Latin for "even stronger". Can be used to compare two theorems or proofs. Could be interpreted to mean "in the same way."

Source: econterms

is a relatively permanent disposition of an individual. Traits are inferred from behaviour and are considered to be continuous dimensions on which individual differences can be arranged quantitatively (e.g. extraversion, introversion). Traits are to be distinguished from states.

Source: SFB 504

abbreviation for Arrow-Debreu equilibrium.

Source: econterms

American Agricultural Economics Association. See their web site at http://www.aaea.org.

Source: econterms

A notion claiming that those who can afford to pay the tax should bear a greater weight of paying the tax.

Source: EconPort

Used in the context of stock returns; means the return to a portfolio in excess of the return to a market portfolio. Contrast excess returns which means something else. Note that abnormal returns can be negative.
Example: Suppose average market return to a stock was 10% for some calendar year, meaning stocks overall were 10% higher at the end of the year than at the beginning, and suppose that stock S had risen 12% in that period. Then stock S's abnormal return was 2%.

Source: econterms

An attribute of a utility function. See Arrow-Pratt measure.

Source: econterms

A limit to the rate or quantity of scientific or technological information that a firm can absorb. If such limits exist they provide one explanation for firms to develop internal R&D capacities. R&D departments can not only conduct development along lines they are already familiar with, but they have formal training and external professional connections that make it possible for them to evaluate and incorporate externally generated technical knowledge into the firm better than others in the firm can. In other words a partial explanation for R&D investments by firms is to work around the absorptive capacity constraint.

This term comes from Cohen and Levinthal (1990).

Source: econterms

a phrase that generally means "leaving out". A model abstracts from some elements of the real world in its demonstration of some specific force.

Source: econterms

The information contained in a prototype is an abstraction across several instances of the concept.

Source: SFB 504

That it is the growth of output that induces continuing net investment. That is, net investment is a function of the change in output not its level.

Source: econterms

Occurs in the context of hypothesis testing. Let T be a test statistic. Possible values of T can be divided into two regions, the acceptance region and the rejection region. If the value of T comes out to be in the acceptance region, the null hypothesis being tested is not rejected. If T falls in the rejection region, the null hypothesis is rejected.

The terms 'acceptance region' and 'rejection region' may also refer to the subsets of the sample space that would produce statistics T in the acceptance region or rejection region as defined above.

Source: econterms

Accessibility ? Construct accessibility is the readiness with which a stored construct is utilized in information processing; that is, construct accessibility is concerned with stored constructs, their utilization in information processing, and the likelihood of such utilization.

Source: SFB 504

The explicit costs of production; these include monetary payments to cover the costs of fixed or variable inputs (i.e., fixed costs and variable costs). Some examples include utilities, rent, wages of labor, property taxes, the cost of raw materials, etc. Unlike economic costs, they do not include implicit (opportunity) costs.

Source: EconPort
See also: economic costs, implicit costs, opportunity cost. , 

The profit made from the total revenue received from the sale of the goods less the (explicit) costs of producing these goods. It is calculated as Total Revenue â?? Explicit Costs.

Source: EconPort

Advisory Council on Intergovernmental Relations, in the U.S.

Source: econterms

In the context of combating unemployment: policies designed to improve the access of the unemployed to the labor market and jobs, job-related skills, and the functioning of the labor market. Contrast passive measures.

Source: econterms

The stochastic process {X_t} and information sets {Y_t} are adapted if {X_t} is a martingale difference sequence with respect to {Y_t}.

Source: econterms

American Economics Association

Source: econterms

An abbreviation for the American Economic Review.

Source: econterms

From Milgrom and Weber (Econometrica, 1982, page 1096): Bidders' valuations of a good being auctioned are affiliated if, roughly: "a high value of one bidder's estimate makes high values of the others' estimates more likely."

There may well be good reasons not to use the word correlated in place of affiliated. This editor is advised that there is some mathematical difference.

Source: econterms

adjective, describing a function with a constant slope. Distinguished from linear which sometimes is meant to imply that the function has no constant term; that it is zero when the independent variables are zero. An affine function may have a nonzero value when the independent variables are zero.
Examples: y = 2x is linear in x, whereas y = 2x + 7 is an affine function of x.
And y = 2x + z² is affine in x but not in z.

Source: econterms

A pricing schedule where there is a fixed cost or benefit to the consumer for buying more than zero, and a constant per-unit cost per unit beyond that. Formally, the mapping from quantity purchased to total price is an affine function of quantity.
Using, mostly, Tirole's notation, let q be the quantity in units purchased, T(q) be the total price paid, p be a constant price per unit, and k be the fixed cost, an example of an affine price schedule is T(q)=k+pq.
For alternative ways of pricing see linear pricing schedule and nonlinear pricing.

Source: econterms

Armed Forces Qualifications(?) Test -- a test given to new recruits in the U.S. armed forces. Results from this test are used in regressions of labor market outcomes on possible causes of those outcomes, to control for other causes.

Source: econterms

An abbreviation for Adjusted Gross Income, a line item which appears on the U.S. taxpayer's tax return and is sometimes used as a measure of income which is consistent across taxpayers. AGI does not include any accounting for deductions from income that reduce the tax due, e.g. for family size.

Source: econterms

"Agricultural Economics is an applied social science that deals with how producers, consumers, and societies use scarce resources in the production, processing, marketing, and consumption of food and fiber products." (from Penson, Capps, and Rosson (1996), as cited by Hallam 1998).

Source: econterms

abbreviation for Akaike's Information Criterion

Source: econterms

An abbreviation for the American Journal of Sociology.

Source: econterms

A criterion for selecting among nested econometric models. The AIC is a number associated with each model:
AIC=ln (s_m²) + 2m/T
where m is the number of parameters in the model, and s_m² is (in an AR(m) example) the estimated residual variance: s_m² = (sum of squared residuals for model m)/T. That is, the average squared residual for model m.
The criterion may be minimized over choices of m to form a tradeoff between the fit of the model (which lowers the sum of squared residuals) and the model's complexity, which is measured by m. Thus an AR(m) model versus an AR(m+1) can be compared by this criterion for a given batch of data.
An equivalent formulation is this one: AIC=T ln(RSS) + 2K where K is the number of regressors, T the number of obserations, and RSS the residual sum of squares; minimize over K to pick K.

Source: econterms

A Marxist term. Alienation is the subjugation of people by the artificial creations of people 'which have assumed the guise of independent things.' Because products are thought of as commodities with money prices, the social process of trade and exchange becomes driven by forces operating independently of human will like natural laws.

Source: econterms

The Allais paradox is the most prominent example for behavioral inconsistencies related to the von Neumann Morgenstern axiomatic model of choice under uncertainty. The Allais paradox shows that the significant majority of real decision makers orders uncertain prospects in a way that is inconsistent with the postulate that choices are independent of irrelevant alternatives. Basically, it is this postulate that allows to represent preferences over uncertain prospects as a linear functional of the utilities of the basic outcomes, viz. as the expectation of these utilities.

Consider the following choice situation (A) among two lotteries:

? lottery L1 promises a sure win of $30,
? lottery L2 is a 80% chance to win $45 (and zero in 20% of the cases).

Typically, L1 is strictly preferred to L2 (such observed behavior is called a revealed preference).

Now, consider another choice situation (B):

? lottery K1 promises a 25% chance of winning $30,
? lottery K2 is a 20% chance to win $45.

Here, the typical choice is K2 over K1 although situation B differs from situation A only in that in each lottery, three quarters of the original probability of winning a positive amount are cancelled.

Assume the typical subject decides among lotteries in the following way. To each of the basic outcomes, a number is assigned that indicates its attractiveness; say u(0)=0, u(45)=1, and u(30)=v (0 0.8; while the revealed preference of K2 over K1 in situation B shows that 1/4 v < 1/5, or v < 0.8.

In cognitive psychology, this inconsistency is explained as a certainty effect. In situation A, L2 differs from L1 by a winning probability that is 20% lower, just as lottery K2 differs from K1 in situation B (where 4/5 x 25 = 20). Empirically, it seems that cancelling a fixed proportion of winning probability has a higher cognitive impact in a lottery where winning was extremely likely than in a lottery where winning was "a rather unlikely event, anyway."

By accounting for a misperception of probabilities according to a non-linear weighting function (of the utilities of the elementary outcomes), expected utility can be rescued also in view of the Allais paradox (see prospect theory). The Allais paradox, devised in the 1950's, was the first piece in a series of systematic evidence challenging the traditional concept of von Neumann Morgenstern expected utility, leading to the development of generalized models of ("boundedly rational") choice behavior under uncertainty.

Source: SFB 504

The accepted purview of economics is the allocation of scarce resources. Allocation comprises production and exchange, reflecting a fundamental division between processes that transform commodities (i.e., production) and those that transfer control (i.e., exchange). In general, optimal allocation ensures that scarce resources are driven to their best use.

For both production and consumption, exchange is essential to the efficient use of resources. It allows decentralization and specialization in production; as to consumption, agents with diverse endowments or preferences (tastes) need exchange to obtain maximal benefits, given their resources. If the preferences of two agents differ (formally, if agents have different rates of substitution among the commodities concerned), then there exists a trade benefitting both. Such trades of private goods take place on markets.

The advantages of barter extend widely, e.g. to trade among nations and among legislators ("vote trading"), but it suffices here to emphasize markets with enforceable contracts for trading private property unaffected by externalities. In such markets, voluntary exchange involves trading bundles of commodities or obligations to the mutual advantage of all parties to the transaction.

Source: SFB 504

Simultaneous bidding game where the bidder that has submitted the highest bid is awarded the object, and all bidders pay their own bids. A subvariant is the second price all pay auction, also war of attrition, where each bidder pays his own bid but the winner only pays the second highest bid. For example, campaign spending and political lobbying processes are second-price all pay auctions; liekwise, timing decisions on the private provision of public goods have the structure of second price all pay auctions.

Source: SFB 504

With probability one. In particular, the statement that a series {W_n} limits to W as n goes to infinity, means that Pr{W_n->W}=1.

Source: econterms

"The hypothesis that the restriction or set of restrictions to be tested does NOT hold." Often denoted H₁. Synonym for 'maintained hypothesis.'

Source: econterms

A member of a certain subfield of political science.

Source: econterms

American Stock Exchange, which is in New York City

Source: econterms

A statistical data analysis program, discussed at http://www.smallwaters.com/amos.

Source: econterms

Often means 'algebraic', as opposed to 'numeric'. E.g., in the context of taking a derivative, which could sometimes be calculated numerically on a computer, but is usually done analytically by finding an algebraic expression for the derivative.

Source: econterms

People who have to make judgements under uncertainty use this heuristic by starting with a certain reference point (anchor) and then adjust it insufficiently to reach a final conclusion. Example: If you have to judge another person´s productivity, the anchor for your final (adjusted) judgement may be your own level of productivity. Depending on your own level of productivity you might therefore underestimate or overestimate the productivity of this person.

Source: SFB 504

Denoted []₊ with a lag operator polynomial in the brackets. Has the effect of removing the terms with an L to a negative power; that is, future values in the expression. Their expected value is assumed to be zero by whoever applies the operator.

Source: econterms

If annuity payments over time are (0,P,P,...P) for n periods, and the constant interest rate r>0, then the net present value to the recipient of the annuity can be calculated this way: NPV(A) = (1-(1+r)^-n)P/r

Source: econterms

Stands for analysis-of-variance, a statistical model meant to analyze data. Generally the variables in an ANOVA analysis are categorical, not continuous. The term main effect is used in the ANOVA context. The main effect of x seems to mean the result of an F test to see if the different categories of x have any detectable effect on the dependent variable on average. ANOVA is used often in sociology, but rarely in economics as far as this editor can tell. The terms ANCOVA and ANOCOVA mean analysis-of-covariance. When I understand ANCOVA and main effect better, I'll make separate entries for them. From Kennedy, 3rd edition, pp226-227: 'Analysis of variance is a statistical technique designed to determine whether or not a particular classification of the data is meaningful. The total variation of the dependent variable (the sum of squared differences between each observation and the overall mean) can be expressed as the sum of the variation between classes (the sum of the squared differences between the mean of each class and the overall mean, each times the number of observations in that class) and the variation within each class (the sum of the squared difference between each observation and its class mean). This decomposition is used to structure an F test to test the hypothesis that the between-class variation is large relative to the within-class variation, which implies that the classification is meaningful, i.e., that there is a significant variation in the dependent variable between classes. If dummy variables are used the capture these classifications and a regression is run, the dummy variable coefficients turn out to be the class means, the between-class variation is the regression's 'explained' variation, the within-class variation is the regression's 'unexplained' variation, and the analysis of variance F test is equivalent to testing whether or not the dummy variable coefficients are significantly different from one another. The main advantage of the dummy variable regression is that it provides estimates of he magnitudes of class variation influences on the dependent variables (as well as testing whether or not the classification is meaningful). 'Analysis of covariance is an extension of analysis of variance to handle cases in which there are some uncontrolled variables that could not be standardized between classes. These cases can be analyzed by using dummy variables to capture the classifications and regressing the dependent variable on these dummies and the uncontrollable variables. The analysis of covariance F tests are equivalent to testing whether the coefficient of the dummies are significantly different from one another. These tests can be interpreted in terms of changes in the residual sums of squares caused by adding the dummy variables. Johnston (1972, pp 192-207) has a good discussion. In light of the above, it can be concluded that anyone comfortable with regression analysis and dummy variables can eschew analysis of variance and covariance techniques.' [Except that one needs to understand the academic work out there, not just write one's own. -ed.]

Source: econterms

Arbitrage Pricing Theory; from Stephen Ross, 1976-78. Quoting Sargent, "Ross posited a particular statistical process for asset returns, then derived the restrictions on the process that are implied by the hypothesis that there exist no arbitrage possibilities."

The APT includes multiple risk factors, unlike the CAPM.

Source: econterms

Stands for "autoregressive." Describes a stochastic process (denote here, e_t) that can be described by a weighted sum of its previous values and a white noise error. An AR(1) process is a first-order one, meaning that only the immediately previous value has a direct effect on the current value:
e_t = re_t-1 + u_t
where r is a constant that has absolute value less than one, and u_t is drawn from a distribution with mean zero and finite variance, often a normal distribution.
An AR(2) would have the form:
e_t = r₁e_t-1 + r₂e_t-2 + u_t
and so on. In theory a process might be represented by an AR(infinity).

Source: econterms

A first-order autoregressive process. See AR for details.

Source: econterms

Arbitrage plays a critical role in the analysis of securities markets, bringing prices to fundamental values and keeping markets efficient.

Source: SFB 504

Stands for Autoregressive Conditional Heteroskedasticity. It's a technique used in finance to model asset price volatility over time. It is observed in much time series data on asset prices that there are periods when variance is high and periods where variance is low. The ARCH econometric model for this (introduced by Engle (1982)) is that the variance of the series itself is an AR (autoregressive) time series, often a linear one.
Formally, per Bollerslev et al 1992 and Engle (1982): An ARCH model is a discrete time stochastic process {e_t} of the form: e_t = z_ts_t
where the z_t's are iid over time, E(z_t)=0, var(z_t)=1, and s_t is positive and time-varying. Usually s_t is further modeled to be an autoregressive process.

According to Andersen and Bollerslev 1995/6/7, "ARCH models are usually estimated by maximum likelihood techniques." They almost always give a leptokurtic distrbution of asset returns even if one assumes that each period's returns are normal, because the variance is not the same each period. Even ARCH models, however, do not usually generate enough kurtosis in equity returns to match U.S. stock data.

Source: econterms

Describes a stochastic process or a model of one. Stands for "autoregressive integrated moving-average". An ARIMA process is made up of sums of autoregressive and moving-average components, and may not be stationary.

Source: econterms

Describes a stochastic process or a model of one. Stands for "autoregressive moving-average". An ARMA process is a stationary one made up of sums of autoregressive and moving-average components.

Source: econterms

Measurable risk, that is, measurable variation in possible outcomes, on the basis of knowledge or believed assumptions in advance. Contrast Knightian uncertainty.

Source: econterms

Means, in practice, competitive equilibrium of the kind shown in Debreu's Theory of Value.
The Arrow-Debreu reference may be to a particular paper: "Existence of an Equilibrium for a Competitive Economy", Econometrica. Vol 22 July 1954, pp 265-290. I haven't checked that out.

Source: econterms

An attribute of a utility function.

Denote a utility function by u(c). The Arrow-Pratt measure of absolute risk aversion is defined by:
R_A=-u''(c)/u'(c)
This is a measure of the curvature of the utility function. This measure is invariant to affine transformation of the utility function, which is a useful attributed because such transformation do not affect the preferences expressed by u().

If R_A() is decreasing in c, then u() displays decreasing absolute risk aversion. If R_A() is increasing in c, then u() displays increasing absolute risk aversion. If R_A() is constant with respect to changes in c, then u() displays constant absolute risk aversion.

Source: econterms

An abbreviation for the journal Administrative Science Quarterly which tends to be closer to sociology than to economics.

Source: econterms

An abbreviation for the journal American Sociological Review.

Source: econterms

A way of mapping from abstract states of the world into the prices of financial assets like stocks and bonds. The prices are always conceived of as endogenous; that is, the states of the world cause them, not the other way around, in an asset pricing model.
Several general types are discussed in the research literature. The CAPM is one, distinguished from three that Fama (1991) identifies: (a) the Sharpe-Lintner-Black class of models, (b) the multifactor models like the APT of Ross (1976), and (c) the consumption based models such as Lucas (1978).
An asset pricing model might or might not include the possibility of fads or bubbles.

Source: econterms

maps the state of the economy at time t into the price of a capital asset at time t.

Source: econterms

An adjective meaning 'of a probability distribution as some variable or parameter of it (usually, the size of the sample from another distribution) goes to infinity.'
In particular, see asymptotic distribution.

Source: econterms

A limiting distribution of an estimator is usually normal. (details!)

This is usually proven with a mean value expansion of the score at the estimated parameter value? (details)

Source: econterms

Definition of the asymptotic variance of an estimator may vary from author to author or situation to situation. One standard definition is given in Greene, p 109, equation (4-39) and is described there as "sufficient for nearly all applications." It's

asy var(t_hat) = (1/n) * lim_n->infinity E[ {t_hat - lim_n->infinity E[t_hat] }² ]

Source: econterms

Estimators are asymptotically equivalent if they have the same asymptotic distribution.

Source: econterms

"There are at least three possible definitions of asymptotic unbiasedness:
1. The mean of the limiting distribution of n^.5(t_hat - t) is zero.
2. lim_n->infinity E[t_hat] = t.
3. plim t_hat = t."
Usually an estimator will have all three of these or none of them. Cases exist however in which left hand sides of those three are different. "There is no general agreement among authors as to the precise meaning of asymptotic unbiasedness, perhaps because the term is misleading at the outset; asymptotic refers to an approximation, while unbiasedness is an exact result. Nonetheless the majority view seems to be that (2) is the proper definition of asymptotic unbiasedness. Note, though, that this definition relies upon quantities that are generally unknown and that may not exist." -- Greene, p 107

Source: econterms

An attitude is "a psychological tendency that is expressed by evaluating a particular entity with some degree of favor or disfavor" (Eagly & Chaiken, 1993, p. 1). This tendency can be expressed by different types of evaluative responses. Social psychologists commonly differentiate between affective, cognitive and behavioral responses. Affective responses towards an attitude object manifest themselves in verbal expressions of feelings and physiological changes in the organism (e.g. increase of arousal). Cognitive responses refer to expressions of beliefs (e.g. expectancy-value judgments) and nonverbal reactions such as response latencies. Behavioral responses manifest in behavioral intentions and actions. Attitude theory and research deals with the structure, function, formation and change of attitudes, and is also concerned with the relationship between attitudes and behavior. The model of reasoned action (Fishbein & Ajzen, 1975), for example, provides a comprehensive approach to all of these aspects. In this model, the internal structure of an attitude is described in terms of beliefs (expectations), that relate the attitude object (a behavioral alternative) to evaluated attributes. The function of attitudes is to guide the formation of behavioral intentions. Attitude formation and change is viewed as a process of deliberative evaluation and belief updating. Attitudes are thought to impact behavior indirectly via behavioral intentions. More recent approaches, however, assume that a deliberative calculation of expectancy and values is not a necessary condition for either intention formation or attitude formation and change. There is ample evidence for example, that liking of an attitude object can be enhanced simply by increasing its presentation frequency (Zajonc, 1980) Furthermore, attitudes, if they are frequently activated from memory, tend to become activated automatically in the presence of the attitude object and then directly impact behavioral decisions (Fazio, 1990).

Source: SFB 504

a kind of steady state in a dynamical system. There are three types of attractor: stable steady states, cyclical attractors, and chaotic attractors.

Source: econterms

Competitive exchange process in which each trader from one market side submits a bid, the most favorable one of which is selected by the complementary market side for the transaction. Most commonly, the bidders form the potential buyers of a commodity, and the bid-taker is a monopolistic seller. Also common is the converse constellation, where a monopsonic buyer elicits price offers from competing sellers ( procurement auction). In a narrow sense, auctions form a variety of familiar and less familiar selling and buying mechanisms for goods reaching from objects of art and collectibles to natural resources like minerals and agricultural products, to treasury bonds, construction and supply contracts, oil drilling rights and broadcasting licenses. Also take-over battles for firms or conglomerates are an explicit auction.

In a broader sense, auctions provide an explicit description of price formation processes that arise from strategic interaction in markets. More general auction mechanisms with competition on both market sides, so-called double auctions, form exchange institutions that map competing price bids (buying demands) and price asks (selling offers) into an allocation of the goods among the traders. Given the vector of bids and asks (and some matching rule), the terms of trade for various quantities of one or several goods are endogenously determined. A prototypical example for double auctions are institutionalized markets of financial assets and financial derivatives.

Auctions are models of 'thin markets', making precise the sense in which markets 'find prices' that can 'reveal' an underlying economic value. This is shown distinctively by the fact they are the unique exchange mechanism adopted whenever competitive market prices do not exist but the object sold is of particular uniqueness and size, such as in privatizations of government enterprises, in the the sale of complex procurement contracts, or seldom goods of arts; or when the resource in question does not have a price other than the terms of trade which are revealed through strategic interaction of traders, such as financial assets like stock, options, corporate or government bonds.

In a sense, strategic equilibria of competitive bidding games have many efficiency properties that generalize those of competitive market equilibrium. As it is the highest (buying) asks and the lowest (selling) offers that are selected for the transaction, the resulting allocation of commodites and quantities is efficient ex post. Under appropriate conditions, equilibrium outcomes from double auctions are even efficient in an interim sense (see efficiency). Under reasonable informational assumptions, the equilibrium bids of common value auctions (see below) converge to the competitive equilibrium price as the number of bidders grows large (see also competitive market equilibrium).

Auctions are modelled as bidding games of incomplete information. The bidders' (players') strategies are bid functions converting their private information about the objects in sale, and previous bids observed, into a money amount that is bid. Such bidding games provide unified descriptions of many competitive processes from diverse contexts. Together with the most common auction formats, we mention some examples below.

Source: SFB 504

A test for a unit root in a time series sample. An augmented Dickey-Fuller test is a version of the Dickey-Fuller test for a larger and more complicated set of time series models.

(Ed.: what follows is only my best understanding.) The augmented Dickey-Fuller (ADF) statistic, used in the test, is a negative number. The more negative it is, the stronger the rejection of the hypothesis that there is a unit root at some level of confidence. In one example, with three lags, a value of -3.17 constituted rejection at the p-value of .10.

Source: econterms

A school of thought which "takes as its central concern the problem of human coordination, through which order emerges not from a dictator, but from the decisions and judgments of numerous individuals in a world of highly disperced and sometimes only tacit knowledge." -- Cass R. Sunstein, "The Road from Serfdom" The New Republic Oct 20, 1997, p 42.

Well-known authors along this line include Carl Menger, Ludwig von Mises, and Friedrich von Hayek. See Deborah L. Walker's essay for a clear account.

Source: econterms

The state of an individual who does not trade with anyone.

Source: econterms

the jth autocorrelation of a covariance-stationary process is defined as its jth autocovariance divided by its variance.

In a sample, the kth autocorrelation is the OLS estimate that results from the regression of the data on the kth lags of the data.

Below is Gauss code to calculate autocorrelations from a sample.

  /* This functions calculates autocorrelation estimates for lag k */  
proc autocor(series, k);   
   local rowz,y,x,rho;    
   rowz = rows(series);    
   y = series[k+1:rowz];    
   x = series[1:rowz-k];    
   rho = inv(x'x)*x'y;            /* compute autocorrelation by OLS */    
   retp(rho);  
endp;  

Source: econterms

The jth autocovariance of a stochastic process y_t is the covariance between its time t value and the value at time t-j. It is denoted gamma below, and E[] means expectation, or mean:
gamma_jt = E[(y_t - Ey)(y_t-j-Ey)]
In that equation the process is assumed to be covariance stationary. If there is a trend, then the second Ey should be the expected value of at the time t-j.

Source: econterms

Defined for a vector random process, denoted y_t here. The ij'th element of the autocovariance matrix is cov(y_it, y_j,t-k).

Source: econterms

Information processing that occurs without conscious control.
Mental processes fall on a continuum from more automatic to more controllable. At the most automatic end is preconscious automaticity, followed by post-conscious automaticity and goal-directed automaticity. Next are spontaneous processes, which are activated without consciousness but processed only with effort. Ruminative processes are slightly more controlled, they are conscious but not deliberately directed by goals. At the most controlled end, intentional thoughts are characterized by people having choices, especially if they make the hard (more effortful) choice, and paying attention to that choice to enact it.
Automatic processing can develop in response to stimuli and environments that people habitually encounter, as a way to save cognitive effort. Automatic responses, especially preconscious automaticity, can be defined with several criteria (Bargh, 1984). First, automatic processes are unintentional; they do not require a goal to be activated. Second, they are involuntary, always occuring in the presence of the relevant cue. Third, they are effortless, using no cognitive capacity. Fourth, they are autonomous, running to completion without any conscious monitoring. Finally, they are outside awareness, meaning they are activated and operated without consciousness.

Source: SFB 504

See AR.

Source: econterms

traditionally refers to whether or not a construct is stored in memory (Bruner, 1957). Recently, there has been an increasing tendency to use the term accessibility and availability interchangeably. Some overlap in the application of these terms was introduced in Tversky & Kahneman´s (1973) description of the availability heuristic, where availability referred to the ease of retrieving construct instances. In the availability heuristic, however, availability also referred to the ease of constructing instances of novel classes and events, which is distinct from the traditional meaning of accessibility (see Higgins & King, 1981).

Source: SFB 504

This heuristic is used to evaluate the frequency or likelihood of an event on the basis of how quickly instances or associations come to mind. When examples or associations are easily brought to mind, this fact leads to an overestimation of the frequency or likelihood of this event. Example: People are overestimating the divorce rate if they can quickly find examples of divorced friends.

Source: SFB 504

abbreviation or symbol for the operation of taking the asymptotic variance of an expression, thus: avar().

Source: econterms

The per-unit cost of producing a product, measured as the total cost of production divided by the number of units produced. It is frequently represented on a graph as a U-shaped curve (average costs initially decrease before eventually increasing).

Source: EconPort

The per-unit share of total fixed costs; it is calculated as the total fixed cost of production divided by the number of units produced. Because fixed costs do not depend upon the quantity produced, average fixed costs decline as more is produced.

Source: EconPort
See also: Fixed Costs , 

Total Revenue divided by the number of units that are produced.

Source: EconPort

The sum of variable and fixed costs divided by the number of units produced. It is calculated as Total Costs divided by the number of units produced.

Source: EconPort

Total variable costs divided by the number of units produced.

Source: EconPort

b(n,q) is notation for a binomial distribution with parameters n and q, where n is the number of draws and q is the probability that each is a one; the value of X~b(n,q) is a count of the number of ones drawn.

Source: econterms

Kind of refinement of Perfect Bayesian Equilibrium that puts sharper requirements on the beliefs which cannot be formed by Bayes' rule, but which are hold after moves off the equilibrium path. These beliefs have to be formed in a 'continuous' way from the information available in the extensive form of the game. Further refinements of Perfect Bayesian equilibrium restrict the players' beliefs about moves off the equilibrium path to the set of those types only for which the observed off-equilibrium move could have been worthwhile at all.

Source: SFB 504

B¹ denotes the Borel sigma-algebra of the real line. It will contain every open interval by definition, which implies that it contains every closed interval and every countable union of open, half-open, and closed intervals. What won't it contain? In practice, only obscure sets. Here's an example: Define the equivalence class ~ on the real line such that x~y (read: x is in the same equivalence class as y) if x-y is a rational number. Now consider the set of all numbers in [0,1] such that none of them are in the same equivalence class. How many members of that set are there? Well, it's not a countable number. This set is not in B¹.

Source: econterms

A country's balance of payments is the quantity of its own currency flowing out of of the country (for purchases, for example, but also for gifts and intrafirm transfers) minus the amount flowing in.

[Ed: this next part is partly speculation; feel free to correct it.] For some purposes this term refers to a stock value and for others a flow value. It is well defined over a period in the sense that it has changed from time A to time B.

Source: econterms

A macro model exhibits balanced growth if consumption, investment, and capital grow at at a constant rate while hours of work per time period stays constant.

Source: econterms

Any complete normed vector space is a Banach space.

Source: econterms

In kernel estimation, a scalar argument to the kernel function that determines what range of the nearby data points will be heavily weighted in making an estimate. The choice of bandwidth represents a tradeoff between bias (which is intrinsic to a kernel estimator, and which increases with bandwidth), and variance of the estimates from the data (which decreases with bandwidth).
Cross-validation is one way to choose the bandwidth as a function of the data.
Has a variety of similar definitions in spectral analysis. Generally, a bandwidth is some way of defining the range of frequencies that will be included by the estimation process. In some estimations it is an argument to the estimation process.

Source: econterms

In periods of free banking, such as most states in the U.S. from 1839-1863, banks could issue their own money, called bank notes. A bank note was a risky, perpetual debt claim on a bank which paid no interest, and could be redeemed on demand at the original bank, usually in gold. There was a risk that the bank would not be able or willing to redeem it.

Source: econterms

The obstacles to producers of entering a market. These can be manifested as:
- requiring a specialized type of license (such as having to be a certified electrician to perform electrical work);
- a government-imposed monopoly (such as specifying a single provider of power and electricity);
- the costs of a business license;
- patents;
- having to compete with other well-entrenched firms already in the market (having to compete with economies of scale);
- other things that may prevent a new firm from entering a market.

Source: EconPort

An economy that does not have a medium of exchange, or money, and where trade occurs instead by exchanging useful goods for useful goods.

Source: econterms

The practice of firms setting prices as if their transportation costs to all locations were the same, even if all the vendors are distant from one another and have substantially different costs of transportation to each location. One might interpret this as a form of monitored collusion between the vendor firms.

Source: econterms

In making probabilistic inferences perceivers ought to take account of general, broadly based information about population characteristics, and more specifically the prior probability of an event occuring. The tendency to under use, sometimes even ignore, such information is called the base rate fallacy. Some authors (Kahneman & Tversky, 1973) explain this phenomenon with respect to the representativeness heuristic. Gigerenzer and Hoffrage (1995) argue that the base-rate fallacy is due to the presentation of the information in probability format and that natural sampling reduces the base-rate fallacy.

Source: SFB 504

the region of states, in a dynamical system, around a particular stable steady state, that lead to trajectories going to the stable steady state. (E.g. the region inside the event horizon around a black hole.)

Source: econterms

One-hundredth of a percentage point. Used in the context of interest rates.

Source: econterms

A known set of fixed quantites of known goods, needed for defining a price index.

Source: econterms

This theorem deals with the impact of new information on the revision of probability estimates, and provides a normative model to assess how well people use empirical information to update the probability that a hypothesis is true.

P(H|O) = P(H) x P(O|H) / [ P(H) x P(O|H) + P(nonH) x P(O|nonH) ]

Bayes's theorem tells us that the probability that a hypothesis is true given that we have made some observation (called the "posterior odds") P(H|O) is a function of:

P(H) = The probability you would have assigned to the hypothesis before you made the observation, called the "prior probability" of the hypothesis.
P(O|H) = The probability the observation would occur if the hypothesis were true.
P(nonH) = The prior probability the hypothesisis not true, 1-P(H).
P(O|nonH) = The probability the event would have occured even if the hypothesis were not true.

For example, when the baserates of women having breast cancer and having no breast cancer are known to be 1% and 99%, respectively, and the hit rate is given as P(positive mammography/ breast cancer) = 80 %, applying the Bayes theorem leads to a normative prediction as low as P(breast cancer/ positive mammography) = 7.8%. That means that the probability that a woman who has a positive mammography actually has breast cancer is less than 8%. Studies show (e.g. Gigerenzer & Hoffrage, 1995) that subjective estimates clearly exceed the normative prediction and are often very close to the hit rate (80% in the example).

Source: SFB 504

"In Bayesian analysis all quantities, including the parameters, are random variables. Thus, a model is said to be identified in probability if the posterior distribution for [the parameter to be estimated] is proper."

Source: econterms

In normal form games of incomplete information, the players have no possibility to update their prior beliefs about their opponents payoff-relevant characteristics, called their types. All that a player knows, except from the game itself (and the priors), is his own type, and the fact that the other players do not know his own type as well. As their best responses, however, depend on the players' actual types, a player must see himself through his opponents' eyes and plan an optimal reaction against the possible strategies of his opponents for each potential type of his own. Thus, a strategy in a Bayesian game of incomplete information must map each possible type of each player into a plan of actions. Then, since the other players' types are unknown, each player forms a best response against the expected strategy of each opponent, where he averages over the (well-specified) reactions of all possible types of an opponent, using his prior probability measure on the type space. Such a profile of type-dependent strategies which are unilaterally unimprovable in expectations over the competing types' strategies forms a Bayes Nash equilibrium. Basically, a Bayes Nash equilibrium is thus a Nash equilibrium 'at the interim stage' where each player selects a best response against the average best responses of the competing players.

Source: SFB 504

In neoclassical economic theory, it is assumed that decision makers, given their knowledge of utilities, alternatives, and outcomes, can compute which alternative will yield the greatest subjective (expected) utility. The term bounded rationality is used to designate models of rational choice that take into account the cognitive limitations of both knowledge and cognitive capacity. Bounded rationality is a central theme in behavioral economics. It is concerned with the ways in which the actual decision-making process influences the decisions that are eventually reached. To this end, behavioral economics departs from one or more of the neoclassical assumptions underlying the theory of rational behavior. The two most important questions that can be posed are:


•Are the assumptions of utility or profit maximization good approximations of real behavior?
•Do individuals maximize subjective expected utility?

Simon (1987b) provides an overview of the literature on these issues.

Research in behavioral economics has adopted specific methodological approaches that complement traditional statistical and econometric tests of economic models. For example, experiments are commonly used in behavioral economics, and survey data are also becoming more important in the process of learning about individuals' actual decision-making processes.

Source: SFB 504

Despite strong evidence that securities markets are highly efficient, there have been scores of studies that have documented long-term historical phenomena in securities markets that contradict the efficient market hypothesis and cannot be captured plausibly in models based on perfect investor rationality. Such phenomena are often referred to as stock market anomalies.

Source: SFB 504

In incomplete information games, in order to predict the optimal behavior of his opponent, a player has to form expectations and assessments of his opponent's type. In a simultaneous game of incomplete information, each player's belief about any other player's type is exogenously given, or it is inferred by Bayes' rule from an intial draw by nature that determines the various types of the players. In sequential games of incomplete information, the players' beliefs about their opponents' types must be updated according to Bayes' rule during the play of the game whenever this is possible by having observed another player's move.

Source: SFB 504

Any value or flow value equation. For a discrete problem it can generally be of the form:
v(k) = max over k' of { u(k,k') + b*v(k') }
where:
u() is the one-period return function (e.g., a utility function) and
v() is the value function and
k is the current state and
k' is the state to be chosen and
b is a scalar real parameter, the discount rate, generally slightly less than one.

Source: econterms

The idea that the tax burden should be proportional to an individual's use of government-supplied goods and services.

Source: EconPort

A bidding war in which the bidders end up at a zero-profit price. See Bertrand game.

Source: econterms

The two firms producing in a market modeled as a Bertrand game.

Source: econterms

Model of a bidding war between firms each of which can offer to sell a certain good (say, widgets), but no other firms can. Each firm may choose a price to sell widgets at, and must then supply as many as are demanded. Consumers are assumed to buy the cheaper one, or to purchase half from each if the prices are the same. Best for the firms (both collectively and individually) is to cooperate, charge monopoly price, and split the profits. Each firm could seize the whole market by lowering price slightly, however, and the noncooperative Nash equilibrium outcome of a Bertrand game is that both charge a zero-profit price.

Source: econterms

In a between subjects design the values of the dependent variable for one subject or group of subjects (e.g., the experimental group) are compared with the values for another subject or another group of subjects (e.g., the control group).

Source: SFB 504

The graph of the inverse relation of unemployment to job vacancies.

Source: econterms

A numerical optimization method from Berndt, Hall, Hall, and Hausman (1974). Used in Gauss, for example. The following discussion of BHHH was posted to the newsgroup sci.econ.research by Paul L. Schumann, Ph.D., Professor of Management at Minnesota State University, Mankato (formerly Mankato State University). It is included here without any explicit permission whatsoever.

  BHHH usually refers to the procedure explained in Berndt, E., Hall, B.,  
Hall, R., & Hausman, J. (1974), 'Estimation and Inference in Nonlinear  
Structural Models,' Annals of Economic and Social Measurement, 3/4: 653-665.    

BHHH provides a method of estimating the asymptotic covariance matrix of a  
Maximum Likelihood Estimator. In particular, the covariance matrix for a MLE  
depends on the second derivatives of the log-likelihood function. However,  
the second derivatives tend to be complicated nonlinear functions. BHHH  
estimates the asymptotic covariance matrix using first derivatives instead  
of analytic second derivatives. Thus, BHHH is usually easier to compute than  
other methods.    

In addition to the original BHHH article referenced above, BHHH is also  
discussed in Greene, W.H., Econometric Analysis, 3rd Edition, Prentice-Hall,  
1997. Greene's econometric software program, LIMDEP, uses BHHH for some of  
the estimation routines.    

Someone (perhaps BHHH themselves?) wrote a Fortran subroutine in the 1970's  
to do BHHH. I do not have a copy of this subroutine at the present time. You  
may want to check out Green's econometric software, LIMDEP, to see if it  
will do what you require, rather than writing your own program to use an  
existing BHHH subroutine. The Web address for LIMDEP is:    
  http://www.limdep.com/index.htm    

Cheers,  
Paul.    
--
   Paul L. Schumann, Ph.D., Professor of Management 
   Minnesota State University, Mankato (formerly Mankato State University) 
   Mankato, MN  56002    
   mailto:paul.schumann@mankato.msus.edu    
   http://krypton.mankato.msus.edu/~schumann/www/welcome.html  

Source: econterms

British Household Panel Survey. A British government database going back to 1990. Web page: http://www.iser.essex.ac.uk/bhps/index.php

Source: econterms

the difference between the parameter and the expected value of the estimator of the parameter.

Source: econterms

In an auction analysis, a bidding function (often denoted b()) is a function whose value is the bid that a particular player should make. Often it is a function of the player's value, v, of the good being auctioned. Thus the common notation b(v).

Source: econterms

From the late Middle Ages. A contract entitling an exporter to receive immediate payment in the local currency for goods that would be shipped elsewhere. Time would elapse between payment in one currency and repayment in another, so the interest rate would also be brought into the transaction.

Source: econterms

A mixture of silver and copper, from which small coins were made in medieval Europe. Larger coins were made of silver or gold.

Source: econterms

A commodity money regime in which there is concurrent circulation of coins made from each of two metals and a fixed exchange rate between them. Historically the metals have almost always been gold and silver. Bimetallism was tried many times with varying success but since about 1873 the practice has been generally abandoned.

Source: econterms

Bell Journal of Economics, the previous name of the RAND Journal of Economics or RJE.

Source: econterms

An illegal market. This may include markets for illegal goods and services (for example, illegal drugs or prostitution), or markets for otherwise legal goods that are sold illegally (for example, making cash payments for goods and services to avoid record-keeping and therefore to to avoid paying taxes).

Because of the illegal nature of these markets, they are difficult to study and to obtain a precise measure of the size and extent of black-market activity in an economy.

Source: EconPort

An equation for option securities prices on the basis of an assumed stochastic process for stock prices.

The Black-Scholes algorithm can produce an estimate the value of a call on a stock, using as input:
-- an estimate of the risk-free interest rate now and in the near future
-- current price of the stock
-- exercise price of the option (strike price)
-- expiration date of the option
-- an estimate of the volatility of the stock's price
Click here for a derivation of Black-Scholes equation. From the Black-Scholes equation one can derive the price of an option.

Source: econterms

Abbrevation for the U.S. government's Bureau of Labor Statistics, in the Labor Department.

Source: econterms

Suppose a certain treatment of a patient has no effect. If one runs a test of statistical significance on enough randomly selected subsets of the patient base, one would find some subsets in which statistically significant differences were apparently distinguished by the treatment. The Bonferroni criterion is a redefinition of the statistical signficance criterion for the testing of many subgroups: e.g. if there are five subgroups and one of them shows an effect of the treatment at the .01 significance level, the overall finding is significant at the .05 level. This is discussed in more detail (and probably more correctly) in Bland and Altman (1995) in the statistics notes of the British Medical Journal. Either of these links should go there:
Llink 1.
Link 2; search for Bonferroni.

Source: econterms

The activity of applying estimators to each of many subsamples of a data sample, in the hope that the distribution of the estimator applied to these subsamples is similar to the distribution of the estimator when applied to the distribution that generated the sample.

It is a method that gives a sense of the sampling variability of an estimator. "After the set of coefficients b0 is computed, M randomly drawn samples of T observations are drawn from the original data set with replacement. T may be less than or equal to n, the sample size. With each such sample the ... estimator is recomputed." -- Greene, p 658-9.
The properties of this distribution of estimates of b0 can then be characterized, e.g. its variance. If the estimates are highly variable, the investigator knows not to think of the estimate of b0 as precise.

Bootstrapping could also be used to estimate by simulation, or empirically, the variance of an estimation procedure for which no algebraic expression for the variance exists.

Source: econterms

Any element of a Borel sigma-algebra.

Source: econterms

The Borel sigma-algebra of a set S is the smallest sigma-algebra of S that contains all of the open balls in S. Any element of a Borel sigma-algebra is a Borel set.

Example: The set B¹ is the Borel sigma-algebra of the real line, and thus contains every open interval.

Example: Consider a filled circle in the unit square. It can be constructed by a countable number of non-overlapping open rectangles (since a series of such rectangles can be defined that would cover every point in the circle but no point outside of it. Therefore it is in the smallest sigma-algebra of open subsets of the unit square.

Source: econterms

Models of bounded rationality are defined in a recent book by Ariel Rubinstein as those in which some aspect of the process of choice is explicitly modeled.

Source: econterms

Rational behavior, in economics, means that individuals maximize some target function under the constraints they face (e.g., their utility function) in pursuit of their self-interest. This is reflected in the theory of (subjective) expected utility (Savage, 1954).

The term bounded rationality is used to designate rational choice that takes into account the cognitive limitations of both knowledge and cognitive capacity. Bounded rationality is a central theme in behavioral economics. It is concerned with the ways in which the actual decision-making process influences decisions. Theories of bounded rationality relax one or more assumptions of standard expected utility theory.

Source: SFB 504

The Box-Cox transformation, below, can be applied to a regressor, a combination of regressors, and/or to the dependent variable in a regression. The objective of doing so is usually to make the residuals of the regression more homoskedastic and closer to a normal distribution:

{	y(l) = ((y^l) - 1) / l for l not equal to zero y(l)=log(y) l=0

Box and Cox (1964) developed the transformation.

Estimation of any Box-Cox parameters is by maximum likelihood.

Box and Cox (1964) offered an example in which the data had the form of survival times but the underlying biological structure was of hazard rates, and the transformation identified this.

Source: econterms

A "methodology for identifying, estimating, and forecasting" ARMA models. (Enders, 1996, p 23). The reference in the name is to Box and Jenkins, 1976.

Source: econterms

Defined on a time series sample for each natural number k by the sum of the squares of the first k sample autocorrelations. The k^th sample autocorrelation is denoted r:
BP(k)=S_s=1^k [r_s²]
Used to tell if a time series is nonstationary.
Below is Gauss code with a procedure that calculates the Box-Pierce statistic for a set of residuals.

  
/* A series of residuals eps_hat[] is generated from a regression, e.g.: */    

eps_hat = y - X*betaols;    

/* Then the Box-Pierce statistic for each k can be calculated this way: */    

print 'Box-Pierce statistic for k=1 is' BP(eps_hat,1);  
print 'Box-Pierce statistic for k=2 is' BP(eps_hat,2);  
print 'Box-Pierce statistic for k=3 is' BP(eps_hat,3);    

proc BP(series, k);    
   local beep, rho;    
   beep = 0;    
   do until k < 1;      
     rho = autocor(series, k);      
     beep = beep + rho * rho;      
     k = k - 1;    
   endo;    
   beep = beep * rows(series);     /* BP = T* (the sum) */    
   retp(beep);  
endp;    

/* This functions calculates autocorrelation estimates for lag k */  
proc autocor(series, k);    
   local rowz,y,x,rho;    
   rowz = rows(series);    
   y = series[k+1:rowz];    
   x = series[1:rowz-k];    rho = inv(x'x)*x'y;            /* compute autocorrelation by OLS */    
   retp(rho);  
endp;  

Source: econterms

An abbreviation for the Brookings Papers on Economic Activity.

Source: econterms

Parallel to the extension of Nash equilibrium to subgame perfect equilibrium in games of complete information, the concept of Bayesian Nash equilibrium loses much of its bite in extensive form games and is accordingly refined to 'Perfect Bayesian' equilibrium. In a sequential game, it is often the threats about certain reactions 'off the equilibrium path' that force the players' actions to be best responses to one another 'onto the equilibrium path'. In sequential games with incomplete information, where the players hold beliefs about their opponents' types and optimize given their beliefs, a player then effectively 'threatens by the beliefs' he holds about his opponents' types after moves that deviate from the equilibrium path. Different beliefs about other players' types after deviations typically yield different reactions, some of which force the players back on the (candidate) equilibrium path, some of which lead them even farer away. In the first case, the plans of actions are confirmed by the beliefs about them, and the crucial self-confirming property of equilibrium beliefs and equilibrium strategies is met. The concept of Perfect Bayesian equilibrium makes precise this self-confirming 'interaction' of beliefs about types selecting certain actions and their 'actual' strategies. First, it requires that players forms a complete system of beliefs about the opponents' types at each decision node that can be reached. Next, this system of beliefs is updated according to Bayes' rule whenever possible (in particular, 'along the equilibrium path'), and finally, given each player's system of beliefs, the strategies from best responses to one another in the sense of ordinary Bayesian Nash equilibrium. A Bayesian equilibrium thus is a profile of complete strategies and a profile of complete beliefs such that (i) given the beliefs, the strategies are unilaterally unimprovable at each potential decision node that might be reached, and such that (ii) the beliefs are consistent with the actual evolution of play as prescribed by the equilibrium strategies.

Source: SFB 504

An algorithm for choosing the step lengths when numerically calculating maximum likelihood estimates.

Source: econterms

The international monetary framework of fixed exchange rates after World War II. Drawn up by the U.S. and Britain in 1944. Keynes was one of the architects.
The system ended on August 15, 1971, when President Richard Nixon ended trading of gold at the fixed price of $35/ounce. At that point for the first time in history, formal links between the major world currencies and real commodities were severed.

Source: econterms

A diagnostic test of a regression. It is a statistic for testing whether dependent variable y is heteroskedastic as a function of regressors X. If it is, that suggests use of GLS or SUR estimation in place of OLS. The test statistic is always nonnegative. Large values of test statistic reject the hypothesis that y is homoskedastic in X. The meaning of 'large' varies with the number of variables in X.

Quoting almost directly from the Stata manual: The Breusch and Pagan (1980) chi-squared statistic -- a Lagrange multiplier statistic -- is given by

l = T * [S_m=1^m=M [S_n=1^n=m-1 [r_mn² ]]

where r_mn² is the estimated correlation between the residuals of the M equations and T is the number of observations. It has a chi-squared distribution with M(M-1)/2 degrees of freedom.

Source: econterms

A substantial movement in market price away from a price determined by fundamental value. In practice, "bubble" always refers to a situation where the market price is higher than the conjectured fundamentally supported price. The idea of a fundamental value requires some model or outside knowledge of what the security (or other good) is worth.

Bubbles are often described as speculative and it is conjectured that bubbles could be risky ventures for speculators who earn a fair rate of return on them. [ed: I believe these are "rational" bubbles.]
There exist statistical models of a bubbles. For example, stochastic collapsing bubbles are cited to Blanchard and Watson (1982) -- in this form, "the bubble continues with a certain conditional probability and collapses otherwise."

Source: econterms

A budget is a description of a financial plan. It is a list of estimates of revenues to and expenditures by an agent for a stated period of time. Normally a budget describes a period in the future not the past.

Source: econterms

A budget constraint is the maximum amount an individual can consume, given current income and prices. For an example, suppose one's income is $100 and there are two goods in the economy; The price of Good A is $2 and the price of Good B is $4. Points on the budget constraint include:
50 units of Good A and 0 units of Good B
48 units of Good A and 1 unit of Good B
46 units of Good A and 2 units of Good B
...
2 units of Good A and 24 units of Good B
0 units of Good A and 25 units of Good B

The budget constraint can be represented graphically, in a table, or in words.

Source: EconPort

A consumer's budget line characterizes on a graph the maximum amounts of goods that the consumer can afford. In a two good case, we can think of quantities of good X on the horizontal axis and quantities of good Y on the vertical axis. The term is often used when there are many goods, and without reference to any actual graph.

Source: econterms

The set of bundles of goods an agent can afford. This set is a function of the prices of goods and the agents endownment.

Assuming the agent cannot have a negative quantity of any good, the budget set can be characterized this way. Let e be a vector representing the quantities of the agent's endowment of each possible good, and p be a vector of prices for those goods. Let B(p,e) be the budget set. Let x be an element of R₊^L; that is, the space of nonnegative reals of dimension L, the number of possible goods. Then:
B(p,e) = {x: px <= pe}

Source: econterms

A form of organization in which officeholders have defined positions and (usually) titles. Formal rules specify the duties of the officeholders. Personalistic distinctions are usually discouraged by the rules.

Source: econterms

Has density function (pdf):
f(x) = ckx^c-1(1+x^c)^k+1 for constants c>0, k>0, and for x>0.
Has distribution function (cdf): F(x) = 1 - (1+x^c)^-k.

Source: econterms

business

Source: econterms

Three to five years. Called the business cycle frequency by Burns and Mitchell (1946), and this became standard language.

Source: econterms

Bayesian VAR (Vector Autoregression)

Source: econterms

Cumulative Average Growth Rate

Source: econterms

A model of political voting behavior in which a citizen chooses to vote if the costs of doing so are outweighed by the strength of the citizen's preference for one candidate weighted by the anticipated probability that the citizen's vote will be decisive in the election.

Source: econterms

NOT SURE WHICH OF THESE (IF EITHER) IS RIGHT:
1. The estimation of some parameters of a model, under the assumption that the model is correct, as a middle step in the study of other parameters. Use of this word suggests that the investigator wishes to give those other parameters of the model a 'fair chance' to describe the data, not to get stuck in a side discussion about whether the calibrated parameters are ideally modeled or estimated.

2. Taking parameters that have been estimated for a similar model into one's own model, solving one's own model numerically, and simulating. Attributed to Edward Prescott.

Source: econterms

A call option conveys the right to buy a specified quantity of an underlying security.

Source: econterms

Something owned which provides ongoing services. In the national accounts, or to firms, capital is made up of durable investment goods, normally summed in units of money. Broadly: land plus physical structures plus equipment. The idea is used in models and in the national accounts.

See also human capital and social capital.

Source: econterms

In national accounts, this is the amount by which gross investment exceeds net investment. It is the same as replacement investment.
-- Oulton (2002, p. 13)

Source: econterms

Increase in capital intensity, normally in a macro context where it is measured by something analogous to the capital stock available per labor hour spent. In a micro context, it could mean the amount of capital available for a worker to use, but this use is rare.

Capital deepening is a macroeconomic concept, of a faster-growing magnitude of capital in production than in labor. Industrialization involved capital deepening - that is, more and more expensive equipment with a lesser corresponding rise in wage expenses.

Capital deepening of a certain input (e.g. a certain kind of capital input, a recent key example being computer equipment) can be measured in the following way. Estimate the growth of the services provided by this input, per unit of labor input, in year T and in year T+1. The growth rate of that ratio is one common measure of the rate of capital deepening. Oulton, p. 31

Source: econterms

Amount of capital per unit of labor input.

Source: econterms

A measure of a bank's capital strength used by U.S. regulatory agencies.

Source: econterms

The capital structure of a firm is broadly made up of its amounts of equity and debt.

Source: econterms

One of the ways in which an effectiveness variable could be included in a production function in a Solow model. If effectiveness A is multiplied by capital K but not by labor L, then we say the effectiveness variable is capital-augmenting.
For example, in the model of output Y where Y=(AK)^aL^1-a the effectiveness variable A is capital-augmenting but in the model Y=AK^aL^1-a it is not.
Another example would be a capital utilization variable as measured say by electricity usage. (E.g., as in Eichenbaum). ----------------- An example: in the context of a railroad, automatic railroad signaling, track-switching, and car-coupling devices are capital-augmenting. From Moses Abramovitz and Paul A. David, 1996. 'Convergence and Deferred Catch-up: productivity leadership and the waning of American exceptionalism.' In Mosaic of Economic Growth, edited by Ralph Landau, Timothy Taylor, and Gavin Wright.

Source: econterms

The system of payment for each customer served, rather than by service performed. Both are used in various ways in U.S. medical care.

Source: econterms

Capital Asset Pricing Model

Source: econterms

stands for Cumulative Average Return.

A portfolio's abnormal return (AR) at each time is AR_t=Sum from i=1 to N of each ar_it/N. Here ar_it is the abnormal return at time t of security i.

Over a window from t=1 to T, the CAR is the sum of all the ARs.

Source: econterms

A class of utility functions. Also called exponential utility. Has the form, for some positive constant a:
u(c)=-(1/a)e^-ac
"Under this specification the elasticity of marginal utility is equal to -ac, and the instantaneous elasticity of substitution is equal to 1/ac."
The coefficient of absolute risk aversion is a; thus the abbreviation CARA for Constant Absolute Risk Aversion. "Constant absolute risk aversion is usually thought of as a less plausible description of risk aversion than constant relative risk aversion" (that's the CRRA, which see), but it can be more analytically convenient.

Source: econterms

cumulative average adjusted returns

Source: econterms

A modeling idea. In a basic Arrow-Debreu general equilibrium there is no need for money because exchanges are automatic, through a Walrasian auctioneer. To study monetary phenomena, a class of models was made in which money was required to make purchases of other goods. In such a model the budget constraint is written so that the agent must have enough cash on hand to make any consumption purchase. Using this mechanism money can have a positive price in equilibrium and monetary effects can be seen in such models. Contrast money-in-the-utility function for an alternative modeling approach.

Source: econterms

''Catch-up' refers to the long-run process by which productivity laggards close the proportional gaps that separate them from the productivity leader .... 'Convergence,' in our usage, refers to a reduction of a measure of dispersion in the relative productivity levels of the array of countries under examination.' Like Barro and Sala-i-Martin (92)'s 'sigma-convergence', a narrowing of the dispersion of country productivity levels over time.

Source: econterms

Research on frequency estimation has shown that several factors can influence the subjective frequency of events. One of these factors is the category width. Splitting an event category into smaller subcategories can increase the subjective frequency of events: A total set of events may have less impact, or appear less frequent, subjectively, than the sum of its (exclusive) subsets. For example, imagine you are asked to judge the number of Japanese cars in your own country, or, in another condition, to judge the frequency of Honda, Nissan, Toyota, Mazda, Daihatsu and Mitshubishi cars. The sum of the judged component frequencies from the split-category condition will be higher, under many circumstances, than the compound frequency of the entire category.

Source: SFB 504

Has thicker tails than a normal distribution.
density function (pdf): f(x) = 1/[pi*(1+x²)]. distribution function (cdf): F(x) = .5 + (tan^-1x)/pi.

Source: econterms

A sequence satisfies the Cauchy criterion iff for each positive real epsilon there exists a natural number N such that the distance between any two elements of the sequence past the Nth element is less than epsilon. 'Distance' must be defined in context by the user of the term.

One sometimes hears the construction: 'The sequence is Cauchy' if the sequence satisfies the definition.

Source: econterms

Stands for Consumption-based Capital Asset Pricing Model.
A theory of asset prices. Formulated in Lucas, 1978, and Breeden, 1979.

Source: econterms

Stands for Corporate Data Exchange, an organization which has data on the shareholdings of large U.S. companies.

Source: econterms

cumulative distribution function. This function describes a statistical distribution. It has the value, at each possible outcome, of the probability of receiving that outcome or a lower one. A cdf is usually denoted in capital letters. Consider for example some F(x), with x a real number is the probability of receiving a draw less than or equal to x. A particular form of F(x) will describe the normal distribution, or any other unidimensional distribution.

Source: econterms

Stands for Concavity of distribution function condition.

Source: econterms

A dependent variable in a model is censored if observations of it cannot be seen when it takes on vales in some range. That is, the independent variables are observed for such observations but the dependent variable is not.

A natural example is that if we have data on consumers and prices paid for cars, if a consumer's willingness-to-pay for a car is negative, we will see observations with consumer information but no car price, no matter how low car prices go in the data. Price observations are then censored at zero.

Contrast truncated dependent variables.

Source: econterms

A government bank; a bank for banks.

Source: econterms

Items with greater family resemblance to a category are judged to be more typical of the category.

Source: SFB 504

The reduction of the probability of an outcome by a constant factor has more impact when the outcome was initially certain than when it was merely probable (e.g. Allais paradox).

Source: SFB 504

Imagine that a stochastic objective function is a function only of output and output-squared. Then the solution to the optimization problem of choosing output will have the special characteristic that only the conditional means of the future forcing variables appear in the first order conditions. (By conditional means is meant the set of means for each state of the world.) Then the solution has the "certainty equivalence" property. "That is, the problem can be separated into two stages: first, get minimum mean squared error forecasts of the exogenous [variables], which are the conditional expectations...; second, at time t, solve the nonstochastic optimization problem," using the mean in place of the random variable. "This separation of forecasting from optimization.... is computationally very convenient and explains why quadratic objective functions are assumed in much applied work. For general [functions] the certainty equivalence principle does not hold, so that the forecasting and opt problems do not 'separate.'"

Source: econterms

The amount of payoff (e.g. money or utility) that an agent would have to receive to be indifferent between that payoff and a given gamble is called that gamble's 'certainty equivalent'. For a risk averse agent (as most are assumed to be) the certainty equivalent is less than the expected value of the gamble because the agent prefers to reduce uncertainty.

Source: econterms

CES stands for constant elasticity of substitution. This is a function describing production, usually at a macroeconomic level, with two inputs which are usually capital and labor. As defined by Arrow, Chenery, Minhas, and Solow, 1961 (p. 230), it is written this way:

V = (bK^-r + aL^-r) ^-(1/r)

where V = value-added, (though y for output is more common),
K is a measure of capital input,
L is a measure of labor input,
and the Greek letters are constants. Normally a>0 and b>0 and r>-1. For more details see the source article.

In this function the elasticity of substitution between capital and labor is constant for any value of K and L. It is (1+r)^-1.

Source: econterms

Example, adapted from Caselli and Ventura:
For capital k, labor input n, and constant b<?? (?less that what?)
f(k,n) = (k^b + n^b)^1/b
Here the elasticity of substitution between capital and labor is less than one, i.e. 1/(1-b)<1.

Source: econterms

Stands for Constant Elasticity of Substitution, a kind of utility function. A synonym for CRRA or isoelastic utility function. Often written this way, presuming a constant g not equal to one:
u(c)=c^1-g/(1-g)
This limits to u(c)=ln(c) as g goes to one.
The elasticity of substitution between consumption at any two points in time is constant, equal to 1/g. "The elasticity of marginal utility is equal to" -g. g can also be said to be the coefficient of relative risk aversion, defined as -u"(c)c/u'(c), which is why this function is also called the CRRA (constant relative risk aversion) utility function.

Source: econterms

means "assuming all else is held constant". The author is attempting to distinguish an effect of one kind of change from any others.

Source: econterms

A Latin term meaning â??all else held constantâ?? or â??all else remains the same.â?? In economics, in order to study the effect of a change in one variable, we often employ the ceteris paribus assumption: to isolate the effect of the changing variable we hold everything else constant. For example, in order to study the effect of an increase in income on the equilibrium price and quantity of a good we have to assume that everything else is held constant (tastes and preferences, the price of other goods, etc.).

Source: EconPort

Abbreviation for the U.S. government's Consumer Expenditure Survey

Source: econterms

The U.S. government's Commodities and Futures Trading Commission.

Source: econterms

An occasional abbreviation for 'computable general equilibrium' models.

Source: econterms

Describes an index number that is frequently reweighted. An example is an inflation index made up of prices weighted by frequency with which they are paid, and frequent recomputation of weights makes it a chained inded.

Source: econterms

A description of a dynamic system that is very sensitive to initial conditions and may evolve in wildly different ways from slightly different initial conditions.

Source: econterms

polynomial whose roots are eigenvalues

Source: econterms

Denoted here PSI(t) or PSI_X(t). Is defined for any random variable X with a pdf f(x). PSI(t) is defined to be E[e^itX], which is the integral from minus infinity to infinity of e^itXf(x). This is also the cgf, or cumulant generating function. "Every distribution has a unique characteristic function; and to each characteristic function there corresponds a unique distribution of probability." -- Hogg and Craig, p 64

Source: econterms

Synonym for eigenvalue.

Source: econterms

or "state theory of money" -- 19th century monetary theory, based more on the idea that legal restrictions or customs can or should maintain the value of money, not intrinsic content of valuable metal.

Source: econterms

A continuous distribution, with natural number parameter r. Is the distribution of sums of squares of r standard normal variables. Mean is r, variance is 2r, pdf and cdf is difficult to express in html, and moment-generating function (mgf) is (1-2t)^-r/2.

From older definition in this same database: If n random values z₁, z₂, ..., z_n are drawn from a standard normal distribution, squared, and summed, the resulting statistic is said to have a chi-squared distribution with n degrees of freedom: z₁² + z₂² + ... + z_n²) ~ X²_(n) This is a one-parameter family of distributions, and the parameter, n, is conventionally labeled the degrees of freedom of the distribution. -- quoted and paraphrased from Johnston See also noncentral chi-squared distribution

Source: econterms

Refers to an perspective on economics of the University of Chicago circa 1970. Variously interpreted to imply:
1) A preference for models in which information is perfect, and an associated search for empirical evidence that choices, not institutional limitations, are what result in outcomes for people. (E.g., that committing crime is a career choice; that smoking represents an informed tradeoff between health risk and immediate gratification.)
2) That antitrust law is rarely necessary, because potential competition will limit monopolist abuses.

Source: econterms

The lowest price at which the quantity demanded is zero.

Source: econterms

Given a symmetric positive definite square matrix X, the Cholesky decomposition of X is the factorization X=U'U, where U is the square root matrix of X, and satisfies:
(1) U'U = X
(2) U is upper triangular (that is, it has all zeros below the diagonal) Once U has been computed, one can calculate the inverse of X more easily, because X^-1 = U^-1(U')^-1, and the inverses of U and U' are easier to compute.

Source: econterms

Same as Cholesky decomposition.

Source: econterms

A particular test for structural change; an econometric test to determine whether the coefficients in a regression model are the same in separate subsamples. In reference to a paper of G.C. Chow (1960), "the standard F test for the equality of two sets of coefficients in linear regression models" is called a Chow test. See derivation and explanation in Davidson and MacKinnon, p. 375-376. More info in Greene, 2nd edition, p 211-2.

Homoskedasticity of errors is assumed although this can be dubious since we are open to the possibility that the parameter vector (b) has changed.
RSSR = the sum of squared residuals from a linear regression in which b₁ and b₂ are assumed to be the same
SSR₁ = the sum of squared residuals from a linear regression of sample 1
SSR₂ = the sum of squared residuals from a linear regression of sample 2
b has dimension k, and there are n observations in total
Then the F statistic is:
((RSSR-SSR₁-SSR₂)/k ) / ((SSR₁+SSR₂)/(n-2k).
That test statistic is the Chow test.

Source: econterms

flows of value within a production organization. Includes stocks of raw material, work in process, finished goods inventories, and cash on hand needed to pay workers and suppliers before products are sold.

Source: econterms

An abbreviation for the Canadian Journal of Economics.

Source: econterms

Stands for the "Censored Least Absolute Deviations" estimator. If errors are symmetric (with median of zero), this estimator is unbiased and consistent though not efficient. The errors need not be homoskedastic or normally distributed to have those attributes.

CLAD may have been defined for the first time in Powell, 1984.

Source: econterms

According to Lucas (1998), a classical theory would have no explicit reference to preferences. Contrast neoclassical.

Source: econterms

Note that the last paragraph is actually a description of classical econometrics. As in statistics, classical (or frequentist) methods concentrate on testing hypotheses that are derived from theory, using the data available. Bayesian econometrics (and statistics), on the other hand, stresses the role of the data itself in both development and testing of economic theories. While most empirical applications of econometrics use classical methods, Bayesian econometrics has gained importance for applied work in recent years, a fact that is partly due to the increased computer power available for computationally intensive applied work. The classical vs. Bayesian controversy extends to other social sciences as well; for an appreciation of its relevance in psychology, see e.g. Gigerenzer (1987).

Source: SFB 504

A 1914 U.S. law on the subject of antitrust and price discrimination.
Section two prohibits price discrimination.
Section three prohibits sales based on an exclusive dealing contract requirement that may have the effect of lessening competition.
Section seven prohibits mergers where "the effect of such acquisition may be substantially to lessen competition, or tend to create a monopoly" in any line of commerce.

Source: econterms

A verb. A market clears if the vector of prices for goods is such that the excess demand at those prices is zero. That is, the quantity demanded of every good at those prices is met.

Source: econterms

the study of economic history; the 'metrics' at the end was put to emphasize (possibly humorously) the frequent use of regression estimation.

'The cliometric contribution was the application of a systematic body of theory -- neoclassical theory -- to history and the application of sophisticated, quantitative techniques to the specification and testing of historical models.' -- North (1990/1993) p 131.

Source: econterms

Data whose observations are not iid but rather come in clusters that are correlated together -- e.g. a data set of individuals some of whom are siblings of others, and are therefore similar demographically.

Source: econterms

Informally: that in presence of complete competitive markets and the absence of transactions costs, an efficient set of inputs to production and outputs from production will be chosen by agents regardless of how property rights over the inputs were assigned to the agents. A detailed discussion is in the Encyclopedia of Law and Economics, online.

Source: econterms

A standard production function which is applied to describe much output two inputs into a production process make. It is used commonly in both macro and micro examples.

For capital K, labor input L, and constants a, b, and c, the Cobb-Douglas production function is
f(k,n) = bk^an^c

If a+c=1 this production function has constant returns to scale. (Equivalently, in mathematical language, it would then be linearly homogenous.) This is a standard case and one often writes (1-a) in place of c.

Log-linearization simplifies the function, meaning just that taking logs of both sides of a Cobb-Douglass function gives one better separation of the components.

In the Cobb-Douglass function the elasticity of substitution between capital and labor is 1 for all values of capital and labor.

Source: econterms

A theoretical model of an adjustment process that on a price/quantity or supply/demand graph spirals toward equilibrium.

Example, from Ehrenberg and Smith: Suppose the equilibrium labor market wage for engineers is stable over a ten-year period, but at the beginning of that period the wage is above equilibrium for some reason. Operating on the assumption, let's say, that engineering wages will remain that high, too many students then go into engineering. The wage falls suddenly from oversupply when that population graduates. Too few students then choose engineering. Then there is a shortage following their graduation. Adjustment to equilibrium could be slow.

"Critical to cobweb models is the assumption that workers form myopic expectations about the future behavior of wages." "Also critical to cobweb models is that the demand curve be flatter than the supply curve; if it is not, the cobweb 'explodes' when demand shifts and an equilibrium wage is never reached."

Source: econterms

An algorithm for estimating a time series linear regression in the presence of autocorrelated errors. The implicit citation is to Cochrane-Orcutt (1949).

The procedure is nicely explained in the SHAZAM manual section online at the SHAZAM web site. Their procedure includes an improvement to include the first observation attributed to the Prais-Winsten transformation. A summary of their excellent description is below. This version of the algorithm can handle only first-order autocorrelation but the Cochrane-Orcutt method could handle more.

Suppose we wish to regress y[t] on X[t] in the presence of autocorrelated errors. Run an OLS regression of y on X and construct a series of residuals e[t]. Regress e[t] on e[t-1] to estimate the autocorrelation coefficient, denoted p here. Then construct series y^* and X^* by: y^*₁ = sqrt(1-p²)y₁,
X^*₁ = sqrt(1-p²)X₁,

and
y^*_t = y_t - py_t-1,
X^*_t = X_t - pX_t-1

One estimates b in y=bX+u by applying this procedure iteratively -- renaming y^* to y and X^* to X at each step, until estimates of p have converged satisfactorily.

Using the final estimate of p, one can construct an estimate of the covariance matrix of the errors, and apply GLS to get an efficient estimate of b.

Transformed residuals, the covariance matrix of the estimate of b, R², and so forth can be calculated; see source.

Source: econterms

Same as R-squared.

Source: econterms

An attribute of a distribution: its standard deviation divided by its mean.

Example: In a series of wage distributions over time, the standard deviation may rise over time with inflation, but the coefficient of variation may not, and thus the fundamental inequality may not.

Source: econterms

Cognition is a common label for processes and structures which have to do with perception, recognition, recall, imagination, concept, thought, but also supposition, expectation, plan and problem solving. It should be distinguished between cognition as process and cognition as the result of this process (see Dorsch Psychologisches Wörterbuch, 1994).

Source: SFB 504

The cognitive dissonance theory (Festinger, 1957) is a general theoretical framework which explains how people change their opinions or hypotheses about themselves and their environment. An important application of cognitive dissonance theory is research on attitude change.

The basic assumption of cognitive dissonance theory is that people are motivated to reduce inconsistent cognitions. Cognition refers to any kind of knowledge or opinion about oneself or the world.

Two cognitions can be either relevant or irrelevant. If they are relevant, then they must be consonant or dissonant (i.e. that one does not follow from the other). Dissonant cognitions produce an aversive state which the individual will try to reduce by changing one or both of the cognitions. If, for example, a heavy smoker is exposed to statistics showing that smoking leads to lung cancer, he or she can change the cognition about how much he smokes ("I´m really only a light smoker.") or perceive the statistical data as hysterical environmentalist propaganda and discount it.

Cognitive dissonance can be reduced by adding new cognitions, if (a) the new cognitions add weight to one side and thus, decreases the proportion of cognitive elements that are dissonant or (b) the new cognitions change the importance of the cognitive elements that are in dissonant relation with one another. The other way to reduce cognitive dissonance is to change existing cognitions. Changing existing cognitions reduces dissonance if (a) the new content makes them less contradictory to others or (b) their importance is reduced.

If new cognitions cannot be added or the existing ones changed, behaviors that have cognitive consequences favoring consonance will be recruited. Seeking new information is an example of such behavior.

Source: SFB 504

A sub-population going through some specified stage in a process. The term is often applied to describe a population of persons going through some life stage, like a first year in a new school.

Source: econterms

"An (n x 1) vector time series y_t is said to be cointegrated if each of the series taken individually is ... nonstationary with a unit root, while some linear combination of the series a'y is stationary ... for some nonzero (n x 1) vector a."
Hamilton uses the phrasing that y_t is cointegrated with a', and offers a couple of examples. One was that although consumption and income time series have unit roots, consumption tends to be a roughly constant proportion of income over the long term, so (ln income) minus (ln consumption) looks stationary.

Source: econterms

A collar consists of holding an underlying asset and simultaneously buying a put option (long put) and selling a call option (short call) of this underlying asset. Because of the long put, the collar hedges against losses of the underlying asset. But the short call limits the possibility of participation on the gains of the underlying asset.

Source: SFB 504

commoditized short-term corporate debt.

Source: econterms

Instead of having statstically independent information, the bidders' typically obtain private signals about an unknown common value of the resource in sale which are correlated with the underlying (unknown) common value, and correlated with one another. For example, prior to auctions of oil drilling licenses, the bidding companies obtain extensive seismic information on the likely quantity of oil hidden in the earth (or sea). In order to prepare profitable bids, the bidders then have to estimate the likely information obtained by rivalling bidders. In particular, the equilibrium bids must incoporate the fact that given a bidder wins the auction, all rivalling bids will have been lower, and thus the (unknown) common value on average will assessed to be lower than it would have been estimated without having won the auction. In this sense, winning the auction is 'bad news' that must be anticipated and incorporated into the bids, in order to avoid falling prey to a so-called winner's curse.

Source: SFB 504

A set is compact if it is closed and bounded.

The concept comes up most often in economics in the context of a theory in which a function must be maximized. Continuous functions that are well defined on a compact domain have a maximum and minimum; this is the Weierstrauss Theorem. Noncontinuous functions, or functions on a noncompact domain, may not.

Source: econterms

To illustrate the concept of comparative advantage requires at least two goods and at least two places where each good could be produced with scarce resources in each place. The example drawn here is from Ehrenberg and Smith (1997), page 136. Suppose the two goods are food and clothing, and that 'the price of food within the United States is 0.50 units of clothing and the price of clothing is 2 units of food. [Suppose also that] the price of food in China is 1.67 units of clothing and the price of clothing is 0.60 units of food.' Then we can say that 'the United States has a comparative advantage in producing food and China has a comparative advantage in producing clothing. It follows that in a trading relationship the U.S. should allocate at least some of its scarce resources to producing food and China should allocate at least some of its scarce resources to producing clothing, because this is the most efficient allocation of the scarce resources and allows the price of food and clothing to be as low as possible.

Famous economist David Ricardo illustrated this in the 1800s using wool in Britain and wine from Portugal as examples. The comparative advantage concept seems to be one of the really challenging, novel, and useful abstractions in economics.

Source: econterms

The price a consumer would need to be paid, or the price the consumer would need to pay, to be just as well off after (a) a change in prices of products the consumer might buy, and (b) time to adapt to that change. It is assumed the consumer does not benefit or lose from producing the product.

Source: econterms

Competitive, or Walrasian, market equilibrium is the traditional concept of economic equilibrium, appropriate for the analysis of commodity markets with flexible prices and many traders, and serving as the benchmark of efficiency in economic analysis. It relies crucially on the assumption of a competitive environment where buyers and sellers take the terms of trade (prices) as a given parameter of the exchange environment. Basically, each trader decides upon a quantity that is such small compared to the total quantity traded in the market that their individual transactions have no influence on the prices.

A Walrasian or competitive equilibrium consists of a a vector of prices and an allocation such that given the prices, each trader by maximizing his objective function (profit, preferences) subject to his technological possibilities and resource constraints plans to trade into his part of the proposed allocation, and such that the prices make all net trades compatible with one another ('clear the market') by equating aggregate supply and demand for the commodities which are traded.

Although this rather narrow concept of economic equilibrium is inappropriate in many situations, such as oligopolostic market structures, public goods and externalities, collusion, or markets with price rigidities, it hightlights the close connection between unregulated free price formation in competitive markets and allocative efficiency. For a broad variety of preferences, technologies, and ownership structures, competitive equilibria maximize social welfare in the sense of maximizing the sum of aggregate consumer and producer surplus (see economic rents). Not only do Walrasian markets provide an exchange institution that leads to efficient outcomes, but any efficient allocation can be reached as a competitive equilibrium by an appropriate redistribution of the traders' intial resources.

In addition, Walrasian markets minimize the informational requirements to complete a transaction: each trader only has to know the characteristics of the object traded, the price, and his own objective function (preferences, technology). However, complete information on prices and on the characteristic of the commodities is necessary to retain the efficiency features of free price formation in competitive markets. If there is asymmetric information on the quality of the commodities, prices only insufficiently signal the relative opportunity costs of economic decisions, and, as a result, allocative decisions will no longer lead to efficient market outcomes. Even worse, the repercussions of adverse quality updating can make markets break down completely, with no voluntary trade taking place at all. (Potential market breakdowns in the presence of commodities of varying quality and asymmetric information have become famous as the lemons problem.)

If markets are 'thin', traders have market power, and the competitive paradigm does no longer apply. Instead, prices are explained from matching strategically formed price 'bids' (buying demands) and price 'asks' (selling offers). Accordingly, more general models of competitive markets are described as auctions. However, as the number of bidders grows large, the strategic equilibrium bids from common value auctions approach the competitive price. A similar result holds for competitive markets with perfect information where the traders are free to form coalitions which maximize the joint gains from trade. Then, the coalitionally stable outcomes form a large set, which includes in particular the (efficient) competitive allocation. Again, as the number of trader becomes large, the set of outcomes which is stable under collusive behavior shrinks, and it approaches the (unique) competitive outcome again. Thus, in the limit, both the coalitional and the strategic approach to describing competitive markets collapse into the simple competitive (Walrasian) paradigma. This fact both underlines the benchmark role of perfectly competitive market equilibrium for the allocation of goods, and the restrictive nature of the Walrasian concept of competitive markets.

Source: SFB 504

See Complements.

Source: EconPort

Goods that are typically consumed together. Examples include guns and bullets, peanut butter and jelly, washers and dryers. If two goods are complements, then an increase in the price of one good, will lead to a decrease in the demand for the other related good (the complement). Similarly, a decrease in the price of one good will lead to an increase in the demand for the complement.

If two goods are complements, the cross-price elasticity of demand is negative.

Source: EconPort
See also: cross-price elasticity of demand , 

(economics theory definition) A model's markets are complete if agents can buy insurance contracts to protect them against any future time and state of the world.

(statistics definition) In a context where a distribution is known except for parameter q, a minimal sufficient statistic is complete if there is only one unbiased estimator of q using that statistic.

Source: econterms

One in which the complete set of possible gambles on future states-of-the-world can be constructed with existing assets.
This is a theoretical ideal against which reality can be found more or less wanting. It is a common assumption in finance or macro models, where the set of states-of-the-world is formally defined.

Source: econterms

a data set used in finance

Source: econterms

A property of a distribution function-utility function pair. (At least, it MAY require specification of the utility function; this editor can't tell well.) It is assumed to hold in some principal-agent models so as to make certain conclusions possible.

Source: econterms

A way of measuring the concentration of market share held by particular suppliers in a market. "It is the percentage of total market sales accounted for by a given number of leading firms." Thus a four-firm concentration ratio is the total market share of the four firms with the largest market shares. (Sometimes this particular statistic is called the CR4.)

Source: econterms

A measure of how close a matrix is to being singular. Relevant in estimation if the matrix of regressors is nearly singular the data are nearly collinear and (a) it will be hard to make an accurate or precise inverse, (b) a linear regression will have large standard errors.

The condition number is computed from the characteristic roots or eigenvalues of the matrix. If the largest characteristic root is denoted L and the smallest characteristic root is S (both being presumed to be positive here, that is, the matrix being diagnosed is presumed to be positive definite), then the condition number is:

gamma = (L/S)^.5

Values larger than 20, according to Greene (93), are observed if and only if the matrix is 'nearly singular'. Greene cites Belsley et al (1980) for this term and the number 20.

Source: econterms

has a special use in finance when used without other modifiers; often means 'conditional on time and previous asset returns'. In that context, one might read 'returns are conditionally normally distributed.'

Source: econterms

a collection of functions that give the optimal demands for each of several inputs as a function of the output expected, and the prices of inputs. Often the prices are taken as given, and incorporated into the functions, and so they are only functions of the output.

Usual forms:

x₁(w₁, w₂, y) is a conditional factor demand for input 1, given input prices w₁ and w₂, and output quantity y

Source: econterms

Shorthand often used in finance to mean, roughly, "variance at time t given that many events up through time t-1 are known."

For example, it has been useful in studying aggregate stock prices, which go through periods of high volatility and periods of low volatility, to model them econometrically as having the variance at time t as coming from an AR process. This is the ARCH idea. In such a statistical model, the conditional variance is generally different from the unconditional variance. That is, the unconditional variance is the variance of the whole process, whereas the 'conditional variance' can be better estimated since in this phrasing it is assumed that we can estimate the immediately previous values of variance.

Source: econterms

A matrix may not have the right dimension or shape to fit into some particular operaton with another matrix. Take matrix addition -- the matrices are supposed to have the same dimensions to be summed. If they don't, we can say that they are not conformable for addition. The most common application of the term comes in the context of multiplication. Multiplying an M x N matrix A by an R x S matrix B directly can only be done if N=R. Otherwise the matrices are not conformable for this purpose. If instead M=R, then the intended operation may be to take the transpose of A and multiply it by B. This operation would properly be denoted A'B, where the prime denotes the transpose of A.

Source: econterms

A firm operating in several industries.

Source: econterms

An estimator for a parameter is consistent iff the estimator converges in probability to the true value of the parameter; that is, the plim of the estimator, as the sample size goes to infinity, is the parameter itself. Another phrasing: an estimator is consistent if it has asymptotic power of one.

"Consistency", without a modifier, is synonymous with weak consistency.

From Davidson and Mackinnon, p. 79: If for any possible value of the parameter q in a region of a parameter space the power of a test goes to one as sample size n goes to infinity, that test is said to be consistent against alternatives in that region of the parameter space. That is, if as the sample size increases we can in the limit reject every false hypothesis about the parameter, the test is consistent.

How does one prove that an estimator is consistent? Here are two ways.
(1) Prove directly that if the model is correct, the estimator has power one in the limit to reject any alternative but the true parameter.
(2) Sufficient conditions for proving that an estimator is consistent are (i) that the estimator is asymptotically unbiased and (ii) that its variance collapses to zero as the sample size goes to infinity. This method of proof is usually easier than (1) and is commonly used.

Source: econterms

An attribute of a production function. A production function exhibits constant returns to scale if changing all inputs by a positive proportional factor has the effect of increasing outputs by that factor. This may be true only over some range, in which case one might say that the production function has constant returns over that range.

Source: econterms

If a firm exhibits constant returns to scale, when it increases the use of inputs then output increases by the same proportion. For example, if the firm doubles the use of all inputs, then output will also double. With constant returns to scale, long-run average costs are constant.

Source: EconPort

Games in which for every combination of strategies the sum of players' payoff is the same. For example, auction games for risk neutral bidders and a risk-neutral seller are constant-sum games, where a fixed social surplus from exchange is to be divided between the bidders and the bid-taker. More generally, all exchange situations which do neither allow for production nor for destruction of resources are constant-sum games.

Source: SFB 504

is a type of validity that refers to the degree to which a test captures the underlying construct purportedly measured by the test.

Source: SFB 504

In the theory of consumer demand, demand functions are derived for commodities by considering a model of rational choice based on utility maximization together with a description of underlying economic constraints. In the theory of consumer demand, these constraints include income (which is treated as given here while it might be endogenous in a more general model of household decisions), and commodity prices, which are also fixed from the perspective of an individual household.

Source: SFB 504

Conducted by the U.S. government. See its Web site.

Source: econterms

Household behavior can most easily by characterized by the consumption function, both in in macroeconomics as well as in microeconomics. The consumption function explains how much a household consumes as a function of income (and, in some cases, other explanatory variables). Note that consumption is not only expenditures for goods but also consumption of services like living in the own house or using durables.

Keynes (1936) postulates in his General Theory the consumption function as the relationship between consumption to disposable income. In the early 50s the two dominant models of consumption were developed: the permanent income hypothesis and the life-cycle hypothesis. While these models were once viewed as competing, they can now be seen as complementary with differences in emphasis which serve to illuminate different significant problems. Both models emphasize the distinction between (1) consumer expenditures measured by the national income account and (2) consumption which is explained by optimal allocation of present and future recources over time.

The dependence of consumption on current income is described in the Keynesian consumption function while the dependence of consumption on lifetime income is described in the life cycle hypothesis and the permanent income hypothesis. The interest rate influences consumption via saving because of the intertemporal substitution from one period to a future period: Income that is not used for consumption purposes can be saved and consumed one period later, earning an interest payment and hence allowing for more consumption in the future. This increase in the absolute amount available for consumption, as reflected in the interest rate, has then to be compared with the individual´s rate of time preference (the latter expressing her patience with respect to later consumption, or, more generally, to delayed utility derived from consumption). In the optimum, the interest rate and the rate of time preference have to be equal. This is one of the fundamentals of intertemporal choice (as a special form of rational behavior).

Source: SFB 504

"A security's consumption beta is the slope in the regression of its return on per capita consumption."

Source: econterms

The set of affordable consumption bundles. One way to define a consumption set is by a set of prices, one for each possible good, and a budget. Or a consumption set could be defined in a model by some other set of restrictions on the set of possible consumption bundles.
E.g. if consumer i can consume nonnegative quantities of all goods, it is standard to define x_i as i's consumption set, a member of R₊^L where L is the number of goods. Normally if the agent is endowed with a set of goods, the endowment is in the consumption set.

Source: econterms

The use of questionnaires about valuation to estimate the willingness of respondents to pay for public projects or programs.

Often the question is framed, "Would you accept a tax of x to pay for the program?" Any such survey must be carefully done, and even so there is dispute about the value of the basic method, as is discussed in the issue of the JEP with the Portney (1994) article.

Source: econterms

reverse hindsight bias, implications for further research, theoretical explanations

Source: SFB 504

Same as Pareto set, with the implication that it is drawn in an Edgeworth box.

Source: econterms

Given a metric space S with distance measure d(), and T:S->S mapping S into itself, T is a contraction mapping if for some b ('b') in the range (0,1), d(Tx,Ty) is less than or equal to b*d(x,y) for all x and y in S.

One often abbreviates the phrase 'contraction mapping' by saying simply that T is a contraction.

The function resulting from the applications of a contraction could slope the opposite way of the original function as long as it is less steeply sloped.

A standard way to prove that an operator T is a contraction is to prove that it satisfies Blackwell's conditions.

Source: econterms

A government policy of reducing spending and raising taxes.
In the language of some first courses in macroneconomics, it shifts the IS curve (investment/saving curve) to the left.

Source: econterms

A government policy of raising interest rates charged by the central bank.
In the language of some first courses in macroeconomics, it shifts the LM curve (liquidity/money curve) to the left.

Source: econterms

As used in the following way: "The effect of X on Y disappears when we control for Z", the phrase means to regress Y on both X and Z, together, and to interpret the direct effect of X as the only effect. Here the effect of Z on X has been "controlled for". It is implied that X is not causing changes in Z.

Source: econterms

In an experimental design, which is contrasting two or more groups, the control group of subjects is not given the treatment whose effect is under investigation.

Source: SFB 504

A variable in a model controlled by an agent in order to optimize something.

Source: econterms

Multiple meanings: (1) a mathematical property of a sequence or series that approaches a value;
In macro: ''Catch-up' refers to the long-run process by which productivity laggards close the proportional gaps that separate them from the productivity leader .... 'Convergence,' in our usage, refers to a reduction of a measure of dispersion in the relative productivity levels of the array of countries under examination.' Like Barro and Sala-i-Martin (92)'s 'sigma-convergence', a narrowing of the dispersion of country productivity levels over time.

Source: econterms

A kind of convergence of random variables. If x_t converges in quadratic mean it converges in probability but it does not necessarily converge almost surely.

The following is a best guess, not known to be correct.
Let e_t be a stochastic process and F_t be an information set at time t uncorrelated with e_t:

E[e_t|F_t-m] converges in quadratic mean to zero as m goes to infinity IFF:
E[E[e_t|F_t-m]²] converges to zero as m goes to infinity.

Source: econterms

The convolution of two functions U(x) and V(x) is the function:
U*V(x) = (integral from 0 to x of) U(t)V(x-t) dt

Source: econterms

A metric for deciding whether a particular point alone affects regression estimates much. After a regression is run one can consider for each data point how far it is from the means of the independent variables and the dependent variable. If it is far from the means of the independent variables it may be very influential and one can consider whether the regression results are similar without it.

[Need to add the equation defining the Cook's d here.]

Source: econterms

A game structure in which the players have the option of planning as a group in advance of choosing their actions. Contrast noncooperative game.

Source: econterms

Normal form game where the players have the same number of strategies, which can be indexed such that it is always a strict Nash equilibrium for both players to play strategies having the same index.

Source: SFB 504

Defined in terms of an original allocations of goods among agents with specified utility functions. The core is the set of possible reallocations such that no subset of agents could break off from the others and all do better just by trading among themselves.
Equivalently: The intersection of individually rational allocations with the Pareto efficient allocations. Individually rational, here, means the allocations such that no agent is worse off than with his endowment in the original allocation.

Source: econterms

A choice made by an agent that is at a constraint, and not at the tangency of two classical curves on a graph, one characterizing what the agent could obtain and the other characterizing the imaginable choices that would attain the highest reachable value of the agents' objective.

A classic example is the intersection between a consumer's budget line (characterizing the maximum amounts of good X and good Y that the consumer can afford) and the highest feasible indifference curve. If the agent's best available choice is at a constraint -- e.g. among affordable bundles of good X and good Y the agent prefers quantity zero of good X -- that choice is often not at a tangency of the indifference curve and the budget line, but at a "corner"

Contrast interior solution.

Source: econterms

Two random variables are positively correlated if high values of one are likely to be associated with high values of the other. They are negatively correlated if high values of one are likely to be associated with low values of the other.

Formally, a correlation coefficient is defined between the two random variables (x and y, here). Let s_x and x_y denote the standard devations of x and y. Let s_xy denote the covariance of x and y. The correlation coefficent between x and y, denoted sometimes r_xy, is defined by:

r_xy = s_xy / s_xs_y

Correlation coefficients are between -1 and 1, inclusive, by definition. They are greater than zero for positive correlation and less than zero for negative correlations.

Source: econterms

A graph of total costs of production as a function of total quantity produced.

Source: econterms

is a function of input prices and output quantity. Its value is the cost of making that output given those input prices. A common form: c(w₁, w₂, y) is the cost of making output quantity y using inputs that cost w₁ and w₂ per unit.

Source: econterms

An approach to public decisionmaking. Quotes below from Sugden and Williams, 1978 p. 236, with some reordering: 'Cost-benefit analysis is a 'scientific' technique, or a way of organizing thought, which is used to compare alternative social states or courses of action.' 'Cost-benefit analysis shows how choices should be made so as to pursue some given objective as efficiently as possible.' 'It has two essential characteristics, consistency and explicitness. Consistency is the principle that decisions between alternatives should be consistent with objectives....Cost-benefit analysis is explicit in that it seeks to show that particular decisions are the logical implications of particular, stated, objectives.' 'The analyst's skill is his ability to use this technique. He is hired to use this skill on behalf of his client, the decision-maker..... [The analyst] has the right to refuse offers of employment that would require him to use his skills in ways that he believes to be wrong. But to accept the role of analyst is to agree to work with the client's objectives.' p. 241: Two functions of cost-benefit analysis: It 'assists the decision-maker to pursue objectives that are, by virtue of the community's assent to the decision-making process, social objectives. And by making explicit what these objectives are, it makes the decision-maker more accountable to the community.' 'This view of cost-benefit analysis, unlike the narrower value-free interpretation of the decision-making approach, provides a justification for cost-benefit analysis that is independent of the preferences of the analyst's immediate client. An important consequence of this is that the role of the analyst is not completely subservient to that of the decision-maker. Because the analyst has some responsibility of principles over and above those held by the decision-maker, he may have to ask questions that the decision-maker would prefer not to answer, and which expose to debate conflicts of judgement and of interest that might otherwise comfortably have been concealed.'

Source: econterms

A cost-of-living price index measures the changing cost of a constant standard of living. The index is a scalar measure for each time period. Usually it is a positive number which rises over time to indicate that there was inflation. Two incomes can be compared across time by seeing whether the incomes changed as much as the index did.

Source: econterms

A costate variable is, in practice, a Lagrangian multiplier, or Hamiltonian multiplier.

Source: econterms

the third of the properties of a measure.

Source: econterms

A bond can be resold into two parts that can be thought of as components: (1) a principal component that is the right to receive the principal at the end date, and (2) the right to receive the coupon payments. The components are called strips. The right to receive coupon payments is the coupon strip.

Source: econterms

A pair of firms who split a market, modeled as in the Cournot game.

Source: econterms

A game between two firms. Both produce a certain good, say, widgets. No other firms do. The price they receive is a decreasing function of the total quantity of widgets that the firms produce. That function is known to both firms. Each chooses a quantity to produce without knowing how much the other will produce.

Source: econterms

A generalization of the Cournot game to describe industry structure. Each of N firms will choose a quantity of output. Price is a commonly-known decreasing functions of total output. All firms know N and take the output of the others as given. Each firm has a cost function c_i(q_i). Usually the cost functions are treated as common knowledge. Often the cost functions are assumed to be the same for all firms.

The prediction of the model is that the firms will choose Nash equilibrium output levels.

Formally, from notes given by Michael Whinston to the Economics D50-1 class at Northwestern U. on Sept 23, 1997:
Denote x_i as a quantity that firm i considers,
X as the total quantity (the sum of the x_i's),
x_i* and X* as the Nash equilibrium levels of those quantities,
X_-i as the total quantity chosen by all firms other than firm i,
and p(X) as the function mapping total quantity to price in the market.

Each firm i solves:
max_xi p(x_i+X_-i)-c_i(x_i)

The first order conditions are, for i from 1 to N:

p'(x_i*+X_-i)+p(X*)-c_i'(x_i*)=0

Assuming x_i* is greater than 0 for all i, then the Nash equilibrium output levels are characterized by the N equations:

p'(X*)x_i* + p(X*) = c_i'(x_i*) for each i.

Source: econterms

A stochastic process is covariance stationary if neither its mean nor its autocovariances depend on the index t.

Source: econterms

A covered short call consists of holding an underlying asset and simultaneously selling a call option (short call) of this underlying asset. Although in the literature exists the name call hedge, the covered short call is not an actual hedge strategy. It is only possible to hedge losses of the underelying asset to the amount of the option price, higher losses will be reduced to this amount. On the other hand it is not possible to participate on gains of the underlying asset, because in this case, the option will be exercised, i.e. the seller has to deliver the underlying asset.

Source: SFB 504

A 1950s, probably British, panel on econometrics which focussed attention on the problem of simultaneous equations. In some tellings of the history this had an impact on the field -- other problems such as errors-in-variables (measurement errors in the independent variables), were set aside or given lower priority elsewhere too because of the prestige and influence of the Cowles Commission.

Source: econterms

The Consumer Price Index, which is a measure of the cost of goods purchased by average U.S. household. It is calculated by the U.S. government's Bureau of Labor Statistics.


As a pure measure of inflation, the CPI has some flaws:
1) new product bias (new products are not counted for a while after the appear)
2) discount store bias (consumers who care won't pay full price)
3) substitution bias (variations in price can cause consumers to respond by substituting on the spot, but the basic measure holds their consumption of various goods constant)
4) quality bias (product improvements are under-counted)
5) formula bias (overweighting of sale items in sample rotation)

Source: econterms

The Current Population Survey (of the U.S.) is compiled by the U.S. Bureau of the Census, which is in the Dept of Commerce. The CPS is the source of official government statistics on employment and unemployment in the U.S. Each month 56,500-59,500 households are interviewed about their average weekly earnings and average hours worked. The households are selected by area to represent the states and the nation. "Each household is interviewed once a month for four consecutive months in one year and again for the corresponding time period a year later" to make month-to-month and year-to-year comparisons possible. The March CPS is special. For one thing the respondents are asked about insurance then.

Source: econterms

Whenever the Fisher information I(b) is a well-defined matrix or number, the variance of an unbiased estimator B for b is at least as large as [I(B)]^-1.

Source: econterms

Synonym for loss function. Used in reference to econometrics.

Source: econterms

synonym for rejection region

Source: econterms

A test for a model or survey's internal consistency. Called a 'scale reliability coefficient' sometimes. The remainder of this definition is partial and unconfirmed.

Cronbach's alpha assesses the reliability of a rating summarizing a group of test or survey answers which measure some underlying factor (e.g., some attribute of the test-taker). A score is computed from each test item and the overall rating, called a 'scale' is defined by the sum of these scores over all the test items. Then reliability a is defined to be the square of the correlation between the measured scale and the underlying factor the scale was supposed to measure. (Which implies that one has another measure in test cases of that underlying factor, or that it's imputed from the test results.) (In Stata's examples it remains unclear what the scale is, and how it's measured; apparently alpha can be generated without having a measure of the underlying factor.)

Source: econterms

The cross-price elasticity of demand measures the sensitivity of the demand for one good to a change in the price of another good. It is calculated as:
(Percentage Change in Demand for Good X)/(Percentage Change in Price of Good Y)

If two goods are independent (that is, the price of one good has no effect on the demand for the other good), the cross-price elasticity of demand is zero.

If two goods are complements (they are typically consumed together) an increase in the price of one good will decrease the demand for the other good (and the reverse); therefore for complements the cross-price elasticity of demand is negative

On the other hand, if two goods are substitutes, an increase in the price of one good will increase the demand for the other good (and the reverse); therefore for substitutes, the cross-price elasticity of demand is positive.

Source: EconPort

Parallel data on many units, such as individuals, households, firms, or governments. Contrast panel data or time series data.

Source: econterms

A way of choosing the window width for a kernel estimation. The method is to select, from a set of possible window widths, one that minimizes the sum of errors made in predicting each data point by using kernel regression on the others.

Formally, let J be the number of data points, j an index to each one, from one to J, y_j the dependent variable for each j, X_j the independent variables for that j, Y_j the dependent variable for that j, and {h_i} for i=1 to n the set of candidate window widths. The h_i's might be a set of equally spaced values on a grid. The algorithm for choosing one of the h_i's is:

For each candidate window width h_i
{
..For each j from 1 to J
..{
....Drop the data point (X_j, Y_j) from the sample temporarily
....Run a kernel regression to estimate Y_j using the remaining X's and Y's
....Keep track of the square of the error made in that prediction
..}
..Sum the squares of the errors for every j to get a score for candidate window width h_i
..Record that in a list as the score for h_i
}
Select as the outcome h of this algorithm the h_i with the lowest score

The grid approach is necessary because the problem is not concave. Otherwise one might try a simpler maximization e.g., with the first order conditions.
Note however that a complete execution of the cross-validation method can be very slow because it requires as many kernel regressions as there are data points. E.g. in this author's experience, the cross-validation computation for one window width on 500 data points on a Pentium-90 in Gauss took about five seconds, 1000 data points took circa seventeen seconds, but for 15000 data points it took an hour. (Then it takes another hour to check another window width; so even the very simplest choice, between two window widths, takes two hours.)

Source: econterms

Stands for Constant Relative Risk Aversion, a property of some utility functions, also said to have isoelastic form. CRRA is a synonym for CES.

Example 1: for any real a<1, u(c)=c^a/a is a CRRA utility function. It is a vNM utility function.

Source: econterms

Stands for Constant Returns to Scale.

Source: econterms

Center for Research in Security Prices, a standard database of finance information at the University of Chicago. Has daily returns on NYSE, AMEX, and NASDAQ stocks.

Started in early 1970s by Eugene Fama among others. The data there was so much more convenient than alternatives that it drove the study of security prices for decades afterward. It did not have volume data which meant that volume/volatility tests were rarely done.

Source: econterms

A particular nonparametric estimator of a function. Given a data set {X_i, Y_i} it estimates values of Y for X's other than those in the sample. The process is to construct a function that balances the twin needs of (1) proximity to the actual sample points, (2) smoothness. So a 'roughness penalty' is defined. See Hardle's equation 3.4.1 near p. 56 for exact equation. The cubic spline seems to be the most common kind of spline smoother.

Source: econterms

The difference between a country's savings and its investment. "[If] positive, it measures the portion of a country's saving invested abroad; if negative, the portion of domestic investment financed by foreigners' savings."

Defined by the sum of the value of imports of goods and services plus net returns on investments abroad, minus the value of exports of goods and services, where all these elements are measured in the domestic currency.

Source: econterms

decreasing absolute risk aversion

Source: econterms

data

Source: econterms

Data analysis software, discussed at http://www.datadesk.com.

Source: econterms

Deadweight loss is the loss of consumer and producer surplus that is caused by inefficiency in a market. It may be caused by taxes, monopoly pricing, or other factors that cause inefficiency.

Source: EconPort

All kind of strategies to test the robustness of an observed bias by attempting to eliminate it under controlled conditions (destructive testing).

Source: SFB 504

Either (1) a function that maps from the current state to the agent's decision or choice or (2) a mapping from the expressed preferences of each of a group of agents to a group decision. The first is more relevant to decision theory and dynamic optimization; the second is relevant to game theory.

The phrase allocation rule is sometimes used to mean the same thing as decision rule. The term strategy-proof has been defined in both contexts.

Source: econterms

Decision strategies specify the type and order that information is processed to determine a choice. Some examples for decision strategies are:

Source: SFB 504

Synonym for FWL theorem or Frisch-Waugh-Lovell theorem.

Source: econterms

If a firm exhibits decreasing returns to scale, when it increases the use of inputs then output increases by a smaller proportion. For example, if the firm doubles the use of all inputs, then output will increase by less than double. With decreasing returns to scale, long-run average costs increase as output increases.

Source: EconPort

Characterizing a reasoning process of logical reasoning from stated propositions. Contrast inductive.

Source: econterms

A capital market may be said to be deep if it has great depth (which see).

May less formally be used to describe a market with large total market capitalization.

Source: econterms

As used with respect to options: The rate of change of a financial derivative's price with respect to changes in the price of the underlying asset. Formally this is a partial derivative.

A derivative is perfectly delta-hedged if it is in a portfolio with a delta of zero. Financial firms make some effort to construct delta-hedged portfolios.

Source: econterms

Gives the distribution of a function of random variables for which one has a distribution. In particular, for the function g(b,l), where b and l are estimators for true values b₀ and l₀:
g(b,l) ~ N(g(b₀,l₀), g'(b,l)var(b,l)g'(b,l)')

Source: econterms

A relation between each possible price and the quantity demanded at that price.

[Aspects of the population doing the demanding are often left implicit. An actual supply is not necessary to conceive of demand because demand involves hypothetical quantities.]

Source: econterms

For a given good, the demand curve is a relation between each possible price of the good and the quantity that would be bought at market sale at that price.

Drawn in introductory classes with this arrangement of the axes, although price is thought of as the independent variable:

Price   |  \
        |    \
        |      \
        |        \ Demand
        |________________________
                        Quantity

Source: econterms

The money stored in the form of checking accounts at banks.

Source: econterms

In a model, the set of the most-preferred bundles of goods an agent can afford. This set is a function of the preference relation for this agent, the prices of goods, and the agent's endowment.

Assuming the agent cannot have a negative quantity of any good, the demand set can be characterized this way:
Define L as the number of goods the agent might receive an allocation of. An allocation to the agent is an element of the space R₊^l; that is, the space of nonnegative real vectors of dimension L.
Define >^p as a weak preference relation over goods; that is, x>^px' states that the allocation vector x is weakly preferred to x' .
Let e be a vector representing the quantities of the agent's endowment of each possible good, and p be a vector of prices for those goods. Let D(>^p,p,e) denote the demand set. Then:
D(>^p,p,e) = {x: px <= pe and x >^p x' for all affordable bundles x'}.

Source: econterms

Literally "rule by the people". This is a dictionary definition and is not considered sharp enough for academic use. Schumpeter (1942) contrasts these two definitions below and regards only the second one as useful and plausible enough to work with: "The eighteenth-century philosophy of democracy may be couched in the following definition: the democratic method is that institutional arrangement for arriving at political decisions which realizes the common good by making the people itself decide issues through the election of individuals who are to assemble in order to carry out its will." (p 250) This "classical" definition has the problem that the will of the people is not clearly defined here (e.g. consider voting paradoxes) or known (perhaps even to the people at the time), and this can lead to ambiguity about whether a given political system is democratic. The following definition is preferred for its clarity but has a modern feel that is at some distance from the original dictionary definition. Political representation is assumed to be necessary here. "[T]he democratic method is that institutional arrangement for arriving at political decisions in which individuals acquire the power to decide by means of a competitive struggle for the people's vote." (p 269) More clearly: the democratic method is one in which people campaign competitively for the people's votes to achieve the power to make public decisions. This definition is the sharpest.

Source: econterms

The study of the size, growth, and age and geographical distribution of human populations, and births, deaths, marriages, and migrations.

Source: econterms

A synonym for pdf.

Source: econterms

The decline in price of an asset over time attributable to deterioration, obsolescence, and impending retirement. Applies particularly to physical assets like equipment and structures.

Source: econterms

An attribute of a market.

In securities markets, depth is measured by "the size of an order flow innovation required to change prices a given amount." (Kyle, 1985, p 1316).

Source: econterms

securities whose value is derived from the some other time-varying quantity. Usually that other quantity is the price of some other asset such as bonds, stocks, currencies, or commodities. It could also be an index, or the temperature. Derivatives were created to support an insurance market against fluctuations.

Source: econterms

The process or occurrence of an asset's declining productivity as it ages. This is a component of depreciation.

Source: econterms

An operator defined on square matrices or the value of that operator. For a matrix B the determinant is denoted |B|. Its value is a unique scalar. Calculation of the value of the determinant is discussed in linear algebra books.

Source: econterms

Not random. A deterministic function or variable often means one that is not random, in the context of other variables available.

That is, those other variables determine the variable in question unerringly, by a function that would give the same value every time those other variables were given to it as arguments, unlike a random one which with some probability would give different answers.

Source: econterms

The study of industrialization.
development

Source: econterms

A Dickey-Fuller test is an econometric test for whether a certain kind of time series data has an autoregressive unit root. In particular in the time series econometric model y[t] = by[t-1] + e[t], where t is an integer greater than zero indexing time, and b=1, let b^OLS denote the OLS estimate of b from a particular sample. Let T be the sample size.

Then the test statistic T*(b^OLS -1) has a known, documented distribution. Its value in a particular sample can be compared to that distribution to determine a probability that the original sample came from a unit root autoregressive process; that is, one in which b=1.

Source: econterms

A formal game with two players: Allocator A and Recipient R. They have received a windfall of, say, $1. The allocator, moving first, proposes a split so that A would receive x and R would receive 1-x. The recipient then accepts, no matter what A proposed. In a subgame perfect equilibrium, A would offer R nothing. In experiments with human subjects, however, in which A and R do not know one another, A offers relatively large shares to R (often 50-50). See also Ultimatum Game.

Source: econterms

In Bayesian statistics the investigator has to specify a prior distribution for a parameter, before the experiment or regression that is to update that distribution. A diffuse prior is a distribution of the parameter with equal probability for each possible value, coming as close as possible to representing the notion that the analyst hasn't a clue about the value of the parameter being estimated.

Source: econterms

In a multi-period model, agents may have different utility functions for consumption (or other experiences) in different time periods. Usually in such models they value future experiences, but to a lesser degree than present ones. For simplicity the factor by which they discount next period's utility may be a constant between zero and one, and if so it is called a discount factor. One might interpret the discount factor not as a reduction in the appreciation of future events but as a subjective probability that the agent will die before the next period, and so discounts the future experiences not because they aren't valued, but because they may not occur.

A present-oriented agents discounts the future heavily and so has a LOW discount factor. Contrast discount rate and future-oriented.
In a discrete time model where agents discount the future by a factor of b, one usually lets b=1/(1+r) where r is the discount rate.

Source: econterms

At least two meanings:

(1) The interest rate at which an agent discounts future events in preferences in a multi-period model. Often denoted r. A present-oriented agent discounts the future heavily and so has a HIGH discount rate. Contrast 'discount factor'. See also 'future-oriented'.
In a discrete time model where agents discount the future by a factor of b, one finds r=(1-b)/b, following from b=1/(1+r).

(2) The Discount Rate is the name of the rate at which U.S. banks can borrow from the U.S. Federal Reserve.

Source: econterms

An econometric model: Pr(y_i=1) = F(X_i'b) = X_i'b

Source: econterms

An econometric model in which the actors are presumed to have made a choice from a discrete set. Their decision is modeled as endogenous. Often the choice is denoted y_i.

Source: econterms

Econometrics models in which the dependent variables assumes discrete values.

Source: econterms

See decreasing returns to scale

Source: EconPort

Like economies of scale but with the implication that they are negative, so larger scale would increase cost per unit.

Source: econterms

prevention of banks from flowing money from savers to borrowers as an effect of regulations; e..g the U.S. home mortgage market is partly blocked from banks and left to savings and loan institutions.

Source: econterms

Refers to economics, which because it is so often about tradeoffs, is widely thought to be depressing to study.

Source: econterms

A synonym for cdf.

Source: econterms

A continuous-time index number. "The Divisia index is a weighted sum of growth rates, where the weights are the components' shares in total value." -- Hulten (1973, p. 1017)

See also http://www.geocities.com/jeab_cu/paper2/paper2.htm.

Source: econterms

Abbreviaton for the U.S. national Department of Justice, which does among other things investigations into violations of antitrust law. See also FTC.

Source: econterms

This seems to be the principle that the growth rate of an aggregate is the weighted average of the growth rates of its components, where each component is weighted by the share of the aggregate it makes up. The idea comes up in the context of national accounts and national statistics.

Source: econterms

After a technological innovcation and a subsequent era of ferment in an industry, a basic architecture of product or process that becomes the accepted market standard. From Abernathy& Utterback 1978, cited by A&T 1991. Dominant designs may not be better than alternatives nor innovative. They have the benchmark features to which subsequent designs are compared. Examples include the IBM 360 computer series and Ford's Model T automobile, and the IBM PC.

Source: econterms

In some games, a player can choose a strategy that "dominates" all other strategies in his strategy set: Regardless of what he expects his opponents to do, this strategy always yields a better payoff than any other of his strategies. An example of a game where each player has a dominant strategy is a second-price auction with independent valuations of the bidders: Here bidding one's true valuation is always a best response, regardless of one's opponents' bids.

Source: SFB 504

Synonymous with Functional Central Limit Theorem (FCLT).

Source: econterms

phrasing from Jevons (1893). "[T]he first difficulty in barter is to find two persons whose disposable possessions mutually suit each other's wants. There may be many people wanting, and many possessing those things wanted; but to allow of an act of barter there must be a double coincidence, which will rarely happen." That is, paraphrasing Ostroy and Starr, 1990, p 26, the double coincidence is the situation where the supplier of good A wants good B and the supplier of good B wants good A.
The point is that the institution of money gives us a more flexible approach to trade than barter, which has the double coincidence of wants problem.

Source: econterms

In an econometric model, a variable that marks or encodes a particular attribute. A dummy variable has the value zero or one for each observation, e.g. 1 for male and 0 for female. Same as indicator variables or binary variables.

Source: econterms

An informal name for the practice of selling a product in a foreign country for less than either (a) the price in the domestic country, or (b) the cost of making the product. It is illegal in some countries to dump certain products into them, because they want to protect their own industries from such competition.

Source: econterms

An algorithm for detecting autocorrelation in the errors of a time series regression. The implicit citation is to Durbin (1970). The h statistic is asymptotically distributed normally if the hypothesis that there is no autocorrelation.

Source: econterms

A test for first-order serial correlation in the residuals of a time series regression. A value of 2.0 for the statistic indicates that there is no serial correlation. For tables to interpret the statistic see Greene pgs 738-743, and context discussing them is on pages 424-425.
This result is biased toward the finding that there is no serial correlation if lagged values of the regressors are in the regression. Formally, the statistic is:
d=(sum from t=2 to t=T of: (e_t-e_t-1)²/(sum from t=1 to t=T of: e_t²)
where the series of e_t are the residuals from a regression.

Source: econterms

Sequential biding game where the standing price is gradually lowered, typically by means of an exogenous counting device (a clock, or a pointer), until it is stopped by a bidder. The first bidder to halt the clock wins the item and pays the price where he stopped the wheel. Dutch auctions are strategically equivalent to first price sealed bid auctions. The name derives from the fact that many agricultural products worldwide, but in particular Dutch flowers, are sold in this way.

Source: SFB 504

synonym for dyadic transformation.

Source: econterms

For whole numbers t and initial value x₀ in [0,1], consider the mapping:

x_t+1 = (2x_t) mod 1

"This law of motion is a standard example of chaotic dynamics. It is commonly known as the dyadic transformation. It is mixing (and hence also ergodic)."
-- Domowitz and Muus, 1992, p 2849

All the x_t's will be in [0,1]. Their distribution will depend on the initial value x₀. If x₀ is rational, the mapping will eventually become periodic (for large enough values of t). If x₀ is irrational, the mapping is never periodic.

Source: econterms

means 'changing over time'.

Source: econterms

A possible attribute of a player's strategy in a dynamic decision-making environment (such as a game).
When the best plan that a player can make for some future period will not be optimal when that future period arrives, the plan is dynamically inconsistent.
In one stylized example, addicted smokers face this problem -- each day, their best plan is to smoke today, and to quit (and suffer) tomorrow in order to get health benefits subesquently. But the next day, that is once again the best plan, so they do not quit then either. (In a model this can come about if the planner values the present much more than the near future, -- that is, has a low short-run discount factor -- but has a higher discount factor between two future periods.)
Monetary policy is sometimes said to suffer from a dynamic inconsistency problem. Government policymakers are best off to promise that there will be no inflation tomorrow. But once agents and firms in the economy have fixed nominal contracts, the government would get seigniorage revenues from raising the level of inflation.

Source: econterms

The impulse responses in a distributed lag model.

Source: econterms

dynamic optimization

Source: econterms

maximization problems to which the solution is a function; equivalently, optimization problems in infinite-dimensional spaces.

Source: econterms

The study of dynamic optimization problems through the analysis of functional equations like value equations.

This phrase is normally used, analogously to linear programming to describe the study of discrete problems; e.g. those for which a decision must be made at times t for t=1,2,3,...

Source: econterms

The branch of mathematics describing processes in motion. Some are predictable and others are not. Two reasons a process might be unpredictable are that it might be random, and it might be chaotic.

Source: econterms

Stands for "earnings before interest and taxes" which is used as a measure of earnings performance of firms that is not clouded by changes in debt or equity types, or tax rules.

Source: econterms

An electronic bibliography of economics literature organized by the American Economics Association, derived partly from the Journal of Economic Literature. EconLit is made available through libraries and universities. See http://www.econlit.org for more information.

Source: econterms

An economic model formulated so that its parameters can be estimated if one makes the assumption that the model is correct.

Source: econterms

A journal whose web site is at http://www.econometricsociety.org/es/journal.html .

Source: econterms

econometrics

Source: econterms

Econometrics is the field of economics that is concerned with the application of mathematical statistics and the tools of statistical inference to the empirical measurement of relationships postulated by economic theory. That is, econometrics (hopefully) uses some clever combination of economic theory and mathematical statistics. Typically, application of econometric methods involves the following elements:


• formulating an economic model appropriate to the questions to be answered;
• reviewing the available statistical models and the assumptions underlying these models, and selecting the form most suitable for the problem at hand;
• obtaining appropriate data, properly defined and matching the concepts of the economic model;
• finding suitable computer software to enable the calculations necessary for estimating and testing the econometric model.

The ultimate goal of an econometric exercise is to see whether an economic model is consistent with empirical (observed) behavior as reflected in the data. Note that econometrics is mostly based on large samples, i.e., on observing economic relationships over a long period of time or for a large number of individuals at the same time (or both, as in the case of longitudinal or panel data). Note also that econometricians usually have to use data that were not created in a controlled experiment (as in natural and some other social sciences). An important aspect of applied work is therefore to assess whether the sample used for estimation is actually a random sample drawn from the population for which the underlying model is supposed to be appropriate ? in other words, whether the relationship of interest is empirically identified. For example, this might not be the case if there are selection problems.

Source: SFB 504

A rule in economics asserting that if the marginal benefit of an action is higher than the marginal cost, then one should undertake the action; however if the marginal cost is higher than the marginal benefit of the action, one should not undertake it.

Source: EconPort

in labor markets: the presence of different pay for workers of the same ability but who are in different groups, e.g. black, white; male, female.

Source: econterms

In a model, a specification of preferences, technology, and the stochastic processes underlying the forcing variables.

Source: econterms

Paraphrasing directly from Mokyr, 1990: Economic growth has four basic causes:
1) Investment, meaning increases in the capital stock (Solovian growth)
2) Increases in trade (Smithian growth)
3) Size or scale effects, e.g. by overcoming fixed costs, or achieving specialization
4) Increases in knowledge, most of which is called technological progress (Schumpeterian growth).

Further elaboration is in Mokyr's book.

Source: econterms

Profit that takes into account both explicit and implicit costs of production. It is calculated as Total revenues minus implicit and explicit costs.

Source: EconPort

In equilibrium of a market or game, the traders (or players) participate voluntarily because their payoff exceeds the one from abstaining to engage in the trade (or to play the game): in equilibrium, the participants earn profits. Part of the equilibrium profits is explained by ordinary trading or exchange activity; part of it accrues to a trader (player) by owning a fixed idiosyncratic resource which is not consumed in the transaction (interaction). The last part is called a player's (trader's) rent. An economic rent is thus the 'wage' for some fixed resource which is necessary for and valuable in a transaction but in monopolistic possession of some trader.

Apart from the costs of not using his outside options (i.e. turning to another partner for exchange), it is the rent on such idiosyncratic factors which must be conceded to a player in order to ensure his participation in the exchange process. For example, traders draw a rent from making accessible a fixed resource like 'land' (which is where the term comes from), from uniquely owning a patent or license protecting a technological achievement or professional activity, or from uniquely owning private information about a fact that influences all players' payoffs.

In analogy to rents acrrueing to a trader from possessing idiosyncratic property rights or 'tangible' assets, the equilibrium profits acrrueing to a player solely from possessing payoff-relevant information are called his information rent. The familiar consumer's surplus from microeconomics is a simple example. The consumer is left a surplus from being able to buy all the quantities consumed at the price of the last consumed unit, instead of having to pay higher prices for earlier units consumed. This 'surplus' corresponds to her information rent for knowing her entire schedule of marginal willingnesses-to-pay for different quantities of the object. If the seller instead knew this schedule of marginal valuations, he could squeeze out all the profits from the customer by selling each unit at a different price, just demanding the consumer's marginal valuation for each unit. The fact that the consumer's information is private thus guarantees him a consumer's rent.

If the seller faces a single customer that she knows very well, having observed his choices at varying prices for a long time, she could devise a schedule of quantity discounts that extracts nearly all of the consumer's rent. This changes when the seller faces a set of competing consumers, each of which has private information on his marginal willingness-to-pay for different quantities. The schedule of discounts must now prevent lower-valued consumers from copying the quantity demanded by higher-valued consumers (and thus get much for a small payment). Typically, this is achieved by selling each additional unit of quantity at a slightly lower price than the previous one, thus inducing customers with higher valuations to choose quantities such large that low-valuation customers will find it too costly to mimic choosing a large quantity. (See the entry on incentive compatibility.) In this way, however, the seller thus increases the equilibrium profits of high-valuation customers disproportionately (relative to those for low-valuations customers), i.e. she pays larger information rents to higher marginal valuations (types) of customers.

The upshot of all this is that in a game where the seller designs an incentive compatible price schedule so that the players implicitly 'sell' their private information by revealing it through their equilibrium choices, the players do not loose their information rents. Instead, the very possibility that lower typed customers can mimic the choices of higher typed customers forces the seller to leave higher information rents to higher types, which which own 'more valuable' private information. In this sense, paying information rents to economic agents is intimately related to providing incentives for the revelation private information in strategic contexts.

Source: SFB 504

Piore (1996) writes of two definitions of economics, a narrow one organized around optimization and a broad one organized around scarcity, and suggests that the subjects included by the larger one but not in the smaller one are the subjects of economic sociology discussed in the Handbook (1994).

More specifically, the broad definition of economics is "the study of how people employ scarce resources and distribute them over time and among competing demands" paraphrasing Paul Samuelson (1961). The narrower definition is from Gary Becker (1976): "The combined assumptions of maximizing behavior, market equilibrium, and stable preferences, used relentlessly and unflinchingly . . . [B]ehavior [of] participants who maximize their utility from a stable set of preferences and accumulate an optimal amount of information and other inputs in a variety of markets."

A bit more specifically -- optimization and formal equilibrium are not natural subjects or methods of economic sociology, but the general subjects of economics are. Economic sociology is more likely than economics to use groups or organizations rather than individuals as units of analysis. The practical definition seems to be evolving over time.

Source: econterms

The study of the allocation of scarce (limited) resources.

Source: EconPort

Usually one says there are economies of scale in production of cost per unit made declines with the number of units produced. It is a descriptive, quantitative term. One measure of the economies of scale is the cost per unit made. There can be analosous economies of scale in marketing or distribution of a product or service too. The term may apply only to certain ranges of output quantity.

Source: econterms

See increasing returns to scale

Source: EconPort

European Currency Unit

Source: econterms

A frequent and dangerous mistake for those not familiar with this language is to think that discussion of 'time series' are about data values in a sample. Actually, they are about probability distributions. It has taken this author years to get used to that, which may just be normal.

An example of the error is to think that a discussion about E[X_t] is testable or measurable. Usually it's not. It's assumed in the discussion. A sample has a computable mean, but whether a time series has a trend, or a unit root, or heteroskedasticity are statements about a conjectured process, not statements about data.

Source: econterms

Usually a function mapping quantities of measured inputs to a school and student characteristics to some measure of school output, like the test scores of students from the school.

For empirical purposes one might assume this function is linear and generate the linear regression:

Y = X'b + S'c + e

where Y is a measure of school outputs like a vector of student test scores, X is a set of measures of student attributes (collectively or individually), S is vector of measures of schools those students attend, b and c are coefficients, and e is a disturbance term.

Source: econterms

An abbreviation for the journal Explorations in Economic History.

Source: econterms

An abbreviation for European Economic Review.

Source: econterms

In the context of a Solow model, if labor time is denoted L and labor's effectiveness, or knowledge, is A, then by effective labor we mean AL. In general means 'efficiency units' of labor or 'productive effort' as opposed to time spent.

Source: econterms

Has several meanings. Sometimes used in a theoretical context as a synonym for Pareto efficiency. Below is the econometric/statistical definition. Efficiency is a criterion by which to compare unbiased estimators. For scalar parameters, one estimator is said to be more efficient than another if the first has smaller variance. For multivariate estimators, one estimator is said to be more efficient than another if the covariance matrix of the second minus the covariance matrix of the first is a positive semidefinite matrix. Sometimes properties of the most efficient estimator can be computed; see efficiency bound.

Computation of efficiency is defined on the basis of assumed distributions of errors ('disturbance terms'). It is not calculated directly on the basis of sample information unless the sample information come from a simulation where the actual error distribution was known.

Source: econterms

Analysis of efficiency in the context of resource allocation has always been a central concern of economics, and it is an essential element of modern microeconomic theory. The ends of economic activity are the satisfaction of human needs within resource constraints, preferences, and technological constraints. In this broad sense, an efficient use of scarce resources within a given technological environment is one that maximizes the satisfaction of aggregate needs for a given set of preferences. In a narrower sense, efficiency is a commonly agreed upon criterion to compare the economic desirability of different allocations, or states of the economy, and different allocation mechanisms or institutions. The incomparability of economic preferences gives rise to a criterion that is independent of the distributional characteristics of the allocations (or institutions) compared (Pareto efficiency). Whether construed as a general purpose of economic activity, or as a criterion for evaluating different allocations and exchange institutions, efficiency is a purely technical notion that is neither related to justness or equality criteria, nor to any moral or ethic questions of economic activity.

Source: SFB 504

The minimum possible variance for an estimator given the statistical model in which it applies. An estimator which achieves this variance is called efficient.

Source: econterms

Usually interpretable as "output per worker per hour."
More generally: An abstract measure of the amount produced for a constant production technology by a worker in some time period. Often the context is theoretical and the time period and production technology do not have to be specified.
But efficiency units can be conceived of (and theorized about) as a function of each worker's characteristics, of the vintage of equipment, of the date in history, of the production technology, and so forth.

Source: econterms

The hypothesis that workers' productivity depends positively on their wages. (For reasons this might be the case see the entry on efficiency wages.)
This could explain why employers in some industries pay workers more than employers in other industries do, even if the workers have apparently comparable qualifications and jobs. A contrasting explanation is that of hedonic models in which these differentials are explained by quality differences in the jobs.

Source: econterms

A higher than market-clearing wage set by employers to, for example:
-- discourage shirking by raising the cost of being fired
-- encourage worker loyalty
-- raise group output norms
-- improve the applicant pool
-- raise morale

Labor productivity in efficiency wage models is positively related to wage.

By contrast, consider models in which the wage is equal to labor productivity in equilibrium, or models in which wages are set to reduce the likelihood of unionization (union threat models). In these, productivity is not a function of the wage.

Source: econterms

A description of either:
-- an allocation that is Pareto efficient
or
-- an estimator that has the minimum possible variance given the statistical model; see efficiency bound.

Source: econterms

Market efficiency is one of the major paradigms of financial economics, focussing on informational efficiency as opposed to Pareto efficiency in microeconomic theory.

Market efficiency as applied to securities markets means that it is on average impossible to gain from trading on the basis of generally available public information (information-arbitrage efficiency) and that the valuation of an asset reflects accurately the future payments to which the asset gives title (fundamental-valuation efficiency). It is apparent that market efficiency in this sense is only part of overall market efficiency.

Fama (1970) distinguishes three forms of informational efficiency: He defines weak, semi-strong and strong form efficiency as holding when the stock market prices reflect all historical price information, all publicly available information, and all information (including insider information), respectively. In order for the price to reflect exactly all information about an asset, nothing can impede the purchase or sale of securities, such as brokerage, fees, taxes and so on. To the extent that impediments exist to the trading of an asset, the prices will only imperfectly reflect information of relevance to the valuation of the security.

Most financial markets have generally been shown to be efficient in the weak or semi-strong form, although not necessarily so in the strong sense.

Source: SFB 504

"A market in which prices always 'fully reflect' available information is called 'efficient.'" -- Fama, p. 383

Source: econterms

Exponential GARCH. The EGARCH(p,q) model is attributed to Nelson, (1991).

Source: econterms

An eigenvalue or characteristic root of a square matrix A is a scalar L that satisfies the equation:

det [ A - LI ] = 0

where "det" is the operator that takes a determinant of its argument, and I is the identity matrix with the same dimensions as A.

Source: econterms

Same as spectral decomposition.

Source: econterms

For each eigenvalue L of a square matrix A there is an associated right eigenvector, denoted b that has the dimension of the number of rows of A. The right eigenvector satisfies: Ab = Lb

Source: econterms

An occasional abbreviation for the British academic journal Economic Journal.

Source: econterms

A measure of responsiveness. The responsiveness of behavior measured by variable Z to a change in environment variable Y is the change in Z observed in response to a change in Y. Specifically, this approximation is common:

elasticity = (percentage change in Z) / (percentage change in Y)

The smaller the percentage change in Y is practical, the better the measure is and the closer it is to the intended theoretically perfect measure.

Elasticities are often negative, but are sometimes reported in absolute value (perhaps for brevity) in which case the author is depending on the reader knowing, or quickly applying, some theory. Usually the theory is the theory of supply and demand.

Among the elasticities that show up in the economics literature are:
elasticity of quantity demanded of some product in response to a change in price of that product-- I think this is 'elasticity of demand' or 'price elasticity of demand'. These are ordinarily negative, and when author reports a positive figure it is usually just an absolute value. A reader has to decide whether the true value is negative; hopefully this is obvious.
elasticity of supply, which is analogous
elasticity of quantity demanded in response to a change in the potential consumer's income -- called 'income elasticity of demand'. These are normally positive.

Inventing another kind of elasticity is plausible. Doing so implies a partial theory of behavior -- e.g. that Y creates a reason for the agent to change behavior Z.

Source: econterms

Tversky (1972): This rule begins by determining the most important attribute and then retrieves a cutoff value for that attribute. All alternatives with values below that cutoff are eliminated. The process continues with the most important remaining attribute(s) until only one alternative remains.
Lexicographic Strategy: This strategy first identifies the most important attribute and then selects the alternative that is best on this attribute. In the case of ties, the tied alternatives are compared on the next most important attribute and so on.
Equal Weight Strategy: It examines all alternatives and attribute values but ignores the weights (probabilities). It sums the attribute values for an alternative to get an overall score for that alternative and then selects the alternative with the highest evaluation.
Satisficing Strategy Simon (1955): This strategy considers one alternative at a time, in the order they are presented. Each attribute of the current alternative is compared to a cutoff. If an attribute fails to exceed the cutoff, then the alternative is rejected. The first alternative to pass all the cutoffs is selected.

Source: SFB 504

An occasional abbreviation for the journal Econometrica.

Source: econterms

The tendency of some contingent valuation survey responses to be similar across different survey questions in conflict with theories about what is valued in the utility function.

An example from Diamond and Hausman (1994): A survey might come up with a willingness-to-pay amount that was the same for either (a) one lake or (b) five lakes which include the one that was asked about individually. If lakes have some utility value to the respondent, one would have expected that five lakes would be worth more than one. Possibly the difference arises because the respondent was not expressing a specific preference for the first lake, and/or was not taking a budget constraint into account. Diamond and Hausman argue that for this reason among others contingent valuation surveys cannot arrive at good estimates for values of public goods.

Source: econterms

An attribute of the way technological progress affects productivity. In Solow (1956), any improvement in technology instantaneously affects the productivity of all factors of production. In Solow (1960) however productivity improvements were a property of only of new capital investment. In the second case we say the technologies are embodied in the new equipment, but in the first case they are disembodied.

Source: econterms

European Monetary System -- founded in 1979, its purpose was to reduce currency fluctuations, and evolved toward offering a common currency.

Source: econterms

European Monetary Union.

Source: econterms

A variable is endogenous in a model if it is at least partly function of other parameters and variables in a model. Contrast exogenous.

Source: econterms

An endogenous growth macro model is one in which the long-run growth rate of output per worker is determined by variables within the model, not an exogenous rate of technological progress as in a neoclassical growth model like those following from Ramsey (1928), Solow (1956), Swan (1956), Cass (1965), Koopmans (1965). Influential early endogenous growth models are Romer (1986), Lucas (1988), and Rebelo (1991). See the sources for this entry for more information. Hulten (2000) says 'What is new in endogenous growth theory is the assumption that the marginal product of (generalized) capital is constant, rather than diminishing as in classical theories.' Generalized capital includes the result of investments in research and development (R&D).

Source: econterms

In a general equilibrium model, an individual's endowment is a vector made up of quantities of every possible good that the individual starts out with.

Source: econterms

energy consumption relative to total output (GDP or GNP).

Source: econterms

On a graph with good 1 on the horizontal axis and good 2 on the vertical axis, envision a convex indifference curve, and a diagonal budget constraint that meets it at one point. Now move the budget constraint in and out and mark the points where the tangencies with indifference curves are. The locus of such points is the Engel curve -- it's the mapping from wealth into the space of the two goods. That is, the Engel curve is (x(w), y(w)) where w is wealth and x() and y() are the amounts of each of the goods purchased at those levels of wealth.

Hardle (1990) p 18 defines the Engel curve as the graph of average expenditure (e.g. on food) as a function of income. And on p 118, defines food expenditure as a function of total expenditure.

The name refers to 19th century Prussian statistician Ernst Engel, according to Fogel (1979).

Source: econterms

Changes in commodity demands by people because their incomes are rising. A generalization of Engel's law.

Source: econterms

The observation that "the proportion of a family's budget devoted to food declines as the family's income increases."

See also Engel effects.

Source: econterms

Sequential bidding game where the standing bid wins the item unless another, higher bid is submitted. Bidders can submit bids as often as they want to, and they observe (hear) all previous bids. Often, a new bid has to increase the standing bid by some minimal amount (advance). The English auction is known to have been in use since antique times; from this auction format the word derives: the latin word augere means to increase. With stastitically independent private valuations, an English auction is equivalent in terms of payoffs to a second price sealed bid auction.

Source: SFB 504

A possible description of the actions of managers of firms. Managers can make investments that are more valuable under themselves than under alternative managers. Those investments might not maximize shareholder value. So shareholders have a moral hazard in contracting with managers.

Or, in the phrasing of Weisbach (1988): "Managerial entrenchment occurs when managers gain so much power that they are able to use the firm to further their own interests rather than the interests of shareholders."

The abstract to Shleifer and Vishny, 1989, p 123, is nicely explicit: "By making manager-specific investments, managers can reduce the probability of being replaced, extract higher wages and larger perquisities from shareholders, and obtain more latitude in determining corporate strategy."

Source: econterms

European Options Exchange

Source: econterms

The Epanechnikov kernel is this function: (3/4)(1-u²) for -1<u<1 and zero for u outside that range. Here u=(x-x_i)/h, where h is the window width and x_i are the values of the independent variable in the data, and x is the value of the scalar independent variable for which one seeks an estimate.
For kernel estimation.

Source: econterms

"Of, relating to; or involving knowledge or the act of knowing." An economic theory might take aspects of human understanding or belief as fundamental to economic processes or outcomes.

Source: econterms

"1. The division of philosophy that investigates the nature and origin of knowledge. 2. A theory of the nature of knowledge."

Source: econterms

(Usually written with a true epsilon character.)

In a noncooperative game, for any small positive number epsilon, an epsilon-equilibrium is a profile of totally mixed strategies such that each player gives more probability weight than epsilon only to strategies that are best responses to the profile of strategies the others are playing.

For a more formal definition see sources. This is a rough paraphrase.

Source: econterms

In a noncooperative game, a profile of strategies is an epsilon-proper equilibrium if "every player is giving his better responses much more probability weight than his worse responses (by a factor 1/epsilon), whether or not those 'better' responses are 'best'."
-- Myerson (1978), p 78.

For a more formal definition see sources. This is a rough paraphrase.

Source: econterms

Some balance that can occur in a model, which can represent a prediction if the model has a real-world analogue. The standard case is the price-quantity balance found in a supply and demand model. If the term is not otherwise qualified it often refers to the supply and demand balance. But there also exist Nash equilibria in games, search equilibria in search models, and so forth.

Source: econterms

In economics, an equilibrium is a situation in which no agent has an incentive to change any of her choices, given the constraints she faces (constraints being interpreted in a broad sense here):


•her perceptions of the behavior of other agents;
•the terms of trade (prices);
•the strategic environment;
•her individual characteristics such as perferences (or production technologies), wealth, and computing capabilities.

In addition to this central property, it is also required that every agent makes optimal choices based on correct expectations of these constraints. Important applications of the concept of an (economic) equilibrium are the formation of prices on markets (the competitve market equilibrium), and the strategic equilibria used in game theory.

Source: SFB 504

Real returns to investors from the purchases of U.S. government bonds have been estimated at one percent per year, while real returns from stock ("equity") in U.S. companies have been estimated at seven percent per year (Kocherlakota, 1996). General utility-based theories of asset prices have difficulty explaining (or fitting, empirically) why the first rate is so low and the second rate so high, not only in the U.S. but in other countries too. The phrase equity premium puzzle comes from the framing of this problem (why is the difference so great?) and the attention focused on it by Mehra and Prescott (1985); sometimes the phrase risk free rate puzzle is used to describe the closely related question: why is the bonds rate so low? The problem can be inverted to ask: why do investors not reject the low-returning bonds in order to buy stocks, which would then raise the price of stocks and lower their subsequent returns?

The above is drawn from the excellent review by Kocherlakota (1996) which surveys the substantial literature on this subject. Abbreviating further from it: the theories against which the evidence constitute a "puzzle" (or paradox, which see) tend to have these aspects in common: (1) standard preferences described by standard utility functions, (2) contractually complete asset markets (against possible time- and state-of-the-world contingencies), and (3) costless asset trading (in terms of taxes, trading fees, and presumably information).

Overwhelmingly the discussion in the economics literature has focused on expansions to the formal theory and on refinements and expansions of data sources, rather than survey evidence. A survey of U.S. households would answer (has answered?) the question of why they invest so little in stocks.

[Editorial comment follows.] It is likely (but this is conjecture) that large fractions of the population do not seriously consider investing in stocks, and are thus not rejecting stocks because their returns are low, but rather because they do not know how and think there are some barriers to learning how; and/or they perceive the risks of stocks to be higher than they have historically been; and/or they believe their savings are insufficient to invest. These explanations suggest that as stock trading becomes easier (e.g. over the Web, with heavy marketing and easy interfaces) the theories will fit better because more of the population will buy stocks. Indeed, this has been observed over the last few years. Another class of likely explanations is that people are highly impatient to spend their income (which would conflict with standard constant-discount-rate utility functions, but agree with the evidence; see hyperbolic discounting). Seen this way, the puzzle is not why the evidence looks the way it does, but the hard theoretical problem of getting these factors into the asset pricing models.

Source: econterms

Informally: a stochastic process is ergodic if no sample helps meaningfully to predict values that are very far away in time from that sample. Another way to say that is that the time path of the stochastic process is not sensitive to initial conditions.

Two events A and B (e.g. possible sets of states of the process) are ergodic iff, taking the limit as h goes to infinity:
lim (1/h)SUM_{from i=1}^{to i=h} |Pr(A intersection with L^-iB)-Pr(A)Pr(B)| = 0
Here L is the lag operator. This definition is like that of 'mixing on average'. A stochastic process is ergodic, I believe, if all possible events in it are ergodic by this definition.

If a random process is mixing, it is ergodic.

Priestly, p 340: A process is ergodic iff 'time averages' over a single realization of the process converge in mean square to the corresponding 'ensemble averages' over many realizations.

Example 1: Let x_t (for integer t=0 to infinity) is known to be drawn iid from a standard normal distribution. Then knowing the value of x₁ doesn't help predict the value of x₂, because they are independently drawn. This time series process is ergodic.

Example 2: Suppose the process is x_t=k+sin(t)+e_t where k is unknown and e_t is a white noise error. Then any sample of x_t for a known t gives information about k and that is enough information to make predictions at remote times in the future that are just as good as predictions at nearby times. This process is not ergodic.

Source: econterms

means persistent properties

Source: econterms

In the context of a stochastic processes {x_t}, set E is an ergodic set if:
(i) it is a subset of the state space S of possible values of x_t,
(ii) if x_t is in E, then Pr(x_t+1 is in E}=1, and
(iii) no proper subset of E has the property in (ii).

Source: econterms

The Employee Retirement Income Security Act of 1974, a major U.S. law which guaranteed certain categories of employees a pension after some period at their employer; there had been more ambiguity before about what rules an employer could put on which employees could get a pension. Also ERISA changed the perceived rules about whether pensions could be invested in venture capital.

Source: econterms

A dynamic model in which "the movement of the variables in any periods is related to the previous period's gap from long-run equilibrium."

Source: econterms

A time series process {x_t} is essentially stationary iff E[x_t²] is uniformly bounded. (from Wooldridge)

This definition may not be standard or widely used.

I believe this means that even if the variance wanders around and is different for different t, there is a finite bound to those variances. The variance of the distribution of x_t is never infinite for any t and indeed never exceeds that finite bound. Thus an ARCH-type process might be essentially stationary even though its variance is not constant for all t.

Note that there are strictly stationary processes that have infinite second moments; such processes are not essentially stationary.

Source: econterms

estimation

Source: econterms

A function of data that produces an estimate for an unknown parameter of the distribution that produced the data.
The way estimators are often discussed, they can be thought of as chosen before the data are seen. This can be hard to understand for the person new to the term. Properties of estimators (such as unbiasedness in finite samples, asymptotic unbiasedness, efficiency, and consistency) are discussed without considering any particular sample, by making assumptions about the distribution of the data, and considering the estimator in the context of the distributions.

Source: econterms

A first order condition that is across a time or state boundary. (Across a state boundary means a tradeoff between uncertain events.) That is, a first order condition that is a relation between a variable that has different values in different periods or different states. E.g. k_t = b(1+r)k_t+1 is an Euler equation, but 2n_t² - 3k_t = 0 is not.

Source: econterms

May refer to either the natural logarithm base e, approximately 2.71828, or to the Euler-Mascheroni (sp) constant, which is approximately .57721566.

Source: econterms

"Originally, it was a dollar-denominated deposit created either in a European bank or in the European subsidiary of an American bank, usually located in London." Here's why: (1) Americans overseas might want their deposits in dollars; (2) the dollar being the most common international currency, borrowers and lenders internationally may want to make their accounts in it; (3) the Eurodollar market was "exempt from reserve requirements and other regulatory costs imposed on domestic American banks. Superior terms in the Eurodollar market attracted American borrowers and depositors who would have otherwise patronized domestic institutions." An example of such regulation was the US Regulation Q which limited interest banks could pay.

Source: econterms

a name for the 'disease' of rigid, slow-moving labor markets in Europe in contrast to fast-moving markets, e.g. in North America.

Source: econterms

A function f() is even iff f(x)=f(-x).

Source: econterms

Empirical study of prices of an asset just before and after some event, like an announcement, merger, or dividend. Can be used to discuss whether the market priced the information efficiently, whether there was private information, etc.

This method was developed by Fama, Fisher, Jensen, and Roll (1969) according to Weisbach, 1988, p 455

Source: econterms

Describes game models in which players choose their strategies through a trial-and-error process in which they learn over time that some strategies work better than others.

Source: econterms

Latin for "beforehand". In models where there is uncertainty that is resolved during the course of events, the ex antes values (e.g. of expected gain) are those that are calculated in advance of the resolution of uncertainty.

Source: econterms

Firms pay dividends to those who are shareholders on a certain date. The next day is called the ex dividend date. People who own no shares until the ex dividend date do not receive the dividend. The price of the stocks is often adjusted downward before the start of trading on the ex dividend date because to compensate for this.

Source: econterms

Latin for "after the fact". In models where there is uncertainty that is resolved during the course of events, the ex post values (e.g. of expected gain) are those that are calculated after the uncertainty has been resolved.

Source: econterms

Starting point of the excess chance measures is a target return, for example a one-month market return, defined by the investor. Chance is than to be considered as the possibility to beat the target return. Special cases of excess chance measures are the excess probability, the excess expectation and the excess variance.

Source: SFB 504

Sample kurtosis minus 3, which means when 'excess kurtosis' is positive, there is greater kurtosis than in the normal distribution.

Source: econterms

Asset returns in excess of the risk-free rate. Used especially in the context of the CAPM. Excess returns are negative in those periods in which returns are less than the risk-free rate. Contrast abnormal returns.

Source: econterms

A situation in which the quantity supplied exceeds the quantity demanded. It occurs when the market price is greater than the equilibrium price.

Source: EconPort

In a simultaneous equation system -- that some of the exogenous variables are not in some of the equations; often this idea is expressed by saying the coefficient next to that exogenous variable is zero. This way of putting it may make this restriction (hypothesis) testable, and may make a simultaneous equation system identified.

Source: econterms

A requirement in a contract that the buyer will only buy goods of a certain type from the stated seller.

Source: econterms

data set from Standard and Poors on compensation to American corporate executives, including stock and options ownership.

Source: econterms

The value that individuals may attach to the mere knowledge of the existence of something, as opposed to having direct use of that thing. Synonymous with nonuse value.

For example, knowledge of the existence of rare and diverse species and unique natural environments may have value to environmentalists who do not actually see them.

Source: econterms

A variable is exogenous to a model if it is not determined by other parameters and variables in the model, but is set externally and any changes to it come from external forces. Contrast endogenous.

Source: econterms

There are several, overlapping definitions: 1) The mean of a probability distribution. If the probability distribution function is F(x) then the mean would be calculated by integrating dF(x) over the domain of the probability distribution function. The expectation operator, E[], is a linear operator per Hogg and Craig, 1995, page 55.
2) In a model, the agents may have to anticipate the value of variables whose realizations may occur in the future. The values they anticipate are often called their expectations. The agents may generalize only from past realizations in a way that we can call "adaptive expectations" or they may have other information from which they hypothesize a distribution from which the realization will be drawn. From such a distribution they can calculate the mean value, and variance, and so forth. This process is one of "rational expectations." --- Note: the notation E_x[] means the expectation of the expression taken over the random variable X. The result of the expression could still be a random variable if there are other random variables in the expression.

Source: econterms

That the utility of an agent facing uncertainty is calculated by considering utility in each possible state and constructing a weighted average, where the weights are the agent's estimate of the probability of each state. Arrow, 1963 attributes to Daniel Bernoulli (1738) the earliest known written statement of this hypothesis.

Source: econterms

An axiomatic extension of the ordinal concept of utility to uncertain payoffs. An agent possesses a von Neumann-Morgenstern utility function if she ranks uncertain payoffs according to (higher) expected value of her utility of the individual outcomes that may occur.

Source: SFB 504

The expected value of a random variable is the mean of its distribution.
In its technical use this word does not have exactly the same meaning as in ordinary English. For example, people buying a lottery ticket that has a 1/10,000 chance of paying $10,000 can expect to get zero since that is overwhelmingly the likely outcome. They can be certain they won't get $1. But the expected value of their winnings is $1.
Having said this, it is a standard implementation of 'rational expectations' to assume that agents behave in response to the expected values of the distributions they face.

Source: econterms

e(p,u) -- the minimum income necessary for a consumer to achieve utility level u given a vector of prices for goods p. (The consumer is presumed to get utility from the goods.)

Source: econterms

In the context of studies of employees, length of time employed anywhere. Sometimes narrowed to include only length of time employed in relevant jobs. Contrast tenure.

Source: econterms

An empirical research method used to examine a hypothesized causal relationship between independent and dependent variables. The antecedent event in a proposed causal sequence is called the independent variable. The measured effect in the causal sequence is called the dependent variable. The main methodological rule of experimentation is that the experimenter must have precise control over the experimental situation. Control involves the creation and variation (manipulation) of the independent variables. The values of the independent variable(s) define the experimental conditions or the design of the experiment. At a minimum, the design involves the application of a treatment to one group of participants and the withholding of the treatment from a comparison or control group. Aside this manipulation the situation in both groups must be hold identical. Accordingly, the dependent variable(s) has (have) to be assessed by consistent measures. In order to render the group samples comparable, participants must be randomly assigned to conditions. Differences that then occur on the measures of the dependent variable can be attributed to the factor which differentiates the groups systematically, the presence, absence or level of the independent variable. Without randomization the method is quasi-experimental (e.g. if gender is used as a factor in the design). Experiments can be conducted in the laboratory or in natural settings (field). Because it is easier to precisely control the experimental situation in the laboratory, this kind of experiments allow the experimenter to achieve a higher level of internal validity than in field experiments. However, if it is possible to sufficently control the experimental situation in natural conditions, field experiments are more likely to be externally valid.

Source: SFB 504

A plan for collecting and treating the data of a proposed experiment. It is important that the experimental design provides the opportunity to make appropriate inferences and decisions relating to the hypothesis from the data.

Source: SFB 504

In an experimental design, which is contrasting two or more groups, the experimental group of subjects is given the treatment whose effect is under investigation.

Source: SFB 504

The accounting costs involved in the production of a good or service. Explicit costs include fixed costs and variable costs, but do not include opportunity costs.

Source: EconPort

A particular function form for a continuous distribution with parameter k, a scalar real greater than zero. Has pdf f(x)=ke^-kx.
The mean is E[x]=1/k, and variance var(x)=1/k². Moment-generating function is (1-kt)^-1.

Source: econterms

A distribution is a member of the exponential family of distributions if its log-likelihood function can be written in the form below.

ln L(q | X) = a(X) + b(q) + c₁(X)s₁(q) + c₂(X)s₂(q) + . . . + c_K(X)s_K(q) where a(), b(), and c_j() and s_j() for each j=1 to K are functions; q is the vector of all parameters; X is the matrix of observable data; and L() is the likelihood function as defined by the maximum likelihood procedure.

The members of the exponential family vary from each other in a(), b(), and the c_j()s and s_j()s. Most common named distributions are members of the exponential family.

Quoting from Greene, 1997, page 149: "If the log-likelihood function is of this form, then the functions c_j() are called sufficient statistics [and] the method of moments estimators(s) will be functions of them," Those estimators will be the maximum likelihood estimators which are asymptotically efficient here.

Source: econterms

A particular functional form for the utility function. Some versions of it are used often in finance.

Here is the simplest version. Define U() as the utility function and w as wealth. a is a positive scalar parameter.
U(w) = -e^-aw

is the exponential utility function.

Now consider events over time. An agent might have a utility function mapping possible streams of consumption into utility values. Here is one way this is often parameterized:
Define (b) as a constant discount rate known to the agent. It's a scalar that is between zero and one, and usually thought of as near one.
Define t as a time subscript that starts at zero and increases over the integers, either to some fixed T or to infinity.
Define c(t) as the amount the agent gets to consume at each t, and {c(t)} as the series of consumptions for all relevant t. c(t) is random here. its value is not known but its distribution is assumed known to the agent.
Let E[] be the expectations operator that takes means of distributions.

Using this notation a common dynamic version of exponential utility is:
u({c_t} = the sum over all t of (b)^tE[-e^-ac(t)]

Whether this utility function describes observed investment decisions is discussable and testable. It is not often discussed, however. If clear information on that becomes known to this author, it will be added here.
Most uses of the exponential utility function in finance are driven by these aspects: (a) its analytic tractability; e.g. that it can be differentiated with respect to choice variables that affect future wealth w or consumption c(t); (b) for some applications it aggregates usefully, meaning that if every agent has this exact utility function and they can buy securities then a representative agent can be defined which also has this analytically convenient form and for whom the securities prices would be the same. It's convenient for computing securities prices in some abstract economies to use that representative agent. There are 'no wealth effects' -- that is, the amount of risky securities that the agent wants to hold is not a function of his own wealth, as long as he can borrow infinitely (which is often assumed for tractability in these models.)

Source: econterms

Goods and services that are produced in the home country and sold in other countries.

Source: EconPort

Or, extendend real numbers, or extended real line. The set of reals plus the elements (infinity) and (minus infinity). Addition and multiplication can generally be extended to this set; see Royden, p. 36

Source: econterms

Refers to the range to which a resource is utilized or applied. Example: the number of hours worked by an employee. Contrast intensive margin.

Source: econterms

or criterion related validity is a type of validity that is assessed by the relationship between test scores and an independent, non-test criterion.

Source: SFB 504

An effect of a purchase or use decision by one set of parties on others who did not have a choice and whose interests were not taken into account.
Classic example of a negative externality: pollution, generated by some productive enterprise, and affecting others who had no choice and were probably not taken nto account.
Example of a positive externality: Purchase a car of a certain model increases demand and thus availability for mechanics who know that kind of car, which improves the situation for others owning that model.

Source: econterms

In a general sense, a technological externality is the indirect effect of a consumption activity or a production activity on the consumption or production possibilities available to some other consumer or producer. By the term indirect it is meant that the effect concerns an agent other than the one exerting this economic activity and that this effect does not work through the price system. This effect has first been analyzed by Pigou (1920).

In a non-cooperative game, the utility payoff to one player usually only depends on the profile of strategies taken by all the players, but not on the identity of the players that undertake certain actions or that face certain outcomes. If this is the case, the game is said to contain externalities. In an auction with externalities, for example, the final valuation for the object in sale of each bidder depends on the identity of the player who wins the auction and receives the object. The modification of payoffs due to externalities in a game can be thought of as an immediate consequence of the actions taken during the play of the game, as in production externalities, or as a reduced-form description of expected future interactions among the players (i.e., their equilibrium behavior) after the end of the game, as in the case of an auction with resale possibilities of the object obtained.

Source: SFB 504

The F distribution is defined in terms of two independent chi-squared variables. Let u and v be independently distributed chi-squared variables with u₁ and v₁ degrees of freedom, respectively.
Then the statistic: F=(u/u₁)/(v/v₁) has an F distribution with (u₁,v₁) degrees of freedom. As can be computed from the definition of the t distribution, the square of a t statistic may be written: t²=(z²/1)/(v/v₁), where z², being the square of a standard normal variable, has a chi-squared distribution. Thus the square of a t variable with v1 degrees of freedom is an F variable with (1,v₁) degrees of freedom, that is: t²=F(1,v₁).

Source: econterms

Normally a test for the joint hypothesis that a number of coefficients are zero. Large values (greater than two?) generally reject the hypothesis, depending on the level of significance required.

Source: econterms

Indicates which services come with a price. Stands for 'free on board.' Describes a price which includes goods plus the services of loading those goods onto some vehicle or vessel at a named location, sometimes put in parentheses after the f.o.b.

Source: econterms

"A security's factor loadings are the slopes in a multiple regression of its return on the factors."

Source: econterms

An effect observed in models of international trade -- that the prices of inputs to ("factors of") production in different countries, like wages, are driven towards equality in the absence of barriers to trade. This happens among other reasons because price incentives cause countries to choose to specialize in the production of goods whose factors of production are abundant there, which raises the prices of the factors towards equality with the prices in countries where those factors are not abundant. Shocks to factor availability in a country would cause only a temporary departure from factor price equality.

The basic theorem of this kind is attributed to Samuelson (1948) by Hanson and Slaughter (1999) who also cite Blackorby, Schworm, and Venables (1993). The context of the theorem is a Heckscher-Ohlin model.

Source: econterms

factories may have been more efficient by reducing transactions costs, as argued by Oliver Williamson (1980).

Source: econterms

The conjecture that market prices for securities take long swings away from their fundamental values and tend to return to them.
In a time series of data this suggests that "the market price differs from the fundamental price by a highly serially correlated fad.". This formulation attributed to Shiller(1981, 1994), Summers (1986) and Poterba and Summers (1988) by Bollerslev and Hodrick (1992) p. 13.

Source: econterms

Contrasted with free trader, a holder of the the point of view that one's country's government must prevent foreign companies from having artificial advantages over domestic ones.

The term dates at least as far back as 1886 Britain, where tariffs were recommended by one point of view expressed in a Royal Commission report 'not to countervail any natural and legitimate advantage which foreign manufacturers may possess, but simply to prevent our own industries being placed at an artificial disadvantage by the interference of either home or foreign legislation....' (Carr and Taplin, p 122)

Source: econterms

A panel study of stocks to estimate CAPM or APT parameters

Source: econterms

two or more persons related by blood, marriage, or adoption, and residing together.

Source: econterms

Financial Accounting Standards Board, which sets accounting rules for the US. (public? private?)

Source: econterms

describes a distribution with excess kurtosis.

Source: econterms

Let {X_n} for n=1,2,3,... be a sequence of nonnegative real random variables.
Then lim inf_n->infinity E[X_n] ≥ E[lim inf_n->infinity X_n].

Source: econterms

stands for 'functional central limit theorem', and is synonymous with Donsker's theorem.

Briefly: if {e_t} is a series of independent and mean zero random variables, partial sums (from 1 to T) of the e's converge to a standard Brownian motion process on [0,1] as T goes to infinity. See other sources for a proper formal statement.

Source: econterms

Foreign Direct Investment, a component of a country's national financial accounts. Foreign direct investment is investment of foreign assets into domestic structures, equipment, and organizations. It does not include foreign investment into the stock markets. Foreign direct investment is thought to be more useful to a country than investments in the equity of its companies because equity investments are potentially "hot money" which can leave at the first sign of trouble, whereas FDI is durable and generally useful whether things go well or badly.

Source: econterms

stands for Fixed Effects estimator. That is, a linear regression in which certain kinds of differences are subtracted out so that one can estimate the effects of another kind of difference.

Source: econterms

The interest rate at which U.S. banks lend to one another their excess reserves held on deposit at the U.S. Federal Reserve.

Source: econterms

Feasible GLS. That is, the generalized least squares estimation procedure (see GLS), but with an estimated covariance matrix, not an assumed one.

Source: econterms

is intrinsically useless; is used only as a medium of exchange.

Source: econterms

Most terms are in one of these categories. You can click on one to see a list of terms relevant to it.
fields

Source: econterms

A filter is a way of treating or adjusting data before it is analyzed. Examples are the Hodrick-Prescott filter or Kalman filter.

More exactly, a filter is an algorithm or mathematical operation that is applied to a time series sample to get another sample, often called the 'filtered' data. For example a filter might remove some high-frequency effects from the data; or detrend it; or remove seasonal frequencies but leave monthly frequencies in.

Source: econterms

Full Information Maximum Likelihood, an approach to the estimation of simultaneous equations.

As portrayed in Johnston's book: Define A as the matrix of coefficients in the multiple-equation model, u as the vector of residuals for each choice of A, and s as the covariance matrix E(uu'). FIML consists of maximizing ln(L(A, s)) with respect to the elements of A and s.

Source: econterms

The study of securities, borrowing, and ownership. finance

Source: econterms

Federal Information Processing Standards. These are encodings defined by the U.S. government and used to encode some data (like states and counties) in U.S. data sets. Listings can be found at the NIST FIPS site.

Source: econterms

Defined by Alchian and Demsetz (1972) this way: "The essence of the classical firm is identified here as a contractual structure with: 1) joint input production [see team production]; 2) several input owners [e.g. the workers]; 3) one party [the firm or its owners] who is common to all the contracts of the joint inputs; 4) who has rights to renegotiate any input's contract independently of contracts with other input owners; 5) who holds the residual claim; and 6) who has the right to sell his central contractual residual status. The central agent is call the firm's owner and the employer. No authoritarian control is involved; the arrangement is simply a contractual structure subject to continuous renegotiation with the central agent. The contractual structure arises as a means of enhancing efficient organization of team production." ---------- a firm is a hierarchical organization attempting to make profits.

Source: econterms

Simultaneous bidding game where the bidder that has submitted the highest bid is awarded the object and pays his own bid (which is the 'first highest' bid). The multi-object form of the first price auction is called discriminatory auction . The equilibrium bid functions of first price auctions balance the trade- off that a higher winning probability is 'bought' by a higher expected payment. As a result, the bidders' private information is revealed in the bids in shaded form only. Oligopolistic competition of price setting firms under incomplete information (Betrand competition) is an instance of a first price procurement auction.

Source: SFB 504

The statement that a Walrasian equilibrium is weakly Pareto optimal. Such a theorem is true in a large and important class of general equilibrium models (usually static ones). The standard case is if every agent has a positive quantity of every good, and every agent has a utility function that is convex, continuous, and strictly increasing, the then the First Welfare Theorem holds.

Source: econterms

Usually means stochastic dominance.

Source: econterms

An extreme Keynesian view, that money doesn't matter at all as aggregate demand policy. Assumes that investment demand does not respond to interest rate changes. Relevant only in depression conditions (Branson, p 386).

Source: econterms

This is a necessary condition for maximum likelihood estimation to be consistent. Maximizing the likelihood function L gives an estimate for parameter b that is Fisher-consistent if: E[d(ln L)/db]=0 at b=b₀, where b₀ is the true value of b.

Another interpretation or phrasing: "An estimation procedure is Fisher consistent if the parameters of interest solve the population analog of the estimation problem." (Wooldridge).

Source: econterms

That in a model where inflation is expected to be steady, the nominal interest rate changes one-for-one with the inflation rate; see Fisher equation. The empirical analogy is the Fisher hypothesis.

Source: econterms

nominal rate of interest = real rate of interest + inflation

Source: econterms

That the real rate of interest is constant. So the nominal rate moves with inflation.
The real rate of interest would be determined by the time preferences of the public and technological constraints determining the return on real investment.

Source: econterms

The 'geometric mean of the fixed-weighted Paasche and Laspeyres indexes.' Proposed as a price index by Irving Fisher in 1922. This is a superlative index number formula. -- Triplett, 1992.

Source: econterms

A price index, computed for a given period by taking the square root of the product of the the Paasche index value and the Laspeyres index value.

Source: econterms

The Fisher information is an attribute or property of a distribution with known form but uncertain parameter values. It is only well-defined for distributions satisfying certain assumptions. It is a (k x k) matrix, where k is the number of elements in a vector of parameters b. Thus, for parameter b of pdf f(x):
I(b)=E{ [f'(x)/f(x)]² | b}
That's from DeGroot. I think this is the same as in Greene p 96:
I(b)=E[{d/db(ln L(b))}²]
=-E[d²/db²(ln L(b))]
If the Fisher information is 'large' then the estimated distribution will change radically as new data (x) are incorporated into the estimate of the distribution by maximum likelihood. The Fisher information is the main ingredient in the Cramer-Rao lower bound, and in some maximum likelihood estimators.

Source: econterms

Hypotheses about the value of r, the correlation coefficient between variables x and y of the underlying population, can be tested using the Fisher transformation of a sample's correlation coefficient r. Let N be the sample's size. This transformation is defined by: z = 0.5 * ln ( (1+r)/(1-r) ) z is approximately normally distributed with mean r, and standard error 1/((N-3)^0.5). This is a common way of testing whether a correlation coefficient is significantly different from 0, and hence ascribing a p-value. ------ [Editor: We suspect that for x and y bivariate normal the distribution works exactly in all sample sizes, otherwise only asymptotically.] [See Kennedy, p 369. Bickel and Dobson, 'Mathematical Statistics: Basic Ideas and selected topics' page 221 also gives derivation, but makes no mention of any distribution requirements.]

Source: econterms

for optimal investment by a firm -- that it should invest in real assets until their marginal internal rate of return equals the appropriately risk-adjusted rate of return on securities

Source: econterms

A cost of production that is independent of the quantity produced; a fixed costs must be paid even if nothing is produced. For example, if a trucking company buys a new semi-truck by taking out a 5-year loan to buy the truck, the loan must be paid (i.e., the truck must be paid for) even if the company decides to shut down and not operate at all. This fixed cost of production must be paid whether the company shuts down, reduces its production, or operates at full capacity.

Fixed costs such as this are the opposite of variable costs, which depend on the amount produced. In the example above, gasoline would be a variable cost â?? if the company does not operate, it does will not have to purchase any gasoline, and the amount of gasoline purchased depends on the amount produced.

Source: EconPort
See also: Variable Cost , 

A method of estimating parameters from a panel data set. The fixed effects estimator is obtained by OLS on the deviations from the means of each unit or time period. This approach is relevant when one expects that the averages of the dependent variable will be different for each cross-section unit, or each time period, but the variance of the errors will not. In such a case random effects estimation would give inconsistent estimates of b in the model: y = Xb + e
The fixed effects estimator is: (X'QX)^-1X'Qy
where Q is the matrix that "partials out" the averages from the groups that have different variances.
Example: Define L as I_N x 1_T, where x is the Kronecker cross product operator, T is the number of time periods, and N is the number of cross-section units (individuals, say). Now individual effects can be screened out by premultiplying the model's equation by Q and running OLS, or equivalently using the estimator equation above. Thus estimating b.

Source: econterms

A macro model in which there is a variable relationship between the growth rate of out put and the level of net investment. The relation between the change in output and the level of net investment is the accelerator principle.

Source: econterms

An occasional compressed form of f.o.b..

Source: econterms

The theorem is that a Nash equilibrium exists in repeated games in which sufficiently patient players to reach Pareto optimal payoffs in a Nash equilibrium. (Fudenberg and Tirole, p 150, describes the achievable payoffs as the individually rational ones, not the Pareto optimal ones.) The strategies that achieve this often have the pattern that they 'punish' the other player at length for any defection from the Pareto optimal choice. In equilibrium that encourages the other player not to defect for a short term gain.

Source: econterms

A decision-frame is the decision-maker's subjective conception of the acts, outcomes and contingencies associated with a particular choice. The frame that a decision maker adopts is controlled partly by the formulation of the problem and by the norms, habits, and personal characteristics of the decision maker. It is often possible to frame a given decision problem in more than one way. A framing effect is a change of preferences between options as a function of the variation of frames, for instance through variation of the formulation of the problem. For example, a problem can be presented as a gain (200 of 600 threatened people will be saved) or as a loss (400 of 600 threatened people will die), in the first case people tend to adopt a gain frame, generally leading to risk-aversion, and in the latter people tend to adopt a loss frame, generally leading to risk-seeking behavior.

Source: SFB 504

Informally: A derivative (slope) defined for mappings from one vector space to another.

The first e in Frechet should have an accent aigu.

Formally (this taken more or less directly from Tripathi, 1996):
Let T be a transformation defined on an open domain U in a normed space X and mapping to a range in a normed space Y.
(Does normed space mean normed vector space? Or might it not?)

Holding fixed an x in U and for each h in X, if a linear and continuous operator L (mapping from X to Y) exists such that:

lim_{||h|| falls to 0} (1/||h||) * (||T(x+h)-T(x)-L(h)||) = 0

Then the operator L, often denoted T'(x), is the Frechet derivative of T() and we can say T is Frechet differentiable at x. (Ed.: I believe any such L is unique.)

Source: econterms

Informally: A possible property of mappings from one space to another. For such a transformation, a Frechet derivative may exist at each point and if so we say the transformation is Frechet differentiable at that point.

Properly the first e in Frechet should have an accent aigu.

See the entry at Frechet derivative for a formal definition.

Source: econterms

Shorthand for U.S. Federal Home Loan Mortgage Corporation.

Source: econterms

cash flow to a firm in excess of that required to fund all projects that have positive net present values when discounted at the relevant cost of capital.
Free cash flow can be a source of principal-agent conflict between shareholders and managers, since shareholders would probably want it paid out in some form to them, and managers might want to control it, e.g. to use it for unprofitable projects, for perquisites, to make acquisitions, to create jobs for friends and allies, and so forth. A possible partial solution to the conflict for the shareholders is for the company to have heavy debts on which frequent, heavy payments are due. Those payments keep the managers focused on delivering consistent revenues and clear out the extra cash.

Source: econterms

An assumption posited in a search and matching model of a market. The assumption is that there is no institutional constraint on firms entering the market (e.g. to hire workers). There is no fixed number of firms. The number of firms is determined in equilibrium, by the costs of starting up.

Source: econterms

excess reserves minus borrowed reserves (Branson, p 353).

Source: econterms

Holder of the political point of view that the best policy is to allow free trade into one's own country.

Source: econterms

The frequency function is the probability of drawing each particular value from a discrete distribution: p(x) = Pr(X=x). Here X is the random variable and x is one of its possible values.

Source: econterms

Unemployment that comes from people moving between jobs, careers, and locations. Contrast structural unemployment.

Source: econterms

In a cash-in-advance model of a monetary system, the Friedman rule for monetary policy is to deflate so that it is not costly to those who have money to continue to hold it. Then the cash-in-advance constraint isn't binding on them.

Source: econterms

Abbreviaton for the U.S. national Federal Trade Commission, which rules in some circumstances on some antitrust regulations. See also FTC.

Source: econterms

A 1914 U.S. law creating a regulatory body for antitrust, price discrimination, and regulation. Section five says "Unfair methods of competition in or affecting commerce, and unfair or deceptive acts or practices in or affecting commerce, are hereby declared unlawful."

Source: econterms

a mapping from paths of functions to the reals (e.g. a value function defined by a mapping from possible paths of choices)

Source: econterms

an equation where the unknown is a function. Example: a value function is the solution to the equation that sets the value function equal to the present discounted value of the current period's utility and the discounted value function of next period's state.

Source: econterms

"Being of such a nature or kind that one unit or part may be exchanged or substituted for another unit or equal part to discharge an obligation."
Examples: money or grain. Not examples: works of art.

Source: econterms

A future-oriented agent discounts the future lightly and so has a LOW discount rate, or equivalently a HIGh discount factor. See also present-oriented, discount rate, and discount factor.

Source: econterms

Given a statistical model y = X₁b₁ + X₂b₂+ e
where
y is a vector of values of a dependent variable,
the X's are linearly independent matrices of predetermined variables, and
the e's are errors, we could premultiply the equation by M₁=I-X₁(X₁'X₁)^-1X' which projects vectors in the space spanned by X₁ to zero, and run OLS on the resulting equation M₁y = M₁X₂b₂+ M₁e
and (the theorem says) would get exactly the same estimate of b₂ that OLS on the first equation would have given.
This use of premultiplying is used in the derivation of many estimators: notably IV estimators and FE estimators.

Source: econterms

A game is a model with (1) players who make (2) strategy (or action) choices in a (3) predefined time order, and then (4) receive payoffs, which are usually conceived of in money or utility terms. Classic games are the Prisoner's Dilemma, Matching Pennies, the Battle of the Sexes, the dictator game, the ultimatum game, the Bertrand game, and the Cournot game.

Source: econterms

Theory of rational behavior for interactive decision problems. In a game, several agents strive to maximize their (expected) utility index by chosing particular courses of action, and each agent's final utility payoffs depend on the profile of courses of action chosen by all agents. The interactive situation, specified by the set of participants, the possible courses of action of each agent, and the set of all possible utility payoffs, is called a game; the agents 'playing' a game are called the players.

In denegerate games, the players' payoffs only depend on their own actions. For example, in competitive markets (competitive market equilibrium), it is enough that each player optimizes regardless of the behavior of other traders. As soon as a small number of agents is involved in an economic transaction, however, the payoffs to each of them depend on the other agents' actions. For example in an oligopolistic industry or in a cartel, the price or the quantity set optimally by each firm depends crucially on the prices or quantities set by the competing firms. Similarly, in a market with a small number of traders, the equilibrium price depends on each trader's own actions as well as the one of his fellow traders (see auctions).

Whenever an optimizing agent expects a reaction from other agents to his own actions, his payoff is determined by other player's actions as well, and he is playing a game. Game theory provides general methods of dealing with interactive optimization problems; its methods and concepts, particularly the notion of strategy and strategic equilibrium find a vast number of applications throughout social sciences (including biology). Although the word 'game' suggests peaceful and 'kind' behavior, most situations revelant in politics, psychology, biology, and economics involve rather strong conflicts of interest, competition, and cheating, apart from leaving room for cooperation or mutually benefically actions.

Based on a model of optimizing agents that plan individually optimal course of play, knowing that her opponents will do so as well, the basic objects of interest in strategic (or 'non-cooperative') game theory are the players' strategies. A player's strategy is a complete plan of actions to be taken when the game is actually played; it must be completely specified before the actual play of the game starts, and it prescribe the course of play for each decision that a player might be called upon to take, for each possible piece of information that the player may have at each time where he might be called upon to act. A strategy may also include random moves. It is generally assumed that the players evaluate uncertain payoffs according to von Neumann Morgenstern utility. In addition to the strategic branch of game theory, there is another one that focuses on the interactions of groups of players that jointly strive to maximize their surplus. While this second branch represents the analysis of coalitional games, which centers around notions of 'coalitionally stable' payoff configurations, we focus here on strategic game theory (from which coalitional games are derived).

Given a strategic game, a profile of strategies results in a profile of (expected) utility payoffs. A certain payoff allocation, or a profile of final moves of the players is called an outcome of the game. An outcome is called an equilibrium outcome if no player can unilaterally improve the outcome (in terms of his own payoff) given that the other players stick to their equilibrium strategies. A profile of strategies is called a (strategic) equilibrium if, given that all players conform to the prescribed strategies, no player can gain from unilaterally switching to another strategy. Alternatively, a profile of strategies forms an equilibrium if the strategies form best responses to one another. (Unfortunately, it is impossible to describe what is an equilibrium other than in such a self-referential way. The best way to understand this definition is then to take it literally.) Only equilibrium outcomes are reasonable outcomes for games, because outside an equilibrium there is at least one player that can improve by playing according to another strategy. An implicit assumption of game theory is that the players, being rational, are able to reproduce any equilibrium calculations of anybody else. In particular, all the equilibrium strategies must be known to (as they are computed by) the players. Similarly, it is assumed that the whole structure of the game, in much the same way as the players' social context, is known by each player (and that this knowledge itself is known etc.)

Source: SFB 504

game theory

Source: econterms

Time structure of possible moves describing an extensive form game. A game tree is a set of nodes some which are linked by edges. A tree is a connected graph with no cycles. The first move of the game is identified with a distinguished node that is called the root of the tree. A play of the game consists of a connected chain of edges starting at the root of the tree and ending, if the game is finite, at a terminal node. The nodes in the tree represent the possible moves in the game. The edges leading away from a node represent the choices or actions available at that move. Each node other than the terminal node is assigned a player's name so that it is known who makes the choice at that move. Each terminal node must be labeled with the consequences for each player if the game ends in the outcome corresponding to that terminal node.

Source: SFB 504

As used with respect to options: The rate of change of the portfolio's delta with respect to the price of the underlying asset. Formally this is a partial derivative.

A portfolio is gamma-neutral if it has zero gamma.

Source: econterms

A distribution relevant to, for example, waiting times. Expression of its pdf requires reference to the gamma function which will be called GAMMA(a) here. (When HTML supports math a better display will be possible.) The gamma distribution's pdf has parameters a>0 and b>0, and GAMMA(a) is also greater than zero. The support is on x>0:
f(x)=[x^a-1e^-x/b]/[GAMMA(a)b^a]

Source: econterms

A function of a real a>0. It is the integral over y from zero to infinity of y^a-1e^-y dy. This integral is the gamma function of a, GAMMA(a). (When HTML supports math a better display will be possible.) The gamma distribution is a function that includes the gamma function.

Source: econterms

Generalized ARCH. First paper may have been Bollerslev, 1986, Journal of Econometrics

Source: econterms

abbreviation for the Generalized Axioms of Revealed Preference.

Source: econterms

A matrix programming language and programming environment. Made by Aptech.

Source: econterms

an adjective that describes a random variable, meaning it has a normal distribution.

Source: econterms

The Gaussian kernel is this function: (2PI)^-.5exp(-u²/2). Here u=(x-x_i)/h, where h is the window width and x_i are the values of the independent variable in the data, and x is the value of the independent variable for which one seeks an estimate. Unlike most kernel functions this one is unbounded on x; so every data point will be brought into every estimate in theory, although outside three standard deviations they make hardly any difference.
For kernel estimation.

Source: econterms

A white noise process with a normal distribution.

Source: econterms

Gross domestic product. For a region, the GDP is "the market value of all the goods and services producted by labor and property located in" the region, usually a country. It equals GNP minus the net inflow of labor and property incomes from broad. -- Survey of Current Business

A key example helps. A Japanese-owned automobile factory in the US counts in US GDP but in Japanese GNP.

Source: econterms

A measure of the cost of goods purchased by U.S. households, government, and industry. Differs conceptually from the CPI measure of inflation, but not by much in practice.

Source: econterms

An abbreviation for the journal Games and Economic Behavior.

Source: econterms

general equilibrium

Source: econterms

A model of the form y=g(b'x) where y is a vector of dependent variables, x is a column vector of independent variables, b' is a row vector of parameters (that is, b is not a function of x) and g() is a possibly random function called a link function.

Examples: linear regression (y=b'x+errs) and logistic regression y=1/(1+e^-x)+errs.

An example that is not in the class of generalized linear models is: y=x₁*x₂.

Source: econterms

See GMM.

Source: econterms

Synonym for Heckit.

Source: econterms

A continuous-time random walk with a drift and random jumps at every point in time (roughly speaking). Algebraically:
a(x,t)dt + b(x,t)c(dt)^.5
describes a generalized Wiener process, where:
a and b are deterministic functions
t is a continuous index for time
x is a set of exogenous variables that may change with time
dt is a differential in time
c is a random draw from a standard normal distribution at each instant

Source: econterms

in a dynamical system, the generator function maps the old state N_t into new state N_t+1 E.g. N_t+1 = F(N_t).
A steady state would be an N^* such that F(N^*) = N^*.

Source: econterms

Geometric mean is a kind of average of a set of numbers that is different from the arithmetic average. The geometric mean is well defined only for sets of positive real numbers. Geometric mean of A and B is the square root of (A*B). The geometric mean of A, B, and C is the cube root of (A*B*C). And so forth. Contrast this to the arithmetic means, which are .5*(A+B) and .333*(A+B+C).

Source: econterms

abbrevation for Generalized Extreme Value distribution. The difference between two draws of GEV type 1 variables has a logistic distribution, which is why a GEV distribution for errors gets assumed in certain binary econometric models.

Source: econterms

Refers to a paper by Greenwood, Hercowitz, and Huffman (1988) with utility functions across agents and across time by:
u(C_it, N_it) = C_it - N_it^b
where a>0 and b>1 are constants, and C_it and N_it stand for consumption and hours worked by each agent i at date t.
-- this utility function has Gorman form and so it aggregates
-- it has been successful at matching cross-section data relative to other functions that do.

Source: econterms

A way to generate empirical distributions of two variables from a model. Say the model defines probability distributions F(X|Y) and G(Y|X). Then start with a random set of possible X's, draw Y's from G(), then use those Y's to draw X's, and so on indefinitely. Keep track of the X's and Y's seen, and this will give samples enough to find the unconditional distributions of X and Y.

Source: econterms

A descriptive relationship between size and growth -- that the size of units and their growth percentage statistics are statistically independent. Sometimes Gibrat's law is thought to apply to large firms, and sometimes to cities (Gabaix, May 1999 American Economic Review, page 130).

Source: econterms

A number between zero and one that is a measure of inequality. An example is the concentration of suppliers in a market or industry.

The Gini coefficient is the ratio of the area under the Lorenz curve to the area under the diagonal on a graph of the Lorenz curve, which is 5000 if both axes have percentage units. The meaning of the Gini coefficient: if the suppliers in a market have near-equal market share, the Gini coefficient is near zero. If most of the suppliers have very low market share but there exist one or a few supplies providing most of the market share then the Gini coefficient is near one.,

In labor economics, inequality of the wage distribution can be discussed in terms of a Gini coefficient, where the wages of subgroups are fractions of the total wage bill.

Source: econterms

A 1933 United States national law separating investment banking and commercial banking firms. Also prohibited banks from owning corporate stock. It was designed to confront the problem that banks in the Great Depression collapsed because they held a lot of stock.

Source: econterms

Generalized Least Squares. A generalization of the OLS procedure to make an efficient linear regression estimate of a parameter from a sample in which the disturbances are heteroskedastic. That is, in
y = Xb + e (equation 1)
that the e's vary in magnitude with the X's.
The estimator of b is: (X'O^-1X)^-1X'O^-1y (equation 2)
where O, standing for omega, is the covariance matrix. (As you see in the estimator, the covariance matrix is assumed to be invertible.)
The procedure to derive this is to multiply through the first equation by the square root of the inverse of the covariance matrix (which assumed to be known; if it estimated, one calls this procedure FGLS, for feasible GLS.) Then take OLS of the resulting equation.

Source: econterms

Stands for Generalized Method of Moments, an econometric framework of Hansen, 1982. It is an approach to estimating parameters in an economic model from data. Used often to figure out what standard errors on parameter estimates should be.

Source: econterms

Gross national product. The GDP is "the market value of all the goods and services producted by labor and property belonging to the region, usually a country. It equals GDP plus the net inflow of labor and property incomes from broad. A Japanese-owned automobile factory in the US counts in US GDP but in Japanese GNP.

Source: econterms

f'(k^*)=(1+n) where k^* is optimal capital stock, f() is the aggregate production function, and n is population growth rate. f(k)-k is consumed by the population. 'Golden Rule' may refer to a Solow fairy tale.

Source: econterms

A good is a desired commodity.

Source: econterms

The accounting term to describe the premium that acquiring companies pay over the book value of the firm being acquired. Goodwill can include value for R&D and trademarks.

Source: econterms

Of a stock price. From M. R. Gordon (1962). This model is sometimes used as a baseline for comparison or for intuition.
Assume a constant rate of return r, and a constant dividend growth rate g. Define P_t to be the price of the stock in period t, and D_t to be its dividend in period t. Implication is that price of stock P_t = D_t/(r-g).

Source: econterms

A utility function or indirect utility function is in Gorman form if it is affine with respect to some argument. Which argument should be clear from context. E.g.:
U_i(x_i, z) = A(z)x_i + B_i(z)
Here the utility U_i for individual i is is affine in argument x_i. A critical implication is that the sum of Gorman form utility functions for individuals is a well-defined aggregate utility function under some conditions....

Source: econterms

A situation, usually discussed in a model not in the real world, in which the behavior of optimizing agents in a market with a government would not produce a Pareto optimal allocation. The point is not that a particular government had, or would have, failed at something, but that the problem abstractly put cannot be perfectly solved by the government. The most common source of government failures in models is private information among the agents.

Source: econterms

Informally, if one time series helps predict another, we can say it Granger causes the other. The original definition, for linear predictors, is in Granger, 1980. From Sargent: A stochastic process z_t is said NOT to Granger-cause a random process x_t if E(x_t+1 | x_t,x_t-1,...,z_t,z_t-1,...) = E(x_t+1 | x_t,x_t-1,...) *** NOTE in J Pehkonen, Applied Economics, 1991, 23, 1559-1568, p. 1560. *** Expert treatment of this subject and more formal, less ambiguous definitions are in Chamberlain, Econometrica, May 82

Source: econterms

Conditions on the regressors under which the OLS estimator will be consistent.

The Grenander conditions are weaker than the assumption on the regressor X that lim_n->infinity(X'X)/n is a fixed positive definite matrix, which is a common starting assumption.

See Greene, 2nd ed, 1993, p 295.

Source: econterms

Some version of "Bad money will drive out good." I think the context is that if there are two suppliers of the same money (e.g. if one of them is a counterfeiter) or of two monies with a fixed exchange rate between them (per Hayek, Denationalization of Money, 1976 p. 39), there will be a tendency for overproduction and that the actual money stock will be made up of the bad, or less valuable, one. (Another situation is if one supplier makes coins that are 90% gold and the other has the option of making coins with less gold, Bertrand competition for coins would drive the gold fraction down over time.)

Source: econterms

German Socio-Economic Panel. A German government database going back to at least 1984.

Source: econterms

Stands for Herfindahl-Hirschman index, which is a way of measuring the concentration of market share held by particular suppliers in a market. It is the sum of squares of the percentages of the market shares held by the firms in a market. If there is a monopoly -- one firm with all sales, the H index is 10000. If there is perfect competition, with an infinite number of firms with near-zero market share each, the H index is approximately zero. Other industry structures will have H indices between zero and 10000.
Tirole's version is bounded between zero and one because each of the market shares is between zero and one.

Source: econterms

That high wages and labor scarcity stimulated technological progress in the U.S. in the 1800s, and in particular brought about the American system of manufacturing based on interchangeable parts. (This description from Mokyr, 1990; idea from Habakkuk, 1962).

Source: econterms

Generally, habits are conceptualized as the learning of sequences of acts that have become automatic responses to specific situations, which may be functional in order to achieve a given result, or to obtain certain goals or end states (e.g. James, 1890, Triandis, 1977, Watson, 1914). Habits thus comprise a goal directed type of automaticity; they are instigated by a specific goal directed state of mind on the presence of triggering stimulus cues, for instance taking the car to travel to the supermarket. Once evoked, the behavior will run to completion without the need for attentional control of the process. Habit strenght is proposed to increase as a result of repetitions of positive reinforcements.

Source: SFB 504

Hahn (1965) question: when does there exist an equilibrium in a model in which money has positive value?

Source: econterms

See J statistic

Source: econterms

A synonym for labor-augmenting, in practice.

Source: econterms

Given a model and data in which fixed effects estimation would be appropriate, a Hausman test tests whether random effects estimation would be almost as good. In a fixed-effects kind of case, the Hausman test is a test of H₀: that random effects would be consistent and efficient, versus H₁: that random effects would be inconsistent. (Note that fixed effects would certainly be consistent.) The result of the test is a vector of dimension k (dim(b)) which will be distributed chi-square(k). So if the Hausman test statistic is large, one must use FE. If the statistic is small, one may get away with RE.

Source: econterms

escape rate; rate of transition out of current state

Source: econterms

Is a mapping from the real line to {0, 1}, denoted (at least sometimes) hv(x). hv(x) is zero for x<0, and is one for x>=0.

Source: econterms

An occasional name for generalized Tobit. This approach allows a different set of explanatory variables to predict the binary choice from those which predict the continuous choice. (The data environment is one in which the continuous choice is measured only when the binary choice is nonzero -- e.g., if we have data on people, whether they bought a car, and how expensive it was, we can estimate a statistical model of how expensive a car other people would buy, but only on the basis of the ones who did buy a car in the data sample.) A regular, non-generalized Tobit constrains the two sets of variables to be the same, and the signs of their effects to be the same in the two estimated equations. 'Heck' is for James Heckman.

-- Christopher Baum, Boston College economics department, 20 May 2000, in a broadcast to the statalist, the email list of people interested in the software Stata.

Source: econterms

A way of estimating treatment effects when the treated sample is self-selected and so the effects of the treatment are confounded with the population that chose it because they expected it would help -- the classic example is that college educations may be selected by those most likely to benefit.

Taking that example, we wish to advance past the following regression:
w_i = a + bX_i + dC_i + e_i
where i indexes people, w_i is the wage (or other outcome variable) for agent i, X_i are variables predicting i's wage, and C_i is 1 if i went to college and 0 if not. e_i is the remaining error after least squares estimation of a, b, and d.

Source: econterms

A model of the effects of international trade. "The Heckscher-Ohlin framework typically is presented as a two-country, two-good, two-factor model. The two countries are assumed to share identical, homothetic tastes for the two substitutable goods and identical, constant-returns-to-scale technologies with some factor substitutability. Perfect competition prevails in each market with zero transport costs and no artificial barriers to international trade in goods, although factors are internationally immobile. In this framework, each country will (incompletely) specialize in production and export the good using intensively in production the factor that the country has in relative abundance." That effect is called factor-price equalization across countries, and is used sometimes to explain how rising international trade would lead to greater income inequality in the most developed countries. (from Bergstrand, Cosimano, Houck, and Sheehan, 1994, p 3)
The reference in the name is to "Scandinavian economists Eli Heckscher and Bertil Ohlin early in [the twentieth century]" in work that is rarely cited directly. (from Bluestone, 1994, p 336).

Source: econterms

A hedge strategy is the intentional reduction of the loss risk (downside risk) of an underlying asset to the debit of the gain chance. Usually hedge strategies are done with derivative securities, e.g. options.

Source: SFB 504

of or relating to utility. (Literally, pleasure-related.) A hedonic econometric model is one where the independent variables are related to quality; e.g. the quality of a product that one might buy or the quality of a job one might take.

A hedonic model of wages might correspond to the idea that there are compensating differentials -- that workers would get higher wages for jobs that were more unpleasant.

"A product that meets several needs, or has a variety of features ... generates a number of hedonic services. Each one of these services can be thought of as generating its own demand, along with a resulting hedonic price. Although each separate component is not observable, the aggregation of all the components results in the observed product demand and equilibrium price.... [Q]uality improvements will appear to an observer as an outward shift of the product demand curve, as consumers are willing to purchase more at the prevailing price." -- William J. White, "A Hedonic Index of Farm Tractor Prices: 1910-1955", Ohio State University working paper, October 1998, pp. 3-4.

Source: econterms

A list of fields contained here is below. There is some other advice at this help page: http://econterms.com/help.html

Most terms are in one of these categories. You can click on one to see a list of terms relevant to it.
fields

Source: econterms

See 'H index'.

Source: econterms

The Hermite polynomials are a series of polynomials defined for each natural number r, used for statistical approximations I believe. Click here for the equation and graphs of the first several.

Source: econterms

The matrix of second derivatives of a multivariate function. That is, the gradient of the gradient of a function. Properties of the Hessian matrix at an optimum of differentiable function are relevant in many places in economics: 1) In maximum likelihood estimation, the information matrix is (-1) times the Hessian.

Source: econterms

A stochastic process is heterogeneous if it is not identically distributed every period.

Source: econterms

An alternate spelling of heteroskedastic. McCulloch (1985) argues that the spelling with the k is preferred, on the basis of the pronunciation and etymology (Greek not French derivation) of the term.

Source: econterms

An adjective describing a data sample or data-generating process in which the errors are drawn from different distributions for different values of the independent variables.
Most commonly this takes the form of changes in variance with the magnitude of X. That is, in
y = Xb + e
that the e's vary in magnitude with the X's. (An example is that variance of income across individuals is systematically higher for higher income individuals.)
If the errors are drawn from different distributions, or if higher moments of the error distributions vary systematically, these are also forms of heteroskedasticity.

Source: econterms

A heuristic is a strategy that can be applied to a variety of problems and that usually ? but not always ? yields a correct solution. People often use heuristics (or shortcuts) that reduce complex problem solving to more simple judgmental operations. Three of the most popular heuristics are discussed by Tversky and Kahnemann (1974):

Source: SFB 504

For whether a cost-benefit analysis supports a public project. The criterion is that the gainers from the project could in principle compensate the losers. That is, that total gains from the project exceed the losses. The criterion does not go so far as the Pareto criterion, according to which the gainers would in fact have to compensate the losers.

Source: econterms

An attribute of an effectiveness variable in a production function. The attribute is that it does not affect labor differently from the way it affects capital.

The canonical example is the Solow model production function Y=AF(K,L). There Y is output, L labor, K capital, F a production variable, and A represents some kinds of effectiveness variable. In Y=F(AK,L) the effectiveness variable affects capital but not labor. In Y=F(K,AL) it affects labor but not capital. These two cases can be described as Hicks-biased. In Y=AF(K,L) it is Hicks-neutral.

Source: econterms

Given a production function AF(K,L) changes in A are Hicks-neutral, meaning that they do not affect the optimal choice of K or L. The subject comes up in practice only for aggregate production functions.

Uzawa, H. 'Neutral Inventions and the Stability of Growth Equilibrium,' The Review of Economic Studies 28:2 (Feb., 1961), 117-124 contains the first known published use of the adjective 'Harrod neutral' According to it, the criterion of Harrod-neutrality comes from

Harrod, Roy F., 'Review of Joan Robinson's Essays in the Theory of Employment,' Economic Journal, vol. 47 (1937), 326-330.

Uzawa also proves that AF(K,L) and F(K,AL) are the right functional forms to meet Hicks and Harrod-neutrality, and that only the Cobb-Douglas form accomplishes both.

Source: econterms

h(p,u) -- the amount of a good that demanded by a consumer given that it costs p per unit and that the consumer will have utility u from all goods. h(p,u) is the cost-minimizing amount.

Source: econterms

A panel data set on U.S. high school students.

Source: econterms

reserves plus currency

Source: econterms

A complete normed metric space with an inner product. So the Hilbert spaces are also Banach spaces. L² is an example of a Hilbert space. Any Rⁿ with n finite is another.

Source: econterms

It is a common observation that events in the past appear simple, comprehensible, and predictable in comparison to events in the future. Everyone has had the experience of believing that they knew all along the outcome of a football game, a political election or a business investment. The hindsight bias is the tendency for people with outcome knowledge to believe falsely that they would have predicted the reported outcome of an event. After learning of the occurrence of an event, people tend to exaggerate the extent to which they had foreseen the likelihood of its occurrence.

Source: SFB 504

Contemporary models suggest that the hindsight bias appears due to reconstructive processes while people try to generate their original estimates.
One is loosely based on the response bias hypothesis, originally developed in eyewitness testimony research: People are assumed either to have remembered or to have forgotten their original judgements. Those that do remember their original estimates are likely to reproduce them. Those who have forgotten them are forced to guess and, in the presence of outcome information, are likely to utilize this information as an anchor assuming that their estimates must have been somewhere in the proximity of the true outcome. But since people are generally optimistic about their capacities, they will locate their presumed prior estimates closer to the real outcome than it had actually been, resulting in the hindsight bias.
Other authors concentrate their assumptions on three different stages in the reconstructive process: Selective retrieval, prejudiced interpretation and weighing of different cues.
Finally, the hindsight distortion may be triggered by the heuristic of anchoring and adjustment.

Source: SFB 504

Hindsight Bias is a strong phenomenon which has been observed in many circumstances, and appears to influence every-day decision-making. Researchers are trying to develop hindsight bias models to provide a better theoretical explanation. Another aspect is practical relevance, whereby real-life cases need to be examined for evidence on distortion influence.

Source: SFB 504

Fischhoff´s original explanation of the hindsight bias, Immediate Assimilation Hypothesis, states that memory for original predictions is altered by subsequent outcome (Fischhoff, 1975). When learning about the actual or alleged outcome, the person re-interprets the original evidence in the light of the outcome. They are therefore inadvertently modifying what had been previously stored in memory. Subsequent outcome knowledge is integrated immediately into the existing knowledge structure. This results in a permanent modification of the person´s prior representation of the event. Other variations of the memory impairment hypothesis suggest that the origins of hindsight biases lay in the retrieval stage. The Selective Retrieval Hypothesis maintains that known outcome serves as a retrieval cue for relevant case material. Once an outcome has been learned, information congruent with this outcome will become highly accessible. Incongruent information cannot be retrieved with the same ease. The authors of the Dual Memory Traces Model (Hell, Gigerenzer, Gauggel, Mall & Müller, 1988) suggested an extension of Fischhoff´s model. They assume two separate memory traces for own judgements and subsequent outcome information. The strength of hindsight biases is determined by the relative strength of the memory traces.

Source: SFB 504

Motivational explanations suggest that judgement and decision processes are not only affected by rational cognitions. They are also influenced by actual needs and motives, including need for control, need for cognition, self-relevance and, most importantly self-presentation concerns. In the latter approach, people are motivated to make others believe that their predictions were close to the actual outcome, in an attempt to maintain a high level of public self-esteem. Contrary to the memory impairment hypothesis, this explanation interprets hindsight distortions as adjustments during the response generation state. Several authors showed, that empirical evidence for motivational underpinnings of the knew-it-all-along effect is rather weak.

Source: SFB 504

Every-day life provides numerous examples on the practical relevance of hindsight bias. This was shown in a medical context. A GP´s second opinion does not differ completely from another GP´s opinion, if he/she is aware of the first opinion. This seems to be of serious consequence if one considers that a second opinion is only required when serious illnesses have been diagnosed.

In a legal context, hindsight bias was found to occur when a jury makes a final decision in court. In the course of a trial, the judge is empowered to order the jury to ignore certain testimonials, by disallowing them. It has been proven impossible to ignore such information.

Hindsight bias also plays a role in an economic context. An economic expert may, for example, analyze certain share activity, as if he/she had always known what would happen. This results in them forming a higher opinion of their own judgement. This in turn can have a long-term, restrictive effect on their individual learning capability as well as future decision-making. In addition to this intra-personal effect, it is possible for inter-personal effects to arise. Example: A supervisor may no longer be able to make an undistorted judgement on his employees´ decision-making if he/she got information about some results of their performance. This is a special problem in the case of poor outcome because it could happen, despite them having acted correctly on the information they were given at the time.

Source: SFB 504

This model was originally conceived during eyewitness testimony research. This was to account for the fact that witnesses receiving misleading information about a previously observed event, show a poorer memory for it. Similar to the hindsight bias, the misleading information effect was originally attributed to memory impairment.

Subsequent interpretations offered the following explanation: Rather than altering existing memory traces, the new information may be used as a reference point by those who cannot remember the original information and therefore need to guess. Misleading information does not alter the original representation, but simply serves as an anchor to perceivers who are unable to retrieve it. Parallels between the hindsight bias and the misleading information paradigms are obvious. Both lines of research query whether information stored in the memory might be less accessible after being confronted with inconsistent new information. The experimental designs of both research traditions show strong similarities. Important differences: In the misleading information paradigm, the original information is presented by the experimenter. In hindsight bias studies however, the original estimates are generated by the subjects. Misleading information is presented unobtrusively without the subjects being aware of its misleading nature. Outcome information given in hindsight studies is explicitly labeled as the correct information.

Source: SFB 504

More recent studies have come up with models that enable precise forecasting of the strength and direction of the hindsight distortion, using a quantitative basis. Researchers are also attempting to determine how far hindsight decisions affect a person´s trust in their own judgements. They are also trying to determine how far such decisions affect a person´s impression of their competency in future decision-making on the same subject. Another interesting point to be examined is the relationship between hindsight bias and the attribution of responsibility.

Source: SFB 504

Although there is a wealth of literature on hindsight distortions, the underlying mechanisms are not yet fully understood. Attempts of explanation were given in three major theoretical areas: Models of memory impairment state that outcome knowledge affects memory for previous judgements by either altering or erasing existing memory traces, or by rendering them less accessible. Other attempts to explain the hindsight bias are based on assumptions that these distortions are driven by motivations. An alternative explanation is that people use distorting heuristics while reconstructing their original judgements.

Source: SFB 504

The subject of economic history is anything in history that is subject to economic explanations. Application of formal theory or statistical analysis of data may be relevant, although it is possible to make a contribution without either, e.g. with a case study or a contextual reinterpretation. Historians tend to be focused on what happened, how, and why, not on the question of whether a model fits the evidence.
history

Source: econterms

Statistical software for Hierarchical Linear Modeling, from Scientific Software International.

Source: econterms

Algorithm for choosing smoothed values for a time series. The H-P filter chooses smooth values {s_t} for the series {x_t} of T elements (t=1 to T) that solve the following minimization problem: min { {(x_t-s_t)² ... etc. } Parameter l>0 is the penalty on variation, where variation is measured by the average squared second difference. A larger value of l makes the resulting {s_t} series smoother; less high-frequency noise. The commonly applied value of l is 1600. For the study of business cycles one uses not the smoothed series, but the jagged series of residuals from it. See Cooley, 1995, p 27-29. That H-P filtered data shows less fluctuation than first-differenced data, since the H-P filter pays less attention to high frequency movements. H-P filtered data also shows more serial correlation than first-differenced data. For l=1600: "if the series were stationary, then [this choice] would eliminate fluctuations at frequencies lower than about thirty-two quarters, or eight years."

Source: econterms

One of a certain class of contracting problems.

Imagine a situation where there is profit to be made if agents A and B work together, so they consider an agreement to do so after A buys the necessary equipment. The hold-up problem (in this context) is A might not be willing to take that agreement, even though the outcome would be Pareto efficient, because after A has made that investment, B would have the power might decide to demand a larger share of the profits than before, since A is now deeply invested in the project but B is not, so B has some bargaining power that wasn't there before the investment. B could demand all of the profits, in fact, since A's alternative is to lose the investment entirely.

Other hold-up problems are analogous to this one.

Source: econterms

An attribute of a function g:R^d->R. g can be said to be Holder continuous if there exist constants C and 0<=E<=1 such that for all u and v in R^d:
|g(u)-g(v)| <= C||u-v||^E

So if g is Holder continuous for C=1 then it is Lipschitz continuous? And if g is Holder continuous then it is continuous.

Source: econterms

An alternate spelling of homoskedastic. McCulloch (1985) argues that the spelling with the k is preferred, on the basis of the pronunciation and etymology (Greek not French derivation) of the term.

Source: econterms

An adjective describing a statistical model in which the errors are drawn from the same distribution for all values of the independent variables. Contrast heteroskedastic.
This is a strong assumption, and includes in particular the assumption in a linear regression, for example,
y = Xb + e
that the variance of the e's is the same for all X's.

(The observed variance will differ in almost any sample. But if one believes that the data-generating process does not in principle have greater variances for different values of the independent variable, one would describe the sample as homoskedastic anyway.)

Source: econterms

Let u(x) be a function homogeneous of degree one in x. Let g(y) be a function of one argument that is monotonically increasing in y. Then u(g()) is a homothetic function of y.

So a function is homothetic in y if it can be decomposed into an inner function that is monotonically increasing in y and an outer function that is homogeneous of degree one in its argument.

In consumer theory there are some useful analytic results that can come from studing homothetic utility functions of consumption.

Source: econterms

In traditional microeconomics, household behavior is understood narrowly as the theory of consumer demand for commodities, i.e., household consumption. There are, however, other aspects of household behavior that have also been investigated in the microeconomics literature, such as the household´s supply of labor, the production of commodities (mainly, services) within the household (household production), saving decisions, retirement decisions, and many more.

Source: SFB 504

Health and Retirement Study, a longitudinal panel of older Americans studied by the Survey Research Center at the University of Michigan. Their Web site is at http://www.umich.edu/~hrswww.

Source: econterms

High School and Beyond, a panel data set on U.S. high school students.

Source: econterms

Same as Huber-White standard errors.

Source: econterms

Standard errors which have been adjusted for specified assumed-and-estimated correlations of error terms across observations.

The implicit citations are to Huber, 1967, White, 1980, and White, 1982.

Source: econterms

The attributes of a person that are productive in some economic context. Often refers to formal educational attainment, with the implication that education is investment whose returns are in the form of wage, salary, or other compensation. These are normally measured and conceived of as private returns to the individual but can also be social returns.

''Human capital' was invented by the economist Theodore Schultz in 1960 to refer to all those human capacities, developed by education, that can be used productively -- the capacity to deal in abstractions, to recognize and adhere to rules, to use language at a high level. Human capital, like other forms of capital, accumulates over generations; it is a thing that parents 'give' to their children through their upbringing, and that children then successfully deploy in school, allowing them to bequeath more human capital to their own children.' -- Traub (2000)

Source: econterms

A way of accounting in a model for the difference in the preferences an agent has over consumption now versus consumption in the future.

For a and g scalar real parameters greater than zero, under hyperbolic discounting events t periods in the future are discounted by the factor (1+at)^(-g/a).

That expression describes the "class of generalized hyperbolas". This formulation comes from a 1999 working paper of C. Harris and D. Laibson, which cites Ainslie (1992) and Loewenstein and Prelec (1992).

In dynamic models it is common to use the more convenient assumption that agents have a common discount rate applying for any t-period forecast, starting now or starting in the future. Hyperbolic discounting is less convenient but fits the psychological evidence better, and when contrasted to the constant-discount-rate assumption can get models to fit the noticeable fall in consumption that U.S. workers are observed to experience when they retire. In a constant-discount-rate model the worker would usually have forecast the fall in income and their consumption expenses would be smooth.

One reason hyperbolic preferences are less convenient in a model is not only that there are more parameters but that the agent's decisions are not time-consistent as they are with a constant discount rate. That is, when planning for time two (two periods ahead) the agent might prepare for what looks like the optimal consumption path as seen from time zero; but at time two his preferences would be different.

Contrast quasi-hyperbolic discounting.

Source: econterms

a hypothesized property of unemployment rates -- that there is a ratcheting effect, so a short-term rise in unemployment rates tends to persist.
Theories that would lead to hysteresis:
-- an insider/outsider model of decisionmaking about employment; insiders such as the unionized workers ratchet up wage rates beyond where it is profitable to hire the unemployed; outsiders who are unemployed don't get to be part of the negotiation process.
-- behavioral and human capital changes among the unemployed, such as forgetting the details of work or work behavior, or losing interest or skill in getting new jobs, could lead to declining chances of becoming employed.

Source: econterms

increasing absolute risk aversion

Source: econterms

IC stands for "incentive compatible".
When solving a principal-agent maximization problem for a contract that meets various criteria, the IC constraints are those that require agents to prefer to act in accordance with the solution. If the IC constraint were not imposed, the solution to the problem might be economically meaningless, insofar as it produced an outcome that met some criterion of optimality but which an agent would choose not to act in accord with.
See also IR constraint.

Source: econterms

Intertemporal CAPM. From Merton, 1973.

Source: econterms

A matrix M is idempotent if MM=M. (M times M equals M.)
Example: the identity matrix, denoted I.

Source: econterms

A parameter in a model is identified if and only if complete knowledge of the joint distribution of the observed variables gives enough information to calculate the parameter exactly.

If the model has been written in such a way that its parameters can be consistently estimated from the observables, then the parameters are identified. There exist cases (mostly obscure) where parameters are identified but consistent estimators are not possible. (See, e.g. Gabrielsen, 1978)
A model is identified if there is no observationally equivalent model. That is, potentially observable random variables in the model have different distributions for different values of the parameter.

Formally:
Let h^* be a vector of unknown functions and distributions in an econometric model.
Let H denote a set which h^* is known to belong. H is defined by the model's restrictions.
Let P(h) denote the joint distribution of observable variables of the model for various elements of h in H. The distribution for the actual data will be assumed to be P(h^*).
Now, vector h^* is identified within H if for all h in H such that h<>h^* it is true that P(h)<>P(h^*).
Note: Linear models are either globally identified or there are an infinite number of observably equivalent ones. But for models that are nonlinear in parameters, "we can only talk about local properties." Thus the idea of locally identified models, which can be distinguished in data from any other 'close by' model.

"An identification problem occurs when a specifed set of assumptions combined with unlimited observations drawn by a specified sampling process does not reveal a distribution of interest." -- Manski, Charles F. "Identification problems and decisions under ambiguity: empirical analysis of treatment response and normative analysis of treatment choice" Northwestern University Department of Economics and Institute for Policy Research, September 1998, p. 2

Source: econterms

Charles Manski gave a brilliant example of what identification is all about:

Suppose that you observe the almost simultanous movement of a man his image in a mirror. Does the mirror image cause the man's movements or reflect them? If you don't understand something of optics and human behavior, you will not be able to tell. (Manski, 1995, p. 1)

Methodological research in the social sciences uses statistical theory. The empirical problem is to infer some feature of a population described by a probability distribution. The data available to the researcher (be it field or experimental data) are observations extracted from the population by some sampling process. In this framework, the statistical and identification problems can be separated:


•Identification is about the conlusions that could be drawn if one could use the sampling process to obtain an unlimited number of observations.


•Statistical inference is about the (generally weaker) conclusions that can be drawn from a finite number of observations.

Identification problems cannot be solved by gathering more of the same kind of data. They can be alleviated only by invoking stronger assumptions or by initiating new sampling processes that yield different kinds of data.

Source: SFB 504

An identity matrix is a square matrix of any dimension whose elements are ones on its northwest-to-southeast diagonal and zeroes everywhere else. Any square matrix multiplied by the identity matrix with those dimensions equals itself. One usually says 'the' identity matrix since in most contexts the dimension is unambiguous. It is standard to denote the identity matrix by I.

Source: econterms

Sometimes used to name the state of people who are not in school but also not working. Context is usually industrialized countries with established labor markets, and the idle are often poor.

Source: econterms

An abbreviation for the journal International Economic Review.

Source: econterms

abbreviation for "if and only if"

Source: econterms

Integrated GARCH, a kind of econometric model of a stochastic process in which there is a unit root in a GARCH environment.
The IGARCH(p,q) process was proposed in Engle and Bollerslev (1986).

Source: econterms

stands for Irrelevance of Independent Alternatives, an assumption in a model. In a discrete choice setting, the multinomial logit model is appropriate only if the introduction or removal of a choice has no effect on the proportion of probability assigned to each of the other choices.
This is a strong assumption; a standard example where IIA is not an appropriate assumption is if one compares a model of transportation choices between a car and a red bus, then introduces a blue bus. The blue bus is functionally like the red bus, so presumably its introduction draws ridership more heavily from the red bus than from the car.

Source: econterms

An abbreviation for "independently and identically distributed." One would say this about two or more random variables to describe their joint distribution. A common use is to describe ongoing disturbances to a stochastic process, indicating that they are not correlated to one another.

Source: econterms

An occasional abbreviation for the academic journal International Journal of Industrial Organization.

Source: econterms

Indirect Least Squares, an approach to the estimation of simultaneous equations models. Steps: 1) Rearrange the structural form equations into reduced form 2) Estimate the reduced form parameters 3) Solve for the structural form parameters in terms of the reduced form parameters, and substitute in the estimates of the reduced form parameters to get estimates for the structural ones.

Source: econterms

International Monetary Fund -- an international organization with liquidity services to maintain financial stability.

Source: econterms

A decision rule (a mapping from expressed preferences by each of a group of agents to a common decision) "is implementable (in Nash equilibrium) if there exists a game form whose Nash equilibrium outcome is the desired outcome for the true preferences."

Source: econterms

A non-contractual agreement that corresponds to a Nash equilibrium to the repeated bilateral trading game other than the sequence of Nash equilibria to the one-shot trading game. In the labor market -- an implicit contract is formally represented by a series of games in which the firm pays a salary and the employee works effectively because they expect to play the game again (continue the agreement) if it goes well, not because they have an explicit, enforceable contract. That is, "by implicit contracts is meant nonbinding commitments from employers to offer ... continuity of wages, employment, and working conditions, and from employees to forgo such temptations as shirking and quitting for better opportunities." -- Granovetter, Ch 9

Source: econterms

Goods and services that are produced abroad and purchased in oneâ??s home country.

Source: EconPort

One of a class of theorems following Arrow (1951) showing that social welfare functions cannot have certain collections of desirable attributes in common.

Source: econterms

Consider a shock to a system. A graph of the response of the system over time after the shock is an impulse response function graph. One use is in models of monetary systems. One graphs for example the percentage deviations in output or consumption over time after a one-time one percent increase in the money stock.

Source: econterms

A function f() satisfies the Inada conditions if: f(0) = 0, f'(0) = infinity, and f'(infinity) = 0. f() is usually a production function in this context.

Source: econterms

A possible action by a player in a game may be said to be inadmissible if it is dominated by another feasible actions.
The term comes the view of a game as a math problem. An action is or is not admissible as a candidate solution to the problem of choosing a utility-maximizing strategy for the game player.

As used in Manski, Charles F. "Identification problems and decisions under ambiguity: empirical analysis of treatment response and normative analysis of treatment choice" Northwestern University Department of Economics and Institute for Policy Research, September 1998, p. 2

Source: econterms

In typical strategic interactions under incomplete information, different types (of a player) can choose from among a menu of different actions (strategies) that comprises the possibility that they mimic the behavior of other types (of the same, or of another player). Incentive compatibility conditions ensure that different types (of each player) align themselves such that they can be identified by their equilibrium choices. Typically, they are used to prevent that some type profits from copying another type's action (given the other types do not disguise themselves behind others' choices). More generally, incentive compatibility conditions force a desired constellation of choices to form a strategic equilibrium for a given array of types. In particular, they might as well ensure that it be worthwhile for different types to choose the same action (the types pool on an action). Yet in most economic problems, incentive compatibility conditions serve to induce a strategic equilibrium which reveals the players' private information by having them choose different 'characteristic' equilibrium actions, i.e. they have the types 'sort themselves out'.

For a simple example, suppose several buyers that differ in their private (marginal) valuations of some economic good (their types) select the quantity to buy from a seller. If the seller maximizes his proceeds from sale, he will want the buyers with higher valuations to buy higher quantities, i.e. she will want to separate her customers (or market segments) according to their marginal willingness-to-pay. To have such choices form a strategic equilibrium, the seller has to provide incentives to the high- valuations customers to buy higher quantities and to prevent market segments with lower valuations from profitably micking the choices of high-valuation customers. To meet both ends, it is often enough to simply offer a monotonic reward scheme that links choices to rewards. In the example, it is enough that the seller rewards buying higher quantities by offering a schedule of ever larger price discounts for larger quantities bought.

The basic idea that is with a monotonic reward scheme, lower types cannot find it worthwhile to mimic the choices of higher types because higher types themselves find it worthwhile to choose even more extreme actions which, in the end, are too costly to copy for lower types. Thus, the price of having the types self-select by giving monotonic rewards to them necessitates that higher types are rewarded progressively higher rents for revealing their information, relative to lower types. (For an illustration of this point, see the paragraph on information rents in the entry rents.)

More generally, suppose the types are 'naturally ordered' in terms of increasing marginal profitability (or costliness) of some economic action; e.g., the schedule of marginal willingnesses-to-pay is differently steep for different customers; different candidates have differently steep marginal cost schedules in investing varying amounts in some activity, etc. Then, to put it in jargon, any monotonic reward scheme "provides incentives to the types to separate themselves", i.e. it has the players self-select levels of actions which reveal the natural ordering of their types.

Incentive compatibility conditions occur throughout economics with incomplete information because, as we have tried to argue, they are closely related to strategic equilibria with certain features. Most often, incentive compatibility constraints are used to frame the ways of interaction such as to create equilibria where the players' private information is revealed by their equilibrium choices. Among important applications are the theory of optimal taxation of unobservable behavioral characteristics in public finance, optimal selling schemes in non-linear pricing and auctions, the optimal regulation of firms under incomplete information, or incentive wage contracts eliciting effort inputs from employees that can hide shirking under favorable conditions.

Source: SFB 504

The Concise Oxford Dictionary defines income as "receipts from one's lands, work, investment etc." This definition has been adapted by economic theory, where, for instance, a consumer may be said to maximize utility subject to an income constraint. The meaning of income is somewhat modified in the construction of income statistics, as generalized to national income.

Income in a microeconomic sense is the sum of earnings of all factors of production of an individual. It includes all benefits to consumers as part of income, even benefits arising from non-market activities ? such as the monetary value of the services of owner-occupied housing or food grown and consumed on farms. This definition of income also includes periodic and one-time transfers such as pensions, unemployment benefits, and bequests.

Source: SFB 504

When used without another referent, appears to mean 'of consumption'. That is for income I and consumption C:
income elasticity = (I/C)*(dC/dI)
In one paper estimates were shown of .2 to .6 for a random sample of industrialized country middle class people.
For more details see elasticity.

Source: econterms

If a firm exhibits increasing returns to scale, when it increases the use of inputs then output increases by a greater proportion. For example, if the firm doubles the use of all inputs, then output will more than double. With increasing returns to scale, long-run average costs decrease as output increases.

Source: EconPort

A kind of insurance, in which payment is made (often in previously determined amounts) for injuries suffered, not for the costs of recovery. The payment is designed not to be a dependent on anything the patient can control. From the point of view of the insurer, this mechanism avoids the moral hazard problem of victim spending too much in recovery.

Source: econterms

Two random variables X and Y are statistically independent if and only if their joint density (pdf) is the product of their marginal densities, that is if f(x,y)=f_x(x)f_y(y).

If two random variables are independent they are also uncorrelated.

Source: econterms

If a bidder has independent private values, it means that he is not influenced by the estimates of the other bidders, when determining how much an object is worth to him

In a regression, a variable that is one if a condition is true, and zero if it is false. Approximately synonymous with dummy variable, binary variable, or flag.

Source: econterms

Represented for example on a graph whose horizontal and vertical axes are quantities of goods an individual might consume, an indifference curve represents a contour along which utility for that individual is constant. The curve represents a set of possible consumption bundles between which the individual is indifferent. Normally, with desirable goods on both axes (say, income today and income tomorrow) the curve has a certain shape, further from the origin when both quantities are positive than when one is zero.

Source: econterms

Denoted v(p, m) where p is a vector of prices for goods, and m is a budget in the same units as the prices. This function takes the value of the maximum utility that can be achieved by spending the budget m on the consumption goods with prices p.

Source: econterms

An allocation is individually rational if no agent is worse off in that allocation than with his endowment.

Source: econterms

Characterizing a reasoning process of generalizing from facts, instances, or examples. Contrast deductive.

Source: econterms

A period commonly dated 1760-1830 in Britain (as in Mokyr, 1993, p 3 and Ashton, 1948). Characterized by: "a complex of technological advances: the substitution of machines for human skills and strength; the development of inanimate sources of power (fossil fuels and the steam engine); the invention, production, and use of new materials (iron for wood, vegetable for animal matter, mineral for vegetable matter); and the introduction and spread of a new mode of production, known by contemporaries as the factory system." -- Landes (1993b) p 137.

Source: econterms

A historical phase and experience. The overall change in circumstances accompanying a society's movement population and resources from farm production to manufacturing production and associated services.

Source: econterms

Stands for 'infimum'. A value is an infimum with respect to a set if all elements of the set are at least as large as that value. An infimum exists in context where a minimum does not, because (say) the set is open; e.g. the set (0,1) has no minimum but 0 is an infimum.

inf is a mathematical operator that maps from a set to a value that is syntactically like the members of that set, although the value may not actually be a member of the set.

Source: econterms

Reduction in value of a currency. Measured often by percentage increases in the general price level per year.

Source: econterms

A game is of complete information if the payoffs of each player are common knowledge among all the players, and it is of incomplete information if the utility payoffs of each player, or certain parameters to it, remain private information of each player. Games with incomplete information require the players to form beliefs about their opponents' private information, and to evaluate uncertain streams of payoff according to von Neumann-Morgenstern utility function (or some other concept of expected utility).

A game with a perfect information is a game in which at each move in the game, the player with the move knows the full history of the play of the game thus far. Otherwise the game is called a game with imperfect information. In a game of perfect recall, nobody ever forgets something they once knew. An event A is common knowledge if all the players know that A occurred, and all the players know that all the players know that A occurred, and all the players know that all the players know that all the players know that A occurred, and so on, ad infinitum.

Source: SFB 504

information

Source: econterms

In maximum likelihood estimation, the variance of the score vector. It's a k x k matrix, where k is the dimension of the vector of parameters being estimated. The vector of parameters is denoted q here:
I(q) = var S(q) = E[(S(q)-ES(q))²] = E[S(q)²]
where the score is S(q) = dL(q)/d(q)

The information matrix can also be calculated by multiplying the Hessian of the log-likelihood function by (-1).

Source: econterms

Synonym for Fisher information (which see).

Source: econterms

The information processing approach constitutes an important paradigm in psychology, which evolved from computer science and communication science as an alternative to behaviorism, which was the most influential paradigm from the early decades until the mid of the 20th century. Compared to behaviorist theories, in which observable responses are conceptualized as a function of observable stimuli, theories in the information processing domain focus on mental operations intervening between stimulus and response. Within social psychology this approach emphasizes the cognitive mediation of social behavior, and, vice versa, the social impact on cognitive processes. Personal involvement, affective states, or environmental factors can have a considerable influence on logical thinking, stereotyping, social judgments and decisions. The sequence of cognitive processes are typically decomposed into various stages, such as perception, encoding, organization, inference making, retrieval, and judgment. These stages are highly interdependent and characterized by various feedback loops. At all stages, the individual's expectations or older knowledge structures come to interact with new input information. It is quite typical for human information processing that data-driven processes ("bottom up") and conceptually driven processes ("top down") mesh (see Fiedler, 1996).

Source: SFB 504

"An informational cascade occurs when it is optimal for an individual, having observed the actions of those ahead of him, to follow [that is, imitate] the behavior of the preceding individual without regard to his own information." -- Bikhchandani, Hirshleifer, and Welch, 1992, p 992

Source: econterms

An American-style business school near Paris. Operates in English.

Source: econterms

Any debt that is used as money. Is a liability to the issuer. Total amount of inside money in an economy is zero. Contrast outside money.

Source: econterms

There are several definitions. Here's one: 'An institution is a social mechanism through which men work together for common or like ends. It is a necessary arrangement wherever regulated group behavior over a broad field of activity is found. It is opposed in sociological thought to 'face to face' grouping and to local community forms of life ...' (Ware, p. 6)

For more see new institutionalism.

Source: econterms

(Neo-)Institutionalism is a theoretical school which is concerned with the question of which organizational actions and routines become taken for granted. Within the school of Neo-Institutionalism distinctions between the micro and the macro level of this theory are made.

Source: SFB 504

Either (1) an estimation technique, often abbreviated IV, or (2) the exogenous variables used in the estimation technique.
Suppose one has a model:
y = Xb + e
Here y is a T x 1 vector of dependent variables, X is a T x k matrix of independent variables, b is a k x 1 vector of parameters to estimate, and e is a k x 1 vector of errors. OLS can be imagined, but suppose in the environment being modelled that the matrix of independent variables X may be correlated to the e's. Then using a T x k matrix of independent variables Z, correlated to the X's but uncorrelated to the e's one can construct an IV estimator that will be consistent:
b_IV = (Z'X)^-1Z'y
The two stage least squares estimator is an important extension of this idea.

In that discussion above, the exogenous variables Z are called instrumental variables and the instruments (Z'Z)^-1(Z'X) are estimates of the part of X that is not correlated to the e's.

Source: econterms

When regressors are correlated to errors in a model, one may be able to replace the regressors by estimates for these regressors that are not correlated to the errors. This is the technique of instrumental variables, and the replacement regressors are called instruments.

The replacement regressors are constructed by running regressions of the original regressors on exogenous variables that are called the instrumental variables.

Source: econterms

Said in reference to a random process. A random process is said to be 'integrated of order d' (sometimes denoted I(d)) for some natural number d if the series would be stationary after being first-differenced d times.
Example: a random walk is I(1).
Example: "Most macroeconomic flows and stocks that relate to population size, such as output or employment, are I(1)." They are growing.
Example: "An I(2) series [might] be growing at an ever-increasing rate."

Source: econterms

Refers to the degree (intensity) to which a resource is utilized or applied. For example, the effort put in by a worker or the number of hours the worker works. Contrast extensive margin.

Source: econterms

"Among other things"

Source: econterms

From Latin, 'between lives'. Used to describe gifts beetween people, usually from one generation to the next, which are like bequests except that both parties are alive. Quantities and timing of such gifts are studied empirically in the same way that quantities and purposes of bequests are subjects of empirical study.

Source: econterms

Defined, apparently, in Holmstrom and Myerson (1983) with reference to Rothschild and Stiglitz (1976). In Imderst (2000) this term is used to characterize the set ('family') of Rothschild-Sticlitz contracts in a particular model setting.

Source: econterms

A choice made by an agent that can be characterized as an optimum located at a tangency of two curves on a graph.

A classic example is the tangency between a consumer's budget line (characterizing the maximum amounts of good X and good Y that the consumer can afford) and the highest possible indifference curve. The slope of that tangency is where:

(marginal utility of X)/(price of X) = (marginal utility of Y)/(price of Y)

Contrast corner solution.

Source: econterms

positive learning or knowledge externalities between programs or plants within a production organization.

Source: econterms

Many economic decisions are intertemporal in the sense that current decisions affect also the choices available in the future. Examples are saving and retirement decisions of households, and investment decisions of firms. In the case of saving, the saving decision made today affects not only the household's current consumption but also his future consumption possibilities. If someone saves more today, he can consume less today and hence his current utility declines, but he can consume more in the future, and his future utility increases.

As can be seen from the savings example, intertemporal decisions are characterized by some kind of intertemporal trade-off: If I give up something today, I want to be compensated for the resulting utility loss in the future. The optimal intertemporal decision requires that current and future changes of utility implied by current behavior correspond to the individual's intertemporal preferences ? formally, that the rate of substitution be equal to the rate of time preference.

An number of studies have shown that the standard theory of intertemporal choice is frequently violated in experimental settings, just as standard (static) expected utility (EU) theory of choice is systematically violated (see Camerer, 1995). Intertemporal decisions are therefore an important area of research in behavioral economics.

Source: SFB 504

A function p(q) that maps from a quantity of output to a price in the market; one might model the demand a firm faces by positing an inverse demand function and imagining that the firm chooses a quantity of output.

Source: econterms

Usually denoted l(Z), and defined by l(Z)=phi(Z)/PHI(Z), where phi() is the standard normal pdf and PHI() is the standard normal cdf.

Source: econterms

In context of time series processes, represented for example by a lag polynomial, inverting means to solve for the e's (epsilons) in terms of the y's.
One inverts moving average (MA) processes to get AR representations.

Source: econterms

Any use of resources intended to increase future production output or income.

Source: econterms

stands for 'Industrial Organization', the field of industry structure, conduct, and performance. By structure we usually mean the size of the firms in the industry -- e.g. whether firms have monopoly power. IO

Source: econterms

Stands for "initial public offering", the event of a firm's first sale of stock shares.

Source: econterms

Integrated Public Use Microdata Series. These are collections of U.S. Census data, adapted for easy use by the University of Minnestota Social History Research Laboratory, at its Web site http://www.ipums.umn.edu.

Source: econterms

IR stands for "individually rational".
When solving a principal-agent maximization problem for a contract that meets various criteria, the IR constraints are those that require agents to prefer to sign the contract than not to. If the IR constraint were not imposed, the solution to the problem might be economically meaningless, insofar as it was a contract that met some criterion of optimality but which an agent would refuse to sign.
See also IC constraint.

Source: econterms

The United States national tax collection agency, called the Internal Revenue Service.

Source: econterms

means 'is a consistent estimator of'

Source: econterms

Given a production function, an isoquant is 'the locus of input combinations that yield the same output level.' (Chiang, p. 360) There is an isoquant set for each possible output level. Mathematically the isoquant is a level curve of the production function.

Examples and discussion is at Martin Osborne's web page: http://www.chass.utoronto.ca/~osborne/2x3/tutorial/ISOQUANT.HTM.

Source: econterms

A stochastic process: a generalized Wiener process with normally distributed jumps.

Source: econterms

abbrevation for Instrumental Variables, an estimation technique

Source: econterms

In a GMM context, when there are more moment conditions than parameters to be estimated, a chi-square test can be used to test the overidentifying restrictions. The test statistic can be called the J statistic.
In more detail: Say there are q moment conditions and p parameters to be estimated. Let the weighting matrix be the inverse of the asymptotic covariance matrix. Let T be the sample size. Then T times the minimized value of the objective function (TJ_T(b_T)) is asymptotically distributed with a chi-square distribution with (q-p) degrees of freedom.

Source: econterms

Has multiple, overlapping definitions numbered below: (1) kind of nonparametric estimator for a regression function. A jackknife estimator is a linear combination of kernel estimators with different window widths. Jackknife estimators have higher variance but less bias than kernel estimators. (Hardle, p. 145.) (2) creates a series of statistics, usually a parameter estimate, from a single data set by generating that statistic repeatedly on the data set leaving one data value out each time. This produces a mean estimate of the parameter and a standard deviation of the estimates of the parameter. (Nick Cox, in an email broadcast to Stata users on statalist, circa 7/5/2000.)

Source: econterms

An occasional abbreviation for the academic journal Journal of Econometrics.

Source: econterms

An abbreviation for the Journal of Economic History.

Source: econterms

Journal of Economic Literature. See also JEL classification codes.

Source: econterms

These define a classification system for books and journal articles relevant to the economic researcher. The list has three levels of precision: categories A-Z, subcategories like A0-A2 (these are used to classify books), and sub-subcategories like A10-A14 (which are used to classify journal articles). The second level is detailed here; for the complete set of possible JEL codes see any issue, e.g. in the Sept 1997 issue, pages 1609-1620. The list below comes from that same issue, pages 1437-1439. A more up-to-date list is online at http://www.aeaweb.org/journal/elclasjn.html

A. General Economics and Teaching (A0 General, A1 General Economics, A2 Teaching of Economics)
B. Methodology and History of Economic Thought (B0 General, B1 History of Economic Thought through 1925, B2 History of Economic Thought since 1925, B3 History of Thought: Individuals, B4 Economic Methodology)
C. Mathematical and Quantitative Methods (C0 General, C1 Econometric and Statistical Methods: General, C2 Econometric and Statistical Methods: Single Equation Models, C3 Econometric and Statistical Methods: Multiple Equation Models, C4 Econometric and Statistical Methods: Special Topics, C5 Econometric Modeling, C6 Mathematical Methods and Programming, C7 Game Theory and Bargaining Theory, C8 Data Collection and Data Estimation Methodology; Computer Programs, C9 Design of Experiments)
D. Microeconomics (D0 General, D1 Household Behavior and Family Economics, D2 Production and Organizations, D3 Distribution, D4 Market Structure and Pricing, D5 General Equilibrium and Disequilibrium, D6 Economic Welfare, D7 Analysis of Collective Decision-Making, D8 Information and Uncertainty, D9 Intertemporal Choice and Growth)
E. Macroeconomics and Monetary Economics (E0 General, E1 General Aggregative Models, E2 Consumption, Saving, Production, Employment, and Investment, E3 Prices, Business Fluctuations, and Cycles, E4 Money and Interest Rates, E5 Monetary Policy, Central Banking and the Supply of Money and Credit, E6 Macroeconomic Aspects of Public Finance, Macroeconomic Policy, and General Outlook)
F. International Economics (F0 General, F1 Trade, F2 International Factor Movements and International Business, F3 International Finance, F4 Macroeconomic Aspects of International Trade and Finance) G. Financial Economics (G0 General, G1 General Financial Markets, G2 Financial and Institutions and Services, G3 Corporate Finance and Governance) H. Public Economics (H0 General, H1 Structure and Scope of Government, H2 Taxation and Susidies, H3 Fiscal Policies and Behavior of Economic Agents

Source: econterms

An abbreviation for the Journal of Economics and Management Strategy.

Source: econterms

If X is a real-valued random variable with E(|X|) finite and the function g() is convex, then E[g(X)] >= g(E[X]).
One application: By Jensen's inequality, E[X²] >= (E[X])². Since the difference between these is the variance, we have just shown that any random variable for which E[X²] is finite has a variance and a mean.
This is the inequality one can refer to when showing that an investor with a concave utility function prefers a certain return to the same expected return with uncertainty.

Source: econterms

An abbreviation for the Journal of Economic Perspectives.

Source: econterms

An abbreviation for the Journal of Economic Theory.

Source: econterms

Journal of Finance

Source: econterms

Journal of Financial Economics

Source: econterms

Journal of Financial Intermediation, at http://www.bus.umich.edu/jfi/

Source: econterms

Journal of Human Resources

Source: econterms

An abbreviation for the Journal of Industrial Economics .

Source: econterms

An abbreviation for the Journal of Law and Economics.

Source: econterms

An abbreviation for the Journal of Law, Economics and Organization.

Source: econterms

Describes the situation of a person with a U.S. job who is not free to leave for another job because the first job has medical benefits associated with it that the person needs, and the second one would not, perhaps because 'pre-existing conditions' are often not covered under U.S. health insurance.

Source: econterms

The monthly US publication Job Openings for Economists.

Source: econterms

In the context of research economics these are academic periodicals, usually with peer-reviewed contents. An amazingly complete list of hyperlinks to journals is at the WebEc web site. Some are also in this glossary directly, below.
journals

Source: econterms

Journal of Policy Analysis and Management

Source: econterms

Abbreviation for the Journal of Political Economy

Source: econterms

Journal of Public Economics

Source: econterms

An abbreviation for the Journal of Regulatory Economics.

Source: econterms

A monetary policy rule of keeping the growth of money at a fixed rate of k percent a year. This phrase is often used as stated, without specifying the percentage.

Source: econterms

A kind of nonparametric estimator of a function. Given a data set {X_i, Y_i} it estimates values of Y for X's other than those in the sample. The process is to choose the k values of X_i nearest the X for which one seeks an estimate, and average their Y values. Here k is a parameter to the estimator. The average could be weighted, e.g. with the closest neighbor having the most impact on the estimate.

Source: econterms

The Kalman filter is an algorithm for sequentially updating a linear projection for a dynamic system that is in state-space representation.

Application of the Kalman filter transforms a system of the following two-equation kind into a more solvable form:
x_t+1=Ax_t+Cw_t+1 y_t=Gx_t+v_t in which:
A, C, and G are matrices known as functions of a parameter q about which inference is desired (this is the PROBLEM to be solved),
t is an whole number, usually indexing time,
x_t is a true state variable, hidden from the econometrician,
y_t is a measurement of x with scalings G and measurement errors v_t,
w_t are innovations to the hidden x_t process,
Ew_t+1w_t'=1 by normalization,
Ev_tv_t=R, an unknown matrix, estimation of which is necessary but ancillary to the problem of interest which is to get an estimate of q. The Kalman filter defines two matrices S_t and K_t such that the system described above can be transformed into the one below, in which estimation and inference about q and R is more straightforward, possibly even by OLS:
z_t+1=Az_t+Ka_t y_t=Gz_t+a_t where z_t is defined to be E_t-1x_t,
a_t is defined to be y_t-E_t-1y_t,
K is defined to be lim K_t as t goes to infinity.

The definition of those two matrices S_t and K_t is itself most of the definition of the Kalman filter:
K_t=AS_tG'(GS_tG'+R)^-1 S_t+1=(A-K_tG)S_t(A-K_tG)'+CC'+K_tRK_t'
K_t is called the Kalman gain.

It's not yet clear to me what specific examples there are of problems that the Kalman filter solves.

Source: econterms

One of the two equations that characterizes the application of the Kalman filter process defines an expression sometimes denoted K_t, which is called the Kalman gain.

That equation, using notation from Sargent's lectures, is:

K_t=AS_tG'(GS_tG'+R)^-1

Source: econterms

The framework of relationships in postwar Japan's big banks and big firms. Related companies organized around a big bank (like Mitsui, Mitsubishi, and Sumitomo) which own a lot of equity in one another and in the bank and do much business with one another. This system has the virtue of maintaining long term business relationships and stability in suppliers and customers. It has the disadvantage of reacting slowly to outside events since the players are partly protected from the external market. (p 412)

Source: econterms

Kernel estimation means the estimation of a regression function or probability density function. Such estimators are consistent and asymptotically normal if as the number of observations n goes to infinity, the bandwidth (window width) h goes to zero, and the product nh goes to infinity. In practice, means use of the Nadaraya-Watson estimator, which see.

Source: econterms

A weighting function used in nonparametric function estimation. It gives the weights of the nearby data points in making an estimate. In practice kernel functions are piecewise continuous, bounded, symmetric around zero, concave at zero, real valued, and for convenience often integrate to one. They can be probability density functions. Often they have a bounded domain like [-1,1].

Source: econterms

As prices fall, a given nominal amount of money will be a larger real amount. Consequently the interest rate would fall and investment demanded rise. This Keynes effect disappears in the liquidity trap. Contrast the Pigou effect. Another phrasing: that a change in interest rates affects expenditure spending more than it affects savings.

Source: econterms

Describes a regression where the regressors are not in the opinion of the writer thoroughly 'justified' by an argument or a theory. Often used pejoratively; other times describes an exploratory regression.

Source: econterms

Kullback-Leibler Information Criterion. An unpublished paper by Kitamura (1997) describes this as a distance between probability measures. It is defined in that paper thus. The KLIC between probability measures P and Q is:

I(P||Q) = [integral of] ln(dP/dQ) dP if P << Q
........ = infinity otherwise

Source: econterms

Unmeasurable risk. Contrast Knightian uncertainty.

Source: econterms

If a regression will be run to estimates different linear slopes for different ranges of the independent variables, it's a spline regression, and the endpoints of the ranges are called knots.

The spline regression is designed so that the resulting spline function, estimating the dependent variable, is continuous at the knots.

Source: econterms

If {w_t} is a sequence of iid draws from a distribution and Ew_t exists (call it mu) then the average of the w_t's goes 'almost surely' to mu as t goes to infinity.
Same as strong law of large numbers, I believe.

Source: econterms

This is an operator that takes two matrix arguments. It is denoted by a small circle with an x in it, but will be denoted here by 'o'. Let A be an M x N matrix, and B be an R x S matrix. Then AoB is an MR x NS matrix, formed from A by multiplying each element of a by the entire matrix B and putting it in the place of the element of A, e.g.:
a₁₁B a₁₂B ... a_1nB
. . . . . .
. . . . . .
a_M1B a_M2B ... a_MnB
Kronecker products have the following useful properties:
(AoB)(CoD)=ACoBD
(AoB)^-1 = A^-1oB^-1 (AoB)' = A'oB' (AoB)+(AoC)=Ao(B+C) AoC+BoC = (A+B)oC

Source: econterms

Let X be a set of regressors, y be a vector of dependent variables, and the model be: y=Xb+e where E[ee'] is the matrix OMEGA. The theorem is that if the column space of (OMEGA)X is the same as the column space of X; that is, that there is heteroskedasticity but not cross-correlation, then the GLS estimator of b is the same as the OLS estimator of b.

Source: econterms

An attribute of a distribution, describing 'peakedness'. Kurtosis is calculated as E[(x-mu)⁴]/s⁴ where mu is the mean and s is the standard deviation.

Source: econterms

A graph with measures of increased economic development (presumed to correlate with time) on the horizontal axis, and measures of income inequality on the vertical axis hypothesized by Kuznets (1955) to have an inverted-U-shape. That is, Kuznets made the proposition when an economy is primarily agricultural it has a low level of income inequality, that during early industrialization income inequality increases over time, then at some critical point it starts to decrease over time. Kuznets (1955) showed evidence for this.

Source: econterms

A journal, whose Web site is at http://www.kyklos-review.ch/kyklos/index.html.

Source: econterms

The set of Lebesgue-integrable real-valued functions on [0,1].

Source: econterms

A Hilbert space with inner product (x,y) = integral of x(t)y(t) dt.
Equivalently, L² is the space of real-valued random variables that have variances. This is an infinite dimensional space.

Source: econterms

is the set of continuous bounded functions with domain Rⁿ

Source: econterms

"[L]abor economics is primarily concerned with the behavior of employers and employees in response to the general incentives of wages, prices, profits, and nonpecuniary aspects of the employment relationship, such as working conditions."
labor

Source: econterms

Shorthand for worker (never employer) variables that are often considered endogeneous in a labor market regression. Such variables, which often appear on the right side of such regressions: wage rates, employment dummies or employment rates.

Source: econterms

Quantity of output per time spent or numbers employed. Could be measured in, for example, U.S. dollars per hour.

Source: econterms

"Both Ricardo and Marx say that the value of every commodity is (in perfect equilibrium and perfect competition) proportionaly to the quantity of labor contained in the commodity, provided this labor is in accordance with the existing standard of efficiency of production (the 'socially necessary quantity of labor'). Both measure this quantity in hours of work and use the same method in order to reduce different qualities of work to a single standard." And neither accounts well for monopoly or imperfect competition. (Schumpeter, p 23)

Source: econterms

One of the ways in which an effectiveness variable could be included in a production function in a Solow model. If effectiveness A is multiplied by labor L but not by capital K, then we say the effectiveness variable is labor-augmenting.

Source: econterms

Stands for 'Least absolute deviations' estimation.

LAD estimation can be used to estimate a smooth conditional median function; that is, an estimator for the median of the process given the data. Say the data are stationary {x_t, y_t}. The dependent variable is y and the independent variable is x.The criterion function to be minimized in LAD estimation for each observation t is:
q(x_t,y_t,q) = |y_t=m(x_t,q)|

where m() is a guess at the conditional median function.

Under conditions specified in Wooldridge, p 2657, the LAD estimator here is Fisher-consistent for parameters of the estimator of the median function.

Source: econterms

Denoted L. Operates on an expression by moving the subscripts on a time series back one period, so: Le_t = e_t-1 Why? Well, it can help manipulability of some expressions. For example it turns out one can could write an MA(2) process (which see) to look like this, in lag polynomials (which see): et = (1 + p₁L + p₂L²)u_t and then divide both sides by the lag polynomial, and get a legal, meaningful, correct expression.

Source: econterms

A polynomial expression in lag operators (which see). Example: (1 - p₁L + p₂L²) where L² = LL, or the lag operator L applied twice. These are useful for manipulating time series. For example, one can quickly show an AR(1) is equivalent to an MA(infinity) by dividing both sides by the lag polynomial (1-pL).

Source: econterms

An algebraic term that arises in the context of problems of mathematical optimization subject to constraints, which in economics contexts is sometimes called a shadow price.

A long example: Suppose x represents a quantity of something that an individual might consume, u(x) is the utility (satisfaction) gained by that individual from the consumption of quantity x. We could model the individual's choice of x by supposing that the consumer chooses x to maximize u(x):

x = arg max_x u(x)

Suppose however that the good is not free, so the choice of x must be constrained by the consumer's income. That leads to a constrained optimization problem ............ [Ed.: this entry is unfinished]

Source: econterms

stands for 'locally asymptotically normal', a characteristic of many ('a family of') distributions.

Source: econterms

Usually a synonym for 'asymptotic' rather than a reference to an actual sample magnitude.

Source: econterms

A price index following a particular algorithm.

It is calculated from a set ('basket') of fixed quantities of a finite list of goods. We are assumed to know the prices in two different periods. Let the price index be one in the first period, which is then the base period. Then the value of the index in the second period is equal to this ratio: the total price of the basket of goods in period two divided by the total price of exactly the same basket in period one.

As for any price index, if all prices rise the index rises, and if all prices fall the index falls.

Source: econterms

Often exemplified by E_tE_t+1(.) = E_t(.) That is, "one cannot use limited information [at time t] to predict the forecast error one would make if one had superior information [at t+1]." -- Campbell, Lo, and MacKinlay, p 23.

Source: econterms

Leveraged buy-out. The act of taking a public company private by buying it with revenues from bonds, and using the revenues of the company to pay off the bonds.

Source: econterms

Consider a repeated play of a finite game. In each period, every player observes the history of past actions, and forms a belief about the other players? strategies. He then chooses a best response according to his belief about the other players? strategies. We call such a process a learning process.

Source: SFB 504

The kind of learning that an agent in a model exhibits by adapting to past data by running least squares on it to estimate a hypothesized parameter and behaving as if that parameter were correct.

Source: econterms

In some models, individuals spend some time working and the rest is lumped into a category called leisure, the details of which are usually left out.

Source: econterms

Describes models like that of Akerlof's 1970 paper, in which the fact that a good is available suggests that it is of low quality. For example, why are used cars for sale? In many cases because they are "lemons," that is, they were problematic to their previous owners.

Source: econterms

Has the form q=min{x1,x2} where q is a quantity of output and x1 and x2 are quantities of inputs or functions of the quantities of inputs.

Source: econterms

An adjective describing a distribution with high kurtosis. 'High' means the fourth central moment is more than three times the second central moment; such a distribution has greater kurtosis than a normal distribution. This term is used in Bollerslev-Hodrick 1992 to characterize stock price returns.
Lepto- means 'slim' in Greek and refers to the central part of the distribution.

Source: econterms

A government benefit to the underemployed will presumably reduce their hours of work. The ratio of the actual increase in income to the benefit is the Lerman ratio, which is ordinarily between zero and one. Moffitt (1992) estimates it in regard to the U.S. AFDC program at about .625.

Source: econterms

A measure of the profitability of a firm that sells a good: (price - marginal cost) / price.

One estimate, from Domowitz, Hubbard, and Petersen (1988) is that the average Lerner index for manufacturing firms in their data was .37.

Source: econterms

Meaning differs by context. Often: the ratio of debts to total assets. Can also be the ratio of debts (or long-term debts in particular, excluding for example accounts payable) to equity.

Normally used to describe a firm's but could describe the accounts of some other organization, or an individual, or a collection of organizations.

Source: econterms

The all-powerful kind of state that Hobbes thought "was necessary to solve the problem of social order." -- Cass R. Sunstein, "The Road from Serfdom" The New Republic Oct 20, 1997, p 37.

Source: econterms

The liability of newness phenomenon describes the different risks of dying of an organization during its life course. It states that at the point of founding of an organization the risk of dying is highest and decreases with growing age of the organization. There are basicly three reasons why this might be the case (see Stinchcombe, 1965):
• New organizations which are acting in new areas ask for new roles to be performed by their members. The learning of the new roles takes time and leads to economic inefficencies.
• Trust among the organizational members has yet to be developed since in most cases the new employees of a firm do not know each other when the organization is founded.
• New organizations have not yet built stable portfolios of clients.

These considerations can - at least in some respects - also apply to the new rules of an organization. A new rule also implies new roles that have to be learned and members have to develop trust towards the new rule. According to this theoretical concept a new organizational rule should also have its highest risk of beeing abolished just after its founding (see Schulz, 1993).

Source: SFB 504

The life-cycle hypothesis presents a well-defined linkage between the consumption plans of an individual and her income and income expectations as she passes from childhood, through the work participating years, into retirement and eventual decease. Early attempts to establish such a linkage were made by Irving Fisher (1930) and again by Harrod (1948) with his notion of hump saving, but a sharply defined hypothesis which carried the argument forward both theoretically and empirically with its range of well-specified tests for cross-section and time series evidence was first advanced by Modigliani & Brumberg (1954). Both their paper and advanced copies of the permanent income theory of Milton Friedman (1957) were circulating in 1953. Both the Modigliani-Brumberg and the Friedman theories are referred to as life-cycle theories.

The main building block of life-cycle models is the saving decision, i.e., the division of income between consumption and saving. The saving decision is driven by preferences between present and future consumption (or the utility derived from consumption). Given the income stream the household receives over time, the sequence of optimal consumption and saving decisions over the entire life can be computed. Note that the standard life-cycle model as presented here is firmly grounded in expected utility theory and assumes rational behavior.

The typical shape of the income profile over the life cycle starts with low income during the early years of the working life, then income increases until a peak is reached before retirement, while pension income during retirement is substantially lower. To make up for the lower income during retirement and to avoid a sharp drop in utility at the point of retirement, individuals will save some fraction of their income during their working life and dissave during retirement. This results in a hump-shaped savings profile over the life cycle ? the main prediction of the life-cycle theory.

Unfortunately, this prediction does not hold in actual household behavior. It is fair to say the reasons for this failure of the simple life-cycle model are still not understood. Rodepeter & Winter (1998) provide empirical evidence for Germany and discuss some extensions of the life-cycle model that might help to understand actual savings behavior. An important direction of current research tries to apply elements of behavioral economics to life-cycle savings decisions.

Source: SFB 504

This review of the literature on life-cycle consumption and saving decisions is adapted from Fisher (1987).

The life-cycle hypothesis presents a well-defined linkage between the consumption plans of an individual and her income and income expectations as she passes from childhood, through the work participating years, into retirement and eventual decease. Early attempts to establish such a linkage were made by Irving Fisher (1930) and again by Harrod (1948) with his notion of hump saving, but a sharply defined hypothesis which carried the argument forward both theoretically and empirically with its range of well-specified tests for cross-section and time series evidence was first advanced by Modigliani & Brumberg (1954). Both their paper and advanced copies of the permanent income theory of Milton Friedman (1957) were circulating in 1953 and led M.R. Fisher (1956) to carry out tests of the theories even preceding publication of Friedman´s work. Both the Modigliani-Brumberg and the Friedman Theories are referred to as life-cycle theories and they certainly have many similar implications, but the one that is more closely related to the life cycle with emphasis on age ? Modigliani and Brumberg ? is the one to which the following review concentrates.

The key which rendered the multi-period analysis tractable under subjective certainty was the specification that the life-time utility function be homothetic ? this permitted planned consumption for each future period to be written as a function of expected wealth as seen at the planning date, the functional parameters being in no way dependent upon wealth, but upon age and tastes. The authors further sharpened their hypothesis. They specified that an individual would plan to consume the same amount in real discounted terms each year. Throughout, desired bequest and initial assets were set to zero. However, the authors did show that bequests could be accounted for within the homothetic utility function itself if that became necessary.

From the outset, such sharp hypothesis was desired for empirical testing. For Modigliani at least, a propelling influence had been the debate about the explanatory power of the Keynesian consumption function for forecasting postwar consumption and income. The inadequacies revealed had led already to several refined theories, notably by Duesenberry (1949) and by Modigliani (1949) himself. In the 1940s, cross-section studies had been carefully carried through at the National Bureau of Economic Research (NBER), and empirical results from these studies were promoting theoretical insights. Any new theory had to be consistent with these findings. The tighter specification of the hypothesis enabled the spelling out of the pattern of accumulating savings in the working years to finance the retirement years ? hump savings. Assuming that real income of each member of the populationwide sample remained the same throughout working life, it was shown that the independent of the age and income distribution and dependent only on the proportion of retirement years to expected lifetime. This alerted economists to the fact that cross-section results do not directly translate into estimates of the marginal propensity to save of an individual planning function. This insight is of broader significance not confined to the simple hypothesis. The implications of the hypothesis for time series analysis were disseminated much more slowly as the companion paper to that on cross section interpretation was never published, accounts not being freely available until 1963 and the original text itself not until 1980.

Real consumption, including the depreciation of durable goods, is a proportion of expected real wealth, and wealth is the addition of initial assets at the planning date, current income and expected (discounted) future income. By then assuming that the proportionality factor referred to is identical across individuals, they devised an aggregate relation for each and every age group. Next they proceed to aggregate across age groups. Here the proportionality factor, depending as it does on age, is not independent of assets, and bias may be introduced, if the strictest set of assumptions used in the cross-section analysis is employed, the authors show that when aggregated real income follows an exponential growth trend the parameters of the aggregate relation remain constant over time. They are, however, sensitive to the magnitude of the growth rate of real income (a sum of growth rates in productivity and population), the saving-income ratio being larger the greater the rate of income growth.

If income and/or assets at any time move out of line with previous planning expectations, plans can be revised. Suppose income rises, yet income expectations are not revised, the change being viewed as an on-off event. Then the individual marginal propensity to save at that date would rise to finance subsequent consumption at a higher level until death. If income expectations were revised upwards permanently, then the marginal propensity to save would also rise but to a lesser degree than in the on-off case as higher consumption can more easily be provided for out of later-period incomes. Allowance for income variability is straightforward in cross section; with time series expected income, here labor income, may be set equal to a weighted average of aggregated past and expected future income, or subdivided according to whether the reference is to employed or unemployed consumers at any time (Modigliani & Ando (1963)).

Source: SFB 504

Acronym for "Let It Function Today" - a concept very comparable to rationality (for a repeated discussion see Bogart, 1985):

•Everyone believes it exists, although some pessimist critics say it consists only theoretically and has no everyday value whatsoever (e.g. Lotterbottel, 1983);
•It has just one entry (the economist view), but still people can get into it coming from very different places or levels. Superficially, these levels all look the same (red), but they really are dependent on context factors (the psychologist view);
•It is at the core of the SonderForschungsBereich. However, there will never be more than four people being able to use it at the same time. The probability is high that this also is the time when the bell rings and the concept breaks down (Hausmeister, 1952);
•People are really into it and they talk a lot about it (Funk & Stoer, 1997). Behavioral observation has proved, however, that in fact nobody gets in (although some people report spiritual experiences of "being in a flight-like state" or "getting closer to the heavenly Geschäftsstelle" or being "lifted up", while others believe in "the key"). Instead people circle around it using the dissatisficing strategy of climbing the stairs of experimental simulation;
•It is supposed to work perfectly, but it could happen that at some point it wouldn't. Therefore it is not worked with preventively. As one result the concept just never works, as a second result people sweat a whole lot;
•There is some speculation about what would happen if it worked at some point, but empirical evidence for these theories is still weak (Autorenkollektiv, 1997).



Source: SFB 504

In maximum likelihood estimation, the likelihood function (often denoted L()) is the joint probability function of the sample, given the probability distributions that are assumed for the errors. That function is constructed by multiplying the pdf of each of the data points together:
L(q) = L(q; X) = f(X; q) = f(X₀;q)f(X₁;q)...f(X_N;q)