

WACM
abbreviation for the Weak Axiom of Cost Minimization

wage curve
A graph of the relation between the local rate of unemployment, on the horizontal axis, and the local wage rate, on the vertical axis. Blanchflower and Oswald show that this relation is downward sloping. That is, locally high wages and locally low unemployment are correlated.

Wallis statistic
A test for fourthorder serial correlation in the residuals of a regression, from Wallis (1972) Econometrica 40:617636. Fourthorder serial correlation comes up in the context of quarterly data; e.g., seasonality. Formally, the statistic is: d_{4}=(sum from t=5 to t=T of: (e_{t}e_{t4})^{2}/(sum from t=1 to t=T of: e_{t}^{2}) where the series of e_{t} are the residuals from a regression. Tables for interpreting the statistic are in Wallis (1972).

Walrasian auctioneer
A hypothetical marketmaker who matches suppliers and demanders to get a single price for a good. One imagines such a marketmaker when modeling a market as having a single price at which all parties can trade.
Such an auctioneer makes the process of finding trading opportunities perfect and cost free; consider by contrast a "search problem" in which there is a stochastic cost of finding a partner to trade with and transactions costs when one does meet such a partner.

Walrasian equilibrium
An allocation vector pair (x,p), where x are the quantities held of each good by each agent, and p is a vector of prices for each good, is a Walrasian equilibrium if (a) it is feasible, and (b) each agent is choosing optimally, given that agent's budget. In a Walrasian equilibrium, if an agent prefers another combination of goods, the agent can't afford it.

Walrasian model
A competitive markets equilibrium model "'without any externalities, asymmetric information, missing markets, or other imperfections." (Romer, 1996, p 151)
'In this general equilibrium model, commodities are identical, themarket is concentrated at a single point [location] in space, and the exchange is instantaneous. [Individuals] are fully informed about the exchange commodity and the terms of trade are known to both parties. [No] effort is required to effect exchange other than to dispense with the appropriate amount of cash. [Prices are] a sufficient allocative device to achieve highest value uses.' (North, 1990, p. 30.)

WAPM
abbreviation for the Weak Axiom of Profit Maximization

WARP
WARP is an acronym for the Weak Axiom of Revealed Preference. This axiom states that when a consumer selects consumption bundle 'a' when bundle 'b' is available, the consumer will not select 'b' when 'a' is available. This axiom has two extensions: the Strong Axiom of Revealed Preference (SARP) and the Generalized Axiom of Revealed Preference (GARP).

wavelet
A wavelet is a function which (a) maps from the real line to the real line, (b) has an average value of zero, (c) has values very near zero except over a bounded domain, and (d) is used for the purpose, analogous to Fourier analysis, implied by the following paragraphs.
Unlike sine waves, wavelets tend to be irregular, asymmetric, and to have values that die out to zero as one approaches positive and negative infinity. "Fourier analysis consists of breaking up a signal into sine waves of various frequencies. Similarly, wavelet analysis is the breaking up of a signal into shifted and scaled versions of the original (or mother) wavelet."
By decomposing a signal into wavelets one hopes not to lose local features of the signal and information about timing. These contrast with Fourier analysis, which tends to reproduce only repeated features of the original function or series.

WE
Walrasian Equilibrium

weak form
Can refer to the weak form of the efficient markets hypothesis, which is that any information in the past prices of a security are fully reflected in its current price. Fama (1991) broadens the category of tests of the weak form hypothesis under the name of 'test for return predictability.'

weak incentive
An incentive that is does not encourage maximization of an objective, because it is ambiguous or satisficeable. For example, payment of weekly wages is a weak incentive since by construction it does not encourage maximum production, but rather the minimal performance of showing up every work day. This can be the best kind of incentive in a contract if the buyer doesn't know exactly what he wants or if output is not straightforwardly measurable. Contrast strong incentive.

weak law of large numbers
Quoted right from Wooldridge chapter: A sequence of random variables {z_{t}} for t=1,2,... satisfies the weak law of large numbers if these three conditions hold: (1) E[z_{t}] is finite for all t, (2) as T goes to infinity, the limit of the average of the first T elements of {z_{t}} 'exists' [unknown: that means it's fixed and finite, right?], (3) as T goes to infinity, the probability limit of the average of the first T elements of the series [z_{t}  E(z_{t})] is zero.
The most important point (I think) is that the weak law of large numbers holds iff the sample average is a consistent estimate for the mean of the process.
Laws of large numbers are proved with Chebyshev's inequality.

weak stationarity
synonym for covariance stationarity. A random process is weakly stationary iff it is covariance stationary.

weakly consistent
synonym for consistent.

weakly dependent
A time series process {x_{t}} is weakly dependent iff these four conditions hold: (1) {x_{t}} is essentially stationary, that is if E[x_{t}^{2}] is uniformly bounded. In any such process, the following 'variance of partial sums' is well defined, and it will be used in the following conditions. Define s_{T}^{2} to be the variance of the sum from t=1 to t=T of x_{t}. (2) s_{T}^{2} is O(T). (3) s_{T}^{2} is O(1/T). (4) The asymptotic distribution of the sum from t=1 to t=T of (x_{t}E(x_{t}))/s_{T} is N(0,1).
These conditions rule out random processes which are serially correlated too positively or negatively or whose partial sums are near zero. Example 1: An iid process IS weakly dependent. (Domowitz, in class 4/14/97.)
Example 2: A stable AR(1) (r<1) with iid innovations.

weakly ergodic
A stochastic process may be weakly ergodic without being strongly ergodic.

weakly Pareto Optimal
An allocation is weakly Pareto optimal (WPO) if a feasible reallocation would be strictly preferred by all agents. WPO <=> SPO if preferences are continuous and strictly increasing (that is, locally nonsatiated).

WebEc
A Web site with indexes to World Wide Web Resources in Economics. Click here to go there.

wedge
The gap between the price paid by the buyer and price received by the seller in an exchange. Might be caused by a tax paid to a third party.

Weibull distribution
in at least one 'standard' specification, has pdf: f(x)=Tx^{T1}exp(x^{T})
where T stands for q. T=1 is the simplest case. It looks like the pdf is zero for x<1 in that case.

Weierstrauss Theorem
that a continuous function on a closed and bounded set will have a maximum and a minimum.
This theorem is often used implicitly, in the assumption that some set is compact, meaning closed and bounded. Examples that may help clarify:
Example 1: Consider a set which is unbounded, like the real line. Say variable x has any value on the real line, and we wish to maximize the function f(x)=2x. It doesn't have a maximum or minimum because values of x further from zero have more and more extreme values of f(x).
Example 2: Consider a set which is not closed, like (0,1). Again, let f(x) be 2x. Again this function has no maximum or minimum because there is no largest or smallest value of x in the set.

Weighted attributes
If the combined weights of a
novel object's attributes' relevance for conferring family
resemblance to the category exceed a certain level (the
mebership criterion), that object will be considered an instance
of the category (Medin, 1983).

weighted least squares
A way of choosing an estimator. Makes a weighted tradeoff between the error in an estimator due to bias and that due to variance. Putting equal weights on the two is the mean square error criterion.

welfare capitalism
welfare capitalism  the practice of employers' voluntary provision of nonwage benefits of to their blue collar employees.

WesVar
A software program for computing estimates and variance estimates from potentially complicated survey data. Made by Westat.

white noise process
a random process of random variables that are uncorrelated, have mean zero, and a finite variance (which is denoted s^{2} below). Formally, e_{t} is a white noise process if E(e_{t}) = 0, E(e_{t}^{2}) = s^{2}, and E(e_{t}e_{j}) = 0 for t<>j, where all those expectations are taken prior to times t and j. A common, slightly stronger condition is that they are independent from one another; this is an "independent white noise process." Often one assumes a normal distribution for the variables, in which case the distribution was completely specified by the mean and variance; these are "normally distributed" or "Gaussian" white noise processes.

White standard errors
Same as HuberWhite standard errors.

Wiener process
A continuoustime random walk with random jumps at every point in time (roughly speaking).

window width
Synonym for bandwidth in the context of kernel estimation

winner's curse
That a winner of an auction may have overestimated the value of the good auctioned. "The winner's curse arises in an auction when the good being sold has a common value to all the bidders (such as an oil field) and each bidder has a privately known unbiased estimate of the value of the good (such as from a geologist's report): the winning bidder [may] be the one who most overestimated the value of the good; this bidder's estimate itself may be unbiased but the estimate conditional on the knowledge that it is the highest of n unbiased estimates is not."  Gibbons and Katz

within estimator
synonym for fixed effects estimator

Within subjects design
In a within subjects design the values of the dependent variable for an item or a set of
items (e.g., the experimental items) are compared with the values for another item or
another set of items (e.g., the control items) within one person.

WLLN
Weak law of large numbers

WLOG
abbreviation for "without loss of generality". This phrase is relevant in the context of a proof or derivation in which the notation becomes simpler, or there are fewer cases to demonstrate, by making an innocuous assumption, for example that the data are in a certain order.

Wold decomposition
Any zero mean, covariance stationary process can be represented as a moving average sum of white noise processes plus a linearly deterministic component that is a function of the index t. That form of expressing the process is its Wold decomposition. Clear expression of this idea requires an equation or two that cannot be put here yet.

Wold's theorem
That any covariance stationary stochastic process with mean zero has a moving average representation, called its Wold decomposition. Let {x_{t}} be that process. See Sargent, 1987, p 286288 for the complete theorem, assumptions, and proof.

World Bank
A collection of international organizations to aid countries in their process of economic development with loans, advice, and research. It was founded in the 1940s to aid Western European countries after World War II with capital.
Click here to go to the World Bank web site.

world systems theory
[What follows is the editor's best understanding, but not definitive.] A category of sociological/historical description and analysis in which aspects of the world's history are thought of as byproducts of the world being an organic whole. Key categories are core and periphery. Core countries, economies, or societies are richer, have more capitalintensive industry, skilled labor and relatively high profits. In a way they exploit the poorer peripheral societies but it may not be a deliberate collusion.

WPO
stands for Weakly Pareto Optimal
