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Glossary


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z (Show all)

k percent rule

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

k-nearest-neighbor estimator

A kind of nonparametric estimator of a function. Given a data set {Xi, Yi} it estimates values of Y for X's other than those in the sample. The process is to choose the k values of Xi 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

Kalman filter

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:
xt+1=Axt+Cwt+1 yt=Gxt+vt 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,
xt is a true state variable, hidden from the econometrician,
yt is a measurement of x with scalings G and measurement errors vt,
wt are innovations to the hidden xt process,
Ewt+1wt'=1 by normalization,
Evtvt=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 St and Kt 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:
zt+1=Azt+Kat yt=Gzt+at where zt is defined to be Et-1xt,
at is defined to be yt-Et-1yt,
K is defined to be lim Kt as t goes to infinity.

The definition of those two matrices St and Kt is itself most of the definition of the Kalman filter:
Kt=AStG'(GStG'+R)-1 St+1=(A-KtG)St(A-KtG)'+CC'+KtRKt'
Kt 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

Kalman gain

One of the two equations that characterizes the application of the Kalman filter process defines an expression sometimes denoted Kt, which is called the Kalman gain.

That equation, using notation from Sargent's lectures, is:

Kt=AStG'(GStG'+R)-1

Source: econterms

keiretsu system

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

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

kernel function

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

Keynes effect

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

kitchen sink regression

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

KLIC

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

Knightian uncertainty

Unmeasurable risk. Contrast Knightian uncertainty.

Source: econterms

knots

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

Kolmogorov's Second Law of Large Numbers

If {wt} is a sequence of iid draws from a distribution and Ewt exists (call it mu) then the average of the wt's goes 'almost surely' to mu as t goes to infinity.
Same as strong law of large numbers, I believe.

Source: econterms

Kronecker product

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 ... a1nB
. . . . . .
. . . . . .
aM1B aM2B ... aMnB
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

Kruskal's theorem

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

kurtosis

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

Kuznets curve

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

Kyklos

A journal, whose Web site is at http://www.kyklos-review.ch/kyklos/index.html.

Source: econterms

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