

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.

knearestneighbor estimator
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.

Kalman filter
The Kalman filter is an algorithm for sequentially updating a linear projection for a dynamic system that is in statespace representation.
Application of the Kalman filter transforms a system of the following twoequation 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+1}w_{t}'=1 by normalization, Ev_{t}v_{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_{t1}x_{t}, a_{t} is defined to be y_{t}E_{t1}y_{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_{t}G'(GS_{t}G'+R)^{1} S_{t+1}=(AK_{t}G)S_{t}(AK_{t}G)'+CC'+K_{t}RK_{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.

Kalman gain
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_{t}G'(GS_{t}G'+R)^{1}

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)

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 NadarayaWatson estimator, which see.

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].

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.

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.

KLIC
KullbackLeibler 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(PQ) = [integral of] ln(dP/dQ) dP if P << Q ........ = infinity otherwise

Knightian uncertainty
Unmeasurable risk. Contrast Knightian uncertainty.

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.

Kolmogorov's Second Law of Large Numbers
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.

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.: a_{11}B a_{12}B ... a_{1n}B . . . . . . . . . . . . a_{M1}B a_{M2}B ... a_{Mn}B Kronecker products have the following useful properties: (AoB)(CoD)=ACoBD (AoB)^{1} = A^{1}oB^{1} (AoB)' = A'oB' (AoB)+(AoC)=Ao(B+C) AoC+BoC = (A+B)oC

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 crosscorrelation, then the GLS estimator of b is the same as the OLS estimator of b.

kurtosis
An attribute of a distribution, describing 'peakedness'. Kurtosis is calculated as E[(xmu)^{4}]/s^{4} where mu is the mean and s is the standard deviation.

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 invertedUshape. 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.

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