# KTest: Compute the K statistics of Kleibergen In gmm: Generalized Method of Moments and Generalized Empirical Likelihood

## Description

The test is proposed by Kleibergen (2005). It is robust to weak identification.

## Usage

 ```1 2 3``` ```KTest(obj, theta0 = NULL, alphaK = 0.04, alphaJ = 0.01) ## S3 method for class 'gmmTests' print(x, digits = 5, ...) ```

## Arguments

 `obj` Object of class "gmm" returned by `gmm` `theta0` The null hypothesis being tested. See details. `alphaK, alphaJ` The size of the J and K tests when combining the two. The overall size is alphaK+alphaJ. `x` An object of class `gmmTests` returned by `KTest` `digits` The number of digits to be printed `...` Other arguments when `print` is applied to another class object

## Details

The function produces the J-test and K-statistics which are robust to weak identification. The test is either H0:θ=theta_0, in which case theta0 must be provided, or β=β_0, where θ=(α', β')', and α is assumed to be identified. In the latter case, theta0 is NULL and obj is a restricted estimation in which β is fixed to β_0. See `gmm` and the option "eqConst" for more details.

## Value

Tests and p-values

## References

Keibergen, F. (2005), Testing Parameters in GMM without assuming that they are identified. Econometrica, 73, 1103-1123,

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```library(mvtnorm) sig <- matrix(c(1,.5,.5,1),2,2) n <- 400 e <- rmvnorm(n,sigma=sig) x4 <- rnorm(n) w <- exp(-x4^2) + e[,1] y <- 0.1*w + e[,2] h <- cbind(x4, x4^2, x4^3, x4^6) g3 <- y~w res <- gmm(g3,h) # Testing the whole vector: KTest(res,theta0=c(0,.1)) # Testing a subset of the vector (See \code{\link{gmm}}) res2 <- gmm(g3, h, eqConst=matrix(c(2,.1),1,2)) res2 KTest(res2) ```

gmm documentation built on June 20, 2017, 3:01 p.m.