KTest function

Compute the K statistics of Kleibergen

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

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 $H0:\theta=theta_0$, in which case theta0 must be provided, or $\beta=\beta_0$, where $\theta=(\alpha', \beta')'$, and $\alpha$ is assumed to be identified. In the latter case, theta0 is NULL and obj is a restricted estimation in which $\beta$ is fixed to $\beta_0$. See gmm and the option "eqConst" for more details.

Returns

Tests and p-values

References

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

Examples

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)