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# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# A copy of the GNU General Public License is available at
# http://www.r-project.org/Licenses/
# This function compute what is needed for the K statistics of KleiBergen (2005)
#####################################################################################
.BigCov <- function(obj,theta0)
{
insertRC <- function(A,w,v)
{
NewA <- matrix(ncol=ncol(A)+length(w),nrow=nrow(A)+length(w))
NewA[-w,-w] <- A
NewA[w,] <- v
NewA[,w] <- v
NewA
}
dg <- function(obj)
{
dat <- obj$dat
x <- dat$x[,(dat$ny+1):(dat$ny+dat$k)]
k <- ncol(x)
h <- dat$x[,(dat$ny+dat$k+1):ncol(dat$x)]
qt <- array(dim=c(dim(obj$gt),k))
for (i in 1:k)
qt[,,i] <- -x[,i]*h
qt}
if (attr(obj$dat,"ModelType") == "nonlinear")
{
Myenv <- new.env()
assign("obj", obj, envir=Myenv)
assign("theta", theta0, envir=Myenv)
gFunct <- obj$g
assign("g",gFunct,envir=Myenv)
res <- numericDeriv(quote(g(theta,obj$dat)),"theta",Myenv)
qT <- attr(res,"gradient")
} else {
qT <- dg(obj)}
qTmat <- apply(qT,3,colSums)
qT <- matrix(qT,nrow=dim(qT)[1])
gt <- obj$g(theta0,obj$dat)
fT <- colSums(gt)
n <- nrow(gt)
q <- ncol(gt)
All <- cbind(gt,qT)
All <- sweep(All,2,colMeans(All),FUN="-")
f <- function(x)
all(abs(x)<1e-7)
w <- which(apply(All,2,f))
if (length(w) != 0)
All <- All[,-w]
if (dim(All)[2] >= dim(All)[1])
stop("Too many moment conditions. Cannot estimate V")
if (attr(obj$dat, "weight")$vcov == "iid")
{
V <- crossprod(All)/nrow(All)
} else {
class(All) <- "gmmFct"
argSand <- attr(obj$dat, "weight")$WSpec$sandwich
argSand$x <- All
argSand$sandwich <- FALSE
V <- do.call(kernHAC,argSand)
}
if (length(w) != 0)
V <- insertRC(V,w,0)
Vff <- V[1:q,1:q]
Vthetaf <- V[(q+1):nrow(V),1:q]
list(Vff=Vff,Vthetaf=Vthetaf,qT=qTmat,fT=fT,n=n,q=q)
}
KTest <- function(obj, theta0=NULL, alphaK = 0.04, alphaJ = 0.01)
{
if (class(obj)[1] != "gmm")
stop("KTest is only for gmm type objects")
if (!is.null(attr(obj$dat,"eqConst")))
{
if (!is.null(theta0))
warning("setting a value for theta0 has no effect when the gmm is already constrained")
resTet <- attr(obj$dat,"eqConst")$eqConst
tet <- obj$coefficients
theta0 <- vector(length=length(tet)+nrow(resTet))
theta0[resTet[,1]] <- resTet[,2]
theta0[-resTet[,1]] <- tet
testName <- paste(rownames(resTet), " = ", resTet[,2], collapse="\n")
if (attr(obj$dat,"ModelType") == "linear")
{
obj$dat$k <- length(theta0)
}
dfK <- nrow(resTet)
which <- resTet[,1]
attr(obj$dat, "eqConst") <- NULL
} else {
if (is.null(theta0))
stop("You must either estimate a restricted model first or set theta0 under H0")
if (length(theta0) != length(obj$coef))
stop("theta0 is only for tests on the whole vector theta when obj is an unrestricted GMM")
dfK <- length(theta0)
testName <- paste(names(obj$coef), " = ", theta0, collapse="\n")
which <- 1:length(theta0)
}
V <- .BigCov(obj, theta0)
Vff <- V$Vff
Vtf <- V$Vthetaf
qT <- V$qT
fT <- V$fT
dfJ <- V$q-length(theta0)
# the following is vec(D)
D <- c(qT)-Vtf%*%solve(Vff,fT)
D <- matrix(D,ncol=length(theta0))
meat <- t(D)%*%solve(Vff,D)
bread <- t(fT)%*%solve(Vff,D)
K <- bread%*%solve(meat,t(bread))/V$n
pv <- 1-pchisq(K,dfK)
S <- t(fT)%*%solve(Vff,fT)/V$n
J <- S-K
dfS <- dfK + dfJ
pvJ <- 1-pchisq(J,dfJ)
type <- c("K statistics","J statistics", "S statistics")
test <- c(K,J,S)
pvS <- 1-pchisq(S,dfS)
test <- cbind(test,c(pv,pvJ,pvS),c(dfK,dfJ,dfS))
dist <- paste("Chi_sq with ", c(dfK,dfJ,dfS), " degrees of freedom", sep="")
if(dfJ>0)
ans <- list(test=test,dist=dist,type=type,testName=testName)
else
ans <- list(test=matrix(test[1,],nrow=1),dist=dist[1],type=type[1],testName=testName)
if (pvJ<alphaJ) {
message <- "reject"
} else {
if (pv < alphaK)
message <- "reject"
else
message <- "do not reject"
}
ans$KJ <- (message == "do not reject")
ans$Matrix <- list(D=D,bread=bread,meat=meat,qT=qT,fT=fT)
ans$message <- paste("KJ-test result: We ", message, " H0 (alphaJ = ", alphaJ, ", alphaK = ", alphaK, ")", sep="")
class(ans) <- "gmmTests"
ans
}
print.gmmTests <- function(x, digits = 5, ...)
{
lab <- paste("%0.",digits,"f",sep="")
cat("\nTest robust to weak identification\n")
cat("**********************************\n\n")
cat("The Null Hypothesis\n")
cat(x$testName,"\n\n")
for (i in 1:length(x$type))
{
cat(x$type[i],"\n")
cat("Test: ", sprintf(lab,x$test[i,1]), "(",x$dist[i],")\n")
cat("P-value: ", sprintf(lab,x$test[i,2]),"\n\n")
}
cat(x$message,"\n")
}
gmmWithConst <- function(obj, which, value)
{
argCall <- obj$allArg
argCall$call = NULL
if (!is.null(attr(obj$w0,"Spec")))
if (is.function(argCall$bw))
argCall$bw <- attr(obj$w0,"Spec")$bw
if (length(which)>=length(obj$coefficients))
stop("Too many constraints")
if (is.character(which))
{
if (any(!(which %in% names(obj$coefficients))))
stop("Wrong coefficient names in eqConst")
if (attr(obj$dat,"ModelType") == "linear")
which <- match(which,names(obj$coefficients))
}
if (!is.null(argCall$t0))
{
argCall$t0 <- obj$coefficients
argCall$t0[which] <- value
}
if (attr(obj$dat,"ModelType") == "nonlinear")
{
eqConst <- which
} else {
eqConst <- cbind(which,value)
}
argCall$eqConst <- eqConst
res <- do.call(gmm,argCall)
res$call <- match.call()
return(res)
}
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