R/heck2steprobVcov.R

In ssmrob: Robust Estimation and Inference in Sample Selection Models

heck2steprobVcov <-
function(y1vec, y2vec, x1Matr, x2Matr, eststage1, eststage2, eststage2sigma, weights = rep(1,nrow(y1vec)), t.c = 1.345)
{
  n <- sum(y1vec == 1)
  sumheck <- 0 #
  for(i in 1:n)  # sandwich estimator of the first term
  {
    sumheck=sumheck+PsiMest(x2Matr[i,],y2vec[i],eststage2,eststage2sigma,t.c,weights[i])%*%t(PsiMest(x2Matr[i,],y2vec[i],eststage2,eststage2sigma,t.c,weights[i]))
  }
  
  s1 <- matrix(0, length(eststage2)-1, length(eststage1$coeff))
  s2 <- 0   
  for(i in 1:n)
  {
    if((y2vec[i] - t(x2Matr[i,]) %*% as.vector(eststage2)) / eststage2sigma < (-t.c))
    {
      s1=s1+0
      s2=s2 - t.c*weights[i]*drop(dLambdadSM(x1Matr[i,],eststage1$coeff))*(x1Matr[i,])
    }
    else if(((y2vec[i] - t(x2Matr[i,]) %*% as.vector(eststage2))) / eststage2sigma > (t.c))
    {
      s1 = s1 + 0
      s2 = s2 + t.c*weights[i]*drop(dLambdadSM(x1Matr[i,],eststage1$coeff))*(x1Matr[i,])
    }
    else {
      s1 = s1 + (x2Matr[i,1:dim(x2Matr)[2]-1])%*%t(x1Matr[i,])*eststage2[dim(x2Matr)[2]]*weights[i]*drop(dLambdadSM(x1Matr[i,],eststage1$coeff))/eststage2sigma
      s2 = s2 + (x2Matr[i,dim(x2Matr)[2]]*eststage2[dim(x2Matr)[2]])*weights[i]*c(dLambdadSM(x1Matr[i,],eststage1$coeff))/eststage2sigma*x1Matr[i,]
      }
  }
  xdx <- rbind(s1,s2)
  term2 <- xdx%*%vcov(eststage1)%*%t(xdx)  
  M2inv <- solve(MmatrM(x2Matr,y2vec,eststage2,eststage2sigma,t.c,weights))
  result <- (M2inv%*%(sumheck+term2)%*%M2inv)  # asymptotic variance for Heckman-M-estimator
  return(result)
}