R/chen_lee.R

In ChenyueLiu/ivqr: Perform inverse quantile regression by solving mixed integer linear programming

#' Generate simulated data using chen_lee 
#' 
#' @param n the number of observations
#' @param pD the number of endongenous variables
#' @return A list containing dependent variable Y, endogenous variable D, instrumental variable Z
#' @details This function produces as many instruments as endogenous variables. 
#' @examples chen_lee(150,3)
chen_lee = function(n, pD){
  B_D      =  rep( 1, pD)
  Z        =  matrix(rnorm(n*pD), ncol = pD)
  firstcol =  c(0.4, 0.6, -0.2, seq(-1,1, len=pD-3))
  firstcol =  sqrt(0.4^2+0.6^2+0.2^2)*firstcol/(norm(firstcol, "2")) 
  V        =  diag(pD+1)
  V[1,2:(pD+1)] = firstcol
  V[2:(pD+1),1] = firstcol
  errors   =  MASS::mvrnorm(n, mu = rep(0, pD+1), Sigma = 0.25*V)
  eps      =  errors[,1]
  nu       =  errors[,-1]# so the Pd nu's correlates with eps respectively while independent with each other
  scale_D  =  c(1, 2, 1.5, seq(1,2, len = pD-3))
  D        =  t(scale_D*t(pnorm(Z + nu)))
  B_errors =  c(1, 0.25, 0.15, seq(0.1, 1, len=pD - 3))
  Y        =  1 + D %*% B_D + (0.5 + D %*% B_errors)*eps
  return(list("Y"= Y, "D"= D, "Z"=Z))
}