```
#' Resample for truncated normal errors
#'
#' @description The truncated multivariate normal errors can be generated
#' in one of two ways. Either we sample the first stage and probit errors
#' first and then resample the linear regression's errors until we have
#' positive values, or we resample the vector of all three errors until
#' the linear value is positive. This is the second method, use cragg_errs1
#' for the second, which is less intuitive.
#'
#'
#' @param cov the covariance matrix. This should be untransformed, the
#' terms will be multiplied by the coefficients within the resampling
#' procedure.
#' @param x1 your exogenous variables (a dataframe)
#' @param z your instrument (a dataframe)
#' @param pi a vector of coefficients for the first stage regression
#' @param gamma a vector of coefficients for the second stage probit
#' @param beta a vector of coefficients for the second stage linear regression
#' @param n the number of errors to be generated
#'
#' @return returns a list of your errors and the three generated variables:
#' the endogenous regressor, the censoring variable and the outcome variable
#'
cragg_errs2<-function(cov,pi,x1,gamma,beta,n,z){
require("MASS")
j=1
endog = c(rep(NA,n))
y0 = c(rep(NA,n))
yStar = c(rep(NA,n))
errors = matrix(c(rep(0,n*dim(cov)[1])),ncol = dim(cov)[1])
while(j<=n){
err = mvrnorm(1,rep(0,dim(cov)[1]),cov)
frame = as.matrix(cbind(1,x1[j,],z[j,]))
endog[j] = frame%*%pi + err[3]
frame2 = as.matrix(cbind(1,x1[j,],endog[j]))
y0[j] = as.numeric(frame2%*%gamma + err[1] > 0)
yStar[j] = frame2%*%beta + err[2]
if(yStar[j]>0){
errors[j,] = err
j = j+1
}
}
return(list(errors = errors, endog = endog, y0 = y0, yStar = yStar))
}
```

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