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st: Two Stage Tobit Covariance Matrix


From   "Leonor Saravia" <[email protected]>
To   [email protected]
Subject   st: Two Stage Tobit Covariance Matrix
Date   Tue, 24 Apr 2007 16:48:22 -0400

Hello Satatlist,

I'm estimating a Two Stage Tobit model manually, because I have
censored variables (at zero) for the first and second stage of the
estimation. I know that when I do this the standar errors are not
valid, but I don't know if it is fine to correct them by the same way
I should do it when is a Two Stage Least Squares manually estimation.

This is the model I have: y1=a+bX1+ bX2 + u, with y1 and X2 as
exogenous variables and X1 as the endogenous variable, but I have an
instrumental variable, Z1, for X1. Both, X1 and y1, are censored at
zero. So, what I�m doing in Stata is:

First step:
              tobit X1 Z1, ll(0)
              predict double X1_hat

Second step:
              tobit y1 X1_hat X2, ll(0)

To correct the standard errors in a Two Stage Least Squares estimation
what I should continue doing is: (from FAQs: Two Least Squares
Regression)

rename X1_hat X1hold
rename X1 X1_hat
predict double res, residual

rename X1_hat X1
rename X1_hold X1_hat
replace res = res^2

summarize res

scalar realmse = r(mean)*r(N)/e(df_r)
matrix bmatrix = e(b)
matrix Vmatrix = e(V)
matrix Vmatrix = e(V) * realmse / e(rmse)^2
ereturn post bmatrix Vmatrix, noclear
ereturn display


This way I correct the variance and covariance matrix.

I should do the same way in the Two Stage Tobit estimation to correct
the var-cov matrix?

Thnak you in advance.

Leonor

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