# st: how to adjust covariance matrix in two-stage model using svy (and iv)?

 From Jennifer Leavy To "Statalist (statalist@hsphsun2.harvard.edu)" Subject st: how to adjust covariance matrix in two-stage model using svy (and iv)? Date Fri, 28 Mar 2008 16:33:45 +0000

```Dear Statalisters
I am trying to estimate a model of market participation (sellers, non-sellers: given that someone sells, how much are they selling?) addressing the following issues:

i) complex survey design (PSUs and pweights only)
ii) sample selection bias
iii) potential reverse causality between regressors and dependent variable

To be able to use instrumental variables I think I will need to estimate the model in two steps (‘by hand’) rather than using the heckman command. However, because of the inverse mills ratio in the outcome equation, this means that I also need to make an adjustment to the covariance matrix of the outcome equation so that I get correct standard errors. I’ve looked through stata FAQs and statalist and trawled the internet and the closest I can find to what I want to do is set out below, minus the IV part of the estimation for now for simplicity (I took the syntax from Vince Wiggins' FAQ post "Must I use all of my exogenous variables as instruments when estimating instrumental variables regression?")

However, there is a problem in that by using svy:regress Stata does not seem to give e(rmse) so the new Vmatrix ends up empty. Is there a way of recovering the estimated rmse so I can plug it into the formula? Or is there a better way for me to do this? I have been grappling with this for some time, so any help (solutions or encouragement to let this one go) very much appreciated.
Many thanks
Jennifer

The syntax:

/*selection equation*/
svy: probit y2 x w
predict Z, xb /*fitted values*/
gen mills=normden(Z)/norm(Z)
/*Outcome equation*/
svy: regress y1 mills x if y2==1
set more off
rename Z y2hold
rename y2 Z
predict double res, residual
rename Z y2
rename y2hold Z
replace res=res^2
summ 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 /*stata does not return e(rmse) - dividing by zero in that case*/
ereturn post bmatrix Vmatrix, noclear /*so the Vmatrix is empty*/
ereturn display

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```