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st: two stage model variance estimators


From   "Rachel Bouvier" <rbouvier@usm.maine.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: two stage model variance estimators
Date   Tue, 13 Sep 2005 16:17:24 -0400

Dear statalisters *

I am confronting a problem much like that described by James Hardin in volume 2, issue 3 of the Stata Journal, "The robust variance estimator for two-stage models," where he gave an illustration of Stata code to construct the Murphy-Topel variance estimator.

I am using a variable (call it yhat), predicted in a first (series of) equations, as a regressor in my second equation.  

In other words, my first (series of) regressions looked like this:
(1) y = b1 x + b2 xsq

Then, I predicted yhat from that regression, and used that in a second regression:
(2) z = b1 yhat + b2 x2 + b2 x3*

I say "series of" regressions because I have a panel of 30 countries.  Rather than run one panel data regression and predict each country's yhat from that, I ran each country as a separate regression, not wanting to assume that they could be pooled.  In other words, I ran equation (1) 30 different times, for each country in the dataset.  (It seemed to make sense at the time, to both me and my committee!)

Therein lies my problem.  I would like to adjust the standard errors for the fact that I predicted yhat, but as I ran a different regression for each country, the solution is not as easy as constructing the Murphy-Topel estimator.  Does anyone have any suggestions? Any help would be much appreciated, before I dive into something that is undoubtedly over my head.  Thanks.


Rachel Bouvier
Assistant Professor of Economics
University of Southern Maine
11 Chamberlain Avenue
Portland, ME 04104
(207) 228-8377


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