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st: Averaging coefficinets across reg3 output

From   Guy Grossman <>
Subject   st: Averaging coefficinets across reg3 output
Date   Mon, 11 Jul 2011 12:29:13 -0400

Hi -

I am reposting a question that was not responded. Assistance would be
highly appreciated. In short, I am using Stata 11.2 on mac to estimate
the following system of equations:

Y1 = alpha_1*T+beta_1*X +e_1
Y2 = alpha_2*T+beta_2*X +e_2
Y3 = alpha_3*T+beta_3*X +e_3
Yk = alpha_k*T+beta_k*X +e_k

where Y1-Yk are standardized dependent variables, X is an exogenous
covariate and T is a binary endogenous variable, instrumented by Z. I
am using reg3 (three-stage estimation). My main interest is the
coefficients on T (the alphas). Y1--Yk are thought to be from the same
family of outcomes. My goal is to conduct the following analysis:

1. calculate a mean effect value that captures the average
relationship between T and the K different outcomes that belong to the
same family

2. calculate the standard error of the mean effect value which depends
on the variance of of each of the individual alpha and the covariance
alpha_1,k and alpha_1, --k

3. test the cross equation hypothesis that the average effect of the K
coefficients equals zero

My Stata code starts with:
global y1 "(q1: y1 t x)"
global y2 "(q2: y2 t x)"
global y3 "(q3: y3 t x)"
global y4 "(q4: y4 t x)"

reg3 $y1 $y2 $y3 $y4, endog(t) exog(z)

I am not sure however, how to continue to stages (2) and (3).
suggestions would be highly appreciated!

Guy Grossman
Dept. of Political Science
Columbia University, NY

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