st: reg3: averaging across K equations and testing that average coeff equals zero

[Guy Grossman <guygrossman1@gmail.com>]

Hi -
I am hoping someone can assist me with the following question. I am
estimating 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 Y 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 (say, political participation). I am hoping to
conduct the following analysis (similar to the one described in the
fantastic Working Paper by Casey, Glennerster and Miguel (2011)
"Reshaping Institutions: Evidence on External Aid and Local Collective
Action", p. 22)

1. calculate a mean effect index that captures the average
relationship between T and the K different outcomes that belong to the
same family
2. calculate the standard error of this index which depends on the
variance of of each of the individual alpha and the covariance between
alpha_1,k and alpha_1, --k
3. test the cross equation hypothesis that the average index of 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 from here. suggestions would be
highly appreciated!
Regards,
Guy

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