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st: puzzling suest test of coefficients across equations


From   henry.sauermann@duke.edu
To   statalist@hsphsun2.harvard.edu
Subject   st: puzzling suest test of coefficients across equations
Date   Tue, 23 Oct 2007 21:39:50 -0400

Dear all,

I am estimating two equations of the following (simplified) form.

Equation1: Y=b0+b1x1+e
Equation2: Y=b0+b1x1+b2x2+e

I now want to test whether adding x2 in equation two significantly
changes the coefficient of x1 (i.e., a mediation analysis a la Baron and Kenny).
It should be straightforward using suest, but I get counterintuitive results.
Both equations are estimated using NBREG (negative binomial) and here are
the relevant estimates for x1 after suest:

Suest one two

Variable            coeff                 SE     
  z          p(z)

One_uspapp (equation 1):
orgtype_4 |  -.2912678   .1595529    -1.83   0.068

Two_uspapp (equation 2):
orgtype_4 |   -.183896   .1528182    -1.20   0.229

So, orgtype_4 (my variable x1) is not significant in equation 1 and
not significant in equation 2, and the coefficient is negative in both
equations. Yet, according to ?test? the difference between the two
coefficients is significant at 5%:

. test [one_uspapp]orgtype_4=[two_uspapp]orgtype_4;

( 1)  [one_uspapp]orgtype_4 - [two_uspapp]orgtype_4 = 0

           chi2(  1) =    4.82
         Prob > chi2 =    0.0281

I don?t see how the difference can be significant when both
coefficients are negative and not different from zero ? does anybody have an
explanation?

Thanks a lot for your help,
Henry


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