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st: Difference-in-Difference of Binary Outcomes with Margins


From   Jonathan Stoeterau <jonathanstoeterau@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Difference-in-Difference of Binary Outcomes with Margins
Date   Fri, 28 Sep 2012 15:41:36 +0200

Dear Statalist,

to reassure my correct understanding of the interpretation of
interaction effects with binary outcome variables:
I have a panel of three institutions from 2008-2012. Reforms where
undertaken at different times in these institutions.
The outcome variable is a job-finding dummy of individuals from these
institutions.

To get the Difference-in-Difference Estimator of the effect of reforms
on the probability of finding a job I used a logit approach:

. logit  employed i.reform i.year covars, robust
. margins reform##year, atmeans

(Where reform is a dummy variable and year a categorial variable)

Which will get me:

|            Delta-method
|     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------------------------------------------------
q1_reform
0     .0346368    .0125651    2.76    0.006    .0100096    .059264
1     .2882842    .0566586    5.09    0.000    .1772354    .399333
--------------------------------------------------------
q1_year
2011     .0372282    .0142733    2.61    0.009    .0092531    .0652033
2012     .1824044    .0214199    8.52    0.000    .1404222    .2243867
--------------------------------------------------------
q1_reform#
q1_year
0 2011     .0099831    .0068771    1.45    0.147    -.0034958    .023462
0 2012     .0549811    .0148792    3.70    0.000    .0258185    .0841437
1 2011     .1022044    .0249878    4.09    0.000    .0532292    .1511795
1 2012     .3964308    .0921924    4.30    0.000    .215737    .5771245

Which of these coefficients identifies the effect of the reforms? And
what is the correct way of interpreting it?

In advance: Thank you for your help. I was trying to googling this out
for a long while...

Jonathan
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