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# Re: st: Stata implementation of difference-in-differences with binary outcomes

 From Maarten buis To statalist@hsphsun2.harvard.edu Subject Re: st: Stata implementation of difference-in-differences with binary outcomes Date Fri, 16 Apr 2010 07:57:03 -0700 (PDT)

```--- On Fri, 16/4/10, C Engelbrecht wrote:
> But what if the outcome variable is binary? How should I
> model the difference of two latent variables, as is the
> case in Probit / Logit? The usual DID is based on
> differencing Y across these groups, but what should we
> do now that we only have a latent Y*?

Difference in difference is all about getting at a causal
effect, which is usually difined as a difference in
averages. This also exists and is meaningful when the
dependent variable is binary, that is the risk difference.
You can calculate it using a linear probability model,
which is just a fancy name of using -regress- on a binary
variable (possibly with the -vce(robust)- option.

There is often some uneasyness in specifying "the effect"
as linear in the probability metric, as that can
eventually lead to predictions outside the range [0, 1].
However, if you define the effect interms of odds ratios
or probit coefficients, you won't get the causal effects
either, see for example: Mood 2010, Allison 1999, or
Neuhaus and Jewell 1993.

So my guess would be that the linear probability model
is in this case the lesser of two evils.

Hope this helps,
Maarten

Allison, Paul D. 1999. "Comparing Logit and Probit
Coefficients Across Groups." Sociological Methods &
Research 28:186–208.

Mood, Carina. 2010. "Logistic regression: Why we cannot
do what we think we can do, and what we can do about
it." European Sociological Review 26:67–82.

Neuhaus, John M. and Nicholas P. Jewell. 1993. "A
Geometric Approach to Assess Bias Due to Omited
Covariates in Generalized Linear Models." Biometrika
80:807–815.

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------

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