# Restricted sample regression vs. Interaction term

To set up the question, I am evaluating a simple linear model as part of a generalized differences-in-differences study design like so:

The study is evaluating state statutory changes from 1990s to 2012 with main variable of interest a dummy for whether policy is adopted or not (lagged one-year), also a set of dummy variables for state- year- fixed effects. The outcome is derived from a national survey.

$Y_{it} = \alpha_0 + \delta*Policy_{it} + year_t + state_i$

Huber-White covariance matrix clustered at state-level, with probability weights from the survey.

The overall policy effect coefficient, $\delta$, is 0.009.

To evaluate effects on subgroups, I created two samples with only elderly and non-elderly respondents respectively. If I do restricted dataset,

Ex code. areg outc policy i.year [pw=wgt] if elderly==1, absorb(state) vce(cluster state)

I get coefficients of 0.011 and 0.012 on $\delta$ for young and old samples respectively, which was weird to me because the overall sample effect was 0.009.

If I do a interaction model,

Ex. code: areg outc i.year i.policy##i.elderly [pw=wgt], absorb(state) vce(cluster state)

margins elderly, dydx(policy)

I get 0.011 for young and 0.003 for old, which makes more sense to me given overall effect and survey has more young people.

I assume the fixed effects are the issue here, but I guess what I am trying to consider is: What is the difference between doing a subgroup only regression or an interaction in this context? How could you observe these "non-collapsible" coefficients for the restricted sample regressions?

Sincerely thanks you for any comments!

• Could you actually include the two commands and such that you used to estimate these models in Stata in the question? Might be useful for us to see that. – RickyB Nov 5 '15 at 17:34
• Added code examples above – user94189 Nov 5 '15 at 17:43