Too stable regression coefficients

[Andrea Tulli]

Hi all,

I have a weird problem with my regression results. In particular, I run a simple diff-in-diff regression where the treatment should have a differential effect on different units (i.e. municipalities in my case). To show the robustness of my results I have run the same regression including/excluding year fixed effects and province specific linear trend.
What surprise me is that even though all coefficients do change on the different specification, my relevant coefficient is absolutely the same up to the third digit.
This sounds too weird to me, so I have checked trying with a subsample of my data and results are now different. How should I interpret this finding then?

Honestly, I don't know what to think about it. I know that the stability of the coefficient is a very positive result but this looks "too much" stable! I would really appreciate if you could give me some feedback on why this might be the case and suggestions to understand the cause/solve any issue.

My specification is the following:

l_n i.treat_m5##i.tbin i.treat_m4##i.tbin  i.treat_m3##i.tbin ///
                         i.treat_m2##i.tbin i.treat_m1##i.tbin ////
                      i.treat_p1##i.tbin i.treat_p2##i.tbin i.treat_p3##i.tbin ///
                      i.treat_p4##i.tbin i.treat_p5##i.tbin ///
                      l_pop financial_aut ///
                      i.year i.province_id#c.year  , fe robust cluster(id)

The interaction between the variables treat and tbin is for measuring the differential effects (i.e. the usual interaction term in diff-in-diff). The outcome variable is the inverse hyperbolic sine of my main outcome, since n has many zeros. In particular, my specification is for a dynamic diff-in-diff, i.e. the treatment does not happen always at the same time for all the treated units.

Thanks a lot for you help

Andrea

[Phil Bromiley]

You'll increase your changes of a helpful answer by following the FAQ on asking questions - provide Stata code in code delimiters (which you partially did), readable Stata output, and sample data using dataex. Also, providing the simplest representation that generates your problem makes it easier on the reader. You have a very complex model and the real meaning of it depends on things like what is in tbin. I couldn't find l_n as an estimator. But the options look like you're doing xtreg or something.

It is odd you don't get a change just as a matter of fitting additional parameters. Are the year effects significant? Whether you should worry about it is not clear to me. Part of the supposed power of d-i-d is that it takes care of a bunch of the exogenous noise so finding that the year fixed effects don't change things much doesn't worry me. That is, you're comparing the change in the treated to the change in the untreated so the year effect (that influences both) may be irrelevant.

The linear trend by province likewise influences both treated and untreated equally so it may not add much in explaining the difference between treated and untreated.