Comparing coefficients from different Event Study specifications

[Kathrin Me]

Hi all,

I aim at estimating the effect of job loss on the labor supply of the spouse using an event study. I estimate the effect once using not yet treated units as my control units and once using never treated individuals as my control units. My question is concerning how to compare the different estimates.

The estimation with not yet treated units yields the following:

When repeating it with never treated units, I get:

While with never treated units I make one normalization (i.e. I set period -1 to zero), I make two restrictions with not yet treated units (cf. Baker, Larcker and Wang, 2022). Here, I set lag -1 and -4 to zero.

My question: How can I compare, for example, the coefficient for period +2? Can I simply conclude that 542.23 is smaller than 598.1? Or do I have to see it relative to the pre-event coefficients (which are a bit different between the two specifications)?

Thanks already now!

Kathrin

[Jared Greathouse]

You give no code, so there's nothing to comment on really.

[Daniel Schaefer]

I'm not sure that it's essential that we see the code to answer this question since this is more of a conceptual statistics question than a programing question. Unfortunately I don't really know the answer (or at least I'm not completely confident about the answer I have), but I do think you deserve a serious response.

My intuition is that you can compare the size of two model coefficients under OLS when the unit of measurement for the independent variable X is the same and the unit of measurement for the outcome variable Y is the same across coefficients all else equal. The "all else equal" part is the rub, because if all else is not equal, then whatever you've changed may explain why the coefficient is different. I believe that ideally in an event study, the event itself is that thing that has changed, but if you've made other modifications to the model, then they might explain the difference in the coefficient as well. In that case, a clear and rigorous theoretical argument should help to explain the difference between coefficients. So yes, I think you can meaningfully say that 542.23 is smaller than 598.1 assuming the unit of measurement is the same, but what that difference means will depend on your theoretical framework as well as any confounding differences between the two models for which you want to compare coefficients.

[Jared Greathouse]

The only reason I ask for the code (aside from my usual reasons for doing so) is that there are multiple different event study commands which presumably handle the subtle details differently. I know, because I've used some of these newer event study commands for my masters thesis, for example.

However, I do certainly believe the question deserves a serious response. Indeed, I have many thoughts on using the ever vs never treated units in event studies. In fact, I've written about it.

[Joro Kolev]

From what I understand your two separate regressions have the same dependent variable, and the same meaning in the independent variables.

Then you can use -suest- to estimate the two regressions jointly, and then you can do whatever statistical comparisons of the corresponding coefficients you want.