How to model intensive and extensive margins of doctor's visits?

[Paul Lovelle]

Dear Statalist,

I am trying to model medical use of patients following an intervention. My data is discharge-level inpatient data 2000-2005 with patient identifier. In addition to estimating the effect of the policy intervention on medical usage, I want to test whether it affects both intensive margin (number of doctor's visits by patients with a medical history) and extensive margin (total number of patients).

How do I model/code to distinguish between intensive vs extensive margins? The following is what I, as a beginner, would come up:

• For intensive margin: Can this be done simply by a regression of the number of visits on a set of covariates including the treatment dummy, among the sample of patients with previous medical history?
• For extensive margin: Make a usage dummy for each patient in each year that equals 1 if she visits a doctor, and 0 if not. And regress the binary usage dummy on the set of covariates including the treatment dummy.

Is this what empirical researchers would do? Can you correct if I misunderstood?

Thank you!

Regards,
Paul

[Clyde Schechter]

Your definition of intensive margin seems reasonable.

For the extensive margin, it gives you a total count of patients who use the system, but makes no distinction between those who use it once and those who use it 100 times in a year. If that's what you want, it seems good.

There is one other consideration affecting both of those. You state that you have discharge-level data. That seems to imply that people who don't utilize at all aren't even in the data set. If that's the case, this is fatal to both definitions, and you can't even define these things based on this data.

Moving beyond these outcome definitions, your informally described regression doesn't sound like it will do what you want, unless the treatment variable was assigned by randomization. Controlling for some covariates helps a bit, but I think for policy analysis it is a fairly slender reed on which to rest your case. If it's not randomized, you might want to look into using propensity-score weighting or propensity-score matching (along with covariate adjustment). The -teffects- suite of commands may prove helpful here. And if the intervention began at a single point in time for all those who were subjected to it, and if you have both pre- and post-intervention data, then a difference-in-differences analysis might be appropriate.

[Dimitriy V. Masterov]

You may find the tpm command useful for thinking about this. For count data, like visits, the analog is hurdle regression.

[Paul Lovelle]

Thank you all for your valuable comments.

Dimitriy: I checked the help document for -tpm- and it does not seem to do fixed effects analysis. What can go wrong if I manually do Poisson fixed effects regressions, instead using hurdle regressions, on the variables constructed as I described in my original post?

Regards,
Paul

[Dimitriy V. Masterov]

I am reluctant to advocate the xtpoisson approach because the zeros may come from a different DGP than the non-zeros, so covariates may affect the intensive margin differently from the extensive margin. However, I am not a health economist and I don't know the details of your setting, so you shouldn't take my advice too seriously.

There is a RE effects version of the hurdle command here, which may be suitable depending on how your intervention worked.