CRE in xtlogit

[Sylvie Rod]

Hello,

I’d like to estimate a correlated random-effects specification using an unbalanced panel logit. Stata’s built-in CRE helper exists for xtreg but not for xtlogit, so I’m considering manually adding unit-level means of the time-varying regressors to a random-effects logit as a CRE workaround. However I wonder if this approach is valid indeed, as I think if it's so easy then CRE within xtlogit would have been developed alongside CRE within xtreg.

I’m also unsure how to choose between fixed effects and random effects in unbalanced panel logit, because the FE drops all units whose dependent variable doesn’t vary over time, which produces very different sample sizes and I don't think they should be comparable.

Many thanks.

[Andrew Musau]

I’d like to estimate a correlated random-effects specification using an unbalanced panel logit.

Jeff Wooldridge provides an excellent discussion of correlated random effects (CRE) in nonlinear panel data models, including probit, with code examples of implementation in Stata (see https://conference.iza.org/conferenc...nonlin_iza.pdf).

I’m also unsure how to choose between fixed effects and random effects in unbalanced panel logit, because the FE drops all units whose dependent variable doesn’t vary over time, which produces very different sample sizes and I don't think they should be comparable.

As in the linear case, the conditional fixed-effects (FE) logit estimator is consistent regardless of whether the random-effects (RE) assumption holds. Therefore, you do not need to justify the use of FE on that basis.

For the RE model, you could use a Hausman-type test to assess whether it is consistent, but CRE is usually preferred. The Hausman or CRE comparison focuses on the coefficients of time-varying variables, so the loss of some units due to constant outcomes should not affect the interpretation of the test. However, if most of your sample is dropped because the dependent variable does not change over time, that reflects a limitation of the data rather than a flaw in the FE estimator itself.

[George Ford]

Zero variance observations in Y add nothing, but CRE should retain them as estimation is by RE.

A LPM is usually a valid replacement for logit, as long as you aren't predicting anything.

I'd think you'd be OK with logit, but there may be some distributional issues you need to consider.

For starters, I'd run them both and compare results (using margins on xtlogit to get comparable avg marginal effects), but I'd still investigate it's validity in a logit context.