Panel Probit and Logit Models with double and Triple Interactions

[Endalkachew Mekonen]

I am estimating a regression model where the dependent variable is binary, and the specification includes several interaction terms. The data come from two sequential rounds collected on the same units. One of the key independent variables, a continuous variable capturing beliefs, is first estimated using the round-one model to address potential endogeneity. Following the correlated random effects (Mundlak) approach, the test indicates that fixed effects are preferred over random effects. Therefore, after predicting the belief variable, I use its demeaned value in the binary outcome model to control for unobserved heterogeneity across units.

For the binary outcome, I plan to estimate two models: xtprobit and the fixed-effects conditional logit (CLogit) model. While the conditional logit model estimates successfully, xtprobit cannot estimate the fixed-effects specification. The problem arises when I attempt to compute marginal effects, both for interacted and non-interacted variables, after the CLogit FE model. Stata does not allow marginal effects after the conditional logit because the fixed effects are conditioned out.

Does anyone have suggestions for alternative estimation strategies or methods to obtain marginal effects in this setting? I'm looking for feasible approaches given the FE requirement, the binary outcome, and the need to interpret interaction terms.

[Andrew Musau]

If your interest is on partial effects, just estimate a linear probability model (LPM) with fixed effects (xtreg, fe). Unlike the conditional fixed-effects logit, the LPM allows you to interpret coefficients directly as marginal effects. In addition, cluster-robust standard errors provide robust inference.

[Endalkachew Mekonen]

If your interest is in partial effects, just estimate a linear probability model (LPM) with fixed effects (xtreg, fe). Unlike the conditional fixed-effects logit, the LPM allows you to interpret coefficients directly as marginal effects. In addition, cluster-robust standard errors provide robust inference.

Dear Musau, thank you for your suggestion. I did it exactly as you suggested. But, I thought the LPM alone is not adequate to make a credible inference because of its known limitations.

[Stephen Jenkins]

Endalkachew Mekonen Andrew's advice is, as ever, something to take notice of. I would also say that whereas you refer to "known limitations" of the LPM, there are also some advantages (which are reasonably well-known) ... what Andrew is referring to is an example of these. Whatever, if you are interested in calculating the marginal effects you cite, check out whether ginteff (Marius Radean, SJ) suits your purposes:

net sj 23-2 st0711

[Endalkachew Mekonen]

Endalkachew Mekonen Andrew's advice is, as ever, something to take notice of. I would also say that whereas you refer to "known limitations" of the LPM, there are also some advantages (which are reasonably well-known) ... what Andrew is referring to is an example of these. Whatever, if you are interested in calculating the marginal effects you cite, check out whether ginteff (Marius Radean, SJ) suits your purposes:

net sj 23-2 st0711

Massive thanks. I will refer your suggestion.