Estimation of Some Nonlinear Panel Data Models With Both Time-Varying and Time-Invariant Explanatory Variables

The so-called “fixed effects” approach to the estimation of panel data models suffers from the limitation that it is not possible to estimate the coefficients on explanatory variables that are time-invariant. This is in contrast to a “random effects” approach, which achieves this by making much stronger assumptions on the relationship between the explanatory variables and the individual-specific effect. In a linear model, it is possible to obtain the best of both worlds by making random effects-type assumptions on the time-invariant explanatory variables while maintaining the flexibility of a fixed effects approach when it comes to the time-varying covariates. This article attempts to do the same for some popular nonlinear models.