Partial effects in fixed-effects models

One of the main reasons for the popularity of panel data is that they make it possible to account for the presence of time-invariant unobserved individual characteristics, the so-called fixed effects. Consistent estimation of the fixed effects is only possible if the number of time periods is allowed to pass to infinity, a condition that is often unreasonable in practice. However, in a small number of cases, it is possible to find methods that allow consistent estimation of the remaining parameters of the model, even when the number of time periods is fixed. These methods are based on transformations of the problem that effectively eliminate the fixed effects from the model. A drawback of these estimators is that they do not provide consistent estimates of the fixed effects, and this limits the kind of inference that can be performed. For example, in linear models, it is not possible to use the estimates obtained in this way to make predictions of the variate of interest. This problem is particularly acute in nonlinear models, where often the parameters have little meaning, and it is more interesting to evaluate partial effects on quantities of interest. In this presentation, we show that although it is indeed generally impossible to evaluate the partial effects at points of interest, it is sometimes possible to consistently estimate quantities that are informative and easy to interpret. The problem will be discussed using Stata, centered on a new ado-file for calculating the average logit elasticities.