Estimating Fixed Effect Binary Choice Models with Long Panels: a Practical Approach to the Conditional Logit Model

In this paper we have presented a practical approach for consistent estimation of the binary choice logit model with long panels in the presence of unobserved fixed effects which may be correlated with observables. Our aim is to overcome the computational burden of the standard approach of CML estimation of the model which conditions on the minimal sufficient statistic, a burden which may result in estimation being quite infeasible in a really long panel. Our approach to this problem is (a) to condition the likelihood on a non-minimal sufficient statistic and (b) to factor the likelihood in such a way that it can be maximized in two-stages, the first requiring the use of a standard CML program for each sub-panel for the case of a minimal sufficient statistic, and the second imposing equality restrictions on the resulting estimates using minimum-distance. We have illustrated the technique with German panel data recording the labour force status of a sample of married women for 60 consecutive months. Unobservable fixed effects appeared important and we found, for example, that allowing for them may cause one's view of the association of husband and wife's labour force status to be changed.