p.1859

Panel Binary Variables and Sufficiency: Generalizing Conditional Logit

Thierry Magnac

Abstract

This paper extends the conditional logit approach (Rasch, Andersen, Chamberlain) used in panel data models of binary variables with correlated fixed effects and strictly exogenous regressors. In a two-period two-state model, necessary and sufficient conditions on the joint distribution function of the individual-and-period specific shocks are given such that the sum of individual binary variables across time is a sufficient statistic for the individual effect. By extending a result of Chamberlain, it is shown that root-n consistent regular estimators can be constructed in panel binary models if and only if the property of sufficiency holds. In applied work, the estimation method amounts to quasi-differencing the binary variables as if they were continuous variables and transforming a panel data model into a cross-section model. Semiparametric approaches can then be readily applied.