This paper proposes an exponential class of dynamic binary choice panel data models for the analysis of short T (time dimension) large N (cross section dimension) panel data sets that allow for unobserved heterogeneity (fixed effects) to be arbitrarily correlated with the covariates. The paper derives moment conditions that are invariant to the fixed effects which are then used to identify and estimate the parameters of the model. Accordingly, generalized method of moments (GMM) estimators are proposed that are consistent and asymptotically normally distributed at the root-N rate. We also study the conditional likelihood approach and show that under exponential specification, it can identify the effect of state dependence but not the effects of other covariates. Monte Carlo experiments show satisfactory finite sample performance for the proposed estimators and investigate their robustness to misspecification.
Al-Sadoon, M., Li, T., & Pesaran, M. (2017). Exponential class of dynamic binary choice panel data models with fixed effects. Econometric Reviews, 36(6-9), 898-927. https://doi.org/10.1080/07474938.2017.1307597