A Dynamic Model for Binary Panel Data With Unobserved Heterogeneity Admitting a Root-N Consistent Conditional Estimator

Abstract

A model for binary panel data is introduced which allows for state dependence and unobserved heterogeneity beyond the effect of strictly exogenous covariates. The model is of quadratic exponential type and its structure closely resembles that of the dynamic logit model. An economic interpretation of its assumptions, based on expectation about future outcomes, is provided. The main advantage of the proposed model, with respect to the dynamic logit model, is that each individual-specific parameter for the unobserved heterogeneity may be eliminated by conditioning on the sum of the corresponding response variables. A conditional likelihood results which allows us to identify the structural parameters of the model with at least three observations (included an initial observation assumed to be exogenous), even in the presence of time dummies. A root-n consistent conditional estimator of these parameters also results which is very simple to compute. Its finite sample properties are studied by means of a simulation study. Extensions of the proposed approach are discussed with reference, in particular, to the case of more elaborated structures for the state dependence and to that of categorical response variables with more than two levels.