Recursive Probability Estimators for Count Data

Abstract

This paper discusses statistical models for count data in a unifying framework. In a typical econometric analysis one would assume that the count data one observes have been generated by some parametric distribution for non-negative integers p(y; θ), like for instance the Poisson, geometric, or negative binomial. Individual observed heterogeneity is introduced by letting the population parameter θ depend on observable individual characteristics x _i , in general via some function of a linear predictor x _i ß. This implies a specific conditional meanfunction (regression) E(Y|x;ß) = µ(x,ß), where the objective is then to estimate and draw inference on the ß’s (and possibly some additional parameters). A straightforward way ofestimation is by the method of maximum likelihood. This approach requires, however, the specification of a “true” probability model. The choice of a wrong model may yield inconsistent and inefficient estimates.