Incidental Parameters and Dynamic Panel Modeling

Panel data o¤ers great opportunities for empirical research throughout the social and business sciences, as such data has done for many decades in longitudinal medical studies. In economics and business, just as in medicine, there is often intense interest in the e¤ects of policy measures or treatments on individual consumer and …rm behavior over time. The pooling of data records across wide panels of individuals has the potential to deliver substantial econometric power in estimation through cross section averaging to sharpen estimates of common response patterns. With these great opportunities for studying individual behavior come many challenges. The present chapter focuses on one of these challenges – the role and e¤ects of incidental parameters that capture the idiosyncratic features of individual entities within a panel. Adding a new individual to a panel brings new idiosyncratic elements to be explained in the data just as it also brings observations that enhance the power of cross section averaging for the common elements of behavior. Exploring the e¤ects of such additions is the subject of this chapter. The problem of incidental parameters in statistical inference was …rst pointed out in a classic article by Neyman and Scott (1948)1 . According to their characterization, an incidental parameter only …gures in a …nite dimensional probability law – thereby involving only a …nite number of observations and, in consequence, rendering the corresponding maximum likelihood estimator inconsistent. Interestingly, in its attempt to deliver the best possible estimates of all of the parameters in a model, including incidental parameters that are speci…c

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