Count data models with selectivity

This paper shows how truncated, censored, hurdle, zero inflated and underreported count models can be interpreted as models with selectivity. Until recently, users of such count data models have commonly imposed independence brtween the count generating mechanism and the selection mechanism. Such an assumption is unrealistic in most applications, and various models with endogenous selectivity (correlation between the count and the selection equations) are presented. The methods are illustrated in an application to labor mobility where the dependent variable is the number of individual job changes during a ten year period.