RECENT DEVELOPMENTS IN COUNT zy DATA MODELLING: THEORY AND APPLICATION Rainer Winkelmann zyxw Dartmouth College and SELAPO, University zyx of Munich Klaus F. Zimmermann SELAPO, University of Munich and CEPR Abstract. This paper deals with statistical methods for modelling individual behavior when the endogenous variable is a nonnegative integer. Examples are the number of children, the number of job changes or the number of shopping trips in a given period. Several approaches zyxw - Poisson, robust Poisson, negative binomial (NEGBIN), zyxwvu NEGBIN,, hurdle Poisson, truncated-at-zeroPoisson - are discussed with a focus on specification, estimation, and testing. zy An application to labor mobility data illustrates the gain obtained by carefully taking into account the specific structure of the data. Keywords. Count data models; Poisson; negative binomial. 1. Introduction This paper reviews recent developments in count data methodology. Since the seminal studies by Hausman, Hall and Griliches (1984) and Cameron and Trivedi (1986), both Poisson and negative binomial regressions have become standard in applied research that uses count data. These models have been implemented in software packages (GLIM, LIMDEP, GAUSS) and are well covered in econometrics textbooks like Greene (1990), for instance. Recent count data applications include studies on trip frequencies (Barmby and Doomik 1989, Rickard 1988), turnover in child care arrangements (Blau and Robins 1991), job turnover (Winkelmann and Zimmermann 1993), bank failures (Davutyan 1989), offer arrival rates (Ebmer 1990), recruitment rates (Kostiuk and Follmann 1989), patents (Schwalbach and Zimmermann 1991), market entry (Chappell, Kimenyi, and Mayer 1990), discovery of new drugs (Jensen 1987), violations of safety regulations (Feinstein 1989), and escape clause petitions (Coughlin, Terza and Khalifah 1989). Recently, Delgado and Kniesner (1 992) have discussed semiparametric methods for count data models. In a parallel development, often initiated by empirical problems, several methodological issues have been raised and solved. The hurdle and truncated Poisson models as well as less restrictive specifications of the negative binomial model fall within these developments. Simultaneously, semiparametric approaches have been proposed. This paper outlines and evaluates these models in a unifying framework, where the main focus will be on the statistical properties of the models. To keep the scope within reasonable limits and, more importantly, reflecting the overwhelming predominance of cross sectional studies in empirical 0950-0804/95/010001-24 JOURNAL OF ECONOMIC SURVEYS Vol. 9, No. 1 Q Basil Blackwell Ltd. 1995, 108 Cowley Rd., Oxford OX4 lJF, UK and 238 Main St, Cambridge, MA 02142, USA.