Duration dependence and dispersion in count - data models

This paper explores the relation between non-exponential waiting times between events and the distribution of the number of events in a fixed time interval. It is shown that within this framework the frequently observed phenomenon of overdispersion, i.e. a variance that exceeds the mean, is caused by a decreasing hazard function of the waiting times, while an increasing hazard function leads to underdispersion. Using the assumption of i.i.d. gamma distributed waiting times, a new count data model is derived. Its use is illustrated in two applications: the number of births, and the number of doctor consultations. Duration Dependence and Dispersion in Count-Data Models Author(s): Rainer Winkelmann Source: Journal of Business & Economic Statistics, Vol. 13, No. 4 (Oct., 1995), pp. 467-474 Published by: American Statistical Association Stable URL: http://www.jstor.org/stable/1392392 Accessed: 28/04/2009 06:19 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=astata. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact [email protected]. American Statistical Association is collaborating with JSTOR to digitize, preserve and extend access to Journal of Business & Economic Statistics. http://www.jstor.org @ 1995 American Statistical Association Journal of Business & Economic Statistics, October 1995, Vol. 13, No. 4 Duration Dependence and Dispersion in Count-Data Models Rainer WINKELMANN Department of Economics, University of Canterbury, Christchurch, New Zealand This article xplores the relation between nonexponential waiting times between events and the distribution f the number of events in a fixed time interval. It is shown that within this framework the frequently observed phenomenon of overdispersion-that is, a variance that exceeds the mean-is caused by a decreasing hazard function of the waiting times, whereas an increasing hazard function leads to underdispersion. Using the assumption of lid gamma-distributed waiting times, a new count-data model is derived. Its use is illustrated intwo applications, the number of births and the number of doctor consultations.