Unobserved Heterogeneity
This chapter discusses mixture models for unobserved heterogeneity. The problem of unobserved heterogeneity arises if the explanatory variables do not account for the full amount of individual heterogeneity in the conditional mean of the dependent variabl
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Rainer Winkelmann
Econometric Analysis of Count Data
Fifth edition
123
Prof. Dr. Rainer Winkelmann University of Zurich Socioeconomic Institute Zürichbergstr. 14 8032 Zürich Switzerland [email protected]
ISBN 978-3-540-77648-2
e-ISBN 978-3-540-78389-3
DOI 10.1007/978-3-540-78389-3 Library of Congress Control Number: 2008922297 c 2008 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Production: le-tex Jelonek, Schmidt & Vöckler GbR, Leipzig Cover design: WMX Design GmbH, Heidelberg Printed on acid-free paper 987654321 springer.com
Preface
The “count data” field has further flourished since the previous edition of this book was published in 2003. The development of new methods has not slowed down by any means, and the application of existing ones in applied work has expanded in many areas of social science research. This, in itself, would be reason enough for updating the material in this book, to ensure that it continues to provide a fair representation of the current state of research. In addition, however, I have seized the opportunity to undertake some major changes to the organization of the book itself. The core material on cross-section models for count data is now presented in four chapters, rather than in two as previously. The first of these four chapters introduces the Poisson regression model, and its estimation by maximum likelihood or pseudo maximum likelihood. The second focuses on unobserved heterogeneity, the third on endogeneity and non-random sample selection. The fourth chapter provides an extended and unified discussion of zeros in count data models. This topic deserves, in my view, special emphasis, as it relates to aspects of modeling and estimation that are specific to counts, as opposed to general exponential regression models for non-negative dependent variables. Count distributions put positive probability mass on single outcomes, and thus offer a richer set of interesting inferences. “Marginal probability effects” for zeros – at the “extensive margin” – as well as for any positive outcome – at the “intensive margin” – can be computed, in order to trace the response of the entire count distribution to changes in an explanatory variable. The fourth chapter add
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