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Compound Poisson—Gamma Regression Models for Dollar Outcomes That Are Sometimes Zero

Published online by Cambridge University Press:  04 January 2017

Benjamin E. Lauderdale
Benjamin E. Lauderdale*
Affiliation:
London School of Economics, Methodology Institute, Columbia House, Houghton Street, London, WC2A 2AE, UK. e-mail: b.e.lauderdale@lse.ac.uk
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Abstract

Political scientists often study dollar-denominated outcomes that are zero for some observations. These zeros can arise because the data-generating process is granular: The observed outcome results from aggregation of a small number of discrete projects or grants, each of varying dollar size. This article describes the use of a compound distribution in which each observed outcome is the sum of a Poisson—distributed number of gamma distributed quantities, a special case of the Tweedie distribution. Regression models based on this distribution estimate loglinear marginal effects without either the ad hoc treatment of zeros necessary to use a log-dependent variable regression or the change in quantity of interest necessary to use a tobit or selection model. The compound Poisson—gamma regression is compared with commonly applied approaches in an application to data on high-speed rail grants from the United States federal government to the states, and against simulated data from several data-generating processes.

Type
Research Article
Information
Political Analysis , Volume 20 , Issue 3 , Summer 2012 , pp. 387 - 399
Copyright
Copyright © The Author 2012. Published by Oxford University Press on behalf of the Society for Political Methodology 

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