Hostname: page-component-857557d7f7-ms8jb Total loading time: 0 Render date: 2025-11-23T03:48:44.564Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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.

Information

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Achen, C. H. 2002. Toward a new political methodology: Microfoundations and ART. Annual Review of Political Science 5: 423–50.CrossRefGoogle Scholar
Alesina, A., and Dollar, D. 2000. Who gives foreign aid to whom and why? Journal of Economic Growth 5(1): 33–63.CrossRefGoogle Scholar
Alesina, A., and Weder, B. 2002. Do corrupt governments receive less foreign aid? American Economic Review 92(4): 1126–37.CrossRefGoogle Scholar
Balla, S. J., Lawrence, E. D., Maltzman, F., and Sigelman, L. 2002. Partisanship, blame avoidance, and the distribution of legislative pork. American Journal of Political Science 46(3): 515–25.CrossRefGoogle Scholar
Berthelemy, J.-C. 2006. Bilateral donors' interest vs. recipients' development motives in aid allocation: Do all donors behave the same? Review of Development Economics 10(2): 179–94.CrossRefGoogle Scholar
Berthelemy, J.-C., and Tichit, A. 2004. Bilateral donors' aid allocation decisions—a three-dimensional panel analysis. Internation Review of Economics and Finance 13: 253–74.Google Scholar
de Mesquita, B. B., and Smith, A. 2007. Foreign aid and policy concessions. Journal of Conflict Resolution 51: 251–84.CrossRefGoogle Scholar
Dollar, D., and Levin, V. 2006. The increasing selectivity of foreign aid, 1984-2003. World Development 34(12): 2034–46.CrossRefGoogle Scholar
Dudley, L., and Montmarquette, C. 1976. A model of the supply of bilateral foreign aid. American Economic Review 66(1): 132–42.Google Scholar
Dunn, P. K. 2004. Occurrence and quantity of precipitation can be modeled simultaneously. International Journal of Climatology 24: 1231–9.CrossRefGoogle Scholar
Dunn, P. K., and Smyth, G. K. 2008. Evaluation of Tweedie exponential dispersion model densities by Fourier inversion. Statistics and Computing 18: 73–86.CrossRefGoogle Scholar
Fleck, R. K., and Kilby, C. 2001. Foreign aid and domestic politics: Voting in Congress and the allocation of USAID contracts across congressional districts. Southern Economic Journal 67(3): 598–617.Google Scholar
Fleck, R. K., and Kilby, C. 2006. How do political changes influence US bilateral aid allocations? Evidence from panel data. Review of Development Economics 10(2): 210–23.CrossRefGoogle Scholar
Heckman, J. J. 1976. The common structure of statistical models of truncation, sample selection, and limited dependent variables and a simple estimator for such models. Annals of Economic and Social Measurement 5: 475–92.Google Scholar
Heckman, J. J. 1979. Sample selection bias as a specification error. Econometrica 47(1): 153–61.CrossRefGoogle Scholar
Jorgensen, B., and de Souza, M. C. P. 1994. Fitting Tweedie's compound Poisson model to insurance claims data. Scandanavian Actuarial Journal 1: 69–93.CrossRefGoogle Scholar
Kuziemko, I., and Werker, E. 2006. How much is a seat on the Security Council worth? Foreign aid and bribery at the United Nations. Journal of Political Economy 114(5): 905–30.CrossRefGoogle Scholar
Lauderdale, B. E. 2008. Pass the pork: measuring legislator shares in Congress. Political Analysis 16: 235–49.CrossRefGoogle Scholar
Lee, F. E. 2000. Senate representation and coalition building in distributional politics. American Political Science Review 94(1): 59–72.CrossRefGoogle Scholar
Maizels, A., and Nissanke, M. K. 1984. Motivations for aid to developing countries. World Development 12(9): 879–900.CrossRefGoogle Scholar
McGillivray, M., and Oczkowski, E. 1992. A two-part sample selection model of British bilateral foreign aid allocation. Allied Economics 24(12): 1311–9.Google Scholar
Neumayer, E. 2003. Do human rights matter in bilateral aid allocation? A quantitative analysis of 21 donor countries. Social Science Quarterly 84(3): 650–66.CrossRefGoogle Scholar
Sartori, A. E. 2003. An estimator for some binary-outcome selection models without exclusion restrictions. Political Analysis 11(2): 111–38.CrossRefGoogle Scholar
Shono, H. 2008. Application of the Tweedie distribution to zero-catch data in CPUE analysis. Fisheries Research 93: 154–62.CrossRefGoogle Scholar
Smyth, G. K. 1989. Generalized linear models with varying dispersion. Journal of the Royal Statistical Society (Series B) 51: 47–60.Google Scholar
Smyth, G. K. 1996. Regression analysis of quantity data with exact zeros. In Proceedings of the Second Australia-Japan Workshop on Stochastic Models in Engineering, Techology, and Management, 572–80. Techology Management Center, University of Queensland.Google Scholar
Smyth, G. K., and Jorgensen, B. 2002. Fitting Tweedie's compound Poisson model to insurance claims data: Dispersion modeling. Astin Bulletin 32(1): 143–57.CrossRefGoogle Scholar
Swan, T. 2006. Generalized estimating equations when the response variable has a Tweedie distribution: An application for multi-site rainfall modeling. PhD thesis, University of Southern Queensland.Google Scholar
Tweedie, M. C. K. 1984. An index which distinguishes between some important exponential families. In Statistics: Applications and new directions, eds. Ghosh, J. K. and Roy, J., 579–604. Calcutta: Indian Statistical Institute.Google Scholar
Younas, J. 2008. Motivation for bilateral aid allocation: Altruism or trade benefits. European Journal of Political Economy 24: 661–74.CrossRefGoogle Scholar
Young, K. H., and Young, L. Y. 1975. Estimation of regressions involving logarithmic transformation of zero values in the dependent variable. American Statistician 29(3): 118–20.Google Scholar