Compound poisson-gamma regression models for dollar outcomes that are sometimes zero

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.