Benjamin E Lauderdale, “Compound Poisson-Gamma Regression Models for Dollar Outcomes That Are Sometimes Zero”, Political Analysis, 20(3):387-399.
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 log-linear 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 U.S. federal government to the states, and against simulated data from several data-generating processes.
Note: The MLE code to fit the model as described in the paper is available on request. However, I recommend estimating a Bayesian version of the model by MCMC using R and JAGS (or WinBUGS with slight modifications), as it is substantially faster. Download example JAGS code here