An inverse hyperbolic sine heteroskedastic latent class panel tobit model: An application to modelling charitable donations

Abstract

We apply a latent class tobit framework to the analysis of panel data on charitable donations at the household level where the latent class aspect of the model splits households into two groups, which we subsequently interpret as “low” donators and “high” donators. The tobit part of the model explores the determinants of the amount donated by each household conditional on being in that class. We extend the standard latent class tobit panel approach to simultaneously include random effects, to allow for heteroskedasticity and to incorporate the inverse hyperbolic sine (IHS) transformation of the dependent variable. Our findings, which are based on U.S. panel data drawn from five waves of the Panel Study of Income Dynamics, suggest two distinct classes of donators. There is a clear disparity between the probabilities of zero donations across these classes, with one class dominated by the observed zero givers and associated with relatively low levels of predicted giving. We find clear evidence of both heteroskedasticity and random effects. In addition, all IHS parameters were significantly different from zero and different across classes. In combination, these findings endorse the importance of our three modelling extensions and suggest that treating the population as a single homogeneous group of donors, as is common in the existing literature, may lead to biased parameter estimates and erroneous policy inference. Although we use this model to explain charitable donations, we note that it has wide applicability for researchers across the social sciences.