A Latent Class Panel Tobit Framework:Application to Modelling Charitable Donations

Abstract

We extend the latent class literature by re-examining censored variable analysis within a panel data context. Specifically, 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. The IHS transformation ensures robustness to nonnormality in the original (untransformed) dependent variable. We then apply this framework to modelling charitable donations, an interesting application given the potential for divergent groups of individuals in the population with regard to their donating behaviour, which we uncover by the latent class approach. Our findings, which are based on U.S. panel data drawn from five waves of the Panel Study of Income Dynamics, do suggest two distinct classes. 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. All IHS parameters were significantly different from zero and different across classes. In combination, these findings endorse the importance of our three modelling extensions.