Modeling Costs with Generalized Gamma Regression

There are three broad classes of models used to address the econometric problems caused by skewness in data commonly encountered in health care applications: (1) transformation to deal with skewness (e.g., OLS on ln(y)); (2) alternative weighting approaches based on exponential conditional models (ECM) and generalized linear model (GLM) approaches; and (3) survival models (Cox proportional hazard regression). In this paper, we encompass these three classes of models using the three parameter generalized gamma (GGM) distribution, which includes several of the standard alternatives as special cases – OLS with a normal error, OLS for the log normal, the standard gamma and exponential with a log link, and the Weibull. The test of identifying distributions and that of proportional hazard assumption are found to be robust. The GGM also provides a potentially more robust alternative estimator to the standard alternatives. Examples using inpatient expenditures and labor market earnings are analyzed.