Sensitivity analysis of efficiency rankings to distributional assumptions: applications to Japanese water utilities

This article examines the robustness of efficiency score rankings across four distributional assumptions for trans-log stochastic production-frontier models, using data from 1221 Japanese water utilities (for 2004 and 2005). One-sided error terms considered include the half-normal, truncated normal, exponential and gamma distributions. Results are compared for homoscedastic and doubly heteroscedastic models, where we also introduce a doubly heteroscedastic variable mean model, and examine the sensitivity of the nested models to a stronger heteroscedasticity correction for the one-sided error component. The results support three conclusions regarding the sensitivity of efficiency rankings to distributional assumptions. When four standard distributional assumptions are applied to a homoscedastic stochastic frontier model, the efficiency rankings are quite consistent. When those assumptions are applied to a doubly heteroscedastic stochastic frontier model, the efficiency rankings are consistent when proper and sufficient arguments for the variance functions are included in the model. When a more general model, like a variable mean model is estimated, efficiency rankings are quite sensitive to heteroscedasticity correction schemes.