Sensitivity Analysis of Efficiency Rankings to Distributional Assumptions: Applications to Japanese Water Utilities

Abstract

This paper examines the robustness of efficiency score rankings across four distributional assumptions for trans-log stochastic production-frontier models, using data from 1,221 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.

Measuring Technical Efficiency of Construction Listed Companies Based on Different Distribution using Stochastic Frontier Model

“…According to Greene (1990), different distributions do not have much on impact efficiency score. Yane & Berg (2013) and Altunbas & Molyneux (1994) Gong & Sickles (1992) assumed that technical inefficiency is time-invariant in their studies. One justification is that firm specific inefficiency can be considered as an inherent and structural residual between observed data and the corresponding production frontier.…”