A Simulation Study of Joint Uses of Data Envelopment Analysis and Statistical Regressions for Production Function Estimation and Efficiency Evaluation

A previous paper by Arnold, Bardhan, Cooper and Kumbhakar (1996) introduced a very simple method to estimate a production frontier by proceeding in two stages as follows: Data Envelopment Analysis (DEA) is used in the first stage to identify efficient and inefficient decision-making units (DMUs). In the second stage the thus identified DMUs are incorporated as dummy variables in OLS (ordinary least squares) regressions. This gave very satisfactory results for both the efficient and inefficient DMUs. Here a simulation study provides additional evidence. Using this same two-stage approach with Cobb-Douglas and CES (constant elasticity-of-substitution) production functions, the estimated values for the coefficients associated with efficient DMUs are found to be not significantly different from the true parameter values for the (known) production functions whereas the parameter estimates for the inefficient DMUs are significantly different. A separate section of the present paper is devoted to explanations of these results. Other sections describe methods for estimating input-specific inefficiencies from the first stage use of DEA in the two-stage approaches. A concluding section provides further directions for research and use.