Bias and precision in the DEA two-stage method

In Data Envelopment Analysis (DEA), the two-stage method is a popular procedure for accounting for exogenous influences on efficiency. With the conventional two-stage method, a DEA is first conducted using only traditional (endogenous) inputs and outputs. Then, the first-stage DEA scores are regressed on the environmental/contextual (exogenous) inputs of interest. The regression outcomes are used to identify exogenous inputs that influence the first-stage DEA scores to a statistically significant degree, and to adjust DEA scores to account for these influences. Herein, it is demonstrated empirically that the conventional method exhibits substantial bias and low precision, with the degree of bias and precision affected by input variance and correlation. A reverse two-stage procedure that yields estimates without the bias and precision problems that compromise the validity of the conventional method's estimates is suggested.