One‐stage and two‐stage DEA estimation of the effects of contextual variables

Two‐stage data envelopment analysis (2‐DEA) is commonly used in productive efficiency analysis to estimate the effects of operational conditions and practices on performance. In this method the DEA efficiency estimates are regressed on contextual variables representing the operational conditions. We re‐examine the statistical properties of the 2‐DEA estimator, and find that it is statistically consistent under more general conditions than earlier studies assume. We further show that the finite sample bias of DEA in the first stage carries over to the second stage regression, causing bias in the estimated coefficients of the contextual variables. This bias is particularly severe when the contextual variables are correlated with inputs. To address this shortcoming, we apply the result that DEA can be formulated as a constrained special case of the convex nonparametric least squares (CNLS) regression. Applying the CNLS formulation, we develop a new semi‐nonparametric one‐stage estimator for the coefficients of the contextual variables that directly incorporates contextual variables to the standard DEA problem. The proposed method is hence referred to as one‐stage DEA (1‐DEA). Evidence from Monte Carlo simulations suggests that the new 1‐DEA estimator performs systematically better than the conventional 2‐DEA estimator both in deterministic and noisy scenarios.