How Operational Conditions and Practices Affect Productive Performance? Efficient Semi-Parametric One-Stage Estimators

Abstract

Understanding the effects of operational conditions and practices on productive efficiency can provide insights that lead to improved managerial strategies. Previous studies have employed a two-stage data envelopment analysis (DEA) method where the DEA efficiency estimates are regressed on contextual variables representing the operational conditions. We re-examine the statistical properties of the two-stage DEA estimator, and find that it is statistically consistent under more general conditions than earlier studies assume. However, 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 insights from Kuosmanen and Johnson (2009), who showed that DEA can be formulated as a constrained special case of the Convex Nonparametric Least Squares (CNLS) regression. Utilizing this link between DEA and the regression analysis, we develop two new semi-parametric one-stage estimators for the coefficients of the contextual variables. The first estimator directly incorporates contextual variables to the standard DEA model, and is hence referred to as one-stage DEA. The second estimator introduces contextual variables to the CNLS regression, relaxing the sign-constraint of DEA. We show that both one-stage estimators are statistically consistent, but the CNLS-estimator requires less restrictive assumptions. The CNLS-estimator for the contextual variables is shown to be unbiased, asymptotically efficient, asymptotically normally distributed, and converge at the standard parametric rate of order n-1/2. Therefore, the conventional methods of statistical inference can be applied to the CNLS-estimator. Finite sample performance of the proposed estimators is examined through Monte Carlo simulations and demonstrates benefits over two-stage DEA.

Keywords: Data Envelopment Analysis, two-stage method, partial linear model