Evaluating contextual variables affecting productivity using data envelopment analysis

A DEA-based stochastic frontier estimation framework is presented to evaluate contextual variables affecting productivity that allows for both one-sided inefficiency deviations as well as two-sided random noise. Conditions are identified under which a two-stage procedure consisting of DEA followed by ordinary least squares (OLS) regression analysis yields consistent estimators of the impact of contextual variables. Conditions are also identified under which DEA in the first stage followed by maximum likelihood estimation (MLE) in the second stage yields consistent estimators of the impact of contextual variables. This requires the contextual variables to be independent of the input variables, but the contextual variables may be correlated with each other. Monte Carlo simulations are carried out to compare the performance of our two-stage approach with one-stage and two-stage parametric approaches. Simulation results indicate that DEA-based procedures with OLS, maximum likelihood, or even Tobit estimation in the second stage perform as well as the best of the parametric methods in the estimation of the impact of contextual variables on productivity. Simulation results also indicate that DEA-based procedures perform better than parametric methods in the estimation of individual decision-making unit (DMU) productivity. Overall, the results establish DEA as a nonparametric stochastic frontier estimation (SFE) methodology.