Evaluating Contextual Variables Affecting Productivity Using Data Envelopment Analysis

TLDR

The study introduces a DEA‑based stochastic frontier estimation framework to assess how contextual variables affect productivity, accounting for one‑sided inefficiency and two‑sided random noise. The authors identify conditions under which a two‑stage procedure—DEA followed by OLS or MLE—yields consistent estimators of contextual variable impacts, requiring contextual variables to be independent of inputs (though they may be correlated with each other), and they use Monte Carlo simulations to compare this approach with one‑stage and parametric methods. Simulation results show that DEA‑based procedures with OLS, MLE, or Tobit in the second stage perform as well as the best parametric methods for estimating contextual variable impacts, outperform parametric methods in estimating individual DMU productivity, and overall establish DEA as a nonparametric stochastic frontier estimation methodology.

Abstract

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.