Stochastic Nonparametric Envelopment of Data: Frontier Estimation Subject to Shape Constraints

Literature of productive efficiency analysis is currently divided between two main paradigms: the parametric Stochastic Frontier Analysis (SFA) and the deterministic, nonparametric Data Envelopment Analysis (DEA). This paper develops a new encompassing framework that melds the SFA-style stochastic composite error term to the DEA-type nonparametric frontier that satisfies monotonicity and concavity. The new approach is referred to as Stochastic Nonparametric Envelopment of Data (StoNED). StoNED method utilizes convex nonparametric least squares (CNLS), which estimates the shape of the frontier without any assumptions about its functional form or smoothness. In crosssectional settings, distinguishing inefficiency from noise requires distributional assumptions, which can be relaxed in the case of panel data. We estimate the conditional expectations of inefficiency based on the CNLS residuals, using the method of moments and pseudolikelihood techniques. Performance of the StoNED procedure is examined using Monte Carlo simulations.