Stochastic non-smooth envelopment of data: semi-parametric frontier estimation subject to shape constraints

• Published in: Journal of productivity analysis Vol. 38; no. 1; pp. 11 - 28
• Main Authors: Kuosmanen, Timo, Kortelainen, Mika
• Format: Journal Article
• Language: English
• Published: Boston Spring Science+Business Media 01.08.2012; Springer US; Springer; Springer Nature B.V
• Subjects: Accounting/Auditing; Compound terms; Consistent estimators; Cost functions; Data envelopment analysis; Data-Envelopment-Analyse; Econometrics; Economics; Economics and Finance; Estimating techniques; Estimation methods; Estimators; Heteroskedasticity; Microeconomics; Nichtparametrisches Verfahren; Noise; Operations Research/Decision Theory; Production estimates; Production functions; Productivity measurement; Signal noise; Stochastic models; Studies; Technische Effizienz; Theorie; Europe; Stochastic frontier analysis (SFA); Nonparametric least squares; C14; D24; Data envelopment analysis (DEA); Productive efficiency analysis; Frontier estimation; C51
• ISSN: 0895-562X; 1573-0441
• DOI: 10.1007/s11123-010-0201-3

The field of productive efficiency analysis is currently divided between two main paradigms: the deterministic, nonparametric Data Envelopment Analysis (DEA) and the parametric Stochastic Frontier Analysis (SFA). This paper examines an encompassing semiparametric frontier model that combines the DEA-type nonparametric frontier, which satisfies monotonicity and concavity, with the SFA-style stochastic homoskedastic composite error term. To estimate this model, a new twostage method is proposed, referred to as Stochastic Nonsmooth Envelopment of Data (StoNED). The first stage of the StoNED method applies convex nonparametric least squares (CNLS) to estimate the shape of the frontier without any assumptions about its functional form or smoothness. In the second stage, the conditional expectations of inefficiency are estimated based on the CNLS residuals, using the method of moments or pseudolikelihood techniques. Although in a cross-sectional setting distinguishing inefficiency from noise in general requires distributional assumptions, we also show how these can be relaxed in our approach if panel data are available. Performance of the StoNED method is examined using Monte Carlo simulations.