Summary: Aggregation of environmental pressures into a single environmental damage index is a major challenge of eco‐efficiency measurement. This article examines how the data envelopment analysis (DEA) method can be adapted for this purpose. DEA accounts for substitution possibilities between different natural resources and emissions and does not require subjective judgment about the weights. Although DEA does not require subjective or normative judgment, soft weight restrictions can be incorporated into the framework. The proposed approach is illustrated by an application to assessing ecoefficiency of road transportation in the three largest towns of eastern Finland.

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 two-stage method is proposed, referred to as Stochastic Non-smooth 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.

Data envelopment analysis (DEA) is known as a nonparametric mathematical programming approach to productive efficiency analysis. In this paper, we show that DEA can be alternatively interpreted as nonparametric least-squares regression subject to shape constraints on the frontier and sign constraints on residuals. This reinterpretation reveals the classic parametric programming model by Aigner and Chu [Aigner, D., S. Chu. 1968. On estimating the industry production function. Amer. Econom. Rev. 58 826–839] as a constrained special case of DEA. Applying these insights, we develop a nonparametric variant of the corrected ordinary least-squares (COLS) method. We show that this new method, referred to as corrected concave nonparametric least squares (C²NLS), is consistent and asymptotically unbiased. The linkages established in this paper contribute to further integration of the econometric and axiomatic approaches to efficiency analysis.

This paper develops the first operational tests of portfolio efficiency based on the general stochastic dominance (SD) criteria that account for an infinite set of diversification strategies. The main insight is to preserve the cross-sectional dependence of asset returns when forming portfolios by reexpressing the SD criteria in T-dimensional Euclidean space, with elements representing rates of return in T different states of nature. We characterize subsets of this state-space that dominate a given evaluated return vector by first- and second-order SD. This allows us to derive simple SD efficiency measures and test statistics, computable by standard mathematical programming algorithms. The SD tests and efficiency measures are illustrated by an empirical application that analyzes industrial diversification of the market portfolio.