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.

Weak disposability of outputs means that firms can abate harmful emissions by decreasing the activity level. Modeling weak disposability in nonparametric production analysis has caused some confusion. This article identifies a dilemma in these approaches: conventional formulations implicitly and unintentionally assume all firms apply uniform abatement factors. However, it is usually cost-effective to abate emissions in those firms where the marginal abatement costs are lowest. This article presents a simple formulation of weak disposability that allows for non-uniform abatement factors and preserves the linear structure of the model. Copyright 2005, Oxford University Press.

T his 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 secondorder 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.

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.

We examine a nonparametric least squares regression model where the regression function is endogenously selected from the family of continuous, monotonic increasing and globally concave functions that can be nondifferentiable. We show that this family of functions is perfectly represented by a subset of continuous, piece-wise linear functions whose intercept and slope coefficients are constrained to satisfy the required monotonicity and concavity conditions. This representation theorem is useful at least in three respects. First, it enables is to derive an explicit representation for the regression function, which can be used for assessing marginal properties and for the purposes of forecasting and ex post economic modeling.Second, it enables us to transform the infinite dimensional regression problem into a tractable quadratic programming (QP) form, which can be solved by standard QP algorithms and solver software. Importantly, the QP formulation applies to the general multiple regression setting. Third, an operational computational procedure enables us to apply bootstrap techniques to draw statistical inference.

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Färe and Grosskopf (this issue) claim that a single abatement factor suffices for modeling weak disposability in nonparametric production models, and that the Kuosmanen (2005) technology that uses multiple abatement factors is larger than necessary. This article demonstrates by a numerical example that a single abatement factor does not suffice to capture all feasible production plans, and that its use leads to the violation of convexity, one of the maintained assumptions of the model. We also prove that the Kuosmanen technology is the correct minimum extrapolation technology under the stated axioms.