Non-parametric production analysis in non-competitive environments

We extend the non-parametric methodology for empirical production analysis to deal with endogenous prices. As price endogeneity is often complemented by price uncertainty, we consider both the case of certain prices and the case of uncertain prices. The extensions are fully compatible with existing tools for eliciting and representing technology and price information, and preserves the tractable mathematical programming structure of the original methodology. An empirical application to the Dutch electricity distribution sector illustrates our extension.     

Neoclassical versus Frontier Production Models? Testing for the Skewness of Regression Residuals*

The empirical literature on production and cost functions is divided into two strands. The neoclassical approach concentrates on model parameters, while the frontier approach decomposes the disturbance term to a symmetric noise term and a positively skewed inefficiency term. We propose a theoretical justification for the skewness of the inefficiency term, arguing that this skewness is the key testable hypothesis of the frontier approach. We propose to test the regression residuals for skewness in order to distinguish the two competing approaches. Our test builds directly upon the asymmetry of regression residuals and does not require any prior distributional assumptions.     

Weak Disposability in Nonparametric Production Analysis: Reply to Färe and Grosskopf

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.     

One-stage estimation of the effects of operational conditions and practices on productive performance: asymptotically normal and efficient,root-<Emphasis Type="Italic">n</Emphasis> consistent StoNEZD method

Understanding the effects of operational conditions and practices on productive efficiency can provide valuable economic and managerial insights. The conventional approach is to use a two-stage method where the efficiency estimates are regressed on contextual variables representing the operational conditions. The main problem of the two-stage approach is that it ignores the correlations between inputs and contextual variables. To address this shortcoming, we build on the recently developed regression interpretation of data envelopment analysis (DEA) to develop a new one-stage semi-nonparametric estimator that combines the nonparametric DEA-style frontier with a regression model of the contextual variables. The new method is referred to as stochastic semi-nonparametric envelopment of z variables data (StoNEZD). The StoNEZD estimator for the contextual variables is shown to be statistically consistent under less restrictive assumptions than those required by the two-stage DEA estimator. Further, the StoNEZD estimator is shown to be unbiased, asymptotically efficient, asymptotically normally distributed, and converge at the standard parametric rate of order n ^−1/2. Therefore, the conventional methods of statistical testing and confidence intervals apply for asymptotic inference. Finite sample performance of the proposed estimators is examined through Monte Carlo simulations.     

Exact decomposition of the Fisher ideal total factor productivity index

Decompositions of total factor productivity (TFP) shed light on the driving factors behind productivity change. We develop the first exact decomposition of the Fisher ideal TFP index which contains no debatable mixed-period components or residuals. We systematically isolate five effects of (1) technical change, (2) technical efficiency, (3) scale efficiency, (4) allocative efficiency, and (5) price effect. The three efficiency components (2–4) represent the efficiency of achieving a given target point. Components (1) and (5) capture the changes of the target point. While the technical change component is well-established, changes in the relative input–output prices can have real effects on the scale and scope of the target. Such changes are captured by the new price effect component (5). The new decomposition is compared with existing decompositions both in theory and by means of an empirical application to a panel data of 459 Finnish farms in years 1992–2000.

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

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.     

Weak Disposability in Nonparametric Production Analysis with Undesirable Outputs

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.     

(In)Efficient Environmental Policy with Interacting Pollutants

Many environmental problems involve the transformation of multiple harmful substances into one or more damage agents much in the same way as a firm transforms inputs into outputs. Yet environmental management differs from a firm’s production in one important respect: while a firm seeks efficient input allocation to maximize profit, an environmental planner allocates abatement efforts to render the production of damage agents as inefficient as possible. We characterize a solution to the multiple pollutants problem and show that the optimal policy is often a corner solution, in which abatement is focused on a single pollutant. Corner solutions may arise even in well-behaved problems with concave production functions and convex damage and cost functions. Furthermore, even concentrating on a wrong pollutant may yield greater net benefits than setting uniform abatement targets for all harmful substances. Our general theoretical results on the management of flow and stock pollutants are complemented by two numerical examples illustrating the abatement of eutrophying nutrients and greenhouse gases.     

Eco-efficiency analysis of consumer durables using absolute shadow prices

We develop a method for eco-efficiency analysis of consumer durables that is based on Data Envelopment Analysis (DEA). In contrast to previous product efficiency studies, we consider the measurement problem from the policy perspective. The innovation of the paper is to measure efficiency in terms of absolute shadow prices that are optimized endogenously within the model to maximize efficiency of the good. Thus, the efficiency measure has a direct economic interpretation as a monetary loss due to inefficiency, expressed in some currency unit. The advantages as well as technical differences between the proposed approach and the traditional production-side methods are discussed in detail. We illustrate the approach by an application to eco-efficiency evaluation of Sport Utility Vehicles.     

Environmental cost-benefit analysis of alternative timing strategies in greenhouse gas abatement: A data envelopment analysis approach

Assessing the benefits of climate policies is complicated due to ancillary benefits: abatement of greenhouse gases also reduces local air pollution. The timing of the abatement measures influences both the economic costs and ancillary benefits. This paper conducts efficiency analysis of ten alternative timing strategies, taking into account the ancillary benefits. We apply the approach by Kuosmanen and Kortelainen [Valuing Environmental Factors in Cost-Benefit Analysis Using Data Envelopment Analysis, Ecological Economics 62 (2007), 56-65], which does not require prior valuation of the environmental impacts. The assessment is based on synthetic data from a dynamic applied general equilibrium model calibrated to The Netherlands. Our assessment shows that if one is only interested in GHG abatement at the lowest economic cost, then equal reduction of GHGs over time is preferred. If society is willing to pay a premium for higher ancillary benefits, an early mid-intensive reduction strategy is optimal.