Conditional Nonparametric Frontier Models for Convex and Non Convex Technologies: a Unifying Approach

The explanation of productivity differentials is very important to identify the economic conditions that create inefficiency and to improve managerial performance. In literature two main approaches have been developed: one-stage approaches and two-stage approaches. Daraio and Simar (2003) propose a full nonparametric methodology based on conditional FDH and conditional order-m frontiers without any convexity assumption on the technology. On the one hand, convexity has always been assumed in mainstream production theory and general equilibrium. On the other hand, in many empirical applications, the convexity assumption can be reasonable and sometimes natural. Leading by these considerations, in this paper we propose a unifying approach to introduce external-environmental variables in nonparametric frontier models for convex and non convex technologies. Developing further the work done in Daraio and Simar (2003) we introduce a conditional DEA estimator, i.e., an estimator of production frontier of DEA type conditioned to some external-environmental variables which are neither inputs nor outputs under the control of the producer. A robust version of this conditional estimator is also proposed. These various measures of efficiency provide also indicators of convexity. Illustrations through simulated and real data (mutual funds) examples are reported.Convexity, External-Environmental Factors, Production Frontier, Nonparametric Estimation, Robust Estimation.

On testing equality of distributions of technical efficiency scores

The challenge of the econometric problem in production efficiency analysis is that the very efficiency scores to be analyzed are unobserved. Recently, statistical properties have been discovered for a class of estimators popular in the literature, known as data envelopment analysis (DEA) approach. This opens a wide range of possibilities for a well-grounded statistical inference about the true efficiency scores from their DEA-estimates. In this paper we investigate possibility of using existing tests for equality of two distributions for such a context. Considering statistical complications pertinent to our context, we consider several approaches to adapt the Li (1996) test to the context and explore their performance in terms of the size and the power of the test in various Monte Carlo experiments. One of these approaches showed good performance both in the size and in the power, thus encouraging for its wide use in empirical studies.Kernel Density Estimation and Tests, Bootstrap, DEA

Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach

This paper proposes a general formulation of a nonparametric frontier model introducingexternal environmental factors that might influence the production process butare neither inputs nor outputs under the control of the producer. A representation isproposed in terms of a probabilistic model which defines the data generating process.Our approach extends the basic ideas from Cazals, Florens and Simar (2002) to thefull multivariate case. We introduce the concepts of conditional efficiency measure andof conditional efficiency measure of order-m. Afterwards we suggest a practical wayfor computing the nonparametric estimators. Finally, a simple methodology to investigatethe influence of these external factors on the production process is proposed.Numerical illustrations through some simulated examples and through a real data seton Mutual Funds show the usefulness of the approach.production function, frontier, nonparametric estimation, environmental factors,robust estimation.

Optimal Bandwidth Selection for Conditional Efficiency Measures: a Data-driven Approach

In productivity analysis an important issue is to detect how external (environmental) factors, exogenous to the production process and not under the control of the producer, might influence the production process and the resulting efficiency of the firms. Most of the traditional approaches proposed in the literature have serious drawbacks. An alternative approach is to describe the production process as being conditioned by a given value of the environmental variables (Cazals, Florens and Simar, 2002, Daraio and Simar, 2005). This defines conditional efficiency measures where the production set in the input × output space may depend on the value of the external variables. The statistical properties of nonparametric estimators of these conditional measures are now established (Jeong, Park and Simar, 2008). These involve the estimation of a nonstandard conditional distribution function which requires the specification of a smoothing parameter (a bandwidth). So far, only the asymptotic optimal order of this bandwidth has been established. This is of little interest for the practitioner. In this paper we fill this gap and we propose a data-driven technique for selecting this parameter in practice. The approach, based on a Least Squares Cross Validation procedure (LSCV), provides an optimal bandwidth that minimizes an appropriate integrated Mean Squared Error (MSE). The method is carefully described and exemplified with some simulated data with univariate and multivariate environmental factors. An application on real data (performances of Mutual Funds) illustrates how this new optimal method of bandwidth selection outperforms former methods.Nonparametric efficiency estimation, conditional efficiency measures, environmental factors, conditional distribution function, bandwidth.

Asymptotic distribution of conical-hull estimators of directional edges

Nonparametric data envelopment analysis (DEA) estimators have been widely applied in analysis of productive efficiency. Typically they are defined in terms of convex-hulls of the observed combinations of $\mathrm{inputs}\times\mathrm{outputs}$ in a sample of enterprises. The shape of the convex-hull relies on a hypothesis on the shape of the technology, defined as the boundary of the set of technically attainable points in the $\mathrm{inputs}\times\mathrm{outputs}$ space. So far, only the statistical properties of the smallest convex polyhedron enveloping the data points has been considered which corresponds to a situation where the technology presents variable returns-to-scale (VRS). This paper analyzes the case where the most common constant returns-to-scale (CRS) hypothesis is assumed. Here the DEA is defined as the smallest conical-hull with vertex at the origin enveloping the cloud of observed points. In this paper we determine the asymptotic properties of this estimator, showing that the rate of convergence is better than for the VRS estimator. We derive also its asymptotic sampling distribution with a practical way to simulate it. This allows to define a bias-corrected estimator and to build confidence intervals for the frontier. We compare in a simulated example the bias-corrected estimator with the original conical-hull estimator and show its superiority in terms of median squared error.Comment: Published in at http://dx.doi.org/10.1214/09-AOS746 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotics and Consistent Bootstraps for DEA Estimators in Non-parametric Frontier Models

Non-parametric data envelopment analysis (DEA) estimators based on linear programming methods have been widely applied in analyses of productive efficiency. The distributions of these estimators remain unknown except in the simple case of one input and one output, and previous bootstrap methods proposed for inference have not been proven consistent, making inference doubtful. This paper derives the asymptotic distribution of DEA estimators under variable returns-to-scale. This result is then used to prove that two different bootstrap procedures (one based on sub-sampling, the other based on smoothing) provide consistent inference. The smooth bootstrap requires smoothing the irregularly-bounded density of inputs and outputs as well as smoothing of the DEA frontier estimate. Both bootstrap procedures allow for dependence of the inefficiency process on output levels and the mix of inputs in the case of input-oriented measures, or on inputs levels and the mix of outputs in the case of output-oriented measures.bootstrap, frontier, efficiency, data envelopment analysis, DEA

Local Likelihood Estimation of Truncated Regression and Its Partial Derivatives: Theory and Application

In this paper we propose a very flexible estimator in the context of truncated regression that does not require parametric assumptions. To do this, we adapt the theory of local maximum likelihood estimation. We provide the asymptotic results and illustrate the performance of our estimator on simulated and real data sets. Our estimator performs as good as the fully parametric estimator when the assumptions for the latter hold, but as expected, much better when they do not (provided that the curse of dimensionality problem is not the issue). Overall, our estimator exhibits a fair degree of robustness to various deviations from linearity in the regression equation and also to deviations from the specification of the error term. So the approach shall prove to be very useful in practical applications, where the parametric form of the regression or of the distribution is rarely known.Nonparametric Truncated Regression, Local Likelihood

Forecasting the Malmquist Productivity Index

The Malmquist Productivity Index (MPI) suggests a convenient way of measuring the productivity change of a given unit between two consequent time periods. Until now, only a static approach for analyzing the MPI was available in the literature. However, this hides a potentially valuable information given by the evolution of productivity over time. In this paper, we introduce a dynamic procedure for forecasting the MPI. We compare several approaches and give credit to a method based on the assumption of circularity. Because the MPI is not circular, we present a new decomposition of the MPI, in which the time-varying indices are circular. Based on that decomposition, a new working dynamic forecasting procedure is proposed and illustrated. To construct prediction intervals of the MPI, we extend the bootstrap method in order to take into account potential serial correlation in the data. We illustrate all the new techniques described above by forecasting the productivityt index of 17 OCDE countries, constructed from their GDP, labor and capital stock.Malmquist Productivity Index, circularity efficiency, smooth bootstrap

Efficiency and University Size: Discipline-wise Evidence from European Universities

Strategic management of universities must build the best possible relation between inputs and outputs. One relevant question, in this perspective, is whether the unit is making the best use of existing resources, or whether technical efficiency is in place. Here we address the question of technical efficiency with respect to university’s size. The crucial concept in this analysis is conditional efficiency and the ratio of size-conditional to unconditional efficiency measures. In particular we take use of robust order-m efficiency scores presented in Cazals, Florens and Simar (2002) and generalized in Daraio and Simar (2005a,b) to analyze data from four European countries and four different research fields. Our results are still explorative and mainly show how heterogeneous international datasets could be used to analyze productivity differences.Universities;efficiency;International comparisons