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.

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.

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.

On the comparative performance of socially responsible and Islamic mutual funds

This is the first study to provide comprehensive analyses of the relative performance of both socially responsible investment (SRI) and Islamic mutual funds. The analysis proceeds in two stages. In the first, the performance of the two categories of funds is measured using partial frontier methods. In the second stage, we use quantile regression techniques. By combining two variants of the Free Disposal Hull (FDH) methods (order-m and order-α) in the first stage of analysis and quantile regression in the second stage, we provide detailed analyses of the impact of different covariates across methods and across different quantiles. In spite of the differences in the screening criteria and portfolio management of both types of funds, variation in the performance is only found for some of the quantiles of the conditional distribution of mutual fund performance. We established that for the most inefficient funds the superior performance of SRI funds is significant. In contrast, for the best mutual funds this evidence vanished and even Islamic funds perform better than SRI. These results show the benefits of performing the analysis using quantile regression

On the informativeness of persistence for evaluating mutual fund performance using partial frontiers

The last few years have witnessed a rapid evolution in the literature evaluating mutual fund performance using frontier techniques. The instruments applied, mostly DEA (Data Envelopment Analysis) and, to a lesser extent, FDH (Free Disposal Hull), are able to encompass several dimensions of performance, but they also have some disadvantages that might be preventing a wider acceptance. The recently developed order-m and order-α partial frontiers overcome some of the disadvantages (they are robust with respect to extreme values and noise, and do not suffer from the well-known curse of dimensionality) while keeping the main virtues of DEA and FDH (they are fully nonparametric). In this article we apply not only the non-convex counterpart of DEA (FDH) but also order-m and order-α partial frontiers to a sample of US mutual funds. The results obtained for both order-m and order-α are useful, since a full ranking of the mutual funds' performance can be obtained. We merge these methods with the literature on mutual fund performance persistence. By combining the two literatures we derive an algorithm which establishes how the choice of m and α parameters intrinsic to order-m and order-α (respectively) relate to the existence of performance persistence and the contrarian effect

Do ethics imply persistence? The case of Islamic and socially responsible funds

We analyze the performance persistence of Islamic and Socially Responsible Investment (SRI) mutual funds. We adopt a multi-stage strategy in which, in the first stage, partial frontiers’ approaches are considered to measure the performance of the different funds in the sample. In the second stage, the results yielded by the partial frontiers are plugged into different investment strategies based on a recursive estimation methodology whose persistence performance is evaluated in the third stage of the analysis. Results indicate that, for both types of funds, performance persistence actually exists, but only for the worst and, most notably, best funds. This result is robust not only across methods (and different choices of tuning parameters within each method) but also across both SRI and Islamic funds—although in the case of the latter persistence was stronger for the best funds. The persistence of SRI and Islamic funds represents an important result for investors and the market, since it provides information on both which funds to invest in and which funds to avoid. Last but not least, the use of the aforementioned techniques in the context of mutual funds could also be of interest for the non-conclusive literature

Blaming the exogenous environment? Conditional efficiency estimation with continuous and discrete exogenous variables

This paper proposes a fully nonparametric framework to estimate relative efficiency of entities while accounting for a mixed set of continuous and discrete (both ordered and unordered) exogenous variables. Using robust partial frontier techniques, the probabilistic and conditional characterization of the production process, as well as insights from the recent developments in nonparametric econometrics, we present a generalized approach for conditional efficiency measurement. To do so, we utilize a tailored mixed kernel function with a data-driven bandwidth selection. So far only descriptive analysis for studying the effect of heterogeneity in conditional efficiency estimation has been suggested. We show how to use and interpret nonparametric bootstrap-based significance tests in a generalized conditional efficiency framework. This allows us to study statistical significance of continuous and discrete exogenous variables on production process. The proposed approach is illustrated using simulated examples as well as a sample of British pupils from the OECD Pisa data set. The results of the empirical application show that several exogenous discrete factors have a statistically significant effect on the educational process.Nonparametric estimation, Conditional efficiency measures, Exogenous factors, Generalized kernel function, Education

Does active management add value? New evidence from a quantile regression approach

While it has long been recognised that active management is an important issue in the area of mutual fund performance, little consensus has been reached about the value managers’ abilities can add. This study examines funds’ and managers’ characteristics in an attempt to understand their influence on mutual fund efficiency. We explore these issues in a twostage approach, considering partial frontier estimators (order-m, order-α) to assess performance in the first stage, and quantile regression in the second stage to isolate the determinants of efficiency. This combination of methodologies has barely been considered to date in the field of operations research. Our findings are of interest to both academics and practitioners as they shed light on the differences among funds as well as among managers. Our analysis provides some arguments to guide fund selection and points to some managerial features investors might consider taking into account. In addition, some of the differences in performance among funds are rather intricate because both the magnitude of the estimated regression coefficients and their significance varies depending on the quantile of the distribution of fund performance, suggesting that some relevant trends might be concealed by conditional-mean models such as Tobit or OLS

Blaming the exogenous environment? Conditional efficiency estimation with continuous and discrete environmental variables.

This paper proposes a fully nonparametric framework to estimate relative efficiency of entities while accounting for a mixed set of continuous and discrete (both ordered and unordered) exogenous variables. Using robust partial frontier techniques, the probabilistic and conditional characterization of the production process, as well as insights from the recent developments in nonparametric econometrics, we present a generalized approach for conditional efficiency measurement. To do so, we utilize a tailored mixed kernel function with a data-driven bandwidth selection. So far only descriptive analysis for studying the effect of heterogeneity in conditional efficiency estimation has been suggested. We show how to use and interpret nonparametric bootstrap-based significance tests in a generalized conditional efficiency framework. This allows us to study statistical significance of continuous and discrete environmental variables. The proposed approach is illustrated by a sample of British pupils from the OECD Pisa data set. The results show that several exogenous discrete factors have a significant effect on the educational process.