Optimal bandwidth selection for conditional efficiency measures: A data-driven approach

Abstract

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 andSimar, 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.

Efficiency assessment of primary care providers: A conditional nonparametric approach

“…Hence, it is possible to find works using this approach to measure the efficiency of units operating in multiple frameworks such as the educational sector (Bonaccorsi et al, 2006;Cherchye et al, 2010;De Witte and Rogge, 2011;Haelermans and De Witte, 2012;De Witte and Kortelainen, 2013;, banks and mutual funds (Daraio and Simar, 2005;Daouia and Simar, 2007;Blass et al, 2008;Badin et al, 2010), post offices (Cazals et al, 2008), public libraries (De Witte and Geys, 2011;, regional welfare or environment Tzeremes, 2011a, Halkos andTzeremes, 2013), local services (Rogge and De Jaeger, 2012;Verschelde and Rogge, 2012) or the water sector Marques, 2010a, 2010b;Carvalho and Marques, 2011;Vidoli, 2011). However, to the best of our best knowledge, this methodology has only been applied previously in the health sector to measure the efficiency of health administrative districts in Greece (Halkos and Tzeremes, 2011b) considering only continuous exogenous variables.…”

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“…Nevertheless, like all the methodologies, this one also has some weaknesses. One is related to its sensitivity to the estimated values for the bandwidth although this weakness has been studied and solutions have been proposed [39]. The incapacity to analyse panel data is also a drawback.…”

“…One of the greatest potential of this approach is related to the fact of not using a separability condition or any assumption on the direction of the effect of the environmental variable [39], as opposed to the methods usually applied in the literature. Nevertheless, like all the methodologies, this one also has some weaknesses.…”

Finding the Right Yardstick: Regulation Under Heterogeneous Environments

“…The conditional DEA estimator is based on an attainable production set, Ψ z , conditioned on a set of z-variables and implies the estimation of a conditional distribution function where the production process is conditional to a particular level of z (Daraio and Simar, 2007b;Bȃdin et al, 2010). 8 The latter requires applying a smoothing technique.…”