Asymptotics and Consistent Bootstraps for Dea Estimators in Nonparametric Frontier Models

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract 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. Terms of use: Documents in

ICT capital and labour productivity growth: A non-parametric analysis of 14 OECD countries

“…That is, it is not possible to make an inference, in the classical sense (Kneip, Simar, & Wilson, 2008), about the estimated components of the decomposition of labour productivity growth defined by relation (10). In fact, the components for a given sample of countries are only estimates of the true population values (Simar & Wilson, 1998, 1999 and are affected by uncertainty due to sampling variation.…”

Nonparametric conditional efficiency measures: asymptotic properties

“…Gijbels et al (1999) derived the explicit form of the limit distribution of the DEA estimator when the input and output variables are all scalar. Methods for approximating the sampling distribution of the DEA estimator in a general multidimensional setup were investigated by Kneip, Simar and Wilson (2003), Jeong (2004), Jeong and Park (2006). Jeong and Simar (2006) proposed a hybrid version of FDH and DEA, say LFDH, which is defined by interpolating the vertices of FDH.…”

Finding the Right Yardstick: Regulation Under Heterogeneous Environments

“…Therefore, the sizes of the selected bandwidths themselves already contain information about the impact of particular z-variables on the production 2012). 8 The statistical properties of this estimator are derived in Kneip et al (2008) and its consistency is established in Jeong et al (2010). 9 The authors suggest using kernels with compact support in the framework of conditional boundary estimation.…”

“…by construction they are upward-biased Simar and Wilson (1998). We correct for the bias inθ andθ c by applying the m-bootstrap first proposed by Kneip et al (2008), and extended by Simar and Wilson (2011). 11 Unlike the naive bootstrap, this approach allows consistent bias-correction by drawing bootstrap subsamples of size m = n κ from 11 As a variant of the original procedure, we also use the kernel probabilities in order to construct the bootstrap samples for the conditional case, which is consistent with the idea of conditioning the production process and is supposed to give even more precise insights the given sample of size n with κ ∈ (0, 1).…”