DOCSLIB.ORG

Efficiency Measurement with the Weibull Stochastic Frontier*

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Efficiency Measurement with the Weibull Stochastic Frontier* OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 69, 5 (2007) 0305-9049 doi: 10.1111/j.1468-0084.2007.00475.x Efficiency Measurement with the Weibull Stochastic Frontier* Efthymios G. Tsionas Department of Economics, Athens University of Economics and Business, Athens, Greece (e-mail: [email protected]) Abstract In this paper we consider the Weibull distribution as a model for technical efficiency. The distribution has a shape and scale parameter like the gamma distribution and can be a reasonable competitor in practice. The techniques are illustrated using artificial data as well as a panel of Spanish dairy farms. I. Introduction Beginning with Aigner, Lovell and Schmidt (1977) and Meeusen and van den Broeck (1977) stochastic frontier models with half-normal or exponential one-sided error terms have become popular in the measurement of production efficiency. Greene (1990) has proposed the gamma distribution as a plausible model, and Stevenson (1980) the truncated normal distribution. In production frontiers one would nor- mally expect to find negative skewness in the composed error term. The standard way to generate negative skewness is to assume a positively skewed inefficiency distribution. However, it is often the case in practice that estimated production frontiers show positive skewness, which certain authors (Green and Mayes, 1991) interpret as evi- dence in favour of ‘super-efficiency’. Carree (2002) suggested an alternative ex- planation by pointing out that there are in fact negatively skewed distributions for the one-sided error term which are reasonable on a priori grounds and, naturally, generate positively skewed composed errors. One such distribution is the binomial and another is the Weibull. Carree (2002) points out that ‘[i]n contrast to the *Many thanks are due to an anonymous referee for several helpful comments and suggestions on earlier versions of this paper and to Subal Kumbhakar for providing the data. JEL Classification numbers: C13, D24. 693 © Blackwell Publishing Ltd and the Department of Economics, University of Oxford, 2007. Published by Blackwell Publishing Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA. 694 Bulletin conclusion of “super-efficiency” in case of a positive skewness, the example of the binomial distribution shows that a positive skewness suggests a one-sided distribu- tion that has low probabilities for small inefficiencies and high probabilities of large inefficiencies. (...) Hence, (...) a large fraction attains considerable inefficiencies’ (p. 105).1 Carree (2002) proposes a simple method of moments estimator when the one-sided distribution is binomial but did not consider estimation under the assump- tion of a Weibull distribution for inefficiencies because this model is more complex. Considering the Weibull is important because the binomial is a discrete distribution and thus it is difficult to argue that it can be a reasonable model in practice. In this paper, we consider Bayesian analysis of the stochastic frontier model when the one-sided error follows a Weibull distribution. With the exception of Misra (2002) who uses maximum simulated likelihood to estimate the parameters, this distribu- tion has not been analysed before because of computational problems. We show that this is, in fact, not a serious problem because computations can be performed using Markov chain Monte Carlo (MCMC) techniques, and we provide finite sample infer- ences on all parameters of the model, as well as predictive and actual inefficiencies. The model and inference techniques are presented in section II. An illustration using artificial data is presented in section III. An empirical application to Spanish dairy farms is discussed in section IV. II. The model and inference techniques The model considered in this paper applies to panel data and is given by the following = + v + yit xit it J tui,(1) 2 vit | ∼ IN(0, ), (2) | = c−1 − c p(ui c, ) c ui exp( ui ), c, , ui > 0, (3) t = 1, ..., T, i = 1, ..., n. Here, T is the number of observations for firm i, xit a k ×1 vector of explanatory vari- ables, vit the measurement error, and the ui values independent non-negative random variables independent of vit with a Weibull distribution whose density is given by equation (3). Moreover, t ≥ 0 is a time-specific component that we parameterize = as t exp((t − 1)), a parameter representing the rate of change of technical inefficiency over time (Battese and Coelli, 1992), and J = −1 or +1 depending on whether we have a production or cost frontier respectively. Technical inefficiency2 is given by tui and is allowed to vary in a parametric way over time thus avoiding the 1This discussion applies to cost frontiers as well. The composed error of cost frontiers must be positively skewed so a positively skewed one-sided distribution is often assumed. The finding of negative skewness in least squares residuals might be taken as evidence that the one-sided distribution is, in fact, negatively skewed. 2For a detailed discussion of the problems arising in Bayesian cross-sectional stochastic frontiers, see Fernandez, Osiewalski and Steel (1997). © Blackwell Publishing Ltd and the Department of Economics, University of Oxford 2007 Efficiency measurement with the Weibull stochastsic frontier 695 3 assumption of time-invariance. Furthermore, it is assumed that both vit and ui are independent of xit. (For more details on stochastic frontier analysis, see Kumbhakar and Lovell, 2000.) In equation (3), is a scale parameter and c a shape parameter. For c = 1 the distribution reduces to exponential. The distribution has a positive mode for c > 1, otherwise the mode is zero. The important feature of the distribution is that it ex- = × hibits negative skewness for c > 3.602. Let yi [yi1, yi2, ..., yiTi ] be the Ti 1 vector of observations for the dependent variable of the i the firm, Xi the associated Ti × k matrix of explanatory variables, and y and X denote the data in obvious notation. The joint probability density of yi is given by ∞ 1 T p(y | X , , , c, , ) = (22)−T/ 2c exp − (y − x − J u )2 i i 2 it it t i 2 = 0 t 1 × c−1 − c ui exp( ui )dui. (4) The integral in equation (4) is not available in closed form (unless c = 1), so the likelihood function n = L(, , c, , ; y, X ) p(yi | Xi, , , c, , ) i = 1 cannot be computed in closed form. For that reason, we treat the ui values as param- eters, and integrate them out using Monte Carlo methods. The kernel of the posterior = distribution augmented by the latent inefficiencies, u [u1, ..., un] , is given by 1 n T p(, , c, , , u | y, X ) ∝−N (c)N exp − (y − x − J u )2 22 it it t i i = 1 t = 1 n × c−1 − c ui exp( ui ) p( , , c, , )(5) i = 1 where p(, , c, , ) is the prior distribution and N = nT denotes the total number of observations. We will assume that ¯ p(, | c, , ) ∝ −(N + 1) exp(−Q/¯ 22) ¯ ¯ ¯ 2 ∼ 2 2 where N and Q are parameters. In this prior we have Q/ χN¯ , where χ denotes the chi-squared distribution with degrees of freedom, and p( | , c, , ) ∝ const.4 For Q¯ = N¯ = 0 we obtain the familiar default prior p(, | c, , )∝−1. The proposed prior for provides some flexibility relative to the default prior and is the condition- ally conjugate prior (see equation 7 below). For the remaining parameters, we specify gamma priors of the form 3 = = It is possible to set 0 and Ti 1 so that we treat the panel as a cross-section. 4The conditions for existence of the posterior from this model in spite of the improper prior on are given in Fernandez et al. (1997). © Blackwell Publishing Ltd and the Department of Economics, University of Oxford 2007 696 Bulletin ∼ G(A, B), c ∼ G(C, D), p() ∝ const., (6) where G(a, b) denotes the gamma distribution with density ba f (x | a, b) = xa−1 exp(−bx)(a, b, x > 0). (a) It should be noted that our numerical techniques allow us to specify an arbitrary prior distribution for parameter . Based on the kernel posterior distribution we can use Gibbs sampling5 to perform the computations. To that end, we extract the following conditional distributions: ˜ 2 −1 | , c, , , u, y, X ∼ Nk ((u, ), (X X ) )(7) (y˜(u, ) − X )(y˜(u, ) − X ) | , c, , , u, y, X ∼ χ2 (8) 2 N n | ∼ + c + , , c, , u, y, X G n A, ui B (9) i = 1 n n | ∝ n + C−1 − c + − p(c , , , , u, y, X ) c exp ui c ln ui D (10) i = 1 i = 1 Å (u − m )2 p(u | , , c, , , y, X ) ∝ exp − i i uc−1 exp(−uc), u > 0(11) i 2 i i i 2 Åi 1 n T p( | , , c, , u, y, X ) ∝ exp − [y − x − J exp((t − 1))u ]2 , (12) 22 it it i i = 1 t = 1 where ˜(u, ) = (X X )−1X y˜(u, ), and y˜(u, ) is a vector whose elements are = y˜it(u, ) yit − J tui. Moreover, Å J Ti t−1(y − x ) 2 = t = 1 it it 2 = mi , Åi , Ci Ci T 1 − 2T C = 2(t−1) = and = exp(). i 1 − 2 t = 1 The distributions in equations (6)–(8) are well known, and random number generation from them is straightforward. For the distribution in equation (9) we use acceptance sampling from a gamma distribution, G(n + C, ) where the scale parameter is given by = (n + C − 1)/ c¯, and c¯ solves the nonlinear equation 5For Bayesian analysis in the context of stochastic frontiers, see van den Broeck et al. (1994), Koop, Osiewalski and Steel (1997), Koop, Steel and Osiewalski (1995), and Osiewalski and Steel (1998).
Load more

Recommended publications
  • Lectures on Nonparametric Bayesian Statistics
    Lectures on Nonparametric Bayesian Statistics Notes for the course by Bas Kleijn, Aad van der Vaart, Harry van Zanten (Text partly extracted from a forthcoming book by S. Ghosal and A. van der Vaart) version 4-12-2012 UNDER CONSTRUCTION 1 Introduction Why adopt the nonparametric Bayesian approach for inference? The answer lies in the si- multaneous preference for nonparametric modeling and desire to follow a Bayesian proce- dure. Nonparametric (and semiparametric) models can avoid the arbitrary and possibly un- verifiable assumptions inherent in parametric models. Bayesian procedures may be desired for the conceptual simplicity of the Bayesian paradigm, easy interpretability of Bayesian quantities or philosopohical reasons. 1.1 Motivation Bayesian nonparametrics is the study of Bayesian inference methods for nonparametric and semiparametric models. In the Bayesian nonparametric paradigm a prior distribution is assigned to all unknown quantities (parameters) involved in the modeling, whether finite or infinite dimensional. Inference is made from the “posterior distribution”, the conditional distribution of all parameters given the data. A model completely specifies the conditional distribution of all observable given all unobserved quantities, or parameters, while a prior distribution specifies the distribution of all unobservables. From this point of view, random effects and latent variables also qualify as parameters, and distributions of these quantities, often considered as part of the model itself from the classical point of view, are considered part of the prior. The posterior distribution involves an inversion of the order of conditioning. Existence of a regular version of the posterior is guaranteed under mild conditions on the relevant spaces (see Section 2).
    [Show full text]
  • Download (4Mb)
    University of Warwick institutional repository: http://go.warwick.ac.uk/wrap A Thesis Submitted for the Degree of PhD at the University of Warwick http://go.warwick.ac.uk/wrap/58404 This thesis is made available online and is protected by original copyright. Please scroll down to view the document itself. Please refer to the repository record for this item for information to help you to cite it. Our policy information is available from the repository home page. Library Declaration and Deposit Agreement 1. STUDENT DETAILS Please complete the following: Full name: …………………………………………………………………………………………….Gui Pedro Araújo de Mendonça University ID number: ………………………………………………………………………………0759252 2. THESIS DEPOSIT 2.1 I understand that under my registration at the University, I am required to deposit my thesis with the University in BOTH hard copy and in digital format. The digital version should normally be saved as a single pdf file. 2.2 The hard copy will be housed in the University Library. The digital version will be deposited in the University’s Institutional Repository (WRAP). Unless otherwise indicated (see 2.3 below) this will be made openly accessible on the Internet and will be supplied to the British Library to be made available online via its Electronic Theses Online Service (EThOS) service. [At present, theses submitted for a Master’s degree by Research (MA, MSc, LLM, MS or MMedSci) are not being deposited in WRAP and not being made available via EthOS. This may change in future.] 2.3 In exceptional circumstances, the Chair of the Board of Graduate Studies may grant permission for an embargo to be placed on public access to the hard copy thesis for a limited period.
    [Show full text]
  • Robust Numerical Bayesian Unit Root Test for Model
    ROBUST NUMERICAL BAYESIAN UNIT ROOT TEST FOR MODEL UNCERTAINTY by XUEDONG WU (Under the Direction of Jeffrey H. Dorfman) ABSTRACT Unit root testing is an important procedure when performing time series analysis, since all the succeeding inferences should be performed based on a stationary series. Thus, it is crucial to test the stationarity of the time series in hand accurately and efficiently. One issue among the existing popular unit root testing methods is that they all require certain assumptions about the model specification, whether on the functional form or the stochastic term distribution; then all the analyses are performed based on the pre- determined model. However, various circumstances such as data incompleteness, variable selection, and distribution misspecification which may lead to an inappropriate model specification that will produce an erroneous conclusion since the test result depends on the particular model considered. This dissertation focuses on confronting this issue by proposing a new numerical Bayesian unit root test incorporating model averaging which can take model uncertainty as well as variable transformation into account. The first chapter introduces a broad literature review of all the building blocks need for the development of the new methods, including traditional frequentist unit root tests, Bayesian unit root tests, and Bayesian model averaging. Following chapter II elaborates the mathematical derivation of the proposed methods, Monte Carlo simulation study and results, as well as testing conclusions on the benchmark Nelson and Plosser (1982) macroeconomic time series. Chapter III applies the method to investigate the effect of data frequency on unit root test results particularly for financial data.
    [Show full text]
  • Bayesian Treatments to Panel Data Models with an Application To
    Bayesian Treatments to Panel Data Models with an Application to Models of Productivity Junrong Liu Department of Economics/Rice University Robin Sickles Department of Economics/Rice University E. G. Tsionas University of Athens This Draft November 25, 2013 Abstract This paper considers two models for uncovering information about technical change in large heterogeneous panels. The first is a panel data model with nonparametric time effects. Second, we consider a panel data model with common factors whose number is unknown and their effects are firm-specific. This paper proposes a Bayesian approach to estimate the two models. Bayesian inference techniques organized around MCMC are applied to implement the models. Monte Carlo experiments are performed to examine the finite-sample performance of this approach, which dominates a variety of estimators that rely on parametric assumptions. In order to illustrate the new method, the Bayesian approach has been applied to the analysis of efficiency trends in the U.S. largest banks using a dataset based on the Call Report data from FDIC over the period from 1990 to 2009. Keywords: Panel data, time-varying heterogeneity, Bayesian econometrics, banking studies, productivity JEL Classification: C23; C11; G21; D24 1 1. Introduction In this paper, we consider two panel data models with unobserved heterogeneous time-varying effects, one with individual effects treated as random functions of time, the other with common factors whose number is unknown and their effects are firm-specific. This paper has two distinctive features and can be considered as a generalization of traditional panel data models. Firstly, the individual effects that are assumed to be heterogeneous across units as well as to be time varying are treated nonparametrically, following the spirit of the model from Bai (2009) and Kneip et al.
    [Show full text]
  • Acebayes: an R Package for Bayesian Optimal Design of Experiments Via Approximate Coordinate Exchange
    acebayes: An R Package for Bayesian Optimal Design of Experiments via Approximate Coordinate Exchange Antony M. Overstall David C. Woods Maria Adamou University of Southampton University of Southampton University of Southampton Abstract We describe the R package acebayes and demonstrate its use to find Bayesian optimal experimental designs. A decision-theoretic approach is adopted, with the optimal design maximising an expected utility. Finding Bayesian optimal designs for realistic problems is challenging, as the expected utility is typically intractable and the design space may be high-dimensional. The package implements the approximate coordinate exchange algo- rithm to optimise (an approximation to) the expected utility via a sequence of conditional one-dimensional optimisation steps. At each step, a Gaussian process regression model is used to approximate, and subsequently optimise, the expected utility as the function of a single design coordinate (the value taken by one controllable variable for one run of the experiment). In addition to functions for bespoke design problems with user-defined utility functions, acebayes provides new functions tailored to finding designs for common generalised linear and nonlinear models. The package provides a step-change in the com- plexity of problems that can be addressed, enabling designs to be found for much larger numbers of variables and runs than previously possible. We provide tutorials on the ap- plication of the methodology for four illustrative examples of varying complexity where designs are found for the goals of parameter estimation, model selection and prediction. These examples demonstrate previously unseen functionality of acebayes. Keywords: A-optimality, computer experiments, D-optimality, decision-theoretic design, Gaus- sian process regression, generalised linear models, high-dimensional design, model selection, nonlinear models, prediction, pseudo-Bayesian design.
    [Show full text]
  • Arxiv:1503.04493V1 [Math.ST] 16 Mar 2015 a Nsbaia Tpictnwiepr Fti Okwsfina Was Work This of Part Hospitality
    Semiparametric Bernstein-von Mises Theorem: Second Order Studies Yun Yang∗, Guang Cheng† and David B. Dunson‡ March 17, 2015 Abstract The major goal of this paper is to study the second order frequentist properties of the marginal posterior distribution of the parametric component in semiparametric Bayesian mod- els, in particular, a second order semiparametric Bernstein-von Mises (BvM) Theorem. Our first contribution is to discover an interesting interference phenomenon between Bayesian esti- mation and frequentist inferential accuracy: more accurate Bayesian estimation on the nuisance function leads to higher frequentist inferential accuracy on the parametric component. As the second contribution, we propose a new class of dependent priors under which Bayesian inference procedures for the parametric component are not only efficient but also adaptive (w.r.t. the smoothness of nonparametric component) up to the second order frequentist validity. However, commonly used independent priors may even fail to produce a desirable root-n contraction rate for the parametric component in this adaptive case unless some stringent assumption is imposed. Three important classes of semiparametric models are examined, and extensive simulations are also provided. Key words: Bernstein-von Mises theorem; second order asymptotics; semiparametric model. 1. Introduction A semiparametric model is indexed by a Euclidean parameter of interest θ Θ Rp and an ∈ ⊂ infinite-dimensional nuisance function η belonging to a Banach space . For example, in the Cox H proportional hazards model, θ is a regression covariate vector corresponding to the log hazard ratio, while η is a cumulative hazard function. By introducing a joint prior Π on the product space Θ , we can make Bayesian inferences for the parameter of interest, e.g., credible set, ×H through MCMC sampling from the marginal posterior distribution.
    [Show full text]
  • Année 1995) Fethy Mili
    Document generated on 09/30/2021 10:44 p.m. L'Actualité économique Liste des cahiers de recherche des Universités et centres de recherche francophones (année 1995) Fethy Mili Volume 72, Number 2, juin 1996 URI: https://id.erudit.org/iderudit/602204ar DOI: https://doi.org/10.7202/602204ar See table of contents Publisher(s) HEC Montréal ISSN 0001-771X (print) 1710-3991 (digital) Explore this journal Cite this document Mili, F. (1996). Liste des cahiers de recherche des Universités et centres de recherche francophones (année 1995). L'Actualité économique, 72(2), 217–242. https://doi.org/10.7202/602204ar Tous droits réservés © HEC Montréal, 1996 This document is protected by copyright law. Use of the services of Érudit (including reproduction) is subject to its terms and conditions, which can be viewed online. https://apropos.erudit.org/en/users/policy-on-use/ This article is disseminated and preserved by Érudit. Érudit is a non-profit inter-university consortium of the Université de Montréal, Université Laval, and the Université du Québec à Montréal. Its mission is to promote and disseminate research. https://www.erudit.org/en/ L'Actualité économique, Revue d'analyse économique, vol. 72, n° 2, juin 1996 LISTE DES CAHIERS DE RECHERCHE DES UNIVERSITÉS ET CENTRES DE RECHERCHE FRANCOPHONES (ANNÉE 1995) Note de la rédaction. Nous remercions M. Fethy MiIi, du département de sciences économiques de l'Université de Montréal, pour son aide dans la préparation de cette liste. G.R.KQAM. (GROUPE DE RECHERCHE EN ÉCONOMIE QUANTITATIVE D'AIX-MARSEILLE), CENTRE DE LA VIEILLE CHARITÉ, 2 RUE DE LA CHARITÉ, 13002 MARSEILLE, FRANCE.
    [Show full text]
  • Bayesian Model Averaging and Prior Sensitivity in Stochastic Frontier Analysis
    econometrics Article Bayesian Model Averaging and Prior Sensitivity in Stochastic Frontier Analysis Kamil Makieła 1,* and Bła˙zejMazur 2 1 Department of Econometrics and Operational Research, Cracow University of Economics, Rakowicka 27, 31-510 Krakow, Poland 2 Department of Empirical Analyses of Economic Stability, Cracow University of Economics, Rakowicka 27, 31-510 Krakow, Poland; [email protected] * Correspondence: [email protected]; Tel.: +48-122937469 Received: 13 December 2019; Accepted: 14 April 2020; Published: 20 April 2020 Abstract: This paper discusses Bayesian model averaging (BMA) in Stochastic Frontier Analysis and investigates inference sensitivity to prior assumptions made about the scale parameter of (in)efficiency. We turn our attention to the “standard” prior specifications for the popular normal-half-normal and normal-exponential models. To facilitate formal model comparison, we propose a model that nests both sampling models and generalizes the symmetric term of the compound error. Within this setup it is possible to develop coherent priors for model parameters in an explicit way. We analyze sensitivity of different prior specifications on the aforementioned scale parameter with respect to posterior characteristics of technology, stochastic parameters, latent variables and—especially—the models’ posterior probabilities, which are crucial for adequate inference pooling. We find that using incoherent priors on the scale parameter of inefficiency has (i) virtually no impact on the technology parameters; (ii) some impact on inference about the stochastic parameters and latent variables and (iii) substantial impact on marginal data densities, which are crucial in BMA. Keywords: stochastic frontier analysis; Bayesian model averaging; Bayesian inference; model uncertainty; efficiency analysis; public policy JEL Classification: C11; C44; C52; C54 1.
    [Show full text]
  • Optimal Design of Non-Linear Multi-Factor Experiments
    University of Southampton Research Repository ePrints Soton Copyright © and Moral Rights for this thesis are retained by the author and/or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This thesis cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder/s. The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders. When referring to this work, full bibliographic details including the author, title, awarding institution and date of the thesis must be given e.g. AUTHOR (year of submission) "Full thesis title", University of Southampton, name of the University School or Department, PhD Thesis, pagination http://eprints.soton.ac.uk UNIVERSITY OF SOUTHAMPTON FACULTY OF SOCIAL, HUMAN AND MATHEMATICAL SCIENCES Mathematical Sciences Optimal Design of Nonlinear Multifactor Experiments by Yuanzhi Huang Thesis for the degree of Doctor of Philosophy February 2016 UNIVERSITY OF SOUTHAMPTON ABSTRACT FACULTY OF SOCIAL, HUMAN AND MATHEMATICAL SCIENCES Mathematical Sciences Doctor of Philosophy OPTIMAL DESIGN OF NONLINEAR MULTIFACTOR EXPERIMENTS by Yuanzhi Huang Optimal design is useful in improving the efficiencies of experiments with respect to a specified optimality criterion, which is often related to one or more statistical models assumed. In particular, sometimes chemical and biological studies could involve multiple experimental factors. Often, it is convenient to fit a nonlinear model in these factors. This nonlinear model can be either mechanistic or empirical, as long as it describes the unknown mechanism behind the response surface.
    [Show full text]
  • Tilburg University International Price Discrimination in the European Car Market Verboven, F.L
    Tilburg University International price discrimination in the European car market Verboven, F.L. Publication date: 1994 Link to publication in Tilburg University Research Portal Citation for published version (APA): Verboven, F. L. (1994). International price discrimination in the European car market: An econometric model of oligopoly behavior with product differentiation. (CentER Discussion Paper; Vol. 1994-51). Unknown Publisher. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 02. okt. 2021 ~ CBM R r~Z Discussion 8414 1994 ~,Res~~~n paper N~i.51 uii iiiiiiiiiimin i ~ C i I N iiiiuiiiNiMiiii 0 1 5 5 7~ ~~ ;~ ,~P i ' 1~~0JQ~Ja ,, Center for Economic Research No. 9451 International Price Discrimination In the European Car Market: An Econometric Model of Oligopoly Behavior with Product Differentiation by Frank Verboven June 1994 ISSN 0924-7815 International Price Discrimination in the European Car Market An econometric model of oligopoly behavior with product differentiation by Frank Verboven CentER for Economic Reseazch Tilburg University P.O.
    [Show full text]
  • 2019 Conference on Economic Design Programme
    2019 Conference on Economic Design Programme , Budapest, 12-14 June Organised by the Mechanism Design research group, Hungarian Academy of Sciences https://mechanismdesign.eu/ Conference on Economic Design is the bi-annual conference of the Society of Economic Design. The Keynote Speakers are: Leonid-Hurwicz Lecture: Philippe Jehiel (Paris School of Economics) Murat Sertel Lecture: Bhaskar Dutta (University of Warwick) Paul Kleindorfer Lecture: Bumin Yenmez (Boston College) PC-members: Lars Ehlers (chair), Deniz Dizdar and Sean Horan (Université de Montréal), Dip Majumdar and Szilvia Papai (Concordia), Ata Atay, Péter Biró, and Ágnes Cseh (Hungarian Academy of Sciences), Attila Tasnádi and Tamás Solymosi (Corvinus University of Budapest) Local organisers: Péter Biró and the Mechanism Design research group. Contact address: [email protected] Summer School: On the Engineering Aspects of Economic Design: Voting and Matching (10-11 June). Tutorials on voting: Markus Brill, Sylvain Bouveret and Piotr Faliszewski; and on matchings: John P. Dickerson, Victor Hiller, David Manlove, Ana Viana, and Bumin Yenmez. See its programme here: https://drive.google.com/file/d/1i7fMJtGTpenySuzxH_Q6RCvuJ0f1x2D3/view Co-located events of the ENCKEP COST Action: The ENCKEP (European Network for Collaboration on Kidney Exchange Programmes) COST Action will have the following co-located events: Workshop: 10 June, internal for ENCKEP members Training School: 11 June, tutorials within the CED summer school Conference: 12 June, two embedded sessions in CED Venues: The venue of CED is Corvinus University of Budapest, main building, at 1093 Budapest, Fővám tér 8. The venue of the summer school and the ENCKEP events (10-11 June) is the HTK building of the Hungarian Academy of Sciences, 1097 Tóth Kálmán u.
    [Show full text]
  • Semiparametric Bayesian Inference for Stochastic Frontier Models
    Semiparametric Bayesian Inference for Stochastic Frontier Models J.E. Griffin and M.F.J. Steel£ Institute of Mathematics and Statistics University of Kent at Canterbury, CT2 7NF, U.K. Abstract In this paper we propose a semiparametric Bayesian framework for the analysis of stochastic frontiers and efficiency measurement. The distribution of inefficiencies is modelled nonparametrically through a Dirichlet process prior. We suggest prior distributions and implement a Bayesian analysis through an efficient Markov chain Monte Carlo sampler, which allows us to deal with practically relevant sample sizes. We also allow for the efficiency distribution to vary with firm characteristics. The methodology is applied to a cost frontier, estimated from a panel data set on 382 U.S. hospitals. Keywords: Dirichlet process, Efficiency measurement, Hospital cost frontiers, Markov chain Monte Carlo JEL classification: C11; C14; C23 1 Introduction Stochastic frontier models have been commonly used in the empirical study of firm efficiency and pro- ductivity, since the seminal work of Aigner, Lovell and Schmidt (1977) and Meeusen and van den Broeck (1977). A production frontier represents the maximum amount of output that can be obtained from a given level of inputs. Similarly, cost frontiers describe the minimum level of cost given a certain out- put level and certain input prices. In practice, the actual output of a firm will typically fall below the maximum that is technically possible. The deviation of actual from maximum output is a measure of inefficiency and is the focus of interest in many applications. These models, thus, typically combine £ Corresponding author: Mark Steel, Institute of Mathematics and Statistics, University of Kent at Canterbury, CT2 7NF, U.K.
    [Show full text]