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One-Step and Two-Step Estimation of the Effects of Exogenous Variables on Technical Efficiency Levels

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  • Hung-jen Wang
  • Peter Schmidt

Abstract

Consider a stochastic frontier model with one-sided inefficiency u, and suppose that the scale of u depends on some variables (firm characteristics) z. A “one-step” model specifies both the stochastic frontier and the way in which u depends on z, and can be estimated in a single step, for example by maximum likelihood. This is in contrast to a “two-step” procedure, where the first step is to estimate a standard stochastic frontier model, and the second step is to estimate the relationship between (estimated) u and z. In this paper we propose a class of one-step models based on the “scaling property” that u equals a function of z times a one-sided error u * whose distribution does not depend on z. We explain theoretically why two-step procedures are biased, and we present Monte Carlo evidence showing that the bias can be very severe. This evidence argues strongly for one-step models whenever one is interested in the effects of firm characteristics on efficiency levels. Copyright Kluwer Academic Publishers 2002

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File URL: http://hdl.handle.net/10.1023/A:1016565719882
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Bibliographic Info

Article provided by Springer in its journal Journal of Productivity Analysis.

Volume (Year): 18 (2002)
Issue (Month): 2 (September)
Pages: 129-144

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Handle: RePEc:kap:jproda:v:18:y:2002:i:2:p:129-144

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Web page: http://www.springerlink.com/link.asp?id=100296

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Keywords: technical efficiency; stochastic frontiers;

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  1. Battese, G E & Coelli, T J, 1995. "A Model for Technical Inefficiency Effects in a Stochastic Frontier Production Function for Panel Data," Empirical Economics, Springer, vol. 20(2), pages 325-32.
  2. Caudill, Steven B & Ford, Jon M & Gropper, Daniel M, 1995. "Frontier Estimation and Firm-Specific Inefficiency Measures in the Presence of Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 105-11, January.
  3. Kumbhakar, Subal C & Ghosh, Soumendra & McGuckin, J Thomas, 1991. "A Generalized Production Frontier Approach for Estimating Determinants of Inefficiency in U.S. Dairy Farms," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(3), pages 279-86, July.
  4. RITTER, Christian & SIMAR, Leopold, 1994. "Pitfalls of Normal-Gamma Stochastic Frontier Models," CORE Discussion Papers 1994041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Reifschneider, David & Stevenson, Rodney, 1991. "Systematic Departures from the Frontier: A Framework for the Analysis of Firm Inefficiency," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(3), pages 715-23, August.
  6. Battese, George E. & Coelli, Tim J., 1988. "Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data," Journal of Econometrics, Elsevier, vol. 38(3), pages 387-399, July.
  7. Caudill, Steven B. & Ford, Jon M., 1993. "Biases in frontier estimation due to heteroscedasticity," Economics Letters, Elsevier, vol. 41(1), pages 17-20.
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