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Spatial stochastic frontier models: accounting for unobserved local determinants of inefficiency

  • Alexandra Schmidt

    ()

  • Ajax Moreira
  • Steven Helfand
  • Thais Fonseca

In this paper, we analyze the productivity of farms across n = 370 municipalities located in the Center-West region of Brazil. We propose a stochastic frontier model with a latent spatial structure to account for possible unknown geographical variation of the outputs. This spatial component is included in the one-sided disturbance term. We explore two different distributions for this term, the exponential and the truncated normal. We use the Bayesian paradigm to fit the proposed models. We also compare between an independent normal prior and a conditional autoregressive prior for these spatial effects. The inference procedure takes explicit account of the uncertainty when considering these spatial effects. As the resultant posterior distribution does not have a closed form, we make use of stochastic simulation techniques to obtain samples from it. Two different model comparison criteria provide support for the importance of including these latent spatial effects, even after considering covariates at the municipal level. Neste texto, analisamos a produtividade de estabelecimentos agrícolas localizados em 370 municípios da região Centro-Oeste do Brasil. Propomos um modelo de fronteira estocástica de produção com estrutura espacial latente que representa os determinantes não-observados da ineficiência da produtividade da agropecuária. Esse componente espacial condiciona a distribuição da ineficiência. Usamos o paradigma bayesiano para estimar os modelos propostos. Foram exploradas duas distribuições diferentes para este termo, a normal truncada e a exponencial, e utilizamos duas especificações para a variável latente, suposta independente entre os municípios, ou dependente dos municípios vizinhos segundo um modelo auto-regressivo espacial. O procedimento de inferência considera explicitamente todas as incertezas quando incluímos o termo espacial. Como a distribuição a posteriori não tem uma expressão analítica, utilizamos técnicas estocásticas da simulação para obter a

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

Volume (Year): 31 (2009)
Issue (Month): 2 (April)
Pages: 101-112

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Handle: RePEc:kap:jproda:v:31:y:2009:i:2:p:101-112
Contact details of provider: Web page: http://www.springerlink.com/link.asp?id=100296

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  1. Julian Besag & Jeremy York & Annie Mollié, 1991. "Bayesian image restoration, with two applications in spatial statistics," Annals of the Institute of Statistical Mathematics, Springer, vol. 43(1), pages 1-20, March.
  2. van den Broeck, Julien & Koop, Gary & Osiewalski, Jacek & Steel, Mark F. J., 1994. "Stochastic frontier models : A Bayesian perspective," Journal of Econometrics, Elsevier, vol. 61(2), pages 273-303, April.
  3. Stevenson, Rodney E., 1980. "Likelihood functions for generalized stochastic frontier estimation," Journal of Econometrics, Elsevier, vol. 13(1), pages 57-66, May.
  4. Tsionas, E.G., 2001. "Stochastic Frontier Models with Random Coefficients," Athens University of Economics and Business 130, Athens University of Economics and Business, Department of International and European Economic Studies.
  5. Greene, William H., 1990. "A Gamma-distributed stochastic frontier model," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 141-163.
  6. Viliam Druska & William C. Horrace, 2002. "Generalized Moments Estimation for Spatial Panel Data: Indonesian Rice Farming," Econometrics 0206004, EconWPA, revised 11 May 2003.
  7. Kumbhakar, Subal C. & Tsionas, Efthymios G., 2005. "Measuring technical and allocative inefficiency in the translog cost system: a Bayesian approach," Journal of Econometrics, Elsevier, vol. 126(2), pages 355-384, June.
  8. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika van der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639.
  9. Helfand, Steven M. & Levine, Edward S., 2004. "Farm size and the determinants of productive efficiency in the Brazilian Center-West," Agricultural Economics, Blackwell, vol. 31(2-3), pages 241-249, December.
  10. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
  11. Alan Gelfand & Alexandra Schmidt & Sudipto Banerjee & C. Sirmans, 2004. "Nonstationary multivariate process modeling through spatially varying coregionalization," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 13(2), pages 263-312, December.
  12. Gamerman, Dani & Moreira, Ajax R. B., 2004. "Multivariate spatial regression models," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 262-281, November.
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