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Spatial Stochastic Frontier Models: accounting for unobserved local determinants of inefficiency

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  • Alexandra M. Schmidt
  • Ajax R. B. Moreira
  • Thais C. O. Fonseca
  • Steven M. Helfand

Abstract

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.

Suggested Citation

  • Alexandra M. Schmidt & Ajax R. B. Moreira & Thais C. O. Fonseca & Steven M. Helfand, 2006. "Spatial Stochastic Frontier Models: accounting for unobserved local determinants of inefficiency," Discussion Papers 1220, Instituto de Pesquisa Econômica Aplicada - IPEA.
  • Handle: RePEc:ipe:ipetds:1220
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    Cited by:

    1. Orea, Luis & Álvarez, Inmaculada C., 2019. "A new stochastic frontier model with cross-sectional effects in both noise and inefficiency terms," Journal of Econometrics, Elsevier, vol. 213(2), pages 556-577.
    2. Alberto Gude & Inmaculada Álvarez & Luis Orea, 2018. "Heterogeneous spillovers among Spanish provinces: a generalized spatial stochastic frontier model," Journal of Productivity Analysis, Springer, vol. 50(3), pages 155-173, December.
    3. Francisco José Areal & Kelvin Balcombe & Richard Tiffin, 2012. "Integrating spatial dependence into Stochastic Frontier Analysis," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 56(4), pages 521-541, October.
    4. Fei Jin & Lung-fei Lee, 2020. "Asymptotic properties of a spatial autoregressive stochastic frontier model," Journal in Spatial Econometrics, Springer, vol. 1(1), pages 1-40, December.
    5. Maria Olivares & Heike Wetzel, 2014. "Editor's Choice Competing in the Higher Education Market: Empirical Evidence for Economies of Scale and Scope in German Higher Education Institutions," CESifo Economic Studies, CESifo, vol. 60(4), pages 653-680.
    6. Areal, Francisco Jose & Balcombe, Kelvin & Tiffin, Richard, 2012. "Integrated spatial dependence into Stochastic Frontier Analysis," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 56(4), pages 1-21, December.
    7. Klein, Nadja & Herwartz, Helmut & Kneib, Thomas, 2020. "Modelling regional patterns of inefficiency: A Bayesian approach to geoadditive panel stochastic frontier analysis with an application to cereal production in England and Wales," Journal of Econometrics, Elsevier, vol. 214(2), pages 513-539.
    8. Alejandro Puerta & Andr'es Ram'irez-Hassan, 2020. "Inferring hidden potentials in analytical regions: uncovering crime suspect communities in Medell\'in," Papers 2009.05360, arXiv.org.
    9. Ioannis Skevas & Alfons Oude Lansink, 2020. "Dynamic Inefficiency and Spatial Spillovers in Dutch Dairy Farming," Journal of Agricultural Economics, Wiley Blackwell, vol. 71(3), pages 742-759, September.
    10. Thomas Graaff, 2020. "On the estimation of spatial stochastic frontier models: an alternative skew-normal approach," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 64(2), pages 267-285, April.
    11. Maria Olivares & Heike Wetzel, 2011. "Competing in the Higher Education Market: Empirical Evidence for Economies of Scale and Scope in German Higher Education Institutions," Economics of Education Working Paper Series 0070, University of Zurich, Department of Business Administration (IBW).
    12. Anthony J. Glass & Karligash Kenjegalieva & Robin Sickles, 2012. "The Effects of Efficiency and TFP Growth on Nitrogen and Sulphur Emissions in Europe: A Multistage Spatial Analysis," Discussion Paper Series 2012_11, Department of Economics, Loughborough University, revised Oct 2012.
    13. Federico Belotti & Giuseppe Ilardi & Andrea Piano Mortari, 2019. "Estimation of Stochastic Frontier Panel Data Models with Spatial Inefficiency," CEIS Research Paper 459, Tor Vergata University, CEIS, revised 30 May 2019.
    14. Pavlyuk, Dmitry, 2011. "Efficiency of broadband internet adoption in European Union member states," MPRA Paper 34183, University Library of Munich, Germany.
    15. Ricardo S. Ehlers, 2011. "Comparison of Bayesian models for production efficiency," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2433-2443, January.
    16. Mari Maté-Sánchez-Val & Antonia Madrid-Guijarro, 2011. "A spatial efficiency index proposal: an empirical application to SMEs productivity," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 47(2), pages 353-371, October.
    17. Gil, Guilherme Dôco Roberti & Costa, Marcelo Azevedo & Lopes, Ana Lúcia Miranda & Mayrink, Vinícius Diniz, 2017. "Spatial statistical methods applied to the 2015 Brazilian energy distribution benchmarking model: Accounting for unobserved determinants of inefficiencies," Energy Economics, Elsevier, vol. 64(C), pages 373-383.
    18. Theodoros Skevas & Jasper Grashuis, 2020. "Technical efficiency and spatial spillovers: Evidence from grain marketing cooperatives in the US Midwest," Agribusiness, John Wiley & Sons, Ltd., vol. 36(1), pages 111-126, January.
    19. Yiorgos Gadanakis & Francisco José Areal, 2020. "Accounting for rainfall and the length of growing season in technical efficiency analysis," Operational Research, Springer, vol. 20(4), pages 2583-2608, December.
    20. A. G. Billé & C. Salvioni & R. Benedetti, 2018. "Modelling spatial regimes in farms technologies," Journal of Productivity Analysis, Springer, vol. 49(2), pages 173-185, June.

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    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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