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A Stochastic Frontier Model with short-run and long-run inefficiency random effects


  • Roberto Colombi


  • Gianmaria Martini


  • Giorgio Vittadini



This paper presents a new stochastic frontier model for panel data. The model takes into account firm unobservable heterogeneity and short-run and long-run sources of inefficiency. Each of these features is modeled by a specific random effect. In this way, firms’ latent heterogeneity is not wrongly modeled as inefficiency, and it is possible to disentangle a time-persistent component from the total inefficiency. Under reasonable assumptions, we show that the closed-skew normal distribution allows us to derive both the log-likelihood function of the model and the posterior expected values of the random effects. The new model is compared with nested models by analyzing the efficiency of firms belonging to different sectors.

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  • Roberto Colombi & Gianmaria Martini & Giorgio Vittadini, 2011. "A Stochastic Frontier Model with short-run and long-run inefficiency random effects," Working Papers 1101, Department of Economics and Technology Management, University of Bergamo.
  • Handle: RePEc:brh:wpaper:1101

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    References listed on IDEAS

    1. Paolo Malighetti & Gianmaria Martini & Stefano Paleari & Renato Redondi, 2007. "An Empirical Investigation on the Efficiency, Capacity and Ownership of Italian Airports," Working Papers 0703, Department of Economics and Technology Management, University of Bergamo.
    2. Subal C. Kumbhakar & Almas Heshmati, 1995. "Efficiency Measurement in Swedish Dairy Farms: An Application of Rotating Panel Data, 1976–88," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 77(3), pages 660-674.
    3. Berta, Paolo & Callea, Giuditta & Martini, Gianmaria & Vittadini, Giorgio, 2010. "The effects of upcoding, cream skimming and readmissions on the Italian hospitals efficiency: A population-based investigation," Economic Modelling, Elsevier, vol. 27(4), pages 812-821, July.
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    Cited by:

    1. Massimo Filippini & William Greene, 2016. "Persistent and transient productive inefficiency: a maximum simulated likelihood approach," Journal of Productivity Analysis, Springer, vol. 45(2), pages 187-196, April.
    2. repec:eee:econom:v:202:y:2018:i:2:p:161-177 is not listed on IDEAS
    3. Chen, Yi-Yi & Schmidt, Peter & Wang, Hung-Jen, 2014. "Consistent estimation of the fixed effects stochastic frontier model," Journal of Econometrics, Elsevier, vol. 181(2), pages 65-76.
    4. Glass, Anthony J. & Kenjegalieva, Karligash & Sickles, Robin C. & Weyman-Jones, Thomas, 2016. "The Spatial Efficiency Multiplier and Random Effects in Spatial Stochastic Frontier Models," Working Papers 16-002, Rice University, Department of Economics.
    5. Lachaud, Michee & Bravo-Ureta, Boris & Ludena, Carlos, 2015. "Agricultural Productivity Growth in Latin America and the Caribbean (LAC): An analysis of Climatic Effects, Convergence, and Catch-up," 2015 Conference, August 9-14, 2015, Milan, Italy 211721, International Association of Agricultural Economists.
    6. Subal Kumbhakar & Anatoly Peresetsky, 2013. "Cost efficiency of Kazakhstan and Russian banks: results from competing panel data models-super-1," Macroeconomics and Finance in Emerging Market Economies, Taylor & Francis Journals, vol. 6(1), pages 88-113, March.
    7. Belotti, Federico & Ilardi, Giuseppe, 2018. "Consistent inference in fixed-effects stochastic frontier models," Journal of Econometrics, Elsevier, vol. 202(2), pages 161-177.
    8. Subal Kumbhakar & Gudbrand Lien & J. Hardaker, 2014. "Technical efficiency in competing panel data models: a study of Norwegian grain farming," Journal of Productivity Analysis, Springer, vol. 41(2), pages 321-337, April.
    9. Roberto Colombi & Subal Kumbhakar & Gianmaria Martini & Giorgio Vittadini, 2014. "Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency," Journal of Productivity Analysis, Springer, vol. 42(2), pages 123-136, October.
    10. Lachaud, Michee Arnold & Bravo-Ureta, Boris E. & Ludena, Carlos E., 2015. "Agricultural productivity growth in Latin America and the Caribbean and other world regions: An analysis of climatic effects, convergence and catch-up," Working Papers 40, University of Connecticut, Department of Agricultural and Resource Economics, Charles J. Zwick Center for Food and Resource Policy.
    11. Makieła, Kamil, 2016. "Bayesian inference in generalized true random-effects model and Gibbs sampling," MPRA Paper 69389, University Library of Munich, Germany.
    12. repec:eee:enepol:v:108:y:2017:i:c:p:606-616 is not listed on IDEAS
    13. William E. Griffiths & Gholamreza Hajargasht, 2015. "Welfare Consequences of Information Aggregation and Optimal Market Size," Department of Economics - Working Papers Series 1190, The University of Melbourne.
    14. Thomas Geissmann & Massimo Filippini & William Greene, 2014. "Persistent and Transient Cost Efficiency – An Application to the Swiss Hydropower Sector," CER-ETH Economics working paper series 16/251, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    15. Kamil Makieła, 2017. "Bayesian Inference and Gibbs Sampling in Generalized True Random-Effects Models," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 9(1), pages 69-95, March.
    16. Griffiths, William E. & Hajargasht, Gholamreza, 2016. "Some models for stochastic frontiers with endogeneity," Journal of Econometrics, Elsevier, vol. 190(2), pages 341-348.

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    Closed-Skew Normal Distribution; Longitudinal Data Analysis; Mixed Models; Stochastic Frontiers;

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