IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v292y2021i3p1115-1132.html
   My bibliography  Save this article

Stochastic frontier models with time-varying conditional variances

Author

Listed:
  • Tsionas, Mike G.
  • Kumbhakar, Subal C.

Abstract

In this paper we introduce stochastic frontier models in which either the inefficiency or the noise component or both the components follow Generalized AutoRegressive Conditional Heteroskedasticity GARCH(1,1) process. Bayesian estimation of the technology parameters are proposed using a half-normal (exponential) distribution for the inefficiency component, and a normal distribution for the noise component. We show, in simulations, that predictions of inefficiency ignoring the GARCH(1,1) process are not aligned with their true values. We use real panel data on electricity distribution and show how to estimate our proposed model, and predict inefficiency. Moreover, we examine the effect of ignoring GARCH specification on economic measures like input elasticities, technical change and returns to scale. We also provide test for GARCH vs no GARCH models using Bayes factors. Finally, we examine variants of the GARCH family such as the ARCH and EGARCH models and we compared GARCH models of different orders.

Suggested Citation

  • Tsionas, Mike G. & Kumbhakar, Subal C., 2021. "Stochastic frontier models with time-varying conditional variances," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1115-1132.
  • Handle: RePEc:eee:ejores:v:292:y:2021:i:3:p:1115-1132
    DOI: 10.1016/j.ejor.2020.11.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221720309541
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2020.11.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Efthymios G. Tsionas, 2006. "Inference in dynamic stochastic frontier models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(5), pages 669-676, July.
    3. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 115(1), pages 147-180.
    4. Caballero, Ricardo J. & Lyons, Richard K., 1992. "External effects in U.S. procyclical productivity," Journal of Monetary Economics, Elsevier, vol. 29(2), pages 209-225, April.
    5. James H. Stock & Mark W. Watson, 2003. "Has the Business Cycle Changed and Why?," NBER Chapters, in: NBER Macroeconomics Annual 2002, Volume 17, pages 159-230, National Bureau of Economic Research, Inc.
    6. Lai, Hung-pin & Kumbhakar, Subal C., 2018. "Panel data stochastic frontier model with determinants of persistent and transient inefficiency," European Journal of Operational Research, Elsevier, vol. 271(2), pages 746-755.
    7. Badunenko, Oleg & Kumbhakar, Subal C., 2017. "Economies of scale, technical change and persistent and time-varying cost efficiency in Indian banking: Do ownership, regulation and heterogeneity matter?," European Journal of Operational Research, Elsevier, vol. 260(2), pages 789-803.
    8. Olivier Blanchard & John Simon, 2001. "The Long and Large Decline in U.S. Output Volatility," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 32(1), pages 135-174.
    9. Kumbhakar, Subal C. & Tsionas, Mike G., 2020. "On the estimation of technical and allocative efficiency in a panel stochastic production frontier system model: Some new formulations and generalizations," European Journal of Operational Research, Elsevier, vol. 287(2), pages 762-775.
    10. Banker, Rajiv D. & Janakiraman, Surya & Natarajan, Ram, 2004. "Analysis of trends in technical and allocative efficiency: An application to Texas public school districts," European Journal of Operational Research, Elsevier, vol. 154(2), pages 477-491, April.
    11. Hung‐pin Lai & Subal C. Kumbhakar, 2020. "Estimation of a dynamic stochastic frontier model using likelihood‐based approaches," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(2), pages 217-247, March.
    12. Margaret M. McConnell & Gabriel Perez-Quiros, 2000. "Output fluctuations in the United States: what has changed since the early 1980s?," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
    13. Jondrow, James & Knox Lovell, C. A. & Materov, Ivan S. & Schmidt, Peter, 1982. "On the estimation of technical inefficiency in the stochastic frontier production function model," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 233-238, August.
    14. James A. Kahn & Margaret M. McConnell & Gabriel Perez-Quiros, 2002. "On the causes of the increased stability of the U.S. economy," Economic Policy Review, Federal Reserve Bank of New York, vol. 8(May), pages 183-202.
    15. Basu, Susanto, 1995. "Intermediate Goods and Business Cycles: Implications for Productivity and Welfare," American Economic Review, American Economic Association, vol. 85(3), pages 512-531, June.
    16. Meeusen, Wim & van den Broeck, Julien, 1977. "Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 435-444, June.
    17. Lai, Hung-pin & Kumbhakar, Subal C., 2019. "Technical and allocative efficiency in a panel stochastic production frontier system model," European Journal of Operational Research, Elsevier, vol. 278(1), pages 255-265.
    18. Peter Bogetoft & Jens Hougaard, 2003. "Rational Inefficiencies," Journal of Productivity Analysis, Springer, vol. 20(3), pages 243-271, November.
    19. Susanto Basu, 1996. "Procyclical Productivity: Increasing Returns or Cyclical Utilization?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 111(3), pages 719-751.
    20. Haelermans, Carla & Ruggiero, John, 2013. "Estimating technical and allocative efficiency in the public sector: A nonparametric analysis of Dutch schools," European Journal of Operational Research, Elsevier, vol. 227(1), pages 174-181.
    21. Banker, Rajiv & Forsund, Finn R. & Zhang, Daqun, 2017. "Use of Data Envelopment Analysis for Incentive Regulation of Electric Distribution Firms," Data Envelopment Analysis Journal, now publishers, vol. 3(1-2), pages 1-47, November.
    22. 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.
    23. Athanassopoulos, Antreas & Gounaris, Chrysostomos, 2001. "Assessing the technical and allocative efficiency of hospital operations in Greece and its resource allocation implications," European Journal of Operational Research, Elsevier, vol. 133(2), pages 416-431, January.
    24. Lai, Hung-pin & Kumbhakar, Subal C., 2018. "Endogeneity in panel data stochastic frontier model with determinants of persistent and transient inefficiency," Economics Letters, Elsevier, vol. 162(C), pages 5-9.
    25. Chang-Jin Kim & Charles R. Nelson, 1999. "Has The U.S. Economy Become More Stable? A Bayesian Approach Based On A Markov-Switching Model Of The Business Cycle," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 608-616, November.
    26. Kumbhakar, Subal C., 2013. "Specification and estimation of multiple output technologies: A primal approach," European Journal of Operational Research, Elsevier, vol. 231(2), pages 465-473.
    27. Peter Bogetoft, 1994. "Incentive Efficient Production Frontiers: An Agency Perspective on DEA," Management Science, INFORMS, vol. 40(8), pages 959-968, August.
    28. Bjørndal, Endre & Bjørndal, Mette & Cullmann, Astrid & Nieswand, Maria, 2018. "Finding the right yardstick: Regulation of electricity networks under heterogeneous environments," European Journal of Operational Research, Elsevier, vol. 265(2), pages 710-722.
    29. 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.
    30. Greene, William, 2005. "Reconsidering heterogeneity in panel data estimators of the stochastic frontier model," Journal of Econometrics, Elsevier, vol. 126(2), pages 269-303, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nicholas Apergis & Stephen M. Miller, 2007. "Total Factor Productivity and Monetary Policy: Evidence from Conditional Volatility," International Finance, Wiley Blackwell, vol. 10(2), pages 131-152, July.
    2. Pontus Mattsson & Jonas Mansson & William H. Greene, 2018. "TFP Change and its Components for Swedish Manufacturing Firms During the 2008-2009 Financial Crisis," Working Papers 18-27, New York University, Leonard N. Stern School of Business, Department of Economics.
    3. Valentin Zelenyuk & Zhichao Wang, 2023. "Random vs. Explained Inefficiency in Stochastic Frontier Analysis: The Case of Queensland Hospitals," CEPA Working Papers Series WP052023, School of Economics, University of Queensland, Australia.
    4. Bernstein, David H., 2020. "An updated assessment of technical efficiency and returns to scale for U.S. electric power plants," Energy Policy, Elsevier, vol. 147(C).
    5. Baležentis, Tomas & Sun, Kai, 2020. "Measurement of technical inefficiency and total factor productivity growth: A semiparametric stochastic input distance frontier approach and the case of Lithuanian dairy farms," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1174-1188.
    6. Belotti, Federico & Ilardi, Giuseppe, 2018. "Consistent inference in fixed-effects stochastic frontier models," Journal of Econometrics, Elsevier, vol. 202(2), pages 161-177.
    7. Ángel L. Martín‐Román & Jaime Cuéllar‐Martín & Alfonso Moral, 2023. "Natural and cyclical unemployment: A stochastic frontier decomposition and economic policy implications," Bulletin of Economic Research, Wiley Blackwell, vol. 75(1), pages 5-39, January.
    8. Ali M. Oumer & Amin Mugera & Michael Burton & Atakelty Hailu, 2022. "Technical efficiency and firm heterogeneity in stochastic frontier models: application to smallholder maize farms in Ethiopia," Journal of Productivity Analysis, Springer, vol. 57(2), pages 213-241, April.
    9. Amjadi, Golnaz & Lundgren, Tommy, 2022. "Is industrial energy inefficiency transient or persistent? Evidence from Swedish manufacturing," Applied Energy, Elsevier, vol. 309(C).
    10. Pontus Mattsson & Jonas Månsson & William H. Greene, 2020. "TFP change and its components for Swedish manufacturing firms during the 2008–2009 financial crisis," Journal of Productivity Analysis, Springer, vol. 53(1), pages 79-93, February.
    11. Musau, Andrew & Kumbhakar, Subal C. & Mydland, Ørjan & Lien, Gudbrand, 2021. "Determinants of allocative and technical inefficiency in stochastic frontier models: An analysis of Norwegian electricity distribution firms," European Journal of Operational Research, Elsevier, vol. 288(3), pages 983-991.
    12. Steven J. Davis & James A. Kahn, 2008. "Interpreting the Great Moderation: Changes in the Volatility of Economic Activity at the Macro and Micro Levels," Journal of Economic Perspectives, American Economic Association, vol. 22(4), pages 155-180, Fall.
    13. Orea, Luis, 2019. "The Econometric Measurement of Firms’ Efficiency," Efficiency Series Papers 2019/02, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).
    14. Gerald A. Carlino & Robert Defina & Keith Sill, 2013. "The Long and Large Decline in State Employment Growth Volatility," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(2‐3), pages 521-534, March.
    15. Irvine, F. Owen & Schuh, Scott, 2007. "Interest sensitivity and volatility reductions: Cross-section evidence," International Journal of Production Economics, Elsevier, vol. 108(1-2), pages 31-42, July.
    16. Badunenko, Oleg & D’Inverno, Giovanna & De Witte, Kristof, 2023. "On distinguishing the direct causal effect of an intervention from its efficiency-enhancing effects," European Journal of Operational Research, Elsevier, vol. 310(1), pages 432-447.
    17. Dimitris Korobilis, 2013. "Assessing the Transmission of Monetary Policy Using Time-varying Parameter Dynamic Factor Models-super-," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 75(2), pages 157-179, April.
    18. Cesaroni, Tatiana & Maccini, Louis & Malgarini, Marco, 2011. "Business cycle stylized facts and inventory behaviour: New evidence for the Euro area," International Journal of Production Economics, Elsevier, vol. 133(1), pages 12-24, September.
    19. Luca Gambetti & Jordi Galí, 2009. "On the Sources of the Great Moderation," American Economic Journal: Macroeconomics, American Economic Association, vol. 1(1), pages 26-57, January.
    20. Alejandro Justiniano & Giorgio E. Primiceri, 2008. "The Time-Varying Volatility of Macroeconomic Fluctuations," American Economic Review, American Economic Association, vol. 98(3), pages 604-641, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:292:y:2021:i:3:p:1115-1132. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.