IDEAS home Printed from https://ideas.repec.org/a/kap/jproda/v43y2015i2p199-214.html
   My bibliography  Save this article

Categorical data in local maximum likelihood: theory and applications to productivity analysis

Author

Listed:
  • Byeong Park
  • Léopold Simar
  • Valentin Zelenyuk

Abstract

In this paper we consider estimation of models popular in efficiency and productivity analysis (such as the stochastic frontier model, truncated regression model, etc.) via the local maximum likelihood method, generalizing this method here to allow for not only continuous but also discrete regressors. We provide asymptotic theory, some evidence from simulations, and illustrate the method with an empirical example. Our methodology and theory can also be adapted for other models where a likelihood of the unknown functions can be used to identify and estimate the underlying model. Simulation results indicate flexibility of the approach and good performances in various complex scenarios, even with moderate sample sizes. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Byeong Park & Léopold Simar & Valentin Zelenyuk, 2015. "Categorical data in local maximum likelihood: theory and applications to productivity analysis," Journal of Productivity Analysis, Springer, vol. 43(2), pages 199-214, April.
    • Handle: RePEc:kap:jproda:v:43:y:2015:i:2:p:199-214
    DOI: 10.1007/s11123-014-0394-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11123-014-0394-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11123-014-0394-y?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Léopold Simar & Valentin Zelenyuk, 2011. "Stochastic FDH/DEA estimators for frontier analysis," Journal of Productivity Analysis, Springer, vol. 36(1), pages 1-20, August.
    2. Bădin, Luiza & Simar, Léopold, 2009. "A Bias-Corrected Nonparametric Envelopment Estimator Of Frontiers," Econometric Theory, Cambridge University Press, vol. 25(5), pages 1289-1318, October.
    3. Leopold Simar & Valentin Zelenyuk, 2006. "On Testing Equality of Distributions of Technical Efficiency Scores," Econometric Reviews, Taylor & Francis Journals, vol. 25(4), pages 497-522.
    4. Peter Hall & Qi Li & Jeffrey S. Racine, 2007. "Nonparametric Estimation of Regression Functions in the Presence of Irrelevant Regressors," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 784-789, November.
    5. Park, Byeong U. & Simar, Léopold & Zelenyuk, Valentin, 2008. "Local likelihood estimation of truncated regression and its partial derivatives: Theory and application," Journal of Econometrics, Elsevier, vol. 146(1), pages 185-198, September.
    6. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    7. Subodh Kumar & R. Robert Russell, 2002. "Technological Change, Technological Catch-up, and Capital Deepening: Relative Contributions to Growth and Convergence," American Economic Review, American Economic Association, vol. 92(3), pages 527-548, June.
    8. Markus Frölich, 2006. "Non-parametric regression for binary dependent variables," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 511-540, November.
    9. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    10. 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.
    11. Park, B.U. & Simar, L. & Weiner, Ch., 2000. "The Fdh Estimator For Productivity Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 16(6), pages 855-877, December.
    12. Daniel J. Henderson & Valentin Zelenyuk, 2007. "Testing for (Efficiency) Catching-up," Southern Economic Journal, John Wiley & Sons, vol. 73(4), pages 1003-1019, April.
    13. Valentin Zelenyuk & Vitaliy Zheka, 2006. "Corporate Governance and Firm’s Efficiency: The Case of a Transitional Country, Ukraine," Journal of Productivity Analysis, Springer, vol. 25(1), pages 143-157, April.
    14. Simar, Leopold & Wilson, Paul W., 2007. "Estimation and inference in two-stage, semi-parametric models of production processes," Journal of Econometrics, Elsevier, vol. 136(1), pages 31-64, January.
    15. 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.
    16. Jeffery Racine & Jeffrey Hart & Qi Li, 2006. "Testing the Significance of Categorical Predictor Variables in Nonparametric Regression Models," Econometric Reviews, Taylor & Francis Journals, vol. 25(4), pages 523-544.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cristian Barra & Raffaele Lagravinese & Roberto Zotti, 2022. "Exploring hospital efficiency within and between Italian regions: new empirical evidence," Journal of Productivity Analysis, Springer, vol. 57(3), pages 269-284, June.
    2. Tsionas, Mike & Parmeter, Christopher F. & Zelenyuk, Valentin, 2023. "Bayesian Artificial Neural Networks for frontier efficiency analysis," Journal of Econometrics, Elsevier, vol. 236(2).
    3. Worthington, Andrew C. & Zelenyuk, Valentin, 2018. "Data envelopment analysis, truncated regression and double-bootstrap for panel data with application to Chinese bankingAuthor-Name: Du, Kai," European Journal of Operational Research, Elsevier, vol. 265(2), pages 748-764.
    4. Subal C. Kumbhakar & Christopher F. Parmeter & Valentin Zelenyuk, 2022. "Stochastic Frontier Analysis: Foundations and Advances I," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 8, pages 331-370, Springer.
    5. Tsionas, Mike G., 2021. "Optimal combinations of stochastic frontier and data envelopment analysis models," European Journal of Operational Research, Elsevier, vol. 294(2), pages 790-800.
    6. Taining Wang & Feng Yao & Subal C. Kumbhakar, 2024. "A flexible stochastic production frontier model with panel data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(4), pages 564-588, June.
    7. Fan Zhang & Joshua Hall & Feng Yao, 2018. "Does Economic Freedom Affect The Production Frontier? A Semiparametric Approach With Panel Data," Economic Inquiry, Western Economic Association International, vol. 56(2), pages 1380-1395, April.
    8. Robin C. Sickles & Wonho Song & Valentin Zelenyuk, 2018. "Econometric Analysis of Productivity: Theory and Implementation in R," CEPA Working Papers Series WP082018, School of Economics, University of Queensland, Australia.
    9. Valentin Zelenyuk, 2019. "Data Envelopment Analysis and Business Analytics: The Big Data Challenges and Some Solutions," CEPA Working Papers Series WP072019, School of Economics, University of Queensland, Australia.
    10. Kelly D.T.Trinh & Valentin Zelenyuk, 2015. "Productivity Growth and Convergence: Revisiting Kumar and Russell (2002)," CEPA Working Papers Series WP112015, School of Economics, University of Queensland, Australia.
    11. Yao, Feng & Wang, Taining & Tian, Jinjing & Kumbhakar, Subal C., 2018. "Estimation of a smooth coefficient zero-inefficiency panel stochastic frontier model: A semiparametric approach," Economics Letters, Elsevier, vol. 166(C), pages 25-30.
    12. Christopher F. Parmeter & Léopold Simar & Ingrid Van Keilegom & Valentin Zelenyuk, 2024. "Inference in the nonparametric stochastic frontier model," Econometric Reviews, Taylor & Francis Journals, vol. 43(7), pages 518-539, August.
    13. Lopez Gomez, Daniel & Parmeter, Christopher F., 2020. "Smooth coefficient estimation of stochastic frontier models," Economics Letters, Elsevier, vol. 193(C).
    14. 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.
    15. Christopher F. Parmeter & Valentin Zelenyuk, 2019. "Combining the Virtues of Stochastic Frontier and Data Envelopment Analysis," Operations Research, INFORMS, vol. 67(6), pages 1628-1658, November.
    16. Bao Hoang Nguyen & Robin C. Sickles & Valentin Zelenyuk, 2022. "Efficiency Analysis with Stochastic Frontier Models Using Popular Statistical Softwares," Springer Books, in: Duangkamon Chotikapanich & Alicia N. Rambaldi & Nicholas Rohde (ed.), Advances in Economic Measurement, chapter 0, pages 129-171, Springer.
    17. Kok Fong See & Shawna Grosskopf & Vivian Valdmanis & Valentin Zelenyuk, 2021. "What do we know from the vast literature on efficiency and productivity in healthcare? A Systematic Review and Bibliometric Analysis," CEPA Working Papers Series WP072021, School of Economics, University of Queensland, Australia.
    18. Léopold Simar & Paul W. Wilson, 2023. "Nonparametric, Stochastic Frontier Models with Multiple Inputs and Outputs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(4), pages 1391-1403, October.
    19. Christopher F. Parmeter & Valentin Zelenyuk, 2016. "A Bridge Too Far? The State of the Art in Combining the Virtues of Stochastic Frontier Analysis and Data Envelopement Analysis," Working Papers 2016-10, University of Miami, Department of Economics.
    20. Quaranta, Anna Grazia & Raffoni, Anna & Visani, Franco, 2018. "A multidimensional approach to measuring bank branch efficiency," European Journal of Operational Research, Elsevier, vol. 266(2), pages 746-760.
    21. Mike Tsionas & Christopher F. Parmeter & Valentin Zelenyuk, 2021. "Bridging the Divide? Bayesian Artificial Neural Networks for Frontier Efficiency Analysis," CEPA Working Papers Series WP082021, School of Economics, University of Queensland, Australia.

    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. Léopold Simar & Ingrid Keilegom & Valentin Zelenyuk, 2017. "Nonparametric least squares methods for stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 47(3), pages 189-204, June.
    2. Sickles, Robin C. & Song, Wonho & Zelenyuk, Valentin, 2018. "Econometric Analysis of Productivity: Theory and Implementation in R," Working Papers 18-008, Rice University, Department of Economics.
    3. Simar, Leopold & Zelenyuk, Valentin, 2011. "To Smooth or Not to Smooth? The Case of Discrete Variables in Nonparametric Regressions," LIDAM Discussion Papers ISBA 2011042, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Klishchuk Bogdan & Zelenyuk Valentin, 2012. "Impact of Services LIberalization on Firm Level Productivity in Eastern Europe and Central Asia," EERC Working Paper Series 12/03e, EERC Research Network, Russia and CIS.
    5. Shiu, Alice & Zelenyuk, Valentin, 2009. "Production Efficiency versus Ownership: The Case of China," MPRA Paper 23760, University Library of Munich, Germany, revised 22 Mar 2010.
    6. Chowdhury, Hedayet & Zelenyuk, Valentin, 2016. "Performance of hospital services in Ontario: DEA with truncated regression approach," Omega, Elsevier, vol. 63(C), pages 111-122.
    7. Léopold Simar & Paul W. Wilson, 2015. "Statistical Approaches for Non-parametric Frontier Models: A Guided Tour," International Statistical Review, International Statistical Institute, vol. 83(1), pages 77-110, April.
    8. Li, Degui & Simar, Léopold & Zelenyuk, Valentin, 2016. "Generalized nonparametric smoothing with mixed discrete and continuous data," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 424-444.
    9. Valentin Zelenyuk, 2019. "Data Envelopment Analysis and Business Analytics: The Big Data Challenges and Some Solutions," CEPA Working Papers Series WP072019, School of Economics, University of Queensland, Australia.
    10. Subal C. Kumbhakar & Christopher F. Parmeter & Valentin Zelenyuk, 2022. "Stochastic Frontier Analysis: Foundations and Advances I," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 8, pages 331-370, Springer.
    11. Halkos, George E. & Tzeremes, Nickolaos G., 2013. "A conditional directional distance function approach for measuring regional environmental efficiency: Evidence from UK regions," European Journal of Operational Research, Elsevier, vol. 227(1), pages 182-189.
    12. Minegishi, Kota, 2013. "Explaining Production Heterogeneity By Contextual Environments: Two-Stage DEA Application to Technical Change Measurement," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 150289, Agricultural and Applied Economics Association.
    13. Natalya Zelenyuk & Valentin Zelenyuk, 2015. "Productivity Drivers of Efficiency in Banking: Importance of Model Specifications," CEPA Working Papers Series WP082015, School of Economics, University of Queensland, Australia.
    14. Camilla Mastromarco & Léopold Simar, 2015. "Effect of FDI and Time on Catching Up: New Insights from a Conditional Nonparametric Frontier Analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(5), pages 826-847, August.
    15. Natalya Zelenyuk & Valentin Zelenyuk, 2014. "Regional and Ownership Drivers of Bank Efficiency," CEPA Working Papers Series WP112014, School of Economics, University of Queensland, Australia.
    16. George Halkos & Nickolaos Tzeremes, 2014. "Measuring the effect of Kyoto protocol agreement on countries’ environmental efficiency in CO 2 emissions: an application of conditional full frontiers," Journal of Productivity Analysis, Springer, vol. 41(3), pages 367-382, June.
    17. Pavlo Demchuk & Valentin Zelenyuk, 2009. "Testing differences in efficiency of regions within a country: the case of Ukraine," Journal of Productivity Analysis, Springer, vol. 32(2), pages 81-102, October.
    18. De Witte, Kristof & Mika, Kortelainen, 2009. "Blaming the exogenous environment? Conditional efficiency estimation with continuous and discrete exogenous variables," MPRA Paper 14034, University Library of Munich, Germany.
    19. Camilla Mastromarco & Léopold Simar, 2021. "Latent heterogeneity to evaluate the effect of human capital on world technology frontier," Journal of Productivity Analysis, Springer, vol. 55(2), pages 71-89, April.
    20. Christopher F. Parmeter & Hung-Jen Wang & Subal C. Kumbhakar, 2017. "Nonparametric estimation of the determinants of inefficiency," Journal of Productivity Analysis, Springer, vol. 47(3), pages 205-221, June.

    More about this item

    Keywords

    Stochastic frontier models; Truncated regression; Local maximum likelihood; Nonparametric smoothing; Categorical variables; C13; C14; C2;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables

    Statistics

    Access and download statistics

    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:kap:jproda:v:43:y:2015:i:2:p:199-214. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.