IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v321y2025i2p644-663.html
   My bibliography  Save this article

Likelihood-ratio test for technological differences in two-stage data envelopment analysis for panel data

Author

Listed:
  • Du, Kai
  • Zelenyuk, Valentin

Abstract

This study explores the question of adapting a likelihood-ratio test in the two-stage data envelopment analysis (DEA) framework, where DEA estimates are regressed against external factors. We focus on the hypotheses of testing the technological difference across time periods (or groups) and propose two bootstrapping procedures. Our Monte Carlo (MC) simulation shows that the proposed test has a substantially better-estimated size for the case of smoothing the ‘spurious ones’, rather than removing them. MC simulation also confirms the curse of dimensionality when the input and output variables increase in the production model. Finally, the proposed test is demonstrated in an empirical illustration.

Suggested Citation

  • Du, Kai & Zelenyuk, Valentin, 2025. "Likelihood-ratio test for technological differences in two-stage data envelopment analysis for panel data," European Journal of Operational Research, Elsevier, vol. 321(2), pages 644-663.
    • Handle: RePEc:eee:ejores:v:321:y:2025:i:2:p:644-663
    DOI: 10.1016/j.ejor.2024.09.039
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221724007409
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2024.09.039?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. Tsionas, Mike & Parmeter, Christopher F. & Zelenyuk, Valentin, 2023. "Bayesian Artificial Neural Networks for frontier efficiency analysis," Journal of Econometrics, Elsevier, vol. 236(2).
    2. Robert C. Feenstra & Robert Inklaar & Marcel P. Timmer, 2015. "The Next Generation of the Penn World Table," American Economic Review, American Economic Association, vol. 105(10), pages 3150-3182, October.
    3. Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2021. "Inference In Dynamic, Nonparametric Models Of Production: Central Limit Theorems For Malmquist Indices," Econometric Theory, Cambridge University Press, vol. 37(3), pages 537-572, June.
    4. Manh Pham & Léopold Simar & Valentin Zelenyuk, 2024. "Statistical Inference for Aggregation of Malmquist Productivity Indices," Operations Research, INFORMS, vol. 72(4), pages 1615-1629, July.
    5. Bădin, Luiza & Daraio, Cinzia & Simar, Léopold, 2012. "How to measure the impact of environmental factors in a nonparametric production model," European Journal of Operational Research, Elsevier, vol. 223(3), pages 818-833.
    6. 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.
    7. Lampe, Hannes W. & Hilgers, Dennis, 2015. "Trajectories of efficiency measurement: A bibliometric analysis of DEA and SFA," European Journal of Operational Research, Elsevier, vol. 240(1), pages 1-21.
    8. 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.
    9. 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.
    10. John S. Liu & Louis Y. Y. Lu & Wen-Min Lu, 2016. "Research Fronts and Prevailing Applications in Data Envelopment Analysis," International Series in Operations Research & Management Science, in: Joe Zhu (ed.), Data Envelopment Analysis, chapter 0, pages 543-574, Springer.
    11. Alois Kneip & Léopold Simar & Paul Wilson, 2011. "A Computationally Efficient, Consistent Bootstrap for Inference with Non-parametric DEA Estimators," Computational Economics, Springer;Society for Computational Economics, vol. 38(4), pages 483-515, November.
    12. Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2008. "Asymptotics And Consistent Bootstraps For Dea Estimators In Nonparametric Frontier Models," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1663-1697, December.
    13. Daraio, Cinzia & Simar, Léopold, 2014. "Directional distances and their robust versions: Computational and testing issues," European Journal of Operational Research, Elsevier, vol. 237(1), pages 358-369.
    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. Alois Kneip & Léopold Simar & Paul W. Wilson, 2016. "Testing Hypotheses in Nonparametric Models of Production," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 435-456, July.
    16. Léopold Simar & Valentin Zelenyuk, 2018. "Central Limit Theorems for Aggregate Efficiency," Operations Research, INFORMS, vol. 66(1), pages 137-149, January.
    17. Cinzia Daraio & Léopold Simar & Paul W. Wilson, 2018. "Central limit theorems for conditional efficiency measures and tests of the ‘separability’ condition in non‐parametric, two‐stage models of production," Econometrics Journal, Royal Economic Society, vol. 21(2), pages 170-191, June.
    18. Simar, Léopold & Zelenyuk, Valentin & Zhao, Shirong, 2024. "Inference for aggregate efficiency: Theory and guidelines for practitioners," European Journal of Operational Research, Elsevier, vol. 316(1), pages 240-254.
    19. 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.
    20. 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.
    21. Liu, John S. & Lu, Louis Y.Y. & Lu, Wen-Min & Lin, Bruce J.Y., 2013. "A survey of DEA applications," Omega, Elsevier, vol. 41(5), pages 893-902.
    22. Daraio, Cinzia & Simar, Leopold & Wilson, Paul, 2018. "Central limit theorems for conditional efficiency measures and tests of the ‘separability’ condition in non-parametric, two-stage models of production," LIDAM Reprints ISBA 2018023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    23. Léopold Simar & Valentin Zelenyuk, 2018. "Improving Finite Sample Approximation by Central Limit Theorems for DEA and FDH efficiency scores," CEPA Working Papers Series WP072018, School of Economics, University of Queensland, Australia.
    24. 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.
    25. Simar, Léopold & W. Wilson, Paul, 2019. "Central limit theorems and inference for sources of productivity change measured by nonparametric Malmquist indices," European Journal of Operational Research, Elsevier, vol. 277(2), pages 756-769.
    26. Tzeremes, Nickolaos G., 2014. "The effect of human capital on countries’ economic efficiency," Economics Letters, Elsevier, vol. 124(1), pages 127-131.
    27. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    28. Robert E. Hall & Charles I. Jones, "undated". "The Productivity of Nations," Working Papers 96012, Stanford University, Department of Economics.
    29. Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2015. "When Bias Kills The Variance: Central Limit Theorems For Dea And Fdh Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 31(2), pages 394-422, April.
    30. Nguyen, Bao Hoang & Simar, Léopold & Zelenyuk, Valentin, 2022. "Data sharpening for improving central limit theorem approximations for data envelopment analysis–type efficiency estimators," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1469-1480.
    31. 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.
    32. Fare, Rolf & Shawna Grosskopf & Mary Norris & Zhongyang Zhang, 1994. "Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries," American Economic Review, American Economic Association, vol. 84(1), pages 66-83, March.
    33. Léopold Simar & Paul Wilson, 2011. "Two-stage DEA: caveat emptor," Journal of Productivity Analysis, Springer, vol. 36(2), pages 205-218, October.
    34. Barro, Robert J. & Lee, Jong Wha, 2013. "A new data set of educational attainment in the world, 1950–2010," Journal of Development Economics, Elsevier, vol. 104(C), pages 184-198.
    35. Psacharopoulos, George, 1994. "Returns to investment in education: A global update," World Development, Elsevier, vol. 22(9), pages 1325-1343, September.
    36. Cinzia Daraio & Léopold Simar, 2007. "Conditional nonparametric frontier models for convex and nonconvex technologies: a unifying approach," Journal of Productivity Analysis, Springer, vol. 28(1), pages 13-32, October.
    37. Zelenyuk, Valentin & Zhao, Shirong, 2024. "Russell and slack-based measures of efficiency: A unifying framework," European Journal of Operational Research, Elsevier, vol. 318(3), pages 867-876.
    38. 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.
    39. Arora, Suchit, 2001. "Health, Human Productivity, And Long-Term Economic Growth," The Journal of Economic History, Cambridge University Press, vol. 61(3), pages 699-749, September.
    40. 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.
    41. Oleg Badunenko & Daniel J. Henderson & Valentin Zelenyuk, 2017. "The Productivity of Nations," Working Papers in Economics & Finance 2017-05, University of Portsmouth, Portsmouth Business School, Economics and Finance Subject Group.
    42. 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.
    43. Simar, Léopold & Zelenyuk, Valentin, 2020. "Improving finite sample approximation by central limit theorems for estimates from Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1002-1015.
    44. Park, B.U. & Jeong, S.-O. & Simar, L., 2010. "Asymptotic distribution of conical-hull estimators of directional edges," LIDAM Reprints ISBA 2010025, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    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. Simar, Léopold & Zelenyuk, Valentin & Zhao, Shirong, 2024. "Inference for aggregate efficiency: Theory and guidelines for practitioners," European Journal of Operational Research, Elsevier, vol. 316(1), pages 240-254.
    2. 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.
    3. Amir Moradi-Motlagh & Ali Emrouznejad, 2022. "The origins and development of statistical approaches in non-parametric frontier models: a survey of the first two decades of scholarly literature (1998–2020)," Annals of Operations Research, Springer, vol. 318(1), pages 713-741, November.
    4. Nguyen, Bao Hoang & Simar, Léopold & Zelenyuk, Valentin, 2022. "Data sharpening for improving central limit theorem approximations for data envelopment analysis–type efficiency estimators," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1469-1480.
    5. Zhichao Wang & Bao Hoang Nguyen & Valentin Zelenyuk, 2024. "Performance analysis of hospitals in Australia and its peers: a systematic and critical review," Journal of Productivity Analysis, Springer, vol. 62(2), pages 139-173, October.
    6. Léopold Simar & Paul W. Wilson, 2023. "Another look at productivity growth in industrialized countries," Journal of Productivity Analysis, Springer, vol. 60(3), pages 257-272, December.
    7. 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.
    8. 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.
    9. Léopold Simar & Paul W. Wilson, 2020. "Hypothesis testing in nonparametric models of production using multiple sample splits," Journal of Productivity Analysis, Springer, vol. 53(3), pages 287-303, June.
    10. Caitlin T. O’Loughlin & Paul W. Wilson, 2021. "Benchmarking the performance of US Municipalities," Empirical Economics, Springer, vol. 60(6), pages 2665-2700, June.
    11. Bao Hoang Nguyen & Léopold Simar & Valentin Zelenyuk, 2021. "Data Sharpening for improving CLT approximations for DEA-type efficiency estimators," CEPA Working Papers Series WP142021, School of Economics, University of Queensland, Australia.
    12. López-Torres, Laura & Johnes, Jill & Elliott, Caroline & Polo, Cristina, 2021. "The effects of competition and collaboration on efficiency in the UK independent school sector," Economic Modelling, Elsevier, vol. 96(C), pages 40-53.
    13. Simar, Léopold & Wilson, Paul W., 2020. "Technical, allocative and overall efficiency: Estimation and inference," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1164-1176.
    14. Kai Du & Allan O’Connor, 2021. "Examining economic complexity as a holistic innovation system effect," Small Business Economics, Springer, vol. 56(1), pages 237-257, January.
    15. Marc Aliana & Diego Prior & Emili Tortosa-Ausina, 2025. "Environmental factors in cross-country productivity growth: A conditional Malmquist Index," Working Papers 2025/01, Economics Department, Universitat Jaume I, Castellón (Spain).
    16. Mike Tsionas & Valentin Zelenyuk, 2021. "Goodness-of-fit in Optimizing Models of Production: A Generalization with a Bayesian Perspective," CEPA Working Papers Series WP182021, School of Economics, University of Queensland, Australia.
    17. Zelenyuk, Valentin & Zhao, Shirong, 2024. "Russell and slack-based measures of efficiency: A unifying framework," European Journal of Operational Research, Elsevier, vol. 318(3), pages 867-876.
    18. José Solana‐Ibáñez & Manuel Caravaca‐Garratón, 2021. "Stakeholder engagement and corporate social reputation: The influence of exogenous factors on efficiency performance (stakeholder engagement and exogenous factors): Stakeholder engagement and exogenou," Corporate Social Responsibility and Environmental Management, John Wiley & Sons, vol. 28(6), pages 1891-1905, November.
    19. Daraio, Cinzia & Simar, Leopold & Wilson, Paul, 2019. "Quality and its impact on efficiency," LIDAM Discussion Papers ISBA 2019004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    20. Léopold Simar & Valentin Zelenyuk & Shirong Zhao, 2023. "Further improvements of finite sample approximation of central limit theorems for envelopment estimators," Journal of Productivity Analysis, Springer, vol. 59(2), pages 189-194, April.

    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:321:y:2025:i:2:p:644-663. 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.