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Exploring horizontal mergers in Swedish district courts using technical and scale efficiency: rejecting convexity in favour of nonconvexity

Author

Listed:
  • Xiaoqing Chen

    (NUIST - Nanjing University of Information Science and Technology)

  • Kristiaan Kerstens

    (LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - ULCO - Université du Littoral Côte d'Opale - Université de Lille - CNRS - Centre National de la Recherche Scientifique)

  • Qingyuan Zhu

    (NUAA - Nanjing University of Aeronautics and Astronautics [Nanjing])

Abstract

Swedish district courts have undergone a major mergers and acquisitions program between 2000 and 2010 to centralize activity in larger and fewer courts. The purpose of this contribution is to conduct an efficiency analysis of these courts to identify the eventual efficiency gains. Distinguishing mainly between technical and scale efficiency and determining the returns to scale of individual observations, we try to find the potential rationales behind this merger wave. We are to the best of our knowledge the first to combine traditional convex with nonconvex nonparametric frontier methods to calculate efficiency before and after the mergers. It turns out that the nonconvex methods provide a more cogent ex post explanation of this historical merger wave aimed at increasing the size of operations. A battery of recent test statistics rejects convexity in favour of nonconvexity.

Suggested Citation

  • Xiaoqing Chen & Kristiaan Kerstens & Qingyuan Zhu, 2025. "Exploring horizontal mergers in Swedish district courts using technical and scale efficiency: rejecting convexity in favour of nonconvexity," Post-Print hal-05368965, HAL.
    • Handle: RePEc:hal:journl:hal-05368965
    DOI: 10.1007/s10479-025-06508-9
    Note: View the original document on HAL open archive server: https://hal.science/hal-05368965v1
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    as
    1. Caves, Richard E., 2007. "In praise of the Old I.O," International Journal of Industrial Organization, Elsevier, vol. 25(1), pages 1-12, February.
    2. Bogetoft, Peter & Wittrup, Jesper, 2021. "Benefit-of-the-doubt approach to workload indicators: Simplifying the use of case weights in court evaluations," Omega, Elsevier, vol. 103(C).
    3. Kerstens, Kristiaan & Vanden Eeckaut, Philippe, 1999. "Estimating returns to scale using non-parametric deterministic technologies: A new method based on goodness-of-fit," European Journal of Operational Research, Elsevier, vol. 113(1), pages 206-214, February.
    4. 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.
    5. Stefan Voigt, 2016. "Determinants of judicial efficiency: a survey," European Journal of Law and Economics, Springer, vol. 42(2), pages 183-208, October.
    6. Cinzia Daraio & Kristiaan H.J. Kerstens & Thyago Celso Cavalcante Nepomuceno & Robin Sickles, 2019. "Productivity And Efficiency Analysis Software: An Exploratory Bibliographical Survey Of The Options," Journal of Economic Surveys, Wiley Blackwell, vol. 33(1), pages 85-100, February.
    7. Dominique Deprins & Léopold Simar & Henry Tulkens, 2006. "Measuring Labor-Efficiency in Post Offices," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 285-309, Springer.
    8. Qianying Jin & Kristiaan Kerstens & Ignace Van de Woestyne, 2024. "Convex and nonconvex nonparametric frontier-based classification methods for anomaly detection," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 46(4), pages 1213-1239, December.
    9. Cinzia Daraio & Kristiaan H.J. Kerstens & Thyago Celso Cavalcante Nepomuceno & Robin Sickles, 2019. "Productivity And Efficiency Analysis Software: An Exploratory Bibliographical Survey Of The Options," Journal of Economic Surveys, Wiley Blackwell, vol. 33(1), pages 85-100, February.
    10. Leleu, Herve, 2006. "A linear programming framework for free disposal hull technologies and cost functions: Primal and dual models," European Journal of Operational Research, Elsevier, vol. 168(2), pages 340-344, January.
    11. 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.
    12. Monastyrenko, Evgenii, 2017. "Eco-efficiency outcomes of mergers and acquisitions in the European electricity industry," Energy Policy, Elsevier, vol. 107(C), pages 258-277.
    13. Troels Kristensen & Peter Bogetoft & Kjeld Pedersen, 2010. "Potential gains from hospital mergers in Denmark," Health Care Management Science, Springer, vol. 13(4), pages 334-345, December.
    14. repec:bla:scandj:v:85:y:1983:i:2:p:181-90 is not listed on IDEAS
    15. Silva, Maria Conceição A., 2018. "Output-specific inputs in DEA: An application to courts of justice in Portugal," Omega, Elsevier, vol. 79(C), pages 43-53.
    16. Podinovski, V. V., 2004. "On the linearisation of reference technologies for testing returns to scale in FDH models," European Journal of Operational Research, Elsevier, vol. 152(3), pages 800-802, February.
    17. Scott E. Atkinson & Jeffrey H. Dorfman, 2009. "Feasible estimation of firm-specific allocative inefficiency through Bayesian numerical methods," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(4), pages 675-697.
    18. Peter Bogetoft & Dexiang Wang, 2005. "Estimating the Potential Gains from Mergers," Journal of Productivity Analysis, Springer, vol. 23(2), pages 145-171, May.
    19. 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.
    20. Chen, Xiaoqing & Kerstens, Kristiaan & Tsionas, Mike, 2024. "Does productivity change at all in Swedish district courts? Empirical analysis focusing on horizontal mergers," Socio-Economic Planning Sciences, Elsevier, vol. 91(C).
    21. Per J. Agrell & Pontus Mattsson & Jonas Månsson, 2020. "Impacts on efficiency of merging the Swedish district courts," Annals of Operations Research, Springer, vol. 288(2), pages 653-679, May.
    22. Michael Gorman & John Ruggiero, 2009. "Evaluating U.S. judicial district prosecutor performance using DEA: are disadvantaged counties more inefficient?," European Journal of Law and Economics, Springer, vol. 27(3), pages 275-283, June.
    23. Massimo Finocchiaro Castro & Calogero Guccio, 2018. "Measuring Potential Efficiency Gains from Mergers of Italian First Instance Courts through Nonparametric Model," Public Finance Review, , vol. 46(1), pages 83-116, January.
    24. Mattsson, Pontus & Tidanå, Claes, 2019. "Potential efficiency effects of merging the Swedish district courts," Socio-Economic Planning Sciences, Elsevier, vol. 67(C), pages 58-68.
    25. Massimo Finocchiaro Castro & Calogero Guccio, 2014. "Searching for the source of technical inefficiency in Italian judicial districts: an empirical investigation," European Journal of Law and Economics, Springer, vol. 38(3), pages 369-391, December.
    26. Cummins, J. David & Tennyson, Sharon & Weiss, Mary A., 1999. "Consolidation and efficiency in the US life insurance industry," Journal of Banking & Finance, Elsevier, vol. 23(2-4), pages 325-357, February.
    27. Kerstens, Kristiaan & Sadeghi, Jafar & Van de Woestyne, Ignace, 2019. "Convex and nonconvex input-oriented technical and economic capacity measures: An empirical comparison," European Journal of Operational Research, Elsevier, vol. 276(2), pages 699-709.
    28. Kristiaan Kerstens & Ignace Van de Woestyne, 2021. "Cost functions are nonconvex in the outputs when the technology is nonconvex: convexification is not harmless," Annals of Operations Research, Springer, vol. 305(1), pages 81-106, October.
    29. Li, Qi & Maasoumi, Esfandiar & Racine, Jeffrey S., 2009. "A nonparametric test for equality of distributions with mixed categorical and continuous data," Journal of Econometrics, Elsevier, vol. 148(2), pages 186-200, February.
    30. Pontus Mattsson & Jonas Månsson & Christian Andersson & Fredrik Bonander, 2018. "A bootstrapped Malmquist index applied to Swedish district courts," European Journal of Law and Economics, Springer, vol. 46(1), pages 109-139, August.
    31. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    32. J Harris & H Ozgen & Y Ozcan, 2000. "Do mergers enhance the performance of hospital efficiency?," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(7), pages 801-811, July.
    33. Oliver Budzinski & Isabel Ruhmer, 2010. "Merger Simulation In Competition Policy: A Survey," Journal of Competition Law and Economics, Oxford University Press, vol. 6(2), pages 277-319.
    34. W. Kip Viscusi & Joseph E. Harrington & John M. Vernon, 2005. "Economics of Regulation and Antitrust, 4th Edition," MIT Press Books, The MIT Press, edition 4, volume 1, number 026222075x, December.
    35. Giacalone, Massimiliano & Nissi, Eugenia & Cusatelli, Carlo, 2020. "Dynamic efficiency evaluation of Italian judicial system using DEA based Malmquist productivity indexes," Socio-Economic Planning Sciences, Elsevier, vol. 72(C).
    36. Caitlin T. O’Loughlin & Paul W. Wilson, 2021. "Benchmarking the performance of US Municipalities," Empirical Economics, Springer, vol. 60(6), pages 2665-2700, June.
    37. Saastamoinen, Antti & Bjørndal, Endre & Bjørndal, Mette, 2017. "Specification of merger gains in the Norwegian electricity distribution industry," Energy Policy, Elsevier, vol. 102(C), pages 96-107.
    38. Matthew Weinberg, 2008. "The Price Effects Of Horizontal Mergers," Journal of Competition Law and Economics, Oxford University Press, vol. 4(2), pages 433-447.
    39. Cesaroni, Giovanni & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2017. "Global and local scale characteristics in convex and nonconvex nonparametric technologies: A first empirical exploration," European Journal of Operational Research, Elsevier, vol. 259(2), pages 576-586.
    40. M. J. Farrell, 1959. "The Convexity Assumption in the Theory of Competitive Markets," Journal of Political Economy, University of Chicago Press, vol. 67(4), pages 377-377.
    41. Paul W. Wilson & Shirong Zhao, 2023. "Investigating the performance of Chinese banks over 2007–2014," Annals of Operations Research, Springer, vol. 321(1), pages 663-692, February.
    42. Walter Briec & Kristiaan Kerstens & Philippe Venden Eeckaut, 2004. "Non-convex Technologies and Cost Functions: Definitions, Duality and Nonparametric Tests of Convexity," Journal of Economics, Springer, vol. 81(2), pages 155-192, February.
    43. Peyrache, Antonio & Zago, Angelo, 2016. "Large courts, small justice!," Omega, Elsevier, vol. 64(C), pages 42-56.
    44. Francesco Aiello & Graziella Bonanno & Francesco Foglia, 2024. "A meta-regression analysis on judicial efficiency literature: the role of methodological and courts diversity," Journal of Applied Economics, Taylor & Francis Journals, vol. 27(1), pages 2284010-228, December.
    45. Kristiaan Kerstens & Ignace Van De Woestyne, 2014. "Solution Methods For Nonconvex Free Disposal Hull Models: A Review And Some Critical Comments," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(01), pages 1-13.
    46. Rezitis, Anthony N., 2008. "Efficiency and productivity effects of bank mergers: Evidence from the Greek banking industry," Economic Modelling, Elsevier, vol. 25(2), pages 236-254, March.
    47. Seiford, Lawrence M. & Zhu, Joe, 1999. "An investigation of returns to scale in data envelopment analysis," Omega, Elsevier, vol. 27(1), pages 1-11, February.
    48. Jacobsen, S E, 1970. "Production Correspondences," Econometrica, Econometric Society, vol. 38(5), pages 754-771, September.
    49. Daraio, Cinzia & Kerstens, Kristiaan & Nepomuceno, Thyago & Sickles, Robin C., 2019. "Empirical Surveys of Frontier Applications: A Meta-Review," Working Papers 19-005, Rice University, Department of Economics.
    50. Farrell, Joseph & Shapiro, Carl, 1990. "Horizontal Mergers: An Equilibrium Analysis," American Economic Review, American Economic Association, vol. 80(1), pages 107-126, March.
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