IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v351y2025i2d10.1007_s10479-025-06508-9.html
   My bibliography  Save this article

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

Author

Listed:
  • Xiaoqing Chen

    (Nanjing University of Information Science and Technology)

  • Kristiaan Kerstens

    (UMR 9221 - LEM - Lille Économie Management)

  • Qingyuan Zhu

    (Nanjing University of Aeronautics & Astronautics)

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," Annals of Operations Research, Springer, vol. 351(2), pages 1319-1351, August.
  • Handle: RePEc:spr:annopr:v:351:y:2025:i:2:d:10.1007_s10479-025-06508-9
    DOI: 10.1007/s10479-025-06508-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-025-06508-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10479-025-06508-9?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

    for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Monastyrenko, Evgenii, 2017. "Eco-efficiency outcomes of mergers and acquisitions in the European electricity industry," Energy Policy, Elsevier, vol. 107(C), pages 258-277.
    8. 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.
    9. repec:bla:scandj:v:85:y:1983:i:2:p:181-90 is not listed on IDEAS
    10. 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.
    11. 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.
    12. Farrell, Joseph & Shapiro, Carl, 1990. "Horizontal Mergers: An Equilibrium Analysis," American Economic Review, American Economic Association, vol. 80(1), pages 107-126, March.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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).
    18. 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.
    19. 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.
    20. 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.
    21. 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).
    22. 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.
    23. 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.
    24. Pontus Mattsson & Jonas Månsson & Christian Andersson & Fredrik Bonander, 2018. "Correction to: A bootstrapped Malmquist index applied to Swedish district courts," European Journal of Law and Economics, Springer, vol. 46(1), pages 141-142, August.
    25. Jacobsen, S E, 1970. "Production Correspondences," Econometrica, Econometric Society, vol. 38(5), pages 754-771, September.
    26. Stefan Voigt, 2016. "Determinants of judicial efficiency: a survey," European Journal of Law and Economics, Springer, vol. 42(2), pages 183-208, October.
    27. 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.
    28. 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.
    29. 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.
    30. Peter Bogetoft & Dexiang Wang, 2005. "Estimating the Potential Gains from Mergers," Journal of Productivity Analysis, Springer, vol. 23(2), pages 145-171, May.
    31. 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.
    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. 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.
    34. 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.
    35. 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.
    36. 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.
    37. 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.
    38. 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.
    39. Caitlin T. O’Loughlin & Paul W. Wilson, 2021. "Benchmarking the performance of US Municipalities," Empirical Economics, Springer, vol. 60(6), pages 2665-2700, June.
    40. 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.
    41. Caves, Richard E., 2007. "In praise of the Old I.O," International Journal of Industrial Organization, Elsevier, vol. 25(1), pages 1-12, February.
    42. 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).
    43. 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.
    44. 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.
    45. 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.
    46. 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.
    47. 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.
    48. Matthew Weinberg, 2008. "The Price Effects Of Horizontal Mergers," Journal of Competition Law and Economics, Oxford University Press, vol. 4(2), pages 433-447.
    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. Ali Emrouznejad & Victor Podinovski, 2025. "In memoriam of Professor Rajiv Banker: New developments in data envelopment analysis and its applications," Annals of Operations Research, Springer, vol. 351(2), pages 1221-1224, August.

    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. 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).
    2. Xiaoqing Chen & Kristiaan Kerstens & Qingyuan Zhu, 2021. "Exploring Horizontal Mergers in Swedish District Courts Using Convex and Nonconvex Technologies: Usefulness of a Conservative Approach," Working Papers 2021-EQM-05, IESEG School of Management.
    3. Kristiaan KERSTENS & Xiaoqing CHEN, 2022. "Evaluating Horizontal Mergers in Swedish District Courts Using Plant Capacity Concepts: With a Focus on Nonconvexity," Working Papers 2022-EQM-02, IESEG School of Management.
    4. Pereira, Miguel Alves & Bădin, Luiza & Kerstens, Kristiaan & Silva, Maria Conceição, 2025. "An integrative approach to reviewing the literature on judicial efficiency in Europe," Socio-Economic Planning Sciences, Elsevier, vol. 98(C).
    5. 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.
    6. Lopes, Nuno Q.M. & Silva, Maria C.A., 2024. "Scale and scope economies in first-instance courts: Portuguese specialized vs non-specialized courts," International Review of Law and Economics, Elsevier, vol. 79(C).
    7. Grammatoula Papaioannou & Victor V. Podinovski, 2025. "Free disposal hull models of multicomponent technologies," Annals of Operations Research, Springer, vol. 351(2), pages 1559-1587, August.
    8. 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.
    9. Jonas Månsson & Christian Andersson & Fredrik Bonander, 2022. "What lessons can be learned from cost efficiency? The case of Swedish district courts," European Journal of Law and Economics, Springer, vol. 54(3), pages 431-451, December.
    10. Kerstens, Kristiaan & Sadeghi, Jafar & Toloo, Mehdi & Van de Woestyne, Ignace, 2022. "Procedures for ranking technical and cost efficient units: With a focus on nonconvexity," European Journal of Operational Research, Elsevier, vol. 300(1), pages 269-281.
    11. 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.
    12. Kerstens, Kristiaan & O’Donnell, Christopher & Van de Woestyne, Ignace, 2019. "Metatechnology frontier and convexity: A restatement," European Journal of Operational Research, Elsevier, vol. 275(2), pages 780-792.
    13. 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.
    14. Zhou, Wenzhuo & Shen, Zhiyang & Vardanyan, Michael & Song, Malin, 2025. "Assessing energy transition using exponential production technology under different convexity assumptions," Energy Economics, Elsevier, vol. 146(C).
    15. Kristiaan Kerstens & Ignace Van de Woestyne, 2018. "Enumeration algorithms for FDH directional distance functions under different returns to scale assumptions," Annals of Operations Research, Springer, vol. 271(2), pages 1067-1078, December.
    16. 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.
    17. Tavakoli, Ibrahim M. & Mostafaee, Amin, 2019. "Free disposal hull efficiency scores of units with network structures," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1027-1036.
    18. Mahmood Mehdiloo & Jafar Sadeghi & Kristiaan Kerstens, 2024. "Top Down Axiomatic Modeling of Metatechnologies and Evaluating Directional Economic Efficiency," Working Papers 2024-EQM-03, IESEG School of Management.
    19. Nguyen, Bao Hoang & Simar, Léopold & Zelenyuk, Valentin, 2021. "Data sharpening for improving CLT approximations for DEA-type efficiency estimators," LIDAM Discussion Papers ISBA 2021033, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    20. Kristof Witte & Rui Marques, 2011. "Big and beautiful? On non-parametrically measuring scale economies in non-convex technologies," Journal of Productivity Analysis, Springer, vol. 35(3), pages 213-226, June.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:spr:annopr:v:351:y:2025:i:2:d:10.1007_s10479-025-06508-9. 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.