IDEAS home Printed from https://ideas.repec.org/a/spr/cejnor/v25y2017i2d10.1007_s10100-016-0465-4.html
   My bibliography  Save this article

Stochastic sensitivity analysis of concentration measures

Author

Listed:
  • Martin Bod’a

    (Matej Bel University, Faculty of Economics)

Abstract

The paper extends the traditional approach to measuring market concentration by embracing an element of stochasticity that should reflect the analyst’s uncertainty associated with the future development regarding concentration on the market. Whereas conventional practice relies on deterministic assessments of a market concentration measure with the use of current market shares, this says nothing about possible changes that may happen even in a near future. The paper proposes to model the analyst’s beliefs by dint of a suitable joint probability distribution for future market shares and demonstrates how this analytic framework may be employed for regulatory purposes. A total of four candidates for the joint probability distribution of market shares are considered—the Dirichlet distribution, the conditional normal distribution, the Gaussian copula with conditional beta marginals and the predictive distribution arising from the market share attraction model—and it is shown how their hyperparameters can be elicited so that a minimum burden is placed on the analyst. The proposed procedure for stochastic sensitivity analysis of concentration measures is demonstrated in a case study oriented on the Slovak banking sector.

Suggested Citation

  • Martin Bod’a, 2017. "Stochastic sensitivity analysis of concentration measures," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(2), pages 441-471, June.
    • Handle: RePEc:spr:cejnor:v:25:y:2017:i:2:d:10.1007_s10100-016-0465-4
    DOI: 10.1007/s10100-016-0465-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10100-016-0465-4
    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/s10100-016-0465-4?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. Ashraf Gouda & Tamás Szántai, 2010. "On numerical calculation of probabilities according to Dirichlet distribution," Annals of Operations Research, Springer, vol. 177(1), pages 185-200, June.
    2. Golan, Amos & Judge, George & Perloff, Jeffrey M, 1996. "Estimating the Size Distribution of Firms Using Government Summary Statistics," Journal of Industrial Economics, Wiley Blackwell, vol. 44(1), pages 69-80, March.
    3. Nicola Cetorelli, 1999. "Competitive analysis in banking: appraisal of the methodologies," Economic Perspectives, Federal Reserve Bank of Chicago, vol. 23(Q I), pages 2-15.
    4. I. Brezina & J. Pekár & Z. Čičková & M. Reiff, 2016. "Herfindahl–Hirschman index level of concentration values modification and analysis of their change," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 24(1), pages 49-72, March.
    5. Opgen-Rhein Rainer & Strimmer Korbinian, 2007. "Accurate Ranking of Differentially Expressed Genes by a Distribution-Free Shrinkage Approach," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 6(1), pages 1-20, February.
    6. Schäfer Juliane & Strimmer Korbinian, 2005. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
    7. Dirk Knol & Jos Berge, 1989. "Least-squares approximation of an improper correlation matrix by a proper one," Psychometrika, Springer;The Psychometric Society, vol. 54(1), pages 53-61, March.
    8. Qichang Ye & Zongling Xu & Dan Fang, 2012. "Market structure, performance, and efficiency of the Chinese banking sector," Economic Change and Restructuring, Springer, vol. 45(4), pages 337-358, November.
    9. Fry, Jane M. & Fry, Tim R. L. & McLaren, Keith R., 1996. "The stochastic specification of demand share equations: Restricting budget shares to the unit simplex," Journal of Econometrics, Elsevier, vol. 73(2), pages 377-385, August.
    10. Woodland, A. D., 1979. "Stochastic specification and the estimation of share equations," Journal of Econometrics, Elsevier, vol. 10(3), pages 361-383, August.
    11. Serge Provost & Edmund Rudiuk, 1996. "The exact distribution of indefinite quadratic forms in noncentral normal vectors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(2), pages 381-394, June.
    12. Eric Nauenberg & Kisalaya Basu & Harish Chand, 1997. "Hirschman-Herfindahl index determination under incomplete information," Applied Economics Letters, Taylor & Francis Journals, vol. 4(10), pages 639-642.
    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. Martin Boďa & Emília Zimková, 2021. "A DEA model for measuring financial intermediation," Economic Change and Restructuring, Springer, vol. 54(2), pages 339-370, May.

    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. Maurizio Naldi & Marta Flamini, 2018. "Dynamics of the Hirschman–Herfindahl Index under New Market Entries," Economic Papers, The Economic Society of Australia, vol. 37(3), pages 344-362, September.
    2. Mr. Jorge A Chan-Lau, 2017. "Variance Decomposition Networks: Potential Pitfalls and a Simple Solution," IMF Working Papers 2017/107, International Monetary Fund.
    3. Korbinian Strimmer, 2008. "Comments on: Augmenting the bootstrap to analyze high dimensional genomic data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 25-27, May.
    4. José M. R. Murteira & Joaquim J. S. Ramalho, 2016. "Regression Analysis of Multivariate Fractional Data," Econometric Reviews, Taylor & Francis Journals, vol. 35(4), pages 515-552, April.
    5. Lim Johan & Kim Jayoun & Kim Sang-cheol & Yu Donghyeon & Kim Kyunga & Kim Byung Soo, 2012. "Detection of Differentially Expressed Gene Sets in a Partially Paired Microarray Data Set," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(3), pages 1-30, February.
    6. John Mullahy, 2010. "Multivariate Fractional Regression Estimation of Econometric Share Models," NBER Working Papers 16354, National Bureau of Economic Research, Inc.
    7. Ján Derco, 2022. "The Impacts of the COVID-19 Pandemic on the Tour Operator Market—The Case of Slovakia," JRFM, MDPI, vol. 15(10), pages 1-8, October.
    8. Vera Djordjilović & Monica Chiogna & Chiara Romualdi, 2020. "Simulating gene silencing through intervention analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 887-907, August.
    9. Hannart, Alexis & Naveau, Philippe, 2014. "Estimating high dimensional covariance matrices: A new look at the Gaussian conjugate framework," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 149-162.
    10. Avagyan, Vahe & Nogales, Francisco J., 2015. "D-trace Precision Matrix Estimation Using Adaptive Lasso Penalties," DES - Working Papers. Statistics and Econometrics. WS 21775, Universidad Carlos III de Madrid. Departamento de Estadística.
    11. Paris, Quirino & Caracciolo, Francesco, 2012. "Quantity Versus Shares in Estimating Demand Systems," Working Papers 124575, University of California, Davis, Department of Agricultural and Resource Economics.
    12. Chotikapanich, Duangkamon & Griffiths, William E, 2002. "Estimating Lorenz Curves Using a Dirichlet Distribution," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 290-295, April.
    13. Jianqing Fan & Xu Han, 2017. "Estimation of the false discovery proportion with unknown dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1143-1164, September.
    14. Wang Xiaoming & Dinu Irina & Liu Wei & Yasui Yutaka, 2011. "Linear Combination Test for Hierarchical Gene Set Analysis," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-18, March.
    15. Kim, Michael Jong & Jiang, Rui & Makis, Viliam & Lee, Chi-Guhn, 2011. "Optimal Bayesian fault prediction scheme for a partially observable system subject to random failure," European Journal of Operational Research, Elsevier, vol. 214(2), pages 331-339, October.
    16. René Henrion & Andris Möller, 2012. "A Gradient Formula for Linear Chance Constraints Under Gaussian Distribution," Mathematics of Operations Research, INFORMS, vol. 37(3), pages 475-488, August.
    17. Marcello Messori, 2009. "Consolidation, Ownership Structure and Efficiency in the Italian Banking System," Springer Books, in: Damiano Bruno Silipo (ed.), The Banks and the Italian Economy, chapter 0, pages 211-243, Springer.
    18. Seunghwan Lee & Sang Cheol Kim & Donghyeon Yu, 2023. "An efficient GPU-parallel coordinate descent algorithm for sparse precision matrix estimation via scaled lasso," Computational Statistics, Springer, vol. 38(1), pages 217-242, March.
    19. Sherrill Shaffer, 2002. "Conduct in a Banking Monopoly," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 20(3), pages 221-238, May.
    20. Bala Rajaratnam & Dario Vincenzi, 2016. "A theoretical study of Stein's covariance estimator," Biometrika, Biometrika Trust, vol. 103(3), pages 653-666.

    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:cejnor:v:25:y:2017:i:2:d:10.1007_s10100-016-0465-4. 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.