IDEAS home Printed from https://ideas.repec.org/p/hhs/nhhfms/2020_005.html
   My bibliography  Save this paper

Sampling risk evaluations in a tax fraud case: Some modelling issues

Author

Listed:

Abstract

This work is a follow-up to Lillestøl (2019). The context is the use of sample data to support claims of tax fraud at eateries, where the possibilities of embezzlement are overreporting of take-away sales and underreporting of cash payments. Ratios of sales amounts of opposing types are computed from the sample and used as estimates for the true yearly ratios. Decisions are made by comparison with the reported ratios in the taxpayer’s yearly income statement, allowing for sampling risk. To this end, a “risk distribution” is established and its quantiles used as decision limits. There are different ways of doing the calculation and to establish the accompanying risk distribution, among them models based on Gamma-assumptions, as detailed in Lillestøl (2019). They may lead to different results, more or less favorable to the taxpayer. The chosen method therefore must be fair and defensible. In this connection, some relevant issues have surfaced, mainly related to independence and conditioning. The objective of this paper is to explore these issues and provide some recommendations on the choice of method.

Suggested Citation

  • Lillestøl, Jostein, 2020. "Sampling risk evaluations in a tax fraud case: Some modelling issues," Discussion Papers 2020/5, Norwegian School of Economics, Department of Business and Management Science.
    • Handle: RePEc:hhs:nhhfms:2020_005
    as

    Download full text from publisher

    File URL: https://hdl.handle.net/11250/2654220
    File Function: Full text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dimitris Karlis, 2003. "An EM algorithm for multivariate Poisson distribution and related models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(1), pages 63-77.
    2. Karlis, Dimitris & Ntzoufras, Ioannis, 2005. "Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i10).
    3. Sturtz, Sibylle & Ligges, Uwe & Gelman, Andrew, 2005. "R2WinBUGS: A Package for Running WinBUGS from R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i03).
    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. Sobom M. Somé & Célestin C. Kokonendji & Nawel Belaid & Smail Adjabi & Rahma Abid, 2023. "Bayesian local bandwidths in a flexible semiparametric kernel estimation for multivariate count data with diagnostics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 843-865, September.
    2. Su Pei-Fang & Mau Yu-Lin & Guo Yan & Li Chung-I & Liu Qi & Boice John D. & Shyr Yu, 2017. "Bivariate Poisson models with varying offsets: an application to the paired mitochondrial DNA dataset," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 16(1), pages 47-58, March.
    3. Lachaud, Michée A. & Bravo-Ureta, Boris E., 2022. "A Bayesian statistical analysis of return to agricultural R&D investment in Latin America: Implications for food security," Technology in Society, Elsevier, vol. 70(C).
    4. Luke S. Benz & Michael J. Lopez, 2023. "Estimating the change in soccer’s home advantage during the Covid-19 pandemic using bivariate Poisson regression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(1), pages 205-232, March.
    5. Liang, Zhongyao & Qian, Song S. & Wu, Sifeng & Chen, Huili & Liu, Yong & Yu, Yanhong & Yi, Xuan, 2019. "Using Bayesian change point model to enhance understanding of the shifting nutrients-phytoplankton relationship," Ecological Modelling, Elsevier, vol. 393(C), pages 120-126.
    6. Marc Marí-Dell’Olmo & Miguel Ángel Martínez-Beneito, 2015. "A Multilevel Regression Model for Geographical Studies in Sets of Non-Adjacent Cities," PLOS ONE, Public Library of Science, vol. 10(8), pages 1-12, August.
    7. Zhao, Qing & Boomer, G. Scott & Silverman, Emily & Fleming, Kathy, 2017. "Accounting for the temporal variation of spatial effect improves inference and projection of population dynamics models," Ecological Modelling, Elsevier, vol. 360(C), pages 252-259.
    8. Adrian D Vickers & Claire Ainsworth & Reema Mody & Annika Bergman & Caroline S Ling & Jasmina Medjedovic & Michael Smyth, 2016. "Systematic Review with Network Meta-Analysis: Comparative Efficacy of Biologics in the Treatment of Moderately to Severely Active Ulcerative Colitis," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-21, October.
    9. Marco Gramatica & Peter Congdon & Silvia Liverani, 2021. "Bayesian modelling for spatially misaligned health areal data: A multiple membership approach," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(3), pages 645-666, June.
    10. Yong Li & Zeng Tao & Jun Yu, "undated". "Robust Deviance Information Criterion for Latent Variable Models," Working Papers CoFie-04-2012, Singapore Management University, Sim Kee Boon Institute for Financial Economics.
    11. repec:jss:jstsof:36:c01 is not listed on IDEAS
    12. Abadi, Fitsum & Gimenez, Olivier & Jakober, Hans & Stauber, Wolfgang & Arlettaz, Raphaël & Schaub, Michael, 2012. "Estimating the strength of density dependence in the presence of observation errors using integrated population models," Ecological Modelling, Elsevier, vol. 242(C), pages 1-9.
    13. Bermúdez i Morata, Lluís, 2009. "A priori ratemaking using bivariate Poisson regression models," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 135-141, February.
    14. Chan, Jennifer So Kuen & Wan, Wai Yin, 2014. "Multivariate generalized Poisson geometric process model with scale mixtures of normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 72-87.
    15. Lluis Bermúdez i Morata, 2008. "A priori ratemaking using bivariate poisson regression models," Working Papers XREAP2008-09, Xarxa de Referència en Economia Aplicada (XREAP), revised Jul 2008.
    16. Mirjana Glisovic‐Bensa & Walter W. Piegorsch & Edward J. Bedrick, 2024. "Bayesian benchmark dose risk assessment with mixed‐factor quantal data," Environmetrics, John Wiley & Sons, Ltd., vol. 35(5), August.
    17. Tom Brijs & Dimitris Karlis & Filip Van den Bossche & Geert Wets, 2007. "A Bayesian model for ranking hazardous road sites," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(4), pages 1001-1017, October.
    18. Yang, Ying & Kang, Jian, 2010. "Joint analysis of mixed Poisson and continuous longitudinal data with nonignorable missing values," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 193-207, January.
    19. Będowska-Sójka, Barbara & Kliber, Agata, 2022. "Can cryptocurrencies hedge oil price fluctuations? A pandemic perspective," Energy Economics, Elsevier, vol. 115(C).
    20. Earl W Duncan & Kerrie L Mengersen, 2020. "Comparing Bayesian spatial models: Goodness-of-smoothing criteria for assessing under- and over-smoothing," PLOS ONE, Public Library of Science, vol. 15(5), pages 1-28, May.
    21. repec:jss:jstsof:40:i05 is not listed on IDEAS
    22. Guy Abel & Jakub Bijak & Jonathan J. Forster & James Raymer & Peter W.F. Smith & Jackie S.T. Wong, 2013. "Integrating uncertainty in time series population forecasts: An illustration using a simple projection model," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 29(43), pages 1187-1226.

    More about this item

    Keywords

    Gamma-Beta analysis; Bayesian Gamma-analysis; Risk analysis; Beta-prime distribution; Random arrival models;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hhs:nhhfms:2020_005. 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: Stein Fossen (email available below). General contact details of provider: https://edirc.repec.org/data/dfnhhno.html .

    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.