IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/100217.html

Type I and Type II Error Probabilities in the Courtroom

Author

Listed:
  • Kanaya, Shin
  • Taylor, Luke

Abstract

We estimate the likelihood of miscarriages of justice by reframing the problem in the context of misclassified binary choice models. The estimator is based on new nonparametric identification results, for which we provide methods to empirically test the key identifying assumptions and alternative identification schemes for when these checks fail. Blacks are found to have both a higher probability of conviction when innocent and a higher probability of acquittal when guilty, relative to whites. We go on to show that this seemingly contradictory result is, in fact, consistent with a model where both police and judges discriminate against blacks.

Suggested Citation

  • Kanaya, Shin & Taylor, Luke, 2020. "Type I and Type II Error Probabilities in the Courtroom," MPRA Paper 100217, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:100217
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/100217/1/MPRA_paper_100217.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gordon B. Dahl & Andreas Ravndal Kostøl & Magne Mogstad, 2014. "Family Welfare Cultures," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(4), pages 1711-1752.
    2. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
    3. Magnac, Thierry & Maurin, Eric, 2007. "Identification and information in monotone binary models," Journal of Econometrics, Elsevier, vol. 139(1), pages 76-104, July.
    4. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
    5. A. Belloni & D. Chen & V. Chernozhukov & C. Hansen, 2012. "Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain," Econometrica, Econometric Society, vol. 80(6), pages 2369-2429, November.
    6. Steven T. Berry & Philip A. Haile, 2014. "Identification in Differentiated Products Markets Using Market Level Data," Econometrica, Econometric Society, vol. 82, pages 1749-1797, September.
    7. Chuan Goh, 2017. "Rate-Optimal Estimation of the Intercept in a Semiparametric Sample-Selection Model," Papers 1710.01423, arXiv.org, revised Sep 2018.
    8. Anna Aizer & Joseph J. Doyle, 2015. "Juvenile Incarceration, Human Capital, and Future Crime: Evidence from Randomly Assigned Judges," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 130(2), pages 759-803.
    9. Joseph G. Altonji & Richard K. Mansfield, 2018. "Estimating Group Effects Using Averages of Observables to Control for Sorting on Unobservables: School and Neighborhood Effects," American Economic Review, American Economic Association, vol. 108(10), pages 2902-2946, October.
    10. Manudeep Bhuller & Gordon B. Dahl & Katrine V. Løken & Magne Mogstad, 2020. "Incarceration, Recidivism, and Employment," Journal of Political Economy, University of Chicago Press, vol. 128(4), pages 1269-1324.
    11. Hausman, J. A. & Abrevaya, Jason & Scott-Morton, F. M., 1998. "Misclassification of the dependent variable in a discrete-response setting," Journal of Econometrics, Elsevier, vol. 87(2), pages 239-269, September.
    12. Lewbel, Arthur, 2000. "Identification Of The Binary Choice Model With Misclassification," Econometric Theory, Cambridge University Press, vol. 16(4), pages 603-609, August.
    13. Bruce D. Spencer, 2007. "Estimating the Accuracy of Jury Verdicts," Journal of Empirical Legal Studies, John Wiley & Sons, vol. 4(2), pages 305-329, July.
    14. Arthur Lewbel & Xun Tang, 2010. "Identification and Estimation of Games with Incomplete Information Using Excluded Regressors, Second Version," PIER Working Paper Archive 12-018, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 20 Mar 2012.
    15. Lewbel, Arthur & Tang, Xun, 2015. "Identification and estimation of games with incomplete information using excluded regressors," Journal of Econometrics, Elsevier, vol. 189(1), pages 229-244.
    16. Shakeeb Khan & Denis Nekipelov, 2018. "Information structure and statistical information in discrete response models," Quantitative Economics, Econometric Society, vol. 9(2), pages 995-1017, July.
    17. Will Dobbie & Jacob Goldin & Crystal S. Yang, 2018. "The Effects of Pretrial Detention on Conviction, Future Crime, and Employment: Evidence from Randomly Assigned Judges," American Economic Review, American Economic Association, vol. 108(2), pages 201-240, February.
    18. Heckman, James J. & Navarro, Salvador, 2007. "Dynamic discrete choice and dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 136(2), pages 341-396, February.
    19. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    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. Paul Bose & Eberhard Feess & Helge Mueller, 2022. "Favoritism towards High-Status Clubs: Evidence from German Soccer," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 38(2), pages 422-478.

    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. Lewbel, Arthur & Tang, Xun, 2015. "Identification and estimation of games with incomplete information using excluded regressors," Journal of Econometrics, Elsevier, vol. 189(1), pages 229-244.
    2. Yingying Dong & Arthur Lewbel, 2015. "A Simple Estimator for Binary Choice Models with Endogenous Regressors," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 82-105, February.
    3. Arthur Lewbel, 2019. "The Identification Zoo: Meanings of Identification in Econometrics," Journal of Economic Literature, American Economic Association, vol. 57(4), pages 835-903, December.
    4. Arthur Lewbel, 2012. "An Overview of the Special Regressor Method," Boston College Working Papers in Economics 810, Boston College Department of Economics.
    5. Chen, Songnian & Khan, Shakeeb & Tang, Xun, 2016. "Informational content of special regressors in heteroskedastic binary response models," Journal of Econometrics, Elsevier, vol. 193(1), pages 162-182.
    6. Sofia Amaral & Gordon B. Dahl & Victoria Endl-Geyer & Timo Hener & Helmut Rainer, 2023. "Deterrence or Backlash? Arrests and the Dynamics of Domestic Violence," NBER Working Papers 30855, National Bureau of Economic Research, Inc.
    7. Matzkin, Rosa L., 2012. "Identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 166(1), pages 106-115.
    8. Jeremy T. Fox & Natalia Lazzati, 2012. "Identification of Potential Games and Demand Models for Bundles," NBER Working Papers 18155, National Bureau of Economic Research, Inc.
    9. David Arnold & Will Dobbie & Crystal S Yang, 2018. "Racial Bias in Bail Decisions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(4), pages 1885-1932.
    10. Ofek-Shanny, Yuval & Strulov-Shlain, Avner & Zeltzer, Dan, 2025. "Impacts of home-care subsidies: Evidence from quasi-random assignment," Journal of Public Economics, Elsevier, vol. 248(C).
    11. Johannes W. Ligtenberg & Tiemen Woutersen, 2024. "Multidimensional clustering in judge designs," Papers 2406.09473, arXiv.org.
    12. Lewbel, Arthur & Schennach, Susanne M., 2007. "A simple ordered data estimator for inverse density weighted expectations," Journal of Econometrics, Elsevier, vol. 136(1), pages 189-211, January.
    13. Manudeep Bhuller & Gordon B. Dahl & Katrine V. Løken & Magne Mogstad, 2020. "Incarceration, Recidivism, and Employment," Journal of Political Economy, University of Chicago Press, vol. 128(4), pages 1269-1324.
    14. Anthony Bald & Eric Chyn & Justine Hastings & Margarita Machelett, 2022. "The Causal Impact of Removing Children from Abusive and Neglectful Homes," Journal of Political Economy, University of Chicago Press, vol. 130(7), pages 1919-1962.
    15. Manudeep Bhuller & Gordon B. Dahl & Katrine V. Løken & Magne Mogstad, 2018. "Incarceration Spillovers in Criminal and Family Networks," NBER Working Papers 24878, National Bureau of Economic Research, Inc.
    16. Jeremy Fox & Natalia Lazzati, 2013. "Identification of discrete choice models for bundles and binary games," CeMMAP working papers 04/13, Institute for Fiscal Studies.
    17. Hirvonen, Johannes & Kässi, Otto & Ropponen, Olli, 2023. "Jobs, Workers, and Firms: Dissecting the Labour Market Effects of Finland’s COVID-19 Subsidy Program," ETLA Working Papers 111, The Research Institute of the Finnish Economy.
    18. Nail Kashaev, 2018. "Identification and estimation of multinomial choice models with latent special covariates," Papers 1811.05555, arXiv.org, revised Mar 2022.
    19. Hjalmarsson, Randi & Machin, Stephen & Pinotti, Paolo, 2024. "Crime and the labor market," Handbook of Labor Economics,, Elsevier.
    20. Robert Collinson & John Eric Humphries & Nicholas Mader & Davin Reed & Daniel Tannenbaum & Winnie van Dijk, 2024. "Eviction and Poverty in American Cities," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 139(1), pages 57-120.

    More about this item

    Keywords

    ;
    ;
    ;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • K14 - Law and Economics - - Basic Areas of Law - - - Criminal Law
    • K41 - Law and Economics - - Legal Procedure, the Legal System, and Illegal Behavior - - - Litigation Process

    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:pra:mprapa:100217. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.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.