Type I and Type II Error Probabilities in the Courtroom

Kanaya, Shin and Taylor, Luke (2020): Type I and Type II Error Probabilities in the Courtroom.

Abstract

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Miscarriages of justice; Nonparametric identification; misclassification
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C25 - Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions ; Probabilities; K - Law and Economics > K1 - Basic Areas of Law > K14 - Criminal Law; K - Law and Economics > K4 - Legal Procedure, the Legal System, and Illegal Behavior > K41 - Litigation Process

References

Acker, J.R. (2017) Taking stock of innocence: Movements, mountains, and wrongful convictions. Journal of Contemporary Criminal Justice. 33(1), pp. 8–25.

References Aizer, A. and J.J. Doyle Jr (2015) Juvenile incarceration, human capital, and future crime: Evidence from randomly assigned judges. Quarterly Journal of Economics. 130(2), pp. 759-803.

References Altonji, J.G. and R.K. Mansfield (2018) Estimating group effects using averages of observables to control for sorting on unobservables: School and neighborhood effects. American Economic Review. 108(10), pp. 2902-46.

References Belloni, A., Chen, D., Chernozhukov, V. and C. Hansen (2012) Sparse models and methods for optimal instruments with an application to eminent domain. Econometrica. 80(6), pp. 2369-2429.

References Berry, S.T. and P.A. Haile (2014) Identification in differentiated products markets using market level data. Econometrica. 82(5), pp. 1749-1797.

References Bhuller, M., Dahl, G.B., Løken, K.V. and Mogstad, M. (2020) Incarceration, recidivism, and employment. Journal of Political Economy. 128(4), pp.1269-1324.

References Bjerk, D. and E. Helland (2019) What can DNA exonerations tell us about racial differences in wrongful conviction rates? Journal of Law and Economics (Forthcoming).

References Chiricos, T., Barrick, K., Bales, W. and S. Bontrager (2007) The labeling of convicted felons and its consequences for recidivism. Criminology. 45(3), pp. 547-581.

References Dahl, G.B., Kostøl, A.R. and M. Mogstad (2014) Family welfare cultures. Quarterly Journal of Economics. 129(4), pp.1711-1752.

References Dobbie, W., Goldin, J. and C.S. Yang (2018) The effects of pretrial detention on conviction, future crime, and employment: Evidence from randomly assigned judges. American Economic Review. 108(2), pp. 201-40.

References Frölich, M. (2006) Non‐parametric regression for binary dependent variables. The Econometrics Journal. 9(3), pp. 511-540.

References Goh, C. (2018) Rate-optimal estimation of the intercept in a semiparametric sample-selection model. Econometric Theory (Forthcoming).

References Gross, S.R. and B. O’Brien (2008) Frequency and predictors of false conviction: Why we know so little, and new data on capital cases. Journal of Empirical Legal Studies, 5(4), pp. 927-962.

References Gross, S.R., O’Brien, B., Hu, C. and E.H. Kennedy (2014) Rate of false conviction of criminal defendants who are sentenced to death. Proceedings of the National Academy of Sciences. 111(20), pp. 7230-7235.

References Hartford, J., Lewis, G., Leyton-Brown, K. and M. Taddy (2017) Deep IV: A flexible approach for counterfactual prediction. Proceedings of the 34th International Conference on Machine Learning. 70, pp. 1414-1423.

References Hausman, J.A., Abrevaya, J. and F.M. Scott-Morton (1998) Misclassification of the dependent variable in a discrete-response setting. Journal of Econometrics. 87, pp. 239-269.

References Heckman, J. J. and S. Navarro (2007) Dynamic discrete choice and dynamic treatment effects. Journal of Econometrics. 136, pp. 341-396.

References Khan, S. and D. Nekipelov (2018) Information structure and statistical information in discrete response models. Quantitative Economics. 9(2), pp.995-1017.

References Klein, R.W. and R.H. Spady (1993) An efficient semiparametric estimator for binary response models. Econometrica. pp. 387-421.

References Lee, B.K., Lessler, J. and E. A. Stuart (2010) Improving propensity score weighting using machine learning. Statistics in Medicine. 29(3), pp. 337-346.

References Lewbel, A. (1998) Semiparametric latent variable model estimation with endogenous or mismeasured regressors. Econometrica. pp. 105-121.

References Lewbel, A. (2000a) Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables. Journal of Econometrics. 97(1), pp. 145-177.

References Lewbel, A. (2000b) Identification of the binary choice model with misclassification. Econometric Theory. 16(4), pp. 603-609.

References Lewbel, A. and X. Tang (2015) Identification and estimation of games with incomplete information using excluded regressors. Journal of Econometrics. 189(1), pp. 229-244.

References Loader, C. (2006) Local Regression and Likelihood. Springer Science & Business Media.

References Magnac, T. and E. Maurin (2007) Identification and information on monotone binary models. Journal of Econometrics. 139(1), pp. 76-104.

References Manski, C.F. (1988) Identification of binary response models. Journal of the American Statistical Association. 83(403), pp. 729-738.

References Mitchell, O., Cochran, J.C., Mears, D.P. and W.D. Bales (2017) Examining prison effects on recidivism: A regression discontinuity approach. Justice Quarterly. 34(4), pp. 571-596.

References Mueller-Smith, M. (2015) The criminal and labor market impacts of incarceration. Working Paper.

References Risinger, D.M. (2006) Innocents convicted: An empirical justified factual wrongful conviction rate. Journal of Criminal Law and Criminology. 97, pp. 761.

References Spencer, B.D. (2007) Estimating the accuracy of jury verdicts. Journal of Empirical Legal Studies. 4(2), pp. 305-329.

References Ventura, L.A. and G. Davis (2005) Domestic violence: Court case conviction and recidivism. Violence Against Women. 11(2), pp. 255-277.

References Zalman, M. (2017) Wrongful Convictions: A Comparative Perspective. Journal of Contemporary Criminal Justice. 33(1), pp. 1-7.