Using a Special Regressor to Identify Type I and Type II Error Probabilities, With an Illustrative Application to Miscarriages of Justice
本文提出一种非参数方法，利用特殊回归变量识别未观测到的第一类和第二类错误概率，并应用于弗吉尼亚州司法误判估计，发现无罪判决错误率因犯罪类型、种族和性别而异。
We nonparametrically identify Type I and Type II error rates when mistakes are unobserved. Our strategy reframes the setting as a misclassified binary choice model, using a special regressor to identify the misclassification probabilities. Identification requires an exclusion restriction and a large support condition. When the exclusion restriction is in doubt, we show how our estimands can be interpreted as bounds under a weaker monotonicity condition. Bounds are also provided when the large support condition is violated. We apply our method to estimate miscarriages of justice in Virginia. Among defendants who proceeded to trial, the estimated probability of wrongful acquittal ranges from 18 to 42%, depending on offense type, race, and gender. Our method also produces estimates of wrongful conviction probabilities; however, these are very high, potentially reflecting the restriction of our sample to trial defendants and/or violations of key assumptions.