Using a Special Regressor to Identify Type I and Type II Error Probabilities, With an Illustrative Application to Miscarriages of Justice

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.