Crime and Mismeasured Punishment: Marginal Treatment Effect with Misclassification

TL;DR

This paper develops methods to partially identify the marginal treatment effect when treatment is misclassified, using restrictions on dependence and derivative signs, with an application to criminal sentencing and recidivism in Brazil.

Contribution

It introduces new identification strategies for the MTE under misclassification, allowing for dependence between instruments and misclassification decisions.

Findings

Misclassification bias can be as large as 10% of the maximum MTE.

Bounds on MTE contain the true MTE under certain derivative conditions.

Application shows the importance of accounting for misclassification in policy analysis.

Abstract

I partially identify the marginal treatment effect (MTE) when the treatment is misclassified. I explore two restrictions, allowing for dependence between the instrument and the misclassification decision. If the signs of the derivatives of the propensity scores are equal, I identify the MTE sign. If those derivatives are similar, I bound the MTE. To illustrate, I analyze the impact of alternative sentences (fines and community service v. no punishment) on recidivism in Brazil, where Appeals processes generate misclassification. The estimated misclassification bias may be as large as 10% of the largest possible MTE, and the bounds contain the correctly estimated MTE.