Recently many papers have used the arrest rate to measure punishments in crime-rate regressions. However, arrest rates account for only a portion of the criminal sanction. Conviction rates and time served are theoretically important, but rarely used, and excluding them generates omitted variable bias if they are correlated with the arrest rate. This paper uses the most complete set of conviction and sentencing data to show that arrest rates are negatively correlated with these normally excluded variables. Consequently, previous estimates of arrest-rate effects are understated by as much as 50%. Also, conviction rates, but not sentence lengths, have significant explanatory power in standard crime-rate regressions.

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