Mueller-Smith sets out to measure the causal impact of incarceration on an individual’s criminal and economic activity. He relies on records of 1.1 million Harris County defendants, state prison and county jail administrative data, unemployment insurance wage records, and public assistance benefit data.
The complexity of this kind of work is that you can’t just plot, say, an individual’s recidivism against years spent incarcerated, and measure the slope as a causal effect. If you had randomly assigned different sentence lengths to people who otherwise bore identical characteristics, then you could: but sentencing, we as a society maintain, is not randomly assigned. The same factors associated with prison sentence length (eg. a person’s propensity to commit crime, as reflected in the nature of the first crime and thus its punishment) may have a causal effect on the second.
To address this, Mueller-Smith exploits a depressing fact: a defendant’s courtroom is randomly assigned, and can be used to predict the criminal sentence. Some judges may be “tougher” than others, even when given the same caseload. Thus, he uses courtroom assignment as an instrumental variable: 1) he uses the randomly assigned courtroom assignment to predict sentence length (accounting, of course, for measurable defendant characteristics); 2) he regresses the dependent variable of choice against this predicted sentence length.
To use courtroom assignment as a valid instrument, it has to satisfy:
- Exclusion restriction: Even though we care about the effects of incarceration, judges may impose other penalties, such as fines. If a “tougher” judge also imposes higher fines, then the post-incarceration impact would capture a combined effect of the longer incarceration and higher fines–violating the exclusion restriction.
To address this, Mueller-Smith includes in his instrumentation analysis not just incarceration status and incarceration length, but also fine status and amount, probation status and length, and alternative sentencing (electronic monitoring, drug treatment, boot-camps, drivers’ education).
- Monotonicity assumption: Judges have to be consistent in how they treat defendants: if they respond differently to different types of defendants and that is not included in the model, then it can distort the measured effects.
To address this, Mueller-Smith’s first stage of the regression allows for the calculated coefficient of judicial preference to be a function of specific defendant characteristics. He picks the most important characteristics through statistical wizardry, settling on type of crime, degree of charge, criminal history, age, and race.
I listed his results above. Mueller-Smith explicitly did not account for the “deterrence” effect of incarceration in these regressions: proponents might argue that the unmeasured benefit lies in preventing other people in the community from committing crimes. I would be skeptical of that claim: it doesn’t explain why America’s incarceration rates are so much higher than the developed world.
But as a thought experiment, Mueller-Smith calculates the deterrent effect that would make a one-year prison sentence worth it, accounting for prison cost and economic effects. It would need to prevent 0.4 rapes, 2.2 assaults, 2.5 robberies, 62 larcenies, or 4.8 people from becoming habitual drug users. According to current literature, this large of deterrent effect is unlikely.