Prisons and Crime, Backwards in High Heels - Spelman, William (Journal of quantitative criminology, 2013)
Objectives Prisons reduce crime rates, but crime increases prison populations. OLS estimates of the effects of prisons on crime combine the two effects and are biased toward zero. The standard solution—to identify the crime equation by finding instruments for prison—is suspect, because most variables that predict prison populations can be expected to affect crime, as well. An alternative is to identify the prison equation by finding instruments for crime, allowing an unbiased estimate of the effect of crime on prisons. Because the two coefficients in a simultaneous system are related through simple algebra, we can then work backward to obtain an unbiased estimate of the effect of prisons on crime. Methods Potential instruments for crime are tested and used to identify the prison equation for the 50 U.S. states for the period 1978–2009. The effect of prisons on crime consistent with this relationship is obtained through algebra; standard errors are obtained through Monte Carlo simulation. Results Resulting estimates of the effect of prisons on crime are around −0.25 ± 0.15. This is larger than biased OLS estimates, but similar in size to previous estimates based on standard instruments. Conclusions When estimating the effect of a public policy response on a public problem, it may be more productive to find instruments for the problem and work backward than to find instruments for the response and work forward.