To answer this question with some kind of scientific certainty, what you'd really like to do is conduct an experiment. Pretend you could randomly select a group of states and command each of them to release 10,000 prisoners. At the same time, you could randomly select a different group of states and have them lock up 10,000 people, misdemeanor offenders perhaps, who otherwise wouldn't have gone to prison. Now sit back, wait a few years, and measure the crime rate in those two sets of states. Voila! You've just run the kind of randomized, controlled experiment that lets you determine the relationship between variables. Unfortunately, the governors of those random states probably wouldn't take too kindly to your experiment. Nor would the people you sent to prison in some states or the next-door neighbors of the prisoners you freed in others. So your chances of actually conducting this experiment are zero. That's why researchers often rely on what is known as a natural experiment, a set of conditions that mimic the experiment you want to conduct but, for whatever reason, cannot. In this instance, what you want is a radical change in the prison population of various states for reasons that have nothing to do with the amount of crime in those states.