One obvious answer is that many more people are in prison than in the past. Experts differ on the size of the effect, but I think that William Spelman and Steven Levitt have it about right in believing that greater incarceration can explain about one-quarter or more of the crime decline. Yes, many thoughtful observers think that we put too many offenders in prison for too long. For some criminals, such as low-level drug dealers and former inmates returned to prison for parole violations, that may be so. But it's true nevertheless that when prisoners are kept off the street, they can attack only one another, not you or your family.
The poverty-crime connection doesn't hold water anymore.