In a 2004 paper, Steven D. Levitt argues, honestly and with some statistically rigor, that the decline in crime in the 1990s was largely a product of more cops, greater incarceration, the end of the crack cocaine epidemic, and legalized abortion. He largely rules out other factors such as gun control, the death penalty, policing methods, economic prosperity, and baby boom demographics as factors. Thus, his approach endorses several key tenants of the conservative approach to crime management, while ruling out a couple of conservative favorites (policing methods and the death penalty). And, he largely rules out most liberal favorites to explain what happened.
Neither conservatives nor liberals are comfortable touting legalized abortion as important in reducing crime. Conservatives are reluctant because increased abortion is off the table in their political agenda; in their view, abortion is a crime. Liberals because the pitch for legalized abortion has largely been rooted in female autonomy, rather than utilitarian benefits, and because liberals aren't comfortable describing crime as the fate of poor, unwanted children.
The trouble is that when Levitt looks at those same figures for the period 1973-1991, increased incarceration in that period suggests that there should also have been a major decline in crime in that period which didn't materialize; instead that period witnessed a major increase in crime. This potentially discredits his entire analysis, and he deserves credit for raising the problem himself in the body of his paper.
One missing factor that could remedy his analysis could be the deinstitutionalization of the mentally ill (from roughly 600 people per 100,000 in 1961 to roughly 50 per 100,000 in 1991, with most of the change from 1968 to 1977), although I doubt that this would be a sufficient explanation. Another factor or two, perhaps lead exposure or the impact of the Vietnam War on a crime prone young non-collegiate male demographic (first removing it from the U.S. and artificially depressing domestic crime via the draft, and possibly the returning it to the U.S. mentally scarred by the war experiment at the end of the war, but possibly not), would probably be necessary to reasonably accurately post-dict the entire post-World War II data set. If one goes back to the early part of the 20th century, does Prohibition need to be considered? What about the Great Depression? Is statistical parsing of the impact of such events possible, even theoretically? What data would be needed?
His study is as good at any, however, at illustrating the difference between heuristic post hoc explanation and genuine prediction. Almost everybody predicted that crime would go up in the 1990s, when in fact, it declined dramatically. But, they were wrong.
It is much easier to fit multiple factors to actual results post-hoc in a statistically plausible way, for a particular set of data, than it is to produce a rigorous model that holds up with a different data set. Obviously, Levitt's model is wrong as an overall cause of crime rate model, because it doesn't come even close to success in the 1973-1991 time period.
But, even if fitting in another plausible factor or two could explain 1973-1991 as well, who is to say that it would accurately capture what was going on in the 2007-2017 time period? Will the Flynn effect, or a decriminalization of illegal drugs create period specific changes in crime rates?