Andrew Gelman at Columbia University writes on his statistics blog here that the findings I discussed yesterday seem correct and don't surprise him in the least. (He also has some entertaining reactions to some of the comments from yesterday).

I'll confess that I not only find the results surprising, I also think that, if they are indeed right, they have farreaching implications for our existing (and future) research on prisons and their effect on unemployment, crime, education, and poverty, as well as our research on gun laws (think of the right-to-carry debates here, here, and here), the effect of abortions (think of the Donohue/Levitt thesis), the deterrent effect of the death penalty (think of the recent debates here), social control and disorganization theories, collective efficacy -- and the list goes on.

In practically all those studies, we have used the imprisonment rate to measure society's level of incapacitation. But the prison rate alone may not capture what we were trying to measure. The most straightforward interpretation of my findings is that neither the rate of imprisonment alone, nor the rate of mental hospitalization alone are good predictors of serious violent crime over the period 1934-2001. In contrast, the aggregated institutionalization rate (aggregating the mental hospitalization and prison rates) is a strong predictor of homicides. This suggests that there is something going on in the relationship between mental hospitalization and prison — perhaps a form of substitution — that should make us rethink entirely how we measure social control and incapacitation.

But since practically none of our studies on prisons, guns, abortion, education, unemployment, capital punishment, etc., controls for institutionalization writ large, most of what we claim to know about these effects may be on shaky ground.

Here's a good example. My colleague Steve Levitt at the University of Chicago has a great paper on the crime decline of the 1990s published in the Journal of Economic Perspectives called Understanding Why Crime Fell in the 1990s: Four Factors that Explain the Decline and Six that Do Not. In the paper, Levitt identifies the prison-population build up as one of the four factors that explains the crime drop of the 1990s.

Levitt estimates that the increased prison population over the 1990s accounted for a 12% reduction of homicide and violent crime, and an 8% reduction in property crime — for a total of about one-third of the overall drop in crime in the 1990s (see pages 178-79). The paper and its progeny have given rise to fascinating debates over the role of the police (Malcolm Gladwell takes Levitt to task in an interesting post here), the abortion thesis, and the role of broken-windows policing vs. the crack epidemic.

What interests me here, though, is that when Levitt extends his analysis to discuss the period 1973--1991, he sticks to the prison population exclusively and does not consider the contribution of the declining mental hospital population (see pages 183-86). As a result, Levitt is surprised that the drop in crime did not start sooner (see page 186). Regarding the period 1973--1991, Levitt writes:

"The one factor that dominates all others in terms of predicted impact on crime in this earlier [1973--1991] period is the growth in the prison population. Between 1973 and 1991, the incarceration rate more than tripled, rising from 96 to 313 inmates per 100,000 residents. By my estimates, that should have reduced violent crime and homicide by over 30 percent and property crime by more than 20 percent. Note that this predicted impact of incarceration is much larger than for the latter [1990s] period." (page 184)

Based on prison data alone, Levitt is left with a significant gap between projected and actual crime rates for the period 1973--1991. Levitt concludes: "The real puzzle in my opinion, therefore, is not why crime fell in the 1990s, but why it did not start falling sooner" (see page 186).

The unexplained difference, though, vanishes if we include mental hospitalization with the prison rate in an aggregated institutionalization variable. I do the math in this paper here at page 1775. The increase in confinement from 1973 to 1991 would have been smaller (because of deinstitutionalization) and, based on Levitt's estimates, this would have translated into a 12% decrease in homicides, not a 35% decrease. Levitt's revised estimate for the total effect of his ten factors on homicide during the 1973--1991 period would be an increase in homicides of 3%, which is not far from the actual reported change in the UCR of a positive 5%.

In other words, using aggregated institutionalization data rather than prison data would eliminate Levitt's disparity regarding the change in homicides. This is just one example that explains a gap. But think of all the other areas where the difference might undermine the results.

Here's another example from the death penalty deterrence debates. The fact is that none of the existing extensive research on the deterrent effect of capital punishment has included mental hospitalization within an aggregated institutionalization rate. Instead, all the studies use prison rates only to get at a measure of incapacitation.

My study includes, as a control variable in the regressions, the execution rate for each state over the period 1934 to 2001. So we can get some idea of what happens when you use aggregated institutionalization rather than the prison rate. The results are interesting: in my fourth model (Model 4 of Table III.1 at page 33), the execution rate is positively related to homicide and statistically significant at .05, suggesting that, controlling for aggregated institutionalization, there may be evidence of a brutalization effect from executions: more executions, more homicide. The statistical significance does not withstand the introduction of demographic and urban variables, and in my most complete model (Model 6 same page) the coefficient is positive but unreliable.

Much has been written recently about the deterrent effects of capital punishment. John Donohue and Justin Wolfers have reviewed the recent studies, including state-level panel data analyses, and conclude that "none of these approaches suggested that the death penalty has large effects on the murder date" (page 841). When I include mental hospitalization, my findings are consistent with these conclusions, but in the process they undermine a lot of other research.

Practically all our criminology has failed to connect the prison to the asylum. For instance, Alfred Blumstein and Joel Wallman, in their account of crime trends in the introduction to The Crime Drop in America — generally perceived as an authoritative compilation — never address aggregated institutionalization. With regard to the sharp increase in crime in the 1960s, Blumstein and Wallman hit on all the usual suspects — the baby-boom generation, political legitimacy, economics — and include later the usual explanations for the 1990s crime drop — changing drug use patterns, decreased gun violence, New York-style policing, the federal COPS program, and increased incarceration. Notably absent in all of this, though, is the relationship between mental health and prison populations.

With the exception of research that specifically explores the interdependence of the mental hospital and prison populations, including some public health studies and some empirical research into the causes of the prison explosion (for instance here, here and here) published empirical research does not conceptualize the level of confinement in society through the lens of aggregated institutionalization (asylum + prison) but rather simply through imprisonment rates.

Even the most rigorous, recent analyses of the prison-crime relationship use only imprisonment data. Though a tremendous amount of empirical work has been done on long-term crime trends, structural covariates of homicide, unemployment, and the prison expansion, none of this literature conceptualizes confinement through the larger prism of institutionalization, and none of it aggregates mental hospitalization data with prison rates.

So in contrast to Andrew Gelman, I'm not only surprised by the results of the regression, I'm also extremely concerned about the implications regarding the state of our current knowledge and existing research. And, unhappily, in contrast to Gelman's just-so post, I expect a huge amount of resistance.