Yesterday's post triggered a lot of comments regarding this graph -- it's on page 23 of the new study on asylums and prisons that I was discussing previously. The figure graphs two time-series using national-level data: the overall rate of institutionalization in the United States (in mental hospitals and prisons) and the homicide rate over the period 1934 to 2001. The institutionalization trend line is scaled to the left-hand side and is high throughout the 1930s, 40s, and 50s; the homicide trend line is scaled to the right-hand side and rises sharply in the 1970s and 80s.

FIGURE: Rates of Aggregated Institutionalization and Homicide in the United States (per 100,000 adults).

In an earlier paper, I analyzed these data using a Prais-Winsten regression model to correct for autocorrelation in the time-series data. I found a large, robust, and statistically significant relationship between aggregated institutionalization (asylums and prisons) and homicide rates at the national level, holding constant three leading structural covariates of homicide (youth demographics, unemployment, and poverty).

The problem with using time-series data for a single jurisdiction (in this case, the entire United States) is that they typically provide weak power to rule out alternative explanations for the patterns observed in the data. This is something I've observed and written about in the context of Giuliani-style policing. (In an article with Jens Ludwig testing the broken-windows policing hypothesis, we showed that the time-series data for crime in New York City was not just compatible with a broken-windows policing theory, but also with what we call the "Broken Yankees Hypothesis" (BYH). It turns out that the strong performance of Billy Martin's Yankees teams during the late 1970s coincided with a drop in homicides, and the consistent excellence of Joe Torre's squads beginning in the late 1990s accompanied an even greater decline in homicides).

In order to test the national-level findings, I collected state-level panel data and ran clustered regressions. The results were truly remarkable. Using state-level panel data spanning the entire period from 1934 to 2001, including all 50 states, and controlling for economic, demographic, and criminal justice variables, I again found a large, robust, and statistically significant relationship between aggregated institutionalization and homicide rates. The findings are not sensitive to weighting by population and hold under a number of permutations, including when I aggregate jail populations as well.

To help visualize the relationship, I plotted the predicted values of homicide in the final model (Model 6) against the aggregated institutionalization rate. These, then, are the predicted values of homicide from the model including all the independent variables (aggregated institutionalization, real per capita income, demographics, execution rate, proportion urban, proportion black, and state and year fixed effects). The data are clustered by state, resulting in what appear to be some strings of observations.

Some readers have suggested that the study should include a model with the prison rate and the mental hospitalization rate as separate independent variables. John Lott recently wrote to me "I don't understand why prison population and [mental hospitalization] only seemed to be entered in as a sum." Eric Rasmusen similarly argues here that "There is another regression you absolutely must do: regress murder on [aggregated institutionalization], prison, and asylums all in one regression. That will separate out the effects."

These are interesting points and something my superb colleagues at the University of Chicago, Tom Miles and Jake Gersen, had batted around with me earlier. My concern is the contribution of aggregated institutionalization and I am really not concerned about the relationship of the parts. I had included some of these regressions in the study, but for the sake of completeness, I just now reran the regressions using every possible permutation of aggregated institutionalization, mental hospitalization alone, and prison rates alone. Every possible permutation — all three, each alone, and every dual-combination.

Here's a table summarizing my results. I'll just note for those who are not steeped in stats that the first model, which includes all three independent variables is going to drop one of them. It's actually impossible to use all three in the same regression. If you include the sum of two variables and each of those two variables, there is a co-linearity problem (since the sum is of course a linear combination of the two). Statistics programs fix this problem by tossing out one of the variables. In this case, STATA dropped the mental hospitalization alone variable. So Model 1 is really identical to Model 6.

But I've presented them all for full and complete disclosure. They do not affect my conclusions. Models 2 and 4 are in the draft of the study. Model 5 represents a race-horse comparison of mental hospitalization and prison rates. Notice that mental hospitalization alone is slightly less significant, but still significant, whereas prison rates alone are not. Again, my concern is not with the relative contribution of the parts, but of the whole. Model 6 includes aggregated institutionalization and prison rates -- and here too, aggregated institutionalization remains statistically significant with a coefficient about the same size (slightly larger).

New Table: Harcourt Results on State-level Panel Data (All Permutations)

These additional specifications do not change the bottom line: Aggregated institutionalization is the best predictor of homicide rates. In studying the prison today, we need to aggregate mental hospitalization and prison rates.

Not only that, but there is in all likelihood an endogeneity problem that actually attenuates the relationship that I am finding in my data. The fact is, there is, if anything, simultaneity bias. The relationship between crime and institutionalization is likely to be two-way. Although increased institutionalization is likely to decrease crime rates through incapacitation, increased crime is also likely to increase institutionalization through convictions and sentencing.

As a result, the incapacitation effect of institutionalization on crime is probably diminished and the statistical estimates are likely to understate the effect. The effect of the bias would be to underestimate the effect of aggregated institutionalization on crime. This would only increase the effect of aggregated institutionalization on homicide.

A former student of mine who also studied under Gary Becker, John Pfaff at Fordham, has a terrific new paper on the methodological problems in the prison literature. He extensively reviews the existing "first generation" studies and raises a number of methodological problems — from endogeneity to omitted variable biases and colinearity.

To be sure, like those other studies, the statistical analyses in my study may be missing some control variables. Few if any of the studies that John reviews in his paper go as far back as the 1930s and the fact is, it is practically impossible to find any more reliable data at the state level that go back that far — though I am continuing to search for more.

But the findings are nevertheless remarkable — actually astounding. These regressions cover an extremely lengthy time period (back to 1934) for all fifty state, resulting in a large number of observations (almost 3,300), controlling for economic, criminal justice, youth and demographic variables, and the results remain robust and statistically significant in the most complete models. That is amazing.

One final point. At a conference last week at Yale where I first presented this work, some participants argued that I have to guide the use of this research and address the policy implications.

I resisted the invitation then, but want to emphasize why here. The reason is that the policy implications of this study could lead in any number of directions. Some readers could argue that my findings show there is no reason to have prisons. Instead of prisons, we should have treatment facilities. Others could argue that we should incapacitate more women — remember, there were far more women in mental hospitals, almost 50 percent. Some might argue that we are now at the right level of institutionalization. But this study tells us nothing about the costs and trade-offs to society involved in imprisoning so many people, and whether the harm to the individuals affected by incarceration does not outweigh the harms to the victims of crime.

So I want to emphasize that we all need to proceed with caution. A study finding correlations is not enough to start drawing policy conclusions.