pageok
pageok
pageok
[Bernard Harcourt, guest-blogging, May 1, 2007 at 7:10am] Trackbacks
Mental Hospital, Prison, and Homicide Rates: Some More Analyses.

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.

Mahan Atma (mail):
I don't understand why you're including standard errors and p-values in your results.

What is your stochastic model, exactly? If I understand correctly, the underlying data (e.g. the crime rates) are population statistics, not sample estimates, correct?

So where is the randomness coming from?
5.1.2007 8:40am
Kieran (mail) (www):
Graphs with two y-axes on different scales make Baby Jesus cry, especially when the axes aren't labeled.

As for the models, it seems to me that there are two substantive issues:

(a) Is the MH rate a better predictor of the homicide rate than the incarceration rate? Based on the comparisons in Models (3), (4) and (5) It looks like it is, whether the variables are considered separately or jointly. Which is pretty interesting. (b) Is the

(b) Is there a reason for preferring the aggregate/combined measure in Model 2 over counting them separately as in Model 5. The aggregate measure in Model 2 does better than the separate measures in Model 5 in terms of conventional significance. But is there an argument that the aggregate measure is picking up something substantive that the separate measures do not? (I haven't read the paper, so apologies if I'm asking for something that's addressed directly there.)

Finally, when making these kinds of significance comparisons within and between models of this sort, bear in mind that (confusingly) the difference between significant and non-significant effects need not itself be statistically significant.
5.1.2007 9:59am
none (mail):
Can you explain your findings in English for people like me who do not speak graph?
5.1.2007 11:08am
No mas!:
Remember when this blog was all sweetness and light and Eugene's insightful comments on a variety of topics and puzzleblogger Kevan Choset's interesting observations and Adler's/Juan's snarky comments?

This blog used to be fun. Now, whoa, Ilya thinks he probably didn't (but maybe did!) change US policy on drug eradication in Afghanistan, and we've got graphs with two Y-axes on different scales, and it's all wonk all the time. Why have we abandoned the idea that posts should be entertaining and interesting to someone other than the author?

Include me out!
5.1.2007 11:10am
rjwaldmann (mail) (www):
Dear Dr Harcourt

Your results are totally new and astonishing to me (I am an economist who doesn't study crime at all). I have a technical question.

Do you state level panel results include time dummies and/or state dummies ? Results with such dummies would be much more convincing than results without.
5.1.2007 11:39am
rjwaldmann (mail) (www):
I have just downloaded the pdf and see that tables III.1 and III.2 include exactly the regression I wanted. Very impressive. Sorry to bother readers which a question I answered just be clicking and reading. As Emily Letella said "never mind."
5.1.2007 11:51am
Andy Freeman (mail):
"Guide the use of this research" suggests that the proponents believe that the folks at Los Alamos should be consulted about nuke use policy.
5.1.2007 1:28pm
George Weiss:
Your getting inconsistent within 1 day of you own posts:

the other day you write:

"It's impossible to make sense of the debate, though, without understanding the extent to which we've dismantled our mental health system in this country. Brick-by-brick, cell-by-cell, we reconstructed what was once a massive mental hospital complex and built in its place a huge prison."

Now you write:

My concern is the contribution of aggregated institutionalization and I am really not concerned about the relationship of the parts. [i.e...how much is prison and hwo much is hospitalization]


make up yourmind
5.1.2007 2:15pm
Bernard E. Harcourt (mail) (www):
In response to Kieran's excellent comment here, I think there is a lot to be gained from using the aggregated measure of asylums and prisons in Model 2 rather than the disaggregated measures in Model 5. The point of aggregating is to think of these two populations as related and in some sense fungible. Neither one of them alone does a good job of predicting homicide, probably because they seem to substitute for each other. It's only when you think of them as a whole that the measure becomes important. As you suggest correctly, we are talking about incremental levels of significance, but at some point that starts to make a difference. I'd say, we've reached that point in Model 2.

Now, let me step back from the trees and comment on the forest for a minute. The relative contribution of the parts (asylum and prisons separately) is not really important to the analysis. The whole (aggregated institutionalization), rather than the parts, is the best predictor of homicides and is what we need to focus on. In effect, we need to redo all our studies of the prison, unemployment, abortion, gun laws, etc., using aggregated institutionalization rather than just imprisonment as the measure of incarceration. I think this is pretty radical and may have wide ranging implications.
5.1.2007 2:17pm
Ignorance is Bliss:
Thank you for the interesting data, analysis, and explanation.

And thank you even more for not using it to advance a specific policy. It is amazing how many 'researchers' do their studies and find that, whatever the results, they prove we must immediately implement whatever policies the researchers favored before they started their research.
5.1.2007 2:19pm
Scot Echols (mail):
Indeed. Our good friends at the UN's IPCC could learn a thing or two from Dr. Harcourt about the differences between science and activism.

That said, I still disagree with the suggestion that there is a relationship, but I admire and respect the objectivity that the author displays in the process.
5.1.2007 2:40pm
David Walser:
Just a comment on why aggregating prison and mental health populations for purposes of the study may make sense: I believe that during the period covered, the US changed the way in which it deals with individuals who are incarcerated. In some years some action was treated as a "crime" and the individual was sent to prison; in other years the same action was treated as a "mental health issue" and the person was hospitalized. If society's treatment of these individuals really has ebbed and flowed between prison and hospitalization, then the study needs to aggregate the two populations to have any validity.
5.1.2007 2:40pm
dwshelf:
Can you discuss what seem to some of us to be dominant historic events.

1. The emergence during the 1960s of effective psychosomatic drugs, which, for the first time, created the potential that psychotic people could "go home", so long as they continued taking their medication.

2. Court decisions ca 1968..1975(sorry, no citations) which ruled that a mental patient could not be involuntarily held in a mental hospital, so long as there was no reason to believe the patient was a danger to himself or others.

These two events are, in "common knowledge", given credit for the demise of the mental hospital system starting ca 1970.

On the prison front, we have:

1. The penetration of hard drugs into American society starting ca 1975. Starting around then, the career "drug seller" became available as an alternative to high school, but also came the violence associated with competition. What percentage of people now in prison are there due to the "war on drugs", which wouldn't have been there prior to 1975?

2. The "liberal experiment" of the 1970s, during which the death penalty was revoked, and violent criminals were released after having been "rehabilitated". By the mid 80s, it had become clear that these people were far from rehabilitated, and needed continued isolation to protect society.

===
The real point is that while these two trends, one with mental hospitals, one with prisons were happening simultaneously, they were not obviously connected. In particular, it's not that people were being shifted from a mental hospital to a prison.

===
Yet another factor. The farm->city migration + the American divorce revolution of the 1950s.

75 years ago, most Americans lived on farms. When life on a farm came to be unbearable for the farm wife, she had exactly one way out: a nervous breakdown. She couldn't get a divorce. She couldn't leave (where would she go?). But she could get out to the mental hospital, where life was peaceful.

Post WWII began the great farm->city migration, combined with the availability of divorce. Today, for one, there are fewer than 1/10 as many farm wives as there were 75 years ago, and when things get tough, they just climb into the car and drive to somewhere else.

Further, nervous breakdowns aren't as much fun these days. They fill you up with dulling drugs and stick you in a warehouse until you're ready to go home.
5.1.2007 3:06pm
Clayton E. Cramer (mail) (www):
No surprise; Sunday's mass murder was a person with a long history of mental illness and alcohol abuse who was hospitalized in October because he was suicidal--but only for six hours.


Can you discuss what seem to some of us to be dominant historic events.

1. The emergence during the 1960s of effective psychosomatic drugs, which, for the first time, created the potential that psychotic people could "go home", so long as they continued taking their medication.

2. Court decisions ca 1968..1975(sorry, no citations) which ruled that a mental patient could not be involuntarily held in a mental hospital, so long as there was no reason to believe the patient was a danger to himself or others.
I'm researching this subject for a book, and you don't have it completely right, but not completely wrong, either. More detail: see this series of blog posts here.
5.1.2007 3:43pm
Clayton E. Cramer (mail) (www):
Scot Echols writes:

That said, I still disagree with the suggestion that there is a relationship, but I admire and respect the objectivity that the author displays in the process.
Based on what? It might well be that the apparent casual relationship is simply a coincidence--but with the high rates of violent crime (and especially murder) arrests of mental patients and an awful lot of murders committed in the 1980s and through Sunday (in Kansas City) by people who, in 1950, would have been hospitalized instead--why do you think that there is no relationship? Based on what evidence?
5.1.2007 5:05pm
PDXLawyer (mail):
Thanks again for resisting the call to "guide" the use of your research. The fact that you are able to identify the underlying trends and causes here does not in itself give you the authority to decide moral/policy questions which your work raises. If you were to try to do so, the result for me is that I would suspect you were "spinning" your analysis. This seems like an area where the facts might be counterintuitive, so it is important to keep their presentation as clear as you can.

If you have ideas about the policy implications, I think many of us would be interested in knowing them, provided they are kept separate from the factual analysis.
5.1.2007 5:05pm
allwrits (mail):
no mas!

I know this is boring stuff, but welcome to the world of the law. The research's policy implications (lockup crazy / violent people in a psych ward or prison - I favor the first others the second) are clear.

I should note, I favor wider uses of psychiatric probation (ie take your meds or go to jail) which I suspect without empirical data would also produce a favorable decrease in homicide rates.
5.1.2007 5:48pm
Clayton E. Cramer (mail) (www):

I should note, I favor wider uses of psychiatric probation (ie take your meds or go to jail) which I suspect without empirical data would also produce a favorable decrease in homicide rates.
Some counties in California are experimenting with such an approach, and at least two counties in Idaho (Ada and Canyon) have established Mental Health Courts which have this as one of their options for dealing with mentally ill persons who have committed nonsexual, nonviolent misdemeanors and felonies.
5.1.2007 6:38pm
Benjamin Davis (mail):
Took SPSS far too long ago, but did think of these things.

The assumption appears to be that these homicides are committed by people who are out of prisons or asylums.

How do you capture that space between those incarcerated unable to commit homicides on the outside and those on the outside committing the homicides? Is there some type of lag/lead analysis and is there an optimal number of months/years to lag/lead?

Do the figures leave out homicides in prison or asylums by persons in asylums or prisons? Is that significant.

Best,
Ben
5.1.2007 10:26pm
Benjamin Davis (mail):
Took SPSS far too long ago, but did think of these things.

The assumption appears to be that these homicides are committed by people who are out of prisons or asylums.

How do you capture that space between those incarcerated unable to commit homicides on the outside and those on the outside committing the homicides? Is there some type of lag/lead analysis and is there an optimal number of months/years to lag/lead?

Do the figures leave out homicides in prison or asylums by persons in asylums or prisons? Is that significant.

Best,
Ben
5.1.2007 10:26pm
dwshelf:
Clayton Cramer writes:

an awful lot of murders committed in the 1980s and through Sunday (in Kansas City) by people who, in 1950, would have been hospitalized instead...

At the very least, take on one form of the null hypothesis, that being common wisdom.

The high murder rates of the 1980s were the result of opening prisons starting during the 70s, combined with the spread of illegal hard drug sales which created plenty of problems for which murder seemed the appropriate solution.

You could show that false by showing that convicted murderers were wildly disproportionately the products of mental institutions rather than prisons, combined with a demonstration that a significant percentage of drug traffic murders are committed by the mentally ill.

Such a case seems unlikely.
5.2.2007 3:38am
No mas!:
All writs

Thanks for welcoming me to the world of law.

Except that I'm a lawyer ... who is perfectly comfortable with boring analyses with policy implications ... who used to come to this blog for a bit of often-law-related entertainment. But this isn't entertaining.

Volokh used to be entertaining. Now it attracts people who say things like "Welcome to the world of law." You can have it.
5.2.2007 11:03pm
Jeff Yates (mail) (www):
I have taken a brief look at the national level data paper "From the Asylum to the Prison" and it is very interesting. However, I didn't see anything suggesting a test for stationarity (or possible co-integration) of the time series. Certainly Professor Harcourt deals with first order autocorrelation by employing a prais winsten regression model, however this doesn't necessarily fully correct for higher ordered autocorrelation concerns, if they exist. A quick look at the national level time series (graph) at issue suggests, at least at first blush, that there may likely exist non-stationarity in both time series. Of course this could have problematic implications for the findings. An interesting discussion of stationarity issues in a law topic setting can be found in the debate between Mishler &Sheehan and Segal &Norpoth in the American Political Science Review (1993) in which they discuss the implications of stationarity for the premise that aggregate Supreme Court decision liberalism is influenced by aggregate national public opinion.
5.4.2007 12:48pm