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Monday, September 23, 2013

Longer Sentences and Prison Growth, Part 2

In my last post, I made a broad—but vulnerable—argument for the claim that longer sentences have not driven prison growth. So I want to provide some stronger evidence for this point over the next few posts.

I want to start by looking at what we can learn from the National Corrections Reporting Program, a powerful and strangely-underused dataset compiled by the Bureau of Justice Statistics. Almost all work on prison growth simply uses the BJS’s aggregate annual admissions, stock, and release data. But the NCRP provides us with the ability to examine the role of time served more precisely.

The NCRP, unlike the aggregate data, reports information on individual inmates. States gather data on the inmate when he enters and then again when he leaves prison. With a bit of work, it is possible to construct the entire distribution of time served by an entering cohort: that of those admitted in, say, 1994, 35% were released within one year of admission, 15% between one to two years after admission, and, as of 2011, 4% of that cohort is still in prison.1 (Technically, this distribution can be calculated down to the number of days in prison.) 

This granularity allows us to do two things that we can’t really do with the aggregate data: compute how the distributions in time served have changed over time, and consider how much different our prison population would look had our admissions or release policies been different. I’ll address the first point in this post, the second in my next one.

Now, there are two major limitations to the NCRP that I need to acknowledge up front.

First, participation in the NCRP is voluntary, and while about 40 states contribute now, in its early years only about thirteen or so states sent in data. Moreover, much of the data they sent in was flawed in one way or the other,  producing any sort of long time series requires dropping a lot of states. The upshot of these limits is that my paper from which these results come can use only 11 states, and these are all disproportionately “Blue”: more urban, more industrial, more Democratic. My sample here is highly self-selected. 

(Don’t dismiss my results yet: in a later post, I’ll produce some results that replicate my basic findings here using all fifty states. Self-selection does not guarantee bias, just increases the risk of it.)

And second, the NCRP does not begin to provide consistently reliable data until the mid- to late-1980s or early 1990s (depending on the state). So if a major factor in prison growth was a one-time upward shift in time served in the mid-1980s—as my caveats in my last post suggested could not be ruled out at first—my results here will miss that and thus undersell the importance of changes in time served.

But there are two important counter-points to the limitations as well. First, the results I mention above that extent 11 states to 50 also extend my starting years from the late 1980s to 1977. And those results seem to show no real change in time served. And second, just showing that time served hasn’t grown since the late 1980s is still a surprising result. Observers as astute as Frank Zimring have argued that the 1990s represent the period where we shift from “lock ‘em up” to “throw away the key.” That’s just not the case.

Enough qualifications and hedging and counter-hedging. On to the results.

The following figure plots the median, 75th and 90th percentiles of time served for each entering cohort. In other words, a value of, say, 2.5 for the median and 4.25 for the 75th percentile in 1995 means that half of all prisoners admitted in 1995 were released within 2.5 years, and 75% were released within 4.25 years. Not surprisingly, as we reach the end of the time series some values can’t be computed: for many latter cohorts, the 90th-percentile prisoner was not released by the time my data ends (in 2004, for the paper I from which these results come).

Screen Shot 2013-09-23 at 10.02.12 AM

Two clear trends appear here:

First, the quantiles all appears fairly constant over time.

And second, the three quantiles plotted here are not really all that long. In many states, the 90th-percentile time-to-release is four to seven years, and the median is often about 1.5 to two years.2

Neither of these results is consistent with the Standard Story, and both argue against viewing changes in time served—or time served in general—as the primary, or even a major engine of prison growth.

In my next post on sentence length, I’ll employ the NCRP data to make the case against sentence length even stronger, using it to generate some counterfactual thought experiments which indicate that changes in time served simply do not explain the growth in prison population, at least since 1990.

That said, these results are not conclusive, and at least one major statistical caveat needs to be addressed up front. Time served can stay flat or fall even during a period where almost all growth is due to longer sentences. This is, I think, an example of Simpson’s Paradox.

Consider a world that has serious drug dealers and minor drug dealers. In Year 1, the state convicts one serious dealer and sentences him to 10 years and ignores the minor dealers, and it repeats this every year. After a while, the prison has an equilibrium prison population of 10. Then, in Year 20, the state increases the sanction for series dealing to 20 years, but it also decides to crack down on the minor dealers and convicts 2 of them every year to serve one-year sentences. The prison population rises to 22 in the long run, although the median falls from 10 years to 1, and the mean from 10 to 7.3. All this despite the fact that 10/12 of the growth is due to longer sentences.

As I’ll argue in the near future, Simpson’s Paradox may be playing some role in these results—particularly in California (which, given the size of its population, is a major concession on my part)—but it does not explain all the stability: even if the “real” effect isn’t as flat as my results suggest, it is more flat than we generally think it to be.

That said, at least as a first step away from the overly-simple argument in my earlier post, these results continue to argue against longer sentences as the main engine of prison growth.


1 Recent, impressive revisions to the NCRP make these calculations quite easy to make for post-2000 data. Which is great, although this renders two long statistical appendices I had written on how to make them moot.

2 The low median in California is driven by its disproportionate reliance on short-serving parole revocations.

Posted by John Pfaff on September 23, 2013 at 10:13 AM | Permalink


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