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Monday, September 16, 2013

Longer Sentences and Prison Growth, Part 1

Over several future posts, I am going to argue that despite all the academic, political, and media attention they receive, long prison sentences are not driving prison growth. Sentences are not that long, and time served has been fairly stable over the years. It is a counter-intuitive and contrarian position to be sure, but I think I have the data on my side.

I want to start, though, with a very simple argument for why we should be skeptical of the longer-sentences-are-central-to-prison-growth argument. And it is one that requires almost no real statistical digging at all.

It’s this graph:

Screen Shot 2013-09-16 at 11.18.05 AM

All this graph plots is total annual admissions to prison in blue, and total annual releases from prison in red. Intuitively, if states were forcing entering cohorts to serve longer and longer sentences, we should expect to see the red releases line flatten relative to the admission line. And maybe that happens to some degree around the late 1980s/early 1990s, but it disappears by the end of the 1990s.

This at least suggests, with some strength, that any sort of lengthening was short-run in duration, and thus that increases in time served in prison--regardless of whatever the legislatures have done to the sentencing--is not at the heart of prison growth. And I think this is generally the right way think about prison growth.

But I don’t want to oversell this point. In fact, let me undermine it a bit right out of the gate. I decided recently to run a simulation. I assumed that a state used one release schedule for all prisoners and then made a permanent one-time change to that schedule, and plotted the admissions and releases trends for this hypothetical jurisdiction.

Specifically, I initially assumed that all inmates were released over 6 years: of all the inmates admitted to prison in year t, 40% are released in t, 20% in t+1, 15% in t+2, 15% in t+3, 5% in t+4, and 5% in t+5. I then assumed that the state toughened sentencing laws so that it took 11 years for all inmates to be released: of those admitted in t, 35% are released in t, 15% in t+1, 12.5% in t+2 and t+3, 5% each in t+4,t+5, and t+6, and 2.5% each in t+7 through t+11.

In other words, under the first sentencing regime, the median time served in prison is 1 year and the mean 2.4 years, while under the second regime the median is exactly 1 again and the mean 3.375. 

Then, to make my simulated admissions data track the actual admissions data more closely, I assume that admissions increase every year by 100 (from an initial value of 1000) for the first 13 years, by 200 for the next 7 years, and then again by 100 for the rest of the years. This is to capture the admissions increase that appears in the real data from the mid-1980s to 1990.

Here are the simulated results:

Screen Shot 2013-09-16 at 11.20.11 AM

What immediately stands out, of course, is that this simulation seems to produce a bulge similar to the one we see in the real data in the 1990s. So close-tracking/bulge/close-tracking can arise in the presence of toughening sentencing lengths. 

In other words, the real data is not a slam-dunk argument for the fact that tougher sentencing laws are not behind prison growth.

But I have three major caveats to my caveat:

  1. In the simulation, even though the admissions and releases lines return to tracking each other closely in the end, as a result of the tougher sentencing regime the gap between them has grown. We don’t see that in the real data, where the gap actually narrows in the mid-2000s.
  2. I have other approaches using other data that all seem to substantiate the idea that tougher sentences are not driving prison growth. I’ll being working through all these in future posts.
  3. The simulation may suggest that tougher sentencing has contributed more to prison growth than I sometimes give it credit, but that does not necessarily imply that it has been more important than admissions.

All of which is to say the following: I don’t think tougher sentences are driving prison growth. And I think I have the data to back up that claim in the main. But I also want to fight off epistemic closure and confirmation bias, and to keep an open mind to the possibility that sentence lengths are playing a bigger role than I sometimes acknowledge.1

So, it seems pretty clear to me that we overstate the importance of longer sentences. Even more, I feel that the data appear to strongly support the claim that admissions increases are doing most if not close to all the heavy lifting. But the complete story will almost surely be a (fair?) bit more confusing and convoluted. 


1I think it is too easy, when one finds oneself sincerely convinced of a contrarian position, to oversimplify it (“your argument that time served matters is completely wrong. It is just admissions!”) and then defend it to the death. That’s what gets people’s attention. “The conventional wisdom isn’t entirely right, though often it does have its merits” just doesn’t excite people at all.

I don’t want to do either, despite the fact that refusing to fanatically defend an extreme position must violate some part of the Law of Blogging.


Posted by John Pfaff on September 16, 2013 at 11:30 AM in Criminal Law | Permalink


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John --

Interesting posts. But I think there's an error in your initial assertion that "we should expect to see the red releases line flatten relative to the admission line", at least to the extent you suggest the flattening should be permanent. (You do undermine this point a bit yourself, but I think the problem with it might run even deeper.) I would expect a change in sentencing practices to only temporarily flatten the release line (at least assuming constant rate of admits). In a very simple world, say, a shift in which courts shift from imposing uniform sentences of 2 years to imposing uniform sentences of 3 years the two lines would diverge temporarily (releases would drop to zero) in year 2 but the lines would re-converge the following year. The prison population would also balloon, permanently (by 50 percent) as long as the new 3 year sentencing regime were in place.
I might be getting something wrong here, but your initial premise just struck me as odd.
Perhaps the real problem is that admissions didn't drop over this time period. After all, I imagine many would expect longer sentences to have an incapacitative effect -- keeping criminals off the streets longer should reduce the number of offenses and thus the number of admits into the system. But your data suggest (and your model assumes) otherwise.

Posted by: Rob Mikos | Sep 16, 2013 1:26:21 PM

Rob--I think you're right. What you explain is basically what my simulation is modeling. As long as sentences *continue* to get tougher, the releases line should continually flatten relative to admissions. But a one-time toughening will result in a brief flattening and the reconvergence, like in the simulation, although the post-hike gap between admissions and releases will be larger (which is not what we see in the mid-2000s onward).

Perhaps a better initial premise would be: if there was a period of toughening in time served, we should see a gradual divergence followed by a reconvergence to a new equilibrium in which the two lines end up further apart. We may see the first effect, but we don't appear to see the second.

And yeah, the real puzzle is why admissions kept climbing. My own works shows that it seems like prosecutors simply ramped up the percent of arrests resulting in felony charges, which raises the question I still have no answer for of "why?"

Posted by: John Pfaff | Sep 16, 2013 2:11:13 PM

> the question I still have no answer for of "why?"

I have a working theory: prosecutors charging "inflation" in recent decades is the result of rational (albeit not coordinated in any systemic way) institutional response for the lack of commensurate funding in the criminal justice system for the increased demand for its services. my thinking is that the inflation helps all parties in the process because it fundamentally changes the cost/benefit of going to trial. That allows dockets to flow because the "trial penalty" crowds out any rational consideration by individual defendants of actually going to trial. (defense bar benefits too by being able to ethically advise against trial in an "inflation" environment where, say, a nonviolent vice repeat offense can be bootstrapped into a serious 10-20 year potential trial result) Thus, the system can process more cases without additional funding.

One way to test this would be to review data that shows the trajectory from, say, 1975 of how many criminal cases are resolved by trial to today's figure of state 94%/fed 97%. My theory is that the number of has steadily increased and that it tracks with the increase in prosecutorial inflation that allowed more "efficient" processing (this has obvious potential problems if "just outcomes" are your goal - efficiency and justice are often in tension in a fiscal wasteland.)

I'm not suggesting that this was some insidiously designed policy and, rather, the result of a host of actors that are responding to an environment with a lot more defendants than the system can meaningfully process in an adversarial criminal trial process without adequate resources. According to my theory, the inflation is a result of an unwillingness of voters to pay the "effective" cost of the system so prosecutors (vast majority are elected) respond to this constituency by depositing the externality onto defendants by overcharging and foreclosing expensive trials to the dustbin of history.

One thought experiment I've toyed with in this area is to imagine a criminal justice system that has adequate funding to _require_ all felony cases to go to trial.

anything to this?

Posted by: Will Coy-Geeslin | Sep 17, 2013 4:20:49 PM

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