Estimating Prison Stays Among Current Prison Populations

Published date01 June 2019
Date01 June 2019
Subject MatterArticles
Estimating Prison Stays Among
Current Prison Populations
Jeremy Luallen
, Gerald Gaes
, and Christopher Cutler
Background: Reporting estimates of length of stay in prison populations is a common objective in
corrections research. Researchers and prison administrators use these estimates for many
different purposes. These include projecting future prison operational and capacity needs,
describing levels of punitiveness among states, and explaining the drivers of prison growth or
decline. Because of their critical importance to so many dimensions of corrections and criminal
justice, researchers have compared the merits of various methods to estimate prison length of
stay. Objective: This article revisits a survival-based approach for estimating length of stay originally
described in Patterson and Preston and uses historical prison data from the Bureau of
Justice Statistics National Corrections Reporting Program to compare this method to alternatives. It
also describes and tests the merits of extending this method to parametric frameworks. Method:
Using 20 years of data in nine states, we model estimates of (1) average length of stay for the 1995
prison admission cohort and (2) length of stay distributions for the 1995 prison stock and compare
estimates to true values for these samples over a 20-year period. We compare results derived from
adjusted and unadjusted stock-flow calculations, release cohorts, and nonparametric and
parametric survival models. Results: We demonstrate that estimates of length of stay using survival-
based estimators consistently perform much better than other estimators and that there are
advantages to using parametric estimation techniques over nonparametric ones. Parametric-based
estimates are less variable and more reliable on average. Conclusion: We conclude that in the future,
stay length estimates should be estimated using survival models like the ones we describe and that
data exist which provide the means to do so effectively.
methodology, analytic methods, modeling prison populations, time served
athenahealth Inc., Watertown, MA, USA
Florida State University, Tallahassee, FL, USA
Abt Associates Inc., Cambridge, MA, USA
Corresponding Author:
Jeremy Luallen, athenahealth Inc., Watertown, MA 02472, USA.
Criminal Justice Review
2019, Vol. 44(2) 119-147
ª2018 Georgia State University
Article reuse guidelines:
DOI: 10.1177/0734016818769705
Estimating the time that inmates spend in prison—alternatively called length of stay, time served,
prison spell, or stay length—is important from both a research and public policy perspective. It is a
prerequisite for accurate population projections.
Jurisdictions use those projections to budget
operational and capital expenses. Projection results can also be used to forecast inmate composition
such as future age or custody-level mixtures. Jurisdictions can use these forecasts to plan more
precisely to address medical and security needs. Time served has been the center of debate on the
causes of mass incarceration. Some scholars argue that increases in the level of the U.S. prison
population are attributable to changes in length of stay as well as changes in rates of admissions
(National Research Council, 2014), while others argue length of stay has had little or no impact (see
especially Pfaff, 2011, 2017). It is possible that this argument could be resolved by better length of
stay estimates over time. Stay length is also a key statistic when comparing trends in punitiveness
among states at a point in time or within a state over time (Pew, 2012). If the stay length estimates
are inaccurate, the jurisdiction comparisons or trends may be meaningless.
To measure length of stay, criminal justice researchers have adopted different estimation strate-
gies. One common practice is to use stock-flow calculations (either as the ratio of prison entries to
the current stock or as the ratio of prison exits to the current stock) to calculate average length of stay
(Blumstein & Beck 1999, 2005; Butts & Adams, 2001; Lynch, 1993; Patterson & Preston, 2008;
Pew, 2012).
The strength of such estimators is that they are easy to estimate and only require
aggregate values of the prison stock, and the total number of admissions or releases over some
specified time frame. However, these estimators require strong steady-state assumptions about the
flow of prisoners both into and out of prison over time (Patterson & Preston, 2008). Moreover,
although these estimators represent mean length of stay, they do not provide estimates of the time-
served distribution.
Another common practice is to estimate time served using the observed stay lengths of offenders
in release cohorts. Release cohorts are a convenient source of data commonly used in criminal
justice studies, such as studies of recidivism, and are widely available. They also have the advantage
that they can be used to describe the distribution of stay lengths rather than simply the average of the
entire population. However, to be unbiased, they require strong steady-state assumptions about the
flow of prisoners both into and out of prison over time (Patterson & Preston, 2008). They have also
been shown to understate the number of long-stay offenders (Lynch, 1993) and, in some cases, can
be highly variable from 1 year to the next. Nevertheless, estimates of stay length derived from
release cohorts are relatively unbiased compared to estimates drawn from the entire prison stock
(Akerlof & Main, 1981).
A recent paper by Patterson and Preston (2008) discusses the application of these estimators in the
context of criminal justice research and describes the assumptions and limitations of each. That
paper also proposes an alternative estimator that adjusts estimates to account for prison population
growth and mitigates the strong steady-state assumptions that are made about entry and exit rates.
Simulations by the authors demonstrate that their adjustment improves estimates of average time-
served over existing methods, though their method (1) requires an additional source of data on prison
growth, (2) assumes constant rates of growth in the adjustment, and (3) does not produce a distri-
bution of stay length. Patterson and Preston’s proposed adjustments are clearly a superior choice to
standard stock-flow calculations, but not without its limits.
Another method discussed briefly in Patterson and Preston is the use of life table/survival models
as a tool for estimating stay length. That method is the focus of this article. At the outset of their
discussion, Patterson and Preston argue that life table/survival models are a superior means for
producing statistics but that effective applications of these methods require longitudinal data that are
120 Criminal Justice Review 44(2)

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