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The Effect of Legislated Reductions in the Prison
Population on Crime Rates
Roisin McCord
March 28, 2013
Abstract
As a major aim of incarceration is to reduce crime, it is important to understand the extent to
which it does so. Isolating the effect of prison on crime can be difficult because of reverse
causation: higher crime rates also tend to lead to larger prison populations. This paper utilizes
state legislated reductions in the prison population to address this question. These policy changes
were adopted because of budget or prison overcrowding concerns, and the legislation achieved
its goals by shortening sentences and releasing from prison many nonviolent offenders. Using
state level data from 1982 to 2009, I estimate that these actions lead to a 9.2 percent decline in
state prison populations. In two stage least squares models that use the release legislation as an
instrument for prison population, results indicate that a decline in the prison population leads to a
statistically significant increase in nonviolent crime rates, with an elasticity of approximately
0.367. There is no statistically significant impact of release on violent crime, which is expected
given the prison population impacted by the laws.
Notre Dame Economics Honors Program
Senior Thesis
Advised by Dr. William Evans
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Introduction
The United States incarcerates more people than any other nation, accounting for nearly a
quarter of the world’s prison population while comprising only 5% of the world’s population
(ACLU, 2011). Since the 1970s, the prison population in the United States has grown
continually. Between 1986 and 2001, prison expenditures increased 150% from $11.7 billion to
$29.5 billion in constant 2001 dollars (Stephan, 2004). Since a major aim of incarceration is to
reduce crime, the extent to which it does so is an important but unsettled question.
There are mixed opinions on the relationship between crime and imprisonment. Some
theorize that incarceration can actually increase crime because of its negative impact on social
structures. Supporting these theories, county level studies have indicated that incarceration
disrupts family structure and leads to economic struggles for former inmates who have difficulty
finding employment because of their criminal records (Lynch and Sabol, 2000).
On the other hand, some research suggests that increased incarceration is correlated with
lower crime rates. There are two ways in which increased incarceration is believed to cause such
reductions. One is through incapacitation, as a prisoner does not have the opportunity to commit
crimes while in jail. To quantify the impact of incapacitation, a key research question is
estimating the crimes inmates would have committed during their sentences, had they not been
incarcerated (Piquero, 2007). This is difficult to do because it requires estimating how people
would have behaved if they were not in prison. Bhati (2007) uses the criminal trajectories once
released from prison of those with shorter sentences to infer how much crime is prevented by
incapacitation for those with longer stays. He finds that increasing the length of prison sentences
by 1% prevents an approximately proportional number of crimes. This method will, however,
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understate the impact of incarceration if those released are less active criminals than those with
longer sentences.
Incarceration is also believed to lower crime through deterrence. Levitt (1998) provides
evidence that deterrence accounts for more than 75% of the reduction in property crime that
results from arrests, and there is a fairly equal mix between deterrence and incapacitation effects
in violent crime arrests. Incarceration has been found to both deter criminals from committing
crimes after they are released from prison and deter those who have never been to prison from
committing crimes. Despite these results, Levitt cautions that the evidence is far from conclusive
because he does not deal with the issue of reverse causation. On page 365 of the paper, Levitt
adds the notes that “the results in the paper must be interpreted with the caveat that endogeneity
is present.” It is believed that longer prison terms deter criminals more effectively than do
shorter ones (Kuziemko, 2007).
Despite these few studies that attempt to distinguish between the effects of deterrence and
incapacitation, making such a distinction can be difficult. Estimations of incapacitation such as
those in Bhati (2007) can be inaccurate as they largely rely on surveys of inmates, which are not
necessarily reliable. Also, while changes in rates of reported crimes can be observed in the
Uniform Crime Reports, estimates do not guarantee what crimes would have been committed
had prospective criminals and former inmates not been deterred by fear of incarceration. Trends
in crime rates can also be affected by changing social conditions, such as family structures or
urban populations that are independent of prison population, leading to inaccurate estimates of
the incarceration effect.
A number of economists have attempted to identify the overall effect of incarceration on
crime. Marvel and Moody (1994) regress crime rates on prison populations and conclude that
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prison population growth leads to lower crime rates with elasticities of -0.099 for violent crimes
and -0.071 for property crimes. This study is limited, however, in that it does not control for the
tendency for increased crime rates to raise prison populations. The work of Marvel and Moody
is therefore subject to a simultaneity bias, which would bias down the estimates in absolute
value.
Levitt (1996) attempts to avoid the simultaneity bias by computing elasticities of crime
rates following large prison releases resulting from overcrowding litigation. Levitt argues this
approach effectively avoids the simultaneity bias since such releases caused a change in prison
populations that was the result of successful legal suits rather than a change in crime rate.
Levitt’s elasticities indicate a much stronger incarceration effect on crime than had been
previously seen. Specifically, he found elasticities between -0.424 and -0.379 for violent crime
and between -0.321 and -0.261 for property crime.
The estimates obtained by Levitt are, however, now rather dated. Levitt used data from
1970 to 1993, but per-capita prison population in the United States increased by 41% from 1993
to 2009. In this paper, I utilize the methodology of Levitt and consider the impact of changing
prison population on crime. The exogenous shocks to prison populations that I utilize are recent
state changes that have led to mass release of prisoners. As I establish below, most of these
changes in incarceration laws, were initiated because of state fiscal reasons and are not a result of
changes in crime rates
Penal policy changes, such as mandatory minimum sentencing, three-strike laws, and
truth-in sentencing legislation have resulted in much longer prison terms. Likewise, the war on
drugs has led to a much larger fraction of those convicted actually serving prison time. As a
result of these trends, the United States prison population has increased considerably over the
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past 40 years, so that prison populations in 1997 were five times as large as those in 1973. By
1997, 645 of every 100,000 United States residents were incarcerated (Caplow & Simon, 1999;
Sabol, 2002; King and Mauer, 2006). This growth in prison populations has led to overcrowded
prisons and increased law enforcement spending. In 2008, the states spent $47 billion on
corrections. While about two-thirds of offenders are on parole or probation as opposed to in
prison, prison expenditures account for approximately 90% of corrections expenditures (Moore,
2009).
Generally, prisoners with a higher risk of recidivism are sentenced to longer terms.
Findings are that parole boards can fairly accurately predict an inmate’s chance of recidivism and
design a sentence so that he is released when this risk falls to a predetermined level (Kuziemko,
2007). By this reasoning, shortening these predetermined sentences should lead to a higher
recidivism and, therefore, higher crime rates, as higher risk criminals are subsequently left out on
the street. An earlier study concluded that while early release proved to be cost-effective, it did
have the negative effect of increasing crime (Austin, 1986). However, in recent years, much of
the increase in prison population has been generated by longer minimum sentences and hence, it
has been difficult to compare the marginal criminal released today to one released in previous
periods. The large prison populations in many states and the strain that prison spending puts on
state budgets have led states to reform prison sentence and parole laws, allowing shorter terms
and early release for prisoners. By shortening the length of time served by prisoners, states can
reduce their prison populations, cutting prison spending and relieving overcrowding.
With the implementation of such changes, the growth in the prison populations has
slowed since the turn of the century, dropping from over 2% per year in 2000 to less than 0.3%
in 2009. Detecting the impact of these reforms on crime is made more difficult because these
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years of slowed growth in prison populations have occurred during a period when crime rates
were declining persistently over time. Quantifying the change in crime rates that resulted from
such reforms would provide evidence as to the social costs of such laws and budget cuts. Doing
so would also provide evidence similar to Levitt’s (1996) that avoids the simultaneity bias
resulting when one does not control for the causal effect of crime rate on incarceration rate.
This paper aims to determine the effect of incarceration rates on crime in recent years by
examining 13 states that have changed parole and sentencing laws, resulting in the early release
of prisoners, and as a result, a noticeable reduction in prison populations. It will utilize a
difference in difference methodology that studies the changes in crime rates in these 13 states
before and after the new legislation, and compare these estimates to trends in states that have not
adopted large scale prisoner releases. Looking at the impact of these laws on crime rates avoids
the simultaneity bias that crime has on prison population, as the change in sentencing laws acts
as an exogenous factor that is not influenced by crime. This study analyzes the effect of state-
initiated changes to prison population on crime, differing from Levitt’s1996 paper, which looked
at cases where a state’s prison population was under federal control. While the means of
downsizing populations differ among states, this paper does not distinguish between such
methods but rather looks solely at the extent to which incarceration impacts crime rates. It aims
to determine if the effect of incarceration on crime that Levitt found has persisted in the years
since his study and if this effect is found when considering cases where states made financial
decisions to downsize prison populations.
Regression analysis presented later in this paper, indicates that the legislative changes
examined in this study did effectively reduce prison population by about 9.2%. Using such
changes as an instrument for prison population, nonviolent crime is seen to increase as prison
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population decreases. Nonviolent crime has an elasticity of -0.367 with respect to prison
population, which is very similar to the results of Levitt (1996). No change is observed in
violent crime when legislative changes are enacted, which is not unexpected, as these laws were
specifically intended for the release of nonviolent criminals.
State Prison Downsizing, 2003-2009
The states examined in this study all made some changes to prison, sentencing, or parole
laws between the years of 2003 and 2009. In all cases, the goal of reducing prison populations
was motivated by state budgets. While there have been similar reforms since then in other states,
prison population data was only available through 2010. Table I gives the states and the years of
the penal policy changes used in this study. The observed legislative changes were obtained by
systematically “googling” each individual state name along with specific phrases such as “prison
early release,” “parole reform laws,” and “prison reform laws.” The resulting sources were then
examined to determine if the given state enacted legislation aimed at reducing prison populations
in the study time period. All states that were found by this systematic search to have enacted
such legislation were put into the treatment group in this study. All control states were
researched individually in this same way, through “Google” searches of several different phrases
relating to prison reform along with the specific state’s name. The control states were not found
to have passed prison legislation in the studied years. A short explanation of the methods of and
reasons for legislative changes is given below for each of the 13 states included in the treatment
group.
In 2003, the Michigan Prisoner Reentry Initiative was enacted to help transition prisoners
back into the community. It led to the closing of over 20 correctional facilities and an estimated
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12% drop in prison population (NGA Center for Best Practices, 2011). A 2003 Washington
Senate Bill allowed for increased earned early release for nonviolent offenders, reducing
spending by approximately $7200 per criminal (Washington State Institute for Public Policy,
2009; NGA Center for Best Practices, 2011). In 2003, Arkansas’s “Emergency Powers Act”
allowed county jails to release nonviolent offenders earlier in order to relieve overcrowding
(Arkansas, 2003). In 2007, faced with prison overcrowding and the prospect of needing to build
new prisons to accommodate prisoners, Texas and Kansas passed legislation reforming and
“reinvestment packages,” investing in treatment programs as alternatives to prison. They also
reformed probation laws, encouraging shorter prison stays for certain nonviolent offenders and
allowed for earned good time credits (ACLU, 2011; Garland). In 2008, aiming to reduce prison
overcrowding, Mississippi passed Senate Bill 2136, changing its truth-in-sentencing laws and
granting parole eligibility to nonviolent offenders who had served 25 percent of their sentences
(Justice Policy Institute, 2011). Wisconsin also modified its truth-in-sentencing laws in 2009,
allowing inmates to earn early release in return for good behavior (Wisconsin Legislative
Reference Bureau, 2009).
In 2008, in response to prison overcrowding and high costs of incarceration, Kentucky
passed House Bill 683, “allowing the parole board to review more cases…so that prisoners might
be eligible for release earlier” (Kentucky Justice and Public Safety Cabinet, 2008). Vermont’s
2008 House Bill addressed the state’s overcrowding and high prison spending by releasing
inmates to rehabilitation programs, allowing for the closing of state prisons. In 2008,
Pennsylvania reduced prison spending by enacting legislation allowing early release from prison
if prisoners showed good behavior and participated in treatment (Pennsylvania Department of
Corrections). Vermont passed the “War on Recidivism Act” in 2008, allowing early parole for
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low-level offenders in response to high prison overcrowding and spending (Vermont, 2008). In
2008, Arizona passed Senate Bill 1476, “The Safe Communities Act,” allowing for earned time
credits and financially encouraging probation officers to keep parolees out of prison (Waters,
2008).
In 2009, Illinois Governor Pat Quinn released 1,700 prisoners in an effort to cut spending
but changed back to a more rigorous sentencing policy months later, when faced with criticism
because of high recidivism rates of those released (Garcia, 2009). California was ordered to
release 30,000 prisoners by the Supreme Court in 2011. This paper does not cover the effect of
this decision because there is no crime and prison population data available from after 2010.
However, California’s growth in prison population was first slowed in 2007, when the state
formed a three-judge panel with the purpose of reducing overcrowding in California prisons
(California Budget Project). The forming of the panel in 2007 is employed in this study.
Data Description
The key goal of this study is to analyze how trends in state prison population were altered
as a result of mass prison release legislation. Because the enabling legislation was passed in
specific states and in particular years, annual state-level observations on prison population and
crime were required. Prison populations are defined as all prisoners under jurisdiction of Federal
or State Correctional Authorities, and are taken from the Statistical Abstract of the United States
(United States Census Bureau).1 The data cover years from 1982 until 2009. Because prison
population data are not available past the year 2009, the study does not include years after that.
1 Data available from:
http://www.census.gov/compendia/statab/cats/law_enforcement_courts_prisons/correctional_faci
lities_prisoners.html and http://www.census.gov/prod/www/statistical_abstract.html
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Likewise, because state prison population data are not available for 1981, the observations in this
paper begin in 1982. The crime data are annual rates of reported crimes, as listed by the Federal
Bureau of Investigation, in its Uniform Crime Reports.2 The crime rates in this paper are broken
into categories of violent and nonviolent crime. Violent crime includes robbery, rape, murder,
and assault. Nonviolent or property crime includes burglary, motor theft, and larceny. Annual,
state prison populations are given presented per 100,000 state residents.
Annual, per capita income is taken from the US Bureau of Economic Analysis.3 Race and
age data for state and year are calculated as a percent of state population and are as compiled by
the National Cancer Institute in Surveillance Epidemiology and End Results.4 Annual state
unemployment rates are as published by the Bureau of Labor Statistics in the Geographic Profile
of Employment and Unemployment.5
Methods
This paper employs a two-stage least squares (2SLS) regression model to determine the
effect of incarceration rates on crime rates. A 2SLS model can be used to avoid omitted
variables and a simultaneity bias in linear regression models. It utilizes a third variable that is
correlated with the original predictor variable but is uncorrelated with the error in the original
model (i.e. there is no simultaneity between this third variable and the outcome variable). The
new variable (in this case prison legislation changes) acts as an exogenous shock, allowing for
2 Data available from: http://www.ucrdatatool.gov/Search/Crime/Crime.cfm 3 Data available from:
http://www.bea.gov/iTable/iTable.cfm?ReqID=70&step=1&isuri=1&acrdn=4#reqid=70&step=1
&isuri=1 4 Data available from: http://seer.cancer.gov/popdata/download.html 5 Data available in print version of Geographic Profiles of Employment and Unemployment
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observation of the impact of the original variable (prison population) on the outcome variable
(crime rates).
The outcome variable of interest is ln(crime ratest), which is the natural log of state s’s
crime rate in year t. Crime rates are defined as reported crimes per 100,000 residents. The
equation of interest is similar to that used by Marvel and Moody (1994) and takes the form:
ln(𝑐𝑟𝑖𝑚𝑒)𝑠𝑡 = 𝛽1ln (𝑝𝑟𝑖𝑠𝑜𝑛)𝑠𝑡 + 𝛽2 ln(𝑖𝑛𝑐𝑜𝑚𝑒)𝑠𝑡 + 𝛽3𝑢𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠𝑡
+ 𝛽4𝑝𝑒𝑟𝑐𝑒𝑛𝑡1524𝑠𝑡 + 𝛽5𝑝𝑒𝑟𝑐𝑒𝑛𝑡65𝑠𝑡 + 𝛽6𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑏𝑙𝑎𝑐𝑘𝑠𝑡
+ 𝛾𝑡 + 𝜉𝑠 + 𝜀𝑠𝑡
(1)
in which ln_prison is the ln(prisoners per 100,000 state residents) in a given year, ln_income is
the ln(per-capita income) in a given state and year, unemployment is the state unemployment
rate, percent1524 is the percentage of state residents between the ages of 15 and 24, percent65 is
the percentage of state residents who are at least 65 years old, and percentblack is the percentage
of state residents who are black. The variable γ is a set of dummy variables used to control for
permanent differences in crime across states. For example, the per capita motor theft rate is
consistently higher in Arizona than in Alabama. The variable ξ represents year effects that are
shocks common to all states in a year but are allowed to vary across time. For example, per
capita motor theft rates were in lower in most states in 2008 than in 2007. These covariates were
included in the model to control for unexplained external factors affecting crime rates that are
common to a state or a year. For example, a national occurrence such as the start of an economic
recession could affect the crime rates across all states in a given year. The key covariate of
interest is β1 which represents the elasticity of crime with respect to the prison population.
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As discussed above, while this model can indicate the correlation between crime and
prison populations, because of the simultaneity bias that exists between these two variables, it
does not isolate an unbiased estimate of the effect of incarceration rates on crime rates. If crime
rises, independent of prison populations, there will be more criminals to arrest, leading to higher
incarceration rates. This will bias down the elasticity estimated in the above model. To isolate
this effect, a two-stage least squares model was created. For this model, the dummy variable
release was generated, using the previously presented information on state legislation changes.
The variable releasest = 1 for a specific state in the year of and the years following the
implementation of a law aimed at reducing prison population, and 0, otherwise. To determine
the efficacy of such changes in reducing prison populations, the following first-stage model was
created:
ln (𝑝𝑟𝑖𝑠𝑜𝑛)𝑠𝑡 = 𝜋1𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑠𝑡 + 𝜋2ln (𝑖𝑛𝑐𝑜𝑚𝑒)𝑠𝑡 + 𝜋3𝑢𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠𝑡
+ 𝜋4𝑝𝑒𝑟𝑐𝑒𝑛𝑡1524𝑠𝑡 + 𝜋5𝑝𝑒𝑟𝑐𝑒𝑛𝑡65𝑠𝑡 + 𝜋6𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑏𝑙𝑎𝑐𝑘𝑠𝑡
+ 𝛾𝑡 + 𝜉𝑠 + 𝜀𝑠𝑡
(2)
which gives an elasticity of prison populations dependent on the legislation changes that are
examined in this study.
Finally, the variable release was employed to act as an exogenous shock to prison
population size and so determine the effect of incarceration rates on crime rates. The reduced-
form model was of the form:
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ln (𝑐𝑟𝑖𝑚𝑒)𝑠𝑡 = 𝜃1𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑠𝑡 + 𝜃2 ∗ ln (𝑖𝑛𝑐𝑜𝑚𝑒)𝑠𝑡 + 𝜃3𝑢𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠𝑡
+ 𝜃4𝑝𝑒𝑟𝑐𝑒𝑛𝑡1524𝑠𝑡 + 𝜃5𝑝𝑒𝑟𝑐𝑒𝑛𝑡65𝑠𝑡 + 𝜃6𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑏𝑙𝑎𝑐𝑘𝑠𝑡
+ 𝛾𝑡 + 𝜉𝑠 + 𝜀𝑠𝑡
(3)
Here, 𝜃1 represents the percent change in a crime category given the implementation of a law to
reduce prison size, or ∂ln(crime)/∂(release). Since the model assumes that crime will only be
impacted by a change in the prison population brought about by prisoner release, then 𝜃1 =
∂ln(crime)/∂release = [∂ln(crime)/∂ln(prison)][∂ln(prison)/∂release]. Since the parameter 𝜋1 in
equation (2) provides an estimate of [∂ln(prison)/∂release], in this exactly identified 2SLS model,
β1 = 𝜃1 / 𝜋1. Therefore, the ratio of the coefficient on release in the reduced form model
equation (3) to the same parameter in the first stage model from equation (2) gives the elasticity
of the effect of per-capita state prison populations on state crime rates, avoiding the effect of
crime rates on prison populations.
Limitations
While the states in the treatment group took steps to reduce their prison populations
because of overcrowding and high costs of incarceration, specific changes in legislation and
methods of reducing prison population vary among states. Many states reinvested money in
treatment programs for parolees, which cost less than incarceration and reduce overcrowding.
These programs aimed, however, to reduce recidivism. If they were effective in doing so, then
these programs would likely lower crime rates as well as prison population. This would then be
an outside factor contributing to crime and correlated with prison populations and reform. If,
however, the programs do reduce crime, they would actually cause an observed increase in crime
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upon reduction in prison size to be understated. Recognizing the change in crime after the
implementations of such programs can be valuable to policy makers, but the specific programs
and, therefore, their efficacy differ from state to state. This study does, however, examine the
effect of simply imprisoning criminals and so determine the net effect of changes in prison
policy.
There is also a concern that a selection bias may affect the states included in the
experimental group. That is, some factor that is correlated with crime could have led to the
changes in prison legislation. It is plausible that a decline in crime rates led states to feel that
they could reduce prison population sides and so led to the passage of new legislation. While
this would explain the observed lower crime rates at the time of release, it would in fact
understate the effect observed in the reduced form model, decreasing the observed effect of
prison releases on crime. This problem is, however, addressed in Table VI, which shows that
there was no statistically significant decrease in crime in the experimental states in any of the
three years before the legislation changes.
If the budget problems that led to many of the changes were caused by increasing prison
populations, resulting from rise in crime rates, there would again be autocorrelation in the data.
This would explain an observed increase in crime in states at the time of legislative changes, but
it would not account for the observed positive coefficient in the first stage model (why prison
population was decreasing at the time of changes). Again, this problem of the possibility of
increasing crime in the years before changes is unlikely, given the results presented in Table VI.
The concern that increasing prison populations led to financial problems and thus legislation
changes is addressed in Table III which shows there to be no statistically significant change in
prison populations in the years preceding the changes.
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While the data analyze trends in prison population over time, numbers of releases
resulting from changes in legislation as opposed to other factors are not available. Because of
this, the study analyzes the effect that legislation had on the trend of incarceration rates. The
data also do not account for what specific groups of prisoners were released. For example, ages
and crime types of released prisoners are not specified. What types of criminals are released
could have an effect on recidivism, but legislation changes aimed to release nonviolent criminals.
While the study aims to determine changes in crime, it can only account for reported
crimes, as reflected in published crime rates. As the crime types given do not include drug
offenses, changes in penal policy regarding drug offenders specifically, are also not included in
the study. Because prison population data is only available through 2009, and the legislation
changes examined happened in recent years, the study can only analyze the short-term effect of
changes in penal policy but cannot draw conclusions about long-lasting results of such policies.
It is likely, however, that in the long-term policies would continue to change.
Results
There are 1400 observations used in this study, corresponding to specific states and years.
Table II provides summary statistics for each variable for each of the 50 states and for all years
from 1982 to 2009. The summary statistics include observations from both treatment and control
states, without distinction. Prison populations are given per 100,000 residents. Prison
populations and crime rates are natural logs. The mean ln(prison population) is 5.65 with a
minimum of 3.85, occurring in New Hampshire in1982 and a maximum of 7.84, occurring in
Alaska in 1989. The ln(violent crime) has a mean of 5.98 and ranges from 3.85 to 7.13, while
than ln(property crime) has a mean of 8.26 and ranges from 7.44 to 8.96. Property crime rates
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(defined as the combination of motor theft, burglary, and larceny) are higher than violent crime
rates (consisting of robbery, assault, rape, and murder) in every state and year and by a wide
amount.
Graphical analysis is useful in visualizing the change in trending crime rates upon
legislation changes. The appendix contains graphs that present the trend in nonviolent crime in
Michigan over time in comparison to the trend in non-violent crime in all 49 of the other states
over this time. Michigan enacted legislative changes to reduce the prison population in 2003.
Because this is one of the earliest changes examined and Michigan is a large state, it provides a
good visual of the change in nonviolent crime trends relative to the time trends of other states
after legislative changes. A vertical line denotes the year of the change (2003) on the time plots.
The first plot presents the rate of total non-violent crime, while the second and third present the
trends in motor theft and burglary, respectively. In each plot, the crime rate in Michigan is seen
to increase in the years following the legislation, while crime rates continue a downward trend in
other states at this same time. Before the change, the crime rates in each of the presented
categories in Michigan seemed to trend in a similar manner to those in other states. This
suggests that the legislative changes did lead to an increase in nonviolent crime.
As the two-stage least squares model used in this study employs prison legislation as a
shock to incarceration rates, it was necessary to check that such changes did in fact reduce prison
populations. This first-stage regression model is presented in the first column of Table III. As is
outlined in the text above, the variable release is a dummy that takes on a value of one in the
year of and the years following a legislative change in a particular state. Regressing ln(Prison)
on release, while controlling for state and year effects plus the other control variables there is a
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statistically significant decrease of about 9.1 percent in prison population after legislation
changes.
The model would present biased estimates if the prison release legislation were adopted
because of secular changes in the prison population. For example, if states adopted these laws
because of changing crime rates, then the results would be biased in a similar way to the basic
results of Marvel and Moody. To ensure that this effect was the result of the legislative changes
and not simply correlated (i.e. that the shock was indeed exogenous), the dummy variables
release1, release2, and release3 were created, indicating an observation to be one, two, or three
years respectively before a prison legislation change. The coefficients on these variables should
be statistically insignificant, indicating that the laws are not a reaction to pre-treatment trends in
the prison population. Regressions that add these three covariates to the first-stage model are
summarized in the second column of Table III. The coefficients on these pre-treatment dummy
variables are all small and statistically insignificant, and the results from this model indicate that
these legislation changes do indeed act as an external shock and so the release variable can serve
as an effective instrument in the model.
Table IV gives estimates of outcomes obtained through regression analysis, according to
the models presented above. The second and forth columns present ordinary least squares
estimates of the effect of prison populations on rates of violent and property crimes. These
models are similar in spirit to those estimated by Marvel and Moody. These values are obtained
by OLS estimates of Model 1 and do not control for the simultaneity bias between prison and
crime. All crime rates are given in log forms so that the estimates take the form of elasticities.
The model produces an estimated elasticity of 0.205 for violent crime and 0.026 for property
crime. The estimate obtained for violent crime can be seen to be significant, having a standard
18
error of only 0.025. With a standard error of 0.018, the estimate for property crime can also be
considered significant, although not at the 95% confidence level. It is somewhat surprising that
these estimates are positive. Positive elasticities suggest that crime rates actually fall when
prison population decreases. This effect is likely due to the simultaneity bias discussed above,
through which higher crime rates can lead to an increase in prison populations. These estimates
do not, however, resemble those found in the studies of either Marvel and Moody (1994) or
Levitt (1996). Both of those studies found negative correlation between prison and crime rates.
It is unclear why this more recent data would not present the same effect, although the positive
relationship seen observed here could be the result of the effect of crime rates on prison rates,
which this study aims to avoid.
The third and fifth columns present reactions of crime rates to prison population changes
in the form of elasticities, as seen through the two-stage least squares model. Both violent and
property crime are listed. While there is a negative coefficient on violent crime, it is not
statistically significant. Therefore, it cannot be deduced from this data that these legislation
changes had any effect on levels of violent crime. This is to be expected, as the legislative
changes examined led to the release of nonviolent rather than violent offenders. Therefore, the
prison population of violent offenders should not be affected. Property crime however has a
coefficient of -0.367 given a change in prison population, and the standard error allows us to
reject the null that the parameter equals zero. This estimate is slightly higher than the estimate of
-0.261 obtained for nonviolent crime by Levitt (1996). The estimate suggests that a decrease in
prison population led to an increase in nonviolent crime.
Table V gives the two-stage least squares estimates for each of the subcategories of
nonviolent crime. Because no effect was observed in any of the subcategories of violent crime,
19
they are not listed here. Prison population changes do not appear to have a statistically
significant effect on larceny rates, but both motor theft and burglary are seen to increase upon a
reduction in prison populations, with elasticities of -0.97 and -0.83 respectively. These estimates
are between two and four times those of -0.26 and -0.40 obtained by Levitt, but this study sees
the prison effect concentrated solely in these two crime categories, mostly likely because of the
prisoners released by legislation changes, while the effect observed by Levitt is spread across
categories.
The estimates obtained through the two-stage-least-squares model of elasticities for
property crime and its subcategories differ dramatically from those obtained using ordinary least
squares regression while treating prison population as exogenous. The ordinary least squares
model produces estimates that, while not significant, are actually positive and, therefore, would
suggest that if prison populations did affect property, crime it would be to increase it. This
points to the existence of a simultaneity bias and highlights the importance of instrumenting for
prison population. The R-squared values in all of the included regressions are above 0.765.
These high values suggest that the variables included in the model effectively explain the trends
in crime rates.
Additional covariates are also listed in the table, as they are included in the model to
control for other characteristics that could affect crime in states over time. Regressing these
other covariates on release shows income to be negatively correlated with the release variable.
While this might in fact, lead to an underestimation of the impact of release on crime rates since
release and income are both negatively correlated with crime, correlation between covariates can
interfere with the model. Because of this, it was necessary to check that release of prisoners had
an effect on non-violent crime that was independent of trends in time. To do so, regressions
20
were run calculating the effect of timing on crime. These regressions used the variable release
that is an instrument in the two-stage least squares model to indicate years of and after a
legislation change as well as dummy variables indicating the status of one, two, or three years
before a legislation change in a particular state. The coefficients obtained in these regressions
are summarized in Table VI. The regressions also controlled for the covariates used above. It
can be seen that legislation changes did significantly affect property crime, burglary, and motor
theft, as is observed above. No pattern in change of crime rates in the years before the changes is
observed. Running an F-test on the dummy variables indicating the years before a change yields
high p-values, suggesting that these variables do not affect crime rates. This suggests that the
effect observed was a result of the legislation changes rather than some other correlated factor.
Conclusion
This study aims to determine the effect that reducing prison populations has on crime
rates. It examines this effect using a two-stage least squares model that uses changes in state
prison laws as an exogenous shock to prison populations, while controlling for fixed state and
year effects. Using both violent and property crime rates as outcome variables, the results of this
study indicate that the decrease in prison populations resulting from these legislative reforms had
no effect on violent crime rates but led to a significant rise in property crime rates with an
elasticity of -0.37. The observed elasticity on property crime is similar to, though slightly higher
than, that observed by Levitt (1996). The increase in crime was concentrated in two categories,
burglary and motor theft, with elasticities of -0.83 and -0.97, respectively.
These results do not, however, contradict findings in earlier studies that showed violent
crime increases in response to prison reductions. Because the instrument used in this paper was
21
legislative changes made by states, the prisoners being released by these laws were generally
nonviolent offenders, which would explain why violent crime is unaffected. The estimates
obtained for the response of property crime rates to prison reductions were higher than those
found in previous studies. This suggests a concentration of the prison release effect within the
categories of crimes for which more criminals are being released, reinforcing the conclusion that
prison populations are directly affecting crime rates. While increased crime is not optimal, this
knowledge can allow states that are facing overcrowding and budget problems to consider which
criminals to release if necessary, based on the types of crimes viewed to have the lowest social
cost.
The findings of this study indicate that incarceration reduces crime. However, it does not
conclude that incarceration is the only effective crime-reduction strategy, nor does this study do
a formal cost-benefit analysis of the prisoner release program. The results are a necessary first
step in considering the costs of this fiscal cost-saving program. The results of regression analysis
suggest that legislation enacted by states to reduce prison populations led to increased crime, but
this does not mean that there are not effective alternative methods of controlling crime. It would
be useful to examine the effects of individual policies to see if any successfully reduce crime.
States could then weigh the costs and benefits of such policies, considering the money saved by
investing in these policies as opposed to prison as well as how effectively they control crime.
Also, as most of the data in this study analyzes short-term effects, it could be that over time these
policies will develop and become more effective. Whether or not these policies can be refined
and made more successful, it is evident from the results of this paper that decreasing prison sizes
causes crime rates to rise, indicating that incarceration effectively reduces crime.
22
Table I
State Prison Population Response to Legislation
State Year of
Change
Citation
Arizona 2008 http://www.azcourts.gov/Portals/25/SafeCommunitiesAct/FINAL_
SB_1476_RPT_FY08.pdf
Arkansas 2003 http://adc.arkansas.gov/resources/Documents/adcar_pdf/AR1316.pdf
California 2007 http://www.cbp.org/pdfs/2011/110914_Corrections_Spending_BB.pdf
Illinois 2009 http://articles.chicagotribune.com/2009-12-31/news/chi-quinn-parole-program-31dec31_1_early-release-major-state-agency-michael-
randle
Kansas 2007 http://www.aca.org/publications/pdf/Garland.pdf
Kentucky 2008 http://justice.ky.gov/nr/rdonlyres/9c0abcaa-02cc-4b55-ac6e-c13a3b0a71de/0/microsoftwordjusticecabinetlegislativeinitiatives.pdf
Michigan 2003 http://www.nga.org/files/live/sites/NGA/files/pdf/1110SENTENCINGREFORM.PDF
Mississippi 2008 http://www.justicepolicy.org/uploads/justicepolicy/documents/due_south_-_mississippi.pdf
Pennsylvania 2008 http://www.cor.state.pa.us/portal/server.pt/community/major_initiatives/21262/recidivism_risk_reduction_incentive/1354883
Texas 2007 ://www.aclu.org/files/assets/smartreformispossible.pdf
Vermont
Washington
Wisconsin
2008
2003
2009
http://www.leg.state.vt.us/docs/2012/Acts/ACT041.pdf
http://www.wsipp.wa.gov/rptfiles/09-04-1201.pdf
http://legis.wisconsin.gov/lrb/pubs/budbriefs/09bb1.pdf
Table I provides a list of included states and the years of prison legislation changes.
Table II
Summary Statistics, 50 States 1982-2009
Variable Number of
Observations
Mean Standard
Deviation
Minimum Maximum
ln(Prison Population) 1400 5.65 0.57 3.85 7.84
ln(Total Crime)
ln(Violent Crime)
1400
1400
8.37
5.98
0.29
0.58
7.57
3.85
9.10
7.13
ln(Rape) 1400 3.50 0.37 1.99 4.62
ln(Assault) 1400 5.50 0.60 3.44 6.67
ln(Robbery)
ln(Murder)
1400
1400
4.56
1.59
0.89
0.64
1.86
-1.61
6.44
3.01
ln(Property Crime) 1400 8.26 0.29 7.44 8.96
ln(Burglary) 1400 6.75 0.40 5.73 7.79
ln(Larceny) 1400 7.87 0.27 7.15 8.54
ln(Motor Theft)
Release
1400
1400
5.81
0.03
0.55
0.17
4.28
0
7.05
1
ln(Per Capita Income)
Unemployment Rate
Percent Black
Percent Age 15-24
Percent Age 65 and Over
1400
1400
1400
1400
1400
10.02
5.75
0.10
0.15
0.17
0.39
2.01
0.095
0.016
0.026
9.02
2.2
0.00
0.12
0.05
10.95
15.7
0.38
0.20
0.29
23
Table III
OLS Estimates of the First-Stage Relationship
Dependent Variable:
ln(Prison Population)
Covariate First-Stage First-Stage with
Lags
Release
Release1
Release2
Release3
-0.092
(0.031)
-
-
-
-
-
-
-0.083
(0.032)
0.046
(0.049)
0.039
(0.049)
0.036
(0.049)
ln(Income) 0.303
(0.123)
0.311
(0.123)
Unemployment -0.001
(0.123)
-0.001
(0.005)
Percent black 0.262
(0.598)
0.290
(0.599)
Percent 15-24 3.048
(0.678)
3.049
(0.678)
Percent 65 -0.095
(0.687)
-0.026
(0.689)
R2 0.9224 0.9225
F-test 190.88 0.59
P-value 0.0000 0.6233
Numbers in parentheses are standard errors. All models include a complete set of state and year
effects.
24
Table IV
OLS and 2SLS Estimates of ln(Crime Rate) Equation
Variable Violent
Crime
OLS
Violent
Crime
2SLS
Property
Crime
OLS
Property
Crime
2SLS
ln(Prison) 0.205
(0.025)
0.209
(0.302)
0.026
(0.018)
-0.367
(0.247)
ln(Income) 0.533
(0.114)
0.532
(0.147)
0.202
(0.080)
0.329
(0.121)
Unemployment -0.017
(0.004)
-0.017
(0.004)
-0.008
(0.003)
-0.008
(0.003)
Percent black -1.772
(0.553)
-1.774
(.548)
-1.416
(0.387)
-1.271
(0.448)
Percent 15-24 5.678
(0.633)
5.665
(1.108)
0.710
(0.387)
1.918
(0.907)
Percent 65 3.908
(0.636)
3.908
(0.617)
1.405
(0.444)
1.407
(0.505)
R2 0.934 0.934 0.869 0.821
F-test 228.58 19855.69 106.69 6782.37
P-value 0.0000 0.0000 0.0000 0.0000
Numbers in parentheses are standard errors. All models include a complete set of state and year
effects.
Table V
2SLS Estimates of ln(Non-violent crime rate) Models
Variable Larceny Motortheft Burglary
ln(Prison)
ln(Income)
-0.077
(0.210)
0.191
(0.191)
-0.970
(0.544)
1.004
(1.004)
-0.835
(0.389)
0.560
(0.190)
Unemployment -0.010
(0.003)
-0.010
(0.007)
-0.005
(0.005)
Percent black -0.782
(0.103)
-2.147
(0.988)
-1.871
(0.707)
Percent 15-24 0.222
(0.773)
8.579
(1.999)
3.801
(1.431)
Percent 65 0.310
(0.430)
2.428
(1.112)
3.087
(3.087)
R2 0.848 0.765 0.776
Chi2 7842.21 5050.53 5623.32
P-value 0.0000 0.0000 0.0000
Numbers in parentheses are standard errors. All models include a complete set of state and year effects.
25
Table VI
Reduced-Form Estimates
Dependent Variable:
ln(Crime Rate)
Variable Property Burglary Motor Theft
Release
Release1
Release2
Release3
0.038
(.020)
0.021
(0.032)
0.023
(0.032)
0.014
(0.032)
0.079
(0.026)
0.013
(0.040)
0.011
(0.040)
0.000
(0.039)
0.099
(0.043)
0.048
(0.066)
0.056
(0.066)
0.029
(0.066)
ln(Income) 0.222
(0.080)
0.308
(0.100)
0.718
(0.166)
Unemployment -0.008
(0.003)
-0.003
(0.004)
-0.008
(0.006)
Percent black -1.353
(0.388)
-2.084
(0.484)
-2.370
(0.806)
Percent 15-24 0.800
(0.439)
1.256
(0.584)
5.623
(0.913)
Percent 65 1.476
(0.446)
3.180
(0.557)
2.596
(0.929)
R2 0.8693 0.8980 0.8476
F-test 0.35 0.06 0.24
P-value 0.7919 0.9820 0.8685
Table VI presents crime trends in the years before and after legislative changes. The F-test and p-
values test release1=release2=release3=0.
26
7.8
8.0
8.2
8.4
8.6
8.8
19821984198619881990199219941996199820002002200420062008
ln(P
rop
ert
y cr
ime
rat
e)
Year
Michigan Property Crime Trend
All other states Michigan
5.0
5.5
6.0
6.5
7.0
19821984198619881990199219941996199820002002200420062008
ln(M
oto
r Th
eft
Rat
e)
Year
Michigan Motor Theft Trend
All other states Michigan
27
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