Measuring the determinants of crime and the benefits of law enforcement

The effect of police on the crime rate

To determine the optimal amount of investment in law enforcement, we would want to compare the marginal cost of the investment with its marginal benefit, e.g., the effect on the crime rate of hiring additional police officers. However, these benefits are usually very hard to measure. Hiring more police should increase p, the probability of arrest for a given level of crime, and this in him should reduce the crime rate, through a deterrent effect and also through the effect of incapacitation.¹³ That is, even if the deterrent impact is small (because, for example, criminals do not have good information about the increase in law enforcement efforts), there may be a substantial benefit from incarceration (“getting criminals off the sheets”), since it is much less likely that criminals will commit crimes while in prison. Tlius we would expect the crime rate to fall with an increase in the police force.¹⁴ We might also expect that, following an increase in the police force, there would be an mitial increase in the arrest rate, followed by a decline as the crime rate was reduced by the effects of deterrence and incarceration.

However, attempts to measure the benefits of a greater investment in law enforcement must deal with problems of simultaneity and possible displacement effects. The simultaneity problem arises because it often happens that more police are lined in response to a crime wave - an unusually high crime rate or recent rapid growth of crime. Thus a researcher who examines the data, but fails to take this into account, might (incorrectly) conclude that the crime rate increases with the size of the police force. The displacement effect arises because, for example, an increase in the police force in suburb A may well reduce crime there, but might also increase crime in adjacent communities by diverting criminals to areas where the probability of apprehension is lower.

For all the foregoing reasons the benefits of an investment in law enforcement, even if substantial, are often hard to determine from the data. However Levitt (1997) devised a method to deal with the simultaneity problem. Fust, he found that there were significant increases in the police force in U.S. cities in years when there was an election for mayor or governor; it appears that incumbents have an incentive to line more police in advance of an election, to either reduce crime or at least appear to be striving to do so. Thus, if crime is indeed reduced by a larger police presence, election years should have the effect of reducing crime through an increase in the police force, but should not otherwise affect the crime rate. Ushig statistical methods to exploit this property of electoral cycles (instrumental variables and two-stage least squares), Levitt found that additional police had large negative effects on crime. Comparing the marginal cost of a police officer to his estimate of the marginal benefit through crime reduction, he found the former smaller than the latter, suggesting that the number of police in large cities was below the optimal level.

The effect of the prison population on the crime rate

Since imprisonment is generally the most severe punishment imposed on crimes, we would expect the crime rate to be lower when upon conviction the probability of imprisonment is relatively high, and the expected duration of a prison term is long. Of course, one consequence of an increase in these variables is that at any given time, a relatively large fraction of the population will be in prison. This raises the question whether there is evidence that the crime rate declines when the prison population increases.

Increasing a State’s prison population (its prisoners per capita) might reduce the crime rate either through deterrence (potential criminals are deterred by a gr eater expected period of imprisonment) or through incapacitation (since persons cannot commit crimes while in prison). It is important to distinguish between the effects of deterrence and incapacitation to determine the optimal type of law enforcement and sentencing policy. Kessler and Levitt (1999) were able to distinguish between the effects of deterrence and incapacitation by analyzing the introduction of sentence enhancement laws hr California in 1994. These laws increased the length of the prior sentence for crimes of a particular type, such as crimes committed with a gun. An increase in deterrence should take effect immediately after the law is passed. Suppose, for example, a sentence enhancement law passed in 1994 increased the sentence for felonious assault from 10 to 20 years. During the first ten years there should be a reduction hr such assaults resulting front the increased deterrent effect of the more severe penalty; sitppose there was in fact a 20 percent reduction. After ten years, if incapacitation is important, there should be a greater reduction of assaults, smce there would now be a combined effect of deterrence and incapacitation that did not exist under prior law. If after 2014 we see a 35 percent reduction hr assaults relative to the situation before 1994, we can attribute 15 percent of the reduction to the effect of incapacitation. If hrcapacitation has the dominant effect in reducing crime, the best policy is to have long sentences, which will lead to a large increase in the prison population, and eventually to an aged prison population that poses a minimal thr eat to society and requires a gr eat deal of health care. If, on the other hand, deterrence is the primary factor, more police should be lured to maximize the probability of apprehension, sentences may be shorter and the steady-state prison population will be smaller.

Studies of the effect of the prison population on the crime rate have been plagued by a simultaneity problem quite similar to the one we encountered above, when considering the effect on crime of the size of the police force: while an increase in the state’s prison population may reduce the crime rate, an increase in crime caused by unrelated factors (an increase in gang activity, or in the number of single-parent families, or a decline in economic opportunities for youths) will increase the state’s prison population. Thus the causation between crime and the prison population runs in both directions. This reciprocal causation makes it difficult to identify the effect of the size of the prison population on crime. Indeed, some studies have found that an increase in the prison population has been accompanied by an increase in the crime rate. Some commentators have argued that a policy of law enforcement that relies heavily on imprisonment doesn’t work, since over the period 1973-1992 the crime rate in the United States did not decline much, if at all, even though the rate of incarceration more than tripled. It is therefore important to determine whether, and if so, how much, crime is reduced by an increase in the prison population.

Levitt (1996) found a way to break the simultaneity of crime and the prison population. His approach is based on the observation that many lawsuits have been brought against state prison systems based on the claim that overcrowding of prisons is cruel and unusual punishment. Not surprisingly, these lawsuits reduced the rate of growth of prison populations in the states where they were filed. Levitt noted that litigation based on prison overcrowding could, by reducing the growth of the state’s prison population, increase the crime rate, but should not otherwise have any effect on crime. This insight led him to exploit a statistical technique (instrumental variables) that made it possible to isolate the effect of the size of the prison population on crime. His estimates suggested that the effect of adding one prisoner was to eliminate fifteen crimes per year.

Comparing the marginal social cost of imprisonment to the marginal benefit from reducing crime, he found the former smaller than the latter, and concluded that there should be greater use of incarceration. Levitt also stressed, however, that an}' increased use of imprisonment should occur at the intensive, rather than the extensive, margin, i.e., in the form of longer sentences for ctmeut prisoners, rather than by adding more inmates. His reasoning was that there is great variation among criminals, in terms of the number and seriousness of the crimes they are likely to commit if not in prison. Consequently there is a greater benefit in terms of crime reduction to be had by prolonging the sentences of the most serious offenders, e.g. those who repeatedly commit violent crimes, than by adding to the prison system those from the bottom of the crime distribution, such as nonviolent petty thieves.

The effect of abortion laws on the crime rate

The United States experienced dramatic declines in the crime rate during the period from 1991 to 2005. In the decade after 1991, homicides fell by more than 40 percent, while violent crime and property crime declined by more than 30 percent. Researchers have investigated a number of possible reasons for this development: the increased use of imprisonment, increases in the number of police officers, a decline in the use of crack cocaine, improvements in the economy, changes in gun control laws, and increased expenditures on precautions such as security guards, locks, and alarms. However Donohue and Levitt (2001) have proposed another explanation, which they find to be more important than any of the foregoing factors: the nationwide increase hi abortions following the 1973 Supreme Court decision in Roe v. Wade. With that decision, the Court struck down state criminal laws against abortion, holding that they violated a woman’s constitutional right to privacy, which included a right to terminate her pregnancy.¹³

The argument by Donohue and Levitt runs as follows. Women choose to have abortions when children are unwanted or mistimed. A large proportion of women in this situation are teenagers, unmarried, or living in poverty. Unwanted children who are bom only because their mothers were unable to obtain abortions are more likely than other children to be raised in a single-parent household, to live in poverty, and to be part of a household on welfare. In addition, their mothers are more likely to have been drinking, smoking, or using drugs during pregnancy. These unwanted children are also more apt to be abused and neglected. Research shows that children bom and living under these conditions have a high propensity to be involved in juvenile delinquency and later, criminal activity. Abortions prevent unwanted children from being bom, and enable women to postpone births until they can provide a child with a more favorable home environment.

Donohue and Levitt examined whether differences in the crime rate could be explained by differences in the abortion rate. They used various statistical methods to analyze the effect of the abortion rate on crime, taking into account other factors that might affect crime such as prisoners and police per capita, economic conditions, state welfare payments, whether state law allowed the carrying of concealed handguns, and per capita beer consumption. Their analysis took into account that most abortions are performed six to seven mouths before birth would have occurred, and that the likelihood of criminal activity depends on the individual’s age; thus, an increase in abortions in a given state would not be expected to have much of an impact on the state’s crime rate until about fifteen years later. They found that legalized abortion was a factor of great importance in explaining the nationwide decline in crime, possibly accounting for one-half of the overall reduction in crime observed in their data.

Several studies have found other noteworthy effects of the legalization of abortion. Kalist and Molinari (2006) analyzed the effect of legalized abortion on the rate of homicides of infants (children less than one year old). They found that an increase in the abortion ratio

(the number of abortions divided by live births) by 10 percent reduced the number of unwanted births by 3.5 percent, and thereby reduced the rate of infant homicides.

Another study found that the legalization of abortion reduced the rate of childbearing by unmarried teenage females. After forty-one consecutive years of increase, the rate of childbearing out of wedlock by teenage females in the United States began to decline in 1991, and by 2002 was 20 percent below its peak. Donohue et al. (2009) estimated that the legalization of abortion in the mid-1970s caused fewer female babies to be bom into situations where their parents were unable or unwilling to provide nurturing and supportive environments. The support that girls bom hi the 1970s received from their parents made them less likely to become out-of-wedlock mothers when they reached their teenage years in the 1990s. In other words, because abortion was available in the 1970s, the childhood background of girls who were bom was substantially more favorable than it would have been for the cohort that would have been bom had abortion not been legalized. Donohue et al. estimated that the legalization of abortion accounted for 25 percent of the decline in the birth rates of unmarried teenage females during the period 1991-2002.