# Prison Math

## What are the costs and benefits of leading the world in locking up human beings?

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In 2009, according to the Bureau of Justice Statistics, there were 1,524,513 prisoners in state and federal prisons. When local jails are included, the total climbs to 2,284,913. These numbers are not just staggering; they are far above those of any other liberal democracy in both absolute and per capita terms. The International Centre for Prison Studies at King's College London calculates that the United States has an incarceration rate of 743 per 100,000 people, compared to 325 in Israel, 217 in Poland, 154 in England and Wales, 96 in France, 71 in Denmark, and 32 in India.

America's enormously high incarceration rate is a relatively recent phenomenon. According to a 2010 report from the Center for Economic and Policy Research (CEPR), U.S. incarceration rates between 1880 and 1970 ranged from about 100 to 200 prisoners per 100,000 people. After 1980, however, the inmate population began to grow much more rapidly than the overall population, climbing from about 220 per 100,000 in 1980 to 458 in 1990, 683 in 2000, and 753 in 2008.

Why are American incarceration rates so high by international standards, and why have they increased so much during the last three decades? The simplest explanation would be that the rise in the incarceration rate reflects a commensurate rise in crime. But according to data from the Federal Bureau of Investigation and the Bureau of Justice Statistics (BJS), the total number of violent crimes was only about 3 percent higher in 2008 than it was in 1980, while the violent crime rate was much lower: 19 per 1,000 people in 2008 vs. 49.4 in 1980. Meanwhile, the BJS data shows that the total number of property crimes dropped to 134.7 per 1,000 people in 2008 from 496.1 in 1980. The growth in the prison population mainly reflects changes in the correctional policies that determine who goes to prison and for how long.

Mandatory minimum sentencing laws enacted in the 1980s played an important role. According to the CEPR study, nonviolent offenders make up more than 60 percent of the prison and jail population. Nonviolent drug offenders now account for about one-fourth of all inmates, up from less than 10 percent in 1980. Much of this increase can be traced back to the "three strikes" bills adopted by many states in the 1990s. The laws require state courts to hand down mandatory and extended periods of incarceration to people who have been convicted of felonies on three or more separate occasions. The felonies can include relatively minor crimes such as shoplifting.

What have longer prison sentences accomplished? Research by the Pew Center on the States suggests that expanded incarceration accounts for about 25 percent of the drop in violent crime that began in the mid-1990s—leaving the other 75 percent to be explained by things that have nothing to do with keeping people locked up.

As for the costs, state correctional spending has quadrupled in nominal terms in the last two decades and now totals \$52 billion a year, consuming one out of 14 general fund dollars. Spending on corrections is the second fastest growth area of state budgets, following Medicaid. According to a 2009 report from the Pew Center on the States, keeping an inmate locked up costs an average of \$78.95 per day, more than 20 times the cost of a day on probation.

More important is the long-term impact that the tough-on-crime policies of the last two decades have had on prisoners and society. Housing nonviolent, victimless offenders with violent criminals for years on end can't possibly help them reintegrate into society, which helps explain why four out of 10 released prisoners end up back in jail within three years of their release.

As the Harvard sociologist Bruce Western and the University of Washington sociologist Becky Pettit showed in a 2010 study published by the Pew Center on the States, incarceration has a lasting impact on men's earnings. Taking age, education, school enrollment, and geography into account, they found that past incarceration reduced subsequent wages by 11 percent, cut annual employment by nine weeks, and reduced yearly earnings by 40 percent. Only 2 percent of previously incarcerated men who started in the bottom fifth of the earnings distribution made it to the top fifth 20 years later, compared to 15 percent of never-incarcerated men who started at the bottom.

It isn't just offenders whose lives are damaged. Western and Pettit note that 54 percent of inmates are parents with minor children, including more than 120,000 mothers and 1.1 million fathers. One in every 28 children has a parent incarcerated, up from 1 in 125 just 25 years ago. Two-thirds of these children's parents were incarcerated for nonviolent offenses.

While we don't yet have data on the income mobility of these children, Rucker C. Johnson of the Goldman School of Public Policy found in 2009 that children whose fathers have been incarcerated are significantly more likely than their peers to be expelled or suspended from school (23 percent compared to 4 percent). Johnson found that family income, averaged over the years a father is incarcerated, is 22 percent lower than family income the year before his incarceration. Even in the year after the father is released, family income remains 15 percent lower than it was the year before incarceration. Both education and parental income are strong indicators of a child's future economic mobility.

Attempts to estimate the costs and benefits of prison have proved difficult and controversial. In 1987, for example, the National Institute of Justice economist Edwin Zedlewski used national crime data to calculate that the typical offender commits 187 crimes a year and that the typical crime exacts \$2,300 in property losses or in physical injuries and human suffering. Multiplying these two figures, Zedlewski estimated that the typical imprisoned felon is responsible for \$430,000 in "social costs" each year he is free. Dividing that figure by an annual incarceration cost of \$25,000, he concluded that the public benefits of imprisonment outweigh the costs by 17 to 1.

Zedlewski's findings have been debunked many times. A severe rebuttal came from the Boalt Hall Law School penologists Franklin Zimring and Gordon Hawkins, who argued in a 1988 article published by the National Council of Crime and Delinquency that Zedlewski overstated the net benefit of incarceration by inflating the numerator (crimes per offender and social costs per crime) and deflating the denominator (annual cost of confinement). They cited several studies to bolster their charge, including one indicating that the typical offender commits 15 (as opposed to 187) crimes in a year. According to a 1991 Brookings paper by John J. DiIulio and Anne Morrison Piehl, making this one adjustment to the calculations reduces the benefit/cost ratio to 1.38. In other words, the benefit of incarceration is probably small, especially compared to the high cost of locking people up. Also note that Zedlewski assumed imprisoned offenders were predatory criminals, although a substantial share of real-world convicts are guilty only of victimless crimes.

Fortunately, economists are getting better at understanding how to keep people out of jail. In a 2007 paper for Economic Inquiry, for instance, the U.C.–Santa Barbara economist Jeff Grogger found there are large deterrent effects from increased certainty of punishment and much smaller, generally insignificant effects from increased severity. Such findings call into question the economic rationality of increasingly long prison terms. Who knows how many more millions will be locked up by the time public policy finally catches up with economics?

Contributing Editor Veronique de Rugy (vderugy@gmu.edu) is a senior research fellow at the Mercatus Center at George Mason University. She writes a monthly economics column for reason.