large increases in crime rates between 1965 and 1975 for robbery and murder.

Crime rates will also be affected by changes in levels of criminality toward more or less offending. Increases in criminality—whether they result from increases in the size of the offender population or from higher frequencies of offending by individual offenders—can increase the incarceration rate independently of any changes in imprisonment policies.15 The rise in adult crime rates illustrated in Figure 7 hints at the substantial underlying changes in criminality from 1965 to 1988 reported in Blumstein et al. (1991). Such increases in offending levels, particularly in those crime types that are more vulnerable to imprisonment, will contribute to increases in population incarceration rates.

CHANGES IN SANCTION POLICIES

The incarceration rate is influenced further by changes in sanction policies that either increase (or decrease) the risk of arrest per crime qa, the imprisonment risk per arrest Qi, or the average length of time served in prison S. We used data on reported crimes and arrests for each state in combination with annual data on commitments to state prisons and resident inmates to estimate the sanction variables.

Arrest Risk per Crime, qa

The arrest risk per crime (reported in appendix Table A-2) is estimated from the ratio of adult arrests of persons age 18 and older in each state to the estimated number of adult crimes reported by the police. The arrest risk variable used here is only a proxy measure that overstates the actual risk of arrest following a crime. The upward bias in qa arises from two sources: (1) the number of crimes in the ratio includes only crimes that are reported by the police, and (2) the number of arrests in the ratio often includes the arrest of several offenders for a single offense.

Data that are available from the annual National Crime Survey (NCS) indicate that the upward bias in qa may be substantial. Crime victims responding to the NCS indicate that about one-half of the violent crimes they suffer are reported to the police each year. Although the reporting rate varies somewhat across offense types, it has remained fairly stable at about 55 percent per year for the more serious violent offenses of rape, robbery, and aggravated assault (Bureau of Justice Statistics, 1990b). After adjustment



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