case, the average S for all inmates declines, but individual offenders continue to serve the same or longer prison terms than under previous policies.

Similarly, declines in Q_i that are accompanied by increases in S need not reflect real increases in the time served by individual inmates. Instead, the decline in Q_i might arise from limiting imprisonment only to more serious offenders who continue to serve the same longer-than-average prison terms as they would have under previous values of Q_i. Since offenders who previously served shorter prison terms are no longer committed to prison, the average time served by the remaining inmates increases. In this case, although the average time served increases, individual offenders actually may be spending the same or less time in prison.

In both cases, the changes in S would result primarily from changes in the composition of inmates as Q_i changes, either increasing or decreasing the number of offenders who serve shorter-than-average prison terms. Distinguishing such composition changes from actual changes in S requires individual-level data on various attributes of inmates that are associated with the length of prison terms (e.g., prior criminal record and offense seriousness), and is beyond the scope of this paper. The key question to be answered in such an analysis would be whether or not the length of prison terms has changed, after attributes of the imprisoned offenders are controlled.

We ignore the arrest risk per crime, q_a, which generally remained fairly stable over the study period.

An earlier National Research Council panel provided an extensive review of prior deterrence and incapacitation research (Blumstein et al., 1978). Further reviews of various aspects of deterrence are available in Cook (1977, 1980); Geerken and Gove (1975); Gibbs (1975, 1986); Klepper and Nagin (1989); Paternoster (1987); Tittle (1980); Williams and Hawkins (1986); and Zimring and Hawkins (1973). Subsequent reviews of incapacitation research can be found in Blumstein et al. (1986); Cohen (1983, 1984); and Visher (1987).

Throughout this paper, the estimates of crime reduction from incapacitation assume that while they are incarcerated, the potential crimes of inmates are eliminated entirely. No adjustments are made for crimes that may continue in the community—perhaps because the offender is replaced or offending persists by unincarcerated members of an offending group. Such offsetting effects are likely to be small for violent offenses.

A notable exception is the study of violent offenders in