“The Incapacitation Effect of Incarceration: Evidence from Several Italian Collective Pardons”, Alessandro Barbarino, Giovanni Mastrobuoni2014-02 ()⁠:

We estimate the incapacitation effect on crime using variation in Italian prison population driven by 8 collective pardons passed 196228199034ya. The prison releases are sudden (within one day), very large (up to 35% of the entire prison population), and happen nationwide…For instance, the last collective pardon (which we exploit to some extent but that we do not end up using in our main results due to some missing data), passed on July 31, 2006, led within a day to the release of 22,000 inmates, around 30% of the total

Exploiting this quasi-natural experiment we break the simultaneity of crime and prisoners and, in addition, use the national character of the pardons to separately identify incapacitation from changes in deterrence…pardons lead to an increase in deterrence, since: (1) the next pardon is unlikely to happen very soon, and (2) pardoned sentences might be added to the new sentence (see Drago et al 2009).

The elasticity of total crime with respect to incapacitation is between −17 and −30%.

A cost-benefit analysis suggests that Italy’s prison population is below its optimal level.

…Disregarding deterrence, which they argue should be modest given the high frequency of their data, the number of saved crimes ranges 17–21 crimes per prison year served when the authors exploit the discontinuity in their experiment, and ranges 22–46 crimes when exploiting the dynamic adjustment path for incarceration and crime that is induced by the one-time shock provided by the pardon. Our estimated elasticities imply that a prison year saves around 22 crimes.

Figure 2: Change in Prison Population and Pardoned Prisoners. Notes: Vertical lines represent years in which pardons or amnesties have been passed. The regression line indicates an OLS prediction.

…Overall the fraction of inmates that gets freed can be as high as 35%, and it sometimes reaches 80% in some regions. But the effect of pardons on prison population appears to be short-lived. Within one year, the inmate population recovers more than half of the size of the initial jump. During 195936199529ya, for example, the inmate population increased, on average, by 449 inmates per year, but with large fluctuations that were driven by the pardons. The inmate population decreases by an average of 3,700 inmates after pardons, but increases by an average of 2,944 inmates immediately afterwards. In all other years the average increase is by 1,165 inmates. In other words, in the year immediately after the pardons, and excluding the year of the pardon, the inmate population grows two and a half times faster.