Economics of Estimating the Elasticity of Crime

face of a prisoner

Academics trained in economic analysis, as if controlled by an invisible moderator of disciplined discussion, have vigorously competed to produce the best estimate of the elasticity of crime with respect to imprisonment. On the supply side, regressing is a predominate practice among empirical economists. An elasticity is a single coefficient produced cheaply in a log-linear regression. Since an increase in crime might naturally be associated with a subsequent increase in imprisonment, identifying the effect of imprisonment on crime raises the sort of causality questions that have been central to expertise within the discipline of economics in the second half of the twentieth century. Estimating elasticities thus provides opportunities for high-interest investments in expertise. On the demand side, the elasticity of crime with respect to imprisonment maps directly into summary statements that support a strong claim to policy relevance, e.g. “a 1% increase in the prison population will produce a 0.3% reduction in crime.” Such claims help to stimulate demand for expert quotations in newspaper articles and interviews on television. Scholars seeking value in economic analysis have rationally allocated considerable research effort to estimating elasticities.

The value of estimating elasticities does not lie within the foundations of economic analysis. Paul Samuelson, winner of 1970 Nobel Prize in Economic Sciences and perhaps the most academically influential twentieth-century economist, called elasticities “essentially arbitrary” and “more or less useless.” In a more nuanced evaluation, he stated, “On the whole, it appears that their importance is not very great except possibly as mental exercises for beginning students.”^ Consequences of changes in a control variable could be estimated, predicted, and described in a wide variety of ways. An elasiticity is merely one, particular, highly specific way of describing consequences.

Apart from disciplinary credit, the utility from estimating the elasticity of crime with respect to imprisonment appears astonishingly small. Prior to 1968, scholars had done little work empirically evaluating the effect of deterrence on crime. In the subsequent decade, at least twenty-four empirical studies addressed this question. A literature review, sponsored by the U.S. National Research Council, reported in 1978:

Despite the intensity of the research effort, the empirical evidence is still not sufficient for providing a rigorous confirmation of the existence of a deterrent effect. Perhaps more important, the evidence is woefully inadequate for providing a good estimate of the magnitude of whatever effect may exist.^

The associated report, the U.S. National Research Council’s Report of the Panel on Research on Deterrent and Incapacitive Effects, offered a carefully worded declaration of non-knowledge:

we cannot yet assert that the evidence warrants an affirmative conclusion regarding deterrence. …Our reluctance to draw stronger conclusions does not imply support for a position that deterrence does not exist, since the evidence certainly favors a proposition supporting deterrence more than it favors one asserting that deterrence is absent.^

A book-length study of criminal incapacitation published in 1994 indicated that the state of knowledge had changed little:

Unfortunately, virtually nothing is known about the size of even the aggregate elasticity. Literally dozens of {estimates of the elasticity} have been calculated on the basis of econometric analysis, but the prevailing opinion is that none of these estimates are persuasive^

By 2000, more than 100 scholarly studies had attempted to test for deterrence.^ Through more than two decades of estimating the elasticity of crime, many technical improvements were declared in the scholarly literature. These improvements led to an important conclusion:

The ultimate futility of our analysis is at last revealed. We can be nearly certain the elasticity lies somewhere between -0.1 and -0.5, and we can be fairly sure it lies between -0.2 and –0.4, but we have no idea at all whether it is greater than or less than -0.265.^

The figure of -0.265 comes from the author’s back-of-the-envelope calculation of the elasticity threshold for the cost effectiveness of prison construction. Its three-digit precision, which is not convincingly supported, seems merely illustrative. A literature review in 2010 found relatively little evidence of severity of punishment having a deterrence effect, but found relatively strong evidence that the probability of punishment deters. The researchers concluded, “we see much need for new research.”^

Estimating the elasticity of crime with respect to deterrence isn’t a socially cost-effective contribution to public discussion of criminal justice policy. Almost everyone has almost nothing to say about deterrence when it is described as an elasticity. Public discussion of criminal punishment also commonly includes justifications that are unrelated to deterrence.^

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