Are Changes in U.S. Crime Rates Time Reversible?

David McDowall, University at Albany
Colin Loftin, University at Albany

This paper considers whether changes in annual U.S. crime rates are time reversible. If a series of observations is reversible, the process that generates it forward in time is identical to the process that would generate it backward. Irreversibility can result from a nonlinear process or from a linear process with non-Gaussian innovations. Series with asymmetric cycles are irreversible, as are series that switch between distinct causal regimes. Current thought on why crime rates rise and fall implicitly assumes reversibility, but several recent findings challenge this idea. The paper applies tests for time reversibility to changes in the homicide rate between 1925 and 1999, and to changes in other serious crimes between 1933 and 1999. In each case, the tests are consistent with the reversibility hypothesis. The findings thus support conventional explanations of crime rate trends, and suggest that the past values of each series provide a reasonable guide to the future.

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Updated 05/20/2006