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Are US Crime Rates Really Unit Root Processes?

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Abstract

Existing research has uncovered little evidence against the hypothesis of US crime rates being unit root processes, despite the uncomfortable implications of this assumption. In light of this, the present paper draws upon noted changes in the temporal patterns of US crime rates since 1960 to undertake an informed approach to testing of the unit root hypothesis which incorporates two potential points of structural change. The results obtained show the unit root hypothesis to be rejected for all classifications of criminal activity examined over the period 1960 to 2007. In addition, the dates of the detected breakpoints are supported by a variety of arguments available in the existing criminology literature concerning alternative determinants of crime and their movements. Interestingly, a difference is observed in the nature of the breaks detected for violent and property crimes. However, potential explanations for this are again found in theoretical arguments available in the criminology literature. Finally, the implications of the current findings for the properties of crime, its subsequent statistical analysis and past and future research are discussed.

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Notes

  1. The issues of trends in the mean and variance of a unit root process are discussed further in the following section.

  2. Throughout this study repeated reference will be made to breaks or structural change. In all instances, this refers to breaks in the level and/or trends underlying series under investigation, rather than breaks or changes in other factors such as variance.

  3. The initial version of our current two-break paper was completed independently prior to the publication of, and without knowledge of, the related research of Narayan et al. (2010). The work of Narayan et al. (2010) came to our attention while undertaking revisions to the originally submitted version of our current paper to address a variety of issues suggested to us by the editors and two anonymous referees. However, as the thrust of the current paper concerns consideration of two potential breaks in US crime rates and subsequently the issues of both whether these lead to a reversal in the unit root inference currently present in the literature and how the detected breakpoints relate to existing knowledge of crime, there is a clear difference between our studies.

  4. Simply put, it can be seen that Eq. (3) states that the variance of x is equal to the variance of the constant initial value (which has variance of zero) and the collective variance of the t error terms (each of which has a variance of σ2).

  5. Interested readers can derive the expected value and variance of x t from (8) by considering the sum of a geometric progression and allowing the time period (t) to tend to infinity.

  6. More precisely, the series should be referred to as asymptotically stationarity.

  7. These critical values can be derived via Monte Carlo simulation involving the numerical simulation of artificially derived unit root processes and application of the specified test over a sufficiently large number of replications.

  8. The test is referred to as the KPSS test due to the initials of the authors.

  9. Interested readers will find an excellent and detailed coverage of these and further unit root tests is provided by Maddala and Kim (1998).

  10. The empirical results drawn upon code which is which has generously been provided by Professor Junsoo Lee and is available from http://www.cba.ua.edu/~jlee/.

  11. All series are expressed in per capita terms, measured per 100,000 inhabitants. See http://bjs.ojp.isdoj.govfor further information.

  12. To check the GAUSS code employed to undertake the empirical analysis required for the LM τ test, the results presented in the seminal study of Lee and Strazicich (2003) for US real wages and the Standard and Poor 500 index were replicated. The results for these series were chosen as they employ the particular two-break in intercept and trend model applied in the present analysis.

  13. The method employed here follows that outlined in the seminal study of Lee and Strazicich (2003) and the approach adopted by Strazicich et al. (2004) in an analysis of income convergence in OECD economies. Interestingly, the sample employed is nearly identical in size to the post-World War II sample examined by Strazicich et al. (2004), differing by one observation only.

  14. In the interests of brevity, the significance of individual breakpoints is not reported. However, all breakpoints identified under two-break analysis for crime rate series other than the three series (property crime burglary, larceny) to be discussed are very highly significant with the exception of the second break for rape. The second break for this series just satisfies the rule of significance at the 10% level with the test statistic for this break having a p value of 0.1 to 2 decimal places. In all other cases breakpoints are exceptionally significant with very small p values recorded for their tests of significance.

  15. It should be noted that the single-break LM τ test of Lee and Strazicich (2004) employed is the same as the two-break test of Lee and Strazicich (2003) in every respect other than the fact that it obviously allows for one fewer break.

  16. Levitt (2004) also notes the apparent contradiction of reduced economic stress accompanying the crime boom of the 1960s.

  17. For example, as Levitt (2004) notes, both Cork (1999) and Grogger and Willis (2000) provide evidence suggesting a positive relationship between the prevalence of crack cocaine and crime, with the former focusing upon homicide in particular.

  18. For example, see Saridakis (2004).

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Acknowledgments

The authors are very grateful to the editors and two anonymous referees for numerous comments which have improved both the content and presentation of this paper.

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  1. Cardiff Law School, Cardiff University, Cardiff, UK

    Jemma Cook

  2. School of Business and Economics, Swansea University, Singleton Park, Swansea, SA2 8PP, UK

    Steve Cook

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Correspondence to Steve Cook.

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Cook, J., Cook, S. Are US Crime Rates Really Unit Root Processes?. J Quant Criminol 27, 299–314 (2011). https://doi.org/10.1007/s10940-010-9124-4

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