Abstract
Objective
This paper advances current understanding of the contemporary crime drop by focusing on the changes in the age distribution of arrests from 1990 to 2010. Using the New York State Computerized Criminal History (CCH) file, which tracks every arrest in the state, we apply standard demographic methods to examine age-specific arrest rates over time. We test whether the 25 % drop in the felony arrest rate can be best explained by period or cohort effects with special attention to how the phenomenon varies across crime types and regions within the state.
Methods
Following the analytic approach of O’Brien and Stockard (J Quant Criminol 25(1):79–101, 2009), we fit the age–period–cohort (APC) model using the generalized inverse matrix, which creates an estimable model. We partition the model variation into each factor by subtracting the variation of the two-factor model from the variation of the three-factor model to provide a direct comparison of the two different classes of explanations for crime drop: period and cohort.
Results
Our analysis supports a cohort explanation over a period explanation. Controlling for the (substantial) variation due to age, the cohort effect accounts for twice as much of the remaining variation as the period effect. Specifically, the drop in arrest rates is concentrated in more recent birth cohorts across all ages. Although we found statistically significant age–period interaction effects for the younger age group (ages 16–20) in 1990 and 1995, the cohort effect was still a much stronger predictor of felony arrest rates than the period explanation, even with the age–period interaction.
Conclusions
The current study reports that the overall drop in felony arrest rates from 1990 to 2010 is mostly due to decreased arrests among those who were born after 1970 rather than a universal drop across different age groups. We discuss but do not test two potential explanations—the legalization of abortion and the ban on leaded gasoline—for the underlying factors associated with a different criminal propensity among birth cohorts.
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Notes
Index offense refers to eight crimes that the FBI reports in the annual Uniform Crime Report (UCR): Murder, forcible rape, robbery, aggravated assault, burglary, motor vehicle theft, larceny, and arson. These crime types are selected because they are serious offenses and most likely to be reported to the police. These crimes are now referred to as Type I offenses.
Demographers refer to changes that affect everyone in a given year equally, regardless of age, as period effects. Changes that affect only people from a given birth cohort regardless of age are referred to as cohort effects. Period effects may not be uniform across the entire sample. They may affect only people of a certain age (age–period interactions), or people from certain cohorts (cohort–period interactions).
The share of the older age group (over age 40) in the total felony arrests increases over time: 9.3 % in 1990, 13.0 % in 1995, 18.3 % in 2000, 22.1 % in 2005, and 25.3 % in 2010. Given that the total volume of felony arrests consistently decreases over time, it addresses that the drop in the felony arrest for the younger age group is large enough to compensate the increase in the older age group.
The percent change in the counterfactual scenario is calculated based on assumption that the 2010 felony arrest counts for older age group has not changed since 1990: (Counterfactual arrest volume in 2010 − Actual arrest volume in 1990)/Actual Arrest volume in 1990 × 100 = (105,558–160,140)/160,140 × 100 = −34.1 %.
Appendix 2 shows the age groups by period and corresponding birth cohorts for our study sample.
The cohort effect has a larger number of degrees of freedom than the period effect, which increases the chances of finding statistically significant non-linear effects of period and cohort. Porter et al. (forthcoming) deal with a similar problem by replacing the cohort dummy variables with a more restricted polynomial functional form, essentially restricting the degrees of freedom for both cohort and period to be the same. Their main finding regarding the importance of cohort effects was unchanged, despite the fact that they had far more cohorts (n = 86) in their paper. Their result shows that additional degrees of freedom does not itself lead to the conclusion that cohort explanations are more powerful.
Utilizing the generalized inverse to get the estimates of the model is one of the estimable function approaches, such as the intrinsic estimator using the Moore–Penrose generalized inverse matrix. We address other types of the estimable function approach in conjunction with suggestions for future study in our discussion.
The results table and figure are not included in this paper but available upon request.
Although the coefficients in the age–period–cohort model are not estimable (and therefore not available for statistical testing), the coefficients in the two-factor (AP and AC) models are still estimable and available for hypothesis testing.
We also checked the graphs for the model including age*period interaction and confirmed that it does not do any better job than the age–period model.
The 17 IMPACT counties are: Albany, Broom, Chautauqua, Dutchess, Erie, Monroe, Nassau, Niagara, Oneida, Onondaga, Orange, Rensselaer, Rockland, Schenectady, Suffolk, Ulster, and Westchester; Project IMPACT has been replaced with operation Gun Involved Violence Elimination (GIVE), which remains focused the same 17 counties, but has evolved to focus specifically on gun violence.
Single-age population information at the county level is not available in the Census data. We used new age groups following the grouping of the Census for the APC analysis by region. The new age groups are as follows: 15–19, 20–24, 25–29, 30–34, 35–39, 40–44, 45–49, 50–54, 55–59, 60–64, and 65–69 years.
The felony arrest rates in the rural upstate counties actually increased for the last 20 years. However, the magnitude of increase for the younger age group is much smaller than that for the older age group, which is in accordance with cohort explanation.
We explored the correlation between the number of index crimes reported to the police and the number of index arrests in a given year in New York State between 1990 and 2010. The correlation between the volume of index offenses reported to police and the volume of index arrests is very high (r = 0.931–0.960) across years.
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Acknowledgments
The authors wish to acknowledge the feedback from the National Academy of Sciences Roundtable on Crime Trends. In particular, we wish to thank Richard Rosenfeld and Malay Majmundar for support and encouragement. We also wish to think the New York State Division of Criminal Justice Services, which provided access to the Computerized Criminal History File. Finally, the Center for Social and Demographic Analysis of the University at Albany provided technical and administrative support for this research through a grant from the National Institute of Child Health and Human Development (R24-HD044943).
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Disclaimer This data is provided by the New York State Division of Criminal Justice Services (DCJS) in the interest of information exchange. The opinions, findings, and conclusions expressed in this publication are those of the authors and not those of DCJS. Neither New York State nor DCJS assumes liability for its contents or use thereof.
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Kim, J., Bushway, S. & Tsao, HS. Identifying Classes of Explanations for Crime Drop: Period and Cohort Effects for New York State. J Quant Criminol 32, 357–375 (2016). https://doi.org/10.1007/s10940-015-9274-5
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DOI: https://doi.org/10.1007/s10940-015-9274-5