Abstract
In this study, we use 1980–2019 longitudinal age-arrest data from Taiwan and applied the age-period-cohort-interaction (APC-I) model (Luo & Hodges, 2022) to examine the stability or change in the age-arrest distributions across five offenses. We focus on two research questions: (1) whether the shape of age-arrest curves in Taiwan diverges from the Hirschi and Gottfredson’s (HG) invariant premise after accounting for period and cohort effects; and (2) whether any observed period or cohort effects on age patterns vary depending on offense type. Findings indicate overall consistency in the shape of Taiwan’s age-arrest distributions after adjusting for period and cohort effects, which are characterized by relatively older peak ages and symmetrical spread-out distributions that diverge considerably from HG’s invariant projection and prototypical US age-arrest patterns. In addition, we find that period effects have contributed to higher arrest rates in recent years, and cohort effects have impacted somewhat the shape of Taiwan’s age-arrest distributions. These findings, along with recent cross-sectional evidence from Taiwan, South Korea, and India (Steffensmeier et al., 2017; 2019; 2020), further confirm that the aggregate age-crime relationship is robustly influenced by country-specific processes and historical and social transformations.
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Notes
However, it is beyond the scope of the current study to examine specific mechanisms of period and cohort effects. We focus on testing if the age-crime patterns change when controlling for period and cohort effects.
Robustness check is conducted using the APC-mixed model (O’Brien et al., 2008) and the results support our main findings.
Since 2005, offenses of breach of trust, which was a subcategory of fraud, was classified as a separate category in the CIBP crime statistics. However, because breach of trust cases consitututed a minor portion of the overall fraud cases (less than 5% cases), the impact of this category change on our findings is small or negligible.
There are several important legal changes in drug laws in Taiwan. Notably, the enactment of the Narcotics Hazard Prevention Act in 1998 emphasized treating drug-addicted defendants as “diseased criminal” rather than just a “criminal”(Chen et al., 2021). Subsequent policy and legal revisions included the introduction of new medical treatment programs, new classifications of specific drugs, or changes in the punishment of specific types of drug offenders. These changes have been primarily driven by temporal changes in drug use patterns (e.g., HIV epidemic among people with injection drug use in the early 2000s). While these changes in law and policy may influence age-specific arrest patterns for drug law violations, the effect will be accounted for as either period or cohort effects in the APC analysis.
We do not show a discrete homicide category because this category in Taiwan includes not only lethal homicides (as characterizes the US homicide category), but also offenses such as kidnapping, assisting suicide, and attempted homicide/serious injury (e.g., assaults near to victim’s head or heart). Roughly 70% of homicide arrests in Taiwan are nonlethal based on its mortality statistics. Also, Hsing et al.’s study (2022) found that Taiwan has low a annual rate of lethal homicide (approximately 1/100,000) and the mean age of homicide victims is older than 35.
Details of the interpolation methods are included in Appendix 1. The linear interpolation method has been widely used in social sciences for estimating missing data and for estimating trends with inconsistent age or period intervals (Holly & Jones, 1997; Lidwall & Marklund, 2011; Rudnytskyi et al., 2015; Weden et al., 2015). In addition, we also conduct supplemental analysis with cubic spline interpolation methods(Bergstrom & Lam, 1989; McNeil et al., 1977). Results are presented in Appendix 1, Fig. 4. The overall patterns are similar to our main analysis.
The formula for calculating the PAI is the formula for calculating the PAI is: \({PAI}_{ij}= \frac{{r}_{ij}}{\sum {r}_{ij}}*100\),
where \({r}\) = age-specific arrest rate, \({i }\) = age category, and \(j\) = offense category. In the following analysis, PAI is used to plot the age-crime curves and calculate summary measures of the age-crime distribution (e.g., peak age, one-half peak descending, skewness).
All of the APC-I models are estimated using the sum-to-zero coding in R. Different from the conventional modeling approach that uses an age or period category as the reference group, the coefficients estimated using the sum-to-zero coding represent the deviation from the grand mean of all the observations. This approach also makes the interpretation of interaction terms easier as each coefficient of the interaction term represents the deviation from the expected values based on the main effects. Moreover, this approach also allows us to adjust for the arrest level differences across comparisons (e.g., offense types or vs HG invariance projection)—that is, we can compare the estimated coefficients across countries as the mean differences across countries are held constant in the model.
We aggregate the data into 5-year categories to avoid random yearly fluctuation and also to better measure the concept of cohort and potential cohort effects. As Easterlin (1987) has noted, a 1-year bulge in the population can be easily absorbed by different social institutions (i.e., labor market, schools), but a 5- or 10-year bulge cannot.
We also conducted a series of deviance tests to examine the unique contributions of age, period, and cohort effects in the APC-I model across the five offense types (Luo & Hodges, 2022). Results suggest that the full APC-I model provides significantly better fit to the data than the partial models. Therefore, we conclude that age, period, and cohort effects are significant factors in explaining the age-specific arrest rates across the five offense types in Taiwan. The deviance test results are presented in Appendix 2, Table 3.
There is a small dip observed in the average age distributions of theft, assault, and total which parallel the mandatory military service required for all young males in Taiwan. The dip is followed by an increase in arrests that lasts well into midlife ages.
Note also the age pattern for total arrests is heavily swayed by large volume of arrests for theft.
An additional research pursuit involves the ongoing monitoring of Taiwan age-arrest trends to document whether current age curves become more/less symmetrical in the years ahead as today’s youth and preteen cohorts transition through the life course. Of interest, particularly, is whether the current symmetrical distribution for theft persists in the decades ahead or becomes more adolescent spiked as was observed in the 1980s timeline.
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Both authors contributed to the study conception and design. Material preparation and data collection were performed by Yunmei Lu and Darrell Steffensmeier. Yunmei Lu conducted the data analysis and developed the first draft and Darrell Steffensmeier edited and commented on various versions of the manuscript. Both authors read and approved the final manuscript.
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Appendices
Appendix 1
Interpolation and Robustness Check
The linear interpolation method has been widely used in social sciences for estimating missing data and for estimating trends with inconsistent age or period intervals (Holly & Jones, 1997; Lidwall & Marklund, 2011; Rudnytskyi et al., 2015; Weden et al., 2015). It assumes linear changes between two known data points; thus, it uses linear polynomials to construct new data points between each two known observations. For instance, for data before 2008, we first disaggregate the 10-year age groups of age 30–39, 40–49, and 50–59 using the linear interpolation function in R (“approx” function) and then rearrange the age group to 5-year increments. The same approach is for the 10-year age groups of age 40–49 and 50–59 in the data after 2008.
We opt for linear interpolation in the main analysis for its parsimony, but we also conduct a supplemental analysis with the cubic spline interpolation technique to ensure our results are consistent across different interpolation methods (McNeil et al., 1977). Cubic-spline interpolation is a special case for spline interpolation where a set of piecewise cubic functions are used to interpolate and smooth a set of data points. It is also a commonly used interpolation method in social science research (Bergstrom & Lam, 1989; Fritsch & Carlson, 1980; Kostaki & Panousis, 2001; McNeil et al., 1977). Appendix Fig. 4 replicates Fig. 1 in the main analysis and demonstrates the histogram of the age-crime distribution of four different periods in Taiwan based on cubic-spline interpolation techniques (“spline” function in R with “natural” method). The interpolated results for single-year estimates vary slightly from the same estimates based on the linear-interpolation results, but once we re-arrange the data into 5-year age categories to reduce instability, the interpolated patterns are almost identical across the two interpolation techniques. The patterns depicted in Appendix Fig. 4 (based on cubic spline interpolation) mirror those observed in are the same as the patterns observed in Fig. 1 (based on linear interpolation). Replication of the age-period-cohort analyses also demonstrates consistent findings.
Age-arrest distribution by type of offense across historical periods in Taiwan based on cubic spline interpolation method
Appendix 2
Appendix 3
Estimated period main effects on different offenses in Taiwan. Notes: The horizontal solid line represents zero deviation from the global mean (intercept of the APC-I model). Points above the zero line represent positive deviations from the global mean, suggesting higher-than-expected risks of arrest; points below the zero line represent negative deviations from the global mean, suggesting lower-than-expected risks of arrest
Estimated inter-cohort deviations of different offenses in Taiwan. Notes: The horizontal solid line in each plot represents no deviation from the predicted arrest rate determined by age and period main effects. Points that fall on the zero line represent no cohort effects (i.e., age and period main effects are sufficient to determine the arrest rate). Points above the line indicate cohorts with higher arrest rates than the predicted values determined by age and period main effects. Points below the zero line indicate cohorts with lower arrest rates than the predicted values determined by age and period main effects
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Lu, Y., Steffensmeier, D. Stability or Change in Age-Crime Relation in Taiwan, 1980–2019: Age-Period-Cohort Assessment. Asian J Criminol 18, 433–458 (2023). https://doi.org/10.1007/s11417-023-09412-y
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DOI: https://doi.org/10.1007/s11417-023-09412-y