Abstract
This chapter extends applications of unconditional and conditional β-convergence and unconditional σ-convergence analysis to Part I crime rates in a panel data sample of Pennsylvania counties during the period 1990-2015. Temporal structural breaks at specific points in the business cycle during the time frame and spatial breakpoints between rural and urban counties in Pennsylvania are acknowledged in the analysis in order to avoid spurious inferences regarding convergence behavior. Unit-root testing is performed on measures of dispersion as well as directly on the underlying crime-rate series via panel-data tests for non-stationarity. The findings support the existence of both unconditional and conditional β-convergence in the pooled, urban, and rural samples during 1990-2015. Visual and statistical evidence reveals the presence of σ-convergence in the three samples across the time span as well. The comprehensive convergence analysis of appropriately disaggregated data performed in this study offers strong support for the predictions of modernization theory.
TopIntroduction
In the context of crime, convergence refers to the tendency of existing differences in crime rates across cross-sectional units or time periods to dissipate and effectively close the gap. In other words, disparities in rates of criminal activity will be transitory rather than permanent. The study of crime rate convergence is a relatively new undertaking for researchers in economics (Cook & Winfield 2013, 2016). Empirical results have been mixed thus far, with some studies showing both β-convergence and σ-convergence (Cook & Winfield, 2013), others finding only one of the two present, and still others revealing crime divergence (Cook & Winfield, 2016). Several important facets of crime rate convergence remain understudied, and no single crime theory of convergence (e.g., modernization theory, conflict theory) has distinguished itself as having the most explanatory power. Despite a dearth of empirical investigation, understanding crime rate convergence is important for policy direction and implementation, since criminal behavior remains a matter of ongoing concern for law enforcement officials and policymakers at all geographic levels. Cook and Winfield’s (2013, 2016) findings on crime rate convergence have birthed new empirical questions, because there is ambiguity surrounding the policy implications of crime rate convergence. Questions like, “Is the convergence of crime rates favorable or unfavorable?” and “Can crime convergence be increased or limited?” remain unsatisfactorily answered.
Determining whether or not crime rate convergence exists across time and region may better inform crime rate predictions and offer new avenues of inquiry for criminological theory and ultimately crime-rate-reduction strategies. This research is motivated accordingly and acknowledges both temporal and spatial structural breaks. Cook and Cook (2011) argue that analyses of crime convergence over time that ignore breakpoints resulting from fluctuations in economic conditions, significant social shifts, and governmental regime changes may yield misleading results. They note that the persistent assertions of non-stationary U.S. crime rates in the existing literature may arise from overlooked structural breaks in the underlying series and, consequently, run the risk of advancing spurious inferences. Thus, the analysis separately considers the convergence behavior of crime rates across the expansionary and contractionary phases of the business cycle when structural changes occur. In addition, this study includes separate analyses of rural and urban regions based on a structural break between rural and urban counties in Pennsylvania, because criminal activity is a function of the features of a specific geographic location as emphasized by Buonanno and Montolio (2008). This approach to understanding crime rates in rural and urban Pennsylvania counties is consistent with previous literature (Cook & Winfield, 2016; Frederick & Jozefowicz, 2018), and it heeds the warning that equivalently treating non-metropolitan and metropolitan areas risks a sample selection bias toward finding convergence (Drennan, Lobo, & Strumsky, 2004). If convergence in crime rates varies by levels of economic activity and/or geographic area, then further analysis on the structural differences between rural and urban areas and the facets of business cycle fluctuations is in order.
Key Terms in this Chapter
Unit Root: Its presence indicates that a time series is non-stationary.
Part I Crime Rate: A measure of the number of reported crimes of murder, nonnegligent manslaughter, forcible rape, robbery, assault, burglary, larceny-theft, motor-vehicle theft, and arson per 100,000 people.
Stationarity: The case when the statistical properties, such as mean, variance, etc., of a time series of observations are all constant over time.
ß-Convergence: A cross-sectional phenomenon in which a unit with a lower initial endowment grows faster than a unit with a higher initial endowment until the former “catches up” to the latter.
s-Convergence: A time-series phenomenon in which a reduction in the dispersion measures of a variable occurs across time.
Dickey-Fuller Generalized Least Squares (DF-GLS) Test: A test for the presence of a unit root in which the time series of observations is transformed via a generalized least squares (GLS) regression before performing the test.
Augmented Dickey-Fuller (ADF) Test: A test for the presence of a unit root in a time series of observations while incorporating lags of the dependent variable.
Business Cycle: The fluctuating periods of expansion and contraction in the level of economic activity in an economy around a long-term growth trend.