alternative specifications incorporate time controls, including a linear time trend and year fixed effects (dummy variables for year), which absorb nationwide shocks, policy changes, and secular trends, affecting all states simultaneously.
state in a given year. State-level observations for PM 2.5 concentrations, crime rates, poverty rates, and unemployment rates were retained in long (panel) format, and no aggregation to annual cross-state averages was performed in the final analysis. Regression analyses were conducted sequentially, beginning with pooled OLS mod- els for baseline comparison, followed by fixed effects panel regressions incorporating state fixed effects, year fixed effects, or both. This sequential approach allows for direct compari- son of coefficient estimates across specifica- tions to evaluate the influence of unobserved heterogeneity and common time trends.
approximately 526 to 412–424 per 100,000 population by 2022. Maximum values for both variables also decreased, accompanied by reduced variability across states.
Regression Analysis of Crime Rate Determinants
Fixed Effects and Identification Strategy
Pooled State–Year Regression (Baseline Specification)
A central concern in observational panel analyses is unobserved, time-invariant het- erogeneity across states, such as differences in policing regimes, demographic composi- tion, urban structure, geographic conditions, and crime reporting practices. If correlated with pollution exposure, these factors could bias pooled estimates. To address this concern, this study esti- mated state fixed effects models, which con- trol for all time-invariant state characteris- tics by exploiting within-state variation over time. The preferred specification includes both state fixed effects and year fixed effects, and is expressed as: Crime s,t = β 1 PM 2.5 s,t + β 2 Poverty s,t + β 3 Unemployment s,t + μ s + λ t + ε s,t where μ s denotes state fixed effects and λ t denotes year fixed effects. Identification in this framework arises from within-state variation over time after accounting for common year-specific shocks, providing a more credible basis for inference than pooled cross-sectional correlations. All models are estimated using ordinary least squares (OLS) or fixed effects estima- tors, as appropriate. Standard errors are clus- tered at the state level to account for serial correlation and heteroscedasticity (also called heterogeneity of variance) within states over time. Results are reported sequentially to facilitate comparison across pooled state fixed effects and state-and-year fixed effects specifications, which allows assessment of the sensitivity of estimated coefficients to increasingly stringent controls. Statistical Analysis All statistical analyses were conducted using Stata18 for 64-bit computers. After compil- ing state-level data for the 10 U.S. states over the period 2000–2022, the final dataset was structured as a state–year panel in which each observation represents a specific U.S.
Supplemental Table S2 reports the results of the pooled OLS regression estimated on the full state–year panel ( N = 230), with standard errors clustered at the state level. This speci- fication relates state-level crime rates to PM 2.5 concentrations, poverty rates, and unemploy- ment rates, without controlling for unob- served state-specific or time-specific effects. The estimated coefficient on PM 2.5 is posi- tive ( β = 0.22), indicating that higher pollution levels are associated with marginally higher crime rates; however, the estimate is statisti- cally insignificant ( p = .98), and the 95% con- fidence interval (CI) is wide and includes 0. These findings suggest no robust linear associ- ation between PM 2.5 concentrations and crime rates in the pooled specification. Poverty is positively associated with crime ( β = 3.54), consistent with theoretical expec- tations linking socioeconomic disadvantages to criminal activity. Nonetheless, this coef- ficient is also statistically insignificant ( p = .64), indicating that poverty does not exhibit a strong independent association with crime in the pooled model. Unemployment rates display a negative coefficient ( β = –6.33), suggesting that higher unemployment rates are associated with lower crime rates; however, this estimate is not sta- tistically significant ( p = .34) once standard errors are clustered at the state level. The over- all explanatory power of the model is limited, with R 2 = .021, and the joint significance test fails to reject the null hypothesis that all slope coefficients are 0 ( F -test, p = .40). Interpretation of the Pooled Regression Results The pooled regression results indicate weak and statistically insignificant associations between PM 2.5 , socioeconomic variables, and crime rates when the full state–year variation is retained. Compared with earlier explor- atory analyses based on cross-state averages, the attenuation of coefficient magnitudes and loss of statistical significance suggest that
Results and Discussion
Historical Trend Observations Figure 2 presents annual PM 2.5 concentrations across the 10 U.S. states during 2000–2022, showing a clear downward trend and sus- tained improvements in air quality. California consistently recorded the highest levels, with notable peaks in 2008, 2013, and 2020, likely linked to wildfire activity. In contrast, Nevada maintained the lowest concentrations, typi- cally between 3 and 6 µg/m 3 . Moreover, Texas, Pennsylvania, Illinois, and Ohio exhibited moderate levels, declining from approximately 15 µg/m 3 in the early 2000s to approximately 10 µg/m 3 in more recent years. Overall, both median and extreme values decreased, indicat- ing reduced pollution intensity and variability. Figure 3 presents annual crime rates per 100,000 population across the same U.S. states, also showing a general downward trend. Specifically, California, Nevada, and Illi- nois reported the highest crime levels, whereas Oregon and Ohio reported lower rates. Cali- fornia experienced a steady decline followed by stabilization, whereas Nevada showed consistently elevated rates with peaks in the mid–2000s. Illinois, Pennsylvania, and Geor- gia recorded substantial reductions, declining from approximately >550 to 400. Texas and Oklahoma exhibited more gradual decreases, while Arizona and Oregon showed sharper early declines followed by fluctuations. PM 2.5 concentrations and crime rates dis- play parallel downward trends, reflecting improvements in both environmental condi- tions and public safety. Median PM 2.5 levels declined from 14.25 µg/m 3 in 2000 to 8–9 µg/ m 3 after 2019, while crime medians fell from
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October 2026 • Journal of Environmental Health
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