ADVANCEMENT OF THE SCIENCE
previously observed relationships likely were influenced by data aggregation and shared national trends. The insignificant PM 2.5 coefficient in the pooled model implies that simple cross-state and intertemporal correlations do not provide compelling evidence of a direct association between air pollution and crime. This find- ing highlights the importance of accounting for unobserved heterogeneity and common shocks, because pooled OLS estimates could be biased by omitted variables that vary sys- tematically across states or over time. The positive but insignificant poverty coefficient is directionally consistent with the conceptual framework linking socioeco- nomic stressors to criminal behavior, but its imprecision suggests that poverty alone does not explain cross-state variation in crime rates in the absence of more refined controls. Similarly, the negative unemployment coef- ficient, although not statistically significant, could reflect cyclical effects, changes in eco- nomic activity, or reporting dynamics rather than causal relationships. Overall, the low explanatory power of the pooled model and the lack of statistically sig- nificant coefficients underscore the limitations of naive panel regressions that do not control for state-specific characteristics or time trends. These results motivate the use of fixed effects models that exploit within-state variation over time and absorb unobserved heterogeneity and common national shocks. The following section details how state-and-year fixed effects were incorporated to provide a more credible identification strategy in the study analysis. State-and-Year Fixed Effects Regression Supplemental Table S3 presents estimates from the fixed effects panel regression, includ- ing state fixed effects and year fixed effects, estimated on the full state–year panel ( N = 230; 10 U.S. states observed over 23 years). Standard errors are clustered at the state level to account for within-state serial correlation. Once unobserved state-specific heteroge- neity and common time shocks are controlled for, the association between PM 2.5 concentra- tions and crime rates becomes positive and statistically significant. The estimated coef- ficient on PM 2.5 is 5.05 ( p = .040), indicating that, within a given state, a 1-unit increase in annual mean PM 2.5 concentration is asso- ciated with an increase of approximately 5
crimes per 100,000 population, when keep- ing poverty, unemployment rates, and nation- wide time effects constant. Poverty exhibits a small positive coefficient ( β = 0.25) but is not statistically significant ( p = .917), suggesting that short-run within-state fluctuations in poverty rates are not strongly associated with changes in crime once fixed effects are included. In contrast, unemploy- ment rates retain a negative and statistically significant association with crime ( β = –8.46, p = .036), indicating that increases in unemploy- ment within a state are associated with contem- poraneous declines in reported crime rates. The model explains a substantial share of within-state variation in crime, with R 2 = .71, which highlights the importance of account- ing for persistent state characteristics and common temporal dynamics. Several year- fixed effects are negative and statistically sig- nificant, reflecting the pronounced national decline in crime over the study period. Interpretation of Fixed Effects Results The fixed effects results differ markedly from the pooled OLS estimates, underscoring the importance of accounting for unobserved heterogeneity and shared time trends when analyzing the pollution–crime relationship. In the pooled specification, the PM 2.5 coeffi- cient was small and statistically insignificant, whereas in the state-and-year fixed effects model, it became larger in magnitude and sta- tistically significant. This shift indicates that in simpler models, cross-state differences and national trends masked the within-state asso- ciation between pollution and crime. By controlling for state fixed effects, the analysis removes all time-invariant state char- acteristics (e.g., baseline crime levels, long- standing policing practices, demographic composition, geographic factors) that may be correlated with both pollution exposure and crime. Year fixed effects further absorb nation- wide shocks, policy changes, and secular trends, including the well-documented decline in U.S. crime rates since the early 2000s. Iden- tification, therefore, arises from within-state deviations from long-run averages, providing a more credible basis for inference. The persistence of a negative and statisti- cally significant unemployment rate coeffi- cient in the fixed effects model suggests that the inverse relationship between unemploy- ment and crime is not solely driven by cross-
state differences. This pattern might reflect reduced economic activity, mobility, or report- ing during periods of higher unemployment, rather than a causal deterrent effect, and thus should be interpreted cautiously. The insignificance of poverty in the fixed effects specification contrasts with its posi- tive (though not significant) coefficient in the pooled model, implying that poverty’s associa- tion with crime operates largely through per- sistent cross-state differences rather than short- term within-state changes. This finding is consistent with the view that structural socio- economic conditions influence crime levels over long horizons, whereas year-to-year fluc- tuations can have weaker immediate effects. Overall, the fixed effects results demonstrate that model specification materially affects inference about the pollution–crime relation- ship. The emergence of a statistically signifi- cant PM 2.5 coefficient in the preferred fixed effects model suggests that air pollution might be associated with crime through short-run mechanisms such as cognitive stress, behav- ioral responses, or contemporaneous environ- mental conditions. At the same time, the sensi- tivity of results across specifications reinforces the need for cautious interpretation and high- lights the observational nature of the analysis. Conclusion This study provides robust empirical evi- dence on the relationship between PM 2.5 , socioeconomic factors, and crime rates across 10 highly polluted U.S. states over the period 2000–2022. The study findings reveal that model specifications fundamentally shape the observed relationship between pollution and crime. Although pooled estimates sug- gest no meaningful association, the fixed effects models uncover a positive and statis- tically significant within-state relationship between PM 2.5 and crime rates. In contrast, poverty does not exhibit a signif- icant effect in the fixed effects models, suggest- ing that its influence is largely structural and persistent rather than dynamic. Unemploy- ment rates, however, show a consistent nega- tive association with crime, pointing to more complex cyclical or behavioral interactions that merit further interpretation. Importantly, the preferred specification explains a substan- tial share of within-state variation, reinforcing the analytical strength of controlling for unob- served heterogeneity and common time trends.
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Volume 89 • Number 3
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