Racial similarity in the relationship between poverty and homicide rates: Comparing retransformed coefficients

Criminologists have shown great interest in comparing the strength of the relationship between poverty and violent crime for whites and blacks. The present paper argues that the standard approach of comparing race-specific coefficients from logarithmic metric OLS and/or Poisson-based regressions has led to erroneous conclusions in this literature. Unlike researchers in other disciplines (especially economics), criminologists have largely ignored the need to “retransform” coefficients to their linear-effect representations before making comparisons between groups. The current study illustrates the importance of this methodological issue for the substantive question of whether poverty’s relationship to homicide is racially invariant (N = 134 cities). Similar to previous studies, initial results indicated that poverty’s effect on the natural logarithm of the homicide rate was dramatically stronger for whites than blacks (nearly 300% stronger for whites). However, after applying a broadly useful retransformation formula, poverty’s effect on the homicide rate actually appeared somewhat stronger for blacks. Further application of bootstrap simulations necessary to calculate the standard error of the difference in coefficients suggested that this racial discrepancy was not statistically significant.