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We examine the hypothesis that the heritability of smoking has varied over the course of recent history as a function of associated changes in the composition of the smoking and non-smoking populations. Classical twin-based heritability analysis has suggested that genetic basis of smoking has increased as the information about the harms of tobacco has become more prevalent—particularly after the issuance of the 1964 Surgeon General’s Report. In the present paper we deploy alternative methods to test this claim. We use data from the Health and Retirement Study to estimate cohort differences in the genetic influence on smoking using both genomic-relatedness-matrix restricted maximum likelihood and a modified DeFries–Fulker approach. We perform a similar exercise deploying a polygenic score for smoking using results generated by the Tobacco and Genetics consortium. The results support earlier claims that the genetic influence in smoking behavior has increased over time. Emphasizing historical periods and birth cohorts as environmental factors has benefits over existing GxE research. Our results provide additional support for the idea that anti-smoking policies of the 1980s may not be as effective because of the increasingly important role of genotype as a determinant of smoking status.