Genotype-by-environment interaction (GxE) studies probe heterogeneity in response to risk factors or interventions. Popular methods for estimation of GxE examine multiplicative interactions between individual genetic and environmental measures. However, risk factors and interventions may modulate the total variance of an epidemiological outcome that itself represents the aggregation of many other etiological components. We expand the traditional GxE model to directly model genetic and environmental moderation of the dispersion of the outcome. We derive a test statistic, [Formula: see text], for inferring whether an interaction identified between individual genetic and environmental measures represents a more general pattern of moderation of the total variance in the phenotype by either the genetic or the environmental measure. We validate our method via extensive simulation, and apply it to investigate genotype-by-birth year interactions for Body Mass Index (BMI) with polygenic scores in the Health and Retirement Study (N = 11,586) and individual genetic variants in the UK Biobank (N = 380,605). We find that changes in the penetrance of a genome-wide polygenic score for BMI across birth year are partly representative of a more general pattern of expanding BMI variation across generations. Three individual variants found to be more strongly associated with BMI among later born individuals, were also associated with the magnitude of variability in BMI itself within any given birth year, suggesting that they may confer general sensitivity of BMI to a range of unmeasured factors beyond those captured by birth year. We introduce an expanded GxE regression model that explicitly models genetic and environmental moderation of the dispersion of the outcome under study. This approach can determine whether GxE interactions identified are specific to the measured predictors or represent a more general pattern of moderation of the total variance in the outcome by the genetic and environmental measures.