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If socio-economic status (SES) and genetic variants are both assets in marriage markets, then the two will become associated in spouse pairs, and will be passed on together to future generations. This process provides a new ex- planation for the surprising persistence of inequality across generations, and for the genes-SES gradient: the genetic differences we observe between high- and low-income people. The gradient includes differences related to human capital and to physical and mental health, so understanding its origins is important for understanding inequality in general, and health inequalities in particular. We model social-genetic assortative mating (SGAM) and test for its ex- istence in a large genetically-informed survey. We compare spouses of individuals with different birth order, which is known to affect socio-economic status and which is exogenous to own genetic endowments among siblings. Spouses of earlier-born individuals have genetic variants that predict higher educational attainment. We provide evidence that this effect is mediated by individuals' own educational attainment and income. Thus, environmental shocks to socio-economic status are reflected in the DNA of subsequent generations. Our work uncovers a new channel by which economic institutions can affect long-run inequality, suggests that genes-SES gradients may be historically widespread, and shows that genetic variation is endogenous to social institutions.