We study assortative mating using a stochastic linear bi-dimensional matching model, where individuals match on an additive index of overall marital attractiveness that has two components: an observable component (education) and a non-observable (to the econometrician) component, the latter being an index of other homogeneously assessed attributes. This setting allows us to investigate whether exogenous shocks to the observable component satisfy the exclusion restriction, and if so, to use them to identify the degree of assortative mating on the observable component, and incidentally on the unobservable index of overall marital attractiveness. In particular, we exploit genetic variation in polygenic scores controlling for population stratification as individual exogenous shocks to education: combining them with our model structure we can test the validity of the exclusion restriction. Using data from the Health and Retirement Study, we find that polygenic scores satisfy the exclusion restriction and are relevant instruments, and cannot reject that the estimated degree of assortative mating on education is the same using OLS and IV. Our study illustrates how to combine quasi-experimental variation in spouses' characteristics with parsimonious matching models to investigate assortative mating.