The returns to scale of marriage markets have important behavioral and welfare consequences. It is quantitatively difficult to estimate the returns to scale because, due to endogenous migration, the marriage market size is endogenous. This paper addresses the endogeneity in two ways. First, it estimates the degree of returns to scale in U.S. marriage markets using the 2000 census. Given that in the United States people move to cities to find marriage partners and, therefore, the size of the marriage market is endogenous, we instrument the current size of a cohort in the marriage market with the size of that cohort twenty years earlier. Second, it estimates city scale effects in two societies---early Renaissance Tuscany and pre-reform China---where there was little internal mobility, and thus, the size of the marriage market can be considered exogenous. The main finding is that in all three societies, there is no evidence of increasing returns to scale in marriage markets, whereas the hypothesis of constant returns to scale cannot be rejected. This is true when looking at marriage odds ratios, total gains to marriage, and the quality of marital match. Given the different characteristics of the three societies in terms of population size, time period, economic structure, and social norms characterizing the marriage market, the similarity and precision of the estimates for returns to scale parameters is remarkable.
