Skills, migration, and urban amenities over the life cycle

We examine sorting behavior across metropolitan areas by skill over individuals' life cycles. We show that high-skill workers disproportionately sort into high-amenity areas, but do so relatively early in life. Workers of all skill levels tend to move towards lower-amenity areas during their thirties and forties. Consequently, individuals' time use and expenditures on activities related to local amenities are U-shaped over the life cycle. This contrasts with well-documented life-cycle consumption profiles, which have an opposite inverted-U shape. We present evidence that the move towards lower-amenity (and lower-cost) metropolitan areas is driven by changes in the number of household children over the life cycle: individuals, particularly the college educated, tend to move towards lower-amenity areas after having their first child. We develop an equilibrium model of location choice, labor supply, and amenity consumption and introduce life-cycle changes in household composition that affect leisure preferences, consumption choices, and required home production time. Key to the model is a complementarity between leisure time spent going out and local amenities, which we estimate to be large and significant. Ignoring this complementarity and the distinction between types of leisure misses the dampening effect child rearing has on urban agglomeration. Since the value of local amenities is capitalized into housing prices, individuals will tend to move to lower-cost locations to avoid paying for amenities they are not consuming.