We derive wage equations with individual-specific coefficients from a structural model of human capital investment over the life-cycle. This model allows for interruptions in labour market participation and deals with missing data and attrition problems. We propose a new framework that deals with missingness at random and is based on factor decompositions that allow for flexible control of selection. Our approach leads to an interactive effect wage specification, which we estimate using long administrative panel data on male wages in the private sector in France. A structural function approach shows that interruptions negatively affect average wages. Interestingly, they also negatively affect the inter-decile range of wages after twenty years. This is only partly due to the fact that interruptions are endogenous.

We develop a new methodology to estimate the elasticity of urban costs with respect to city population using French house and land price data. After handling a number of estimation concerns, we find that the elasticity of urban costs increases with city population with an estimate of about 0.03 for an urban area with 100,000 inhabitants to 0.08 for an urban area of the size of Paris. Our approach also yields a number of intermediate outputs of independent interest such as the share of housing in expenditure, the elasticity of unit house and land prices with respect to city population, and within-city distance gradients for house and land prices.