Research

This paper provides a unifying explanation for the lack of supply of skilled teachers in remote locations. I build an empirical model of dynamic two-sided matching to link teachers' and schools' preferences with equilibrium sorting and job-to-job flows. I show that this mapping is invertible such that preferences can be identified and estimated from observed matches. Taking these tools to panel data on the assignment of public teachers in Peru, I show that the spatial disaggregation of labor demand coupled with the concentration of labor supply in cities imply the existence of a spatial job ladder. Low quality teachers get displaced in remote schools and move toward urban schools by climbing up the ladder once they have accumulated experience and skills. Labor mobility thus magnifies the urban-rural gap in teacher quality by one third. Dynamic wage contracts that foster retention can largely mitigate this effect.

We exploit data on the universe of public-school teachers and students in Peru to establish that wage rigidity makes teachers choose schools based on non-pecuniary factors, magnifying the existing urban-rural gap in student achievement. Leveraging a reform in the teacher compensation structure, we provide causal evidence that increasing salaries in less desirable locations is effective at improving student learning by attracting higher-quality teachers. We then build and estimate a model of teacher sorting across schools and student achievement production, whereby teachers are heterogeneous in their preferences over non-wage attributes and their comparative advantages in teaching different student types. Counterfactual compensation policies that leverage information about teachers' preferences and value-added can result in a substantially more efficient and equitable allocation by inducing teachers to sort based on their comparative advantage.

I build a model of many-to-one matching with non-transferable utility involving many agents on both sides of the market, e.g. workers and firms. I provide an analytical mapping between agents' preferences and equilibrium sorting patterns. Under parsimonious assumptions on preferences, one can identify the joint surplus of a match, but cannot separately identify workers' and firms' preferences from data on realized matches. Within-firm variation in worker characteristics, only available in many-to-one matching data, allows to identify latent firm components of the surplus function. I discuss how these results can help identifying the sources of wage inequality and worker-firm sorting.

I build an empirical model of dynamic two-sided matching where a subset of job and worker attributes are contractible, e.g. wages, hours or amenities. I provide a tractable asymptotic characterization of how workers' preferences and firms' technology map into the distribution of equilibrium matches, contracts and job-to-job transitions. I leverage this result to show that search frictions, i.e. non-degenerate meeting probabilities, are not necessary for the model to generate rich predictions on worker-firm sorting and mobility, wage dynamics and inequality, and labor market power. More generally, I find that, without further restrictions, the match surplus function and search frictions are not separately identified from panel data on realized worker-firm matches. I conclude by discussing the implications of this result for empirical work.