Endogenous job destruction and job matching in cities

We propose a spatial search-matching model where both job creation and job destruction are endogenous. Workers are ex ante identical but not ex post since their job can be hit by a technological shock, which decreases their productivity. They reside in a city and commuting to the job center involves both pecuniary and time costs. Thus, workers with high wages are willing to live closer to jobs to save on time commuting costs. We show that, in equilibrium, there is a one-to-one correspondence between the productivity space and the urban location space since high-productivity workers bid away low-productivity workers in order to occupy locations close to jobs. We also show that in the bargaining process, there is a spatial element in the wage setting since firms need to compensate workers for their spatial costs. Compared to the non-spatial model, the unemployment rate and the reservation productivity are lower and the job-creation rate is higher because the urban space through commuting costs and land rent create additional frictions in the labor market.