Firm Sorting and Spatial Inequality

We study the importance of firm sorting for spatial inequality. If productive locations are able to attract the most productive firms, then firm sorting acts as an amplifier of spatial inequality. We develop a novel model of spatial firm sorting, in which heterogeneous firms first choose a location and then hire workers in a frictional local labor market. Firms' location choices are guided by a fundamental trade-off: Operating in productive locations increases output per worker, but sharing a labor market with other productive firms makes it hard to poach and retain workers, and hence limits firm size. We show that sorting between firms and locations is positive--i.e., more productive firms settle in more productive locations--if firm and location productivity are complements and labor market frictions are sufficiently large. We estimate our model using administrative data from Germany and find that highly productive firms indeed sort into the most productive locations. In our main application, we quantify the role of firm sorting for wage differences between East and West Germany, which reveals that firm sorting accounts for 17%-27% of the West-East wage gap