Explaining the size distribution of cities: X-treme economies

The methodology used by theories to explain the size distribution of cities is contrived in that it takes an empirical fact and works backward to first obtain a reduced form of a model, then pushes this reduced form back to assumptions on primitives. The induced assumptions on consumer behavior, particularly about their ability to insure against the city-level productivity shocks in the model, are untenable. With either self insurance or insurance markets, and either an arbitrarily small cost of moving or the assumption that consumers do not perfectly observe the shocks to firms' technologies, the agents will never move. Equilibrium implies a uniform distribution of agents. Even without these frictions, our analysis yields another equilibrium with insurance that gives exactly the same utility level to consumers as the equilibrium studied in the literature, but where consumers never move. Thus, insurance is a substitute for movement. Even aggregate shocks are insufficent to generate consumer movement, since consumers can borrow and save. We propose an alternative class of models, involving extreme risk against which consumers will not insure. Instead, they will move.