History and the sizes of cities

We discuss the tension between some of the recent evidence of path dependence in urban location with recent efforts to analyze calibrated models of city sizes. One strand of recent work, including some of our own, finds evidence of persistent city sizes following the obsolescence of historical advantages. This literature argues that such persistence cannot be understood as the medium-run effect of legacy capital, but rather as the long-run effect of equilibrium selection. In contrast, a different, recent literature uses stylized models that feature a single long-run equilibrium at each site/city. We show this disjunction in a standard model and then propose several modifications that might allow for multiplicity and thereby historical path dependence. We use mixed-integer-programming solvers to construct bounds on the degree of multiplicity of steady states across US Counties. We find, absent strong parametric restrictions, very wide bounds on the scope for multiple long-run equilibria. We then discuss a way forward for tightening these bounds using the obsolete endowments as restrictions on the model. ∗Bleakley: University of Michigan, 611 Tappan, Ann Arbor, MI 48109, [email protected]. Lin: Federal Reserve Bank of Philadelphia, Ten Independence Mall, Philadelphia, PA 19104, [email protected]. The views expressed here are those of the authors and do not necessarily represent the views of the Federal Reserve Bank of Philadelphia or the Federal Reserve System. We thank Jeff Brinkman and Satyajit Chatterjee for comments.