ECONOMIC GROWTH CENTERYALE UNIVERSITYP.O. Box 208269New Haven, CT 06520-8269http://www.econ.yale.edu/~egcenter/CENTER DISCUSSION PAPER NO. 862ESTIMATING EQUILIBRIUM MODELS OF SORTING ACROSS LOCATIONSPatrick BayerYale UniversityandChristopher TimminsYale UniversityJuly 2003Notes: Center Discussion Papers are preliminary materials circulated to stimulate discussions andcritical comments.The authors wish to thank Dan Ackerberg, Steve Berry, William Brock, Don Brown, Greg Crawford, SteveDurlauf, Penny Goldberg, Vernon Henderson, Michael Keane, Robert McMillan, Stephen Morris, MarcRysman, Steven Stern, Chris Udry and two anonymous referees for their helpful comments andsuggestions. We gratefully acknowledge financial support provided from the NSF under grant SES-0137289. Correspondence may be sent to either author at 37 Hillhouse Avenue, Department of Economics,Yale University, New Haven, CT 06511, email: [email protected], [email protected] paper can be downloaded without charge from the Social Science Research Network electronic libraryat: http://ssrn.com/abstract=441320An index to papers in the Economic Growth Center Discussion Paper Series is located at: http://www.econ.yale.edu/~egcenter/research.htmEstimating Equilibrium Models of Sorting Across LocationsPatrick Bayer and Christopher TimminsAbstractWith the growing recognition of the role played by geography in all sorts of economic problems, there is stronginterest in measuring the size and scope of local spillovers (i.e., simple anonymous agglomeration or congestioneffects, or more complicated interactions between individuals or firms of specific types). It is well-understood,however, that such spillovers cannot be distinguished from unobservable local attributes using just the observedlocation decisions of individuals or firms. We propose an empirical strategy for recovering estimates of spilloversin the presence of unobserved local attributes for a broadly applicable class of equilibrium sorting models. Thisapproach relies on an instrumental variables strategy derived from the internal logic of the sorting model itself.We show practically how the strategy is implemented, provide intuition for our instrumental variables, and discussthe role of effective choice-set variation in identifying the model, and carry-out a series of Monte Carloexperiments to demonstrate the instruments’ performance in small samples.JEL Codes: H7, R0, R2, R3Keywords: Local Spillovers, Location Choice, Economic Geography, Natural Advantage, Social Interactions,Network Effects, Endogenous Sorting, Discrete Choice Models, Agglomeration, Congestion21 INTRODUCTIONModels of location choice – whether of firms or households, within or across cities – havelong been central to regional and urban economics. From the inter-jurisdictional sorting models ofTiebout (1956) to the models of segregation developed by Schelling (1969, 1971) to the “neweconomic geography” of Fujita, Krugman, and Venables (2000), a central feature has been the roleof local interactions or spillovers, whereby the payoffs from choosing a location depend in part onthe number or attributes of other individuals or firms that choose the same or nearby locations inequilibrium. In some cases, these local spillovers operate through anonymous channels, withpayoffs depending upon simply the number of other individuals or firms selecting the same location,while in other circumstances, the attributes of one’s neighbors (e.g., race, income, or education inthe case of individuals, and industry classification in the case of firms) might matter as well. It isthe interplay between these sorts of spillovers and the natural advantages embedded in thelandscape of alternative locations that can explain, at a regional level, the geographic and sizedistribution of cities, and at an urban level, the stratification of households across communities onthe basis of income, education, and race, neighborhood density patterns, ethnic enclaves, ghettos,and problems of inner-city decay and suburban sprawl. Ultimately, local spillovers must derive from some underlying mechanism. For example,households may desire to live in large metropolitan areas because of the size and scope of the labormarket or the urban amenities that cities provide. At the same time, congestion operating throughincreased travel times and the increased price of land may detract from the welfare of individualsin large cities. While distinguishing the precise role of each of these mechanisms may be of interest,often the central problem in an empirical application is simply that of distinguishing the aggregatebehavioral effect of local spillovers from that of fixed natural advantages that are tied to locations,particularly when the latter are not observed by the researcher. Recent empirical work attemptingto distinguish the magnitude of local interactions has focused on subjects as diverse as crime in cities3[Glaeser, Sacerdote, and Scheinkman (1996)], racial segregation [Bayer, McMillan, and Rueben(2002)], interjurisdicational sorting related to schooling [Epple and Sieg (1999), Bayer, Ferreira, andMcMillan (2003)], human capital spillovers in the labor market [Morretti(2002)], the generalequilibrium effects of environmental policy [Sieg et. al. (2003), Timmins (2003)], welfareparticipation [Bertrand et. al. (2000)], unemployment spells [Topa (2001)], development economics[Deichmann et. al. (2002), Krugman (1995)] and agglomeration economies in firm locations andinvestment [Henderson (1999)], among many others.It is well-understood that there is nothing in, for example, just the observation of manypeople residing in New York City or numerous high-tech firms locating in Silicon Valley that candistinguish between local spillovers and a distribution of underlying natural advantages acrosslocations [Glaeser and Scheinkman (2002)]. Behavioral data alone provide no guidance as towhether such examples of clustering of individuals or firms should be interpreted as evidence of astrong agglomerating force or the inherent desirability of these locations. Ellison and Glaeser (1997)formalize this as an observational equivalence theorem, stating that “the relationship between meanmeasured levels of concentration and industry characteristics is the same regardless of whetherconcentration is the result of spillovers, natural advantage, or a combination of the two.” In essence,this result is based on the fact