Tipping and the Dynamics of Segregation April 2007

In a classic paper, Schelling (1971) showed that extreme segregation can arise from social interactions in white preferences: once the minority share in a neighborhood exceeds a critical “tipping point”, all the whites leave. We use regression discontinuity methods and Census tract data from 1970 through 2000 to test for discontinuities in the dynamics of neighborhood racial composition. White population flows exhibit tipping-like behavior in most cities, with a distribution of tipping points ranging from 5% to 20% minority share. The estimated discontinuities are robust to controls for a wide variety of neighborhood characteristics, and are as strong in the suburbs as in tracts close to high-minority neighborhoods, ruling out the main alternative explanations for apparent tipping behavior. In contrast to white population flows, there is no systematic evidence that rents or housing prices exhibit non-linearities around the tipping point. Finally, we relate the location of the estimated tipping points in different cities to measures of the racial attitudes of whites, and find that cities with more tolerant whites have higher tipping points. *We are grateful to Edward Glaeser and three anonymous referees for their insightful comments and to Ted Miguel, Joshua Angrist, Jack Porter, Bo Honoré, Mark Watson, Jose Scheinkman, and Roland Benabou for helpful discussions. David Walton, Brad Howells, and Andrew Roland provided outstanding research assistance. We also thank Gregg Carter and Bill Collins for the data used to construct an index of riot severity and Albert Saiz and Susan Wachter for data on land use patterns. This research was funded in part by the Center for Labor Economics and the Fisher Center for Real Estate at UC Berkeley, and by the Industrial Relations Section at Princeton University. Social interaction models have been used to explain segregation (Schelling, 1971, 1978; Becker and Murphy, 2000), collective action (Granovetter, 1978), persistent unemployment (Cooper and John, 1988), and crime (Glaeser, Sacerdote and Scheinkman, 1996). The key feature of these models is that preferences depend on other agents choices, potentially leading to multiple equilibria and tipping (Brock and Durlauf, 2001b; Glaeser and Scheinkman, 2003). Researchers have attempted to identify preference spillovers by estimating the effect of peer characteristics on individual decisions (e.g. Case and Katz, 1991; Evans, Oates and Schwab, 1992; Kling, Ludwig and Katz, 2005); and by testing for excess dispersion in choices across social groups (Glaeser, Sacerdote, and Scheinkman, 1996; Graham 2005). To date, however, there is no direct evidence of the tipping behavior predicted by many social interaction models. In this paper we use regression discontinuity methods (Angrist and Lavy, 1999; Hahn, Todd and van de Klaauw, 2001) to test for race-based tipping in neighborhoods. To illustrate our approach, Figure 1 plots mean percentage changes in the white population of Chicago Census tracts from 1970 to 1980 against the minority share in 1970. The figure also shows predictions from a local linear regression model, estimated with a break at a 5% minority share  the level identified by two alternative procedures as the most likely potential tipping point. The graph shows clear evidence of tipping, with white population gains to the left of the tipping point and substantial outflows just to the right. We find similar (though less extreme) patterns for a broad sample of U.S. cities in each of the past three decades. We begin the paper by outlining a simple model of a local housing market in which whites willingness to pay for homes depends on the neighborhood minority share. Under 1 See Manski (1993) for a discussion of the difficulties in testing for interaction effects, and Glaeser and Scheinkman (2003) for a review of many existing studies. 2 We express the change in white population as a fraction of the total tract population in 1970. Minorities are defined as nonwhites and white Hispanics. -2certain assumptions, shifts in the relative demand of whites and minorities will lead to smooth changes in the minority share of the neighborhood as long as the minority share remains below a critical threshold. Beyond this tipping point all the white households will leave. The location of the tipping point is determined in part by the strength of white preferences for minority contact, and is higher when whites are more tolerant of minority neighbors. We then set out to test for tipping behavior using decadal changes in neighborhood racial/ethnic composition. A major obstacle is that the location of the tipping point is unknown. We use two approaches to identify city-specific potential tipping points. First, drawing from the literature on structural breaks, we select the point that yields the best fitting model for tract-level white population changes. Second, building on the pattern in Figure 1, we fit a flexible model for tract-level changes in white population shares in each city, and find the minority share with a predicted change equal to the city-wide average change. The methods yield very similar tipping points for most cities. The estimated tipping points for a given city are also highly correlated across the three decades in our sample. As suggested by the pattern in Figure 1, we find large, significant discontinuities in the white population growth rate at the identified tipping points. These are robust to the inclusion of flexible controls for other neighborhood characteristics, including poverty, unemployment, and housing attributes. Similar tipping patterns are present in larger and smaller cities in all regions of the country, and in both suburban and central city neighborhoods. Neither rents nor housing prices exhibit sharp discontinuities at the tipping point. Nevertheless, tipping has an important effect on the quantity of new housing units, particularly in 3 In an early study, Laurenti (1960) pointed out that there is little theoretical or empirical support for the widespread belief that home values necessarily fall when neighborhoods undergo racial transition.