Endogenous neighborhood selection , the distribution of income , and the identi cation of neighborhood e ¤ ects

This paper develops a simple model where acquired human capital (training), Ht+1, is a CobbDouglas function of parental training, Ht, neighborhood-average parental training, Ht, (neighborhood quality) and unobserved ability, At+1. As in Loury (1981) and Becker and Tomes (1979, 1986) parental utility depends on own consumption and the expected adult consumption of ones child. However, instead of raising the latter directly, through purchased inputs, parents do so indirectly, by choosing to reside in higher quality neighborhoods. The model induces an equilibrium assignment of families to neighborhoods as well as an associated distribution of childrenstraining. The structure of this distribution reects di¤erences in ability, parental training and endogenously chosen neighborhood quality across individuals. A calibration of the model to the Panel Study of Income Dynamics (PSID) sample used by Kremer (1997) suggests that 19.0% of the variance of schooling in United States is attributable to di¤erences in neighborhood quality across individuals. Using the equilibrium joint distribution of child training, parent training and neighborhood quality induced by the model I analyze the properties of a prototypical neighborhood e¤ects regression analysis. Formally, I solve for the coe¢ cients of the (mean squared error minimizing) linear predictor of lnHt+1 on a constant, lnHt and lnHt. Sorting respectively biases the latter two coe¢ cients downwards and upwards relative to their structural values. I also study the e¤ects of neighborhood sorting on the interpretation of measured intergenerational mobility. Finally, I use the model to evaluate alternative approaches to measuring neighborhood e¤ects in the presence of endogenous neighborhood selection. I study kitchen sink approaches (e.g., Ginther, Haveman, and Wolfe, 2000), social experiments (e.g., Rosenbaum, 1991; Kling, Liebman and Katz, 2007) and various cross-cityresearch designs (e.g., Cutler and Glaeser, 1997; Card and Rothstein, 2007). These analyses both formalize existing intuitions and suggests new approaches to the empirical analysis of neighborhood spillovers. JEL Classification: C31, D58, J24, R13 Key Words: Locational Sorting, Neighborhood E¤ects, Income Distribution, Inequality A preliminary version of this paper, circulated under the title On the identi cation of neighborhood e¤ects in the presence of endogenous neighborhood selection, was initially prepared during a short visit to CEMFI in early June of 2008 (to whom I am thankful for hospitality). I would also like to thank David Card, Larry Katz, Yannis Ioannides, Jesse Rothstein and Giulio Zanella for helpful comments on this earlier draft. All the usual disclaimers apply. yDepartment of Economics, University of California Berkeley, 508-1 Evans Hall #3880, Berkeley, CA 94720 and National Bureau of Economic Research. E-mail: bgraham@econ.berkeley.edu. Web: http://www.econ.berkeley.edu/~bgraham/. That ones life outcomes depend on childhood experiences, particularly the inputs of parents and community, at rst glance, seems self-evident. Nevertheless, it has proven surprisingly di¢ cult to characterize the causal connections between adult outcomes and the childhood inuences of parents and, in particular, community. In recent years, in part driven by the availability of rich geo-coded socioeconomic surveys, sociologists, demographers, educational researchers and economists have produced a sizeable empirical literature on neighborhood e¤ects. Reviewers of this literature have been remarkably pessimistic. While a large body of ethnographic and other types of qualitative evidence strongly suggests that community matters, credible quantitative measurement of such inuences has proved elusive (cf., Manski, 1993; Brock and Durlauf, 2001; Mo¢ tt, 2001; Glaeser and Scheinkman, 2001, 2003; Durlauf, 2004). Endogenous sorting of individuals into communities is often posited as source of bias in neighborhood e¤ects analyses. For example, Brookes-Gunn et al (1993) comment that the process by which families select themselves into di¤erent neighborhoods may impart an unknown bias in our empirical estimates (p. 358). More recently, in a comprehensive review of the sociology literature on neighborhood e¤ects, Sampson, Moreno¤ and Gannon-Rowley (2002) identify di¤erential selection of individuals into communitiesas a key methodological challenge (p. 465, cf., Duncan and Raudenbush, 2001). Evans, Oates and Schwab (1992), Durlauf (2004) and Kling, Liebman and Katz (2007) make related points from an economists perspective. The latter authors argue, for example, that the empirical assessment of. [neighborhood] externalities. has.proven di¢ cult.because individuals sort across neighborhoods for reasons that are likely to be correlated with the underlying determinants of their outcomes(p. 84). If individuals are heterogenous in unobserved ways, then sorting may induce a correlation between a neighborhoods observed characteristics and the unobserved attributes of its residents. Neighborhood-level covariates may help to predict adult outcomes to a degree disproportionate to any causal relationship. While, as the above quotations illustrate, this basic point is widely appreciated I am aware few attempts to analytically characterize sorting bias in the context of neighborhood e¤ects analyses.2 A formal, albeit stylized, characterization of sorting biasis one contribution of this paper. In order to characterize the nature of sorting bias I combine elements of Lourys (1977, 1981) and Becker and Tomes(1979, 1986) theory of income distribution with a simple model of locational sorting along the lines of Benabou (1996), Durlauf (1996a), Epple and Platt (1998) and especially Sarychev (2001) and Nesheim (2002) (see also de Bartolome, 1990; Benabou, 1993; Durlauf, 1996b; Epple and Sieg, 1999; Becker and Murphy, 2000; Fernández, 2003). The model, while stylized, is nevertheless rich enough to generate very direct implications for empirical analysis. It particular it allows for an analytical, and intuitive, characterization of sorting bias. In the model individuals are heterogenous in parental human capital or, following Loury (1981), 2 In the context of demand estimation for local public goods Tiebout bias is frequently discussed. The source of this bias arises from assortative locational matching on willingness-to-pay for a public good and the level of its provision. This is, of course, very similar to sorting biasin the neighborhood e¤ects context. Goldstein and Pauly (1981) analyze Tiebout bias (cf., Rubin eld, Shapiro and Roberts, 1987; Reid, 1990).