Abstract
We develop and estimate a statistical model of neighborhood choice that draws on insights from cognitive science and decision theory as well as qualitative studies of housing search. The model allows for a sequential decision process and the possibility that people consider a small and selective subset of all potential destinations. When combined with data from the Los Angeles Family and Neighborhood Survey, our model reveals that affordability constraints and households’ tendency toward short-distance moves lead blacks and Hispanics to have racially stratified choice sets in which their own group is disproportionately represented. We use an agent-based model to assess how racially stratified choice sets contribute to segregation outcomes. Our results show that cognitive decision strategies can amplify patterns of segregation and inequality.
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Notes
Discrete choice models represent an important advance over earlier strategies for modeling neighborhood mobility. They allow for an explicit representation of the choice process that conditions on the options available, and they permit the analyst to simultaneously represent each choice alternative as a constellation of attributes rather than examining each attribute in isolation (Bruch and Mare 2012; Quillian 2015).
This is consistent with prior studies demonstrating that omission of such a screening process from the model of choice if it actually occurs in observed data leads to significantly biased parameter estimates (Swait 1984; Swait and Ben-Akiva 1986, 1987a; Thill 1992), which in turn lead to misunderstanding of individual decision processes and ultimately to potentially erroneous policy formulation.
Different families of models are specified based on different assumptions about the error distribution. For example, the model most familiar to demographers—the multinomial or conditional logit—assumes that the error terms are independently and identically extreme value (Gumbel) distributed. For a comprehensive introduction to the classic models used in choice modeling, see Ben-Akiva and Lerman (1985), Louviere et al. (2000), and Train (2003).
Typically, social science studies assume the choice set consists of all potential choice alternatives. For example, in their conditional logit models of college application decisions, Hoxby and Avery (2013) assumed that the choice set includes all colleges in the United States. Similarly, in analyses of neighborhood choice, scholars have typically assumed that the choice set includes all neighborhoods within the metro area (e.g., Bayer et al. 2004; Bruch and Mare 2012).
When the number of alternatives is quite large, as is the case with neighborhood choice, analysts may specify the choice set as a random sample of alternatives. However, this is a strategy for consistent (although not efficient) estimation of utility parameters when the number of alternatives is large; it still assumes that the choice set is the universe of all alternatives. This procedure does not reflect any behavioral assumptions about choice set formation.
The conditional choice probability Pn(i | Ck) is defined to be 0 if i ∉ Ck.
Clark and Onaka (Clark and Onaka 1985; Onaka and Clark 1983) provided a forerunner to our work in their model of the joint choice of housing and neighborhood selection. However, they used a nested logit model that did not impose any ordering of the stages of choice or choice set restrictions. This model arises as a modification of the stochastic specification of the original conditional logit model, but it is not a model of behavior (Greene 2002:725).
Our model and earlier CSF models developed by Swait and colleagues (e.g., Swait 1984, Swait and Ben-Akiva 1986, 1987a, 1987b) have the same basic structure as Logan’s (1996, 1998) two-sided logit (TSL), which developed along a parallel track. Both CSF and TSL are designed to capture restrictions on the choice set. In the CSF, we assume that choice set restrictions are imposed by the decision-maker in the deliberation process. In the TSL, supply-side actors, such as firms that decide to hire workers or colleges that decide to admit students, define choice set restrictions.
Our model specifies that choice sets be formed not out of elemental neighborhoods but on larger geographic areas. This assumption is necessary for statistical tractability, but it also has empirical support. A body of work in geography has suggested that people consider units within a bounded area (e.g., Huff 1986). The geographic regions we use in our empirical analysis reflect features of Los Angeles, such as freeways and mountains, that divide the city topographically and socially. These areas represent a sensible compromise between a socially meaningful and statistically tractable number of choice set components.
For example, if we have neighborhoods nested within two geographic regions (Region 1 and Region 2) and two price categories, the set of all possible regional choice sets includes three choice sets: all the neighborhoods in Region 1, all the neighborhoods in Region 2, and all the neighborhoods in both Regions 1 and 2 (the complete choice set). When we cross-classify these with the two price strata, we get K = 6 choice sets in total.
We define the scale factors in Eq. (2) in terms of their component parts associated with geography and affordability: μk = λC · ηg, where λC is the scale factor for a given region combination, and ηg is the scale factor associated with a given stratum of neighborhood median housing costs.
This restriction is also necessary to keep the model statistically tractable; otherwise, we would need to estimate a unique scale factor for every geographic area and affordability group combination, far too many parameters for feasible estimation.
The second condition implies that the only choice set in Γ that has a nonzero probability is the full set of all regions, and it will therefore have unit probability.
Although the conditional logit model assumes independence of irrelevant alternatives (IIA), the CSF model relaxes the IIA assumption through its scale factors (μk) that allow unobservable features of destination alternatives to be correlated within choice sets. In other words, our CSF model allows neighborhoods that are spatially proximate and/or within the same price stratum to be similar based on unmeasured factors.
To construct choice sets for the L.A.FANS respondents, we first categorize neighborhoods based on their median housing price. We calculate housing prices using official records of housing sales, which are not subject to the biases of recollection of survey data, or tenure discounts of long-term residents. Inspection of data reveals sufficient sales per neighborhood to ensure full coverage. We determine the average price of all units sold within a particular neighborhood in 2010 and then divide neighborhoods into affordability groups based on quantiles of housing prices. These define affordability stratum in Wgn; see Eq. (3a) in the online appendix for more details. The average price of housing within each of the four affordability strata is $148,270 (≤25 % quartile), $286,212 (26 % to 50 %), $550,166 (51 % to 75 %), and $1,126,201 (≤76 %).
The coefficient on Size, which is the log of the number of households in the ith neighborhood, is constrained to unity following standard approaches for dealing with aggregated alternatives (Ben-Akiva and Lerman 1985: chapter 9).
Our estimated consideration set drastically reduces the number of options. But with 259 neighborhoods in Los Angeles, it still implies that people consider 38 or 39 of them. From the decision literature, we know that a choice set of this size would outstrip our cognitive capacity. This suggests that although our model is an improvement over the standard choice model, it does not perfectly capture the choice set formation process.
The differences in mobility by race observed in our study are not concordant with findings from the U.S. Census about the mobility rates of Americans as a whole (Mateyka 2015). This may be a result of using the second wave of a panel survey. Respondents who remain in their previous place of residence are easier to find.
As a robustness check, we estimated the model including household tenure at the decision-to-move stage and found that owners are less likely to move, on average, compared with renters. Adding this variable did not change the other substantive results of the model. These results are available from the authors by request.
Empirically, we find that the probability that the respondent’s choice set includes the current housing unit is essentially 1. We fix the dummy variable coefficient on the current housing unit to 10 to stabilize model estimation and avoid this coefficient going to infinity.
The remaining coefficients in the CSF model report the estimated scale factors associated with regions and price strata. Recall that the scale factors capture variation in utility that is not represented systematically by covariates and as such can inflate or deflate the utilities associated with particular neighborhoods in the final stage choice evaluation.
Whites’ reactions to out-group neighbors, especially blacks, are weaker in our L.A.FANS models compared with what earlier studies have found using the Panel Study of Income Dynamics (e.g., Crowder 2000; Quillian 2014). We suspect this stems at least in part from the fact that Los Angeles is multiethnic; earlier work has shown that multiethnic cities in the West and Southwest do not follow the same segregation patterns as cities in the Northeast (Frey and Farley 1996; Lee and Wood 1991). Evidence also suggests that racial residential preferences differ across cities. For example, whites in Los Angeles have less extreme own-group preferences than whites in Detroit (e.g., Farley et al. 1997).
This is consistent with prior work in choice modeling showing that the incorporation of consideration sets that exclude certain options from detailed processing demonstrates superior fit and predictive accuracy (e.g., Horowitz and Louviere 1995; Louviere et al. 2000). Indeed, Hauser and Wernerfelt (1990) attributed in excess of 75 % of their choice model’s fit to choice set formation.
This is not to say that more conventional models—in particular, discrete choice models—should be jettisoned in future modeling of neighborhood choice processes. All models, including the one laid out in this study, are more or less suitable depending on specific research questions and data structure.
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Acknowledgments
This work was supported under NIH K01-HD079554 to the first author and Australian Research Council Discovery Project DP140103966 to the second author. We also gratefully acknowledge use of the services and facilities of the Population Studies Center at the University of Michigan, funded by NICHD Center Grant P2CHD041028. This article benefitted from three anonymous reviewers as well as helpful feedback from Alexandra Murphy, John Allen Logan, and Jeffrey Morenoff.
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Bruch, E., Swait, J. Choice Set Formation in Residential Mobility and Its Implications for Segregation Dynamics. Demography 56, 1665–1692 (2019). https://doi.org/10.1007/s13524-019-00810-5
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DOI: https://doi.org/10.1007/s13524-019-00810-5