Preferences and pathways to segregation: Reply to Van De Rijt, Siegel, and Macy

We are pleased that Van de Rijt, Siegel, and Macy have taken an interest in our work. Since the publication of our article (Bruch and Mare 2006) we too have examined the role of random error in segregation dynamics and formally examined the relationship between residential preferences and segregation (Mare 2007; Tuljapurkar, Bruch, and Mare 2008). We welcome the opportunity to discuss these issues, compare our conclusions to those of Van de Rijt et al., and extend our 2006 argument regarding the preferences of individuals and the dynamics of residential segregation. We also acknowledge and present corrections of errors in our 2006 article. In preparing our software for public release, we found an error in our computer code. Our corrected results show that, as Van de Rijt et al. point out, some continuous functions for individuals’ decisions about whether and where to move that we originally claimed would generate integration in fact lead to segregation. Our original findings regarding continuous functions with varying β parameters (Bruch and Mare 2006, p. 692) were wrong. This reply to Van de Rijt et al. includes corrected versions of our simulations. However, the error in our code notwithstanding, we believe that our original conclusions regarding the effects of the form of individual preferences on segregation dynamics are correct. Our corrected software—including an executable file, the open-source Java code, and a suite of testing software for verifying key features of agent-based models—is publicly available.2 Our software can be extended to look at various dynamic processes (e.g., marriage markets, peer effects, and the spread of innovation), and we encourage interested researchers to build upon our source code. Our 2006 article reported an investigation of the links between how people evaluate neighborhoods and aggregate segregation dynamics. We emphasized that the shape of residential choice functions (i.e., how individuals evaluate and choose neighborhoods) has important implications for segregation dynamics. Simulations based on our corrected code show that, as Van de Rijt et al. report, hypothetical monotonic, continuous functions with a sufficiently strong response to the racial makeup of a neighborhood (the coefficient β in the functions that describe residential choice) can generate segregation and that empirical preference functions based on Detroit Area Study (DAS) data are consistent with high segregation. However, our argument that “regions of indifference” across neighborhoods with varying ethnic composition (a key feature of threshold functions) play an important role in segregation dynamics still holds. Moreover, as we show below, the shape of residential preference functions affects segregation dynamics through other pathways as well. Our reply first summarizes our ideas about preference functions and the effect of random variation on segregation dynamics and then responds more directly to Van de Rijt et al.’s comment. We review the ways that randomness enters into choice processes and argue that the shape of residential choice functions—for example, whether preferences follow a continuous or a threshold function—affects segregation dynamics through three pathways: the baseline level of randomness in the choice process, how random error fades out or cumulates over time, and the speed with which integrated communities converge to an equilibrium level of segregation. Our corrected agent-based models produce the same patterns as the ones shown by Van de Rijt et al., and we agree with them that continuous functions with a sufficiently high β can produce segregation. However, we believe that their claim that “sensitivity to chance” matters more than “sensitivity to change” is misleading because these are not separable dimensions of the choice function. Rather, these factors interact in a complex yet interpretable way. We also show that, contrary to Van de Rijt et al.’s claims, continuous functions with a sufficiently low randomness do not result in higher levels of segregation than threshold functions, although continuous functions do reach equilibrium more rapidly. We also explain an important feature of Van de Rijt’s figures C1 and C2, namely that, above a certain β value, the threshold functions appear less responsive than continuous functions to increases in β. We then address the issue, raised by Van de Rijt et al., of how preferences for racial integration affect segregation. We find their argument regarding “the paradox of strong versus weak preferences” unpersuasive. Van de Rijt et al. argue that stronger preferences for integration result in higher segregation when residential choice follows a continuous rather than a threshold function, but we show that this conclusion is an artifact of their highly stylized specification of these functions. Van de Rijt et al.’s “paradox” occurs only under a narrow set of assumptions. We show that preferences for integration expressed by black respondents in the DAS are consistent with very low segregation and offer a more plausible statement about the link between preferences for integration and segregation dynamics.