Empirically Testing a Computational Model: The Example of Housing Segregation

Thomas Schelling's famous model of housing segregation started with a few coins on an eight by eight grid and some very simple assumptions about individual preferences. Using the SWARM programming environment, we have extended Schelling's concept to examine the contemporary debate about the nature and causes of housing segregation. We begin with basic preferences functions derived from empirical data on neighborhood racial composition and add a variety of putative factors in housing decisions. The result is a computational model of racial housing segregation that provides insight into empirical patterns of segregation and desegregation in the late twentieth century. INTRODUCTION Thirty years ago, the economist Thomas Schelling advanced a theory to explain the persistence of racial segregation in an environment of growing racial tolerance (Schelling, 1971, 1978). Schelling posited a simple model that made a straightforward point: if the racial makeup of one's neighbors is a decisive factor in choosing housing, then the collective interaction of individual preferences will tend to produce segregation, even if many individuals tolerate or even prefer integration. Schelling's use of "micromotives" to explain "macro" phenomena has become a familiar concept, but for many years it did not advance very far as a practical tool for studying segregation. Mathematically, it is much easier to analyze the aggregate behavior of individuals in market models, in which everyone is engaged in the same transaction, than in Schelling's "tipping" model, in which individuals react to their local environment rather than an aggregated market. But the spread and increased accessibility of computational modeling makes it possible to experiment with much more complex models, incorporating both neighborhood-based racial preferences and market-based housing choices into a more complete representation of urban forces. In this paper, we describe our development of a computational model of housing segregation over the past year. We particularly focus here on a problem that has often bedeviled model-builders: how to "test" models with empirical data. We believe our experiments show some progress towards the goal of rigorously testing alternate theories of segregation. The Paradox of Modern Housing Segregation Housing segregation -particularly of African Americans -continues to be a dominant feature of most American cities, and it has been linked to a wide range of urban ills (Massey and Denton, 1994). Scholars in the field generally agree that income differences between blacks and whites only explain a small fraction of current segregation levels (Muth, 1986; Clark, 1986); but beyond this, there is no consensus and little in the way of convincing evidence to demonstrate why housing segregation has remained so high. As an historical matter, it is obvious and widely agreed that black housing segregation came about through organized, mostly private efforts to ghettoize blacks in the early twentieth century -particularly the years between the world wars (Sander, 1988). One can chart the rise of segregation through the index of dissimilarity, which measures the proportion of one group (e.g., blacks) who would have to move to different neighborhoods to achieve the same metropolitan distribution as a second group (e.g., whites). Where an index of 1.00 equals complete apartheid, black/white segregation rose in American cities from an average of .6 in 1910 to .90 in 1940. Intense levels of housing discrimination persisted throughout metropolitan America during the 1940s and 1950s, and it is thus unsurprising that segregation remained extremely high into the 1960s. But in the late 1960s, things changed rather dramatically. The civil rights movement brought a striking change in the answers whites gave to survey questions about integration; many more whites expressed marked levels of tolerance. The same movement brought the Civil Rights Act of 1968, which outlawed a wide range of discriminatory conduct in housing markets. Moreover, some real changes in American cities followed in the 1970s. Measured levels of housing discrimination fell sharply by 1977 (Wienk et al, 1979). Black migration to previously-white housing accelerated (Sander, 1998). Although inner-city poverty remained acute, the black middle-class grew and in many ways flourished. Given these changes, many observers predicted rapid declines in housing segregation. Generally, however, the declines were almost imperceptible. The average black/white index of dissimilarity across a range of cities fell from .88 to .81. Most of the decline was concentrated in a fraction of cities; in many of the nation's largest cities, the black/white index had fallen only a couple of points by 1990 (Sander, 1998). This, then, is the central paradox of segregation: why have levels of black/white separation changed so little when so many related factors changed a lot? Related to the paradox are a number of smaller but important puzzles: why has housing in predominantly black areas "flipped," from being more expensive than white housing prior to 1970 to being less expensive afterwards? Why are Latinos, who experience levels of discrimination similar to those experienced by blacks, and who have about the same incomes as blacks, much less segregated from whites? And why have a few areas (e.g., Santa Clara County in California or Seattle, Washington) experienced sharp declines in segregation? Scholars of segregation have not been able to provide robust theories that account for these related puzzles. While an extended discussion of the literature is beyond the scope of this paper, we believe that there are two central problems: a paucity of attempts to rigorously specify testable hypotheses derived from alternative theories of segregation; and the difficulties noted earlier in operationalizing Schelling's insights. We turned to computational modeling as a way of overcoming both problems. Building a Computational Model of Segregation Although Schelling described his segregation model as a "thought experiment" and focused on simple numerical examples, it lends itself so readily to computational modeling that its has been a standard computational demonstration for many years. In these models, agents are arrayed on an open grid, with each interior agent surrounded by eight squares. Each agent is either black or white, and they are either "happy" or "unhappy", depending on whether no more than some critical threshold of their neighbors are persons of the other race. Some random squares are vacant, and in a series of rounds, each agent who is unhappy moves to a vacant square. The surprising report, as we noted earlier, is that for a wide range of preference levels, integrated neighborhoods will "tip" towards one group or another, leading the outnumbered group to flee and thus producing segregation. We wanted to bring this simple model closer to the real world in two ways. First, rather than have agents be either "happy" or "unhappy", we wanted them to evaluate and compare a wide range of possible states. Second, we wanted racial preferences to be only one of many factors agents used to compare neighborhoods. We achieved both goals by creating a multivariate utility model through which agents are periodically asked to compare a range of neighborhoods, evaluate the overall utility they would achieve at each location (considering several variables), and decide if they would like to move. Since we sought to explore the evolution of segregation after the civil rights revolution, we modeled our schematic city on a prototypical large American metropolis in 1970. The city is biracial (with "reds" and "blues" standing in for "whites" and "blacks"), and the minority group is systematically clustered near the center of the city (that is, the initial index of dissimilarity is 1.00). In the models described in this paper, the population of the city is 2,375 (a number that seems to us, so far, large enough to capture the key 1 The federal Fair Housing Act went fully into effect on January 1, 1970 and decennial census conducted in April 1970 thus captures nicely the state of segregation as society embarked on its experiment in housing desegregation. Please note that though we use the term "city" to describe our model, we envision it as a representation of a metropolitan area, in which the movement choices of agents are limited to the region of the model. dynamics of the simulation). In each period, a randomly selected tenth of the population is given the option of moving to one of five alternative locations (which are randomly selected from the entire city) or remaining at the agent's current location. The agent compares the sites using five different criteria: housing cost, distance of the new site from the present location, local discrimination, the racial makeup of the immediate neighborhood (the eight adjacent agents using Moore's definition), and the racial makeup of the surrounding community. Each factor is closely related to a competing theory of housing segregation. We operationalized each variable as follows: Housing cost: Five percent of the city's cells are vacant at any time, and the 2500 cells in the city at large are divided into 25 communities (demographically analogous to census tracts) each containing 100 cells. Popular communities have fewer vacant cells than unpopular ones. The housing price then becomes a simple inverse function of the vacancy rate. In actual runs of the model, neighborhood vacancies range from zero to over 20%. Distance from existing home: We calculate the distance of each of the five sites to which an agent might move from the agent's present location, using the Pythagorean theorem. We assume that, other things being equal, utility monotonically declines with the distance an agent moves, because we also (simplistically) assume that an agent's relatives, job, friends and church are close to its current location. Discrimination: In our model, some of the majority-group (red) agents discriminate against minority-group (blue) agents. We capture this by allowing a specified proportion of red agents to impose a utility cost on adjacent squares if they are occupied by blues. Racial composition of neighbors: Survey data show substantial variation in what blacks say is their "ideal" neighborhood racial mix; the same is true of whites. We therefore created six different utility functions (three for each race) in which each possible neighborhood racial makeup is characterized by a unique utility for the agents. In evaluating moves, the agent calculates the racial makeup of its Moore neighborhood and considers the associated utility. Racial composition of community: In much the same fashion, agents evaluate the overall racial makeup of their current and alternative communities. Again, we define the community in tracts of 100 agents. Agents use the same utility functions they apply to their Moore neighbors, but to larger groups of neighboring agents. With these combined factors, we generate an overall utility function like this: n io iscriminat d w w ng totalhousi occupancy w pref tract w pref neigh w Utility i i * * ) ( * _ * _ * 5 4 3 2 1 + + + + = distance