An economic efficiency analysis of deconcentrating poverty populations

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Abstract

This paper presents a comparative static analysis using a conceptual model of the social benefits and costs associated with alternative spatial distributions of the poor. This analysis demonstrates that the necessary and sufficient conditions for justifying deconcentration of the poor on the grounds of increasing net social benefits are much more stringent than is commonly believed, fundamentally involving particular sorts of non-linear relationships between neighborhood poverty rates and the propensity of neighboring individuals to engage in problem behaviors and to earn less. The paper then conducts a meta-analysis of the limited empirical evidence available. The weight of the evidence implies that net social benefits would be improved if neighborhoods with greater than about 15% poverty rates were replaced with (an appropriately larger number) of neighborhoods having less than 15% poverty rates. However, net social benefits would be smaller if neighborhoods with greater than about 40% poverty rates were replaced with (an appropriately larger number) of neighborhoods having between about 15–40% poverty rates.

Introduction

Researchers and policy makers have long harbored concerns over the location of low-income (poor hereafter) households, expressing fears that the concentration of poverty contributed to a variety of social maladies (Jargowsky, 1997; Wilson, 1987, Wilson, 1996). More recently, the issues related to the spatial distribution of the poor have been framed more positively. Housing subsidy programs, it has been argued, should be structured to give poor households wider residential options. This enrichment of spatial alternatives would not only serve to improve the well-being of housing subsidy recipients in the short run, but also their families’ prospects for economic self-sufficiency in the long run, by enhancing their access to employment and job information networks, better-quality education, and community social norms more supportive of education and employment (Cisneros, 1995; Polikoff, 1994; Rosenbaum, 1995). It is noteworthy that the arguments have almost entirely been framed in terms of reputed benefits gained by poor households that move from high- to lower-poverty neighborhoods, not in terms of the consequences for households residing in the places from which and to which the poor move.

Nevertheless, this set of arguments has been sufficiently persuasive to generate an array of federal legislative and judicial initiatives. These include replacing high-rise public housing complexes with small-scale, scattered-site units, court-ordered dispersal programs for minority populations as a remedy to past discrimination by public housing authorities, and the encouragement of spatial mobility by section 8 housing subsidy recipients through the Moving To Opportunity demonstration and the Regional Opportunity Counseling Program (Burchell et al., 1994; Goering et al., 1995; Hogan, 1996; Ludwig and Stolzberg, 1995; Peterson and Williams, 1996; US Department of HUD, 1996).

This paper analyzes theoretically and empirically whether the current housing policy emphasis on deconcentrating poor populations can be justified on the grounds of economic efficiency, i.e., does society as a whole gain from switching from a more- to a less-concentrated poverty regime, without recourse to claims of distributional equity? It presents a comparative static analysis using a general model of the social benefits and costs associated with alternative spatial distributions of the poor. It then reviews existing evidence to ascertain which functional form and parameters of the model are most appropriate, and draws implications about the efficiency of alternative spatial distributions of the poor. This represents the paper’s main contribution: synthesizing and interpreting evidence in an economics-based theoretical framework that leads to housing policy conclusions of great current relevance.

More particularly, a graphic analysis first is provided to demonstrate heuristically, using a wide variety of potential functional forms, how differences in the curvature of the function relating neighborhood poverty rates to individuals’ propensities to earn income or engage in problematic behaviors generate different conclusions about the efficiency of deconcentrating the poor. Second, it makes the same argument more formally with a mathematical optimization of a particular class of social benefit and cost functions. Third, it conducts a meta-analysis of empirical work related to the non-linear external effects of neighborhood poverty to see what functional form(s) of social cost and benefit relationships seem most likely and, by implication, the degree to which poverty deconcentration is justified on empirical grounds of social efficiency.

The emphasis on social efficiency in this paper should not be taken as an implicit claim that distributional equity concerns are of less importance. On the contrary, distributional concerns are omitted purely for the purpose of isolating efficiency impacts. The paper concludes that, based on empirical evidence related to a very general set of models that makes no claims about distributional equity, tenuous support can be given for the hypothesis that deconcentrating the poor will improve net social benefits, but only if the result is fewer neighborhoods with extremely high poverty and more with a modicum of poverty, not more with moderate poverty rates.

The current paper intersects with three closely related literatures. First, earlier work on peer group effects in educational production functions (Arnott and Rowse, 1987; Henderson et al., 1978) made the point that the curvature of the function relating educational outcomes to ability diversity within the classroom determined the optimal degree of such diversity. I follow a similar strategy in developing the theoretical and empirical argument as the seminal paper by Arnott and Rowse (1987), but apply it to the case of how to optimally distribute poor and non-poor residents across neighborhoods. Unlike them, who take parameters from two empirical studies to illustrate possible variations in optimal distributions with different peer effects, I conduct a meta-analysis in an attempt to ascertain if there is consensus about the functional form and key parameter values of the neighborhood poverty externality effects.

Second, economic models have been developed (e.g., Benabou, 1993, Benabou, 1996; Fernandez and Rogerson, 1996) of how residential segregation of different income groups, coupled with certain local school finance structures, can have efficiency consequences for the society when there are local complementarities among residents/students in human capital development. Unlike this work, however, I: (1) consider a broader range of neighborhood effects than education, (2) make minimal assumptions about the precise nature of social interactions, and (3) attempt to bound key parameters through a meta-analysis of extant empirical studies on neighborhood effects, instead of doing solely a purely theoretical exercise.

Finally, Johnson and colleagues (Johnson, 2002; Johnson and Hurter, 1999, Johnson and Hurter, 2000; Johnson et al., 2002) have worked to develop a scientific management algorithm for administrators of subsidized housing programs that would help guide their decisions of where to place subsidized units. As is the case in this paper, their algorithms seek to maximize social efficiency by the optimal allocation of the poor across space, they assume externality effects from neighborhood poverty, and they try to bound key parameters by scanning empirical literature. The current paper places more emphasis on the sensitivity of the optimal allocation on the nature of the neighborhood poverty externality function and explores the implications of more variants of this function.

Section snippets

A conceptual framework for evaluating the social benefits and costs of deconcentrating the poor: overview

In the following analysis I compare two static hypothetical situations: one where the distribution of poor households across a fixed number of neighborhoods having fixed residential capacities is less spatially concentrated (segregated) than in another distribution. I typically assess whether a situation in which the poor are evenly distributed among the non-poor provides superior efficiency, i.e., net social benefits (NSB), compared to one in which the poor remain predominantly segregated

General model specification: a graphical interpretation

Assume for simplicity that all households are of identical size and demographic structure, and that each reproduces itself identically and in a fixed residential location, such that each stylized household can be examined unambiguously over a multi-generational period. All subsequent social benefits (incomes) and social costs (problematic behavior costs) associated with households will be specified for this arbitrary, multi-generational period, with the appropriate time discounting being

A more particular model specification: a mathematical interpretation

The foregoing conclusions relating the optimal degree of poverty deconcentration to the curvature of the neighborhood poverty externality function can be derived more formally by adding some specificity to the general functional forms , above. For simplicity I assume a quadratic formulation for N:Iin=Gi+βNn+δNn2+γBin,whereweassume:β<0;δ<?>0;γ<0,Bin=Hi+φNn+θNn2+αIin,whereweassume:φ>0;θ<?>0;α<0.As shown in Appendix A, the difference in TSB between a situation where the poor are evenly

A review of empirical evidence on the non-linear relationships between neighborhood poverty rates, incomes and socially problematic behaviors

I do not attempt here a detailed review of the “neighborhood effects” literature, inasmuch as this has been provided by Jencks and Mayer (1990), Mayer and Jencks (1989), Galster and Killen (1995), Briggs (1997), Turner and Gould Ellen (1997), and Leventhal and Brooks-Gunn (2000). Rather, in the spirit of the above analysis I focus on the evidence that has tested for non-linearities in the marginal relationships between N and either I and/or B that would inform the alternative implications

Conclusions, caveats, and implications

In order to assess the social efficiency of alternative spatial distributions of low-income populations, one must identify the mathematical way in which the percentage of poor residents in a neighborhood affects all residents’ incomes and problem behaviors. It is insufficient to claim that “neighborhood effects are important,” or “the poor benefit when they move to lower poverty neighborhoods.” Only if the relationships between neighborhood poverty rate and individuals’ social costs associated

Acknowledgements

The author wishes to thank Alvaro Cortes, Ron Malega, and Anne Zobel for their excellent research assistance and Cheryl Alston for her help in paper production. The helpful comments offered by Ralph Braid, Allen Goodman, Michael Johnson, Ade Kearns, and Ben Scafidi on an earlier draft are acknowledged with gratitude. Special thanks are due Ralph Braid, who made seminal suggestions about the structure of the mathematical appendix. Three anonymous referees offered extremely helpful insights on an

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