Economic and Statistical Models for Affordable Housing Policy Design

Prescriptive planning models for affordable and subsidized housing policy design that have a local focus and which are intended to reflect aspects of current and/or best practices require detailed estimates of various structural parameters. These estimates should ideally reflect observations of actual housing units, households and development projects. We examine here three classes of structural parameters: dollar-valued benefits and costs of affordable/subsidized housing provision, correlates of measures of housing market strength, and locational outcomes of households participating in housing mobility programs. Current results for dollar-valued housing impacts—provision costs, household benefits and subsidy levels—are based on detailed administrative data from a local housing provider and generate promising forecasting models for use in regional-level planning models. Results for the remaining two classes of structural parameters are currently under development. I. Benefits and Costs of Affordable Housing Development Introduction The goal of the decision models for affordable housing development that I use in my research is to identify policy directions for affordable housing providers who need to decide how many units of various types of housing to develop, and the locations at which the housing should be sited. These decision models typically take the form of integer math programs in which the decision variables represent whether a development of a certain type should be located at a given site, and the number of housing units in that development to be located. These models are generally multiobjective in nature: one goal is to choose configurations of affordable housing across a study area to maximize economic efficiency, e.g. net social benefit, while another goal is to choose configurations of affordable housing to maximize a measure of equity or fairness, e.g. minimize the variance in the number of housing units allocated to target neighborhoods across the study area. Central to these decision models is the notion that there is spatial variation in the various outcome measures (net social benefit, equity) under consideration. However, developing realistic datasets for these decision models is challenging: there are no standard sources of data for social impacts of affordable housing. Therefore, I compute dollar-valued social impact measures using the framework of cost-benefit analysis and analytical methods of microeconomics. This research note is intended to describe a number of recent analyses to estimate and analyze the dollar-valued impacts of affordable ownerand renter-occupied housing developed by a Economic Analysis for Flexible Models 1 4/26/2007 FlexibleModelsAnalysis09.doc Pittsburgh-area non-profit organization. The service area for this provider is shown in Figure 1, below. [Figure 1: Affordable Housing Provider Service Area] The provider’s service region is comprised of the colored Census tracts to the south and west of the city of Pittsburgh. Analysis of housing market and demographic characteristics of this service area (Table 1) reveal that it is generally less affluent, has lower quality of housing and has higher levels of distress than the Pittsburgh metropolitan statistical area overall. [Table 1: Affordable Housing Provider and Pittsburgh MSA Population and Housing Characteristics] Cost-Benefit Analysis Framework for Affordable Housing Social impacts of subsidized housing are numerous and can be classified (Johnson, Ladd and Ludwig 2002) according to two broad categories: program participants and non-participants, as in Table 1. [Table 2: Social Impacts of Affordable/Subsidized Housing] Impacts on program participants can be divided into those whose origin lies, in part, in neighborhood and social characteristics, such as criminal offending, and those whose origin lies primarily in the quality and quantity of housing consumed, e.g. consumer surplus. Impacts on program non-participants can be classified according to a number of constituent groups, e.g. residents of communities in which subsidized housing is located and taxpayers. In principle, these social impacts could be measured using well-known evaluation methods and monetized using economic analyses of markets in which impacts, or complements to or substitutes for them are traded. Alternatively, when markets don’t exist, or suffer significant imperfections, or when relevant economic data are hard to measure, one can use shadow prices to estimate social impacts. Although the research literature on subsidized housing programs such as Moving to Opportunity (U.S. Department of Housing and Urban Development 2003) and HOPE VI (Popkin et al. 2004) is well-developed, no comprehensive cost-benefit analysis of such programs is known to this author. In addition, collecting the large volume of outcomes data associated with the affordable housing programs that are the subject of this paper is a logistically daunting task. Therefore, we concentrate efforts for social impacts measurement of affordable housing on two measures that may be computed using participantand unit-level data: consumer surplus associated with consuming more housing under the program than in the private market, and subsidy levels associated with housing provision. This strategy is similar to that pursued by Johnson and Hurter (1999) when examining the social impacts of a hypothetical housing Economic Analysis for Flexible Models 2 4/26/2007 FlexibleModelsAnalysis09.doc mobility program in the Chicago area. However, in contrast to that work, the present study addresses construction and/or rehabilitation of housing, as compared to allocation of families across a study area using housing vouchers. Therefore, the category of housing subsidies includes both operating subsidies and the fixed costs of housing provision. Construction Costs In the theory of the firm (Henderson and Quandt 1980), a company that produces a single product from two inputs according to the production function q = f(x1, x2) faces costs that are a function of output level q, input prices r1 and r2 and the level of fixed costs, b, as: C = φ(q, r1, r2) + b (1) Cost functions can be shown to be nondecreasing, homogeneous of degree 1 and concave as a function of input prices. If input prices are constant, then the cost function can be stated more simply as C = φ(q) + b (2) Cost functions can take on a variety of forms; they are commonly shown as cubic, demonstrating increasing economies of scale up to an inflection point, and decreasing economies of scale afterwards (Figure 1). [Figure 1: Cost Function] If a production function is assumed to take the form of a Cobb-Douglas function, i.e. q = Ax1x2 (3) then it can be shown that the resulting total cost function is linear if α + β = 1, convex if α + β < 1 and concave if α + β > 1. The affordable housing planning model of Johnson (2007) assumes that cost functions for affordable housing are linear over all output levels. Such assumptions are not unreasonable: current literature on housing production functions assumes constant returns to scale (see e.g. Epple, Gordon and Sieg 2006), which can result in a linear cost function. However, as argued in Johnson (2006), it is possible that production functions for housing development projects might enjoy increasing returns to scale, i.e. output quantities that increase at an increasing rate as a function of inputs such as building materials and labor as compared to smaller projects. This could result in a cost function that shows economies of scale over some levels of output. It may also be the case that for projects larger than a certain level, the cost function might display diseconomies of scale due to difficulties of coordinating various construction tasks. The present analysis supposes that the cost function for affordable housing development shows economies of scale, i.e. that the total cost function is strictly concave. To test this hypothesis, we collected data on construction costs of projects developed or under development by a Pittsburgharea affordable housing provider. These data, in paper form as well as spreadsheets, often Economic Analysis for Flexible Models 3 4/26/2007 FlexibleModelsAnalysis09.doc recorded only estimates of future production costs. In 18 cases, though, we were able to record actual construction expenditures of the affordable housing provider for construction of new owner-occupied housing as well as multi-family rental housing. Construction costs are typically classified in two broad categories: “hard costs”, e.g. materials and on-site labor, and “soft costs”, e.g. architectural drawings, appraisals and various fees. We report results only for total construction costs, as data in component categories were often incomplete and incompatible across projects. Table 3 contains descriptive statistics for construction costs. Note that total construction costs varied widely, from a minimum of $47,000 for a five-unit multi-family rental rehabilitation project, to a maximum of $1,185,765 for an eight-unit owner-occupied new construction project. Thirteen of the eighteen projects studied were new construction for owner-occupied units. [Table 3: Descriptive Statistics, Affordable Housing Construction Data] We tested the possibility that construction costs differ significantly according to the number of units in the project using a set of t-tests. We found (Table 4) that the breakpoint for project size with the greatest statistical significance was that for 5 units or less, versus 6 units or more. [Table 4: T-Test for Affordable Housing Construction Data: 5 Units and Less vs. 6 and Greater] In addition, we regressed total construction costs on the number of units in a project, the number of units squared and a dummy variable indicating whether a project was new construction or not (Table 5). Since the coefficient of the number of units squared is negative for our sample, we can show that marginal costs are less than average costs. This is additional evidence for economies of scale enjoyed by this affordable housing provider. [Table 5: Economies of Scale: Affordable Housing Construction Data (Dependent Variable: Construction)] In order to use these results in a math programming model for affordable housing provision, it is necessary to forecast construction costs in all neighborhoods across a defined service area, including those neighborhoods in which the affordable housing provider has not yet built housing. Thus, we developed a forecasting model using ordinary least squares in which the log of observed construction costs is regressed upon projectand neighborhood-level variables. Characteristics of these variables are shown in Table 6. [Table 6: Construction Costs Forecasting Model Variables] To ensure that the estimated coefficients of explanatory variables could be interpreted in a straightforward way, we divided some neighborhood-level independent variables by average values for the Pittsburgh MSA. Regression results using ordinary least squares (Table 7) indicate that signs and magnitudes of many of the estimated coefficients correspond with intuition. For example, construction costs for this housing provider increase for projects that are newconstruction and those that have more then 5 units. Construction costs also increase in neighborhoods with stronger housing markets and larger housing units. However, construction Economic Analysis for Flexible Models 4 4/26/2007 FlexibleModelsAnalysis09.doc costs are higher in neighborhoods that are more distant from the central business district, perhaps due to scarcity in construction firms. They are also higher in neighborhoods with larger concentrations of rental housing units and older housing. If larger concentrations of older, renteroccupied housing units are associated with neighborhood disadvantage (not unreasonable, given the economically-depressed nature of the affordable housing provider’s study area), then costs that increase in rental housing concentrations may illustrate the expenses associated with demolishing dilapidated housing and replacing it with new housing. [Table 7: Regression Results: Construction Costs Forecasting Model] These results can be used in a prescriptive planning model by developing estimates of projectlevel construction costs for two types of housing: New Construction (New = 1) or Rehab-forResale (New = 0), of two size categories: Small, i.e. 5 units or less (GreaterThan5 = 0) and Large, i.e. 6 units or more (GreaterThan5 = 1) located in Census tracts throughout the affordable housing provider’s service area. These estimates are summarized in Table 8 below. [Table 8: Forecasting Results: Construction Costs] The significant increase in mean construction cost estimates as compared to the administrative data reported in Table 1 is due to the greater economic diversity in 80 Census tracts that comprise the affordable housing provider’s study area, as compared to the 10 relatively distressed 10 Census tracts in which the 18 projects that yielded observations of construction costs are actually located. Note the high computed values of standard deviation for the construction cost measures, an indication of spatial variation in estimated construction costs that may contribute to a decision model for facility location yielding results with policy insights. Social Impacts: Consumer Surplus and Operating Subsidy As discussed in the first section, we are limited in our examination of short-term impacts of affordable housing to consider only benefits associated with increases in housing consumption (consumer surplus) and costs associated with ongoing subsidies associated with each unit. To compute these measures, we extend the methodology of Johnson and Hurter (1999), who applied standard housing economics models of e.g. Olsen and Barton (1983) to address consumer surplus and subsidy measurement for a hypothetical housing mobility program. Rental housing for which monthly rents are subsidized via payments from a public housing authority to the landlord results in an increase in housing consumption by families who participate in the housing voucher program. A stylized, conventional representation of the consumption tradeoffs faced by typical participant families before and after receiving subsidized housing is shown in Figure 3. [Figure 3: Consumption of Housing via a Housing Voucher] Economic Analysis for Flexible Models 5 4/26/2007 FlexibleModelsAnalysis09.doc A participant family with income Y0 initially consumes a bundle of housing and non-housing goods (H0, X0) at prices (ph, px) (px is usually set to 1 for simplicity). This yields satisfaction associated with indifference curve I0 just tangent to the family’s income constraint at point a before entering the housing voucher program. Upon entering the program, the family’s consumption of subsidized housing changes to (H’s, X’s), yielding satisfaction associated with indifference curve Is (point d) with H’s > H0 and X’s > X0. Housing consumption in this program is assumed to be limited to at most Hmax. The effect of the housing subsidy is to decrease the effective cost of housing by α%, rotating the income constraint counterclockwise. Now, the income that would be necessary to purchase the bundle (H’s, X’s) on the private market is given by the income line joining (Ym/px and Ym/ph). That is, the subsidy associated with this below-market rate housing is (Ym/px – Y0/px). However, this line is not tangent to point d, indicating a non-optimal consumption bundle. Point e, on the same indifference curve as point d, represents a different consumption bundle (H, X) yielding the same satisfaction as the bundle at point d, that could be purchased with income Ys/px. The difference (Ys/px Y0/px) is the additional income necessary to make the family as satisfied consuming housing on the private market as they would be consuming the housing they do under the voucher program at their current income. This difference is called equivalent variation (EV). In this analysis, the demand schedule is a Hicksian demand schedule: it holds utility constant, rather than holding purchasing power constant, as is the case with the conventional Marshallian demand schedule. However, Hicksian demand schedules cannot usually be estimated directly using market data. If one were to estimate a demand schedule for housing as shown in Figure 3 using a Marshallian demand schedule, equivalent variation and consumer surplus will differ. If there is a significant income effect from changes in consumption of the non-numeraire good (housing in this case), and a Marshallian demand schedule is used, then EV can be shown to be a good approximation to Marshallian consumer surplus (Boardman et al. 2006, p. 69). Thus, we wish to compute an approximation to consumer surplus, (Ys/px Y0/px) and subsidy, (Ym/px – Y0/px), based on administrative data. Johnson and Hurter (1999) do so by proposing that families choose consumption bundles by optimizing a Stone-Geary utility function subject to an income constraint. This problem can be expressed as: max U = (H θh)βh(X θx)βx (4) s.t. Y0 = phH + pxX (5) where parameters θh and θx represent “subsistence levels” of consumption for goods H and X, parameters βh and βx measure the family's propensity to consume housing and nonhousing above their respective subsistence levels and βh +βx = 1. The first-order necessary conditions for this optimization problem can be manipulated to yield closed-form expressions for consumer surplus (B) and subsidy (B), as follows: Bf = ⎣ ⎢ ⎡ ⎦ ⎥ ⎤ Rm phθh β β ⎣ ⎢ ⎡ ⎦ ⎥ ⎤ Y0 Rs θx 1-β 1−β + phθh + θx Y0 (6) Bs = Rm Rs (7) Economic Analysis for Flexible Models 6 4/26/2007 FlexibleModelsAnalysis09.doc where β ≡ βh and 1 – β = βx from the Stone-Geary utility function, R is the market rent of the subsidized housing unit currently occupied by the family, R is the family’s monthly housing contribution and all other parameters are as defined above. In the current study, the affordable housing provider builds ownerand renter-occupied housing, and manages the renter-occupied housing. The subsidies used by the affordable housing provider are project-based, meaning that they are associated with the housing unit, rather than beingtenant-based, as is the case with housing vouchers. This complicates our analysis in two ways: it is not clear that the analysis culminating in equations (6) and (7) can be extended to owner-occupied housing, and it not clear what the market rents (for renter-occupied housing) or mortgages (for owner-occupied) housing ought to be. Current analyses of housing investments by individuals stress its multi-period nature: in each period, individuals may choose the level of commodity consumption, financial investments and level of housing consumption to maximize discounted utility (Bajari, Benkard and Krainer 2004). This analysis assumes that housing is an investment good as well as a consumption good. The resulting consumer utility maximization problem is difficult to solve, and the data requirements are substantial. Based on discussions with housing managers at the affordable housing provider that has supplied data for this study, it is likely that participants in heavily-subsidized owner-occupied housing programs as are managed by community development corporations have such limited incomes and housing opportunities that the decision problem they face—once they have decided to purchase housing rather than rent—is very similar to that faced by similarly situated low-income families who relocate to subsidized renter-occupied housing. A fuller discussion of these assumptions is contained in (Kim 2006). Between November 2003 and May 2006, we collected data on approximately 219 housing units managed by a Pittsburgh-area affordable housing provider. For renter-occupied housing, these data included number of bedrooms and monthly rent. For owner-occupied housing, these data included amount of the first and second (deferred) mortgage and the selling price. For all program participants, we had data on race and gender of the head of household and the number of persons in the household. In addition, we received detailed data on 110 participant families for the purposes of calibrating a utility function, including household income, amount spent on rent and utilities, race and gender of all household members. We computed the subsidies associated with each housing unit as follows. For new construction owner-occupied housing, we used data from the “sources and uses” financial statement to infer the total provision cost of each unit, which we then defined as the market value of each unit. For rehabilitated owner-occupied housing, we used a rule of thumb, also verified by the affordable housing provider, that the market value of each unit is equal to the sum of the first and (usually deferred) second mortgages. In both cases, we computed a standard mortgage payment, accounting for first-time homeowner programs that drastically reduced the down-payment requirements as compared to market-rate borrowers, using 7.5% for the interest rate, 30 years for the term and administrative data from the affordable housing provider as to the actual amount of the mortgage. The difference between the imputed market value for each owner-occupied unit, converted into a monthly payment also using 7.5% for the interest rate, a 30-year term and a 5% down payment, and the estimated actual monthly mortgage payments made by affordable housing program participants, constituted the monthly subsidy value. Economic Analysis for Flexible Models 7 4/26/2007 FlexibleModelsAnalysis09.doc For renter-occupied units, we reasoned as follows. The market value for each affordable housing unit is the rent that would be charged if the developer did not use below-market interest rate loans or grants as did the affordable housing provider and wished to enjoy a moderate financial return on his or her investment—say 10%. Using administrative data on provision costs for the renter-occupied multi-family buildings developed by the affordable housing provider, we computed the rents on each unit that would be sufficient for net income to meet mortgage payment obligations and supply profit to the developer. The difference between these ‘market’ rents and the rents actually charged to program participant families is the per-unit monthly subsidy associated with each renter-occupied housing unit. We now describe the computational results. Table 9 defines the variables used to compute the equivalent variation estimate of consumer surplus according to equation (6); Table 10 provides descriptive statistics for these variables, classified by housing type. [Table 9: Variable Definitions: Affordable Housing Households] [Table 10: Descriptive Statistics: Affordable Housing Households] Johnson and Hurter (1999) show that one of the first-order necessary conditions to the utility maximization problem solved by families moving from market-rate housing to subsidized housing can be rearranged to resemble a demand function for housing. By estimating the parameters of this demand function using statistical regression and administrative data, it is possible to recover the parameters of the Stone-Geary utility function used on the consumer utility maximization problem and thus compute values for consumer surplus as in equation (3). This demand function can be expressed in two ways: as a regression of observed housing payment upon monthly income, per Mayo (1981): R = (θh (1 β)ph β θx ) + βY0 + ε (8) or as a regression of the ratio of housing expenditure to income upon the inverse of monthly income, per Olsen and Barton (1983): 0 Y R = β0 + γ 0 1 Y + z. (9) Characteristics of affordable housing families within and across housing type categories (new construction, rehab for resale, multi-family rental) influence the modeler’s decision of categories of observations for which equations (8) or (9) should be estimated. T-tests for housing expenditure showed significant differences among the three tenure types for housing expenditures but not for household demographic characteristics within tenure types. Therefore, we retain our conventional housing type categories, and reject the possibility that subgroups of affordable housing clients within those housing type categories have distinct utility function parameters. Computational results for the estimated demand function across three housing tenure types indicated greater statistical robustness for the transformed demand function (9) than for the direct demand function (8). The details of the regression results for (9), reported separately for new Economic Analysis for Flexible Models 8 4/26/2007 FlexibleModelsAnalysis09.doc construction and rehab for resale owner-occupied housing, as well as multi-family rental housing, are reported in Table (11). A small sample size and lack of variation in the variables required us to use robust weighted least squares, which does not result in a conventional R performance measure. [Table 11: Robust WLS Regression Results: Affordable Housing Households; Dependent Variable = HousingPayment/IncomeMonth] To compute point estimates for consumer surplus, we follow the convention of Olsen and Barton (1983) as applied in Johnson and Hurter (1999): the sample minimum housing expenditure is used to estimate the subsistence level of housing θh, and the subsistence level of nonhousing θx is computed from θx = ((1 – α)θh – γ)/α, where α and γ are estimated coefficients from regression equation (9). Results for the estimated utility function parameters are contained in Table (12): [Table 12: Estimates of Stone-Geary Utility Function Parameters: Affordable Housing Households; Olsen and Barton (1983) Interpretation] These findings are in line with both Johnson and Hurter (1999) and Olsen and Barton (1983): the previous studies found values for β between 0.03 and 0.08 and 0.02 and 0.15, respectively. They also both found large negative estimates for θx (approximately -4,000 for Johnson and Hurter (1999) and between -1,700 and -63,992 (yearly data) for Olsen and Barton (1983)). These estimates are interpreted by both sets of authors as evidence that families borrow against future earnings for non-housing consumption. Next, we use equations (6) and (7) to compute consumer surplus and subsidy values for the three different housing tenure types in our sample. The results are contained in Table (13), below: [Table 13: Point Estimates of Consumer Surplus and Subsidy] These results are consistent with those of Johnson and Hurter (1999) and Olsen and Barton (1983) in that average subsidy values are significantly greater than average consumer surplus values, as predicted by the theory illustrated in Figure (2). As DeSalvo (1971) noted, the implication of the theory of consumer utility maximization for subsidized housing requires positive social impact measures, such as a neighborhood upgrading effect, in order that social benefits of a subsidized housing program exceed its costs. However, in this study we make no effort to identify such ancillary benefits. In order to use these point estimates of consumer surplus and operating subsidy in a planning optimization model, we must, as for construction costs in the previous section, construct a forecasting model that regresses estimates of consumer surplus and subsidy upon participant household, housing unit and neighborhood characteristics. T-tests for point estimates of consumer surplus showed no difference between New Construction and Rehab-for-Resale Economic Analysis for Flexible Models 9 4/26/2007 FlexibleModelsAnalysis09.doc housing observations. T-tests for point estimates of subsidy showed differences at 1% level between New Construction and Rehab-for-Resale housing. Table (14) contains definitions and descriptive statistics for the explanatory variables we use in consumer surplus and subsidy forecasting models. These variables are chosen to reflect theory on impacts of neighborhoods, housing units and housing tenure types upon consumer surplus and subsidy levels. [Table 14: Explanatory Variables: Housing Impact Measures Forecasting Model Table (15) contains regression results. We perform a single regression for consumer surplus and for subsidy by including dummy variables for the different housing types. In the consumer surplus regression, statistically significant measures of most measures of neighborhood disadvantage negatively affect measures of consumer surplus. However, the estimated coefficient of the square of the percentage of persons below poverty, which is statistically significant, is positive, contrary to our expectations. Note that the estimated coefficient for the Type=2 variable, distinguishing Rehab-for-Resale from other housing tenure types, is significant at the 5 percent level, in contrast to T-test results reported above. In the subsidy regression, statistically significant measures of neighborhood disadvantage and housing market distress negatively affect measures of subsidy. The estimated coefficient for the Type=2 variable is significant at the 1 percent level, consistent with T-test results reported above. [Table 15: OLS Regressions: Housing Impact Measures Forecasting Model] We note that the data for Multi-Family Rental housing lack sufficient variation according to various explanatory variables; all observations come from just three Census tracts. Thus, forecasts of consumer surplus and subsidy for rental housing should be used with extreme caution. Applying results from the forecasting regressions in Table (15) to explanatory variables in Table 14, we compute estimates of consumer surplus and subsidy across all Census tracts in the affordable housing provider’s study area, including those tracts in which no housing produced by the provider currently exists. As mentioned above, forecasting results for Multi-Family Rental housing should be used with caution as the underlying data show little variation. [Table 16: Forecast Results: Monthly Housing Impact Measures The average estimated consumer surplus values from the forecasting model show lower mean values than the point estimates, while average estimated subsidy values are of a similar magnitude to the point estimates. As was the case for forecast values of construction costs, these data appear to show sufficient variation to be of use in an optimization planning model incorporating spatial features. Economic Analysis for Flexible Models 10 4/26/2007 FlexibleModelsAnalysis09.doc Use of Forecasting Results in a Planning Optimization Model The results of the previous two sections indicate that appropriate data can be constructed for use in a prescriptive planning model that provides guidance to affordable housing providers regarding the type, number and location of affordable housing to build across their service area. Recall that the forecasting results for construction costs summarized in Table (8) included estimated tract-level values for all three housing tenure types—New Construction, Rehab-forResale and Multi-Family Rental, according to project size: Small (5 units or less) or Large (6 units or more). Also, forecasting results for consumer surplus and operating subsidy in summarized in Table (16) indicate that Multi-Family Rental estimates are of questionable validity due to lack of variation in the underlying observations. These results can be used in a prescriptive planning model in the following way. The decision problem will be to choose sites for development of New Construction and/or Rehab-for-Resale owner-occupied housing units across a study area. A development of a particular owneroccupied housing type in a given Census tract can be of two size categories: Small and Large. The decision variables allowing such a range of development values will be of the following types: xij = 1, if a size-j housing development is located in neighborhood i = 0, otherwise; zij = number of units built in a size-j development located in neighborhood i Decision model structural parameters include housing unit-level and housing development-level values, as follows: bij: Per-unit net social benefit (consumer surplus less operating subsidy) for a size-j development in neighborhood i; fij: Fixed provision cost for a size-j development in neighborhood i; As we have demonstrated significant spatial variation in estimated tract-level values of consumer surplus, operating subsidy and fixed provision costs, the decision problem to be formulated is expected to yield non-trivial allocations of housing across the study area. In addition, our computational results indicate that consumer surplus measures are likely to be strongly outweighed by operating subsidy and fixed cost measures. This is not a surprising result as we have made no effort to identify and model other, positive, impacts of affordable housing development as listed in Table 2. Therefore, any decision model that uses these values must take care to ensure that the number of units sited is not set to zero to minimize net social costs. Analytical results for decision models calibrated using these data are currently under development. In addition, detailed descriptions of the decision models themselves are beyond the scope of this paper. However, details are available in (Johnson 2006, 2007). II. Indicators of Neighborhood Housing Market Strength Another research project of interest for its use of economic and statistical methods is one that seeks to choose parcels under the control of a local organization to develop into housing in order to maximize net social welfare, subject to a budget constraint. As described in Johnson, Fisher and Kim (2006), the optimization problem to be solved may be framed in two ways: addressing, Economic Analysis for Flexible Models 11 4/26/2007 FlexibleModelsAnalysis09.doc or ignoring, spatial interaction effects. In the former case, households who would live in housing developed from current vacant parcels derive benefit from proximity to multiple nearby neighborhoods according to a measure of residential real estate market strength. In the latter case, families derive benefit from proximity only to the closest neighborhood. The math programming model addressing the former modeling assumption is a nonlinear integer program similar to one solved in Fotheringham and O’Kelly (1989, p. 155); the math programming model addressing the latter modeling assumption is a linear integer program similar to the well-known fixed-charge facility location problem (Balinski 1964). Central to both of these optimization problems is the presence of a scalar measure of residential real estate market strength. One convenient measure of real estate market strength is average value of residential property within a neighborhood. However, the diversity of housing types makes computation of such a composite measure problematic. One approach to this problem would be to estimate hedonic models that relate housing unit and neighborhood characteristics to measured property values, and to use the estimated coefficients, with appropriately chosen weights, to generate an index of housing market strength. Though hedonic models are wellstudied in economics, the analytic and technical demands of such an enterprise, which would incorporate spatial concerns, is substantial. In contrast, factor analysis (Basilevsky 1994) offer a promising research direction. Here, the goal would be to collect data on a wide variety of housing unit and neighborhood characteristics, as well as a measure of market value, and through data reduction identify a few dimensions that account for variations in the observed variables. The resulting factor scores could be combined using expert-provided weights to create the composite housing market index we seek. Application of principal components and factor analysis to data from neighborhoods in the city of Pittsburgh is ongoing. III. Social Impacts of Housing Mobility An issue of great interest to housing researchers is individual and neighborhood impacts of housing mobility programs. The substantial literature on programs such as the Gautreaux Assisted Housing Program and the Moving to Opportunity experiment have demonstrated, to a greater or lesser extent, the significant impacts upon life outcomes of low-income families associated with relocation from disadvantaged neighborhoods to more opportunity-rich neighborhoods. As indicated in §1, there appears to be very little literature on social benefits and costs of housing mobility. However, I am involved in two research projects that may enable me to contribute to such an analysis. The first is associated with an initiative by the Chicago Housing Authority in the mid-1990s to revamp its Section 8 housing voucher program. As a result, the existing waiting list was cleared and re-populated, and families on the new list chosen at random to receive housing vouchers. This has the effect of a natural experiment in which one might compare life outcomes for families that received vouchers with similar families who did not. With Jens Ludwig of Georgetown and others, I have contributed to a rigorous outcomes evaluation of this novel intervention. While the initial focus has been on changes in levels of criminal offending associated with housing mobility (Ludwig et al. 2004), current research is addressing a broader range of outcomes. This longitudinal dataset, available to me, along with estimated participant outcomes, may allow me to develop a social cost-benefit analysis of the conventional Section 8 Economic Analysis for Flexible Models 12 4/26/2007 FlexibleModelsAnalysis09.doc program. This might serve as a benchmark against which other programs in which families receive directed counseling to relocate to low-poverty neighborhoods might be compared. The second research project is inspired by public housing redevelopment in the city of Pittsburgh from the mid-1990s to the present, much of which is related to the HOPE VI program. A grant from the Centers for Disease Control (Jacqueline Cohen, Carnegie Mellon University, principal investigator) has provided support for a research team, of which I am part, to estimate neighborhood-level criminal offending outcomes associated with family relocation in the wake of public housing redevelopment. A substantial administrative dataset from the Housing Authority of the City of Pittsburgh may enable me to estimate the social benefits and costs of public housing redevelopment, including family relocation. IV. Conclusion This working paper has presented current research results on dollar-valued impacts of affordable and subsidized housing in urban areas using well-established economic models of the firm and the consumer. These dollar-valued impacts—provision costs, household benefits, subsidies—are the basis for forecasting models that provide estimates of potential neighborhood-level impacts even in the absence of data on existing affordable housing programs. Moreover, the results of these forecasting models exhibit expected variation according to programmatic, housing unit, household and neighborhood-level characteristics. The next step for this research is to incorporate these forecasts into multi-objective planning models for affordable housing as in Johnson (2007), appropriately modified to account for scale economies in impacts. This paper has also introduced research initiatives that attempt to better understand the nature of local housing markets in order to inform planning models for parcel-level housing development decisions, as well as analyzing the locational outcomes of households who use tenant-based vouchers. AcknowledgementsI am deeply grateful to the dedicated assistance of Heinz School master’s students Jiyoung Kimand Julius Snell, and University of Pittsburgh doctoral student Helen Lafferty. ReferencesBajari, P., Benkard, C.L. and J. Krainer. 2005. House Prices and Consumer Welfare. 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Economic Analysis for Flexible Models154/26/2007 FlexibleModelsAnalysis09.doc Tables, Charts and Graphs Washington CountyAllegheny County