¹ St. Joseph County, Indiana, (whose central city is South Bend) and Brown County, Wisconsin, (whose central city is Green Bay) are the two housing markets being studied by HASE to help the U.S. Department of Housing and Urban Development assess the desirability and feasibility of using housing allowances to enable low–income families to afford safe, decent, and sanitary dwellings. HASE was explicitly undertaken to measure the price effects of a full–scale housing allowance program.

² See Barnett, C. Lance, Using Hedonic Indexes to Measure Housing Quantity, R–2450–HUD (Santa Monica, Calif.: The Rand Corporation, 10 1979)Google Scholar.

³ The existence of competitive equilibrium and the equality of core and competitive allocations in the context of indivisible, heterogeneous commodities is demonstrated in Mas-Collel, Andreu, “A Model of Equilibrium with Differentiated Commodities,” Journal of Mathematical Economics, Vol. 2 (1975), pp. 263–295CrossRefGoogle Scholar. For an application to urban housing markets, see Ellickson, Bryan (with Barry Fishman and Peter A. Morrison), Economic Analysis of Urban Housing Markets: A New Approach, R–2024–NSF (Santa Monica, Calif.: The Rand Corporation, 07 1977)Google Scholar.

⁴ See, for example, Rosen, Sherwin, “Hedonic Prices and Implicit Markets,” Journal of Political Economy, Vol. 82 (1974), pp. 34–55CrossRefGoogle Scholar.

⁵ In practice the error term contains the effects of excluded attributes as well as random variation.

⁶ Those surveys were fielded in 1975 at the beginning of the allowance program to provide a benchmark for assessing its effect. The landlord survey was addressed to owners of a marketwide probability sample of rental residential properties. The household survey solicited information from the occupants of dwellings on those properties. Trained fieldworkers described and evaluated building exteriors for the residential building survey. As part of the neighborhood survey, local public sources were used to obtain facts on each of the 86 neighborhoods in which St. Joseph County was divided. The neighborhood survey also includes fieldworkers' reports on the characteristics of each blockface in the county.

⁷ For a more detailed description and assessment of the index, see Noland, Charles W., Assessing Hedonic Indexes for Housing, N–1305–HUD (Santa Monica, Calif.: The Rand Corporation, forthcoming)CrossRefGoogle Scholar.

⁸ See, for example, Kain, John F. and Quigley, John M., “Measuring the Value of Housing Quality,” Journal of the American Statistical Association, Vol. 65 (06 1970), pp. 532–548CrossRefGoogle Scholar; King, A. Thomas, Property Taxes, Amenities, and Residential Land Values (Cambridge, Mass.: Ballinger Publishing Company, 1973)Google Scholar; Straszheim, Mahlon R., An Econometric Analysis of the Urban Housing Market (New York: National Bureau of Economic Research, 1975)Google Scholar; Little, James T., “Residential Preferences, Neighborhood Filtering and Neighborhood Change,” Journal of Urban Economics, Vol. 3 (01 1976), pp. 68–81CrossRefGoogle Scholar; Goodman, Allen C., “Hedonic Prices, Price Indices, and Housing Markets,” Journal of Urban Economics, Vol. 5 (10 1978), pp. 471–484CrossRefGoogle Scholar.

⁹ For example, if additional rooms have declining marginal value in the market, then rooms should be rescaled to account for that. Here the natural logarithm of the number of rooms is used, a transformation that incorporates declining marginal value.

¹⁰ See Haitovsky, Yoel, “A Note on the Maximization of R⁻², The American Statistician, Vol. 23 (1969), pp, 20–21Google Scholar.

¹¹ The regression results presented in Table 1 were obtained using a generalized least-squares procedure to account for the fact that the standard error of the residuals varied systematically by property type.

¹² This specification, used by King in his study of New Haven, was substantiated by analysis of the residuals.

¹³ In rural areas, blockface variables refer to the area within a quartermile radius of the dwelling.

¹⁴ See Alonso, William, Location and Land Use (Cambridge, Mass.: Harvard University Press, 1964)CrossRefGoogle Scholar; and Muth, Richard F., Cities and Housing (Chicago: University of Chicago Press, 1969)Google Scholar.

¹⁵ Spline functions are piecewise linear. Along the j^th piece the slope equals the sum of slopes of the previous j–1 pieces plus the slope of the jpiece. When length of stay exceeds 3.5 years, the slope is -4.37 + 3.42 = -.95, which is not significantly different from zero.

¹⁶ An alternative explanation (argued from the demand rather than the supply side) is that tenants find resident landlords to be a nuisance and will pay less for dwellings on properties with resident landlords.

¹⁷ Merely comparing the coefficients tells us little because they depend on the units of measurement. The usefulness of beta coefficients depends on the independent variables' orthogonality. Given the amount of collinearity in our data, it seems wise not to use beta coefficients.

¹⁸ Dropping a summary group means excluding from the regression all ofthe variables that compose it.

¹⁹ The Brown County index distinguishes interior and exterior quality. There interior quality ranks first, space second, and exterior quality third; location is least important.

²⁰ The t-statistic for the test did not exceed the critical value at the 99 percent confidence level. The small sample size prohibited performing the same test for the southeast suburbs.

²¹ Third Annual Report of the Housing Assistance Supply Experiment, R–2151–HUD (Santa Monica, Calif.: The Rand Corporation, 02 1977), pp. 67–70Google Scholar. admitting that St. Joseph County may contain submarkets that are in short-run equilibrium, we tested for the most likely two submarkets– –central South Bend and the rest of the county. The test is the same as that reported earlier for assessing specification error: The null hypothesis that the coefficients for the two regressions were equal could not be rejected at the 99 percent confidence level.

²² The expenditure for residential services equals monthly gross rent plus the price discount that accrues with length of stay and that is due to the presence of a resident landlord, i.e., the price adjustments.

²³ See Mulford, John, Income Elasticity of Housing Demand, R–2449–HUD (Santa Monica, Calif.: The Rand Corporation, 07 1979)Google Scholar.

²⁴ The number of bathrooms is specified linearly in Brown County but as a squared tern in the St. Joseph County index.

²⁵ These results pertain only to different income classes of renters in our sample. As its income increases, a particular household could change tenure, simultaneously increasing its expenditures for neighborhood and blockface quality (if these items are systematically higher for homeowners).