Hedonic Markets and Explicit Demands: Bid-Function Envelopes for Public Services, Neighborhood Amenities, and Commuting Costs

Abstract

Hedonic regressions with house value as the dependent variable are widely used to study the value of public services and amenities. This paper builds on the theory of household bidding and sorting to derive a bid function envelope, which provides a form for these regressions. This approach uses a general characterization of household heterogeneity, yields estimates of the price elasticities of demand for services and amenities directly from the hedonic with no need for a Rosen two-step procedure, and provides tests of key hypotheses about household sorting. An application to data from Cleveland in 2000 yields precise estimates of price elasticities for school quality, distance from environmental hazards, and neighborhood ethnic composition. The results support the sorting hypotheses and indicate that household preferences are very heterogeneous, with some households placing a negative value on many "amenities."

The capitalization of school quality into house values: A review

“…As discussed earlier, the S 2 term or its equivalent appears in all formally derived envelope specifications that are consistent with sorting. The sign of a 2 is expected to be positive; indeed, Yinger (2010) shows that a positive sign for this coefficient supports the hypothesis that households sort according to the slopes of their bid functions. Moreover, a high value for Y is associated with a steep bid function, so the omission of S 2 is likely to bias upward the coefficient of Y and may lead to an understatement of service capitalization.…”

“…This lesson is supported by Rasmussen and Zuehlke's rejection of a BoxCox in favor of a quadratic specification. Moreover, Yinger (2010) shows that the Box-Cox, log, and semi-log specifications are all inconsistent with sorting, at least given constant-elasticity demand functions for S and H. Overall, the inconclusive and sometimes contradictory results in these studies remind us that more research is still needed to guide the choice of functional forms in empirical studies of school quality capitalization. At this point, it seems reasonable to recommend that capitalization studies should at least examine a specification including S and S 2 , which is consistent with Epple's (1987) and with Yinger's third special case in Eq.…”

“…As shown above, Epple (1987) and Yinger (2010) derive functional forms consistent with sorting under certain assumptions, but other studies have not followed this route. Instead, several studies investigate the performance of various functional forms in the hedonic model in general, instead of focusing on b PfSg.…”

“…This formulation could be applied to housing if all public service and structural traits were brought into the X vector. Yinger (2010) derives bid-function envelopes under the assumptions that the service and housing demand functions take the constant-elasticity form; that sorting is determined by bid-function slopes (as in the standard theorem discussed above); and that the equilibrium relationship between the service level, S, and the bid-function slope, w, can be approximated by S ¼ ðr 1 þ r 2 wÞ r 3 . Three easy-to-estimate special cases of this envelope arise when the price elasticity of demand for housing is minus one and r 3 equals one.…”

“…Marginal willingness to pay is not directly observed. Unless the functional form explicitly identifies the underlying demand parameters, as in Epple (1987) and Yinger (2010), the coefficient of S in a capitalization equation cannot be used to measure marginal willingness to pay.…”