برآورد لذت باورانه از کشش تقاضای مسکن با نشانه گذاری بر هزینه های نهایی

We show that recent developments in hedonic pricing theory allow modeling of the equilibrium pricing function as the marginal cost of an additional housing unit plus a markup that varies inversely with the elasticity of demand. Useful information about demand elasticity at a given point on the envelope function can be recovered from the hedonic regression and limited information on marginal costs. In particular, the elasticity of the envelope with respect to any characteristic such as interior area provides information on the elasticity of demand. Relative price elasticities (i.e., elasticities that vary from a base value in a known way with interior area, unit type or neighborhood characteristics) can be computed from the elasticity of the hedonic envelope. Like Yinger (2010), our method is based on a single hedonic equation. We test our method using sales of new high rise condominiums in two districts within Shenzhen, China: Futian and Longgang. The results strongly confirm the main hypothesis of this paper: price elasticity with respect to size is increasing for more complex types of units. Together with estimates of marginal costs of production, these results imply that relative demand elasticity is declining for larger, more complex units.

It is well established that monopolistic competition implies that firms obtain a markup over the marginal cost of production and that the markup decreases with the absolute value of the price elasticity of demand (Henderson and Quandt, 1980).1 Recent literature has extended this result to hedonic equilibrium (Pakes, 2003). Moreover, the hedonic model has been extended to allow different pairings between supply and demand at each of several discrete points along the hedonic function (Ekeland et al., 2004 and Bajari and Benkard, 2005). These developments allow modeling of disparate demand and supply equilibria with a single hedonic function in a single submarket.2 This paper shows that these seemingly unrelated facts allow estimation of the relative price elasticity of demand for a unit of housing 3 from the hedonic function and limited information on the functional form of marginal cost. In other words, this paper develops the logical relation between the elasticity of the hedonic envelope and the price elasticity of demand. Relative price elasticities are calculated for each hedonic bundle relative to a numeraire bundle. We show that high-rise condominium construction within a given neighborhood provides one case where our hedonic elasticity method can be applied without extensive knowledge about marginal costs. In this case, the land component of an additional square meter of interior area is approximately fixed for a unit of a given type, and construction cost is approximately linear in size, so the functional form of marginal costs is known with reasonable accuracy. The developer can be modeled as supplying units of various sizes and types on a given land area so as to maximize profit from the limited number of households in each demand segment. In our model, demand is segmented by size and type of unit. We show that relative demand elasticities for units of different types and sizes can be estimated from the hedonic function. The intuition behind our analysis is that developers allocate limited floor area to large and small units depending on their expectations about the willingness and ability of each demand segment to pay. For example, the demand for large or luxurious units may be less elastic than that for small units. Our key insight is that the equilibrium hedonic envelope function – e.g., the elasticity of predicted hedonic price with respect to unit size – provides information about the price elasticity of demand for the hedonic bundle. Empirically, we derive a method for estimating the direction, degree, and statistical significance of changes in the price elasticity of demand as a function of hedonic characteristics. We present a new database for Shenzhen China, part of the rapidly growing Guangzhou conurbation near Hong Kong.4 Our data are a very rich and complete representation of free market transactions of ownership units in high-rise buildings (i.e., condominiums) between August 2004 and January 2006. Many of the sales are presales: i.e., sold before the buildings are completed. Thus, we take our results as an approximation to the market for new housing. These condominium sales and construction costs allow us to estimate relative price elasticities of demand for buyers in housing markets both inside and outside Shenzhen’s special economic zone (SEZ). We find that relative demand elasticity is declining for the larger, more complex units. Useful summaries of the American and European literatures are found in Zabel, 2004, Ermisch et al., 1996 and Mayo, 1981, and Hanushek and Quigley (1980). One strand of the literature estimates price elasticity for housing services as a bundle, including structural, neighborhood and location attributes. Several papers have established the importance of allowing price elasticity parameters to differ across market segments, such as structure and land (Ioannides and Zabel, 2008 and Zabel, 2004); income, tenure and location (Garcia and Hernandez, 2008); by demographic group (Ermisch et al., 1996); by degree of neighborhood choice (Ihlanfeldt, 2007); for movers (Bajari and Kahn, 2005); and stayers (Goodman, 2003).5 Our investigation of hedonic equilibrium pairings between demand and supply provides a new approach linking demand for a bundle of characteristics (units of housing or of housing services) to market segments associated with these bundles sold in each of two Shenzhen neighborhoods, and the marginal costs of these bundles. This context allows us to develop a model that associates market segments with price elasticity of demand. Like Yinger’s (2010), ours is a single equation method; multiple market data are not required. Yinger’s model is based on household types sorting by steepness of their bid functions. At each point along the hedonic envelope, willingness to pay is allowed to change. Our model is similar in that each point on the envelope is an equilibrium with a possibly different household type. We allow households to differ by elasticity of demand for units whereas Yinger estimates demand elasticities for separate services and amenities such as safety, school quality or distance from an environmental hazard. Our method is based on the assumption of monopolistic competition whereas Yinger’s is based on constant elasticity of demand utility functions. We allow supply, as represented by marginal cost, to differ at each point on the envelope, as required by hedonic equilibrium.6 The next section discusses the relevance of Shenzhen in Chinese economic and housing development. Section 3 develops the role of equilibrium hedonic pricing theory in identifying the relative price elasticity of housing demand. Section 4 proposes a functional form for the hedonic regression. Section 5 presents the data and empirical results. Section 6 compares our estimates of demand elasticity to those contained in the previous literature. Section 7 concludes.

Recent developments in hedonic pricing theory allow marginal cost and marginal utility to differ in equilibrium (Harding et al., 2003). Moreover, a single hedonic function in a single submarket is consistent with multiple equilibrium pairings between disparate demand segments and monopolistic suppliers (Yinger, 2010, Ekeland et al., 2004 and Bajari and Benkard, 2005). These developments allow hedonic equilibria where demand segments, characterized by possibly different demand elasticities, are paired with landlords. The latter are attempting to maximize profit by choosing the mix by size and unit type of condominiums in a high-rise building on a given plot of land, subject to local planning and zoning restrictions. 35 These theoretical elements allow us to model the hedonic pricing envelope as equal to marginal cost per unit plus a series of markups that vary inversely with the elasticity of demand for each demand segment. Useful information about demand elasticity can be recovered from the hedonic function and limited information on marginal costs. In particular, the elasticity of the hedonic envelope with respect to size and type of unit allows inferences about the variation of the price elasticity of demand with respect to these hedonic characteristics. Relative demand elasticities (e.g., elasticities that vary in a known way with unit type and/or with interior area) can be estimated in these cases. Our method has two new characteristics: (1) a single hedonic equation in a single submarket provides information on demand elasticity; (2) the supply side is introduced explicitly by measuring marginal costs. Our method provides a link between that strand of the literature focused on the price elasticity for the hedonic bundle and that strand dealing with price elasticity with respect to neighborhood characteristics such as pollution, school quality and racial or ethnic composition. We test our hedonic method using sales of new high rise condominiums in two districts within Shenzhen: Futian and Longgang.36 In Futian, results confirm the hypothesis expressed by Fig. 1: larger units with luxury features have significantly higher hedonic elasticity with respect to size. Our data indicate that marginal costs of supplying these units do not increase as much as price, and this is supported by a plausible cost function containing a fixed component. Therefore, we can infer that relative price elasticity of demand declines by about 60 percent as we move from 1-bedroom to 4-bedroom condominium units. This estimate is based on the fact that the markup over the marginal cost of production increases for these more complex units. Interestingly, demand elasticity is somewhat higher for 3-bedroom units than for 2-bedrooms units. The omitted property type for Longgang is the 1-bedroom units. The interaction variables for the 2-bedroom, 3-bedroom, 4-bedroom, and Duplex-and-4-plus-bedroom types are all significant at better than 1% and positive and each adds a substantial amount to the hedonic elasticity with respect to size when compared to 1-bedroom units. Therefore, relative demand elasticity is declining for the larger, more complex units, confirming the main hypothesis of this paper. In Futian, decisions by policy makers and developers are informed by the fact that demand for 4-bedroom and larger units is much less elastic than for other units. Policy makers allocating permissions across the two submarkets should be aware that in Longang relative price elasticities decline at much smaller units than in Futian. Consequently, decisions to change allocations to 3-bedroom (95 square meter) apartments in Longgang will have a bigger impact on price than the same decisions in Futian, where a typical 3-bedroom apartment has 106 square meters. Our method suggests that more attention should be paid in the academic literature to the marginal cost of providing housing, disaggregated into land and structure components. Professional appraisers and tax assessors have long relied on comparable land sales and construction cost estimates from companies such as RS Means Inc. Future research can investigate application of these data sources to marginal cost and elasticity estimates.