Luc Anselin and Nancy Lozano-Gracia 1217example, for environmental characteristicqi, this would yield:
∂U/∂qi
∂U/∂x
=∂Pi/∂qi. (26.2)The hedonic price function is an equilibrium price equation where the price of
houseiis defined as a function of the house characteristics:
Pi=P(qi,Si,Ni,Li). (26.3)With estimates for the coefficients in this function to hand, it then becomes
possible to estimate the individual’s marginal willingness to pay for any character-
istic that enters the utility function. As shown in equation (26.2), differentiating
equation (26.3) with respect to the characteristic of interest yields the desired result.
The marginal willingness to pay can be interpreted as a “price” for the char-
acteristic and exploited to construct an inverse demand function. To accomplish
this, the MWTP is “observed” at different levels of the characteristic, sayqi, and
combined with additonal demand shifter variablesCin a demand function:
MWTPi=f(qi,Ci). (26.4)This allows for the analysis of non-marginal changes in the characteristic.
26.2.2 Estimation
The operational implementation of a hedonic analysis consists of two stages: the
estimation of a hedonic price function and the construction of the inverse demand
function for house characteristics. In most applied work, the second stage is not
carried out.
In the first stage, a hedonic price function is specified in terms of the relevant
characteristics of the house, typically a combination of individual house features
(size, number of rooms, amenities such as air conditioning, etc.), environmen-
tal characteristics, neighborhood characteristics and location. Different functional
forms can be used, either linear or nonlinear, the most commonly being linear,
semi-log and log-log. Alternatively, a flexible Box–Cox approach can be taken. In
a much cited study, Cropperet al. (1988) carried out a large number of simula-
tions to assess the sensitivity of the results to functional specification. They found
that when there are omitted variables or when proxies are used in the absence of
a measure of the real variable, simpler functional forms such as linear or semi-log
perform better than more complex forms. In most applied work, this is the path
taken.
The estimates of the parameters in the price function yield the marginal price
for each characteristic as the partial derivative of the function with respect to the
characteristic. Depending on the functional form, this marginal price may change
with the level of the characteristic. It is interpreted as the marginal willingness to
pay for the characteristic.
The second stage of a hedonic analysis is to relate the marginal willingness to pay
to different levels of the characteristic in order to yield an inverse demand function