The choice of functional forms for hedonic price equations: Comment

Abstract

Rosen [13], Freeman [4], Halvorsen and Pollakowski [6], and others have stressed that economic theory does not suggest an appropriate functional form for hedonic price functions. 1 1 The only theoretical restriction on the hedonic price function is that its price elasticity must lie in between the price elasticities of supply and demand. Since both the supply and demand curves are not observable, even this mild restriction is not very helpful in choosing functional forms. It consequently is reasonable to try several functional forms and utilize the multiple regression equation with the best performance. In this spirit, Halvorsen and Pollakowski [6] recommend using the Box-Cox flexible functional form for hedonic analysis and measuring best performance with a goodness of fit test. The Box-Cox methodology has also been adapted in hedonic studies by Goodman [5], Linneman [10], Blomquist and Worley [1], and Eberts and Gronberg [3]. 2 2 The Box-Cox functional form has been used in several other urban contexts by Kau and Lee [8], Kau and Sirmans [9], Sirmans et al. [14], Sirmans and Redman [15], and McDonald [11]. Some of the problems, for example with prediction, raised in this paper on hedonics apply to these uses as well. The Box-Cox is particularly suited for testing functional forms because many familiar forms such as semilog, log linear, and translog are subsets of the flexible Box-Cox permitting nested hypothesis testing. In this note, we illustrate that the formal hypothesis testing advantage of the Box-Cox functional form is purchased at the expense of other important goals. The goal of most hedonic studies is to estimate the prices of the characteristics, to measure the response to changes in the prices, and/or to predict future expenditures. Using a best fit criterion to choose functional forms does not necessarily lead to more accurate estimates of characteristic prices. In fact, the large number of coefficients estimated with the Box-Cox functional form reduces the accuracy of any single coefficient which could lead to poorer estimates of specific prices. Second, because any negative number raised to a noninteger real power is imaginary, the traditional Box-Cox functional form is not suited to any data set containing negative numbers. Third, the Box-Cox functional form may be inappropriate for prediction. Since the mean predicted value of the untransformed dependent variable need not equal the mean of the sample upon which it is estimated, the predicted untransformed variable (housing value) will be biased. The predicted untransformed dependent variable may also be imaginary. Fourth, the nonlinear transformation results in complex estimates of slopes and elasticities which are often too cumbersome to use properly. We discuss each of these drawbacks and quantify them when possible in the remainder of this note.