A Tractable Framework to Relate Marginal Willingness-to-pay in Hedonic and Discrete Choice Models

The two primary approaches to estimate marginal willingness-to-pay (MWTP) are hedonic (Rosen, 1974) and discrete choice models (McFadden, 1974). This paper provides a tractable framework to investigate the relationship between MWTP in these models. By deriving the hedonic price gradient implicitly from the share function in the discrete choice model, I present an analytical mapping between the hedonic gradient (hence, the hedonic MWTP) and choice probabilities in the discrete choice model. Intuitively, the hedonic MWTP depends on weighted averages of marginal utilities where higher weights are assigned to individuals whose choice probabilities indicate more uncertain choices (marginal individuals). As this choice becomes more certain, the weights start to decrease. Since the hedonic method relies on tangencies between indifference curves and the hedonic price function to identify MWTP, inframarginal individuals (whose bid functions are not tangent to the hedonic price function) have low weights (they have choice probabilities that are close to 0 or 1 and low choice variances). This novel analytical mapping between the hedonic gradient and the share function can be used to identify conditions when MWTP in the two models are similar. (JEL: C01, R21, J23) ∗I am indebted to Fernando Ferreira for his guidance and time. I thank Kenneth Chay, Michael Greenstone, HanMing Fang, Alex Gelber, Joe Gyourko, Mark Jenkins, Jeremy Tobacman and participants at the CSWEP Mentoring Workshop for comments. Hyejin Lee and Xuequan Peng provided excellent research assistance. I am grateful to the Research Sponsors Program of the Zell/Lurie Real Estate Center at Wharton for financial support. All errors are my own. Email: [email protected]. Address: 3620 Locust Walk, 1464 SHDH, Wharton Real Estate, University of Pennsylvania, Philadelphia, PA, 19104-6302.