A tractable approach to compare the hedonic and discrete choice frameworks

The two primary approaches to estimate marginal willingness-to-pay (MWTP) are hedonic (Rosen, 1974) and discrete choice (McFadden, 1974). While both approaches rely on revealed preference methods to estimate MWTP, the primitives underlying both models are different, making it difficult to compare them. This paper establishes the assumptions needed to develop a tractable framework to compare both approaches. I begin with a discrete choice model and show how to derive the gradient of the equilibrium price function implicitly. I then incorporate Rosen's insight that the price gradient is equal to the MWTP of the marginal individual whose indifference curve is tangent to the price function in equilibrium. However, with discrete choices, some individuals may be inframarginal and their indifference curves will not be tangent to the price function. The analytical mapping I derive formalizes this intuition and shows that the price gradient 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. This result shows how choice probabilities and other moments of choice data can be used to distinguish marginal versus inframarginal individuals.