Hedonic price indices

The stratified approach for constructing a constant-quality index partitions goods along observable characteristics to help justify an assumption of conditional independence between potential prices and the time when a good sells. This results in a collection of constant-quality indices for each stratum that can be identified by within-stratum transaction prices. The trick with the stratified approach is finding a coarse enough stratification to justify conditional independence while ensuring that the overlap condition holds. Otherwise, if overlap fails, the overall constant-quality index cannot be constructed from the stratum-specific transaction-price indices because it is not possible to construct a transaction-price index for each stratum.

One motivation for hedonics is to specify a model for prices to extrapolate across strata when overlap fails. There may be a list of characteristics for a good that are agreed to appropriately capture what is confounding changes in price over time with changes in the underlying quality of a good, but it is not possible to stratify prices along this list of characteristics due to a failure of overlap. The idea behind hedonics is to model \(E(\rho | X, t)\) with a parametric model, \(h(X, t)\), that does not require overlap (or requires a weaker form of overlap). With conditional independence, the constant-quality price index is then simply \[\begin{align*} \log(I^{Q}) = E[E(\rho | X, t = 1) - E(\rho | X, t = 0)] = E[h(X, 1) - h(X, 0)]. \end{align*}\] Every geometric hedonic index has this form, and can be thought of as using the model \(h\) to construct modeled price relatives that compare goods with the same characteristics over time, and then aggregating these with a geometric index.

It is worth noting that the hedonic model is usually given a structural interpretation (ILO et al. 2013, chap. 5), so that it captures the structural contribution of each characteristic towards price. This is indeed where the name hedonics comes from. The problem with giving the hedonic model \(h\) a structural interpretation is that it requires a tremendous amount of prior knowledge, essentially understanding how the individual characteristics of a product determine its price. This is entirely unnecessary, however, once an assumption of conditional independence is made—the hedonic model is simply a model for how average transaction prices relate to characteristics and time. Consequently, the label “hedonics” is not very useful, and is potentially misleading. In the interest of keeping with the broader literature, however, the label will be maintained. What’s important to keep in mind is that the hedonic model is simply a model for how average transaction price relates to the characteristics of a good and when it sells.

📖 RPPI Handbook: Chapters 5–6.

📖 PPI Manual: Chapter 21, sections A, C, D.