ISSN (Print) 0473-453X

Discussion Paper No. 1224

ISSN (Online) 2435-0982

HEDONIC PRICE FORMATIONCharles Ka Yui Leung

December 2023

The Institute of Social and Economic ResearchOsaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Hedonic price formation

Charles Ka Yui LeungThis version: December 2023

Abstract
This short article provides a quick summary of the hedonic pricing theory. Some newdevelopments are also discussed.

Keywords: hedonic price, portfolio of attributes, valuation, unobservable, non-tradeable

JEL classification Number: C10, D10, R20



Acknowledgement: This article is prepared for The World of Regional Science, edited byPeter Nijkamp, Karima Kourtit, Kingsley Haynes and Zeynep Elburz, to be published by EdwardElgar. I am very grateful to many colleagues who shaped my thoughts on the topic, especially YifanGong, Rick Hanushek, Steve Malpezzi, Edward Tang, Kuzey Yilmaz, among others. The usualdisclaimer applies.
Department of Economics and Finance, City University of Hong Kong, Kowloon Tong, HongKong. kycleung@cityu.edu.hk

Hedonic price formation

1. Definition
According to the Cambridge Dictionary, hedonic is about the feeling of pleasure(https://dictionary.cambridge.org/dictionary/english/hedonic ). Following the logic, "hedonicprice" is an attempt to interpret the market price of an item (e.g., a smartphone) as the sum of thevalue of its components (e.g., a phone, a camera, a clock, etc.), according to the "pleasure" or"utility" that each part offers to the owner. When we apply this idea to the labor market, we caninterpret a worker's salary as the sum of skills, experience, social network, etc. These items canall bring value to the employer (Ekeland et al., 2004). When we apply hedonic price to thehousing market, we say that the value of a house would depend on its location, size, internalfeatures (e.g., number of bedrooms, number of restrooms), etc. Therefore, one may consider"hedonic pricing" as “component pricing” or "decomposition pricing."
2. History
While the exact origin of hedonic pricing may be controversial(https://en.wikipedia.org/wiki/Hedonic_regression), many economists learn hedonic pricing fromRosen (1974), which has accumulated almost 16,000 Google citations as this article is written.
Since then, the idea has been adopted and extended in many directions. Malpezzi (2003) and Hill(2013), among others, have provided a detailed survey of the related literature.
3. Theory
The theory of hedonic pricing is straightforward. Let us consider that a consumer's "pleasure" or"utility" 𝑈 is defined on a vector of attributes 𝑥 , 𝑥 , … , 𝑥 . In the case of housing, we canconsider those attributes to be housing-related. For instance, consider 𝑥 to be the size of thehouse, 𝑥 to be the commute distance, i.e., the distance between the housing unit and theconsumer's workplace, 𝑥 to be the education quality of the district where the housing unit islocated, etc. We consider two scenarios. In the first scenario, there is a market for each attribute,and attribute 𝑥 ’s unit price is 𝑝 . And assume that the consumer has a budget of 𝑀 to purchase
all these attributes. Thus, the optimization problem of the consumer is𝑚𝑎𝑥 𝑈 𝑥 , 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 ∑ 𝑝 𝑥

𝑀, (1)

where x is a short-hand of the vector of attributes to be purchased, 𝑥𝑥 , 𝑥 , … , 𝑥 . We
assume an interior solution for all attributes, which means that we have the demand for every
attribute to be positive. The optimality condition gives𝑈 ≡𝜆𝑝 .

(2)

It means that the marginal utility of each attribute of the optimal package equates to the productof the marginal utility of an extra dollar 𝜆 and the corresponding unit price 𝑝 . Assume that theconsumer uses up all the money. We have∑𝑀 ∑ 𝑝 𝑥𝑥.
(3)
In the second scenario, imagine a housing unit with the same portfolio of attributes as theoptimal package under the first scenario, with the price 𝑃. The two purchases should be equal invalue as they have the same collection of attributes. It implies that𝑃∑

𝑥.

(4)

In other words, the value of the house 𝑃 is a summation of its attributes, weighted by the ratio of
the marginal utility of the corresponding attribute 𝑈 and the marginal utility of an extra dollar 𝜆.
4. Conceptualisation
Some researchers interpret equation (4) as justifying a simple linear regression of the transaction
price of the house 𝑃 on its attributes 𝑥
𝑥 , 𝑥 , … , 𝑥 . People add time-fixed andgeographically fixed effects when the sample includes transactions in different periods andgeographical units (e.g., cities, regions).
Other researchers provide a different interpretation. First, the marginal utility of an attribute 𝑈
does not need to be constant but depends on the whole package of the attributes. For instance, thevalue of the distance from work may depend on whether there are geographical features (e.g., ariver, a mountain, etc.) and transportation infrastructure (e.g., public transport, highways).
Second, the marginal utility of money 𝜆 depends on the budget and the whole vector of attributeprices 𝑝 , 𝑝 , … , 𝑝 . Thus, putting these together, equation (4) implies a nonlinear relationshipbetween the transaction price 𝑃 with the vector of attributes 𝑥
𝑥 , 𝑥 , … , 𝑥 . Among others,
Ekeland et al. (2004) and Malpezzi (2003) provide a detailed discussion.
5. New developments
There are many developments in the hedonic pricing theory. Limited by the space, only a few arehighlighted here. First, some attributes may not be observable, so some adjustments are neededin estimation (Francke and van de Minne, 2021). Second, the housing market may be spatiallysegmented, and the traditional ordinary least squares (OLS) may be insufficient (Liao and Wang,2012). Third, some attributes may not be directly tradeable. For instance, the high quality ofeducation in a local area is observable but not directly "tradeable" but reserved to the residents.
Hence, people may purchase housing units in an area with complicated motives. Researchers
need to adjust for such a possibility (Hanushek and Yilmaz, 2022). Fourth, when the sample
involves an extended period, separately considering each subperiod may provide superior
statistical performance than adding time-fixed effects (Tang and Leung, 2023). Fifth, the recent
development in machine learning can be combined with the traditional hedonic pricing models(Dutra Calainho et al., 2022).
6. Policy relevanceThe hedonic pricing model is relevant for practical policies. For instance, if a local government
needs to create a new infrastructure (e.g., a bridge, a railway), how much does she need tocompensate the nearby residents if specific housing units must be demolished? And how muchvalue would the new infrastructure create after completion?
7. Application fields
The hedonic pricing model is also applied in development, health, and labor economics.
8. Prospect
With increasing available granular data, more potential applications of the hedonic pricing model
would arise. Since some applications would be new, more caution would also be needed.

Reference
Dutra Calainho, F., Van de Minne, A., and Francke, M. K. (2022). A Machine Learning
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Francke, M., and van de Minne, A. (2021). Modeling unobserved heterogeneity in hedonic pricemodels. Real Estate Economics, 49(4), 1315-1339.
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