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Published in: Mathematics and Financial Economics 4/2014

01-09-2014

Entropy methods for identifying hedonic models

Authors: Arnaud Dupuy, Alfred Galichon, Marc Henry

Published in: Mathematics and Financial Economics | Issue 4/2014

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Abstract

This paper contributes to the literature on hedonic models in two ways. First, it makes use of Queyranne’s reformulation of a hedonic model in the discrete case as a network flow problem in order to provide a proof of existence and integrality of a hedonic equilibrium and efficient computation of hedonic prices. Second, elaborating on entropic methods developed in Galichon and Salanié (Cupid’s invisible hand: social surplus and identification in matching models. Working Paper, 2014), this paper proposes a new identification strategy for hedonic models in a single market. This methodology allows one to introduce heterogeneities in both consumers’ and producers’ attributes and to recover producers’ profits and consumers’ utilities based on the observation of production and consumption patterns and the set of hedonic prices.

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Footnotes
1
We are confident Ivar will approve of this choice of example.
 
2
Note that in this setup, the utility of agents on each side of the market does not depend directly on the type of the agent with whom they match, only through the type of the contract. A more general framework where \(\alpha \) and \(\gamma \) depend simultaneously on \(x\), \(y\) and \(z\) is investigated in [9].
 
3
The node-edge matrix is usually denoted \(A\); our notations \(\nabla ^{*}\) and terminology are chosen to stress the analogy with the corresponding differential operators in the continuous case.
 
4
In most physical systems, mass is conserved and the balance equation has the more usual form of Kirchoff’s law \(\nabla ^{*}\mu =N\). However, in the present setting, producers and consumers have an option not to participate in the market, hence \(\nabla ^{*}\mu =N\) is replaced by Eqs. (2.11)–(2.13).
 
5
However, the ideas presented here extend to the continuous case, see Dupuy and Galichon [8] for a continuous logit approach and Chernozhukov, Galichon and Henry [4] for an approach based on multivariate quantile maps.
 
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Metadata
Title
Entropy methods for identifying hedonic models
Authors
Arnaud Dupuy
Alfred Galichon
Marc Henry
Publication date
01-09-2014
Publisher
Springer Berlin Heidelberg
Published in
Mathematics and Financial Economics / Issue 4/2014
Print ISSN: 1862-9679
Electronic ISSN: 1862-9660
DOI
https://doi.org/10.1007/s11579-014-0125-1

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