Identification of Preferences from Market Data

Abstract

We offer a new proof that the equilibrium manifold (under complete markets) identifies individual demands globally. Moreover, under observation of only a subset of the equilibrium manifold, we find domains on which aggregate and individual demands are identifiable. Our argument avoids the assumption of Balasko (2004) requiring the observation of the complete manifold.

Identification of Individual Demands from Market Data under Uncertainty

“…We obtain those results by first extending the results of Carvajal and Riascos (2005) to the case of uncertainty, in a setting in which all individual budgets are expressed in present value (using no-arbitrage considerations). Since this setting deals with prices that are not (directly) observable in real life, we consider this extension as an intermediary step for the results in the next section.…”

“…5 For differentiable preferences this condition is standard when financial markets are complete, but it is not obvious when markets are incomplete. When needed, we impose the following smoothness condition on preferences:…”

“…For a survey of this literature, see Carvajal et al (2004). 5 The argument of the function and its derivatives is omitted in the expression; the condition is to hold at every (p, w) ∈ {p ∈ R N ++ |p 0,1 = 1} × R N ++ . 6 Functions f i : S N −1 ×R N ++ → R N ++ and F : S N −1 ×R N I ++ → R N ++ are well defined, by assumption 1 guarantees that the range of f i is contained in R N ++ .…”

“…After that, we introduce the concepts of identification: we first define identification of the aggregate demand from the equilibrium manifold, and then define identification of the profile of individual demands from the aggregate demand. The third section is auxiliary: it gives an alternative setting for the problem and extends the main results of Carvajal and Riascos (2005) to that setting. Section 4 then exploits the auxiliary results to obtain identification of aggregate and individual demands from the equilibrium manofold.…”

Identification of Pareto-improving policies: Information as the real invisible hand

“…This idea was exploited by Chiappori et al (2004), Matzkin (2005) and Carvajal and Riascos (2005), to show that, in economies without uncertainty, the graph of the equilibrium correspondence can be used to identify individual preferences.…”