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Ambgiuity, Data and Preferences for Information - Theory and Applications

Final Report Summary - AMBIGUITY AND DATA (Ambgiuity, Data and Preferences for Information - Theory and Applications)

Objectives of the project:
We study decision making informed by data. We examine the relation between objective information provided by data and decision maker's beliefs about uncertain outcomes. We also study the evaluation of information by economic agents. We then apply the derived theoretical insights to models of technological adaptation to climate change and to a study of market participation and market structure.
We start by providing a representation of preferences when decisions are informed by data.
The representation captures the idea that information from data is perceived as ambiguous.

We identify the decision maker's beliefs which combine the objective information in the data (frequency, number and type of observations) with the decision maker's subjective characteristics (perception of similarity and perception of ambiguity). We determine the decision maker's degrees of optimism and pessimism and relate them to his preferences for precision of information. This allows us to derive the value of information.
Next, we apply the representation to a model of technological adaptation in response to a change in climate conditions. We study the role of agent heterogeneity in the process of adoption. By experimenting with new technologies, optimists provide the public good of information, but also obtain lower average returns. Pessimists use this information to choose the optimal technology in the long-run. When the share of optimists is low, steady states are inefficient. We study the impact of subsidies for early adopters and provision of additional information on successful adoption.

While ambiguity-aversion can explain empirically observed patterns in asset prices, standard economic wisdom claims that such deviations will be eliminated by the wealth dynamics in the economy and thus, cannot be sustained in the long-run. We analyze a market populated by expected utility maximizers with correct beliefs and smooth ambiguity-averse consumers. We study conditions under which ambiguity-averse consumers survive and affect prices in the long-run. If ambiguity vanishes with time or if the economy exhibits no aggregate risk, ambiguity-averse consumers survive, but have no long-run impact on prices. In both scenarios, ambiguity-averse consumers are fully insured against ambiguity in equilibrium and, thus, behave as expected utility maximizers with correct beliefs. If ambiguity-averse consumers are not fully insured against ambiguity, they behave as expected utility maximizers with effectively wrong beliefs and an effective discount factor which, for agents with constant relative ambiguity aversion, is higher than their actual discount factor. The latter effect can be shown to offset the former and thus, in a Markov economy with large persistent ambiguity and aggregate risk, these consumers almost surely survive, while driving expected utility maximizers with correct beliefs out of the market. In the long-run, asset prices are thus fully determined by the ambiguity-averse consumers and hence, exhibit many of the empirically observed patterns (high equity premium, excessive saving rates, etc.).