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ERC

INDIMACRO Report Summary

Project ID: 670337
Funded under: H2020-EU.1.1.

Periodic Reporting for period 1 - INDIMACRO (Individual decisions and macroeconomic robustness)

Reporting period: 2015-10-01 to 2017-03-31

Summary of the context and overall objectives of the project

The team has been working on several projects connected to the initial ERC proposal:
1. In the paper “A framework for the Analysis of Self-Confirming Policies” we (henceforth, the PI with his team) provide a general framework for the analysis of self-confirming policies. We do so, first, by studying self-confirming equilibria in recurrent decision problems with incomplete information about the true stochastic model. Then, we illustrate the theory in a monetary policy setting. We conclude by discussing more general cases of self-confirming policies.
2. In the paper “Absolute and Relative Ambiguity Aversion: A Preferential Approach” we provide a framework to address how the uncertainty attitudes of a decision maker change while his/ her wealth changes. The analysis proceeds by characterizing many models of decision making in terms of these attitudes. This is particularly important, since many models in this class are used in economic applications, but until now the treatment of wealth effects had been ignored.
3. In the paper “Learning from Ambiguous and Misspecified Models”, we model intertemporal ambiguity as the scenario in which a Bayesian learner holds more than one prior distributions of beliefs over a set of parameters. We provide necessary and sufficient conditions in which ambiguity fades away because of learning. Our conditions apply to many and diverse learning environments, of different model-classes. Our result highlights a possible tradeoff between model misspecification and ambiguity.
4. Recently, there has been a renewed interest and attention in the study of the process of decision making. In “Rational Preference and Rationalizable Choice”, we focus on the study of the judgements of a decision-maker about his/ her well-being and the choices that he/ she makes. In a decision-theoretic environment under uncertainty, we propose axioms that support this binary-rationality of a decision maker, regarding both his/ her “mental” preferences and his /her “behavioral” ones.
5. In the paper “Learning and Self-confirming Long-Run Biases” we study an uncertainty averse and sophisticated decision maker, who is facing a recurrent decision problem and where information is generated endogenously. In this context, we study self-confirming strategies as the outcomes of a process of active experimentation. We provide, inter alia, a learning foundation for self-confirming equilibrium with model uncertainty. We also argue that ambiguity aversion tends to stifle experimentation, increasing the likelihood that decision makers get stuck into suboptimal “certainty traps”.
6. Both economic and physical phenomena entail some uncertainty and risk, which analysts wish to measure given the observed distribution of characteristics available. In the paper “A Formal Theory of Evidence and Measurement “, we propose the way that one can extract such a measurement from the available evidence. In addition, we provide tools for the comparison of different measurement results.
7. and 8. The papers “On the equality of Clarke-Rockafellar and Greenberg-Pierskalla Differentials for Monotone and Quasiconcave Functionals” and “Orthogonal Decompositions in Hilbert A-Modules” are Math papers. Their motivation is simple: to provide a unifying mathematical theory for some tools used in the economic literature.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

All the projects mentioned above have been described with their obtained outcomes and achieved goals. In terms of results achieved so far:

Paper 1 is a revise and resubmit in a “top five” journal in economics. It has also been presented in several top academic institutions as well as conferences.

Paper 2 is currently under review in a “top five” journal in economics. It has also been presented in several top academic institutions as well as conferences.

Paper 3 is currently under review in a “top field” journal in economics. It has also been presented in few conferences.

Paper 4 is currently under review in a “top field” journal in operations research.

Paper 5 is currently under review in a “top field” journal in economics. It has also been presented in few top academic institutions as well as conferences.

Paper 6 is about to be submitted to a “top field” journal in operations research.

Paper 7 is a revise and resubmit in a “field” journal in mathematics.

Paper 8 is about to be submitted to a “top” journal in mathematics. It has also been presented in few academic institutions as well as conferences.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The potential impact of the current research is big. Inter alia, the current research is truly interdisciplinary as it can be seen in the different targeted outlets. More specifically:

Paper 1 provides a bridge between two strands of literatures, one in game theory and the other in macroeconomics. Such a connection did not exist and allows researchers to use tools from both fields.

Paper 2 provides an analysis that allows researchers to discuss wealth effects on uncertainty attitudes, which is tremendously important in economic applications.

Paper 3 yields to the striking result, in which there are cases that a decision maker should pragmatically choose to learn a wrong model, instead of facing a long-run ambiguity. This is a new result in the literature.

Paper 4 provides a foundation for an existing methodology in decision theory and generalizes it.

Paper 5 provides a learning foundation for self-confirming equilibrium with model uncertainty, something which was suggested by the literature, but was never formalized.

Paper 6 provides a theory of measurement, which was not present in the literature until now.

Paper 8 provides a mathematical theory, which, among other things, allows to unify several different existing approaches in Finance. For example, the description of static, intertemporal, and dynamic financial markets.
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