Periodic Reporting for period 4 - INDIMACRO (Individual decisions and macroeconomic robustness)
Okres sprawozdawczy: 2020-04-01 do 2021-09-30
The nature of the ERC project was the exploration, from a decision theoretic point of view, of the nature of uncertainty and rationality featured in many economic applications.
• Estimation of objective (physical) probabilistic models of the states that are relevant for many economically important decision problems is sometimes very hard, sometimes just impossible due to the lack of data, and in most cases affected by the decision makers’ actual choices. For this reason decision makers (henceforth, DMs) are confronted with a set of possible models rather than a single one and often they are not sure if the true model belongs to this set.
• Rationality requires to deal with the resulting model uncertainty. The analysis then leads to optimal actions/policies that are robust with respect to model uncertainty. Moreover, rationality requires that no mistakes are made in making choices.
A) How do we incorporate the aforementioned uncertainty in the current economic models which often feature only one probability model assumed to the correct one?
B) Can we study DMs who make choices that are often wrong, but share a basic underlying notion of rationality?
The formal environments and modelling choices aim at broadening the scope of modern decision theoretic methods in order to establish a common language for the two fields, which will favor cross fertilization, as well as it will broaden and deepen the understanding of the role of uncertainty in economic decisions.
• Estimation of objective (physical) probabilistic models of the states that are relevant for many economically important decision problems is sometimes very hard, sometimes just impossible due to the lack of data, and in most cases affected by the decision makers’ actual choices. For this reason decision makers (henceforth, DMs) are confronted with a set of possible models rather than a single one and often they are not sure if the true model belongs to this set.
• Rationality requires to deal with the resulting model uncertainty. The analysis then leads to optimal actions/policies that are robust with respect to model uncertainty. Moreover, rationality requires that no mistakes are made in making choices.
A) How do we incorporate the aforementioned uncertainty in the current economic models which often feature only one probability model assumed to the correct one?
B) Can we study DMs who make choices that are often wrong, but share a basic underlying notion of rationality?
The formal environments and modelling choices aim at broadening the scope of modern decision theoretic methods in order to establish a common language for the two fields, which will favor cross fertilization, as well as it will broaden and deepen the understanding of the role of uncertainty in economic decisions.
The team has been working on several projects connected to the initial ERC proposal. In particular, 21 papers have been completed (16 published and 5 at a working paper stage). I am going to only discuss a handful of them, some of them were discussed already in the midterm report.
1. In the paper “Making Decisions under Model Misspecification”, joint with S.Cerreia-Vioglio and L.P.Hansen we use decision theory to confront uncertainty that is sufficiently broad to incorporate models as approximations. We presume the existence of a featured collection of what we call structured models that have explicit substantive motivations. The decision maker confronts uncertainty through the lens of these models, but also views these models as simplifications, and hence, as misspecified. We extend min-max analysis under model ambiguity to incorporate the uncertainty induced by acknowledging that the models used in decision-making are simplified approximations. Formally, we provide an axiomatic rationale for a decision criterion that incorporates model misspecification concerns. This paper concerns question A.
2. In the paper “Multinomial logit processes and preference discovery” joint with S.Cerreia-Vioglio and A. Rustichini, we study and axiomatically characterize the dependence of choice probabilities on time in the softmax (or Multinomial Logit Process). MLP is the most widely used model of preference discovery in all fields of decision making from Quantal Response Equilibria to Discrete Choice Analysis, from Psychophysics to Combinatorial Optimization. Our axiomatic characterization of softmax permits to understand its conceptual underpinnings as a theory of agents’ behavior, as well as to empirically test its descriptive validity. This paper concerns question B.
3. In the paper “A Canon of Probabilistic Rationality” joint with S. Cerreia-Vioglio, P. O. Lindberg, Fabio Maccheroni, and A. Rustichini, we show how an important property of stochastic choice, if satisfied, makes random choices of agents the result of a tie breaking rule among optimal alternatives. This paper concerns question A.
4. In the paper “Sources of Uncertainty and Subjective Prices” joint with V. Cappelli, S. Cerreia-Vioglio, F. Maccheroni and S. Minardi, we develop a general framework to study source-dependent preferences in economic contexts. Our model evaluates profiles source-wise, by computing the source-dependent certainty equivalents; the latter are converted into the unit of account of a common source and then aggregated into a unique evaluation. By viewing time and location as instances of sources, we show that subjective discount factors and subjective exchange rates are emblematic examples of subjective prices. Finally, we use the model to explore the implications on optimal portfolio allocations and home bias. This paper concerns questions A and B.
5. In the paper “Absolute and Relative Ambiguity Aversion: A Preferential Approach” joint with S. Cerreia-Vioglio and F. Maccheroni, we provide a framework to address how the uncertainty attitudes of a decision maker change while 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. This paper concerns question A.
6. 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 AND e illustrate the theory in a monetary policy setting. We conclude by discussing more general cases of self-confirming policies. This paper concerns question A and B.
7. In the paper Experimental Cost of Information joint with T. Denti and A. Rustichini, we relate two representations of the cost of acquiring information: a cost that depends on the experiment performed, as in statistical decision theory, and a cost that depends on the distribution of posterior beliefs, as in the theory of rational inattention. In many cases of interests, the two representations prove to be inconsistent with each other. We provide a systematic analysis of the inconsistency, propose a way around it, and apply our findings to information acquisition in games. This paper concerns question A and B.
All the projects mentioned above have been described with their obtained outcomes and achieved goals. In terms of disseminations the papers have all been published in top field journal or are revise and resubmit at Top5 general audiences’ journals with good prospects. Moreover, the papers have been presented in several seminars at different institutions, American and European, as well as conferences.
1. In the paper “Making Decisions under Model Misspecification”, joint with S.Cerreia-Vioglio and L.P.Hansen we use decision theory to confront uncertainty that is sufficiently broad to incorporate models as approximations. We presume the existence of a featured collection of what we call structured models that have explicit substantive motivations. The decision maker confronts uncertainty through the lens of these models, but also views these models as simplifications, and hence, as misspecified. We extend min-max analysis under model ambiguity to incorporate the uncertainty induced by acknowledging that the models used in decision-making are simplified approximations. Formally, we provide an axiomatic rationale for a decision criterion that incorporates model misspecification concerns. This paper concerns question A.
2. In the paper “Multinomial logit processes and preference discovery” joint with S.Cerreia-Vioglio and A. Rustichini, we study and axiomatically characterize the dependence of choice probabilities on time in the softmax (or Multinomial Logit Process). MLP is the most widely used model of preference discovery in all fields of decision making from Quantal Response Equilibria to Discrete Choice Analysis, from Psychophysics to Combinatorial Optimization. Our axiomatic characterization of softmax permits to understand its conceptual underpinnings as a theory of agents’ behavior, as well as to empirically test its descriptive validity. This paper concerns question B.
3. In the paper “A Canon of Probabilistic Rationality” joint with S. Cerreia-Vioglio, P. O. Lindberg, Fabio Maccheroni, and A. Rustichini, we show how an important property of stochastic choice, if satisfied, makes random choices of agents the result of a tie breaking rule among optimal alternatives. This paper concerns question A.
4. In the paper “Sources of Uncertainty and Subjective Prices” joint with V. Cappelli, S. Cerreia-Vioglio, F. Maccheroni and S. Minardi, we develop a general framework to study source-dependent preferences in economic contexts. Our model evaluates profiles source-wise, by computing the source-dependent certainty equivalents; the latter are converted into the unit of account of a common source and then aggregated into a unique evaluation. By viewing time and location as instances of sources, we show that subjective discount factors and subjective exchange rates are emblematic examples of subjective prices. Finally, we use the model to explore the implications on optimal portfolio allocations and home bias. This paper concerns questions A and B.
5. In the paper “Absolute and Relative Ambiguity Aversion: A Preferential Approach” joint with S. Cerreia-Vioglio and F. Maccheroni, we provide a framework to address how the uncertainty attitudes of a decision maker change while 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. This paper concerns question A.
6. 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 AND e illustrate the theory in a monetary policy setting. We conclude by discussing more general cases of self-confirming policies. This paper concerns question A and B.
7. In the paper Experimental Cost of Information joint with T. Denti and A. Rustichini, we relate two representations of the cost of acquiring information: a cost that depends on the experiment performed, as in statistical decision theory, and a cost that depends on the distribution of posterior beliefs, as in the theory of rational inattention. In many cases of interests, the two representations prove to be inconsistent with each other. We provide a systematic analysis of the inconsistency, propose a way around it, and apply our findings to information acquisition in games. This paper concerns question A and B.
All the projects mentioned above have been described with their obtained outcomes and achieved goals. In terms of disseminations the papers have all been published in top field journal or are revise and resubmit at Top5 general audiences’ journals with good prospects. Moreover, the papers have been presented in several seminars at different institutions, American and European, as well as conferences.
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.
Pertaining question A, all the papers described above and many others decribed in the previous report have pushed the frontier in the study of choice under uncertainty and their applications. Compared to the existing literature, we now have viable models, descriptive and normative, that allow for the possibility of discussing and taking into account the fact that the probabilistic information of the decision maker is imprecise and her attitudes toward uncertainty might vary as the underlying wealth is changing or the source of information might be changing. None of this was possible before.
Pertaining question B, we developed a model which described apparent random choices as the result of an optimal algorithm which features pairwise choices with a tiny component of error. In doing so, we advanced the current understanding of stochastic choices, that typically only feature binary choices to a setup of choice over many alternatives: a much more common framework in Economics.
Pertaining question A, all the papers described above and many others decribed in the previous report have pushed the frontier in the study of choice under uncertainty and their applications. Compared to the existing literature, we now have viable models, descriptive and normative, that allow for the possibility of discussing and taking into account the fact that the probabilistic information of the decision maker is imprecise and her attitudes toward uncertainty might vary as the underlying wealth is changing or the source of information might be changing. None of this was possible before.
Pertaining question B, we developed a model which described apparent random choices as the result of an optimal algorithm which features pairwise choices with a tiny component of error. In doing so, we advanced the current understanding of stochastic choices, that typically only feature binary choices to a setup of choice over many alternatives: a much more common framework in Economics.