Learning as a rational foundation for macroeconomics and finance

Expectations play a central role in modern macroeconomics. The econometric learning approach, in line with the cognitive consistency principle, models agents as forming expectations by estimating and updating subjective forecasting models in real time. This approach provides a stability test for RE equilibria and a selection criterion in models with multiple equilibria. Further features of learning – such as discounting of older data, use of misspecified models or heterogeneous choice by agents between competing models – generate novel learning dynamics. Empirical applications are reviewed and the roles of the planning horizon and structural knowledge are discussed. We develop several applications of learning with relevance to macroeconomic policy: the scope of Ricardian equivalence, appropriate specification of interest-rate rules, implementation of price-level targeting to achieve learning stability of the optimal RE equilibrium and whether, under learning, price-level targeting can rule out the deflation trap at the zero lower bound.cognitive consistency; E-stability; least-squares; persistent learning dynamics; business cycles; monetary policy; asset prices

Automata and rational expressions

This text is an extended version of the chapter 'Automata and rational expressions' in the AutoMathA Handbook that will appear soon, published by the European Science Foundation and edited by JeanEricPin

Rational foundation of GR in terms of statistical mechanic in the AdS/CFT framework

In this article, we work out the microscopic statistical foundation of the supergravity description of the simplest 1/2 BPS sector in the AdS(5)/CFT(4). Then, all the corresponding supergravity observables are related to thermodynamical observables, and General Relativity is understood as a mean-field theory. In particular, and as an example, the Superstar is studied and its thermodynamical properties clarified.Comment: 13 pages, 6 eps figures, latex, some improvements introduced, reference added, typos correcte

Modular invariance of trace functions in orbifold theory

The goal of the present paper is to provide a mathematically rigorous foundation to certain aspects of rational orbifold conformal field theory, in other words the theory of rational vertex operator algebras and their automorphisms. Under a certain finiteness condition on a rational vertex operator algebra V which holds in all known examples, we determine the precise numbers of g-twisted sectors for any automorphism g of V of finite order. We prove that the trace functions and correlations functions associated with such twisted sectors are holomorphic functions in the upper half-plane and, under suitable conditions, afford a representations of the modular group of the type prescribed in string theory. We establish the rationality of conformal weights and central charge. In addition to conformal field theory itself, where our conclusions are required on physical grounds, there are applications to the generalized Moonshine conjectures of Conway-Norton-Queen and to equivariant elliptic cohomology.Comment: Latex 58 pages, several typos are corrected and the statements of some main results are clarifie

Learning without Recall: A Case for Log-Linear Learning

We analyze a model of learning and belief formation in networks in which agents follow Bayes rule yet they do not recall their history of past observations and cannot reason about how other agents' beliefs are formed. They do so by making rational inferences about their observations which include a sequence of independent and identically distributed private signals as well as the beliefs of their neighboring agents at each time. Fully rational agents would successively apply Bayes rule to the entire history of observations. This leads to forebodingly complex inferences due to lack of knowledge about the global network structure that causes those observations. To address these complexities, we consider a Learning without Recall model, which in addition to providing a tractable framework for analyzing the behavior of rational agents in social networks, can also provide a behavioral foundation for the variety of non-Bayesian update rules in the literature. We present the implications of various choices for time-varying priors of such agents and how this choice affects learning and its rate.Comment: in 5th IFAC Workshop on Distributed Estimation and Control in Networked Systems, (NecSys 2015

On the Micro-foundations of Money: The Capitol Hill Baby-Sitting Co-op.

This paper contributes to the micro-foundation of money in centralized markets with idiosyncratic uncertainty. It shows existence of stationary monetary equilibria and ensures that there is an optimum quantity of money. The rational solution of our model is compared with actual behavior in a laboratory experiment. The experiment gives support to the theoretical approach.micro foundations of money; optimal quantity of money

A Theory of Natural Addiction

Economic theories of rational addiction aim to describe consumer behavior in the presence of habit-forming goods. We provide a biological foundation for this body of work by formally specifying conditions under which it is optimal to form a habit. We demonstrate the empirical validity of our thesis with an in-depth review and synthesis of the biomedical literature concerning the action of opiates in the mammalian brain and their eects on behavior. Our results lend credence to many of the unconventional behavioral assumptions employed by theories of rational addiction, including adjacent complementarity and the importance of cues, attention, and self-control in determining the behavior of addicts. We oer evidence for the special case of the opiates that "harmful" addiction is the manifestation of a mismatch between behavioral algorithms encoded in the human genome and the expanded menu of choices faced by consumers in the modern world

Being Rational and Being Wrong

Do people tend to be overconfident in their opinions? Many think so. They’ve run studies to test whether people are calibrated: whether their confidence in their opinions matches the proportion of those opinions that are true. Under certain conditions, people are systematically “over-calibrated”—for example, of the opinions they’re 80% confident in, only 60% are true. From this observed over-calibration, it’s inferred that people are irrationally overconfident. My question: When—and why—is this inference warranted? Answering this question requires articulating a general connection between being rational and being right—something extant studies have not done. I show how to do so using the notion of deference. This provides a theoretical foundation to calibration research, but also reveals a flaw: the connection between being rational and being right is much weaker than is commonly assumed; as a result, rational people can often be expected to be miscalibrated. Thus we can’t test whether people are overconfident by simply testing whether they are over-calibrated; instead, we must first predict the expected rational deviations from calibration, and then compare those predictions to people’s performance. I show how in principle this can be done—and that doing so has the potential to overturn the standard interpretation of robust empirical effects. In short: rational people can be expected to be wrong more often than you might think

Punishment diminishes the benefits of network reciprocity in social dilemma experiments

Network reciprocity has been widely advertised in theoretical studies as one of the basic cooperation-promoting mechanisms, but experimental evidence favoring this type of reciprocity was published only recently. When organized in an unchanging network of social contacts, human subjects cooperate provided the following strict condition is satisfied: The benefit of cooperation must outweigh the total cost of cooperating with all neighbors. In an attempt to relax this condition, we perform social dilemma experiments wherein network reciprocity is aided with another theoretically hypothesized cooperation-promoting mechanism—costly punishment. The results reveal how networks promote and stabilize cooperation. This stabilizing effect is stronger in a smaller-size neighborhood, as expected from theory and experiments. Contrary to expectations, punishment diminishes the benefits of network reciprocity by lowering assortment, payoff per round, and award for cooperative behavior. This diminishing effect is stronger in a larger-size neighborhood. An immediate implication is that the psychological effects of enduring punishment override the rational response anticipated in quantitative models of cooperation in networks.We thank J. H. Lee for useful discussions. M.J. and Z.W. were, respectively, supported by the Research Grant Program of Inamori Foundation and the Chinese Young 1000 Talents Plan. B.P. received support from the Slovenian Research Agency (ARRS) and the Croatian Science Foundation through Projects J5-8236 and 5349, respectively. S.H. thanks the Israel-Italian collaborative project Network Cyber Security (NECST), Israel Science Foundation, Office of Naval Research (ONR), Japan Science Foundation, and the US-Israel Binational Science Foundation and the US National Science Foundation (BSF-NSF) for financial support. The Boston University Center for Polymer Studies is supported by NSF Grants PHY-1505000, CMMI-1125290, and CHE-1213217, by Defense Threat Reduction Agency (DTRA) Grant HDTRA1-14-1-0017, and by Department of Energy (DOE) Contract DE-AC07-05Id14517. (Inamori Foundation; Chinese Young 1000 Talents Plan; J5-8236 - Slovenian Research Agency (ARRS); 5349 - Croatian Science Foundation; Israel-Italian collaborative project Network Cyber Security (NECST); Israel Science Foundation; Office of Naval Research (ONR); Japan Science Foundation; US-Israel Binational Science Foundation; US National Science Foundation (BSF-NSF); PHY-1505000 - NSF; CMMI-1125290 - NSF; CHE-1213217 - NSF; HDTRA1-14-1-0017 - Defense Threat Reduction Agency (DTRA); DE-AC07-05Id14517 - Department of Energy (DOE))Published versio