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pendence of choice probabilities on deadlines in the softmax form
pt (a;A) =
e(t)u(a)+(a)
P
b2A e(t)u(b)+(b)
where: pt (a;A) is the probability that alternative a is selected from the set A of feasible
alternatives if t is the time available to decide, is a time dependent accuracy para-
meter/unit cost of information, u is a time independent utility function, and is an
alternative-speci c bias that determines the initial choice probability and reects prior
information.1
Softmax (also known as Multinomial Logit Model, when is constant) is the most
widely used model of preference discovery in all elds of decision making, from Rational
Inattention to Discrete Choice Analysis, from Neuroscience to Quantal Response Equilib-
rium. Our axiomatic characterization of softmax permits to test empirically its descriptive
validity as a theory of agents(possibly bounded) rationality, and to elicit its parameters.
Moreover, it sheds light on the behavioral features of the Heteroscedastic Multinomial
Logit Model and re nes its testable implications. Our neuro-computational foundation provides a biologically inspired algorithm that may explain softmax emergence in intelligent behavior and that naturally relates multi-alternative choice with the classical Drift Di¤usion Model paradigm of binary choice.
Learning, Uncertainty and Choices
Paper Session
Friday, Jan. 3, 2020 10:15 AM - 12:15 PM (PDT)
- Chair: Fabio Angelo Maccheroni, Bocconi University
Ambiguous Information
Abstract
How do agents react to ambiguous information? We test this in an experiment in which a piece of information can be truthful or not based on the draw from a 2-color Ellsberg urn. We measure subjects’ attitude after the information and their willingness to pay for the information itself. In one treatment, the information pertains to the draw from a 50/50 risky urn; in the other, it pertains to the draw from an ambiguous urn. We also measure subjects’ ambiguity aversion. Different theories of updating under ambiguity make different predictions for our experiment, allowing us to test them. We find that when the information pertains to the draw from a risky urn, ambiguity averse and neutral subjects 1) do not react to the information and 2) value it (on average) zero. Ambiguity loving subjects, instead, do increase their valuation. When the information pertains to the draw from an ambiguous urn, ambiguity averse subjects increase their valuation; while ambiguity seeking ones decrease it. Overall, our results are not compatible with Full-Bayesian or Maximum-Likelihood updating of sets of priors; they instead support the Proxy Updating rule.Macroeconomics with Misspecification and Learning: A General Theory and Applications
Abstract
This paper explores a form of bounded rationality where agents learn about the economy with possibly misspecified models. I consider a recursive general-equilibrium framework that nests a large class of macroeconomic models. Misspecification is represented as a constraint on the set of beliefs agents can entertain. I introduce the solution concept of constrained-rational-expectations equilibrium (CREE), in which each agent selects the belief from her constrained set that is closest to the endogenous distribution of observables in the Kullback–Leibler divergence. If the set of permissible beliefs contains the rational-expectations equilibria (REE), then the REE are CREE; otherwise, they are not. I show that a CREE exists, that it arises naturally as the limit of adaptive and Bayesian learning, and that it incorporates a version of the Lucas critique. I then apply CREE to a particular novel form of bounded rationality where beliefs are constrained to factor models with a small number of endogenously chosen factors. Misspecification leads to amplification or dampening of shocks and history dependence. The calibrated economy exhibits hump-shaped impulse responses and co-movements in consumption, output, hours, and investment that resemble business-cycle fluctuations.Short and Long Run Uncertainty
Abstract
Uncertainty appears to have both a short-run and a long-run component, which we measure using firm and macro implied volatility data from equity options of 30 days to 5 years duration. We ask what may be driving uncertainty over these different time horizons, finding that policy uncertainty, interest rate volatility, and currency volatility are particularly associated with long-run uncertainty, while oil price volatility and CEO turnover appear to impact short- and long-run uncertainty about equally. Examining a panel of over 4,000 firms from 1996 to 2016 we find that investment is relatively more sensitive to long-run uncertainty than hiring, and about as sensitive to long-run uncertainty as R&D. Investment is also more sensitive to the overall level of uncertainty than both R&D and hiring, holding fixed the relative magnitude of short- versus longrun uncertainty. We investigate the channels underlying these different sensitivies to short- versus long-run uncertainty, and show empirically and in simulations that lower depreciation rates and higher adjustment costs explain why investment is more sensitive to longer-run uncertainty. Collectively, these results suggest that recent events that have raised long-run policy uncertainty may be particularly damaging to growth by reducing investment and R&D.Multinomial Logit Processes and Preference Discovery: Outside and Inside the Black Box
Abstract
We provide both an axiomatic and a neuro-computational characterization of the de-pendence of choice probabilities on deadlines in the softmax form
pt (a;A) =
e(t)u(a)+(a)
P
b2A e(t)u(b)+(b)
where: pt (a;A) is the probability that alternative a is selected from the set A of feasible
alternatives if t is the time available to decide, is a time dependent accuracy para-
meter/unit cost of information, u is a time independent utility function, and is an
alternative-speci c bias that determines the initial choice probability and reects prior
information.1
Softmax (also known as Multinomial Logit Model, when is constant) is the most
widely used model of preference discovery in all elds of decision making, from Rational
Inattention to Discrete Choice Analysis, from Neuroscience to Quantal Response Equilib-
rium. Our axiomatic characterization of softmax permits to test empirically its descriptive
validity as a theory of agents(possibly bounded) rationality, and to elicit its parameters.
Moreover, it sheds light on the behavioral features of the Heteroscedastic Multinomial
Logit Model and re nes its testable implications. Our neuro-computational foundation provides a biologically inspired algorithm that may explain softmax emergence in intelligent behavior and that naturally relates multi-alternative choice with the classical Drift Di¤usion Model paradigm of binary choice.
JEL Classifications
- D8 - Information, Knowledge, and Uncertainty
- D9 - Micro-Based Behavioral Economics