Asymptotic behavior of Bayesian learners with misspecified models

Esponda, Ignacio; Pouzo, Demián; Yamamoto, Yuichi

doi:10.1016/j.jet.2021.105260

Cited by 20 publications

(11 citation statements)

References 50 publications

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“…The third issue involves the combination of our multiple dimensions of policies and continuous actions. Esponda et al (2021) use stochastic approximation methods to characterise conditions for stability of steady state. These conditions rely on a discrete set of actions and are moreover easier to check and apply when a unidimensional state space is involved.…”

Section: E Convergencementioning

confidence: 99%

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Misspecified Politics and the Recurrence of Populism

Levy

Razin

Young

2022

American Economic Review

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We develop a dynamic model of political competition between two groups that differ in their subjective model of the data generating process for a common outcome. One group has a simpler model than the other group as they ignore some relevant policy variables. We show that policy cycles must arise and that simple world views—which can be interpreted as populist world views—imply extreme policy choices. Periods in which those with a more complex model govern increase the specification error of the simpler world view, leading the latter to overestimate the positive impact of a few extreme policy actions. (JEL D72, D83, K42)

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Section: E Convergencementioning

confidence: 99%

“…Hauser 2019, Esponda et al 2021, andFrick et al 2020). Our paper provides an example of how convergence can be proven in a model with multiple agents, a multidimensional state space and continuous actions.…”

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confidence: 99%

Misspecified Politics and the Recurrence of Populism

Levy

Razin

Young

2022

American Economic Review

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“…Agents' stopping decisions determine how many signals they observe about the fundamentals. Other recent papers (Esponda, Pouzo, and Yamamoto (2021), Fudenberg, Lanzani, and Strack (2021), Frick, Iijima, and Ishii (2021a), Heidhues, Kőszegi, and Strack (2021)) prove general theorems about the convergence of misspecified learning in different settings. Though not the primary contribution of this work, the convergence result in Proposition 7 deals with a setting that is not covered by these papers: a multi‐dimensional inference problem with a continuum of states, signals, and actions.…”

Section: Related Theoretical Literaturementioning

confidence: 99%

Mislearning from censored data: The gambler's fallacy and other correlational mistakes in optimal‐stopping problems

2022

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I study endogenous learning dynamics for people who misperceive intertemporal correlations in random sequences. Biased agents face an optimal‐stopping problem. They are uncertain about the underlying distribution and learn its parameters from predecessors. Agents stop when early draws are “good enough,” so predecessors' experiences contain negative streaks but not positive streaks. When agents wrongly expect systematic reversals (the “gambler's fallacy”), they understate the likelihood of consecutive below‐average draws, converge to overpessimistic beliefs about the distribution's mean, and stop too early. Agents uncertain about the distribution's variance overestimate it to an extent that depends on predecessors' stopping thresholds. I also analyze how other misperceptions of intertemporal correlation interact with endogenous data censoring.

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“…Most prior work on misspecified Bayesian learning study implications of particular errors in specific active-learning environments (i.e., when actions affect observations), including both single-agent decision problems (Nyarko, 1991;Fudenberg, Romanyuk, and Strack, 2017;Heidhues, Koszegi, and Strack, 2018;He, 2020) and multi-agent games (Bohren, 2016;Bohren and Hauser, 2018;Jehiel, 2018;Molavi, 2019;Dasaratha and He, 2020;Ba and Gindin, 2020;Frick, Iijima, and Ishii, 2021). A number of papers establish general convergence properties of misspecified learning (Esponda and Pouzo, 2016;Esponda, Pouzo, and Yamamoto, 2019;Frick, Iijima, and Ishii, 2019;Fudenberg, Lanzani, and Strack, 2020). All of the above papers take misspecifications as exogenously given.…”

Section: Related Literaturementioning

confidence: 99%

Evolutionarily Stable (Mis)specifications: Theory and Applications

Libgober

2020

Preprint

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We introduce an evolutionary framework to evaluate competing (mis)specifications in strategic situations, focusing on which misspecifications can persist over a correct specification. Agents with heterogeneous specifications coexist in a society and repeatedly match against random opponents to play a stage game. They draw Bayesian inferences about the environment based on personal experience, so their learning depends on the distribution of specifications and matching assortativity in the society. One specification is evolutionarily stable against another if, whenever sufficiently prevalent, its adherents obtain higher expected objective payoffs than their counterparts. The learning channel leads to novel stability phenomena compared to frameworks where the heritable unit of cultural transmission is a single belief instead of a specification (i.e., set of feasible beliefs). We apply the framework to linear-quadratic-normal games where players receive correlated signals but possibly misperceive the information structure. The correct specification is not evolutionarily stable against a correlational error, whose direction depends on matching assortativity. As another application, the framework also endogenizes coarse analogy classes in centipede games.

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Asymptotic behavior of Bayesian learners with misspecified models

Cited by 20 publications

References 50 publications

Misspecified Politics and the Recurrence of Populism

Misspecified Politics and the Recurrence of Populism

Mislearning from censored data: The gambler's fallacy and other correlational mistakes in optimal‐stopping problems

Evolutionarily Stable (Mis)specifications: Theory and Applications

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