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Misspecified Beliefs

Paper Session

Friday, Jan. 3, 2025 8:00 AM - 10:00 AM (PST)

Hilton San Francisco Union Square
Hosted By: Econometric Society
  • Chair: Aislinn Bohren, University of Pennsylvania

Evolutionarily Stable (Mis)specifications: Theory and Applications

Kevin He
,
University of Pennsylvania
Jonathan Alan Libgober
,
University of Southern California

Abstract

Toward explaining the persistence of biased inferences, we propose a framework to evaluate competing (mis)specifications in strategic settings. Agents with heterogeneous (mis)specifications coexist and draw Bayesian inferences about their environment through repeated play. The relative stability of (mis)specifications depends on their adherents’ equilibrium payoffs. A key mechanism is the learning channel: the endogeneity of perceived best replies due to inference. We characterize when a rational society is only vulnerable to invasion by some misspecification through the learning channel. The learning channel leads to new stability phenomena, and can confer an evolutionary advantage to otherwise detrimental biases in economically relevant applications.

Dynamic Concern for Misspecification

Giacomo Lanzani
,
Harvard University

Abstract

We consider an agent who posits a set of probabilistic models for the
payoff-relevant outcomes. The agent has a prior over this set but fears the
actual model is omitted and hedges against this possibility. The concern for
misspecification is endogenous: If a model explains the previous
observations well, the concern attenuates. We show that different static
preferences under uncertainty (subjective expected utility, maxmin, robust
control) arise in the long run, depending on how quickly the agent becomes
unsatisfied with unexplained evidence and whether they are misspecified. The
misspecification concern's endogeneity naturally induces behavior cycles,
and we characterize the limit action frequency. This model is consistent
with the evidence on monetary policy cycles and choices in the face of
complex tax schedules. Finally, we axiomatize in terms of observable choices
this decision criterion and how quickly the agent adjusts their
misspecification concern.

Robust Comparative Statics with Misspecified Bayesian Learning

Aniruddha Ghosh
,
Johns Hopkins University

Abstract

We present novel monotone comparative statics results for steady state behavior in a dynamic optimization environment with misspecified Bayesian learning. We consider a
generalized framework, based on Esponda and Pouzo (2021), wherein a Bayesian learner facing a dynamic optimization problem has a prior on a set of parameterized transition
probability functions (models) but is misspecified in the sense that the true process is not within this set. In the steady state, the learner infers the model that best-fits the data generated by their actions, and in turn, their actions are optimally chosen given their inferred model. We characterize conditions on the primitives of the environment, and in particular, over the set of models under which the steady state distribution over
states and actions and inferred models exhibit monotonic behavior. Further, we offer a new theorem on the existence of a steady state on the basis of a monotonicity argument.
Lastly, we provide an upper bound on the cost of misspecification, again in terms of
the primitives of the environment. We demonstrate the utility of our results for several
environments of general interest, including forecasting models, dynamic effort-task, and
optimal consumption-savings problems

The Empirical Content of Bayesianism

Pooya Molavi
,
Northwestern University

Abstract

This paper characterizes the conditions under which the observed beliefs of a group of agents are consistent with Bayesian updating. Beliefs are consistent with Bayesianism if they arise from the application of Bayes’ rule given some subjective distribution for the state and the signals agents observe between periods. The paper’s main finding is that beliefs are consistent with Bayesianism if and only if the mean of the distribution of poste- riors is uniformly absolutely continuous with respect to the prior. Furthermore, the paper shows that the existing results on the empirical content of Bayesianism rely on additional restrictions on permissible subjective distributions, such as the requirement that agents have correct beliefs about the distribution of signals.
JEL Classifications
  • D8 - Information, Knowledge, and Uncertainty