3

Individuals use models to guide decisions, but many models are wrong. This paper studies which misspecified models are likely to persist when individuals also entertain alternative models. Consider an agent who uses her model to learn the relationship between action choices and outcomes. The agent exhibits sticky model switching, captured by a threshold rule such that she switches to an alternative model when it is a sufficiently better fit for the data she observes. The main result provides a characterization of whether a model persists based on two key features that are straightforward to derive from the primitives of the learning environment, namely, the model’s asymptotic accuracy in predicting the equilibrium pattern of observed outcomes and the `tightness’ of the prior around this equilibrium. I show that misspecified models can be robust in that they persist against a wide range of competing models—including the correct model—despite individuals observing an infinite amount of data. Moreover, simple misspecified models with entrenched priors can be even more robust than correctly specified models. I use this characterization to provide a learning foundation for the persistence of systemic biases in two applications. First, in an effort-choice problem, I show that overconfidence in one’s ability is more robust than underconfidence. Second, a simplistic binary view of politics is more robust than the more complex correct view when individuals consume media without fully recognizing reporting bias.

This paper explores how properties of the learning environment determine how people react to information. We develop a two-stage model of belief formation where people first reduce complexity by channeling attention to a subset of states that are representative of the observed information, then evaluate this information using Bayes’ rule subject to cognitive imprecision. The model predicts overreaction when environments are complex, signals are noisy, or priors are concentrated on intermediate states; it predicts underreaction when environments are simple, signals are precise, or priors concentrated on more extreme states. Results from a series of pre-registered experiments provide direct support for these predictions, as well as the proposed attentional mechanism. We show that the two-stage model is highly complete in capturing explainable variation in belief-updating; in particular, the interaction between the two psychological mechanisms is critical to explaining belief-formation in more complex settings. These results connect disparate findings in prior work: underreaction is typically found in laboratory studies, which feature simple learning settings, while overreaction is prevalent in financial markets, which feature more complex environments.

Social media influencers often endorse products under brand sponsorships without disclosing the nature of their relationship with the brand. This paper explores the incentives for truth-telling when influencers face private sponsorship opportunities and the potential consequences for consumers. While reputation concerns can encourage influencers to be truthful when promoting sponsored products, they may also lead to under-endorsement when no sponsorship opportunity exists. As sponsorship opportunities become more abundant, the quality of information transmission initially decreases before increasing. Therefore, new technologies that efficiently match influencers with sponsors may improve consumer welfare. The Federal Trade Commission’s mandatory disclosure rules are also shown to benefit consumers without necessarily harming influencers.