[Paper Review] Robust Misspecified Models and Paradigm Shifts

Cuimin Ba|arXiv (Cornell University)|Jun 24, 2021

Opinion Dynamics and Social Influence4 citations

TL;DR

This paper introduces a model-switching framework in which agents evaluate and switch between competing models based on a thresholded Bayes factor, showing that misspecified models can persist robustly due to high asymptotic accuracy and tight priors—even outperforming correct models. The key contribution is a characterization of model persistence in terms of two primitives: predictive accuracy and prior concentration around equilibrium outcomes.

ABSTRACT

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 the reporting bias.

Motivation & Objective

• To address the gap in misspecified learning literature by modeling active model switching rather than dogmatic model use.
• To understand under what conditions misspecified models persist despite observing infinite data and having access to better alternatives.
• To provide a learning foundation for systemic biases by analyzing model persistence in real-world contexts like overconfidence and political polarization.
• To characterize model robustness using two measurable primitives: asymptotic accuracy and prior tightness around equilibrium outcomes.
• To show that simple, misspecified models with entrenched priors can be more robust than correctly specified models.

Proposed method

• Agents use a threshold rule to switch between two models based on the Bayes factor comparing the competing model to the current one.
• The agent updates beliefs using Bayesian updating within the current model and selects actions based on posterior expectations.
• Model persistence is analyzed through three robustness notions: local, global, and p-absorbing robustness, with p-absorbing being central to long-run persistence.
• The framework uses self-confirming equilibria (SCEs) as the target outcome patterns, where model predictions align with observed data under the model's assumptions.
• Theoretical analysis derives conditions under which a model remains persistent, focusing on the interplay between the model's predictive accuracy and the concentration of the prior around equilibrium outcomes.
• The paper constructs counterfactual models with additional DGPs to test the robustness of persistence, showing that back-and-forth switching does not invalidate the core results.

Experimental results

Research questions

• RQ1 Under what conditions does a misspecified model persist even when the correct model is available and infinitely many data points are observed?
• RQ2 Why do simple, biased models such as overconfidence or binary political views persist despite being factually incorrect?
• RQ3 How does the stickiness of model switching—controlled by a threshold on the Bayes factor—affect the long-run persistence of a model?
• RQ4 What role does prior concentration around equilibrium outcomes play in determining model robustness?
• RQ5 Can a misspecified model be more robust than a correctly specified one, and if so, under what conditions?

Key findings

• Misspecified models can be robustly persistent even when the correct model is available and infinitely many data points are observed, due to high asymptotic accuracy and tight priors.
• A model is globally robust if and only if it is p-absorbing and has high prior tightness around the set of p-absorbing self-confirming equilibria.
• Overconfidence in one’s ability is more robust than underconfidence in an effort-choice problem because it leads to higher asymptotic accuracy in predicting outcomes.
• A simplistic binary view of politics is more robust than the correct, nuanced view when individuals consume media with reporting bias, due to better alignment with observed data patterns.
• Simple, misspecified models with entrenched priors can be more robust than correctly specified models, challenging the assumption that correctness guarantees persistence.
• Theoretical results hold even under a conservative definition of persistence requiring no model switching, as long as the agent eventually settles on a model and remains there.