This paper develops a general framework to study how misinterpreting information impacts learning. Our main result is a simple criterion to characterize long‐run beliefs based on the underlying form of misspecification. We present this characterization in the context of social learning, then highlight how it applies to other learning environments, including individual learning. A key contribution is that our characterization applies to settings with model heterogeneity and provides conditions for entrenched disagreement. Our characterization can be used to determine whether a representative agent approach is valid in the face of heterogeneity, study how differing levels of bias or unawareness of others' biases impact learning, and explore whether the impact of a bias is sensitive to parametric specification or the source of information. This unified framework synthesizes insights gleaned from previously studied forms of misspecification and provides novel insights in specific applications, as we demonstrate in settings with partisan bias, overreaction, naive learning, and level‐k reasoning.

Economists often measure discrimination as disparities arising from the direct effects of group identity. We develop new tools to model and measure systemic discrimination, capturing how discrimination in other decisions indirectly contributes to disparities. A novel experimental design, the iterated audit, identifies systemic discrimination. We illustrate these new tools in two field experiments. The first experiment shows how racial discrimination can accumulate across multiple rounds of hiring through the interaction of two forces: greater discrimination against inexperienced workers, which affects the opportunity to obtain experience, and high subsequent returns to experience. The second experiment shows how gender-based differences in the language of recommendation letters can translate into systemic gender discrimination in STEM hiring. We discuss how our findings qualify previous results on direct discrimination and how our tools can be used to target policy interventions.

We model the dynamics of discrimination and show how its evolution can identify the underlying source. We test these theoretical predictions in a field experiment on a large online platform where users post content that is evaluated by other users on the platform. We assign posts to accounts that exogenously vary by gender and evaluation histories. With no prior evaluations, women face significant discrimination. However, following a sequence of positive evaluations, the direction of discrimination reverses: women’s posts are favored over men’s. Interpreting these results through the lens of our model, this dynamic reversal implies discrimination driven by biased beliefs.

We formalize the optimal design of experiments when there is interference between units, i.e. an individual's outcome depends on the outcomes of others in her group. We focus on randomized saturation designs, two-stage experiments that first randomize treatment saturation of a group, then individual treatment assignment. We map the potential outcomes framework with partial interference to a regression model with clustered errors, calculate standard errors of randomized saturation designs, and derive analytical insights about the optimal design. We show that the power to detect average treatment effects declines precisely with the ability to identify novel treatment and spillover effects.