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“Big data” gives markets access to previously unmeasured characteristics of individual agents. Policymakers must decide whether and how to regulate the use of this data. We study how new data affects incentives for agents to exert effort in settings such as the labor market, where an agent's quality is initially unknown but is forecast from an observable outcome. We show that measurement of a new covariate has a systematic effect on the average effort exerted by agents, with the direction of the effect determined by whether the covariate is informative about long‐run quality versus a shock to short‐run outcomes. For a class of covariates satisfying a statistical property that we callstrong homoskedasticity, this effect is uniform across agents. More generally, new measurements can impact agents unequally, and we show that these distributional effects have a first‐order impact on social welfare. 

Model misspecification is a common approach to model belief formation distortions. Misspecified models can be decomposed into two classes of distortions: prospective and retrospective biases (Bohren and Hauser 2023). Prospective biases correspond to distortions in forecasting future beliefs, while retrospective biases correspond to distortions in interpreting information ex post. We disentangle the impact of these two distortions on optimal lending contracts in the context of an entrepreneur who borrows to invest in a project. The entrepreneur learns about project quality from a signal, which she interprets with a misspecified model. A lender leverages each form of bias in distinct ways. 

An agent has access to multiple information sources, each modeled as a Brownian motion whose drift provides information about a different component of an unknown Gaussian state. Information is acquired continuously—where the agent chooses both which sources to sample from, and also how to allocate attention across them—until an endogenously chosen time, at which point a decision is taken. We demonstrate conditions on the agent's prior belief under which it is possible to exactly characterize the optimal information acquisition strategy. We then apply this characterization to derive new results regarding: (1) endogenous information acquisition for binary choice, (2) the dynamic consequences of attention manipulation, and (3) strategic information provision by biased news sources. 

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. 

Abstract We develop a model of social learning from complementary information: short-lived agents sequentially choose from a large set of flexibly correlated information sources for prediction of an unknown state, and information is passed down across periods. Will the community collectively acquire the best kinds of information? Long-run outcomes fall into one of two cases: (i) efficient information aggregation, where the community eventually learns as fast as possible; (ii) “learning traps,” where the community gets stuck observing suboptimal sources and information aggregation is inefficient. Our main results identify a simple property of the underlying informational complementarities that determines which occurs. In both regimes, we characterize which sources are observed in the long run and how often.