Abstract We develop a general theory of omitted variable bias for a wide range of common causal parameters, including average treatment effects, average causal derivatives, and policy effects from covariate shifts. We show how plausibility judgments on the maximum explanatory power of omitted variables are sufficient to bound the bias, facilitating sensitivity analysis in otherwise complex models. Finally, we provide statistical inference methods that can leverage modern machine learning algorithms for estimation. These results allow empirical researchers to perform sensitivity analyses in a flexible class of machine-learned causal models using very simple tools. Empirical examples demonstrate the utility of our approach.

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.