Constrained data-fitters

We study maximum-likelihood estimation and updating, subject to computational, cognitive, or behavioral constraints. We jointly characterize constrained estimates and updating within a framework reminiscent of a machine learning algorithm. Without frictions, the framework simplifies to standard maximum-likelihood estimation and Bayesian updating. Our central finding is that under certain intuitive cognitive constraints, simple models yield the most effective constrained fit to data - more complex models offer a superior fit, but the agent may lack the capability to assess this fit accurately. With some additional structure, the agent's problem is isomorphic to a familiar rational inattention problem.