Andrew Ellis

Working papers

  • Limited belief propagation and contingent thinking, with R. Spiegler. [slides]
    Abstract. An agent updates her beliefs over a set of variables after observing some of them. We provide a representation of updated beliefs that captures limited propagation of her observation's implications through the directed acyclic graph that represents the relations between all variables. Failure of contingent thinking occurs when she performs fewer inference steps from unobserved variables than observed ones, leading to correlation neglect and violations of iterated expectations. Our framework offers a new perspective on existing experiments about contingent thinking and suggests new directions. We characterize the model's relationship with familiar Bayesian and non-Bayesian benchmarks, and illustrate it with applications to public-good provision and social learning games.
  • Equilibrium Information Aggregation under Machine Learning, with M. Piccione and S. Zhang. [slides]
    Abstract. We introduce a framework for studying the equilibrium effects of machine learning. Agents process information using a Chow and Liu (1968) tree, a widely-used machine learning procedure that admits a closed-form solution. We apply the model to an asset market with dispersed information based on Hellwig (1980). The price mechanism fails to aggregate the information extracted by the algorithm, even approximately. While there are partial equilibrium benefits from access to algorithms, the equilibrium price aggregates less information than the rational equilibrium. Equilibrium typically features diverse world-models, demands, and utilities, even with ex ante identical agents.
  • Subjective Causality in Choice, with H. C. Thysen.
    Abstract. An agent makes a stochastic choice from a set of lotteries. She infers the outcomes of her options using a subjective causal model represented by a directed acyclic graph, and consequently may misinterpret correlation as causation. Her choices affect her inferences which in turn affect her choices, so the two together must form a personal equilibrium. We show how an analyst can identify the agent's subjective causal model from her random choice rule. In addition, we provide necessary and sufficient conditions that allow an analyst to test whether the agent's behavior is compatible with the model.
  • Identifying Assumptions and Research Dynamics, with R. Spiegler. [slides]
    Abstract. Abstract. A representative researcher has repeated opportunities for empirical research. To process findings, she must impose an "identifying assumption." She conducts research when the assumption is sufficiently plausible (taking into account both current beliefs and the quality of the opportunity), and updates beliefs as if the assumption were perfectly valid. We study the dynamics of this learning process. While the rate of research cannot always increase over time, research slowdown is possible. We characterize environments in which the rate is constant. Long-run beliefs can exhibit history-dependence and "false certitude." We apply the model to stylized examples of empirical methodologies: experiments, various causal-inference techniques, and "calibration."
  • Misspecified Higher-Order Beliefs and Failures of Social Learning, with M.R. Levy and B. Szentes [pdf coming soon].
    Abstract. We study a model of social learning with misspecified higher-order beliefs. The environment is such that with rational beliefs, players' actions would converge to the public information optimal action. A small misperception at an arbitrarily high level of the belief hierarchy may lead to predetermined learning: agents become arbitrarily convinced that a given state obtains, independently of the true state of the world.