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Behavioural Causal Inference

Review of Economic Studies 2026 93(2), 1323-1353
When inferring causal effects from correlational data, a common practice by professional researchers but also lay people is to control for potential confounders. Inappropriate controls produce erroneous causal inferences. I model decision-makers (DMs) who use endogenous observational data to learn actions’ causal effect on payoff-relevant outcomes. Different DM types use different controls. Their resulting choices affect the very correlations they learn from, thus calling for an equilibrium analysis of the steady-state welfare cost of bad controls. I obtain tight upper bounds on this cost. Equilibrium forces drastically reduce it when types’ sets of controls contain one another.

“Data Monkeys”: A Procedural Model of Extrapolation from Partial Statistics*

Review of Economic Studies 2017 84(4), rdx004
I present a behavioural model of a “data analyst” who extrapolates a fully specified probability distribution over observable variables from a collection of statistical data sets that cover partially overlapping sets of variables. The analyst employs an iterative extrapolation procedure, whose individual rounds are akin to the stochastic regression method of imputing missing data. Users of the procedure’s output fail to distinguish between raw and imputed data, and it functions as their practical belief. I characterize the ways in which this belief distorts the correlation structure of the underlying data generating process—focusing on cases in which the distortion can be described as the imposition of a causal model (represented by a directed acyclic graph over observable variables) on the true distribution.

The Market for Quacks

Review of Economic Studies 2006 73(4), 1113-1131
A group of n “quacks” plays a price-competition game, facing a continuum of “patients” who recover with probability α, whether they acquire a quack's “treatment”. If patients chose rationally, the market would be inactive. I assume, however, that patients choose according to a boundedly rational procedure, which reflects “anecdotal” reasoning. This element of bounded rationality has significant implications. The market for quacks is active, and patients suffer a welfare loss which behaves non-monotonically w.r.t. n and α. In an extended model that endogenizes the quacks' choice of “treatments”, the quacks minimize the force of price competition by offering maximally differentiated treatments. The patients' welfare loss is robust to market interventions, which would crowd out low-quality firms in standard models. Thus, as long as the patients' quality of reasoning is not lifted above the anecdotal level, ordinary competition policies may be ineffective.

Equilibrium in Justifiable Strategies: A Model of Reason-based Choice in Extensive-form Games

Review of Economic Studies 2002 69(3), 691-706
I explore the idea that people care about the justifiability of their decisions in the context of two-person extensive games. Each player justifies his strategy s with a belief b of the opponent's strategy which is consistent with the play path and maximally plausible (according to some exogenous criterion). We say that s is justifiable if against the ex post criticism that some other strategy s′ outperforms s against b, the player can argue that playing s′ would have exposed him to similar criticism in the opposite direction. Under a simplicity-based plausibility criterion, this concept implies systematic departures from maximizing behaviour in familiar games.

Bayesian Networks and Boundedly Rational Expectations *

Quarterly Journal of Economics 2016 131(3), 1243-1290 open access
I present a framework for analyzing decision making under imperfect understanding of correlation structures and causal relations. A decision maker (DM) faces an objective long-run probability distribution p over several variables (including the action taken by previous DMs). The DM is characterized by a subjective causal model, represented by a directed acyclic graph over the set of variable labels. The DM attempts to fit this model to p , resulting in a subjective belief that distorts p by factorizing it according to the graph via the standard Bayesian network formula. As a result of this belief distortion, the DM’s evaluation of actions can vary with their long-run frequencies. Accordingly, I define a ”personal equilibrium” notion of individual behavior. The framework enables simple graphical representations of causal-attribution errors (such as coarseness or reverse causation), and provides tools for checking rationality properties of the DM’s behavior. I demonstrate the framework’s scope of applications with examples covering diverse areas, from demand for education to public policy.

Placebo Reforms

American Economic Review 2013 103(4), 1490-1506
I study a dynamic model of strategic reform decisions that potentially affect the stochastic evolution of a publicly observed economic variable. Policy makers maximize their evaluation by a boundedly rational public. Specifically, the public follows a rule that attributes recent changes to the most recent intervention. I analyze subgame perfect equilibrium in this model when the economic variable follows a linear growth trend with noise. Equilibrium is essentially unique and stationary, bearing a subtle formal relation to optimal search models. Policy makers tend to act during crises, display risk aversion conditional on acting, and prefer interventions that induce permanent noise.

Contracting with Diversely Naive Agents

Review of Economic Studies 2006 73(3), 689-714
In standard contract-theoretic models, the underlying assumption is that agent types differ in their preference or cost parameters, and the principal's objective is to design contracts in order to screen this type. We study a contract-theoretic model in which the heterogeneity among agent types is of a “cognitive” nature. In our model, the agent has dynamically inconsistent preferences. Agent types differ only in their degree of “sophistication”, that is, their ability to forecast the change in their future tastes. We fully characterize the menu of contracts which the principal offers in order to screen the agent's sophistication. The menu does not exclude any type: it provides a perfect commitment device for relatively sophisticated types, and “exploitative” contracts which involve speculation with relatively naive types. More naive types are more heavily exploited and generate a greater profit for the principal. Our results allow us to interpret real-life contractual arrangements in a variety of industries.

A Mechanism-Design Approach to Speculative Trade

Econometrica 2007 75(3), 875-884 open access
When two parties have different prior beliefs about some future event, they can realize gains through speculative trade. Can these gains be realized when the parties' prior beliefs are not common knowledge? We examine a simple example in which two parties having heterogeneous prior beliefs, independently drawn from some distribution, bet on what future action one of them will choose. We define a notion of "constrained interim-efficient" best and ask whether they can be implemented in Bayesian equilibrium by some mechanism. Our main result establishes that as the costs of unilaterally manipulating the bet's outcome become more symmetric across states, implementation becomes easier. In particular, when these costs are equal in both states, implementation is possible for any distribution.

A Model of Competing Narratives

American Economic Review 2020 110(12), 3786-3816
We formalize the argument that political disagreements can be traced to a “clash of narratives.” Drawing on the “Bayesian Networks” literature, we represent a narrative by a causal model that maps actions into consequences, weaving a selection of other random variables into the story. Narratives generate beliefs by interpreting long-run correlations between these variables. An equilibrium is defined as a probability distribution over narrative-policy pairs that maximize a representative agent's anticipatory utility, capturing the idea that people are drawn to hopeful narratives. Our equilibrium analysis sheds light on the structure of prevailing narratives, the variables they involve, the policies they sustain, and their contribution to political polarization.

Search Design and Broad Matching

American Economic Review 2016 106(3), 563-586 open access
We study decentralized mechanisms for allocating firms into search pools. The pools are created in response to noisy preference signals provided by consumers, who then browse the pools via costly random sequential search. Surplus-maximizing search pools are implementable in symmetric Nash equilibrium. Full extraction of the maximal surplus is implementable if and only if the distribution of consumer types satisfies a set of simple inequalities, which involve the relative fractions of consumers who like different products and the Bhattacharyya coefficient of similarity between their conditional signal distributions. The optimal mechanism can be simulated by a keyword auction with broad matching.