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Report

Teaser, summary, work performed and final results

Periodic Reporting for period 2 - BAYNET (Bayesian Networks and Non-Rational Expectations)

Teaser

Summary

\"The main objective of this project is to make causal reasoning an integral part of economic theory. The basic idea is that when people make decisions, they establish a causal mapping from actions to consequences, which is based on an intuitive subjective causal model. For example, when a parent decides how much to invest in his child\'s education, he may have in mind an intuitive causal model that can be represented by the following graphical diagram: investment in child\'s education --> child\'s performance at school --> child\'s subsequent performance in the labor market. The decision maker then uses this subjective causal model to make sense of statistical regularities in his environment and form beliefs that guide his action. In the above example, this means that the parent will measure the observed correlation between investment and school performance as well as the observed correlation between school performance and subsequent labor-market performance, and he will combine these correlations in accordance with his causal model. If the decision maker\'s causal model is incorrect - e.g., when he reverses the true direction of causality between two variables, or when he omits certain variables from his model - then his beliefs may exhibit systematic biases. This in turn can lead to interesting behavioral effects. In the above example, the parent\'s subjective causal model neglects the possibility that both school and labor-market performance may be affected by unobserved exogenous characteristics of the child. This error may result in over-investment in the child\'s education.

In its exploration of behavioral implications of erroneous causal reasoning, this project is related to the behavioral economics and bounded rationality literatures. In particular, it adds a novel dimension to the literature on \"\"non-rational expectations\"\". While behavioral economics has studied a variety of biases in belief formation, it has not yet dealt with the problem of erroneous causal reasoning. However, causal inference is fundamental to decision making, especially in modern societies. We are constantly bombarded with observational data and correlations between variables, and whether we are able to draw correct causal inferences from this type of data is an important question. The motto \"\"correlation does not imply causation\"\" is so well-known precisely because people do tend to draw wrong causal inferences from mere correlations. These errors could make them vulnerable to exploitation by third parties.

From a technical point of view, the project draws on the rich literature in statistics and artificial intelligence (AI) on so-called \"\"Bayesian networks\"\". This literature offers tools that enable us to formalize types of errors of causal reasoning and analyze their behavioral consequences. Thus, if successful, the project may also contribute to the influence of graphical probabilistic models in economics, which could be particularly relevant for econometric theory.
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Work performed

\"The paper that initiated this research agenda and was the basis for the original grant proposal (authored by the PI and eventually published in 2016 in QJE, under the title \"\"Bayesian Networks and Boundedly Rational Expectations\"\") presented a model of individual decision making that was based on the above description. This model has several non-trivial properties (mainly the possibility that individual decision making exhibits \"\"equilibrium\"\" effects that we normally associate with interactive models), which the formalism of Bayesian networks helps illuminating. The subsequent papers that belong to this project have already been supported by this ERC grant.

The paper \"\"Can agents with causal misperceptions be systematically fooled?\"\" (authored by the PI and accepted for publication in JEEA) considers interaction between a rational \"\"principal\"\" and an agent with a wrong causal model. The question is whether the principal can exploit the agent\'s causal misperception to attain objectives that would be impossible if the agent had so-called \"\"rational expectations\"\". A key application in this paper involves interaction between a central bank and the private sector. The question is whether the central bank can use monetary policy to get long-run effects on the real economy, under the assumption that only unexpected inflation has real effects. This is a familiar problem from 1970s marcoeconomic theory. When the private sector has rational expectations, the central bank cannot systematically surprise it and therefore monetary policy cannot have long-run real effects. The question is whether this conclusion breaks down when the private sector\'s beliefs are based on a wrong causal model of the economy. The paper analyzes this theoretical question and provides answers in terms of structural properties of the private sector\'s causal model.

The paper \"\"Data monkeys\"\" (authored by the PI and published in Restud 2017) proposes an alternative interpretation of the beliefs that result from the above behavioral model. According to this alternative model, the decision maker does not have a prior causal model. Instead, he has access to partial data regarding the probability distribution that characterizes his environment. He uses a behaviorally motivated procedure to extrapolate a probabilistic belief from the partial data. Under certain conditions on the type of data the decision maker receives, the outcome of this belief-extrapolation procedure looks as if the decision maker fits a subjective causal model to the true distribution.

In addition to these two publications, the project has generated four working papers.

In \"\"News and archival information in games\"\" (authored by the PI), the decision model presented in the QJE 2016 paper - reinterpreted along the lines of the Restud 2017 paper - is extended to game-theoretic settings. This paper offers a theoretical framework for modeling games in which players have limited information of two kinds. First, they receive \"\"news\"\" - i.e. information regarding the current realization of relevant variables. This is the standard type of information in Game Theory. Second, the player receives \"\"archival information\"\" - i.e. partial statistical data regarding the steady-state distribution of various variables. The idea that a player\'s type can also be defined by his \"\"archival information\"\" is novel in Game Theory. The new formalism can express situations that so far have been outside the scope of Game Theory. For example, it can formalize situations in which one firm in a market has news regarding a rival firm\'s archival information. The paper\'s contribution lies in the introduction of this new modeling framework.

The paper \"\"Strategic interpretations\"\" (authored by the PI, team member Heidi Thysen and Kfir Eliaz) applies this framework to a standard model of strategic communication, where a sender who is informed of the state of Nature sends costless messages (\"\"cheap talk\"\") to a receiver who then needs to decide whether\"

Final results

What the above papers have delivered so far can be classified into several categories:

1. Creating modeling frameworks that provide a language and some basic results that will guide theorists who want to analyze the implications of causal misperceptions in various economic settings.

2. Providing analytical results about the situations in which wrong causal models lead to wrong beliefs, and some results about the magnitude of such belief errors.

3. A variety of applications in various fields of economics (monetary theory, contract theory, strategic communication) that demonstrate the scope of the modeling frameworks.

I expect that by the end of the project, I will have a richer collection of results in categories (2) and (3). In particular, I plan to apply the framework to richer models of monetary economics, industrial organization and asset markets. I also want to make progress in exploring more sophisticated models of how people use subjective causal models to draw causal inferences from observational data, possibly using the do-calculus framework of Pearl (2009).