Economist trying to model optimal choosing, under- and over-reaction, mental accounting, rational inattention, etc., under cognitive constraints

A Theory of Narrow Thinking. Chen Lian. MIT, May 24, 2019. https://economics.mit.edu/files/15186

Abstract: I develop an approach, which I term narrow thinking, to break the decision-maker’s ability to perfectly coordinate her multiple decisions. For a narrow thinker, different decisions are based on different, non-nested, information. The narrow thinker then makes each decision with an imperfect understanding of the others. Formally, it is as if the decision-maker is a collection of multiple selves playing an incomplete-information game. The friction effectively attenuates the degree of interaction across decisions and can translate into either over- or under-reaction depending on the environment. Narrow thinking leads to a violation of the fungibility principle and a smooth model of mental accounting. Narrow thinking also reconciles other seemingly disparate phenomena ina unified framework, suchas excess smoothness to taste shocks, the small wage elasticity of daily labor supply, and the label effect. Finally, I study an endogenous narrow thinking problem: the decision maker chooses optimally what information each decision is based upon, subject to a cognitive constraint.

Keywords: boundedrationality,narrowbracketing,incompleteinformation,multipleselves, mental accounting

7 Conclusion
Each decision maker faces multiple economic decisions, and makes these decisions separately. Nevertheless, in standard modeling practice, we implicitly assume perfect self-coordination among all these decisions. It is as if the decision maker determines all her decisions together. In this paper, I try to break such perfection. I develop an approach, narrow thinking, to capture the decision maker’s difficulty in coordinating her multiple decisions. The notion of narrow thinking is that differentdecisionsarebasedondifferent, non-nested, information. This notion is motivated by the psychological observation that the decision maker may not incorporate all the relevant information when making each decision. Under narrow thinking, each decision of the decision maker is made with an imperfect understanding of other decisions. In response to shocks to the fundamental, it is as if each decision is made caring less about the influence of other decisions. I then show how narrow thinking can provide a unified explanation to seemingly disparate behavioral phenomena, including both under-reaction and over-reaction. A general principle is: when the indirect effect works in the same direction as the direct effect, narrow thinking leads to under-reaction; when the indirect effect works in the opposite direction to the direct effect, a dampening of the indirect effect under narrow thinking leads to over-reaction. Finally, let me outline two potential avenues for future research. A first possibility is to explore the general equilibrium implications of narrow thinking. A second possibility is to conduct an experimental test of narrow thinking, along the line of the potential experiment I discussed at the end of Section 3.

1.1 Related Literature
This paper builds on, and adds to, the growing literature on rational inattention (Sims, 2003; Mackowiak and Wiederholt, 2009; Matejka, 2015, 2016; Matejka and McKay, 2015; Koszegi and Matejka, 2018)3 and sparsity (Gabaix, 2014, 2017). There, the key friction is the decision maker’s imperfect perception of the fundamental, while the decision maker perfectly knows her other decisions when making a particular decision. On the other hand, the narrow thinking approach lets different decisions be based on different, non-nested, information and captures the friction that each decision can be made with an imperfect understanding of other decisions. As the decision problem under narrow thinking is equivalent to multiple selves playing an incomplete information game, the paper also builds upon the literature on incomplete information “beauty contests” (Morris and Shin, 2002; Angeletos and Pavan, 2007; Bergemann and Morris, 2013). This literature studies linear best-response games under incomplete information. A key insightfromtheliteratureisthatincompleteinformationcanattenuatetheequilibriuminteraction (Angeletos and Lian, 2016, 2018; Bergemann, Heumann and Morris, 2017). In these works, the behavior of each individual is frictionless and the focus is on inter-personal coordination friction and macroeconomic applications. The current paper, on the other hand, focuses on intra-personal friction in coordinating a decision maker’s multiple decisions and behavioral applications. This change of focus permits me to build a bridge between the incomplete information literature and the bounded rationality literature. The paper then shows how such intra-personal frictions can deliver a novel theory to reconcile seemingly disparate behavioral phenomena. By viewing the decision maker as a team of multiple selves, the paper also connects to the literature on multiple-selves and team theory. The multiple-selves literature (Piccione and Rubinstein, 1997; Benabou and Tirole, 2002, 2003, 2004; Gottlieb, 2014, 2017) uses environments in which multiple selves have conflicted interests to model motivated beliefs and reasoning, and explores reasons why the decision maker’s beliefs and behavior can be systematically biased. The multiple selves of the narrow thinker, on the other hand, have common interests, and the focus of the current paper is about frictional behavior in response to shocks. Narrow thinking does not necessarily lead to systematical bias on average. The team theory literature (Marschak and Radner, 1972; Dessein, Galeotti and Santos, 2016), on the other hand, mostly focuses on optimal information design in an organization. Angeletos and Pavan (2007) develop a method to use team theory to find the constrained efficient allocation in an economy with dispersed information. Angeletos and Pavan (2009), Lorenzoni (2010) and Angeletos and La’O (2018) then use the method to characterize optimal policy with informational frictions. Multiple cognitive frictions can let different decisions be made based on different, non-nested, information. For example, Gennaioli and Shleifer (2010), Kahana (2012), Wilson (2014), Bordalo, Gennaioli and Shleifer (2017) and Jehiel and Steiner (2018) on bounded recall, and Tversky and Kahneman(1973)andKahneman(2011)onheuristics,biases,andselectiveretrievalfrommemory. These works therefore provide complementarity justification for the kind of frictions that define narrow thinking. Gennaioli and Shleifer (2010) use the term “local thinker” to describe a decision maker whose bounded recall follows the representativeness heuristic, and study the implication for single-decision problems. The current paper, on the other hand, focuses on the decision maker’s difficulty in coordinating her multiple decisions. On the applied side, narrow thinking provides a unified framework to explain different behavioral phenomena. Depending on the environment, narrow thinking can translate into either over- or under-reaction. Applications studied in the paper connect to the literature on narrow bracketing (Rabin and Weizsacker, 2009), mental accounting (Thaler, 1985, 1999; Heath and Soll, 1996; Hastings and Shapiro, 2013; Abeler and Marklein, 2016), excessive sensitivity to temporary income shock (Parker et al., 2013; Kueng, 2018), the small cross-price demand elasticity (Gabaix and Laibson, 2006; Abaluck and Gruber, 2011, 2016; Allcott and Taubinsky, 2015) and the small wage elasticity of daily labor supply (Camerer et al., 1997; Farber, 2015; Thakral and To, 2017). For each application, narrow thinking’s distinct economic implications and testable predictions will be discussed. Koszegi and Matejka (2018) is a recent, complementary, paper that shares the focus on an information-based theory of mental accounting. That paper stays within the rational inattention paradigm, and different decisions are based on the same, imperfect, information.