Job Market Paper|
The Cost of Optimally Acquired Information (with Weijie Zhong) [Slides]
This paper develops a theory for the expected cost of optimally acquired information when information can be acquired sequentially and there is no explicit cost of delay. We study the "reduced-form" Indirect Cost functions for information generated by sequential minimization of a "primitive" Direct Cost function. The class of Indirect Costs is characterized by a recursive condition called Sequential Learning-Proofness. This condition is inconsistent with Prior Invariance: Indirect Costs must depend on the decision-maker's prior beliefs.
We show that Sequential Learning-Proofness provides partial optimality foundations for the Uniformly Posterior Separable (UPS) cost functions used in the rational inattention literature: a cost function is UPS if and only if it is an Indirect Cost that (i) satisfies a mild regularity condition or, equivalently, (ii) is generated (only) by Direct Costs for which the optimal sequential strategy involves observing only Gaussian diffusion signals, a property we call Preference for Incremental Learning. We characterize the unique UPS cost function that is generated by a Prior Invariant Direct Cost; it exists only when there are exactly two states.
We also propose two specific UPS cost functions based on additional optimality principles. We introduce and characterize Total Information as the unique Indirect Cost that is Process Invariant when information can be decomposed both sequentially and "simultaneously": it is uniquely invariant to the "merging" and "splitting" of experiments. Under regularity conditions, Mutual Information is the unique Indirect Cost that is Compression Invariant when aspects of the state space can be "freely ignored": it is uniquely invariant to the to the "merging" and "splitting" of states. We argue that Total Information and Mutual Information represent the normatively ideal costs of, respectively, "producing" and "processing" information.
Persuading a Rationally Inattentive Agent (with Ilya Segal) [Slides]
How should information be disclosed to an inattentive audience? We develop a model in which a Sender transmits signals about an uncertain state to a rationally inattentive Receiver, who privately bears a mutual information cost (Sims 2003) to process these signals before taking an action. Information disclosure serves dual purposes: to persuade Receiver when preferences over actions are misaligned, and to manipulate Receiver's attention, which is subject to moral hazard. The latter friction causes the standard Obedience Principle to fail: Sender cannot simply provide an action recommendation because Receiver would sometimes ignore it. We characterize the optimal form of disclosure in a canonical binary-action setting using a first-order approach. Under aligned preferences, full disclosure is generically suboptimal: Sender instead attracts Receiver's attention by pooling intermediate- and high-stakes states (in which taking the correct action is most valuable) while fully revealing low-stakes states (in which it is least valuable). Under misaligned preferences, Sender may also distract Receiver by providing detailed information about states in which their preferred actions differ. We show that higher attention costs tend to induce more informative disclosure and that, when Sender lacks commitment power, her incentive to exaggerate hinders communication. We also explore broader modeling issues, such as the importance of Sender's "language" when Receiver's cost function differs from mutual information, and the difference between Receiver learning about Sender's signal ("communication") vs. directly about the state ("delegated information acquisition").
Augmented Stochastic Choice and Optimal Sequential Learning [Slides] [draft coming soon]
Many theories of information acquisition make joint predictions about final choices and observable "process" variables, such as decision times or search histories. This paper provides revealed preference foundations for such theories using the augmented stochastic choice data (inclusive of process variables) generated by a decision maker's (DM's) underlying learning process, as is common in lab experiments on decision times and eye/mouse-tracking and in field studies of consumer search. We introduce classes of Delay/Search Cost Representations in which incremental delay/search is the only source of learning costs, as in most models of sequential sampling/search. We provide behavioral characterizations and conditions under which the delay/search cost parameters can be uniquely identified separately from DM's feasible set of learning strategies. We also characterize the more general class of Sequential Costly Information Representations in which DM's cost function over learning strategies is unrestricted, encompassing various models of dynamic rational inattention. We uniquely identify the discount factor and characterize the extent to which the cost function is (partially) identified; discounting is essential for process data to impose meaningful new restrictions. We discuss implications for applied models of sequential information acquisition and empirical tests thereof.
Insurance and Inequality with Persistent Private Information (with R. Vijay Krishna and Oksana Leukhina)
This paper studies the optimal tradeoff between insurance and inequality in economies with persistent
private information. We consider a principal-agent model in which the principal insures the agent against
privately-observed shocks to his endowment, which follows an ergodic finite-state Markov chain that
may exhibit arbitrary serial correlation. The optimal contract always induces immiseration: the agent's
consumption and utility become arbitrarily negative in the long run. When the endowment is positively
serially correlated, the optimal contract provides increasingly high-powered incentives: the sensitivity
of the agent's utility with respect to his report increases without bound. These results generalize the
classic immiseration results established under the assumption of iid types, and extend to settings in
which the agent's private type concerns his tastes or productivity (as in optimal taxation). In a solved
example, we additionally show that, with persistence, the optimal contract (i) is not renegotiation-proof
and (ii) exhibits qualitatively novel short-run dynamics and quantitatively worse risk-sharing relative to
the iid information benchmark.
Persistent Private Information Revisited (with R. Vijay Krishna and Bruno Strulovici) [Supplement]
This paper revisits Williams' (2011) continuous-time model of optimal dynamic insurance with
persistent private information and corrects several errors in that paper's analysis. We introduce and
study the class of self-insurance contracts that are implementable as consumption-saving problems for
the agent with constant taxes on savings chosen by the principal. We show that the contract asserted to
be optimal in Williams (2011) is the special self-insurance contract with zero taxes. When the agent's
private endowment is mean-reverting, that contract is strictly dominated by the optimal self-insurance
contract, which imposes a strictly positive tax, induces immiseration when the rate of mean-reversion is
high, and sends the agent to bliss when the rate of mean-reversion is low. When the agent's endowment is
not mean-reverting, the contract derived in that paper is, in fact, optimal among all incentive compatible
contracts; we provide a new explanation for its properties in terms of the agent's indifference among all
reporting strategies. These results extend to the natural discrete-time analogue of the model. Separately,
Williams' (2011) first-order approach to incentive compatibility relies on an erroneous and unjustified
assumption on the space of feasible reporting strategies; our analysis does not.
Dynamic Attention Manipulation [draft coming soon]
A Sender discloses information about an uncertain state to a rationally inattentive Receiver, who privately bears a mutual information cost to process Sender's signals before taking an action. We show that it is generally optimal for Sender to use multi-stage disclosure mechanisms that reveal information gradually. By conditioning future disclosure on Receiver's past learning, these mechanisms extract more attentional effort from Receiver than is possible in the optimal static mechanism (Bloedel and Segal 2020). Notably, dynamics are optimal despite Sender's commitment power and the inherently static natures of the underlying uncertainty and moral hazard (in attention) problem. We present a sufficient condition under which static disclosure is without loss of optimality.
Work in Progress
Commitment and Flexibility in Agenda Setting (with S. Nageeb Ali, B. Douglas Bernheim, and Silvia Console-Battilana) [draft in preparation]
Many policies are determined by majority rule in legislatures that sequentially consider amendments to a status quo policy. How much power does a (non-voting) agenda-setter wield in such settings? We consider a model of legislative policy-making with three realistic features: (i) voters are sophisticated, (ii) the agenda-setter cannot pre-commit to future amendment proposals, and (iii) deliberations are subject to a deadline. Under mild conditions, the agenda-setter implements her favorite policy in every equilibrium and regardless of the initial status quo: the ability to flexibly set the agenda in real-time, in conjunction with the modicum of commitment afforded by a deadline, leads to absolute agenda-setter power. Our results qualify the conventional wisdom that voter sophistication on its own constrains an agenda-setter's power, and contrast with findings that, absent a deadline, a non-committed agenda-setter's power completely erodes.
Competing for Attention by Withholding Information (with Dong Wei)
Common wisdom suggests that, in games of information disclosure, competition between multiple Senders leads to more informative disclosure. We show that this wisdom may be overturned when the Receiver is attention-constrained. In our model, a single Receiver must take a multi-dimensional action to match a multi-dimensional state; her information comes from multiple Senders, each of whom only cares about and discloses information concerning certain dimensions. Paying attention is not intrinsically costly, but Receiver's total attention expenditure is capacity-constrained. We focus on settings with intra-dimensional preference alignment and separable payoffs, in which Senders have no persuasive motives and interact only through the capacity constraint. Although full disclosure would be the unique equilibrium with a single monopolistic Sender, with competing Senders full disclosure is not an equilibrium over a non-degenerate set of capacity levels due to a novel attentional externality. We discuss applications to organizational economics and the debate over mandated disclosure regulations.
Multi-Source Rational Inattention
In many modern "information-rich" markets, such as those for online goods and media, the process by which agents acquire information is characterized by three features: (i) there are multiple sources (e.g., websites) each with exclusive information, (ii) agents can flexibly learn from each source (e.g., pay partial attention to a webpage's contents), and (iii) the cost of switching between sources (e.g., clicking on a new link) is negligible. We introduce a variant of the rational inattention framework that accounts for the multi-source nature of such environments. We geometrically characterize the value of information acquisition via a generalized concavification operation. While the optimal strategy is generally dynamic, we identify sufficient conditions under which optimal information acquisition is static and can be tractably characterized. These conditions encompass Gaussian-Quadratic settings previously studied in macro and finance applications under ad hoc restrictions on feasible information acquisition strategies. We discuss information-theoretic foundations for this approach and an alternative interpretation of the model in terms of costly interactive communication.