Some Thoughts on Inattention

Maher Said

February 3, 2006

1 Background

The vast majority of important economic decisions are taken infrequently and discontinuously;

for example, producers do not update their prices instantaneously when they observe a change in

demand or in their cost structure – they set prices periodically. “Sticky” prices and other decisions

are a fact of our economic existence.

With this in mind, a recent trend within the macroeconomic literature has been to attempt

to model this stickiness as the outcome of rational behavior instead of simply assuming that, say,

wages are exogenously taken to be sticky. There are two main strands within the current literature

on this topic: stickiness due to information acquisition and processing costs, and stickiness due to

limited informational capacity.

1.1 Information Acquisition and Processing Costs

Mankiw and Reis (2002) propose a replacement to the “New Keynesian Phillips Curve” that is

based on a somewhat ad hoc “sticky information” model. They assume that in each period, a

fraction of firms obtain new information about the state of the economy and computes a new path

of optimal prices; meanwhile, the remaining firms continue to set prices based on old plans and

outdated information. Using this basic framework, they derive several results concerning the link

between inflation and output that seem to match observed empirical regularities rather well.

The microfoundations for such a model are developed in Reis (2004) and (2006). Here, the

author assumes that agents are fully rational and make optimal choices; however, the agent incurs

a cost whenever she acquires information and makes optimal decisions. This cost is interpreted

as the cost of obtaining information, processing and interpreting it, and then deciding how to

optimally update their plans.

Facing these costs, a person setting a plan of action for consumption, for example, must choose

not only what to consume, but also when to again incur costs of learning about the state of the

economy and to readjust their consumption plan. This process then leads to “optimal inattentive-

ness” – the agent balances the tradeoffs between making potentially sub-optimal choices for some

length of time and the costs of ensuring that future choices are optimal.

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1.2 Limited Informational Capacity

The second recent strand of literature is due in large part to Sims (1998) and (2003), where he argues

for modeling the inertia of economic agents as the outcome of informational capacity constraints.

In particular, he assumes that agents’ payoffs are dependent upon a number of stochastic state

variables; however, agents have only limited capacity to observe these variables. This limited

capacity is modeled by Shannon capacity, a measure of information flow that uses the reduction in

the entropy of a probability distribution.

Mackowiak and Wiederholt (2005) build a model of firm behavior that is based upon Sims’ ideas

– firms optimally decide what to observe, choosing the number of signals that they receive each

period as well as the stochastic properties of these signals. However, firms face the constraint that

the information flow between the sequence of signals and the sequence of states of the economy are

bounded. In particular, this implies that firms may decide which state variables to observe with

greater precision, and which variables to observe with lesser precision. This model seems to be

rather successful in explaining observed price-setting behavior by firms.

2 Possible Directions for Future Work

Where can we go from here? It is interesting that Sims (2003) praises Keynes’ original stickiness

idea because it is “inconsistent with the assumption of continuously optimizing agents interacting

in continuously clearing markets.” He, along with Mankiw, Reis, Mackowiak, and Wiederholt,

seem to be interested in heading towards models of somewhat bounded rationality, where agents

do not have perfect information and face cognitive constraints. However, in terms of modeling

the behavior of these agents, these authors build in what could be interpreted as extra layers of 

rationality – agents no longer solve one optimal control problem; instead, they solve an entire

family of such problems, and then choose the maximal solution among these optima. Thus, in

Reis’ models, agents must solve for the optimal consumption path given a set of periods in which

state variables may be observed. Then, they must optimize over the set of all possible observation

periods. Similarly, Mackowiak and Wiederholt’s firms solve for the optimal pricing paths given an

informational structure, and then solve a constrained optimization problem in selecting the optimal

information acquisition mechanism. Frankly, these methods seem to miss the point.

One alternative approach that could combine limited information acquisition or processing

ability with more boundedly rational behavior would be to introduce a reinforcement learning

rule-of-thumb type procedure. For example, consider an infinitely-lived consumer in a stochastic

environment – one in which future income and interest rates are unknown. We may further assume

that the consumer does not know the distributions governing these two stochastic processes. How-

ever, in each period, the consumer can choose the relative precision with which to observe signals

of the next realization of the variables – they can reduce the variance of one observation or the

other. Given this choice, the consumer then chooses a level of consumption and receives a benefit

according to some instantaneous utility function. The innovation here would be allowing the re-

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alized utility to act as the payoff from one play on a 2-armed bandit; the consumer will “learn”

whether it is more beneficial to observe future income or to observe future interest rates, and adjust

their choices accordingly. Such a process can then act in place of the second level of optimization

found in the rational inattention literature, serving as an alternative (less rational) rationalization

for “inattentiveness” to economic variables.

References

[1] Mackowiak, Bartosz and Mirko Wiederholt (2005). “Optimal Sticky Prices Under Rational

Inattention.” Mimeo, Humboldt University Berlin.

[2] Mankiw, N. Gregory and Ricardo Reis (2002). “Sticky Information versus Sticky Prices: A

Proposal to Replace the New Keynesian Phillips Curve.” Quarterly Journal of Economics  117:

1295-1328.

[3] Reis, Ricardo (2004). “Inattentive Consumers.” Mimeo, Princeton University.

[4] Reis, Ricardo (2006). “Inattentive Producers.” Review of Economic Studies, forthcoming.

[5] Sims, Christopher (1998). “Stickiness.” Carnegie-Rochester Conference Series on Public Policy 

49: 317-356.

[6] Sims, Christopher (2003). “Implications of Rational Inattention.” Journal of Monetary Eco-

nomics  50: 665-690.

[7] Sims, Christopher (2006). “Rational Inattention: A Research Agenda.” American Economic 

Review, forthcoming.

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