Dynamic coordination with timing frictions: Theory and applications

• Author: Ana E. Pereira,Bernardo Guimaraes,Caio Machado
• Date: 01 June 2020
• Published date: 01 June 2020
• DOI: http://doi.org/10.1111/jpet.12427

J Public Econ Theory. 2020;22:656–697.wileyonlinelibrary.com/journal/jpet656

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© 2020 Wiley Periodicals, Inc.

Received: 13 November 2019

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Accepted: 30 December 2019

DOI: 10.1111/jpet.12427

ORIGINAL ARTICLE

Dynamic coordination with timing frictions:

Theory and applications

Bernardo Guimaraes

1

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Caio Machado

2

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Ana E. Pereira

3

1

Sao Paulo School of Economics—FGV,

Sao Paulo, Brazil

2

Instituto de Economía, Pontificia

Universidad Católica de Chile, Santiago,

Chile

3

School of Business and Economics,

Universidad de los Andes, Santiago, Chile

Correspondence

Ana E. Pereira, School of Business and

Economics, Universidad de los Andes,

Santiago, Chile.

Email: apereira@uandes.cl

Funding information

Fondo Nacional de Desarrollo Científico

y Tecnológico, Grant/Award Numbers:

11180046, 11190202; Conselho Nacional

de Desenvolvimento Científico e

Tecnológico

Abstract

We present a general framework of dynamic coordina-

tion with timing frictions. A continuum of agents

receive random chances to choose between two actions

and remain locked in the selected action until their next

opportunity to reoptimize. The instantaneous utility

from each action depends on an exogenous fundamental

that moves stochastically and on the mass of agents

currently playing each action. Agents' decisions are

strategic complements and history matters. We review

some key theoretical results and show a general method

to solve the social planner's problem. We then review

applications of this framework to different economic

problems: network externalities, statistical discrimina-

tion, and business cycles. The positive implications of

these models are very similar, but the social planner's

solution points to very different results for efficiency in

each case. Last, we review extensions of the framework

that allow for endogenous hazard rates and ex ante

heterogeneous agents.

1

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INTRODUCTION

Several problems in economics exhibit strategic complementarities. For example, in a scenario

of bank runs, withdrawing deposits from the bank might be the optimal action only if others

also do so.

1

The decision about joining and posting on Facebook depends crucially on whether

other people are doing the same.

2

For firms considering whether to invest or not, one important

factor is the demand for their goods, which in turn depends on whether other firms choose to

1

See Diamond and Dybvig (1983).

2

See Katz and Shapiro (1985) for a model of network externalities.

invest.

3

Adopting a new technology may not be the best decision if others in the production

chain will keep working with an old technology.

4

Strategic complementarities are also common in the field of public economics. Evading taxes

might be the optimal choice only if many others do so because the stigma associated with

evasion and the probability of punishment are both smaller when many others are also

evading.

5

More generally, complying with social norms is more important if most people follow

them.

6

Donating for a charitable project may pay off only if the charity is able to attract enough

donations to realize its projects.

7

The incentives for a high‐skill and honest citizen to become a

politician depend on whether there are sufficiently many good politicians out there.

8

Tax

exemptions are particularly important for a firm if tax breaks are pervasive and the tax base is

small. This yields strategic complementarities in lobbying activity.

9

A variety of models that capture these economic problems give rise to multiple equilibria. In a

range of parameters, different outcomes can arise in equilibrium depending on what agents expect

others will do. For example, in models of tax evasion, for an intermediate range of fundamentals,

there is an equilibrium where agents evade taxes and another where they do not; in models of

network externalities, equilibria predicting the prevalence of different networks coexist; in

macroeconomic models, economic activity might depend on arbitrary shifts on expectations.

One important question left unanswered by models with multiple equilibria is what

determines which equilibrium will be played. Will firms evade taxes? Will competent and

honest citizens choose a career as politicians? Will people coordinate on Facebook, Orkut or

Google+? Will economic activity recover next year?

Different approaches to deal with equilibrium multiplicity have been proposed. This survey

focuses on the literature of dynamic games with timing frictions, which follows the seminal

contribution of Frankel and Pauzner (2000). Time is continuous. Agents choose between two

states (say, low and high) and get opportunities to revise their behavior according to a Poisson

clock. Their instantaneous utility gain from being in the high state increases in an exogenous

fundamental variable and in the fraction of agents in the high state. The fundamental moves

according to a Brownian motion.

10

As an illustration, firms might choose procedures that comply with tax regulations or not.

The net benefit from evading taxes depends on exogenous factors and on how many people are

complying with tax rules. At some random points in time, firms decide whether they want to

change their procedures. Here, the Poisson clock can be seen as an attention friction modeled in

a reduced‐form way. In other applications, the Poisson clock could be related to the maturity of

a bond or an investment, or to the obsolescence of a machine.

Many economic problems are naturally described as dynamic environments with

coordination motives and evolving fundamentals. Examples include compliance with rules,

investment dynamics, technology adoption, bank runs, political behavior, and many others.

This modeling approach provides a suitable framework for all these problems. As an alternative,

3

See Cooper and John (1988) and Kiyotaki (1988). Investment in human capital can also feature coordination motives (see Palivos & Varvarigos,2013).

4

See Matsuyama (1991).

5

See the models in Kim (2003), Nyborg and Telle (2004), and Sanchez‐Villalba (2015).

6

See the models in Bethencourt and Kunze (2019) and Meunier and Schumacher (2019).

7

See the model in Andreoni (1998).

8

See Caselli and Morelli (2004) for a model.

9

See Ilzetzki (2018) for a model.

10

See also Burdzy, Frankel, and Pauzner (2001).

GUIMARAES ET AL.

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one could introduce dynamics in global games. However, in general, dynamic global games are

not very tractable—and might exhibit equilibrium multiplicity.

11

An alternative stream of the

literature incorporates dynamics in coordination games through learning, but typically

fundamentals are assumed to be fixed.

12

One key aspect of the class of models studied here is that history matters. Incentives to pick

one state are positively affected by thestock of agents in that state. Hence agents might stick to an

action for longer periods of time simply because this is what they have been doing in the past.

This feature of the model captures some well known dynamic coordination problems. One classic

example is the prevalence of QWERTY keyboards (David, 1985), but this is likely to be important

in a wide range of applications. The model also fits well caseswhere we coordinate on a patternof

behavior for such a long time that we may fail to notice a coordination problem.

13

One important question is about the economic inefficiencies in these problems. We show a

general formulation of the planner's problem that allows for a clean comparison between the

socially optimal solution and the decentralized equilibrium. As it turns out, the planner's

solution is given by a problem very similar to the agents' one, as if the planner were playing a

game with its future selves, but with a different utility flow that takes into account the

externalities of an agent on others.

The literature has used this framework to study several economic settings. Naturally, in all

these applications, the positive implications are qualitatively similar. However, interestingly,

the welfare implications are substantially different across applications and are often not obvious

at all. For example, in a model of network externalities, a situation with agents stuck in a low‐

quality network is actually efficient: in the decentralized equilibrium, agents move too soon to a

higher‐quality network. At the moment agents start to switch, the social future gains from being

in a higher‐quality network are strictly smaller than the social transition costs. In a business

cycle model with a fixed investment cost, firms' investment decisions depend on whether others

have been investing, so the economy might get stuck in a situation where firms choose not to

invest, but would invest if only others had been doing so. Nevertheless, the planner is not

particularly concerned with stimulating investment in these occasions.

Section 2 presents the framework proposed by Frankel and Pauzner (2000) and some results for

the general model. First, it presents results on equilibrium multiplicity and equilibrium uniqueness.

Then, it shows a method to solve the social planner's problem and applies mathematical results

about bifurcation probabilities from Burdzy, Frankel, and Pauzner (1998) to derive expressions for

the equilibrium threshold in the limiting cases of vanishing shocks and vanishing frictions. We

compare this framework to two popular approaches that deal with equilibrium selection in

coordination games: global games and dynamic models with perfect foresight.

With this toolkit in hand, Section 3 shows analytical results for a case with linear preferences

and presents applications of the basic framework to a variety of settings such as network

externalities, statistical discrimination and stimulus policies in macroeconomics. Besides

generating insights for specific questions, the applications illustrate the potential of the model

to accommodate a large set of economic problems and the different results regarding efficiency.

11

For a class of tractable dynamic global games, see Mathevet and Steiner (2013).

12

See, for example, Ennis and Keister (2005), Amir and Lazzati (2011), and Amir, Gabszewicz, and Resende (2014).

13

For example, in 1918, the trade publication Earnshaw's Infants' Department stated that “the generally accepted rule is pink for the boys, and blue for the girls.

The reason is that pink, being a more decided and stronger color, is more suitable for the boy, while blue, which is more delicate and dainty, is prettier for the

girl.”A hundred years later, we might have the impression that we have always coordinated on blue for boys—and some argue that this coordination pattern

might be ripe for change.

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