Fernando E. Alvarez and David Argente are exploring a central question in macroeconomics: when many decision-makers influence one another, what makes the overall economy adjust slowly—or quickly—after a change?
In a new study, the authors analyze “strategic complementarities” in linear-quadratic mean field games, a class of models designed for settings with large numbers of similar agents whose choices interact through economy-wide aggregates. These models are especially useful because they provide tractable, local approximations to familiar macroeconomic environments. Alvarez and Argente point to applications ranging from capital accumulation problems to pricing decisions by firms with multiple products.
Their main theoretical result is a simplification: despite the presence of strategic interactions across agents, the evolution of aggregate variables in equilibrium can be represented as if it came from a single-agent linear-quadratic control problem. The twist is that the parameters of this representative control problem—specifically, the “curvatures” governing how costly movements in states and actions are—must be modified to reflect the underlying strategic interactions. This mapping does more than tidy up the mathematics. It delivers practical conditions under which an equilibrium exists, and it also helps establish when that equilibrium is unique.
With that foundation in place, the paper connects the nature of complementarities to aggregate persistence, meaning how long the impact of shocks or policy changes lingers in the macro data. The authors separate two channels. When complementarities operate through states—for example, when today’s state is more valuable because others are in certain states as well—stronger complementarities tend to make aggregate dynamics more persistent. In contrast, when complementarities operate through actions—when taking an action is more attractive because others take related actions—strengthening these interactions can make adjustment less persistent. Importantly, the authors show these conclusions can be extended beyond simple one-dimensional cases: the results can hold even in multidimensional settings where the matrices describing the system cannot be diagonalized together, a technical obstacle that often blocks clean comparative statics.
The same logic also clarifies how a utilitarian social planner’s allocation differs from the decentralized equilibrium. If the planner internalizes state complementarities that individuals ignore, the planner’s chosen aggregate path becomes more persistent. But if the key wedge is action complementarities, internalization pushes the planner toward less persistence.
The paper also considers economies subject to common shocks. In that environment, Alvarez and Argente provide conditions under which researchers can use the joint behavior of individual-level and aggregate outcomes to identify both the strategic interaction terms and other model parameters—a step toward empirical implementation rather than purely theoretical characterization.
Finally, the analysis is extended beyond interactions through averages: the authors discuss how to incorporate strategic links that run through higher moments of the cross-sectional distribution of states.
A preliminary version of the project was initially pursued with Thomas J. Sargent, whom the authors credit for early guidance. They also acknowledge extensive feedback from a wide set of economists and seminar audiences, including presentations at SED 2024 in Buenos Aires and several macro and mean-field conferences and workshops. The first draft is dated October 2024, and the authors note that the views expressed do not necessarily reflect those of the National Bureau of Economic Research.
Why it matters
Persistence shapes how long recessions last, how quickly inflation returns to target, and how fast investment and prices respond to policy. By isolating when complementarities in states versus actions amplify or dampen persistence—even in complex, multidimensional settings—the paper offers a sharper lens for building and estimating macro models. The identification results under common shocks also point to what kinds of data could help measure strategic interaction strengths in practice.