Friday, July 12, 2013

Divided Fed, Broken Models

This week, it has become abundantly clear that the Fed is "deeply divided." In speeches and public communications, FOMC committee members and  Fed Chairman Ben Bernanke have revealed significant differences in their outlooks and intentions for the economy. Tim Duy writes that "The growing division makes it increasingly difficult to think of "the Fed" as a single entity with regards to policy intentions." This is an extremely important point, because most macroeconomic models do consider the Fed as a single entity, and would have different implications if they did not.

Monetary policy is often modeled as a dynamic game in which the two players are the central banker and the public. Typically, the central banker can choose what private information to reveal to the public. Monetary policymakers' preferences and reputational concerns determine their optimal communication strategy in the equilibrium of this dynamic credibility game (see for example Faust and Svensson 2001). Depending on the exact "rules of the game," the optimal strategy turns out to be something less than full information revelation. This game-theoretic political economy paradigm for thinking about monetary policy became hugely influential after seminal papers by Kydland and Prescott in 1977 and Barro in 1986, and has shaped the way economists think about the merits of central bank independence, rules versus discretion, transparency, and explicit inflation targets, with. Insights from this huge literature have been thoroughly integrated into the policymaking sphere.

In reality, of course, in almost every country, monetary policy is not made by a single representative agent, but rather by a committee of very non-representative agents, each with their own, sometimes conflicting, preferences and reputational concerns. With multiple central bankers, monetary policy is a dynamic game between more than two players-- which makes computing optimal strategies dauntingly complex. Strategic behavior between members of the committee will influence each member's communication strategy with the public and with each other. And the public, aware of these strategic interactions, will have quite a complex task computing their best response.

I'm not quite sure where we go from here. One of the most brilliant and famous game theorists, John Nash, proved that non-cooperative games with an arbitrary finite number of players have a Nash equilibrium. But actually finding such an equilibrium is a huge challenge (plus, the non-cooperative assumption is kind of restrictive.) A pair of computer scientists at Berkeley and Stanford note that "even less is known about computing equilibria in multi-player games than in the (still mysterious) special case of two-player games." Even more telling is the title of another paper by Berkeley computer scientists: "Three-Player Games are Hard."


  1. On the topic of game theory, Nash proved that his equilibria exist, but there are generically many of them in applied problems. Multiplicity is why we see so many refinements -- subgame perfect, satisfy the intuitive criterion, etc. The thing is, Nash equilibria are a small subset of the rationalizable set, loosely the set of plays which can occur if all players are rational. Game theory has very little predictive power, even after 60 years of development.

  2. Hmm! In the beginning of your argument you mentioned conflict between Fed governor and the FOMC committee. If we treat FOMC as one player at this level, then we have two players. However, at a deeper level the FOMC members may be divided in their opinion; some may support the governor. Hence, this may describe a nested game. One can still use two player strategy by assuming one set of players, in support and the other set in opposition to set the game theoretic problem. In nested game one has to solve the game between committee members, which may result in a game between two polarized groups. The wining group may be used in solving the game between Fed governor and the group, perhaps. No doubt, the game will not be an easy one solution and may require several iterations.

  3. Yasin, I'm not sure that the game would be nested. If FOMC members are in opposition, they could reveal information to the public as part of their strategy before solving the game between committee members. There is no reason they would solve the game between committee members before the game between the committee and the public. Committee members express different opinions in public communications long before it is clear who has "won."

  4. In that case, one can assume that the committee members release opinion in public communications to get public response and continually restructure their strategy before a final outcome is reached.


Comments appreciated!