write down the likelihood. But there has been a lot of progress here

thanks to Tony Smith, Ron Gallant, and George Tauchen and others,

who have ¬gured out ways to get estimates as good, or almost as good,

as maximum likelihood. I like the Gallant“Tauchen idea of using moment

conditions from the ¬rst-order conditions for maximizing the likelihood

function of a well ¬tting auxiliary model whose likelihood function is

easy to write down.

Evans and Honkapohja: Do you see any drawbacks to likelihood-

based approaches for macro models?

Sargent: Yes. For one thing, without leaving the framework, it seems

dif¬cult to complete a self-contained analysis of sensitivity to key features

of a speci¬cation.

Evans and Honkapohja: Do you think that these likelihood-based

methods are going to sweep away GMM-based methods that don™t use

complete likelihoods?

Sargent: No. GMM and other calibration strategies will have a big

role to play whenever a researcher distrusts part of his speci¬cation and

so long as concerns about robustness endure.

Learning

Evans and Honkapohja: Why did you get interested in nonrational

learning theories in macroeconomics?

Sargent: Initially, to strengthen the case for and extend our under-

standing of rational expectations. In the 1970s, rational expectations was

severely criticized because, it was claimed, it endowed people with too

much knowledge about the economy. It was fun to be doing rational

316 George W. Evans and Seppo Honkapohja

expectations macro in the mid-seventies because there was lots of skept-

icism, even hostility, toward rational expectations. Critics claimed that

an equilibrium concept in which everyone shared “God™s model” was

incredible. To help meet that criticism, I enlisted in Margaret Bray™s and

David Kreps™s research program. Their idea was to push agents™ beliefs

away from a rational expectations equilibrium, then endow them with

learning algorithms and histories of data. Let them adapt their behavior

in a way that David Kreps later called “anticipated utility” behavior: here

you optimize, taking your latest estimate of the transition equation as

though it were permanent; update your transition equation; optimize

again; update again; and so on. (This is something like “¬ctitious play”

in game theory. Kreps argues that while it is “irrational,” it can be a

smart way to proceed in contexts in which it is dif¬cult to ¬gure out

what it means to be rational. Kreps™s Schwartz lecture has some fascinat-

ing games that convince you that his anticipated utility view is attractive.)

Margaret Bray, Albert Marcet, Mike Woodford, you two, Xiaohong Chen

and Hal White, and the rest of us wanted to know whether such a system

of adaptive agents would converge to a rational expectations equilibrium.

Together, we discovered a broad set of conditions on the environment

under which beliefs converge. Something like a rational expectations

equilibrium is the only possible limit point for a system with adaptive

agents. Analogous results prevail in evolutionary and adaptive theories

of games.

Evans and Honkapohja: What do you mean “something like”?

Sargent: The limit point depends on how much prompting you

give agents in terms of functional forms and conditioning variables.

The early work in the least squares learning literature initially endowed

agents with wrong coef¬cients, but with correct functional forms and

correct conditioning variables. With those endowments, the systems

typically converged to a rational expectations equilibrium. Subsequent

work by you two, and by Albert Marcet and me, withheld some per-

tinent conditioning variables from agents, e.g., by prematurely trun-

cating pertinent histories. We found convergence to objects that could

be thought of as “rational expectations equilibria with people con-

ditioning on restricted information sets.” Chen and White studied

situations in which agents permanently have wrong functional forms.

Their adaptive systems converge to a kind of equilibrium in which

agents™ forecasts are optimal within the class of information ¬ltrations

that can be supported by the functional forms to which they have

restricted agents.

Evans and Honkapohja: How different are these equilibria with sub-

tly misspeci¬ed expectations from rational expectations equilibria?

An Interview with Thomas J. Sargent 317

Sargent: They are like rational expectations equilibria in many ways.

They are like complete rational expectations equilibria in terms of many

of their operating characteristics. For example, they have their own set of

cross-equation restrictions that should guide policy analysis.

They are “self-con¬rming” within the class of forecasting functions

agents are allowed. They can also be characterized as having forecasting

functions that are as close as possible to mathematical expectations con-

ditioned on pertinent histories that are implied by the model, where

proximity is measured by a Kullback“Leibler measure of model discrep-

ancy (that is, an expected log-likelihood ratio). If they are close enough

in this sense, it means that it could take a very long time for an agent

living within one of these equilibria to detect that his forecasting func-

tion could be improved.

However, suboptimal forecasting functions could not be sustained in

the limit if you were to endow agents with suf¬ciently ¬‚exible functional

forms, e.g., the sieve estimation strategies like those studied by Xiaohong

Chen. Chen and White have an example in which a system with agents

who have the ability to ¬t ¬‚exible functional forms will converge to a

nonlinear rational expectations equilibrium.

Evans and Honkapohja: Were those who challenged the plausibility

of rational expectations equilibria right or wrong?

Sargent: It depends on how generous you want to be to them. We

know that if you endow agents with correct functional forms and condi-

tioning variables, even then only some rational expectations equilibria are

limit points of adaptive economies. As you two have developed fully in

your book, other rational expectations equilibria are unstable under the

learning dynamics and are eradicated under least squares learning. Maybe

those unstable rational expectations equilibria were the only ones the

critics meant to question, although this is being generous to them. In my

opinion, some of the equilibria that least squares learning eradicates

deserved extermination: for example, the “bad” Laffer curve equilibria in

models of hyperin¬‚ations that Albert Marcet and I, and Stan Fischer and

Michael Bruno also, found would not be stable under various adaptive

schemes. That ¬nding is important for designing ¬scal policies to stabil-

ize big in¬‚ations.

Evans and Honkapohja: Are stability results that dispose of some

rational expectations equilibria, and that retain others, the main useful

outcome of adaptive learning theory?

Sargent: They are among the useful results that learning theory has

contributed. But I think that the stability theorems have contributed

something even more important than equilibrium selection. If you stare

at the stability theorems, you see that learning theory has caused us to

318 George W. Evans and Seppo Honkapohja

re¬ne what we mean by rational expectations equilibria. In addition to

the equilibria with “optimal misspeci¬ed beliefs” that I mentioned a little

while ago, it has introduced a type of rational expectations equilibrium

that enables us to think about disputes involving different models of the

economy in ways that we couldn™t before.

Evans and Honkapohja: What do you mean?

Sargent: Originally, we de¬ned a rational expectations equilibrium in

terms of the “communism of models” that I alluded to earlier. By “model,”

I mean a probability distribution over all of the inputs and outcomes of

the economic model at hand. Within such a rational expectations equilib-

rium, agents can have different information, but they share the same

model. Learning theories in both macroeconomics and game theory

have discovered that the natural limit points of a variety of least squares

learning schemes are what Kreps, Fudenberg, and Levine call “self-

con¬rming equilibria.” In a self-con¬rming equilibrium, agents can have

different models of the economy, but they must agree about events that

occur suf¬ciently often within the equilibrium. That restriction leaves

agents free to disagree about off-equilibrium outcomes. The reason is

that a law of large numbers doesn™t have enough chances to act on such

infrequent events. In the types of competitive settings that we often use

in macroeconomics, disagreement about off-equilibrium-path outcomes

among small private agents don™t matter. Those private agents need only

to predict distributions of outcomes along an equilibrium path. But

the government is a large player. If it has the wrong model about off-

equilibrium-path outcomes, it can make wrong policy choices, simply

because it is wrong about the counterfactual thought experiments that

go into solving a Ramsey problem, for example. No amount of empirical

evidence drawn from within a self-con¬rming equilibrium can convince a