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-confirming’ 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 conditioned on per-
tinent histories that are implied by the model, where proximity is measured
by a Kullback-Leibler measure of model discrepancy (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 function could be improved.
However, suboptimal forecasting functions could not be sustained in the
limit if you were to endow agents with sufficiently flexible 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
fit flexible 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 conditioning
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 hyperinflations that Albert Marcet and I,
and Stan Fischer and Michael Bruno also, found would not be stable under
various adaptive schemes. That finding is important for designing fiscal policies
to stabilize big inflations.
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 refine what we mean
by rational expectations equilibria. In addition to the equilibria with ‘optimal
misspecified 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.