scarcity of resources at our disposal. Creating dynamic equilibrium macro the-
ories and building a time series econometrics suitable for estimating them were
both big tasks. It was a sensible opinion that the time had come to specialize
and to use a sequential plan of attack: let’s first devote resources to learning
how to create a range of compelling equilibrium models to incorporate interest-
ing mechanisms. We’ll be careful about the estimation in later years when we
have mastered the modelling technology.
Evans and Honkapohja: Aren’t applications of likelihood based meth-
ods in macroeconomics now making something of a comeback?
Sargent: Yes, because, of course, a rational expectations equilibrium is
a likelihood function, so you couldn’t ignore it forever. In the 1980s, there were
occasions when it made sense to say, ‘it is too difficult to maximize the likeli-
hood function, and besides if we do, it will blow our model out of the water.’
In the 2000s, there are fewer occasions when you can get by saying this. First,
computers have gotten much faster, and the Markov Chain Monte Carlo algo-
rithm, which can be viewed as a clever random search algorithm for climbing a
likelihood function, or building up a posterior, is now often practical. Further-
more, a number of researchers have constructed rational expectations models
with enough shocks and wedges that they believe it is appropriate to fit the
data well with complete likelihood based procedures. Examples are the recent
models of Otrok and Smets and Wouters. By using log-linear approximations,
they can use the same recursive representation of a Gaussian likelihood function
that we were using in the late 1970s and early 80s.
Of course, for some nonlinear equilibrium models, it can be difficult to 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 figured 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 first-order conditions
for maximizing the likelihood function of a well fitting 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
difficult to complete a self-contained analysis of sensitivity to key features of a
specification.
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 specification and so long as
concerns about robustness endure.
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