| by Jeffrey
C. Fuhrer and Giovanni
P. Olivei
No. 1, January 2004 - August 2004
Motivation for the Research
The basic framework for macroeconomic analysis has the structure
of a simple model consisting of a demand or “IS”
equation, an inflation or “AS” equation, and a
monetary policy reaction function. Over time, this model has
evolved from the static Keynesian model into a micro-founded,
rational expectations model — often labeled the “New
Keynesian” model — in which expectations play
a dominant role in the structural equations. Expectations
of current and future interest rates affect current aggregate
demand, and expectations of current and future aggregate demand
affect current inflation.
Different empirical studies have reached different conclusions
concerning the importance of expectations regarding future
interest rates and future demand in determining the dynamics
of current output and inflation in applying the “New
Keynesian” model to real-world analysis.
This paper aims to resolve the differences by providing an
explanation for the disparate nature of the empirical results
on forward-looking demand and inflation relations.
Research Approach
The authors compare different methods for estimating forward-looking
output and inflation Euler equations and show that weak identification
can be an issue in conventional Generalized Method of Moments
(GMM) estimation. Weak instruments lead to GMM point estimates,
hypothesis tests, and confidence intervals that are unreliable.
The authors then propose a GMM procedure that uses projections
that impose the dynamic constraints implied by the forward-looking
relation instead of instrumenting by means of simple linear
projections on the instruments set. They label this procedure
an “optimal” instruments approach.
Finally, the authors use Monte Carlo simulations to test
the performance of the optimal
instruments approach against conventional GMM estimation.
Key Findings
- The authors find weak identification in the GMM estimation
of these macroeconomic relations (as in previous research),
and they demonstrate that in a weak instruments context
conventional GMM estimates may be biased.
- In contrast to conventional GMM estimation, GMM estimation
with optimal instruments produces estimates that are properly
centered around the true values.
- Estimates obtained by GMM with optimal instruments are
comparable to the estimates obtained via maximum likelihood
(ML), and, in contrast to ML estimation, GMM estimation
does not require assumptions about the type of distribution
for the structural shocks.
Implications
The authors argue that the disparate nature of the extant
empirical findings is largely dependent on the estimation
methodology. Since weak identification can be an issue in
conventional GMM estimation of output and inflation forward-looking
relations, it is important to employ methods that are more
reliable than GMM when instruments are weak. Overall, the
findings support the use of optimal instruments techniques
when estimating output or inflation Euler relations. Optimal
instruments methods also provide a tighter test of the Euler
relation because they impose a constrained reduced form that
is the rational-expectations solution to the relation at hand.
In so doing, optimal instruments methods exploit the most
distinguishing feature of dynamic rational-expectations models.
Full text of Working
Paper 04-2 
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