922 Monetary Policy, Beliefs, Unemployment and Inflation
inferences from equations like (18.4) is possible only if future expected inflation
and output gaps were actually exogenous, which they are not. Complete system
adjustments are needed to judge what the interest rate response to changes in either
of the right-hand-side variables would be. This interpretative issue is addressed by
Dennis (2004), who argues that judgments on the relative weights attached to
inflation versus output stabilization require that central bank preferences be esti-
mated, and this requires that all the parameters in the system be estimated.^5 A
further econometric issue in these single-equation studies (both the NKPC and the
estimated Taylor rules) is the problem of weak instruments. Often, large numbers
of instrumental variables are used, and the risk is that the equations may be “over-
fitted,” with predicted values being very close to actual values, with results that are
close to ordinary least squares (OLS), as noted by Henry and Pagan (2004).
Moving to complete model estimates, there have been many studies using vector
autoregressive models (VARs) and structural vector auto regressive models (SVARs)
to evaluate the relative statistical contribution that changes in exogenous shocks
versus changes in model structures play in accounting for the changes in output
and inflation dynamics. Representative examples used here are Stock and Watson
(2002) (henceforth SW) and Boivan and Giannoni (2003) (henceforth BG). SW
provide decomposition results for the observed changes in inflation and output
volatility in the US, using estimated reduced form VARs of structural models akin
to (18.1)–(18.3) above,^6
X ̃t=#(L)X ̃t− 1 +ut, (18.5)whereX ̃tis a four variable vector of gross domestic product (GDP) growth, inflation,
the Federal Funds rate and the growth in commodity prices.^7 This latter equation
is appended as anad hocequation, so the set of variables in (18.5),X ̃t, differs from
those in the baseline NKPM (18.1)–(18.3) above. SW’s VAR estimates are fourth-
order VARs for two sub-samples of the period 1960–2001, pre- and post-1984Q1,
and the empirical results are noteworthy in that they show that it was changes in
the covariance matrix of the unforecastable components of the VARs that account
for almost all of the changes in the observed volatility of output. BG also report
unrestricted VAR estimates over two sub-samples divided at the end of the 1970s.
Broadly speaking, their findings are in line with the results of SW in that BG’s
unrestricted VAR results show that, if anything, monetary policy effects appear
weaker in the second sample.
However, comparative results from the SVARs reported by SW and BG give dif-
ferent conclusions as to the effectiveness of monetary policy over time in the US,
although each use a related, but different, version of the NKPM to identify their
structural VAR. Thus SW usea priorivalues of the slope of the AD curve, the slope
of the AS curve and the weight on forward-looking inflation in the AS curve. When
estimated over the two periods, their structurally identified decomposition of out-
put variability implies that most of the reduction in the second period is accounted
for by changes in the variability of shocks, not changes in monetary policy coeffi-
cients. Although the paper by BG also takes a model based on the closed-economy