problems. This amounts to choosing in each period the instrument it such as to minimize:
ee∏πt-π*)] - α (∏t - ∏*) - 1
Et-1 α2
+ λEt-1
e(^γyt ) — γyt — i
Y 2
+ 2 (it — i*)2 + Ft
subject to ∏t = kyt + ft and yt = -φit + gt, where Ft ≡ Et-i ∑∞=1 δτLt+τ, ft ≡ θEtπw + εf
and gt ≡ Etyt+i + φEtπt+ι + εd are taken as given reflecting the fact that the monetary
authorities cannot directly manipulate expectations. The first order condition reads
and it implicitly describes the optimal, possibly nonlinear response of the central bank to the
developments in the economy. Equation (5) nests the linear form as a special case and when
both α and γ tend to zero the reaction function collapses to an implicit interest rate rule of
the type analyzed in Rudebusch (2002), and Clarida, Gali' and Gertler (2000):
-Et-i
e[α(πt-π*)]
α
-1
kφ - Et-1
e(γyt)
λφ + μ (it — i*) — 0
(5)
-kφFt-i (∏t - π*) - λφEt-i (yt) + μ (it — i*) — 0
This feature is attractive as it implies that the hypothesis of symmetric central bank
preferences can be tested simply by evaluating the functional form of the reaction function.
3 Empirical results
This section reports the estimates and the relevant tests of the targeting rule. The analysis
is conducted on US quarterly data spanning the period 1960:1-2003:2. The data set has been
obtained in July 2003 from the web site of the Federal Reserve Bank of St. Louis and embodies
alternative measures of inflation and output gap. In the baseline case, inflation is measured
as the changes in the log of the personal consumption expenditure (PCE) deflator while the
output gap is constructed using the series of potential output provided by the Congressional
Budget Office (CBO). Figure 2 plots the baseline series. As a way to provide a robustness
check, we also report the results for two alternative measures of inflation and output gap,
namely the GDP deflator and the Hodrick-Prescott filtered real GDP.5
5 The use of a low frequency filter to obtain estimates of the target level of real activities does not contrast
with the model-based definition of flexible-price level of output. As argued by Woodford (2003, ch. 7), the
central bank can make society better off by accommodating technology and preference shocks while offsetting
disturbances to inflation and wage mark-ups. In this vein, Smets and Wouters (2003b) show that if the monetary
authorities wish to hedge against shocks of unknown nature, they would regard persistent disturbances as the