where we have used the fact that the output gap has an unconditional distribution with zero
mean and variance σ2y .
The average inflation bias arises here because policy preferences are asymmetric with
respect to the output gap rather than because the desired level of output is above potential
like in Barro and Gordon (1983). The distortion increases with the degree of asymmetry,
and to the extent that the penalty associated to an output contraction is larger than the
penalty associated to an output expansion of the same size, the model predicts γ<0.Asλ
and k are positive, the difference between the model-based inflation mean and the inflation
target represents an inflation bias rather than a deflation bias. When γ is equal to zero,
the expected marginal benefit of a policy intervention becomes linear and the inflation bias
disappears together with the precautionary motive.
The average inflation bias is proportional to the variance of the output gap and, as shown
by the first equality in (10), it is inversely related to the inflation slope of the targeting rule
(9). Hence, the model is rich enough to confront the explanatory power of a change in the
asymmetric preference parameter over the output gap, γ , with two alternative interpretations
of the behavior of US inflation. The first is a shift in the response to the inflation level as
captured by c1 . The second is a difference in the variance of the shocks as proxied by σy2 .
4.2 Measuring the bias
We estimate equation (9) using GMM with a four lag Newey-West estimate of the covariance
matrix. The measures of inflation and output gaps and the instrumental variables refer to
the baseline case. The only difference relative to Table 1 is that, in line with the restriction
c3 =0, the four lags of the squared inflation are not included here as instruments. The
results are shown in Table 6 and they turn out to be sufficiently close to those reported in
the previous tables that we do not comment further. The restrictions discussed above allows
us to identify the inflation target, which is found to move from 3.61% during the 1960s and
1970s to a statistically lower 2.77% during the last two decades. Interestingly enough, this
result contrasts with most of the empirical literature on monetary policy rules that, neglecting
asymmetric preferences on the output gap and therefore imposing a linear reaction function,
usually find a difference in π* over subsamples of two-to-three percentage points.
We use the estimates of table 6 to compute the inflation bias implied by the model,
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