Inflation Targeting and Nonlinear Policy Rules: The Case of Asymmetric Preferences (new title: The Fed's monetary policy rule and U.S. inflation: The case of asymmetric preferences)

erence over inflation stability is normalized to one so that λ and μ are expressed in relative
terms. The inflation target is π* whereas the parameters α and γ capture any possible asym-
metry in the loss function. Varian (1974) and Zellner (1986) proposed a linex specification
similar to (4) in the context of Bayesian econometric analysis while Nobay and Peel (2003)
introduced this form in the optimal monetary policy literature.⁴

A negative value of γ implies that, everything equals, an output contraction relative to the
potential level is weighted more severely than an output expansion of the same magnitude. To
see this notice that whenever yt < 0 the exponential component of the loss function dominates
the linear component while the converse is true for y_t > 0. A similar reasoning holds for the
coefficient α. However, if the monetary authorities are more concerned about overshooting
π* rather than undershooting it, the value of α would be positive meaning that high inflation
relative to the target is more costly than low inflation. It should be noted that while these sign
predictions seem plausible given the sample we use, the linex specification does not prevent
α to be negative corresponding to a case in which the risk of deflation outweighs the risk
of inflation. Figure 1 compares the standard quadratic with the linex function for both the
inflation (panel a) an the output (panel b) objective.

The linex function nests the quadratic form as a special case so that when both α and γ go
to zero L_t reduces to the symmetric parametrization 2 [(π_t — π*)² + λy_t² + μ (it — i*)2∣. The
latter can be obtained as a second order approximation of the utility-based welfare function in
a New-Keynesian model of the business cycle that involves a zero lower bound for the nominal
interest rate (see Woodford, 2003, ch. 6). It follows that under the null of a quadratic
loss, the policy preferences are functions of some primitive parameters of the model and
therefore potential evidence of asymmetries in the central bank objective may be interepreted
as evidence of asymmetries in the representative agent’s utility. The implication is that
business cycle fluctuations may have important welfare effects beyond the second order.

2.3 A nonlinear policy rule

We solve for the optimal monetary policy under discretion. Because no endogenous state vari-
able enters the model, the intertemporal problem reduces to a sequence of static optimization

⁴ Additional references include Chadha and Schellekens (1999), Ruge-Murcia (2003) and Surico (2003).

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