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)

output gap, the long-short interest rate spread, and the PCE inflation. When the squared,
and then the squared and the cubes of the predictions π_t are added to the original equation,
the corresponding F-tests show that the null hypothesis of non-misspecification is not rejected.
This suggests that the US aggregate supply curve is well approximated by a linear relation,
consistently with the findings in Dolado, Maria-Dolores and Ruge-Murcia (2004).

An additional form of nonlinearity comes from the policy makers’ (mis)perception of the
state of the economy. Suppose that on the basis of the estimates available in real-time the
Fed believed for part of the sample that the output gap was larger than the revised data
indicates. Then, the policy interventions during that period may appear surprisingly activist
given the values of the gap from the 2003 vintage. However, using real-time data Orphanides
(2004) finds that the Fed response to the output gap was actually more activist in the 1970s
when the misperceptions on potential output turned out to be more severe. Moreover, Kuha
and Temple (2003) show that measurement error in quadratic regressions tends to hide the
presence of nonlinearities. In the view of these arguments, this paper takes an essential step
towards asymmetric preferences by extending the available evidence on monetary policy rules
using revised data.

A further reason for nonlinearity is associated with the point estimates of the natural
rate of real activity. Meyer, Swanson and Wieland (2001) show that in periods of heightened
uncertainty about the NAIRU, the central bank may face an incentive to move policy rates
only for sufficiently large deviations of unemployment from the target. While potentially
relevant, this hypothesis testing would require a real-time series for potential output such as
to reflect the policy makers’ beliefs about the state of the economy at the time decisions were
taken. For reasons discussed above, however, we use the official estimates of potential output,
which are actually revised by the CBO on a regular basis. As these revisions sensibly reduce
the uncertainty about the historical measures of the output gap, this form of nonlinearity is
likely to play only a minor role in our analysis.

3.2 Reduced-form estimates

The empirical analysis is complicated by the fact that it is not possible to recover all structural
parameters of the model from the estimates of the central bank Euler equation. In particular,
the preference parameters α and γ are not identified. A simple transformation of the model

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