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)

two specifications only during the pre-1979 regime, and it thus corroborates the results of the
Wald tests for the presence of asymmetric preferences.

3.3 Robustness checks

We assess now the robustness of our findings to alternative measures of inflation and output
gap, and to different normalizations of the ortoghonality condition. Table 2 reports the
estimates obtained using, everything equals, the rate of change in the GDP deflator as measure
of inflation. The squared terms line up with those in Table 1 and translate into meaningful
preference parameters. Specifically, the coefficient on output gap, γ, always takes a negative
sign and is significant only during the pre-Volcker era, while the coefficient on inflation, α,
is never statistically different from zero. Lastly, the Wald statistics confirm that asymmetric
preferences matter before 1979, but not after 1982.

We re-estimate the policy rule (6) using the baseline inflation and the Hodrick-Prescott
filtered output. The results are shown in Table 3 and they bear out those from the previous
tables. A significant, negative value of the feedback coefficient c4 over the first sub-sample
maps into a significant, negative value of the asymmetric preference on output, whereas no
asymmetry is detected for inflation. Once more, the null hypothesis of symmetric preferences
is rejected only during the pre-Volcker regime.

3.4 Structural estimates

One econometric issue we must confront with is that, in small samples, nonlinear GMM may be
sensitive to the normalization of the orthogonality conditions (see Fuhrer, Moore and Schuh,
1995). Moreover, specific parameterizations of the central bank Euler equation may allow us
to draw direct inference on the structural parameters α and γ . To address these issues, we
rearrange the targeting rule in two alternative forms that we view as most natural for the
problem at hand. To keep consistency with the reduced-form specification, we introduce a
lagged interest rate. The first specification normalizes the coefficient on the inflation level to
unity:

^{- π}*)⁺∣yt⁺2 (^πt^{- π}*)^2+γ2∣y²)⁺ρ(it-ι^- i*)]zt-ι}=0

(7)

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