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)

Table 3: Reduced-form Estimates

- alternative measure of output gap -

Specification: i_t = (1 - ρ)i* +c₁ (π_t - π ) + c2y_t + c3 (π_t - π )2 + c4y2 ] + ρ_t-1 + ν_t

Notes: Standard errors using a four lag Newey-West covariance matrix are reported in
brackets. Inflation is measured as changes in the personal consumption deflator and the
output gap is obtained with the Hodrick-Prescott filter (smoothing parameter = 1600).
The instrument set includes four lags of inflation, squared inflation, output gap, squared
output gap, the fed funds rate and gdp inflation. The asymmetric preference parameters
are computed as α=2c₃Zc₁ and γ=2c√c₂ while the standard errors are obtained using the
delta method. W(n) refers to the Wald statistics of the test for n parameter restrictions,
which is distributed as a χ²(n) under the joint null hypothesis c3=c4=0. The latter is
equivalent to the original null of symmetric central bank preferences, α=γ=0. F-stat
refers to the statistics of the hypothesis testing for weak instruments relative to
inflation and output gap, respectively. J(m) refers to the statistics of Hansen’s test for m
overidentifying restrictions which is distributed as a χ²(m) under the null hypothesis of
valid overidentifying restrictions. The superscript ** and * denote the rejection of the
null hypothesis that the true coefficient is zero at the 1 percent and 5 percent significance
levels, respectively.

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