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 2: Reduced-form Estimates

- alternative measure of inflation -

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 the rate change in the gdp deflator and the output gap is
obtained using the CBO potential output. The instrument set includes four lags of
inflation, squared inflation, output gap, squared output gap, the fed funds rate and
personal consumption inflation. The asymmetric preference parameters are computed as
α=2c₃∕c₁ and γ=2c₄∕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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