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)

that confronts directly the issue involves the linearization of the exponential terms in (5) by
means of a first-order Taylor series expansion. We solve the resulting expression for i_t and
prior to GMM estimation we replace expectations with realized values. As customary in the
empirical studies, we introduce a lagged dependent variable to capture interest rate smoothing
for which a number of explanations are provided in the literature (see Woodford, 1999, Sack
and Wieland, 2000, and Castelnuovo, 2003).⁶ We estimate the following policy rule:

it = (1 - ρ) P* + C1 (πt - π*) + c2yt + C3 (∏t - π*)2 + C4 (yt)2] + pit-1 + νt

where the coefficients are given by the expressions

_ kφ _ λφ _ αkφ _ λφγ
μ ’         μ ’          2μ ’          2μ

and the error tems is defined as

c1 (πt - Et-1πt) + c2 (yt - Et-1yt) +
+c3 ^hπ_t² - Et-1 (πt)²ⁱ + c4 ^hy_t² - Et-1 (yt)²ⁱ

The term in curly brackets is a linear combination of the forecast errors while e_t is the
remainder of the Taylor series approximation. Thus, ν_t is orthogonal to any variable in
the information set available at time t - 1.

Equation (6) makes clear that the reaction function parameters can only be interpreted as
convolutions of the coefficients representing policy makers’ preferences and those describing
the structure of the economy. Nevertheless, the estimates of the policy rule can now identify
the asymmetric preferences and - up to an additional assumption discussed below - α =2c3 /c1
and γ = 2c4/c2 . The feedback coefficients c3 and c4 embody the relevant information such that
the joint restriction c3 = c4 =0with c1 6=0 and c2 6=0 implies α = γ =0. Hence, testing the
hypothesis H₀⁰ : c3 = c4 =0in (6) is equivalent to testing the hypothesis H0 : α = γ =0in (5).
Under the null of a linear reaction function, which fully corresponds to the null of symmetric
preferences, the statistics has an asymptotic χ² distribution with as many degrees of freedom
as the number of restrictions, and it can be successfully evaluated through a standard Wald
test.

In the absence of further assumptions our method only identifies the structural parameter
on output gap asymmetry, γ, but neither the one on inflation, α, nor the target π^* , separately.

⁶ Interestingly enough, a policy rule with no interest rate smoothing (estimates not reported but available
upon request) delivers an even stronger evidence of nonlinearity. It follows that the specification adopted in
this paper minimizes, if any, the degree of asymmetries. This observation deserves independent attention.

10

<<   8   9   10   11   12   13   14   >>

More intriguing information