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 -

1960:1 -1979:2

1982:4 2003:2

c1

0.67**

2.63**

(0.09)

(0.34)

c2

1.45**

2.17**

(0.31)

(0.35)

c3

-0.02

0.07

(0.02)

(0.18)

c4

-0.17**

-0.19

(0.04)

(0.10)

ρ

0.72**

0.83**

(0.05)

(0.02)

i*

5.4

6.0

π*

4.1

2.9

α

-0.06

0.06

(0.04)

(0.13)

γ

-0.25**

-0.18

(0.07)

(0.095)

W(2) p-value

.00 0

.16 1

F-stat p-value

.00/.00

.00/.00

J(19) p-value_______

________.969______________

_______________.895_______________

Specification: it = (1 - ρ)i* +c1 (πt - π ) + c2yt + c3 (πt - π )2 + c4y2 ] + ρt-1 + νt

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.

24



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