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)

while the second normalizes the coefficient on the output gap level:

Et-1{[^-^μ (it ^- i*) ⁺ (1 ^{- ρ}) (V (^πt ^{- π}*)^{+ y}t ⁺ TT (^πt ^{- π}*)^{2 +} Y^y2 ) ^{+ ρ}(it-1 ^- i*)]^zt-1} = 0
λφ                λ              2λ           2

(8)

The latter specifications make it possible to estimate α and γ directly, and since these are
the structural parameters of the model, we refer to the values inferred upon (7) and (8) as

structural estimates.

An advantage of these normalizations relative to the reduced-form (6) is that they do not
implicitly impose a non-zero value for the weight on the interest rate level stabilization μ.
Moreover, to the extent that the inflation level and the output gap level significantly enter
the central bank policy rule, as they virtually do in all empirical literature, the reduced-
form coefficient on the interest rate gap (i_t — i*) is informative about μ such that a positive,
significant value of the convolutions (k⅛) and ( j⅛) implies a positive, significant value for μ.
While it is not possible to identify this policy preference parameter, we can evaluate whether
it is statistically different from zero and since the test is performed on the convolution rather
than on μ directly, we refer to it as a t-type test.

We estimate α and γ using nonlinear GMM and the set of instruments, zt-1, which includes
the measures of inflation and output gap in the baseline case. The reduced-form coefficients
are recovered from the estimates of the conditions (7) and (8) while the standard errors are
computed using the delta method. The results for the first and the second normalization are
reported in Table 4 and Table 5 respectively.

The structural estimates confirm, by and large, the reduced-form evidence. The implied
cis (i =1, 2, 3 and 4) are in most cases not statistically different from the estimates of the
previous tables and they provide empirical support for the presence of asymmetric preferences.
The squared variables do never have explanatory power with the exception of the output gap
in the pre-Volcker sample, whose estimate, c4 , is negative and significant. The structural
parameter α is never statistically different from zero whereas the significant values of γ over
the first sample are in line with the reduced-form estimates. In accord with the results of the
previous tables, the joint null of symmetric central bank preferences, which is now directly
tested on α and γ, is rejected before but not after 1979. Lastly, the t-type statistics for the null
hypothesis μ = 0 indicate that the central bank penalizes also the fluctuations of the interest
rate level and therefore they validate the restriction implicitly imposed by the reduced-form

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