As the focus of our analysis is on asymmetric preferences, we choose to fix a value for π*.
Specifically, we conduct a grid search in the 1% neighborhood of the subsample inflation
mean, which is 4.5% for the pre- and 2.8% for the post-1979 period respectively, and we
select the value that provides the best fit. Moreover, as restricting i* appears beneficial for
the convergence of the optimization algorithm, we assume that the subsample average of the
interest rate provides a reasonable approximation for the target.
Table 1 reports the GMM estimates of the interest rate rule (6) for the baseline case, which
corresponds to the CBO output gap and PCE inflation. The squared output gap term, c4 ,
is highly significant over the pre-Volcker regime in the second column but loses most of its
explanatory power during the later period in the third column. The squared inflation term,
c3 , appears relatively more relevant in the post-Volcker sample, though it is never statistically
different from zero at the 5% significance level.
The estimates of the asymmetric preferences parameters are recovered from the feedback
coefficients and the standard errors are computed using the delta method. Interestingly, α
and γ take the expected signs and, in accord to the reduced-form estimates, the asymmetric
preference on output is the significant parameter before 1979.7 Specifically, a 0.3 estimate
of γ implies on impact a 75 point basis cut of the interest rate in response to a negative 2%
output gap but only a 42 point basis rise in response to a positive 2% gap. By contrast, after
1982 both coefficients become of limited importance and the Wald statistics in the second but
last row indicates that the null hypothesis of symmetric preferences is not rejected at the 5%
significance level, although it is rejected at the 10% level.
Finally, in order to gauge the forecasting advantages of the nonlinear (as opposed to
the linear) monetary policy rule, we perform a version of the Diebold and Mariano (1995)
test, which is designed to detect any difference in the predictive accuracy of two competing
forecasts. To this end, we first compute the dynamically simulated fitted values of the two
models and then we calculate the corresponding root-mean-squared error (RMSE) over both
sub-samples. The RMSE of the linear model is 0.96 in the pre-Volcker period and 0.65 in the
post-Volcker period, while the values of the nonlinear model are 0.78 and 0.63, respectively.
The Diebold-Mariano test rejects the null hypothesis of no difference in the accuracy of the
7The results are robust to letting the pre-Volcker sample begin in 1966:1 when the Federal funds rate first
traded consistently ab ove the discount rate.
11