ysis into canonical Vector Autoregressive (VAR) models. We consider a covariance
stationary VAR with identified shocks in which the shocks do not only affect the con-
ditional mean of the variables but also change their conditional distributions, where
the distributional changes are captured by a multivariate-multiquantile model for the
forecast error processes. The suggested quantile model is a multivariate generalization
of the mixture of the quantile autoregression (QAR) and the conditional autoregres-
sive Value at Risk (CAViaR), in which the conditional quantiles are linear functions of
the lagged variables and the lagged conditional quantiles. We propose a new impulse
response function (IRF) to capture possible asymmetric responses of the risk struc-
ture to positive and negative shocks. The IRF consists of two parts; the expected IRF
(EIRF) which is equivalent to the conventional IRF and is symmetric with respect
to the direction of economic shocks, and the IRF in multiple quantiles (QIRF) which
allows for asymmetric responses to positive and negative shocks. The estimation can
be done by applying the quasi maximum likelihood estimation (QMLE) of Komunjer
(2005), and White (1994). We provide conditions for the consistency and derive the
asymptotic distribution of the quantile estimator.
The proposed method is applied to assess the impact of a monetary policy shock
on the US economy. The set of variables in the VAR includes the monthly growth
rate of industrial production index, the monthly inflation rate of PPI final goods,
and the measure of the monetary policy shocks. Following Romer and Romer (2004),
the monetary policy shock is measured by the intended federal funds rate after elim-
inating the systemic response to the observed information. Using the monthly data
spanning from January 1969 to December 2007, the estimated impulse response func-
tions show that a contractionary monetary policy shock associates with 1) a large
decrease in upper side inflation risk, 2) a minor increase in lower side inflation risk,
3) a moderate reduction of lower side growth risk, and 4) no clear change pattern
in upper side growth risk. An expansionary shock results in the opposite changes.
Thus, a tightening monetary policy shock reduces the high inflation risk with a minor
cost, while a loose policy has only a mild risk benefit with a cost of large increase in
high inflation risk. This result indicates that contractionary rather than expansionary
money policy is more effective in reducing risks, and policy makers should be more
cautious when easing money.