Impulse Response Analysis in Conditional Quantile Models and an Application to Monetary Policy

This paper presents a new method to analyze the e¤ect of shocks on time series using quantile impulse response function (QIRF). While conventional impulse response analysis is re- stricted to evaluation using the conditional mean function, here, we propose an alternative impulse response analysis that traces the e¤ect of economic shocks on the conditional quantile function. By changing the quantile index over the unit interval, it is possible to measure the e¤ect of shocks on the entire conditional distribution of a given variable in our framework. Therefore we can observe the complete distributional consequences of policy interventions, especially at the upper and lower tails of the distribution as well as at the mean. Using the new approach, it becomes possible to evaluate two distinct features, namely, (i) the degree of uncertainty of a shock by measuring how the dispersion of the conditional distribution is changed after a shock, and (ii) the asymmetric e¤ect of a shock by comparing the responses to an impulse at the lower tails with those at the upper tails of the conditional distribution. None of these features can be observed in the conventional impulse response analysis exclusively based on the conditional mean function. In addition to proposing the QIRF, our second contribution is to present a new way to jointly estimate a system of multiple quantile functions. Our proposed system quantile estimator is obtained by extending the result of Jun and Pinkse (2009) to the time series context. We illustrate the QIRF on a VAR model in a manner similar to Romer and Romer (2004) in order to assess the impact of a monetary policy shock on the US economy.