Gaussian Mixture Approximations of Impulse Responses and The Non-Linear Effects of Monetary Shocks

This paper proposes a new method to estimate the (possibly non-linear) dynamic effects of structural shocks by using Gaussian basis functions to parametrize impulse response functions. We apply our approach to the study of monetary policy and obtain two main results. First, regardless of whether we identify monetary shocks from (i) a timing restriction, (ii) sign restrictions, or (iii) a narrative approach, the effects of monetary policy are highly asymmetric: A contractionary shock has a strong adverse effect on unemployment, but an expansionary shock has little effect. Second, an expansionary shock may have some expansionary effect, but only when the labor market has some slack. In a tight labor market, an expansionary shock generates a burst of inflation and no significant change in unemployment.