The Analytic Theory of a Monetary Shock

We propose an analytical method to analyze the propagation of a once-and-for-all shock in a broad class of sticky price models. The method is based on the eigenvalue- eigenfunction representation of the dynamics of the cross-sectional distribution of firms’ desired adjustments. A key novelty is that, under assumptions that are appropriate for low-inflation economies, we can approximate the whole profile of the impulse response for any moment of interest in response to an aggregate shock (any displacement of the invariant distribution). We present several applications and discuss extensions.