The Analytic Theory of a Monetary Shock

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