The Analytic Theory of a Monetary Shock

We propose a new 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 cross-sectional process for price adjustments and provides a thorough characterization of the entire impulse response function of any moment or function of interest, in response to a once-and-for-all aggregate shock (any displacement of the initial distribution). We use the method (i) to discuss a general analytic characterization of the “selection effect” in sticky-price models, (ii) to show that the response of the cross-sectional dispersion of prices to a small shock is zero at all horizons, (iii) to derive a parsimonious representation of the output response to monetary shocks, and the key parameters determining its shape, (iv) to study the propagation of monetary shocks after a change in volatility.