Identification, long-run relations, and fundamental innovations in a simple cointegrated system

This paper examines the roles played by innovations identified from a simple four-variable VAR characterized by cointegration. Using knowledge of cointegration rank and "textbook'' relations that link macroeconomic aggregates, we identify distinct "real'' and "nominal'' innovations that dictate the long-run behavior of the model. We also examine the explanatory power of transitory innovations that are orthogonal to these permanent shocks. One of the permanent shocks displays all the characteristics of a technology or "supply'' innovation, while one of the transitory innovations-identified by imposing short-run price rigidity-is interpretable as a "demand'' side impulse. The permanent nominal shock bears the imprint of an innovation in aggregate inflation expectations. Historical decomposition and comparison with variables that are external to the model reveals the relative importance of the shocks at various episodes.