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

This paper examines the roles played by innovations identified from a simpl e four-variable VAR characterized by cointegration. Using knowledge of coin tegration 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 tr ansitory innovations that are orthogonal to these permanent shocks. One of the permanent shocks displays all the characteristics of a technology or "s upply'' innovation, while one of the transitory innovations-identified by i mposing short-run price rigidity-is interpretable as a "demand'' side impul se. The permanent nominal shock bears the imprint of an innovation in aggre gate inflation expectations. Historical decomposition and comparison with v ariables that are external to the model reveals the relative importance of the shocks at various episodes.