VARMA representation of DSGE models

•Simple conditions to determine most concise VARMA representation of a DSGE model.•Smets and Wouters (2007) model has exact VARMA(3,2) representation.•Parameters identifiable from entire likelihood also from identifiable VARMA terms.•Implications for identification, estimation, and inference in DSGE models.

This note develops simple conditions from which to determine the most concise VARMA representation of a given DSGE model. It is proven analytically that the Smets and Wouters (2007) model has exact VARMA(3,2) representation. In this model, the largest possible subset of structural parameters which is locally identifiable from the entire likelihood is also so merely from the subset of identifiable VARMA parameters.