Trend agnostic one step estimation of DSGE models

DSGE models are currently estimated with a two step approach: data is first filtered and then DSGE structural parameters are estimated. Two step procedures have problems, ranging from trend misspecification to wrong assumption about the correlation between trend and cycles. In this paper, I present a one step method, where DSGE structural parameters are jointly estimated with filtering parameters. I show that different data transformations imply different structural estimates; the two step approach lacks a statistical-based criterion to select among them. The one step approach allows to test hypothesis about the most likely trend specification for individual series and/or use the resulting information to construct robust estimates by Bayesian averaging. The role of investment shock as source of GDP volatility is reconsidered.