Bootstrap lag selection in DSGE models with expectations correction

A well known feature of DSGE models is that their dynamic structure is generally not consistent with agents’ forecasts when the latter are computed from ‘unrestricted’ models. The expectations correction approach tries to combine the structural form of DSGE models with the best fitting statistical model for the data, taken the lag structure from dynamically more involved state space models. In doing so, the selection of the lag structure of the state space specification is of key importance in this framework. The problem of lag selection in state space models is quite an open issue and bootstrap techniques are shown to be very useful in small samples. To evaluate the empirical performances of our approach, a Monte Carlo simulation study and an empirical illustration based on U.S. quarterly data are provided.