We study what happens to identified shocks and to dynamic responses when the data generating process features q disturbances but less than q variables are used in the empirical model. Identified shocks are mongrels: they are linear combinations of current and past values of all structural...

We propose a method to estimate time invariant cyclical dynamic stochastic general equilibrium models using the information provided by a variety of filters. We treat data filtered with alternative procedures as contaminated proxies of the relevant model-based quantities and estimate structural...