I just returned from a conference at the San Franciso Fed on Monetary Policy and Financial Markets HERE where I discussed a paper by Fumio Hayashi and Junko Koeda. They use a novel way of identifying the effects of policy during periods of Quantitative Easing which recognizes that policy is different when interest rates are at the lower bound. An interesting take away from their paper is that QE is effective at reducing the output gap.
The Hayashi-Koeda paper suggests the following research topic for Ph.D. Students. H-K use an SVAR, i.e. a vector autoregression that is identified by making assumptions about the covariances of the variables. See Stock and Watson here for a summary of what that means.
The novelty in Hayashi Koeda is to allow for different coefficients of the VAR when the interest rate is at the lower bound. The pitfall here, is that although SVAR stands for "structural vector autoregression", there really isn't anything structural about it. An SVAR is just the reduced form of a DSGE model. And that means that the coefficients of the equations cannot be relied upon to remain constant if the policy rule changes.
Nothing new there -- we've known that for a long time. I was asked to discuss the paper because I've worked here (with Dan Waggoner and Tao Zha) on DSGE models where the parameters switch occasionally from one regime to another. Here is the interesting research topic. How are Regime switching SVARs of the kind estimated by Hayashi and Koeda, related to the Markov switching DSGE models that I studied with Dan and Tao?