Appendix B from John H . Cochrane , “ Determinacy and Identification with Taylor Rules

This appendix contains additional literature review and many extensions left out of the text for reasons of space. Sections A and B critically review more of the literature on identification and determinacy in new-Keynesian and related models. If you want to know " what about x's approach to these issues? " you are likely to find an answer here. In particular, Section A.1 reviews the learnability criterion advanced by McCallum (2003, 2009). Section A.2 reviews recent proposals by Loisel (2007) and Adão, Correia, and Teles (2011), which seem to solve the multiple-equilibrium question. In fact, they propose a limiting case with infinite eigenvalues, a subset of the timing issues reviewed below. Section A.3 reviews Atkeson, Chari, and Kehoe (2010). Section B on identification acknowledges the many papers that have made related points critical of identification in new-Keynesian models. It also tackles some attempts to overcome the identification problems. Lubik and Schorfheide (2004) try to identify the region—determinacy versus indeterminacy—without having to measure specific parameters using likelihood-based measures. I show generally that their identification comes from restrictions on the lag length of the unobservable shocks. Section B.3 shows that in general one sets to zero movement in eigenvectors corresponding to exploding eigenvalues, so the latter cannot be measured. Thus, the problems are not specific to the structure of the three-equation new-Keynesian model. Section B.4 reviews identification in full-system approaches, that is, complete models. Since none of those efforts have been focused on assessing determinacy, I do not cover them in the main text. For now, despite identification problems, the models impose eigenvalues greater than one and study dynamics. Section C collects some extensions of the frictionless model. Section C.1 explores identification in all the equilibria of the frictionless model. I show that for , we still cannot identify f separately from r. For f ! 1 f 1 1 and with a prior that , we can identify f for every equilibrium except the new-Keynesian choice. If the r ! 1 economy does explode, we can measure the speed of that explosion. Section C.2 explores the impulse-response functions of the simple model. The new-Keynesian model produces responses by supposing that endogenous variables jump to a different equilibrium. The subsection contrasts the response function in the new-Keynesian equilibrium, which combines an (implicit) fiscal shock with a monetary policy shock, to the response function in the active-fiscal equilibrium of the same model, which …