Measuring the Effects of a Shock to Monetary Policy - Humboldt ...

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Bayesian FAVARs with Agnostic Identification 15 limN→∞N −1 N N |E(eitejt)| < ∞ i=1 j=1 The decision which approach to choose will depend on the estimation procedure de- sired to apply. The frequentists DPA approach allows for an approximate DFM, the Bayesian requires an exact DFM specification. From my perspective, the question which approach rather to pursue has not yet been sufficiently and conclusively enough answered in the literature. BBE provide results for both specifications and estimation approaches. Based on their results, which favors the classical nonparametric two-step estimation, they conclude implicitly that the approximate specification might be the better one. Here one should be very cautious, because the results BBE compare, might not necessarily be representative enough to draw a conclusion w.r.t. to the model choice. This will become clear when comparing the likelihood based results with the two alternative identification schemes. As the results differ qualitatively the conclusion based on the results becomes invalid. In the section on the empirical results I will show, that with reasonable identify- ing assumptions such as the ”agnostic identification” one can get very reasonable results in an Bayesian framework. This does not give an obvious hint what the correct approach should be, but at least one can conclude that the Bayesian approach does not suffer from the structure it imposes on the idiosyncratic component. Therefore the structure imposed must not be an unreasonable restriction on the model. It remains to further research on this specific issue to prove conclusively. More precise assumptions of DFMs can be found in the section on identification and normalization.
16 Bayesian FAVARs with Agnostic Identification 4 The Econometric Framework 4.1 FAVARs As already stated, the idea behind the FAVARs is to combine the standard structural VAR analysis with the recent developed and advanced features of dynamic factor models estimating a joint VAR that contains factors extracted from large panel of informational data and in addition perfectly observable time series that have pervasive effects on the economy such as the short-term interest rate set by the central. Therefore BBE labeled the model in a straight forward manner ”factor-augmented VAR”. This approach is well suited for structural analysis such as impulse response analysis and variance decomposi- tion (in particular for the problem at hand). For the estimation procedure the model has to be cast into a state-space representation. For the rest of the thesis I will mostly follow the approach and notation of BBE otherwise explicitly stated. The model consists of the two equations (1) and (2) introduced in the previous section. The FAVAR equation (2) already has the form to build the state equation to which one also refers often to as the transition equation. Equation (2) represents the joint dynamics of factors and the observable pervasive variables (Ft, Yt). ⎡ ⎢ ⎣ Ft Yt ⎤ ⎡ ⎥ ⎢ ⎦ = Φ(L) ⎣ Ft−1 Yt−1 ⎤ ⎥ ⎦ + vt (3) vt ∼ N(0, Q) (4) Here the variable Yt denotes the [M × 1] vector of observable economic variables that having pervasive effects throughout the economy. The index t = 1, ..., T represents the time the term Φ(L) represents a conformable lag polynomial of order d. In our specification that follows BBE Yt is assumed to represent the policy instrument,e.g. the
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