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

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Bayesian FAVARs with Agnostic Identification 35 There is the BBE FAVAR identification scheme, also applied in this thesis, and a slightly modified version that is applied by Stock and Watson (2005). Furthermore the approach of Favero and Marcellino (2005) and Favero, Marcello and Neglia (2004) is introduced in the survey by Stock and Watson (2005). Here as in the VAR case the factor’s structural shocks are assumed to be linearly related to the reduced form factor innovations. vt = Qut where Q is a an (orthonormal) invertible [q × q] matrix. For identifying the trans- formation matrix Q there are two ways. The one is the full system identification by Blanchard and Watson (1986) who strive to identify all elements of Q. The other approach is the single-equation identification where only one row of Q is required in order to identify the one respective shock. The latter one is the relevant one for us as, we are interested only in the identification of the shock attributable to monetary policy. There- fore we interested in a single row qs of the orthonormal matrix Q . Uhlig’s Sign Restriction As already introduced the sign restriction approach in its version advanced by Uhlig (2005) is the most reasonable approach in my view. Conventional wisdom says that after a monetary policy contraction the federal funds rate should increase, the prices should fall, and finally real output should fall. In other identification schemes that do not accomplish this wisdom, the researchers tend call this empirical observation a ”puzzle”. There are even some researchers that try to build a model producing such puzzles out of a model as has been done by CEE(2005). This seems unreasonable to me, because here one has to be very certain about the chosen identification scheme, and neglect any possible estimation mistakes not accomplished by the identification scheme chosen. Sims gives the advice to avoid unreasonable identification schemes. The approach by Uhlig seems reasonable,
36 Bayesian FAVARs with Agnostic Identification especially regarding the application FAVARs of DFMs. Because in these frameworks one incorporates by far more relevant information than in the VAR methodology, and therefore one can set more restrictions in that sense that for instance not only CPI should fall after a monetary policy contraction but all the prices considered. Of course this becomes computationally by far more demanding than the other identification schemes and also than in the VAR case, because here we have now by far more information and respectively more ”reasonable” restrictions to set. It is straightforward that this method generates very few relevant candidate impulse responses due to the fact that the set of acceptable impulse responses is reduced due to the increased number of restrictions. It might and in practice is a difficult task to find an impulse vector that satisfies the ”stricter” restriction. This should not be considered as a disadvantage, it simply reflects that the economy is multi-causal where many things happen simultaneously and dynamically interact. From this fact one can deduce that the task to disentangle the effects of one single shock is very difficult, in particular has to satisfy a lot of ”economic conventional wisdom” in order to be identified as a mere effect of a single cause out of many. I would not go so far and state that with this method the shock is perfectly identified, but to me it seems that this approach is one of the more reasonable ones that are available especially with respect to the large set of information available, and furthermore provides at least the possibility to figure out very precise respones after a shock induced by the monetary authority. The task is first to identify the structural shock wt according the FAVAR innovation vt. It is actually the same concept as in the VAR case, except that the innovations one has are factor and not VAR variable innovations. The relation between the reduced form dynamic factor innovation vt and the structural factor innovation wt is given by wt = Avt The matrix A is an orthogonal invertible matrix of order [(K + M) × (K + M)]. We are only interested in identifying one single shock therefore it is sufficient to identify one single row as where s refers to the respective shock. This single-equation identification is the more common approach that most of the recent literature pursue. The alternative
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