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

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Bayesian FAVARs with Agnostic Identification 5 sampling seems to be unfavorable. The aim of this paper is threefold. First I critically examine the result by BBE and provide an answer why they arrive at inferior results and how one should apply this procedure to receive more reasonable results. I like to combine the Bayesian FAVARs with the agnostic identification by Uhlig (2005). To my best knowledge this has not been done yet in the current literature on empirical macroeconomics. Hence I tackle the question raised above in a complete consistent Bayesian framework. Not only the factors and the parameters of interest are estimated with Bayesian methods, more importantly I apply the agnostic identification in order to identify the specific effects induced by contrac- tionary monetary policy. Here I try to be as precise as possible and as close as possible to the conventional wisdom. This is accomplished by setting different ”block criteria” that successively become stricter, while imposing more restrictions. This approach holds an enticing promise in that one can narrow down the space of economically reasonable dynamic reactions as accurate as the data allows. We do not have to set restrictions on only one price variable, one of the monetary aggregates and one short term interest rate as it has been applied so far and is common practice when applying sign-restrictions in the VAR framework. Having available such a large datasets, provides the possibility to be more strict in imposing e.g. not only the CPI to react non-positively after a monetary policy shock but also other price variables that are incorporated in the estimation procedure. This serves the possibility to identify the structurally, reaction of the economy in an more exact manner than other identification approaches common in the literature on empirical macroeconomics. The second contribution and also the most time consuming one was to provide a Mat- lab code that does the estimation and identification. Here the major challenge has been to provide a code that is as efficient as possible, especially with respect to the calculating time and the memory required in a way that also students can run the program on PCs of ”common” capacity without waiting a week for the results. The Gibbs sampling procedure
6 Bayesian FAVARs with Agnostic Identification itself is a very cumbersome computer intensive and memory intensive estimation method that applied to such large datasets might take very long to produce results. The challenge is to combine the Gibbs sampling with the agnostic identification procedure which itself is time consuming. How the code accomplishes this challenge is explained on the section about the Matlab implementation. Third we present results that seem reasonable and consistent with the conventional wisdom in like the ones by BBE. This indicates that the key to the question above is the identification scheme. More importantly the results confirm the lead of Sims to avoid unreasonable identifying assumption. Hence opposed to the conclusion of BBE our results confirm that not only information is very important but one receives reasonable estimation results in combination with economically sound identification schemes such as the agnostic identification using a broader set of sign-restrictions. The main results are that the Bayesian estimation of FAVARs combined with the agnostic identification of Uhlig [2005] deliver results according to the conventional wisdom where no prize puzzle arises. It seems to be the crucial issue why Bernanke, Boivin and Eliasz [2005] arrive at inferior results compared to the two-step principal component estimation. They apply a standard recursive identification scheme. Furthermore the greater information set allows the researcher to be more strict w.r.t. to the sign restrictions im- posed, in order to disentangle the dynamic effects of a shock to monetary policy more exactly. However one should be cautious with the conclusion, due to the fact that one should collect results for longer Gibbs iterations in order to assure the results. One should also try out several number of factors and also report their contribution via variance decom- position. The next section gives an overview of the relevant literature followed by an introdution into dynamic factor models in section 3. Section 4 starts to explain the FAVAR framework with its different identification and various estimation approaches. Furthermore a short
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