DSGE prior weight

How much do we learn from the DSGE model and what is it’s optimal value? The key metric for that is the DSGE prior weight explained before and denoted byλ. It distribu-tion can be found in figure (4.2). The posterior mode value isλ_mode =.87 which is close but slightly less then the applications of Del Negro and Schorfheide [12] who find for their application to the post-world war II US data optimal values ofλ ∈ {.75, 1, 125}. Note that I assume a rather uninformative uniform prior on the interval [0, 5]. Even much wider intervals like[0, 100]resulted in very similar posterior distribution for the weightλwhich is narrowly peaked around the posterior mode. Therefore I stick to the lower range interval as the choice of the optimalλand it’s posterior distribution is not affected. This way the integration on low likelihood parameters is avoided and hence the simulation of the marginal data density is not artificially deteriorated¹³.

Figure 4.2:Posterior distribution of Model weight: λ

13Adjemian et. al [2008].

4.6 Empirical Results

4.6.7 Impulse Response function Analysis: Monetary Policy Shock 4.6.7.1 Comparison: DSGE-DFM vs. DSGE

In order to detect the difference in the monetary transmission mechanism implied by the pure DSGE model and the DSGE-DFM I plot the respective calculated impulse re-sponse functions against each other in figure (4.3). The reaction of the real indicators such as real GDP, real wages and in particular real investment is significantly stronger than implied by the DSGE-DFM. In contrast the impulse response function of infla-tion is less strong. Overall one can observe that the DSGE impulse response funcinfla-tions have a hump-shaped response between 4-6 quarters. An exception is the interest rate response which is strongest on impact and afterwards dies out to the pre-shock level after 8 quarters. The persistence in the DSFE-DFM is less for all variables except for in-terest rates where the reaction is stronger with respect to the scale and shows a higher persistence.

Figure 4.3:IRF of DSGE-DFM-Indicator

4.6.7.2 Identification of DSGE-DFM via DSGE rotation with block-diagonalΛ

As noted before the DSGE rotation based identification of the DSGE-DFM relies on the block-diagonally restrictions imposed on the factor loading matrix to uniquely iden-tify the factors against rotational indeterminacy. Hence by construction there is

homo-geneity in the shape of the impulse response functions as the are multiple scalars of the factor impulse response functions. However differences in the scale can be ana-lyzed which gives insights to the exposure of the single member countries to aggregate shocks. In general I find that this approach is associated with a rather high degree of uncertainty compared to the DSGE-DFM case identified with sign restrictions. The re-sults reported suggest that the impulse response functions of most countries real GDP to a contractionary euro area aggregate monetary policy shock is close to the response of the Euro area GDP factor as regards the scale. Austria and Portugal show a weaker response indicating a lower exposure to the shock. In terms of frequentist language the results do not show a significant price puzzle however there is some probability mass on the positive support. This might be unappealing and we might want to re-strict or penalize a positive price response to a contractionary monetary policy. This is feasible and I employ it in the sign restriction (both in the DSGE-DFM and the DFM approach) version in the next two subsections. The strongest discrepancy regarding the scale of the impulse response functions can be found in the real wages and em-ployment in Finland, Portugal and Spain. The reaction is up to ten mimes stronger than in Germany or France. Overall the conclusion of DSGE-DFM approach with the DSGE rotation is that there is by and large homogeneity in the monetary transmission mechanism though there are some differences in the exposure of some countries’ labor market to a contractionary monetary policy shock.

4.6.7.3 Identification of DSGE-DFM via Sign Restriction with block diagonalΛ

The restrictions imposed are derived from the estimated DSGE model and results in the sign restrictions reported in table (4.5). Following Uhlig [2005] I impose the re-strictions for the contemporaneous period and up to two quarters. Compared to the results of the previous section employing the DSGE rotation to facilitate identification the results of the sign restriction approach within the DSGE-DFM are associated with less uncertainty and the responses show a higher degree of homogeneity regarding the respective scales of the impulse response functions following a contractionary mone-tary policy shock. Most countries real GDP responses are close to the Euro area GDP factor impulse response function. Slightly weaker responses can be found for Austria and stronger responses in Portugal. As discussed in the previous section the prize puz-zle is ruled out by construction without any probability mass on the positive support.

Furthermore the single countries inflation responses are all similar to the Euro area responses. The price puzzle of the previous section is ruled out by construction. How-ever the scale if the responses are rather similar here. The same picture regarding the strongest discrepancy in the scale of the responses emerges for the reaction of employ-ment and real wages across countries. In Finland, Portugal and Spain the reaction is up to 5 times stronger compared to Germany or France. The impulse responses to the interest rates look more reasonable compared to the previous case in that they have a clear positive impact in the initial quarters following the shock. The uncertainty in the previous case is very high.

4.6 Empirical Results

4.6.7.4 Identification of DFM via Sign Restriction

As a third alternative I employ the sign restriction scheme to identify aggregate shocks, however the DSGE model serves only as a tool to derive robust sign restrictions and NOT to estimate the parameters of the empirical model as opposed to the previous two models. This approach shows a higher degree of heterogeneity in particular at longer horizons. At short horizons most of the responses have the same sign though the shape can be somewhat different. Furthermore there a some sign puzzles. The key appeal is that this approach is less restrictive allowing for richer and more complicated dynamics in the transmission of shocks. This is due to the fact that the normalization of the loading matrix is by far less restrictive as no block-diagonally is required. The estimated DSGE model delivers the same sign restriction to be imposed both when based on the euro area aggregate data or on factors. This complexity comes at a cost.

For the results to reasonable more sign restrictions might have to be imposed. From the figures we can see that there are some sign puzzles in particular regarding the re-action of prices. It should be noted that the price puzzle emerge for those variables that are rather badly represented by the data hence the figure might appear less rea-sonable as it actually is. It is obvious that if those indicators that are mostly driven by idiosyncratic dynamics their exposure to surprise changes driving the common factors is negligible even thought the respective impulse response functions have clear effects.

Hence while interpreting the impulse response functions one should always keep in mind how much do the respective indicators depend on the common factors.