Table 5: Estimation Parameters of Data rich DSGE c) Case C vs. Regular DSGE

Note:

parameters	Regular DGE model	Data-Rich DGE Model (Case C)
mean	[ 90 % interval ]	mean	S.E.	S.D.	[ 90 % interval ]	CD
Structural Parameters
h	0.544	[ 0.400	0.692 ]	0.693	0.008	0.112	[ 0.512	0.868 ]	-1.617
$ \sigma_{c} $	1.498	[ 1.043	1.964 ]	0.944	0.043	0.538	[ 0.094	1.611 ]	7.531
$ \sigma_{L} $	0.572	[ 0.441	0.698 ]	0.587	0.004	0.051	[ 0.488	0.669 ]	-15.227
1/ $ \varphi $	5.326	[ 3.562	7.055 ]	6.047	0.145	1.804	[ 3.201	8.916 ]	-11.746
$ \phi $	1.951	[ 1.664	2.239 ]	1.994	0.026	0.336	[ 1.457	2.558 ]	-2.310
$ \psi $	0.151	[ 0.033	0.261 ]	0.225	0.005	0.080	[ 0.089	0.345 ]	-3.088
$ \gamma_{p} $	0.304	[ 0.123	0.481 ]	0.505	0.029	0.341	[ 0.127	0.988 ]	51.413
$ \gamma_{w} $	0.395	[ 0.297	0.409 ]	0.645	0.011	0.180	[ 0.378	0.946 ]	4.523
$ \xi_{p} $	0.768	[ 0.711	0.824 ]	0.838	0.005	0.065	[ 0.723	0.928 ]	8.279
$ \xi_{w} $	0.355	[ 0.297	0.409 ]	0.667	0.011	0.132	[ 0.475	0.856 ]	-15.763
Policy Parameters
$ \rho_{m} $	0.870	[ 0.836	0.907 ]	0.854	0.005	0.064	[ 0.763	0.959 ]	-11.401
$ \mu_{\pi} $	1.618	[ 1.442	1.779 ]	1.623	0.007	0.109	[ 1.456	1.808 ]	2.110
$ \mu_{y} $	0.125	[ 0.041	0.206 ]	0.100	0.004	0.060	[ 0.017	0.209 ]	-3.776
Shock Persistence
$ \rho_{z} $	0.558	[ 0.400	0.715 ]	0.767	0.012	0.152	[ 0.540	0.997 ]	-14.615
$ \rho_{c} $	0.511	[ 0.328	0.696 ]	0.665	0.009	0.127	[ 0.482	0.892 ]	10.297
$ \rho_{g} $	0.841	[ 0.730	0.964 ]	0.834	0.007	0.097	[ 0.704	0.999 ]	4.131
$ \rho_{L} $	0.484	[ 0.230	0.762 ]	0.744	0.019	0.228	[ 0.433	0.999 ]	-24.015
$ \rho_{inv} $	0.677	[ 0.476	0856 ]	0.769	0.010	0.120	[ 0.587	0.970 ]	5.246
S. D. of Shocks
$ \varepsilon_{c} $	3.235	[ 2.245	4.192 ]	3.044	0.118	1.430	[ 0.498	5.017 ]	-7.721
$ \varepsilon_{inv} $	2.465	[ 1.499	3.383 ]	3.449	0.192	2.248	[ 1.225	7.716 ]	10.551
$ \varepsilon_{q} $	5.174	[ 0.182	9.249 ]	0.797	0.078	1.104	[ 0.157	1.391 ]	2.243
$ \varepsilon_{z} $	9.600	[ 9.120	10.000 ]	8.368	0.061	0.730	[ 7.449	9.756 ]	-2.163
$ \varepsilon_{p} $	0.225	[ 0.058	0.421 ]	0.000	NA	NA	NA	NA	NA
$ \varepsilon_{L} $	0.466	[ 0.392	0.538 ]	0.626	0.011	0.130	[ 0.407	0.823 ]	-3.958
$ \varepsilon_{w} $	6.683	[ 3.610	9.723 ]	0.000	NA	NA	NA	NA	NA
$ \varepsilon_{g} $	1.948	[ 1.655	2.234 ]	2.073	0.057	0.691	[ 1.076	3.235 ]	6.381
$ \varepsilon_{m} $	0.131	[ 0.110	0.151 ]	0.108	0.001	0.015	[ 0.083	0.132 ]	-8.360

(a) The first 100,000 draws of MH algorithm are discarded to guarantee convergence and then the next 200,000 draws are used for calculating the posterior means, the standard errors of the posterior means (S.E.), the standard deviations (S.D.), the 90% intervals and the convergence diagnostic (CD) statistics proposed by Geweke (1992).

(b) The posterior mean is computed by averaging the simulated draws.

(c) S.E. is computed using a Parzen window with a bandwidth of 10,000.

(d) S.D. is computed as the sample standard deviation of the simulated draws.

(e) The 90% intervals refer to 90 % posterior probability bands. These bands are calculated using the 5th and 95th percentiles of the simulated draws.

(f) CD is computed using the criterion as follows.

$$ CD=\frac{\bar{\theta}_{A}-\bar{\theta}_{B}}{\sqrt{\hat{\sigma}_{A}^{2}/n_{A}+\hat{\sigma}_{B}^{2}/n_{B}}}, $$

where $ \sqrt{\hat{\sigma}_{A}^{2}/n_{A}} $ and $ \sqrt{\hat{\sigma}_{B}^{2}/n_{B}} $ are the standard errors of $ \bar{\theta}_{A} $ and $ \bar{\theta}_{B} $ , and we set $ n_{A}=40,000 $ and $ n_{B}=100,000 $ and compute $ \hat{\sigma}_{A}^{2} $ and $ \hat{\sigma}_{B}^{2} $ using a Parzen window with bandwidths of 4,000 and 10,000 respectively.