Smets and Wouters' (2003) work. The standard errors were set so that the domain covered a reasonable range of parameter values. For example, means of the priors of the Calve parameters of price and real wage, $ \xi_{p} $ and $ \xi_{w} $ , are set to 0.75 as the average period for updating prices and wages might be around one year according to estimations by Gali et al. (2001). Their standard deviations are set to 0.15 to cover the updating period between 0.75 years and two years.

Similarly, the mean of the intertemporal elasticity of substitution $ \sigma_{c} $ is set equal to one. The elasticity of the capital utilization cost function $ \psi $ has a mean of 0.2, and includes in its domain the value of 0.1, as suggested by King and Rebelo (2000) for the U.S. economy. The share of fixed costs (or the elasticity of the cost of adjusting investment) in total production, $ \phi $ , has a mean of 1.45, which is close to those of Christiano et al. (2005) for the U.S. A wide range of calibrations has been used for the inverse elasticity of labor supply. We took as a starting point a value of two, which falls between the relatively low elasticities that are typically estimated in the micro-labor literature and the higher elasticities typically used in DSGE models. Finally, the priors on the means of the coefficients $ \mu_{\pi} $ in the monetary policy reaction, i.e. 1.7, help to guarantee a unique solution path when solving the model; the prior on the lagged interest rate $ \rho_{m} $ is set at 0.8 and the prior on the output gap reaction coefficient corresponds to the Taylor coefficient $ \mu_{y} $ of 0.125 (which is quarterly based, so the annualized base is 0.5). Table 2 shows the setting of priors.

## 6 Empirical Results

### 6.1 Estimate accuracy of model concepts and measurement errors

We first consider whether increasing the number of data indicators improves separation into model concepts and measurement errors with precision in a data-rich approach. Figure 1 shows an estimation of model concepts and actual observations of primary data indicators $ X_{1,t}^{sensor} $ in three cases, where solid and dashed lines denote data and estimations, respectively. Gray shading denotes 90% credible intervals. (As no measurement errors in the regular DSGE model are assumed, there is no discrepancy between actual data and estimations in Case SW.) From Figure 1, five model concepts, except inflation and real wage, consist of data in broad terms in Cases A and B. As inflation and wages show a large fluctuation with high-frequency, these components are identified as noise and their low-frequency component is employed as their common factor. Note that the i.i.d. wage markup shock is removed and an AR (1) measurement error is introduced in our data-rich approach, in contrast to the regular model. This amendment is likely to exert a significant influence on the estimated concept of wages. Meanwhile, different pictures are drawn in Case C. That is, output, consumption, and labor input are estimated with considerable fluctuations, compared to actual observations, whereas inflation and wages are much closer to the observed values.

To clarify the discrepancy between these three cases, Table 3 shows the correlations between sensor series $ X_{1t}^{sensor} $ , $ X_{2t}^{sensor} $ , $ X_{3t}^{sensor} $ , and the model concept $ \bar{S}_{t}^{link} $ . In the primary indicators $ X_{1t}^{sensor} $ , the correlation of inflation levels stands at 0.38 in