In this equation, the acceptance rate $ \q\ $ is not dependent on proposal density $ p(\pmb{\theta}|\pmb{\theta}^{(g-1)}) $ . As a result, the random walk MH algorithm has the advantage that we do not need to adopt a proposal density close to the posterior density. However, when the proposal value $ \pmb{\theta}^{(\mathrm{proposal})} $ departs from the previous sample $ \pmb{\theta}^{(g-1)} $ , the acceptance rate q becomes small and the efficiency of the MCMC estimation worsens. To avoid this, the adjustment coefficient c should be small, but this narrows the range of sampling space of $ \pmb{\theta}^{(\mathrm{proposal})} $ . Roberts et al. (1997) and Neal and Roberts (2008) report that the optimal acceptance rate q of a random walk MH algorithm is approximately 25%. The optimal acceptance rate q is defined as the acceptance rate maximizing the speed of convergence to invariant distribution, which is the target of MCMC. Roberts et al. (1997) analytically solve the optimal acceptance rate q in a random walk MH algorithm, obtaining a value of 0.234 as the dimension of parameters d becomes $ d \rightarrow \infty $ under the assumption of following identical and independent distribution for any parameter. According to Rosenthal (2011), as long as rate q is between 0.1 and 0.6, the random walk MH algorithm will implement sampling efficiently. However, as our method adopts the hybrid MCMC algorithm (Metropolis-within-Gibbs), we cannot apply their study directly. The survey of the optimal acceptance rate q is given in Rosenthal (2011). Accordingly, the adjustment coefficient c in this study is set so that the acceptance rate is close to around 25%.

## 5 Preliminary Settings and Data Description

### 5.1 Alternative specification of link between the model concepts and the data

It is plausible that observed variables are imperfectly measured in relation to their corresponding model concepts and are contaminated by measurement errors, which are unrelated to the actual model concepts. One drawback of a regular DSGE model is that the estimates of the model parameters and structural shocks are likely to be distorted, as it is usually assumed that no errors are included in the data indicators. The purpose of this paper is to validate whether measurement errors are removed from the data, and whether estimates of the model parameters and structural shocks are extracted using a data-rich approach, or by exploiting the broad range of information in large panel data. To this end, we consider four cases, each of which has different restrictions imposed on the measurement equation $ (2.10) $ , i.e., on the link between the model concepts $ \bar{S}_{t} $ and the data indicators $ X_{t} $ .

## (1) Case SW

The first case is estimated based on a regular DSGE model with a small data set of just seven indicators. This case implies the replication of a DSGE model following Smets and Wouters (2003), as explained in Section 3. The small data set adopted here is standard for estimating regular DSGE models. As the seven model concepts $ \bar{S}_{t}^{link} $ , which link directly to the data, are assumed to be perfectly observed as data indicators, there is no measurement error in this model, i.e., $ e_{t} = 0 $ . In Case SW, the data and model concepts have a one-to-one correspondence so that the measurement equation(2.10) described in Section 2.3 is represented as follows: