## 1 Introduction

Recently, the dynamic stochastic general equilibrium (DSGE) model has continued to grow into the most influential tool for analyzing macroeconomics and evaluating macroeconomic policy. A DSGE model is constructed from a micro foundation under which economic agents, such as households, firms, and governments, behave optimally in allocating their resources and developing rational expectations, and a number of exogenous stochastic shocks are regarded as factors that affect business cycles and price fluctuations. In addition, developing methods that specify a DSGE model and sources of business cycles empirically, and identifying structural shocks, have become hot topics in advanced macroeconometrics. Central banks and government organizations such as the U.S. Federal Reserve, the European Central Bank, and the OECD have made rapid progress in developing large-scale DSGE models and applying them in the analysis and forecasting of economic activities and counterfactual policy simulations. For example, the U.S. Federal Reserve has developed SIGMA, the European Central Bank employs the New Area-Wide Model (NAWM), and the Bank of Japan has the Medium-scale Japanese Economic Model (M-JEM). In Japan, empirical studies of DSGE models for policy analysis have been developed at the core of the Bank of Japan with the enthusiastic participation of researchers. Examples of recent works are those by Hirose (2008), Hirose and Kurozumi (2010), Kaihatsu and Kurozumi (2014) and Fueki et al. (2010).

The importance of adopting existing statistical approaches for macroeconomic analysis has not diminished. This is because there are appreciable amounts of panel data sets concerning macroeconomic time series that have not been incorporated within macroeconomic models such as DSGE models in which only small number (i.e., between three and seven) data indicators can be employed as model variables. In estimating a DSGE model, researchers have so far assumed that all relevant information for estimation is adequately summarized by this small data set. For example, we often see the arbitrary selection of one of three indicators, such as the gross domestic product (GDP) deflator, consumption price index (CPI) or core CPI, as the model variable specifying the concept of inflation. However, it is plausible that each of these data indicators is contaminated by measurement error. Hence, estimation results derived from a small data set selected arbitrarily are likely to contain biases and induce policy simulation toward the wrong calculation incorporating bias.

Central banks and financial market participants monitor and analyze hundreds of data sets. Nowadays, dynamic factor models (DFMs) are widely employed by empirical studies in macroeconomics and show that the inclusion of a large set of macroeconomic variables may be necessary to capture economic dynamics adequately. Such models exploit common factors that are key factors for the fluctuation of primal macroeconomic series from large panel data sets. According to the growing empirical evidence, these common factors might contribute to forecasting in macroeconomics (Stock and Watson 2002a, 2002b), modeling monetary policy (Bernanke and Boivin, 2003) and identifying monetary transmission mechanisms (Bernanke et al., 2005; Boivin et al., 2011). However, these statistical models that use large data series are nonetheless constructed in a non-structural fashion. This is a considerable shortcoming with respect to analyzing the source of business cycles and conducting counterfactual policy simulation. Against this background, to