this approach. As described above, in contrast to the volatile movements in actual observation of wages, the estimate in Case A does not show activity. However, in Case C the estimate is very close to the actual data because of the expanding labor supply shock, which is not identified in Case SW. We can draw certain inferences from this evidence. The relation between real wage and labor input is determined by two movements: labor demand of entrepreneurs and labor supply of households. The shifts in the labor demand function are caused by the productivity shock of the production function managed by firms, but this shock is observed as only a small variation in our three data-rich cases. This is because output, consumption and investment fluctuate mainly due to investment and preference shocks but not productivity shock. Meanwhile, the shift in the labor supply curve is caused by labor supply shock, which means a change to the disutility of household for labor, and this shock seems to determine a large part of the relation between wages and labor. In addition, parameter $ \sigma_{L} $ , which implies the inverse of labor supply elasticity, is smaller (workers' supply of labor is more elastic) and the Calvo wage $ \xi_{w} $ is higher (the nominal wage becomes more rigid), and the labor supply curve becomes more "fluttery" than in Case SW ( $ \partial\hat{w}/\partial\hat{l} $ is smaller). The flat labor supply curve should receive a much larger shock because of the shift in the real wage. Intuitively, the positive labor supply shock makes people less industrious; that is, they will reduce the quantity of labor supply voluntarily given the real wage.

As noted above, the difficulty of applying a Smets and Wouters-type model to the Japanese economy is explaining the reason why the real wage was so high in the Bubble Boom by just expanding workers' disutility for labor but not a change in productivity shock (Fig. 6). In the Bubble Boom, between 1988 and 1991, increases in capital and labor input caused by investment and preference shocks respectively raised output as well as consumption and investment (Fig. 4, Fig. 7 and Fig. 8). However, these shocks do not contribute to the movement of the real wage. As a result, workers' disutility for labor becomes larger, comprising a much higher fit between actual and estimated wages in the data-rich approach for Case C. In addition, the collapse of Bubble Boom is likely to have been caused by an increasing negative labor supply shock prior to a negative preference (or consumption demand) shock according to the historical decomposition of real GDP in Case C (Fig. 4). This implies that in the peak of the boom, reservation wages were kept at high levels in the labor market because of monopolistic households dominating their wages, and they over-consumed, preferred not to work, and voluntarily stopped, all of which induced the collapse. Is this story plausible?

According to the evidence of business cycle accounting in Japan (Kobayashi and Inaba, 2006; Otsu, 2011), wages in the labor market mainly caused fluctuations in output. However, any frictions within the labor market except wage rigidity are not considered in the Smets and Wouters-type DSGE model. Hence, we can infer that the over-evaluation of a labor supply shock shows the limitations of the Smets and Wouters-type DSGE model, which does not address issues such as frictions causing involuntary unemployment. We need to undertake further analysis to reach definitive conclusions for these results.

Finally, we summarize the benefits and limitations of the data-rich approach in DSGE models from the evidence shown above. One major problem is that enriching information by increasing the volume of data does not necessarily improve the accuracy of the discrimination between model concepts and measurement errors, nor