Decomposition of Trend and Cycle; An Application to Real GDP and Unemployment Rate in Japan(in Japanese)

For thirty years since Beveridge and Nelson (1981) decomposition, many decomposition of trend and cycle have been developed. Their estimation, however, have little correspondence with each other. This paper applies to Japanese real GDP and unemployment rate between 1955 and 2000 using decomposition of recent studies such as Morley et al. (2003) and Perron and Wada (2009). Our estimated results show that we cannot get unique decomposition even using the same unobservable component model and that outcome of decomposition depends largely on the ratio of variances of both shocks of trend and cycle as well as the correlation of both shocks shown by Morley et al. (2003). And, when real GDP was estimated from a UC model with structural breaks followed by Perron and Wada (2009) but without specifying distribution of trend 's shock, the cycle component of the GDP was similar to short cycle and small amplitude derived by Morley et al. (2003), unlike by Perron and Wada (2009). Accordingly, we suggest that unique decomposition cannot be derived by only statistical approach.