and the periods are called “a lost decade.” To estimate trends of macroeconomic data, the Hodrick and Prescott (1997) filter is often used. In recent years, the Baxter and King (1999) filter and the Christiano and Fitzgerald (2003) filter are also often used. Our method is an alternative to these filters, and it is “structural” estimation of time-varying economic trends. From the mid-1980s to the mid-1990, $ \pi_{t}^{s} $ is positive, and it is from 1% to 2%. From the early 1990 to present, $ \pi_{t}^{s} $ is negative. The results show the target rate of the inflation of the BOJ is changed in the early 1990s, and the target in the 1990s and 2000s is too low. From the 2006, the BOJ announces “understanding of the price stability,” and it states a stable inflation rate is from 0% to 2%, which is measured by consumer price index, excluding food. This low target rate makes $ \pi_{t}^{s} $ negative because it is well known that CPIs have upward bias. From the mid-1980s to the early 1990s, $ r_{t}^{s} $ is above 2%, and from the early 1990s to present, it is below 1%. The $ r_{t}^{s} $ is an estimate of equilibrium real rate $ ^{26} $ . Krugman (1998) states ERR of the Japanese economy in the late 1990s is negative. However, our estimate of ERR is not negative but quite low in 1997 and 1998. It strongly suggests that the BOJ, which adopted quite low interest rate policy at the time, needed positive inflation rates to stimulate the economy in the late 1990s. Note that the target rate of inflation, $ \pi_{t}^{s} $ , in the 1990s is negative.

### [Figure 1 about here.]

Figure 2 shows the estimates of the endogenous variables. The expectational output gap, $ E_{t}\hat{Y}_{t} $ , and the output gap, $ \hat{Y}_{t} $ , have fundamentally similar shapes. They indicate that the favorable economic situation ends at early 1990s, and serious recessions happen in the early 1990s, 1997-1998, 2000-2001. The large negative spike in 1989 shows that introducing the consumption tax reduced GDP. We would like to emphasize the large negative spike has little influence on the estimates of parameters. The results indicate that our time-varying-parameter approach is relatively robust to outliers. The inflation expectation, $ E_{t}\hat{\pi}_{t} $ , and the inflation rate, $ \hat{\pi}_{t} $ , show that in the mid-1980s and the 1990s negative deviation from the target rate of inflation happen. In particular, the negative deviation in the 1990s is very long, and it indicates the long-term recession of the economy. Interest rate, $ \hat{i}_{t} $ , shows the deviation from the equilibrium real interest rate, and it presents the fact that the BOJ made expansionary monetary policy in the late 1980s and the early 1990s. From 1999, the $ \hat{i}_{t} $ is zero because the Japanese economy is under a liquidity trap. The symbols, $ \hat{W}_{t} $ , and, $ \hat{L}_{t} $ , have similar shapes to $ E_{t}\hat{Y}_{t} $ and $ \hat{Y}_{t} $ . The symbol, $ \hat{Z}_{t} $ , shows the negative technology shocks that happened in the early 1990s, the late 1990s, and the early 2000s, and they correspond to the recessions from 1985 to 2007.

### [Figure 2 about here.]

Fig. 3 shows the estimates of time-varying parameters. These estimates indicate that some “structural” parameters are time-varying. The results indicate that habit persistence, h, the Calvo parameter, $ \xi_{p} $ , and the coefficient of AR(1) technology process, $ \xi_{z} $ , are relatively stable. The parameter, $ \sigma_{C} $ , is above 1 in most periods, and it indicates that the utility function of consumption is concave and not the log-type utility function. The parameter, $ \sigma_{L} $ , is increasing in the all periods, and it indicates that the distortion of labor markets from 1985 to 2006 cannot be captured by our model.