Do the Bank of Japan’s Unconventional Monetary Policies Decrease Real Interest Rates under a Zero Lower Bound?

To test Paul Krugman’s pioneering proposal for escaping from liquidity traps, this study examines whether unconventional monetary policies under a zero lower bound decrease real interest rates in Japan. We find a sizable decline in real interest rates under zero interest rate policy and Abenomics monetary policy. In addition, we find no significant decline in real interest rates under other unconventional monetary policies, such as the first quantitative easing and comprehensive monetary easing.


Introduction
Are unconventional monetary policies effective for an economy stuck at the zero lower bound of short-term nominal interest rates? The Bank of Japan (BOJ) was the world's first central bank to implement several unconventional measures, as shown in Figure  The extant empirical literature explores the effects of those unconventional monetary policies and provides evidence on their effectiveness through various channels. For example, Okina and Shiratsuka (2004) investigate the commitment effect and find that it flattens the yield curve from March 1998 to February 2003. More recently, Honda (2014) finds positive effects of the first QE from 2001 to 2006 on investment and production through Tobin's q channel. Bowman et al. (2015) show that QE has only limited effects on bank lending. Regarding QQE after 2013, Matsuki et al. (2015) point out that quantitative easing leads to a decline in short-term interest rates and increase in prices, while qualitative easing stimulates economic activity. In addition, Miyao and Okimoto (2017) demonstrate that the introduction of QQE substantially raises real output and prices. Moreover, Michaelis and Watzka (2017) compare all the unconventional monetary policies (ZIR, QE, and QQE) and confirm a substantial effect on real output and prices only in Abenomics monetary policy (QQE).
However, while several channels of the BOJ's unconventional monetary policies have been studied up to now, surprisingly, there is no or little empirical evidence about whether those unconventional monetary policies lower real interest rates. Krugman (1998) developed a pioneering theory of unconventional monetary policy in a liquidity trap, suggesting that a radical regime change of monetary easing can boost an economy through an expected rise in inflation and a decline in real interest rates, even at a zero lower bound.
The channel involving real interest rates has yet to be revealed.
In this study, we identify unconventional monetary policies (ZIR policy, QE, CE, and QQE) and examine whether they decrease real interest rates in Japan under a zero lower bound. To this end, we test the validity of the Fisher effect, that is, whether there is high correlation between nominal interest rates and inflation. 1 If an unconventional monetary policy contributes to lowering real interest rates, then the Fisher effect does not hold in the period. Conversely, if real interest rates are not influenced by the expected changes in the inflation rate and remain constant in the period, then the Fisher effect should be validated.
We find a sizable decline in real interest rates under the ZIR policy and Abenomics monetary policy (QQE). On the contrary, a substantial decline in real interest rates cannot be confirmed under the other unconventional monetary policies (i.e., QE and CE).
The rest of the paper is organized as follows. In Section 2, we explain the data used in the analysis and our empirical strategy. In Section 3, we present the empirical results.

Data and methodology
Our data are monthly observations in Japan and cover the time period from October 1997 to December 2015. Since our sample period is required to correspond to the zero lower bound period, the sample begins in the month in which the call rate (or short-term interest rate) falls below 50 basis points, following Iwata and Wu (2006) and Nakajima (2011). The end date of the sample corresponds to the end of the first QQE policy framework, and the sample ends before the negative interest rate policy is introduced. Nominal interest rates are long-term (10-year) government bond yields, which are obtained from the website of the St. Louis Fed's Federal Reserve Economic Data. The inflation rate is calculated as the year-on-year change rate of the core consumer price index. We use two types of core consumer price index: (1) all items less fresh food and energy and (2) all items less food (less alcoholic beverages) and energy. In the consumer price indexes, the effects of the tax hikes are excluded. These consumer price indexes can be retrieved from the website of Japan's Ministry of Internal Affairs and Communications. Following the literature on the Fisher effect (e.g., Mishkin, 1992), the basic model builds on the Fisher equation, as follows: where i t is the nominal interest rate in period t, π t is the inflation rate in period t, and ε t is the error term. Moreover, to verify the abovementioned visual inspection of Figure   2 formally, we incorporate slope dummy variables identifying the periods of Japanese unconventional monetary policies and estimate the following equation: where

Empirical results
We now present our main results. In what follows, π 1 denotes the first inflation rate on all items less fresh food and energy, and π 2 denotes the second inflation rate on all items less food (less alcoholic beverages) and energy. 3 [Insert Table 1 around here] Prior to the estimation, we first check whether our variables are stationary. To do this, we perform two unit root tests: the augmented Dickey-Fuller (ADF) test by Dickey and Fuller (1979) and the refined Dickey-Fuller test by Elliott et al. (1996). The lag lengths are chosen based on the Schwarz information criterion (up to 10 lags). We assume that tests in levels include constants and linear trends (detrended tests) and tests in first differences include constants only (demeaned tests). Table 1 shows the results of unit root tests. Overall, the results indicate that the null hypothesis of the unit roots cannot 2 In order to test the theoretical implications of Krugman (1998), we focus on the zero lower bound period and disregard the most recent period after January 2016, in which the negative interest rate policy is implemented.
3 Note also that, in the following analysis, the time variable t is omitted when not needed for clarity. be rejected in levels, but is strongly rejected in first differences. Hence, we treat all the variables as integrated of the order one.
[Insert Table 2 around here] We next check whether there is a cointegrating relationship between i and π using Johansen's (1988) and Johansen and Juselius's (1990) maximal eigenvalue test. The lag lengths used in the tests are chosen based on the Schwarz information criterion and the Akaike information criterion (up to 10 lags). In both models (i, π 1 ) and (i, π 2 ), the Schwarz information criterion indicates that there are no lags. The Akaike information criterion indicates two lags in model of (i, π 1 ) and four lags in model of (i, π 2 ). The results reported in Table 2 indicate that the null of no cointegration is rejected overall, showing that there is cointegration in both models.
[Insert Table 3 around here] Table 3 reports the estimation results of both (1) and (2), in which slope dummy variables are incorporated, because parameter shifts are suggested from a visual inspection of Figure 2, as already mentioned. We estimate the cointegrating vector using the fully modified ordinary least squares (FMOLS) and dynamic ordinary least squares (DOLS) methods. In the DOLS estimations, the lead and lag lengths are assumed to be unity.
In columns 1 and 2 of Table 3, the results of (1) are reported. In this case, all the estimated coefficients of π are negative, but not significant. Columns 3 and 4 of Table   3 add slope dummy variables of the unconventional monetary policies and display the estimation results. The estimated coefficients of π are affected and are positive values, but again are not significant.
The results of the slope dummy variables of (2) indicate that the ZIR and QQE variables are strongly negatively related to nominal interest rates in all the specifications and methods. This suggests that real interest rates decrease under the ZIR and QQE policies. On the contrary, the estimated coefficients of CE are rather positive and significant.
Under the first QE period, no significant result can be confirmed.
[Insert Table 4 around here]

Conclusion
While several channels of the BOJ's unconventional monetary policies have been studied in the existing literature, little is known about the channel involving real interest rates proposed by Krugman (1998). In this study, we attempted to fill this gap and investigated whether the BOJ's unconventional monetary policies decrease real interest rates. We found a sizable decline in real interest rates only under the ZIR policy and Abenomics monetary policy (QQE). The finding is useful for policymakers in considering which types of unconventional monetary policies are effective for cutting real interest rates, which are a crucial factor for real economic activities, such as private consumption and investment. . The lag lengths are chosen based on the Schwarz information criterion (up to ten lags) and shown in the parentheses. * , * * , and * * * represent the rejection of the null hypothesis at the 10, 5, and 1% significance levels, respectively.  , π 2 ). The lag lengths are chosen based on the Schwarz information criterion and the Akaike information criterion (up to ten lags) and shown in the parentheses. In both models, the Schwarz information criterion indicates that there are no lags. The Akaike information criterion indicates two lags in model of (i, π 1 ) and four lags in model of (i, π 2 ). Critical values are from MacKinnon et al. (1999). * and * * represent the rejection of the null hypothesis at the 10 and 5% significance levels, respectively.  Notes: The values in parentheses are the standard errors. Heteroscedasticity-and autocorrelation-consistent (Newey-West) robust standard errors are used. * and * * represent the rejection of the null hypothesis at the 10 and 5% significance levels, respectively.