# Quantitative and Qualitative Monetary Easing and Long-Term Interest Rates: The Effects through the Stock of "Net Supply" and Maturity Structure of Japanese Government Bonds

Ichiro Fukunaga,^{*} Naoya Kato (Bank of Japan)

Research LAB No.15-E-7, December 11, 2015

Keywords:

Japanese Government Bonds; Term structure of interest rates; Preferred-habitat investors; Quantitative and Qualitative Monetary Easing

JEL Classification:

E43, E52, G12, H63

Contact:

naoya.katou@boj.or.jp (Naoya Kato)

- Currently the International Monetary Fund.

## Abstract

The relationship between the supply-demand structure of government bond markets and long-term interest rates has been studied both theoretically and empirically, motivated by the implementation of large-scale government bond purchases by many central banks in advanced economies. Fukunaga, Kato, and Koeda (2015) [PDF 3,676KB] examined the effects of changes in the holders and maturity structures of Japanese Government Bonds (JGBs) on the term structure of interest rates and the risk premium on long-term bonds. Using a regression approach and a term structure model approach, they confirmed that the "net supply" of JGBs-that is, the amount outstanding of JGBs issued (supplied) by the government minus that held (demanded) by investors with preferences for particular maturities, including the Bank of Japan (BOJ)-had statistically significant effects on long-term interest rates. They also reported calculations based on the two approaches showing that the BOJ's JGB purchases as part of its Quantitative and Qualitative Monetary Easing (QQE) had substantial effects on the long-term interest rates.

## Introduction

It is widely recognized in practice that daily short-term fluctuations in supply and demand conditions of government bond markets affect interest rates, but it is not necessarily clear that these conditions can affect interest rates for somewhat longer periods of time. According to the "(pure) expectations hypothesis", the levels of long-term interest rates and their term structure are determined by the expected future path of short-term interest rates (or the expected future paths of economic activity and inflation as the factors behind it). Even if a shock to the supply and demand conditions of government bonds with particular maturities occurs, the levels of the long-term interest rates with the corresponding maturities are supposed to converge to levels consistent with the expected future path of short-term rates sooner or later through arbitrage trading by market participants, as illustrated in the left panel of Figure 1. This argument implies that government bond purchases by central banks can have effects on long-term interest rates only as a signal to market participants about the future path of short-term rates including the duration of the zero interest rate policy (the signaling channel), but have no direct effects beyond that.

### Figure 1: Yield-curve fluctuation (conceptual examples)

The argument based on the expectations hypothesis, however, does not hold if there exists a certain portion of investors with preferences for particular maturities ("preferred-habitat investors", henceforth) and the associated movements in the risk premium are taken into account. In a situation where a central bank that implements large-scale government bond purchases with maturity extension can be regarded as a kind of preferred-habitat investor, such a policy can have direct and persistent effects on long-term interest rates theoretically through two channels: (1) a shortage of bonds with particular maturities available for trading that lowers the risk premium on bonds with the corresponding maturities (the scarcity channel) and (2) a reduction in the duration risk for market participants incurred by holding long-term bonds that lowers the risk premium on bonds with a wide range of maturities (the duration channel), as illustrated in the right panel of Figure 1.

The existence of preferred-habitat investors, typically insurance companies and pension funds that tend to hold longer-term assets to match their long-duration liabilities, had been recognized prior to the implementation of large-scale government bond purchases by central banks in many advanced economies. Following the development of theoretical studies on the term structure of interest rates that explicitly consider the existence of preferred-habitat investors, many empirical studies have been conducted recently, especially in the United States, to estimate the effects of government bond purchases by central banks on the long-term interest rates.^{1} Fukunaga, Kato, and Koeda (2015, FKK henceforth) conducted an empirical study using Japanese data following these studies based on the preferred-habitat theory.

- There are also many empirical studies that are not necessarily based on the preferred-habitat theory but focused on the announcement effects or daily flow effects (such as event-study analysis) of the Federal Reserve's purchases of U.S. Treasury bonds.

## Holders and maturity structures of JGBs

We first give an overview of FKK's constructed database on the amount outstanding of JGBs categorized by holder and remaining maturity. Figure 2 presents the amount outstanding of (fixed-rate) JGBs divided by nominal GDP from January 1992 to September 2014.^{2} The upper panel shows those with all maturities, and the lower panel shows those with remaining maturities less than 10 years. Besides the total amounts issued by the government, Figure 2 shows those held by the BOJ, insurance companies, pension funds, and the other holders such as banks. FKK regard insurance companies and pension funds as well as the BOJ as preferred-habitat investors, while the other holders are defined as "arbitragers" who have a relatively strong tendency to conduct arbitrage trading based on their expected future path of short-term interest rates. Then FKK define the amount outstanding of JGBs held by the arbitragers, which corresponds to the issuance (supply) by the government minus the demand by the preferred-habitat investors, as the "net supply" of JGBs, and analyze its effects on the long-term interest rates. As shown in Figure 2 (in both the upper and lower panels), the ratio of the amount outstanding of JGBs held by the arbitragers to GDP increased generally in parallel with the total debt-to-GDP ratio before the BOJ introduced QQE in 2013, but started to fall considerably as the BOJ accelerated the pace of its JGB purchases thereafter.

- 2The effects of the expansion of QQE, which was announced in October 2014, are not analyzed in FKK.

### Figure 2: Amount outstanding of fixed-rate JGBs held by each sector

Figure 3 shows the average maturities of JGBs held by each sector of holders as well as the total average maturities. As shown in the upper panel, the arbitragers' average maturity increased from around 2009 in parallel with the total average maturity, but leveled off when the BOJ started to extend its maturity in 2013. More clearly, the lower panel, which extracts the JGBs with maturities less than 10 years, shows that the arbitragers' average maturity started to decline in 2013.

### Figure 3: Average maturities of fixed-rate JGBs held by each sector

According to the preferred-habitat theory mentioned above, these movements in the "net supply" of JGBs after the introduction of QQE were supposed to flatten the yield curve and put downward pressure on the risk premium on bonds with a wide range of maturities through the scarcity and duration channels.

## Main results of empirical analysis

To examine the above "net supply" effects quantitatively, FKK use a regression approach and a term structure model approach. The former can flexibly control various factors that affect long-term interest rates, while the latter is more rigorously related to the preferred-habitat theory.

First, as an example of the regression approach, we show the result on how the arbitragers' average maturities (a "net supply" measure) and the related movements in the BOJ's average maturity have affected the 10-year/3-year yield spread (the difference between zero-coupon yields on 10-year and 3-year JGBs, shown as "actual" in Figure 4), which is part of the slope of the yield curve. As fundamental determinants of the yield spread, FKK control a factor representing economic growth and inflation (the 10-year/3-year spread of nominal GDP trend growth) and investors' risk aversion (the equity premium as a proxy). Then they regress the yield spread on the average maturity of JGBs with maturities less than 10 years held by the arbitragers (shown in the lower panel of Figure 3) as well as the above control variables, and confirm that the effect of the arbitragers' average maturity is statistically significant.^{3}

- 3In the estimation, FKK consider a cointegrating relationship between the dependent and explanatory variables, and address the possible endogeneity in the arbitragers' average maturity. The estimation results are generally robust when they use some alternative dependent and explanatory variables. For details, see Section III of FKK.

### Figure 4: Decomposition of the 10-year/3-year yield spread

Figure 4 shows the decomposition of the yield spread based on the estimation result. We can see that the decrease in the arbitragers' average maturity since 2013, together with a shrinking trend-growth spread (reflecting a long-term decline in the potential growth and short-term improvements in growth prospects and inflation expectations in a 3-year horizon), has contributed to tightening of the yield spread (the flattening of the yield curve). Using the estimated coefficient on the arbitragers' average maturity, FKK calculate the cumulative contribution of the BOJ's maturity extension from 2013 through September 2014 to the tightening of the yield spread. The result is around 11 basis points, which accounts for about half of the actual tightening of the yield spread in the same period, as shown in the upper row of Table 1.

### Table 1: Effects of the BOJ's JGB purchases

Regression approach | Term structure model approach | Actual changes through the period | |
---|---|---|---|

10-year/3-year yield spread | -11.0 | -9.7 to -2.1 | -25.6 |

Term premium (10-year) | -38.0 to -60.0 | -- | -27.0 |

Notes:

- Unit is basis points (bps).
- The cumulative net supply effects from January 2013 through September 2014 are calculated.
- The 10-year/3-year yield spread is based on the zero-coupon yield data provided by Bloomberg.
- The term premium is derived from the term structure model.

In the term structure model approach, although the details cannot be explained here,^{4} yield spreads and risk premium are derived from the model that explicitly incorporates the existence of the preferred-habitat investors, and depend on a factor reflecting the maturity structure of the "net supply" of JGBs as well as other yield-curve factors. According to the estimation results of the model, the former factor (a model-based "net supply" measure) has significant effects on yield spreads and risk premium. As in the regression approach, FKK then calculate the contribution of the BOJ's maturity extension to the tightening of the 10-year/3-year yield spread based on the model. The results are in a range between approximately 2 and 10 basis points, depending on the model assumptions. This range is relatively small compared with the result from the regression approach, because the yields in this model become less responsive to any factors including a factor reflecting the "net supply" effects when the short-term interest rate is constrained by the zero lower bound.

FKK also examine the "net supply" effects on the 10-year term premium (the actual bond yield minus the average expected future short-term interest rates over the life of the bond) derived from the term structure model. As in the regression approach, they regress the term premium on variables including those based on the JGBs held by the arbitragers and their average maturity, and confirm that the effects of these "net supply" measures are statistically significant. The contributions of the BOJ's JGB purchases and maturity extension to the reduction in the term premium are in a range between approximately 38 and 60 basis points, as shown in the lower row of Table 1. These magnitudes of the effects are larger than the actual reduction in the term premium in the same period, which is around 27 basis points. This result is broadly comparable with those in previous studies that estimate the effects of the Federal Reserve's corresponding policy measures.

- 4For details, see Section IV of FKK and Koeda (2015).

## When are the "net supply" effects stronger?

In the following, we touch on FKK's additional analysis of the strength of the "net supply" effects examined above. The preferred-habitat theory predicts that the "net supply" effects are stronger when the arbitragers' risk aversion is higher (for example, when deterioration in their balance sheets weakens their risk-taking ability), because they become reluctant to conduct arbitrage trading based on their expected future path of short-term interest rates. The results from the regression approach imply that the net supply effects were stronger when the equity premium, a proxy of the risk aversion, was higher. The estimation results of the term structure model, which incorporates the above relationship, also support the theoretical prediction.

The two approaches, however, differ in their results on the effectiveness in the period when the short-term interest rate is constrained by the zero lower bound. While the regression approach implies that the "net supply" effects were stronger in the zero interest rate periods, this relationship was not found using the term structure model approach, due to the lower responsiveness of yields under the zero lower bound as mentioned above. In general, the large-scale government bond purchases by a central bank and its maturity extension are implemented in the zero interest rate periods. It is and will be all the more important for policy implications to determine whether these policy measures are more effective in the zero interest rate periods than in the normal periods.

## Concluding remarks

As discussed, FKK confirm the "net supply" effects on long-term interest rates using a regression approach and a term-structure model approach, and also examine quantitatively the effects of the BOJ's JGB purchases and maturity extension under its QQE. Both approaches find statistically significant effects, although their magnitudes vary depending on the time and underlying assumptions.

Based on FKK's analysis, several directions for future research could be pursued. First, they left the problem of when and how the effectiveness of the "net supply" of JGBs on long-term interest rates changed. Second, more details about the mechanisms of the scarcity channel and the duration channel mentioned above could be investigated, including the relationship between the scarcity channel examined above using monthly stock data and daily fluctuations in supply-demand flows and liquidity conditions of JGBs, and heterogeneity among preferred-habitat investors such as the BOJ, insurance companies, and pension funds. Third, implications could be derived from the "net supply" effects in the JGB markets for other financial markets and the whole economy.^{5} Further developments in research on these topics, especially those related to JGB markets, are expected.

- 5Comments and discussion on FKK at the 2015 BOJ-IMES Conference are summarized in Endo
*et al*. (2015).

## References

- Endo, Yushi, Takushi Kurozumi, Takemasa Oda, and Kenichirou Watanabe, (2015), "Monetary Policy: Its Effects and Implementation: Summary of the 2015 BOJ-IMES Conference Organized by the Institute for Monetary and Economic Studies of the Bank of Japan [PDF 128KB],"
*Monetary and Economic Studies*, 33, pp. 1-23. - Fukunaga, Ichiro, Naoya Kato, and Junko Koeda, (2015), "Maturity Structure and Supply Factors in Japanese Government Bond Markets [PDF 3,676KB],"
*Monetary and Economic Studies*, 33, pp. 45-95. - Koeda, Junko, (2015), "Bond Supply and Excess Bond Returns in Zero-Lower Bound and Normal Environments: Evidence from Japan [PDF 1.08MB]," (Link to an external website) Working Paper No. E1506, Faculty of Political Science and Economics, Waseda University.

## Notice

The views expressed herein are those of the authors and do not necessarily reflect those of the Bank of Japan.