Monetary Policy Rules and Term Structure of Interest Rates at Zero Lower Bound

AbstractThe Taylor-type rules of optimal interest rate cannot be used to operate the monetary policy during the zero interest rate policy (ZIRP) period, because the short rate cannot be lowered further. Relying on the joint yields-macro latent factors model, this study empirically examines the effect of non-conventional monetary policy stances on term structure and the possible feed-back effect on the real as well as financial sectors using the Japanese experience of ZIRP and implementation of non-conventional policy instruments. The analysis indicates that it is the entire term structure that transmits the policy shocks to the real economy and financial markets rather than the yield spread only. The monetary policy signals pass through the yield curve level and slope factors to stimulate the economic activity. The curvature factor, besides reflecting the cyclical fluctuations of the economy, acts as a leading indicator for future inflation. In addition, policy influence tends to be low as the short end becomes segmented toward medium/long-term of the yield curve. Furthermore, the expectation hypothesis of the term structure does not hold during the ZIRP period as the estimated term premia vary considerably over time.

Keywords: Monetary policy transmission; Term structure; Latent factors; Curvature; State-space model; Expectation channel.

JEL Classification: C32, C58, E32, E52, E50, E58, G12.

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1. IntroductionThe Taylor-type rules of optimal interest rate consider the short rate as the policy instrument. If the policymakers raise short-term interest rates, long-term rates are usually not increasing one-to-one with them but slightly less. Hence, the spread tightens and even might become negative. As a result, higher longer term rates slow down overall spending and, consequently, stagnates the economic growth. Although, the aim is to alter the long-term rates, policymakers use the short rate or the term spread as policy instrument. The related studies in this regard are Bernanke and Blinder (1992), Estrella and Hardouvelis (1991) and Mishkin (1990), who explore the informational content of the spread between long and short-term yields (as an indicator of monetary policy) to forecast the future economic activity and inflation. They find that the slope of the term structure appears to carry information about future inflation and also provide evidence that an inverted yield curve reflects expectations of a declining rate of real activity.1 The other strand includes Kozicky and Tinsley (2001), Svensson (2003), and Bernanke et al. (2005), who modeled the short-term interest rate as policy instrument into the term structure framework. A common result of this strand is that the relation between the term spread and economic activity may be that the slope of yield curve reflects the stance of monetary policy. The contractionary monetary policy triggers two effects. First, it produces a real economic downturn and second, it generates a fall in inflation with a sufficiently lag. For the shape of the yield curve it implies that it flattens or even gets inverted. In contrast, a monetary expansion causes both a steepening of the yield curve and an improvement of economic activity. A point to stress is that such explanations for the co-movements of the term spread and future output growth can be attributed entirely to the informational role of (expected) monetary policy actions.Despite the justifiable explanations for attributing an instrumental role in monetary policy to short-term interest rates or to term spread, the experiences of Japan during the last fifteen years and the fears of US deflation in 2003 and 2009 have let both policymakers and academicians to rethink about their view on application of the term spread and short end of yield curve as a monetary policy tool. Because these models fail to reflect the stances of monetary policy on real economic activity through the yields spread or short rates due to the unusual shape of yield curve during the ZIRP period. Once the short end of the yield curve hits the zero lower bound, the yields have asymmetric movements and the yield curve becomes flat at the short end. For bond pricing and monetary policy analysis it is critical to account for this asymmetry to accurately capture the yield dynamics near the zero boundary. Furthermore, the short rate— the traditional monetary policy instrument — has been at a lower bound of essentially zero for over last two decades. According to macroeconomic models, the binding constraint on nominal interest rates should have greatly reduced the effectiveness of monetary policy and increased the efficacy of fiscal policy during this period (Christiano, Eichenbaum, and Rebelo, 2011; Woodford, 2011).

1 The term spread contains information about future output growth independent of that contained in various other macro variables. Ang et al. (2006) report that for the US, every recession after the mid-1960s has been predicted by an inverted yield curve within six quarters of the impending recession.

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Since at the zero-lower bound, the short-term rate cannot be used as a policy instrument by the central bank to affect the aggregate demand through long-term yields. The alternative may be monetary easing/contraction, foreign exchange market intervention or some other non-conventional measures to alter the medium and long-term yields.2 The goal of the central bank is, therefore, to affect the economy across the entire term structure, bringing down long-term rates, thereby, boosting the economy. Therefore, it is more appropriate to consider the impact on medium to long-term maturities yields rather than only the term spread, as they are the fundamental conduits for the transmission of monetary policy impulses to the economy.The motivation to include the entire spectrum of interest rates comes from informational requirements. The Taylor rule suggests that the short rate should react to current inflation and to the current output gap. Such a rule can hardly be feasible from an operational point of view. The period a central bank sets its interest rate, current inflation and output, data are measured with heavy noise and they are subject to sampling errors and revisions, whereas the output gap is not observable at all. On the other hand, the term structure of interest rates provides high-quality financial data in real time. Given its informational content, term structure measures can be explicitly incorporated in a modified reaction function. In this case, the real as well as financial sectors of the economy respond to term-structure information that are in nature forward-looking.3 This study addresses this issue by formulating a yield curve model that augments monetary policy as well as real economy factors in the term structure model. The objective is to examine the effectiveness of non-conventional monetary policy (monetary easing and foreign exchange market interventions) in affecting the yield curve, using the Japanese experience of zero interest rate policy (ZIRP) and quantitative easing monetary policy (QEMP). To be precise, we are interested to figure out the transmission mechanism through which the non-conventional monetary policy affects the real economy. For this purpose, we formulate a five-factor term structure model, based on the classic contribution of Nelson and Siegel (1987), which grasps the characteristics of the term structure in the Japanese bond market during ZIRP and QEMP. We incorporate five macroeconomic variables, i.e., the level of economic activity, exchange rate, money supply, inflation rate and stock market activity indicator in the state-space representation of the yield curve model to evaluate the transmission mechanism of policy shocks through the medium and long-term bond yields to the real economy. The motivation to add two more factors, i.e., second slope and curvature factors, in the standard dynamic Nelson-Siegel (DNS) model comes from the distinctive features of JGBs yields during the ZIRP regime. During the normal state, Litterman and Scheinkman, (1991), Christensen et al. (2011) and Diebold and Li (2006) show that the short rates are more volatile than long-term yields and

2 Non-conventional tools include sale/purchases of foreign currency denominated bonds, equities (indexed equity funds listed on the exchange) and real estate (funds), and non-sterilized interventions.3 Against this background, monetary policy itself can be forward-looking in the sense that it reacts to expected inflation and output (Clarida et al. 1999). This specification allows a central bank to consider a broad array of information to form expectations about the future state of the economy. Under a forward-looking regime, interest rate decisions are based upon a broad set of conditioning information in a data-rich environment rather than on a few key aggregate variables (Bernanke and Boivin, 2003).

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three factors are sufficient to model the time variation in the cross section of U.S. Treasury bond yields.4 However, the dynamic Nelson-Siegel (DNS) is not capable to grasp the characteristics of the Japanese government bonds (JGBs) yield curve. For JGBs since 1999, yield curve under the ZIRP and the QEMP is flat near zero at the short-term maturities and the short end of the yield curve seems more volatile than the long end (Ullah et. al. 2015 and Table A-1 in Appendix-II). Moreover, the principal component analysis (PCA) of the JGBs during ZIRP period shows that the three factors accounts only for 98.30% variation of the yields. The five factors together capture about 99.51% of the total variation in JGBs yields (Ullah et al. 2016).5 The loadings on the fourth and fifth factors do not have a structure that match to the pattern of either level, slope, or curvature (first three PCs loadings). The fourth factor has biggest loading at the very short end of the yield curve. It is positive at the very short end (until 3-year maturity) that is helpfully to prevent the short rates from becoming negative during ZIRP. The fifth factor loadings has significant role at very long end of the curve (beyond 20-year maturity). The significant role of fourth and fifth factor during the ZIRP regime provides a motivation for the extension of three-factor Nelson-Siegel (1987) term structure model to a five-factor model for modeling the JGBs yield curve (Ullah et al. 2016; Christensen, 2015). Furthermore, considering the Japanese case is particularly interesting, because its economy has become very unstable and experienced significant institutional and monetary strategy changes during the last two decades. In Japan, where prices have remained sluggish in a lackluster recovery from the country’s worst recession of 1990 since World War II, the government has urged the monetary authorities to stimulate the economy further by flooding the banking sector with cash. With interest rates already close to zero, the Bank of Japan (BOJ) is swelling the monetary base by around 80 trillion Yen ($712 billion) each year, up from ¥60 trillion-70 trillion currently, aimed at increasing liquidity in the Japanese economy.6 To do so, it will hoover up still larger quantities of Japanese government bonds (JGBs). In spite of massive increases in monetary base and adoption of zero nominal interest rate lower bound, economic growth has remained low and deflationary pressure has not abated. These events are raising new questions about the effectiveness of monetary policy under a zero nominal interest rate policy. The monetary authority can still influence economic activity when nominal interest rates are zero by taking actions that affect market expectations about the future time path of variables such as interest rates, inflation or exchange rates (Eggertson and Woodford 2003). One way to assess the ability of a central bank to affect expectations is to look retrospectively and ascertain the extent to which previous monetary policy surprises have affected 4 The first three principal components capture the 99.95% of the total variation in yields.5 The fourth and fifth factors explain 0.89% and 0.32% of the variation in yields in the zero-bound state, respectively.6 The BOJ undertook an initial round of QE in 2013 that doubled its balance sheet. But with inflation continuing to stagnate at well below 1%, the bank has moved into a second, open-ended phase of QE consisting of $660 billion in yearly asset purchases that will continue until the 2% inflation target is achieved. The scale of the purchases is unmatched anywhere in the world: the value of the assets held by the BOJ has exceeded 70% of GDP, while the U.S. Federal Reserve's and European Central Bank's assets, by contrast, both stand below 25% of their respective GDPs. In 2014, the BOJ announced the expansion of its bond buying program, to now buy 80 trillion Yen of bonds a year.

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bond yields of different maturities. The remainder of the study is organized as follows. In the next section, we present the term structure model that integrates the yield curve factors with macroeconomic variables and explains the estimation method, while the data structure and estimation results are presented in section 3. In section 4, we relate our framework to the expectation hypothesis. Finally, section 5 presents the conclusion of the paper.

2. The model and estimation methodThe recent trend in literature about yield-macro interaction is to model the term structure of interest rates and the macroeconomic variables jointly in a single model, such as in Ang and Piazzesi (2003), Diebold et al. (2006) and Ullah et al. (2014a). In the seminal work, Ang and Piazzesi (2003) incorporate macro factors namely inflation and growth in affine terms structure model and show that the macroeconomic variables play an important role in movements especially in the short and middle part of the yield curve. Moreover, Diebold et al. (2006.) and Ullah et al. (2013b, 2014a) among others, have convincingly advocated the case for the existence of bidirectional link between the term structure and rest of economy. They incorporate the macroeconomic factors in the dynamic Nelson-Siegel (DNS) yield curve model and examine their joint interaction in the state-space framework. However, the Nelson-Siegel model and even its affine version are not able to grasp the characteristics of the JGBs yield curve. For JGBs since 1999, yield curves under the zero interest rate policy (ZIRP) and the quantitative easing monetary policy (QEMP) have distinctive features.7 In the JGBs market, for the estimatedλ(which are empirically in the range from 0.025 to 0.019), the factor loading for the curvature factor does not increase sharply to play its due role at the short end, while the slope factor loading is close to one (does not decay rapidly), and thus, the model only has the level and slope factors to fit yields with maturities of 3-month to 36-month (for these maturities the yield curve is flat and also has some humps). Therefore, sometimes the estimated yield becomes negative if much weight is assigned to slope factor than the level factor because of having negative estimate ofβ2 t(due to the fact of observing the upward sloped curve almost for alltduring the ZIRP and QEMP periods). Furthermore, ifλis allowed to vary freely, the model suffers ruthlessly from the lack of fit at the long end of curve. The more carefully and thorough investigation of JGBs yield curve shapes and of the Nelson-Siegel yield curve functional form, suggest that the single decay parameterλin Nelson-Siegel model is at the heart of this problem. The parameterλdetermines the exponential decay rate and there is a trade-off between fitting the curvature at short and at long maturities.

7 During this periods, the yield curve has a flat shape near zero at the short-term maturities. The second feature frequently seen in the JGBs interest rate term structure is that it has a complex shape with multiple inflection points. For example, on February 17, 2009, the seven-year interest rate becomes relatively low compared with the six-year and eight-year rates (Kikuchi and Shintani, 2012). Detail description of these features of JGBs yield curve is given in Ullah et al. (2013a, 2014b), Kim and Singleton, (2012), and Kikuchi and Shintani, (2012). Moreover, at some dates the curve is initially falling and then gradually rising (Ullah et al. 2013a, b). Some models and estimation methods may not grasp this kind of curve features and shapes.

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To overcome this limitation in fitting the cross section of yields and grasp the characteristics of the JGBs yield curve, we consider the extended version of the Nelson-Siegel yield curve with an additional slope as well as curvature factors- the so called generalized dynamic Nelson-Siegel model (GDNS)- that corresponds to a modern five-factor term structure model.8 Furthermore, we incorporate five key macroeconomic variables, i.e., the level of economic activity, exchange rate, money supply, inflation rate and stock market activity indicator in the state-space representation of the yield curve model to evaluate the transmission mechanism of policy shocks through the short, medium, and long-term bond yields to the real economy. The inclusion of second slope will be helpful to fit the very short maturities, as we restrict the role of the newly added slope and curvature factors to the short end of the curve by assuming thatλ1< λ2. In this section, we discuss the yield-macro model, considered to evaluate the effectiveness of non-conventional monetary policy. First, in subsection 2.1, we describe the model that incorporates macroeconomic variables in state-space representation. The latent factors model is considered, because it will be a convenient vehicle for introducing the state-space representation. Second, subsection 2.2 presents the estimation procedure of the model in the state-space framework using the Kalman filter algorithm.

2.1. Yields-macro factors modelAn intuitive way to represent our model is to cast the generalized Nelson-Siegel functional form into state-space framework, which assumes that information about the term structure of interest rates can be summarized by five factors, i.e., the level, two slopes and two curvatures of the yield curve, as:

Rt (m )=β1 t+β2 t [1−exp (− λ1 m)λ1m ]+β3 t [1−exp (− λ2 m)

λ2m ]+β4 t[1−exp (−λ1m )λ1 m

−exp (− λ1 m)]+ β5 t [ 1−exp (−λ2 m )λ2 m

−exp (−λ2m )]+εt (m )(1)

whereRt (m )is the zero-coupon rate for maturitymwithm=1,2 ,…,N andt=1,2 ,…,T .The generalized dynamic version of Nelson-Siegel model, which we denote as the GDNS model, is a five-factor model with one level factor, two slope factors, and two curvature factors. Here β1 t is the asymptotic value of the spot rate function, which can be seen as the long-term interest rate and is assumed to be positive( β1 t>0 ). Furthermore, β2 t and β3 t determines the rate of convergence with which the spot rate function approaches its long-term trend. Furthermore, the factors β4 tand β5 t determine the size and the form of the humps. The two slope and curvature factors are governed by the two different decay rates. In (1), β2 t and β3 trefers to the first slope and second slope factors, while β4 tand β5 tcan

8 Assuming a second-order differential equation, to describe the movements of the yield curve, with the assumption of real and un-equal roots, the solution will be the instantaneous implied forward rate function. The solution for the yield function can be found by integrating the forward rate function. The resulting yield curve function will consists of five factors (one level, two slopes and two curvatures factors) and two decay parameters, i.e.,λ1and λ2, which corresponds to two different roots of the second-order differential equation.

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be termed as first and second curvature factors, respectively. The two decay parameters, i.e.,λ1andλ2

, determines the rates with which the two slopes approaches to its asymptotes values. Ifλ1< λ2, then the value ofλ1will serve to fit the long rates attractively (the first slope and curvature factors, i.e.,β2 t

andβ4 tloading will approach comparatively slowly to its asymptotic values), whileλ2will be helpful to fit the short end of cure more reasonably (the second slope and curvature, i.e.,β3 tandβ5 tloadings will decay more rapidly). The advantage of this extension is that the model can fit curves with special shapes, such as twists. However, there is a trade-off between better fitting and parameter estimation. It is worthwhile to mention that we impose the restriction ofλ1< λ2, which is non-binding due to symmetry. The factor loadings of the two slopes and curvatures in the yield function are illustrated in Ullah et al. (2015) for the JGBs yields in detail.As far as the macro variables are concerned, the term structure includes significant amount of information about the market’s expectations of future inflation, exchange rate, economic growth and state of equity market as suggested by the recent macro-finance literature (Ang and Piazzesi , 2003; Hördahl et al. 2008; Wu, 2002; Diebold et al. 2006 and Ullah et al. 2014a). The promising results in this regard are reported in Ang and Piazzesi (2003), Moench (2006) and Hordahl et al. (2006). Ludvigson and Ng (2009) find that macro factors also help to forecast excess bond returns, indicating that macro factors contain predictive information that is not already contained in forward rates and yields spread. In line with the arguments of the studies that show the dynamic interaction of yield and macroeconomic factors, we expect that yield curve level factor has strong correlation with the exchange rate, money supply and inflation level, while the spread and curvature factors are related to the overall economic activity measures, monetary policy variation and risk premium of stocks. However, Diebold et al. (2006) report negligible responses of macroeconomic variables to shocks in the curvature factor, but conversely, Monch (2006) argues that flattening of the yield curve is associated with the changes in the curvature factor and can be linked to an economic slowdown.9 Given the ability of the five yield curve factors to provide a good representation of the yield curve, we include five key variables: the annual growth rate in industrial production( IPt), exchange rate(EX t), money supply(MS t), annual price inflation( INF t )and stock market index(SI t) in the state equation to analyze their joint dynamics with the yield curve factors and the effectiveness of non-conventional monetary policy. These variables represent, respectively, the level of real economic activity, foreign market competitiveness, monetary policy stances, and the inflation rate, which are widely considered to be the minimum set of fundamentals needed to capture basic macroeconomic dynamics. As for the stock market is concerned, the annual growth rate of stock market aggregate index (SI t) is considered in the model as an indicator of the capital market performance. Though, the stock market aggregate index is an equity market indicator, in this study we call all the five variables( IP t ,EX t , MS t , INFt , SIt )as macroeconomic variable for the ease of interpretation and writing.

9 For the theoretical background and expected relation between the yield curve and macroeconomic factors with support from the recent macro-finance literature, see Diebold et al. (2006) and Ullah et al. (2013b, 2014a).

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The rationale behind including the growth rate of money supply and exchange rate, i.e., MS tandEX t

in the model is to evaluate the effectiveness of non-conventional monetary policy in affecting the yields for various maturities and the reverse effect on the real as well as financial sectors.The non-conventional monetary policy tried by the BOJ includes the so-called “quantitative easing and foreign exchange market intervention”. The quantitative easing (QE) involves an expansion of the monetary base, even when the policy interest rate cannot be driven any lower, either through open market operations on short-term government debt, outright purchase of long-term bonds (or equities), or through unsterilized purchases of foreign currency. The BOJ has been conducting such a policy since March 2001, and more aggressively since December 2001. The recent ample liquidity moves by the BOJ (in late 2012 and 2013) also includes the aggressive use of QE.10 The conventional liquidity trap analysis suggests that when the short-term interest rate hits a floor of zero, short-term bonds become a perfect substitute for money and so expanding the monetary base will have no effect on the economy. However, quantitative easing might be helpful to stimulate the economy if it provided a signal that the monetary base would be higher than it otherwise would be once the deflation is over (Auerbach and Obstfeld, 2005).On the other hand, foreign exchange market intervention to depreciate the currency provides an additional way of exiting from a deflation trap. A fall in the value of the domestic currency makes imports more expensive and exports cheaper. The result is expenditure switching in which exports rise and imports fall, thereby, increasing the demand for domestically produced goods, which stimulates aggregate demand. Intervention in the foreign exchange market, the selling of JP-Yen and purchase of foreign currency, has thus been suggested as a powerful way of getting the Japanese economy moving again (Bernanke, 2000, McCallum, 2000, 2003, 2005, 2009, Meltzer, 1995, Orphanides and Wieland, 2008, and Svensson, 2001, 2003).11 Indeed during the ZIRP period and in recent years, the BOJ is intervening continuously in the foreign exchange market to depreciate the JP-Yen to boost the economy. It shows that the foreign market intervention to depreciate the JP-Yen (EX tincreases) is by analogy has the similar impact as the increase in MS t

(expansionary monetary policy) has on the real sector. Given that the BOJ has used these two tools extensively during the ZIRP period to operate the monetary policy, therefore, we use the growth rate in MS tandEX tas non-conventional monetary policy tools to evaluate the impact of non-conventional monetary policy in affecting the macroeconomic environment in the economy.We assume that the yield curve latent factors vector β talong with the five macroeconomic factors follow a vector autoregressive process of first order, which allows us to formulate the yield curve

10 The monetary base includes the amount of current account at the Bank of Japan. In normal times, excess reserves would be unlikely to help stimulate the economy. However, an expansion of the monetary base might be beneficial even if it does not produce a significant increase in M2 when the interest rate is zero. First, ample liquidity in the system may help to avoid a potential financial crisis that was a concern in 2002-2003. Second, liquidity may encourage financial institutions to take more risk in portfolio management, in particular taking positions in long-term bonds, equities, and foreign bonds, any of which would contribute to stimulating the economy indirectly. The economic recovery in 2003 may be partly due to ample liquidity in the system.11 The JP-Yen means the Japanese local currency Yen (¥).

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latent factor model in the state-space form and to use the Kalman filter for obtaining maximum-likelihood estimates of the hyper-parameters and the implied estimate of β t. In the state-space representation the complete model with observation equation (2) and state equation (3) can be written as:

[Rt

Z t]=[Λ ( λ1, λ2 ) 00 I 5][ β t

~Z t ]+[ε t

0 ] (2)

α t+1=( I 10−A ) μ+ A α t+v t+1 (3)

[ εt

v t+1] N ([00 ] ,[Ω 00 Σv ]) (4)

whereα t=(β t' ,~Z t

' ) ' is (10×1) latent vector,Rtis (N×1) vector of zero-coupon yields,

Z=(IP t , EXt , MS t , INFt , SI t)' is (5×1) vector of macroeconomic factors, β t is (5×1) vector of yield

curve factors, Λ ( λ1 , λ2) is (N×5) matrix of factors loadings, A is (10×10) matrix of parameters, μ is (10×1) mean vector of factors, and I 10 and I 5 are (10×10) and (5×5) identity matrices respectively. Σv is (10×10), the covariance matrix of innovations of the transition system and is assumed to be unrestricted, while the covariance matrix Ω of the innovations to the measurement system of (N×N) dimension is assumed to be diagonal. The latter assumption means that the deviations of the observed yields from those implied by the fitted yield curve are uncorrelated across maturities and time.12 Moreover, in (4), we assume that the innovations,ε tandv t, have Gaussian distribution. While real data are never exactly multivariate normal, the normal density is often a useful approximation to the true population distribution. Additionally, the multivariate normal density is mathematically tractable and nice results can be obtained. Moreover, the distribution of many multivariate statistics is approximately normal, regardless of the form of the parent population because of the central limit theorem.

2.2. Statistical formulation of the models and estimation methodIn this subsection, the estimation procedure based on the Kalman filter for model is explained. For convenience, we introduce some new notations and rewrite the signal and state equations in (2) and (3) respectively, to obtain the generalized form of yield-macro model in state-space form.

y t=H X t+wt , ∀ t=1,2, …,T (5)X t=C+F X t−1+u t+1 (6)

[wt

u t ]∼N ([00 ] ,[G 00 Q ]) (7)

12 Given the large number of observed yields used, the diagonality assumption of covariance matrix of the measurement errors is necessary for computational tractability.

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where the expressions of y t , F , X t ,C , H , G ,Q ,wtandutare given in appendix-I. In (7), the matrixGis assumed to be diagonal for computational traceability, while the covariance matrixQis assumed to be non-diagonal. Moreover, the transition and the measurement errors are assumed to be orthogonal to the initial state.The Kalman filter algorithm is implemented along the lines of Hamilton (1994a) to evaluate the Gaussian likelihood function and obtain the latent factor as well as estimates of the hyper-parameters. Denoting the optimal estimate of latent factors X tgiven the information until time t−1 ort , as X t∨t−1 and X t∨trespectively. Using the transition equation the recursive prediction step can be calculated as:

X t∨t−1=C+F X t−1 (8)Pt∨t−1=F Pt−1 F '+Qt (9)

where Pt∨t−1is the mean square error (MSE) matrix at the prediction step. Using the measurement equation these estimates are improved by observingRt, thus in the update step:

X t∨t=X t∨t−1+P t∨t−1 H ' K t−1 ηt (10)

Pt∨t=Pt∨t−1−Pt∨t−1 H ' K t−1 H Pt∨t−1 (11)

whereηt=Rt−H X t ∨t−1(the forecast error vector) andK t=H P t∨t −1 H '+G(the MSE matrix of ηt). The Kalman Filter iterative process begins with X 0 and P0 being set at theμand unconditional covariance respectively as discussed in Hamilton (1994a). The parameters, the constants vectorμ, coefficients matrix Aand both the co-variance matrices (Ω and Σv) along with both decay parameters ( λ1 , λ2)are treated as unknown coefficients, which are collected in the parameter vectorξ . Estimation ofξis based on the numerical maximization of the log-likelihood function that is constructed via the prediction error decomposition and given by:

log L(ξ )=−NT2

log (2 π )−12∑t

log [|K t (ξ )|]−12∑t

[ηt' [ K t (ξ ) ]−1 ηt ] (12)

The specification in (12) is a function of the parameter setξ=( λ1 , λ2 , μ , A , Ω ,Σv ). The likelihood is comprised of the (N×1) yield prediction error vectorηt , and of the (N×N) conditional covariance matrix of the prediction errorsK t. We use the numerical optimization fminsearch routine of the Matlab, which solves non-linear optimization to maximize the log likelihood function (12) and obtain the estimates of the parameters. We also apply the optimization routine csminwell to ensure global convergence as well as testing the sensitivity to starting values. For inferences, the covariance matrix of the estimates is calculated by inverting the negative of the Hessian evaluated at the optimum, where the Hessian itself was approximated by finite differences after reverting back to the original parameterization, as suggested in Hamilton (1994a).

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Due to the large number of parameters in the models, the optimization problem will be highly sensitive to the initial values of parameters. In order to start the optimization procedure, we choose certain initial values for the model parameters that are expected to be most likely that lead to the global optimum. The process of choosing the initial values is carried out in multiple steps. Initially few parameters are allowed to vary freely (i.e., the mean vector), while all other parameters are fixed to some constant values (fixed values are taken from Ullah et al. 2015) and the log likelihood function is optimized to obtain the optimal estimates for freely varying parameters. In the second stage, the parameters vector is expanded (decay parameters are included) and the log likelihood function is optimized once again. This information is incorporated into the next run. During the second run, the mean vector is seeded with the previous run optimal values. In this way the parameter vector is steadily expanded until it includes the full set of parameters in the model and the parameter vector is fully specified. The full specification includes 192 parameters in the parameters vector. In this incremental progressing, we identify the starting values for almost all the parameters in the fully specified model. This whole process involves running the model 30 times, each time with an expanded parameters vector. These simulated estimates are then used as initial values for the parameters vector to optimize the full models.

3. Empirical resultsIn this section, we provide empirical evidences on the dynamic interrelation of the yield curve and macroeconomic factors as well as the potential role of yield curve factors in monetary policy transmission. In doing so we answer three principle questions: (i) what are the macro-financial linkages between bond yields and macroeconomic variables? (ii) how does the yield curve factors respond to monetary policy stances and transmit the policy shocks to the real sector? (iii) does the non-conventional policy tools adopted during the ZIRP are effective to stimulate the economy and pushed the economy out of the deflationary cycle (liquidity trap)? In evaluating the non-conventional policy tools, we are along the way to show that will the recent momentous move of ample liquidity in the market by the BOJ be capable to clear the clouds hanging over the Japanese economy since the burst of asset bubbles of 1990s? To analyze the joint interaction, the monthly time series panel of unsmoothed Fama-Bliss zero-coupon yields for Japanese treasuries of different maturities between 1996 and 2013 is combined with a data-set of macroeconomic time series for the same sample period. The details of the data-set are provided in section 3.1. The estimation results for the joint interaction of macro and yield curve factors are presented in section 3.2. Section 3.3 presents the results of some formal statistical tests of contemporaneous and lagged interaction between macro and yield curve factors. Finally, in section 3.4 and 3.5, we discuss the estimation results for macroeconomic and yield curve factors impulse response functions and variance decompositions respectively.

3.1. Data descriptionThe empirical results are based on the Japanese interest rates that are constructed by employing the

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Fama-Bliss (1987) methodology of calculating the unsmoothed Fama-Bliss zero-coupon yields from bond pricing data. These have been constructed from average bid-ask price quotes, retrieved from the Japan Securities Dealers Association (JSDA) and the Tokyo Stock Exchange (TSE) bonds files. The bonds with maturity of less than two months and inflation indexed bonds are excluded from the sample.13 The remaining quotes are used to construct forward rates using the Fama and Bliss (1987) methodology. The forward rates are then averaged to construct constant maturity spot rates. These unsmoothed yields exactly price the underlying bonds.The resulting balanced panel data-set consists of 20 maturities over the period January 1996 to December 2013 with maturities of 3, 6, 9, 12, 15, 18, 21, 24, 30, 36, 48, 60, 72, 84, 96, 108, 120, 180, 240 and 300 months (20 maturities). The summary statistics of the yields for various maturities along with a three-dimensional plot of the data-set are discussed in detail in appendix II. The descriptive statistics and three-dimensional plot of the data show that the typical yield curve have been upward sloping and the short rates are almost zero during the prolonged period except with a little rise in late 2006 and early 2007. During the period of a rise in very low maturity interest rates, the fall in the slope is also apparent. Moreover, short maturities are less volatile than long rates.We complement this yield curve data with a monthly panel of macroeconomic time series from January 1996 up to December 2013. Macroeconomic panel consists of variety of variables that should provide a snapshot of the Japanese economic climate over the sampled period. We consider the industrial production, real exchange rate, money supply, consumer price index and Tokyo Stock Exchange share prices index (TOPIX). The data for the former four variables is obtained from the International Financial Statistics (IFS), while for TOPIX the data are taken from annual reports of the Tokyo Stock Exchange for various years. All five variables are measured as the last 12 months’ percentage growth rate. TheIPtis growth rate in industrial production,EX tis the growth in real exchange rate (JP-Yen/US-$),MS t is the growth rate ofM 2monetary aggregate,INF tis the inflation rate and is measured as 12-month percent change in the consumer price index, andSIt is the last 12-month growth rate of TOPIX.14 The descriptive statistics of the macroeconomic variables and capital market indicator are depicted in appendix-II.

3.2. Estimation results of the modelFor given values of the system matrices, we use the Kalman filter to evaluate minimum mean square linear estimates (MMSLE) of the state vector at timetgiven the observation. The Kalman filter is also used to evaluate the log likelihood function via the prediction error decomposition. The maximum likelihood estimates of the unknown parameters are obtained via the numerical optimization of the log likelihood function. The log likelihood is optimized by employing the Simplex algorithm.The Kalman filter is initialized atX 0=μand unconditional covariance matrix of the state vectorP0, which is derived from the Gaussian distribution, given that the innovations of both signal and state equations are normally distributed. The Kalman filter algorithm is sensitive to the initializing values of parameters, we use the estimates of the parameters of the simulation exercise discussed in section 2.3 as the initial values.The estimation results of the parameters of state equation are presented in the first panel of table 1. A reasonably high persistency in the yield curve latent factors can be seen from the diagonal elements of the coefficient matrix A, particularly for the second slope and first curvature factors (being close to one), however, the lagged own dynamics of level, first slope and second curvature 13 The bonds of maturity less than two months have almost same prices because of the very low interest during the sampled period and it implies to some strange estimates of the zero-coupon rates, such as the rate for one-month maturity is higher than of the one and half month maturity bonds. Moreover, the inflation indexed bonds have floating rates (coupon is not fixed) that change in each period. Therefore, the bonds with maturity of less than two months and floating rates are omitted from the sample at the stage of calculating the zero-coupon rates.14 The US-$ means the United States of America local currency dollar ($).

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are not as strong as of the rest two yield curve factors, i.e.,β3 tandβ4 t. The yield curve factors persistency is lower as compared to that of the standard dynamic Nelson-Siegel model factors (shown in related studies, such as, Diebold et al. 2006; Ullah et al. 2013b), might be due to the inclusion of two additional yield factors in the model. The lagged own dynamics of three macroeconomic factors representing the growth of economic activity, exchange rate and the stock market index are also sufficiently large.15 Regarding the cross-factor dynamics among the yield curve factors, the results show that the level factor is affected negatively by the two slope factors, while the two slope factors, i.e.,β2 tandβ3 t have significant negative impact on each other and are positively affected by the level and second curvature factors. Theβ1 tandβ2 tare significantly related toβ4 tandβ5 t, whereas theβ5 ,t−1has positive significant impact on the first curvature. This significant relation encourages the use of a VAR model to describe the dynamics of the latent factors in the yield curve model instead of the more parsimonious AR(1) specification. Moreover, the lagged interaction among the macroeconomic factors show negative significant impact of one period lagged inflation rate on industrial production along with the statistically significant lagged impact of money supply and inflation rate on exchange rate and ofMS t−1andIPt −1on stock market performance index.

<<Table 1>>Turning the focus to yield and macro factors dynamics, which is the main focus of this study, the results in upper right (5×5) and lower left (5×5) blocks of the matrix Aindicate that the impact of yield curve factors on macro factors is stronger than the impact of latter on the former. This suggests that the policy signal passes through the yield curve factors to the macro economy and yield curve shape carries information about the future and can predict the economy. The upper right (5×5) block, which indicate the impact of macro factor on yield curve, reveals that the level factor is negatively affected by the level of economic activity and money supply. The response of level factor is weak but statistically significant. The most important result is that the first slope factor, i.e., β2 tis negatively affected by the growth in industrial production and positively by the monetary aggregate. The negative relation with economic activity is consistent with the idea that during recession an upward sloped yield curve not only indicate bad time today but also better state in the near future. The positive response to the money supply reveals that the monetary policy affects the shape of the yield curve (yield curve become steeper) which in turn influence the other indicators of macroeconomic and financial market performance. This suggests that monetary policy shocks account for significant fluctuations in the yield curve shape and policy shocks are likely to affect the medium- to long-term interest rates. One important channel, through which monetary policy works, is the long end of yield curve, shaping them so that, in turn, they affect the level of economic activity. This relation is consistent with the EH of the yield curve theory. Moreover, the first curvature factor is positively related to the money supply and inflation rate. The positive response to money supply in consistent with the premise that yield curve becomes steeper with an expansionary monetary policy (the fall in the curvature means transition from an upward sloping yield curve to a flat one). The lagged exchange rate and stock market index do not have any statistically significant impact on any yield curve factors.Furthermore, the left lower (5×5) block of matrix A, indicating the response of macroeconomic indicators to yield curve factors, shows that level factor has negative impact on economic activity, exchange rate and stock market index. The negative effect on IPtand SI tconfers that as the long term interest rate goes up, both the flow of spending and investment in equity divert towards the bond market, because of higher certain return on bonds. And as a consequence the inflation rate falls, consistent with the Fisher (1896) hypothesis of expected inflation. The result of EX t is consistent with the economic principle of capital inflow in the economy because of the higher

15 The own-lag coefficient ofβ3 tandEX t are greater than 0.9. However, stationarity is assured, because the largest eigenvalue of the matrix Ais 0.9472. No value lies outside the unit circle.

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profitability in the domestic bond market. Regarding the first slope factor, i.e.,β2 t, there is negative impact on the IPt , while positive on money supply, exchange rate and inflation rate. The negative relation suggests that the yield curve first slope can serve as a leading indicator of the future state of economy. It shows that as the yield curve tends to flatten or negatively sloped, the industrial production falls in the subsequent periods. The positive relation with the money supply confers that the Bank of Japan (BOJ) launches more expansionary monetary policy in order to avoid the upcoming recession and because of the positive relation between inflation and monetary growth, the inflation rate increases. Besides this, the second slope factor can also anticipate the future business fluctuations as it has negative impact on the stock market.16 It means that as the yield curve tends to flatten, the stock market goes into a bearish trend because of the anticipated future economic slowdown. The first curvature factor has statistically significant negative impact on money supply and exchange rate, while positive on the industrial growth. It confers that as the yield curve becomes flatter, the BOJ imputes the liquidity in market, because a fall in curvature shows the transition from steeper to a flatter yield curve, either in the form of an increase in the monetary base (QE) or foreign exchange market intervention. Moreover, the significant positive impact on economic activity indicates that the curvature can also transmit the policy signals to affect the economic indicators. Moreover, the second curvature, i.e., β5 thas negative relation with the exchange rate and inflation rate, while positive with theSI t . This shows that, besides predicting the trend of the stock market, the yield curve curvature factor may be of some importance to predict the future inflation. The significant relation of two curvatures factors with exchange rate confers that as curvature fall (yield curve becomes flatter), the BOJ intervene in the foreign exchange market to devalue the yen (to boost exports) in order to avoid the upcoming recession, because of the export oriented nature of the Japanese economy. The BOJ is operating its monetary policy through the foreign exchange market intervention for the last 20 years, therefore, the two curvatures can be viewed as the transmission paths of monetary and exchange rate policies to the rest of the economy. Finally, the estimate of first decay parameter λ1is 0.0167 with a standard error of 0.0028, indicating that the estimate is highly significant. It implies that the loading on the first curvature factor is maximized at a maturity of about 108-month. This confers that the estimatedλ1serves to fit long rates attractively, because of very low decay rate of the slope and curvature factors loadings. Therefore, the first slope and curvature factors affect the important intermediate range of maturities from 5- to 20-year of maturity. The estimatedλ2(0.1581 with standard error 0.0002) suggests that the second curvature loading peaks at 12-month maturity. Therefore, the second slope and curvature factors take on very different roles in the fit of the model as compared to the standard DNS model. The rapid decay rate of the second slope loading will be helpful to fit the short rates more accurately and precisely, as it is one of the problem with the standard DNS model in fitting the JGBs yield curve during the zero interest rate policy (ZIRP) period. The inclusion of the additional slope and curvature factors to the standard DNS model are also helpful to restrict the very short rates from becoming negative during the ZIRP and QEMP periods (see Ullah et al. 2015, for details)Moreover, many of the coefficients (48 out of 100) in matrix A are statistically insignificant, Wald-test and LR (likelihood ratio) test for their joint significance are employed and the results are presented in the second panel of table 1. Both of the test statistics reject the null-hypothesis of the joint insignificance of the 48 individually insignificant coefficients in the state equation. This suggests that inclusion of macroeconomic factors in the Nelson-Siegel specification of yield curve improves the model’s overall fit and prediction power (Ullah et al. 2013b).Furthermore, the estimated factors of the yield curve are closely related to the macroeconomic variables that are considered fundamental conduits for the fluctuation in economy.17 The time series of the yield curve factors’ estimates of yield-macro model with potentially related macroeconomic 16 Furthermore, the lag of second slope factor, i.e.,β3 ,t−1has positive significant impact on EX t , MStandINF t. The effect is similar to the effect ofβ2 tin terms of sign and statistical significance, but much stronger in terms of magnitude of impact.

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variables are plotted in figure 1. The figure show the time series path of the estimated level β̂1 tand first slope − β̂2 t factors against money supplyMS t, the first curvatureβ̂4 tagainst the inflation rateINF tand second slopeβ̂3 tfactors against the growth rate in industrial production IPt and exchange rateEX t. The pattern of level factor along with the first slope factor is closely related to annual growth of money supply (shown in the top left pane of figure 1), while the second slope factor follows the pattern of variation in exchange rate as depicted in bottom left panel of figure 1. It confers that shocks to monetary policy (both tools, i.e., money supply and exchange rate) are important sources of variation in long end of the yield curve and pricing the long-term maturity bonds. The top figure shows that fall in money growth is accompanied by a rise in the level factors, i.e.,β̂1 tand fall in the slope of yield curve ( β̂2 t rises), while an increase in money supply is reflected by a fall inβ̂1 tandβ̂2 t(yield curve becomes flatter). It means that the monetary policy signal transmits through the yield curve level and spread factors to the real sector. It suggests that the shift of long end and, hence, the slope of yield curve has important information about the state of economy. This mechanism is more obviously illustrated by the second slope factor, i.e., β̂3 t(top right panel of figure 2), which has a very clear relation with the industrial production. The figure shows that decrease in second slope (β̂3 trises) is followed by a fall in the real activity with one period lag and vice-versa, suggesting that decline in the slope of yield curve (becoming flat or more negatively sloped) can be considered as a signal of economic slowdown.18 Moreover, the stances of monetary policy are also depicted by the second slope factor, i.e., β̂3 tas shown in bottom left pane of figure 1. It is a well-known fact that after bounding the short rate to zero, the BOJ was operating the monetary policy through the use of un-conventional monetary policy tools, such monetary easing and more importantly the foreign exchange market intervention. Because of the export based economy, the intervention to devalue yen has similar impact on the real sector as an increase in the money supply has on the domestic economy and vice versa. Therefore, the rise inEX tby analogy acts like the expansionary monetary policy. Furthermore, as we plot − β̂3 t(against exchange rate), therefore, a fall in− β̂3 tdepicts the transition from steeper to flatter or more negatively sloped yield curve. The pattern in figure indicates that in response to an increase in the exchange rate (expansionary monetary policy) the yield curve becomes steeper and fall inEX tis followed by the fall in slope of yield curve. This suggests that monetary policy shocks account for significant fluctuations in the yield curve shape and policy shocks to exchange rate are likely to affect the medium- to long-term interest rates, which, in turn, influence the other indicators of macroeconomic and financial market performance.

<<Figure 1>>

17 We also compare the estimated yield curve factors, i.e., β̂ t vector, with their corresponding empirical proxies (level,

slope, and curvature). The empirical level factor( Lt )is defined as the 25-year yield, slope( St )as the difference between

the 25-year and 3-month yields and curvature slope(C t )as two times the 2-year yield minus the sum of the 25-years and

3-month zero coupon yields. The pairwise correlation of estimated β̂1 twith empirically defined level factor is

ρ ( β̂ t , Lt )=0.8681, whereas the correlation of the estimated slope factors (i.e., β̂2 tand β̂3 t) with the empirical slope is

ρ ( β̂2 t , S t )=−0.8157andρ ( β̂3 t , S t )=−0.7190. The correlation of estimated curvatures (i.e., β̂4 tandβ̂5 t) and

empirical curvature is ρ ( β̂4 t ,C t )=0.7106 ,andρ ( β̂5 t , Ct )=0.5681, while the correlation of second curvature β̂5 t

with the ten-year maturity yields is -0.9246. It shows that the estimated factors are closely related to and also follow the pattern of the empirically defined factors, i.e., level, slope and curvature. Given the fairly large pairwise correlations of yield curve estimated factors with their empirical proxies, the estimated latent variables in our yield-macro model can be termed as level, slope and curvature factors.18 One should be aware of two big fall in industrial production during late 2008 and early 2011. The former corresponds to the global financial crisis, during this period the Japanese exports fall sharply and hence the real activity slows down. The second fall refers to the impact of the great East Japan earthquake and tsunami of 2011.

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Moreover, the variation in inflation is closely explained by the first curvature factor of the yield curve, i.e.,β̂4 t. The CPI based inflation rate closely follows the pattern of curvature factor of yield curve as depicted in the bottom right panel of figure 1. The rise in curvature, indicating the transition from a flatter to an upward sloping yield curve, is followed by an increase in the inflation (consistent with the procyclical behaviour of inflation rate during the business cycle) and vice versa. In addition the curvature factor is also closely related to the growth rate in money supply.Overall, figure 1 suggests that during the initial period of adopting the ZIRP and QEMP and world financial crisis, we observe a decline in the yields of long-term bonds and slope of yield curve and during the period of recovery, the yield curve long end as well as slope are on the increasing trend. In particular, the curvature reflects the cyclical fluctuations of the economy too. Like the yield curve spread, a decrease in curvature is signaling towards economic slowdown and vice versa. Furthermore, the curvature factor seems either to anticipate the future inflation or complemented by inflation rate, suggesting that the curvature factor is the main driving force of the inflation rate, and The estimate of the covariance matrix of the state innovations, as depicted byΣvin (4), along with the results of Wald and LR tests are shown in table 2. The results indicate that the diagonal elements of the matrixΣvthat correspond to the variance of the state innovations are statically significant. Regarding the off-diagonal elements, only 21 out of 45 covariance terms are statistically significant at 5% level of significance. The corresponding covariance terms may also be interpreted as the contemporaneous relation between the yield curve and macroeconomic factors.19 Therefore, the Wald and Likelihood ratio (LR) tests are employed for the joint significance of the off-diagonal elements of the matrixΣv. Both the test statistics are highly significant and reject the null-hypothesis of the diagonality of the Σv(the test statistic for Wald test is 105.4924 (0.000) and 126.9868 (0.000) for the LR test). The result is consistent with our prior expectation that the innovations of transition system are cross correlated and there is contemporaneous relation between the macroeconomic and yield curve factors. Therefore, the covariance matrix Σvshould not be reduced to a diagonal matrix.

<<Table 2>>Regarding the in-sample fit of the model, in table 3 summary statistics for the fitted errors are reported. At first glance, table 3 seem to imply that model has a very good fit, both for short and long maturities. The improvement for the short maturities is consistent with the premise that the second slope and curvature factors operate at short maturities. There is also a slightly better fit with long-term yields in comparison to results presented in Ullah et al. (2014b) for the standard DNS model. The improved fit for the short-maturity yield in the GDNS based models relative to the DNS model reflects the important role of second slope and curvature factors. Moreover, it is evident that the residuals autocorrelations across time for all maturities is considerably smaller. An interesting feature of the residuals is that the standard deviation increases rapidly as the maturity gets longer; this is not the case for US data, at least not to this extent, see Diebold and Li (2006). The reason <<Table 3>>

19 The estimate of covariance matrix and test statistics for diagonality are reported in order to show that the residuals of state innovations are not contemporaneous independent. Therefore, the diagonalization of matrix Σvmay be required to compute the impulse response function and variance decompositions results in section 3.4 and 3.5 respectively.

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3.3. Formal tests for macro and yield curve factors interactionsTo assess the lagged as well as contemporaneous interactions between the yield curve factors and the macroeconomic variables, the (10×10) mean reversion matrixA and the covariance matrix Σv , are partitioned into four (5×5) blocks as:

A=[ A1 A2

A3 A4]Σv=[Σ 1 Σ2'

Σ 2 Σ4] (13)

where A2 and A3show the extent of the lagged linkage from the macro-to-yields and the yields-to-macro factors respectively, and A1 and A4 show the yield curve factors and the macroeconomic variables dynamics with their own lags respectively. Furthermore, all the covariance terms given by the block Σ2 can be attributed to the contemporaneous effect of the yield curve factors on the macro variables in accordance to the order of the yield and the macro factors employed in the state equation (3). As such, there are two links from the yields to the macroeconomy in our setup: the contemporaneous link given byΣ2 and the effects of the lagged yields on the macroeconomy are embodied in A3. Conversely, links from the macroeconomy to yields are symbolized in A2.

<<Table 4>>Table 4 gives the results of likelihood ratio (LR) and the Wald tests for the several restrictions of the yield and the macro dynamics (in the matrix A andΣv). Both of the tests reject the no individual contemporaneous as well as the lagged interaction hypothesis (as the null hypothesis of (i) A2=0, (ii) A3=0, and (iii) Σ2=0 are rejected). Furthermore, the null hypothesis of no interaction of the two joint restrictions and the three joint restrictions are also rejected with a very high probability (as the null hypothesis of (i) A2=A3=0, (ii)A2=Σ2=0, (iii) A3=Σ2=0, and (iv) A2=A3=Σ2=0 are rejected). The results indicate that the restriction that certain blocks of the estimated state transition matrix as well as covariance matrix are zero are rejected. The results suggest that both hypotheses, of “no macro to yields” depicted by A2 and “no yields to macro for contemporaneous as well as lagged impact” depicted by A3 and Σ2 respectively, should be rejected at a very high level of significance. In particular, the last row confirm that there is indeed a dynamic (contemporaneous as well as lagged) interaction between the yield curve factors and the macro variables, in both directions.

3.4. Macroeconomic and yield curve impulse response functionsThis subsection assesses how much the variation in macroeconomic variable depends on the shocks of the yield curve factors and also the feedback effect of macro as well as policy shocks on the yield curve factors. This assessment is meaningful for measuring the degree of integration of the macro-yield factors and evaluating the transmission mechanism of monetary policy. Following Diebold et al. (2006) and Ullah et al. (2014a), we consider the dynamic relationships between the macro and the yield curve factors through impulse response analysis. From an estimated VAR, we compute the variance decomposition (VDCs) and the impulse response functions (IRFs) which serve as tools for evaluating the dynamic interactions and the strength of causal relations among variables in the VAR system.20 In simulating IRFs and VDCs, it should be noted that VAR innovations may be contemporaneously correlated. This means that a shock in one variable may work through the contemporaneous correlation with innovations in other variables. Therefore, the responses of a variable to shocks in another variable of interest cannot be adequately represented and isolated

20 In estimating VAR model, one should be aware of the stationarity consideration of the variable in the system, otherwise the results may be suffered from spurious relationship. A regression involving the levels of I(1) series will produce misleading results (Phillips, 1986). However, in our analysis all the roots of transitional matrix lie inside the unit circle (ensuring the stationarity of all the underlying variables). Furthermore, see Ullah et al. (2014a) for the derivation of VAR model and computation of impulse response functions and variance decompositions.

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shocks to individual variables cannot be identified (Lutkepohl, 1991). As shown in section 3.2 that the diagonality of the estimatedΣvmatrix is strongly rejected, which means that the estimated VAR residuals are correlated. Therefore, we cannot assume that the contagion of shocks is unidirectional and use the Cholesky factorization which orthogonalizes the innovations as suggested in Sims (1980) to avoid this identification difficulty.21 This strategy requires a pre-specified causal ordering of the variables, because the results from VDCs and IRFs may be sensitive to the variables’ ordering. The ordering of variables suggested in Sims (1980) starts with the most exogenous variable in the system and ends with the most endogenous variable.22

To see whether the ordering could be a problem, the contemporaneous correlations of VAR error terms are checked (results are not reported to conserve space). The results show that there are high correlations among the three yield curve factors ( β1 t , β2 t , β4 t )and between the yield curve factors and growth rate of money supply(MSt). Other correlations are mostly less than 0.25. Based on the strength of the correlation, we arrange the variables according to the following order:( IP t , INF t , EX t , SI t , MSt , β5 t , β3 t , β4 t , β2 t , β1t ).23 Furthermore, in estimating the VAR to compute the IRFs and VDCs, Bayesian information criterion (BIC) was considered for the lag length selection, which is particularly useful in small samples as it imposes a stricter penalty for loss of degrees of freedom relative to AIC (Swartz, 1978).24 Hence, BIC is used for lag length selection which considers lag length of 1 as optimal fit.25

There are four blocks of impulse responses, i.e., the yield curve factors responses to macro shocks, the macro variables responses to yield factors shocks, the yield to yield factors shocks, and the macro to macro variables shocks, but given the focus of this study, here we consider only the former two blocks. Particularly, we focus on the yield curve factors responses to monetary policy shocks and back to activity level indicators and inflation rate. The results of impulse response functions of the two blocks along with 90% confidence band are presented in figure 2. Overall, the results convey an interesting message that the response of the macro variables to the yield factors is Considering the responses of the yield curve to the macro shocks, the slope and the level factors show a very little response than the curvature factors to the shocks in all the five macroeconomic

21 For detailed discussion on Cholesky factorization, see Hamilton (1994b). 22 To avoid the subjective criteria of pre-specified ordering of variables, we also computed the generalized impulses (GIRF) as described in Pesaran and Shin (1998). The resulting responses (not reported here to save space) are almost similar to the one obtained from Cholesky factorization.23 In Diebold et al. (2006), the order is reverse as they put yield curve factors before macroeconomic variables. The intuition behind their ordering is that the yield curve observations are dated at the beginning of the month, whereas for the macroeconomic variables, the end of month data is used. Under this identification scheme, yield factors are assumed to be contemporaneously unaffected by the macro factors. But in our case, we do not assume that macroeconomic factors do not contemporaneously cause variation in the yield factors as we use the end of month’s price quotes to calculate the zero-coupon yields and macroeconomic data is also collected at the end of each month.24 Moreover, Inoue and Kilian (2006) compare asymptotic and finite sample properties of various model selecting criteria and conclude that traditional methods tend to over-select the over-parameterized models while the BIC provides the best approximating model among candidate models. Moreover, Diebold (1998) also notes that the disadvantage of larger bias due to model misspecification is often not sufficiently large in practice to justify a departure from consistent model selection procedure as BIC (see also Pesaran et al. 2011).25 The AIC criterion shows that the optimal lag is equal to 8, which makes the estimation very complicated (as we have 10 variables in the VAR system) and may also over-parameterized the model.

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variables. It attributes to the prominent role and the economic interpretation of the curvature factor of the term structure. The results show that a stochastic positive shock in the industrial production immediately push down the long end with an increase in the both slope factors (the yield curve become less positively sloped or more negatively sloped), suggesting that the yield curve becomes flatter in response to the supply side shocks. However, the first curvature factor moves to left with a 4 to 5 months delay, indicating that inflation expectation rises as a result of expansionary monetary policy in subsequent periods during recession. The second curvatureβ5 tjumps down, pointing towards flattening of the yield cuve, and rises after 5 months because of expansionary monetary policy expectations. After 15 months, the long end goes up and the yield curve becomes steeper (as β2 t falls and β4 t reaches to its maximum). This behavior of long rates is consistent with the inflationary expectation hypothesis of Fisher (1896). Furthermore, the behaviour of other four yield curve factors in subsequent periods is consistent with the idea that during recessions, premia on long-term bonds tend to be high and yields on short bonds tend to be low. Hence, during recessions, upward sloping yield curve does not only indicate bad times today, but also better times tomorrow. Since the adoption of ZIRP, the BOJ is operating its monetary policy through an intervention in the foreign exchange market (because of the export oriented nature of the economy, the devaluation of JP-Yen has the similar impact on the real sector as an increase in the money supply have). Therefore, the rise inEX tby analogy acts like the expansionary monetary policy. Positive shocks to money supply and exchange rate induce the long rates to rise and, hence, the slope increases (meaning β2 t falls), however, the first curvature factor reacts much stronger than the former two factors. The fall in the curvature factor is associated with a rise in the inflationary expectation, consistent with the expected positive impact of the expansionary monetary policy on the inflation rate. Recalling that the ultimate objective of the Japanese monetary policy (either by foreign exchange market intervention or quantitative easing) during the last two decades is to affect the yield curve level in order to stimulate the economy, the success of the monetary policy could be defined as a decrease in the long end of the yield curve either via expected short-term rates (policy-duration effect), term premium (portfolio-rebalancing channel) or both of them. However, this represents only an intermediate target in an attempt to generate economic recovery and to stop deflation. The final goal of the BOJ is expected to increase inflation expectations and thus future short-term interest rates, which in turn, will raise the long-term interest rates. As argued by Nagayasu (2004), monetary policy mechanisms take one to two years to achieve their full effects. It seems appropriate to expect that the effectiveness of the QEMP, if any, would result in an increase in the level factor. Therefore, during the ZIRP and the QEMP, the long end immediately jumps up in response to a shock in the monetary policy indicators. The rise in the level factor reflects the strengthening credibility of the BOJ and, thus, the effectiveness of its policy. Indeed, as argued in Diebold et al. (2006) and Bianchi et al. (2009), if the monetary policy is credible, the level factor, other things being equal, should fall after a positive shock to the call rate, because the expectation of future inflation declines. Since, the BOJ commits itself during the QEMP period to maintain the short-term rates to a zero level, the decline in the level factor after an increase in the call rate is by

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analogy equivalent to a rise in this factor to a monetary policy expansion. This can be due to an expectation of the economic recovery and a rise in inflation, indicating a monetary policy success. Moreover, the response of second curvature is virtually zero to both money supply and exchange rate shocks. However, the second slopeβ3 tresponds actively to both types of shocks and points towards an increase in the slope of yield curve, consistent with the expected effect of expansionary monetary policy on the bond market and ultimately the economy.Shocks in inflation rate immediately push up β2 t (decrease the slope) and down the level factor, however, the second slope factor does not respond. Whereas both curvature factors immediately moves to left. The reaction of the slope as well as the level factor is consistent with the behavior of the Japanese economy during the sampled period. The inflation rate is almost zero and the surprise to the actual inflation cannot give a boost to long rates but it falls in accordance to the long-run expectations. However, in response to a change in the level factor, the slope as well as the curvature factors react.Positive shocks to stock market induce the long rates to fall with an increase in the first slope factor (the yield curve become less positively sloped or more negatively sloped), suggesting that the yield curve becomes flatter in response to the stock market shocks. The response ofβ1 tandβ2 tto stock market shock is almost similar to its behaviour to supply side shocks. It suggests that the equity market can serve as a leading indicator of economy, because of its similar impact on yield curve as the industrial growth has. However, the response of rest of three factors stuck to zero to shocks in stock market.

<<Figure 2>>The lower block of figure 2 summarizes impulse response functions of the macroeconomic variables to the unexpected increase in the yield curve factors. The level shock has a negative effect on industrial production, although its impact seems small but statistically significant. It reinforces the idea that the contribution of the macroeconomic variables to the level factor variation, if any, comes from the level of economic activity. Furthermore, a positive surprise change in the level factor indicates an increase of inflation, exchange rate and monetary expansion. However, the inflation increases a little and reverts to zero immediately, but the response of money growth is more prolonged. It suggests that the BOJ adopts an expansionary monetary policy in response to a decline in aggregate spending, results from a sudden increase in the long-term interest rate.26 The response of exchange rate is also points towards the foreign exchange intervention as a tool for monetary policy. The reaction of stock market activity indicator is almost zero in response to variation in long term rates.The responses to an unexpected positive change in the two slope factors are consistent with the monetary policy stances in the Japanese economy. An increase in the slope factor means a reduced spread between long-term and short-term bonds, which indicates a monetary policy tightening and,

26 The increase in the long term interest rate (as a result of an increase in the short rates, according to the expectation hypothesis) causes a decline in aggregate spending.

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thus, economic activity declines within the upcoming 3 to 4 months.27 The direction of reaction of the IPtcontributes to the view that the yield curve slope acts as an indicator of the future state of economy. The reaction of inflation and stock market to shock in second slope β3 tlooks qualitatively

similar to their responses to the level shock (do not respond). However, an unexpected increase of the first slope factor is followed by an increase in inflation rate, consistent with the inflation trend during recession. The money growth rate falls in response to the slope shock but reverts to zero immediately and then increases. It confers that the BOJ implements the expansionary monetary policy, as the spread between the long and short end tightens, to avoid the upcoming recession. Moreover, the exchange rate jumps up to shocks in both slope factors, suggesting that the BOJ intervene in the foreign exchange market to devalue JP-Yen and boost exports to avoid the upcoming slowdown. Furthermore, the stock market goes in the bearish trend in response to the fall in the yield curve slope. Overall the reaction of all five macro variables to sudden shock in β2 tshows

that the first slope factor in our yield-macro factors model can signal out the future state of economy in terms of the trends adopted by the industrial production, stock market, inflation rate, monetary policy and exchange rate, that are considered fundamental conduits for the business cycle.Unlike Diebold et al. (2006), the macroeconomic variables have significant reactions to the positive change in the first curvature factor, however, the reaction to second curvatureβ5 tis virtually zero of

all macroeconomic variable.28 The increase in the curvature means transition from a flat yield curve to a steeper one. The economic activity expands along with an increase in inflation rate in response to an unanticipated positive shock in the curvature of the yield curve. It suggests that the curvature is a leading indicator/main driving force of future inflation and also reflects the cyclical fluctuations of the economy. It advocates that the curvature factor also presents the stances of monetary policy and can predict the future path of economy and inflationary expectations. The reaction of the money supply and exchange rate shows that the contractionary monetary policy (in terms of fall in monetary growth or appreciating JP-Yen) is adopted by the BOJ to cool down the heated inflationary pressure. The behaviour of two monetary policy indicators, i.e.,MS tandEX t, is in

accordance to the economic theory and historical facts that a tightened monetary policy is implanted by most of the central banks during the inflationary pressure. However, keeping in view the prevailing economic situation during the decade in the Japanese economy, the reaction of money supply and exchange rate is not consistent with the expectations. The expected reaction will be zero because of the liquidity trap and stagnation like situation in the Japanese economy for the last 20 years. There may be certain other factor that enforce the BOJ to lower money supply and exchange rate as the yield curve becomes steeper. The reaction of stock market is minor and is not of any importance to variation in the curvature factor.Summarizing, it turns out that the contribution of the macroeconomic variables, though small

27 Normally a decrease in yield curve slope announces an economic slowdown. But, the loading of the slope factor in our model decreases with maturity and corresponds to the difference between short and long-term yields, therefore, an increase in this factor corresponds to a decrease in the term spread.28 The null response to second curvatureβ5 tmay be due to fact that it is related to the short end and the response to short rates is mostly captured by the two slope factors.

21

in magnitude but does not quickly shift to low levels, suggest a significant role in influencing the yield curve during the long-lasting economic stagnation and liquidity trap type like environment in the Japanese economy. The lower block that sums up the reaction of the macroeconomic variables in response to the shocks in the yield curve factors suggests that, after the short-term interest rate has reached zero, the monetary policy signals can be transmitted significantly and with higher probability (as all the responses are statistically significant) to the real sector through the yield curve factors.

3.5. Macroeconomic and yield curve variance decompositionsAnother way of presenting information from a VAR estimation is to calculate variance decompositions, which indicate the portion of the forecast error variance of the VAR variables that can be attributed to the shocks. It shows how much of the forecast error variance for any variable in a system is explained by innovations to each explanatory variable over a series of time horizons. Usually, own series shocks explain most of the error variance, although the shock will also affect other variables in the system.Table 5 shows the results for the four different periods (1-, 12-, 24- and 40-month) ahead forecast variances for all ten yield-macro factors. The results clearly show that the main driving force behind the yield curve factors (particularly level, two slopes and second curvature) are either the money supply or foreign market interventions shocks, while significant portion of variation in macroeconomic factors is explained by the two slope factors. The level factor also play some role in explaining the variance of money supply and exchange rate.From table 5, the VDC substantiates that the first curvature factorβ4 tand exchange rate play an

influential role in the variation of yield level. Furthermore, a significant role is also played by the second slope and money supply in fluctuating the yield level factor in the long run. It confers that, rather than only the monetary easing, the foreign exchange intervention (used as monetary policy tool) shocks also contribute significantly to the variation of the long-term interest rate. This indicates that news about the future evolution of exchange rate variation and supply side shocks (asβ3 thas very close relation with the level of economic activity) might be more important for the

dynamics of the yield curve than inflationary concerns for that period. The variation in the first slope factor mainly comes from the level factor, monetary growth and the exchange rate. The impacts of the monetary and exchange rate policy are consistent with the behaviour of spread and monetary growth in figure 1. The industrial growth and stock market activity indicator also play a significant role than the rest of factors. The second slope factor variance is mainly driven byβ2 t(first slope factor), monetary policy and level of economic activity

(represented by the industrial growth) shocks. This suggests that, rather than only the change monetary policy, the supply side shocks also contribute significantly to the variation in the shape of yield curve, particularly the short end. Furthermore, the changes in the first curvature factor are attributed to the shift of long end of the yield curve and the variation in the inflation rate. However, at the longer horizon forecasts, the second slope factor plays a significant role as well. As for the

22

variation in second curvature is concerned, the level factor plays the dominant role, consistent with the behavior ofβ5 tover time that is close related and follows the pattern of 10-year maturity yield as

shown in Christensen et al. (2009) and Ullah et al. (2014d). The second slope and exchange rate also contribute significantly to the variation in second curvature. The relation with exchange rate (tool for monetary policy) suggests that the monetary policy signals, during the ZIRP, mainly affect the curvature (medium rates) of the yield curve.Regarding the variance decomposition of the extant of the economic activity (represented by the growth rate of the industrial production), it is apparent that the two slope factors play the crucial role at all horizons of forecasts, followed by the stock market activity index. It highlights the idea that the slope of the yield curve signals out the state of economy in the near future. The role of level and two curvatures is negligible at all horizons. The variance appears to be explained about 4 to 6 percent by the inflation innovations. This indicates that the information about the slope of the yield curve might be an important signal about the future evolution of the output than the long rates and the inflationary concerns for that period.

<<Table 5>>The two slopes, i.e.,β2 tandβ3 tfactors are the dominant factors in explaining the variance of

exchange rate. It confers that the future state of activity level in the Japanese economy is the main driving force of the exchange rate. The BOJ intervenes in the foreign exchange market to alter the exchange rate, consistent with the upcoming business fluctuation, means that the BOJ depreciates the JP-Yen as the clouds of economic slowdown hang over the economy. This behavior is further supported by the influential role of industrial production growth in the variation of exchange rate. The role of first curvatureβ4 tin explaining the variability in exchange rate points towards that the

curvature factor is also helpful in transmitting the policy signals to the economy and may reflect the cyclical fluctuation.Looking at the variance decomposition of the money supply, it shows that the first slope factor is the dominant factor, followed by the level factor within the group of yield curve factors. Productivity and stock market shocks also contribute after one period in explaining the variance of monetary growth. The result is consistent with the idea that the shape and particularly the slope of the yield curve represent the stances of the monetary policy to affect the level of the economic activity. The response to the activity level variables (i.e.,IPtandSI t) shows that, taking into

consideration the business condition, the BOJ react with the monetary easing/contraction rather than only the foreign exchange market interventions. Because the BOJ mainly used money supply and foreign exchange market intervention as the monetary tools to achieve its goals during the sampled period.The variation in inflation is explained by the industrial production to a greater extent. It suggests that the supply side shocks are more influential in determining the path of inflation rather than the demand side during the last 20 years in the Japanese economy, because the contribution of monetary policy shocks is negligible during the QEMP and ZIRP periods. This is consistent with the ineffectiveness of the QEMP in affecting the expectation about future inflation as well as the

23

long end of the yield curve, because the inflation response veers to zero and becomes insignificant more rapidly (figure 2).29 Regarding the contribution of the yield curve factors, the variation in the inflation is largely due to the first curvature factor of the yield curve. The remaining factors contribute marginally in the variance decomposition of inflation rate. Finally, the variation in stock market activity can be attributed to the shocks in industrial production and the first slope factor to a greater extent. It further supports the premise that slope of yield curve is the leading indicator of future state of economy, because the slope factor can predict the stock market (considered as the leading indicator of the economy in macro-finance literature). The shocks in exchange rate also affect the activity level in the stock market, because of the variation in the investors’ behavior (to invest in Japanese stocks) due to the exchange rate risk.Overall, the results of VDCs validates the conclusion drawn from the IRFs. Two main findings emerged from the empirical analysis of the preceding two sections. First, a compression in the long- and short-term yield (spread) exerts a powerful effect on both output growth and inflation in the Japanese economy, when the zero lower bound is binding. Second, the impact of the BOJ asset purchase programs of long-term government bond (for monetary easing) and foreign market intervention on yield curve factors indicate that un-conventional monetary policy actions have been successful at mitigating significant risks both of deflation and of further output collapses.

4. Evidence on the expectation hypothesis and time-varying term premiumThe crucial link between the central bank’s instrument and the long-term interest rates is the expectation hypothesis (EH) of the yield curve theory.30 The EH relies on the general proposition that expectations about future interest rates affect the current level of long-term interest rates and, therefore, provides an indication about how anticipation of the future monetary policy decisions affects the economy. The EH states that the long-term rate at timet is the average of the expected future short-term rates plus the term premium.

Rt (m )=( 1m )∑

i=0

m−1

E t Rt+i (1 )+ϕ (m ) (14)

where mis the time to maturity, which ism>0, Rt+i (1 )is the short term rate (one period rate) at time t+ i, Et ( . )is the expectation operator, and ϕ (m )is a term premium that is time invariant. Whenϕ (m )=0, the equation (14) becomes consistent with the pure expectations model. However, ϕ (m )=0represents a very unique situation that does not hold in the real world. Furthermore, there is little evidence to support the EH even in its standard form. Campbell and Hamao (1992) study the short-end of term structure and provide evidence to support the expectations theory, particularly in the

29 It suggests that rather than the demand side, the supply shocks (oil price, fall in exports due to East Asian crisis, US crisis and Eurozone crisis) should also be considered possible reasons for the prolonged deflationary period in Japan.30 The traditional expectation hypothesis of the term structure states that the movements in the long rates are due to the movements in the expected future short rates. Any term or risk premia are assumed to be constant through time, but vary across the maturity spectrum of spot and forward rates as well as holding-period returns.

24

period preceding 1985. However, the performance of the model deteriorates after 1985 when changes in policy dictated by the Plaza Accord, resulted in a regime shift in the data. For the Japanese market case, Thornton (2004), applying a bivariate VAR for long-term and short-term interest rates for the period from March 1981 to January 2003, shows that the EH does not hold. The poor performance and empirical failure of the standard model in (14) may be due to the existence of a time-varying term premium (Shikano 1985; and Shirakawa 1987).31 Time-variation in term premia might arise because of changes in preferences of market participants toward risk. In addition, the term premium could also vary with the business cycle, as investors might be more risk-averse in recessions than in booms. In this vain, Nagayasu (2002), allowing for the stationary time-varying risk premium in the cointegration model for the short-end of term structure, provides evidence in support of the expectations theory. In this study, we use a time-varying risk premium latent factor model to review the validity of the standard EH and the effects of the BOJ’s expectations management on the JGBs yield curve.32 Following McCallum (1994), we re-express (14) to account for time-varying term premium that that follows the AR(1) process, the model can be written as:

Rt (m )=R t (m )EH +ϕt (m )+ηt (15)ϕt (m )=ρ ϕt−1 (m )+ϵ t (16)

[ηt

ϵ t] N ([00] , [Ωη 00 Σϵ]) (17)

Rt (m ) EH=( 1m )∑

i=0

m−1

Et Rt+i (1 ) (18)

where ϕt (m ) is a time-varying term premium that may also vary with the maturity, and the parameter |ρ|<1, which measures the persistency of the term premium.

Specifically, we compare the theoretical bond yieldsRt (m ) EH, constructed via (18), plus ϕt (m )under the assumption that the expectation hypothesis (in its standard form) does not hold, with the actual bond yieldsRt (m ). We construct the expected future 1-month maturity yields by iterating forward the estimated yield model using the measurement equation (2) and the state equation (3) forEt R t+i (1 ); and then compute the theoretical bond yields at each point in time using (18).

Furthermore, the term premium is computed by using the state-space model with the signal equation specified in (15) and the state equation in (16), assuming that the latent factor ϕt (m )follows the

31 Further possible cause of the failure of the expectations model is identified by Saito et al. (2001), who outline the importance of the liquidity effect of periodic settlement on the term structure. They document that such an effect is prevalent at the end of the settlement months (March, September, and December).32 This issue is especially important for the Japanese economy because the principal channel suggested by either the ZIRP or the QEMP is the expectation channel, through which the monetary policy works is the long-term interest rates, shaping them so that in turn they affect the level of economic activity. The expectation that the policy of low short-term interest rates may be maintained for a substantial period of time will likely lower medium to long-term interest rates, which, in turn, will rise inflationary expectations and boost economic activity.

25

stationary AR(1) process. We use the Kalman filter algorithm as discussed in section 2.2 to estimate the time-varying term premia.Figure 3 provides some selected maturities estimated yields together with their actual counterpart. The estimated yields [ Rt (m) EH+ ϕ̂t (m ) ]are tracking actual yields very well, despite of the limited deviation that occurs for the 3-month maturity yield. However, overall the results indicate that the expectation hypothesis of the term structure of the interest rates does not hold during the ZIRP/QEMP period, because the estimated term premia vary considerably during the sampled period.33

<<Figure 3>>Furthermore, the estimated term premia of some selected maturities is shown in figure 4. There is substantial variation over time in the behavior of the term premium for all the maturities. In particular, it is interesting to note that during the ZIRP and the QEMP period (2001-2006), the term premia decline to a lower level. This could be due to the heavy demand for JGBs from the BOJ during that period.

<<Figure 4>>5. ConclusionThis study explores the evolution between the yield curve and the Japanese economy with a special focus on examining the effects of the non-conventional monetary policy, i.e., foreign exchange market intervention and quantitative easing strategies in Japan on the yield curve and the possible feed-back effect on the real sector by applying a yields-macro model during the ZIRP period. The monetary policy targets the short rates in accordance to the Taylor rule of optimal monetary policy; however, during ZIRP, the short end of the yield curve cannot serve as a policy instrument (because the rate cannot be lowered any more). Therefore, the central bank operates the monetary policy through the non-conventional tools (Ullah et al. 2014a).The yield curve model of this study explicitly incorporates both the yields factors (level, two slopes, and two curvatures) and the macroeconomic variables (overall economic activity, exchange rate, money supply, inflation rate and stock market activity index). The Nelson-Siegel type five-factor model of yield curve along with macroeconomic factors in state-space framework is considered to evaluate the impact of policy shocks on yield curve factors and the feedback effect on the real and financial sectors.34 We show that by incorporating the two additional factors the estimated short rates could be restrict from becoming negative, which is one of the troublesome problem is estimating the very short rate in the ZIRP period (Kikuchi and Shintani, 2012). Furthermore, we include the growth rate in monetary aggregate and exchange rate as non-conventional monetary policy tools (in state equation) in the state-space framework, as the BOJ operates its monetary policy through the foreign market intervention and quantitative easing since the adoption of the so called ZIRP policy. The modeling approach provides a framework to evaluate the effectiveness of non-conventional policy tools (QE and foreign exchange market interventions) and measure the degree to which the zero bound affects other yields.Empirical results from the yields-macro factors model show that there is a statistically significant bidirectional linkage between the macroeconomic and the yield curve factors; however, by contrast

33 We tried the model with the fixed term premia, however, the theoretical yield deviate too much from the actual yield. It suggests a supportive evidence in regard to time-varying term premia. Results are not reported to conserve space. The results of the model with fixed term premia indicate that the EH can be rejected –consistent with what followed in the empirical research on the empirical validity of EH –no matter what testing equations, estimation techniques and information sets are used.

34 The Nelson-Siegel three-factor framework of yield curve attractively fits the yield data, however, during the ZIRP it fails to replicate the stylized facts of observed yield data and some time may imply negative estimates of the yields near the short end of curve. Therefore, we extend the model in Diebold et al. (2006) to include the second slope and curvature factors to provide a flexible framework that fits the yield curve attractively and grasps the distinctive characteristics of JGBs yield curve in the ZIRP environment.

26

with conventional wisdom, macro variables play a less prominent role in explaining the yield factors as compared to the strength of effect from the latter to the former. Furthermore, during the ZIRP period, the generalization (extension) of popular Nelson-Siegel yield curve model seems to be a good choice to fit the yield curve and evaluate the dynamic interaction between yield curve and macro economy.The structural decomposition indicates that it is the entire term structure of interest rate that transmits the policy shocks to the real economy rather than only the yield spread (as considered in the previous studies regarding the Japanese economy). The monetary policy signals pass through the yield curve level and the first slope factors to stimulate the economic activity. The (first) curvature factor, besides reflecting the cyclical fluctuations of the economy, acts as a leading indicator for future inflation. The curvature factor seems either to anticipate or to be accompanied by inflation rate. One can infer from the overall results that the first slope and the curvature factors (in our framework) serve as leading counter-cyclical and pro-cyclical indicators respectively. More importantly, the second slope factor is closely related to the variation in the real activity as well as the fluctuation in the stock market. Summarizing, it turns out that monetary policy shocks account for significant fluctuations in the yield curve shape and policy shocks are likely to affect the medium to long-term interest rates. One important channel, through which monetary policy works, is the long end of yield curve, shaping them so that, in turn, they affect the level of economic activity. In addition, the proposed yields-macro factors model does not empirically substantiate the traditional expectation hypothesis during the ZIRP and the QEMP regimes as the estimated term premia vary considerably across time.To preview our results, we find that yields with medium and long maturities are responsive to policy shocks (QE), despite the short rate being at zero. This suggests that the efficacy of monetary policy because of the sensitivity of the 5-year and above maturities yields to policy interventions. We also show that 5-year and beyond maturities yields are essentially unconstrained by the zero bound, while yields of 36-month and less maturity have been severely constrained by the zero lower bound. The BOJ large-scale purchases of long-term bonds and management of monetary policy expectations may have helped offset the effects of the zero bound on medium- and longer-term interest rates.

Appendix-ICoefficients and latent variable in the general state-space formIn the statistical formulation of the models in section 2.2, the matrices and vectors for the state and observations equations should be considered as follows. The matrices and vectors in state-space system in (5-7) should be defined as:

27

y t=(Rt' , Z t

' )'H=Λ ( λ1 , λ2 )

X t=αt=(β t' ,~Z t

' )'

C=[ I 10−A ] μ F=A w t=εt

ut=v t G=Ω Q=Σ v

whereα t=(β1 t , β2 t , β3 t , β4 t , β5 t ,

~IPt ,~EX t ,

~MS t ,~INF t ,

~SI t )' is (10×1) latent vector,Rt

is (N×1) vector of

zero-coupon yields, Z=(IP t , EXt , MS t , INFt , SI t)' is (5×1) vector of macroeconomic factors, β t is

(5×1) vector of yield curve factors, Λ ( λ1 , λ2) is (N×5) matrix of factors loadings, A is (10×10) matrix of parameters, μ is (10×1) mean vector of factors, and I 10 is (10×10) identity matrix. The ε t

and v tare (N×1) and (10×1) innovations vectors of the observation and state equations respectively, Σv is (10×10), the covariance matrix of innovations of the transition system and is assumed to be

unrestricted, while the covariance matrix Ω of the innovations to the measurement system of (N×N) dimension is assumed to be diagonal.

Appendix-IIData descriptionWe consider JGB yields with maturities of 3, 6, 9, 12, 15, 18, 21, 24, 30, 36, 48, 60, 72, 84, 96, 108, 120, 180, 240 and 300 months. The yields are derived from bid/ask average price quotes, from January 1996 through December 2013, using the Fama and Bliss (1987) methodology.Table A1 provides summary statistics for the data-set. For each maturity, we report mean, standard deviation (SD), minimum, maximum, skewness, kurtosis, and autocorrelation coefficients at various displacements. The summary statistics reveal that the average yield curve is upward sloping. Unconditional volatility increases by maturity and yields for all maturities are persistent, however, relatively short rates persistency is higher than those of the long rates.

<<Table A1>><<Figure A1>>

In addition to the findings in table A1, we see few interesting characteristics in figure A1, which plots cross-section of yields over time. The first noticeable fact is that long term yields vary significantly over time. Second, the short rates are almost zero during the prolonged period except with a little rise in late 2006 and early 2007 that causes a fall in the slope of the curves. Moreover, when short rates are stuck at zero, the long end seem more volatile than the short end of the curves.Regarding the macroeconomic variables, we consider the industrial production, real exchange rate, money supply, consumer price index and Tokyo Stock Exchange share prices index (TOPIX). The data for the former four variables is obtained from the International Financial Statistics (IFS), while for TOPIX the data are taken from annual reports of the Tokyo Stock Exchange for various years. All five variables are measured as the last 12 months’ percentage growth rate. The IPtis growth rate in industrial production,EX tis the growth in real exchange rate (JP-Yen/US-$),MS t is the growth rate ofM 2monetary aggregate,INF tis the inflation rate and is measured as 12-month percent change

28

in the consumer price index, andSI tis the last 12-month growth rate of TOPIX. The descriptive

statistics of these variables are presented in table A2.<<Table A2>>

In table A2, the results of augmented Dickey–Fuller (ADF) unit root test suggest that all five macroeconomic variables are stationary at level.

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liquidity trap. Monetary and Economic Studies 19(1): 277–312.Svensson LEO. 2003. Escaping from a liquidity trap and deflation: the foolproof way and others.

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and Economic Studies 22(2):45–69.Ullah W, Matsuda Y, Tsukuda Y. 2013a. Term structure modeling and forecasting of government

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Table 1. Latent and macro factors VAR(1) parameters estimates of the yield-macro model

Panel 1: Estimates of matrix Aand vectorμμ β1 ,t−1 β2 ,t−1 β3 ,t−1 β4 , t−1 β5 ,t−1 IPt−1 EX t−1 MSt−1 INF t−1 SIt−1

β1 t

0.3513

(0.1216)

0.6789

(0.1130)

-0.1448

(0.1009)

-0.1827

(0.0636)

-0.0420

(0.2515)

-0.2108

(0.2015)

-0.0082

(0.0008)

0.0029

(1.8781)

-0.0574

(0.0229)

-0.0318

(0.1597)

-0.0014

(3.4421)

β2 t

1.0176

(0.1086)

0.1746

(0.0956)

0.7226

(0.0854)

-0.2004

(0.0538)

0.0327

(0.2127)

0.2611

(0.1704)

-0.0106

(0.0033)

-0.0001

(1.5880)

0.0247

(0.0110)

0.0227

(0.1351)

0.0018

(2.9105)

β3 t

-1.0957

(0.0684)

0.2637

(0.0796)

-0.1332

(0.0711)

0.9086

(0.0448)

0.0232

(0.1771)

0.2239

(0.1419)

-0.0005

(1.0270)

0.0051

(1.3223)

-0.0011

(0.0865)

-0.0002

(0.0012)

0.0007

(0.0007)

β4 t

-0.2615

(0.1706)

0.0402

(0.0144)

-0.2881

(0.0129)

-0.0890

(0.0081)

0.8460

(0.0321)

0.3513

(0.0257)

0.0017

(0.1863)

0.0006

(0.2399)

0.0451

(0.0157)

0.0745

(0.0204)

0.0007

(0.4397)

β5 t

-0.0561

(0.2168)

-0.1587

(0.0581)

0.1874

(0.0519)

0.0168

(0.0327)

-0.0260

(0.1294)

0.7779

(0.1037)

-0.0043

(0.7503)

-0.0034

(0.9661)

-0.0021

(0.0632)

-0.0025

(0.0822)

0.0000

(1.7707)

IPt

-2.1278

(1.5691)

-0.4910

(0.0028)

-0.1563

(0.0025)

0.0829

(0.0516)

0.4821

(0.0063)

-0.1697

(0.5250)

0.8201

(0.0364)

-0.0180

(0.0468)

-0.3086

(0.0031)

-0.2273

(0.0040)

0.0382

(0.0859)

EX t

3.4706

(1.0203)

-0.0521

(0.0020)

0.1199

(0.0018)

0.2604

(0.0011)

-0.7610

(0.0045)

-0.1985

(0.0036)

-0.0114

(0.0259)

0.9782

(0.0334)

-0.2434

(0.0022)

0.1138

(0.0028)

0.0009

(0.0612)

MS t

0.0064

(0.1322)

0.2151

(0.0185)

0.1448

(0.0166)

0.3541

(0.0104)

-0.0018

(0.0010)

-0.0342

(0.0330)

-0.0089

(0.2392)

0.0051

(0.3079)

0.6971

(0.0201)

0.0010

(0.0262)

0.0001

(0.5644)

INF t

-0.8717

(0.1718)

0.2856

(0. 2405)

0.3090

(0.0214)

0.0871

(0.0135)

-0.0473

(0.0534)

-0.0695

(0.0427)

0.0115

(0.3094)

-0.0002

(0.3983)

-0.0153

(0.0261)

0.5927

(0.0339)

0.0003

(0.7301)

SI t

0.2046

(3.7028)

-0.6163

(0.0008)

-0.4775

(0.0007)

-0.3701

(0.0005)

0.3713

(0.5418)

0.1712

(0.0014)

-0.0950

(0.0103)

-0.0042

(0.0132)

0.0085

(0.0009)

-1.2048

(0.0011)

0.8710

(0.0243)

λ1 0.0167 (0.0028)

λ2 0.1581 (0.0002)

Panel 2: Test for the joint-significance of individually insignificant coefficients in mean reversion matrix ATest Wald Test LR Test

33

Test statistic df P-value Test statistic df P-valueValue 181.4724 48 0.0000 165.7407 48 0.0000

Note: The table reports the estimates for the parameters of the transition equation of yields-macro factors dynamics. Panel 1 presents the estimates for the vector μ and matrix A, while panel 2 shows the results of the Wald-test and likelihood ratio (LR) test for the joint significance of individually insignificant coefficients in matrix A. The null hypothesis is that insignificant coefficients are simultaneously equal to zero. Both the test statistics are Chi-square with their respective degrees of freedom (df). P-value is the probability value of the test statistic. The standard errors are in parenthesis. Bold entries denote parameter estimates are significant at the 5 percent level.

34

Table 2. Estimates of covariance matrixΣvand its diagonality test Panel 1: Estimates of covariance matrixΣv

Σv ( .,1 ) Σv ( .,2 ) Σv ( .,3 ) Σv ( .,4 ) Σv ( .,5 ) Σv ( .,6 ) Σv ( .,7 ) Σv ( .,8 ) Σv ( .,9 ) Σv ( .,10 )

Σv (1, . ) 0.0696(0.0003)

Σv (2, . ) -0.1128(0.0006)

0.1250(0.0007)

Σv (3 ,. ) 0.0002(0.0005)

-0.0002(0.0004)

0.0003(0.0001)

Σv (4 ,. ) -0.0072(0.0005)

0.0220(0.0010)

-0.0015(0.0014)

0.1964(0.0011)

Σv (5 ,. ) -0.0005(0.0010)

0.0009(0.0001)

0.0010(0.0001)

0.0022(0.0002)

0.0009(0.0001)

Σv (6 , . ) -0.0002(0.0002)

0.0170(0.0092)

-0.0006(0.0028)

0.1203(0.0111)

-0.0012(0.0075)

0.7734(0.0111)

Σv (7 , . ) -0.0458(0.0083)

0.0182(0.0079)

-0.0012(0.0024)

0.0086(0.0092)

0.0005(0.0070)

-0.7725(0.0121)

0.3165(0.0083)

Σv (8 , . ) -0.0034(0.0063)

0.0003(0.0027)

0.0002(0.0042)

-0.0106(0.0051)

0.0001(0.0021)

-0.0226(0.0079)

-0.2666(0.0040)

0.0327(0.0068)

Σv (9 , . ) -0.0100(0.0028)

0.0028(0.0023)

-0.0003(0.0032)

0.0058(0.0022)

0.0001(0.0012)

0.0375(0.0044)

-0.0829(0.0012)

0.0034(0.0021)

0.1412(0.0020)

Σv (10 ,. ) -0.2333(0.0022)

0.0279(0.0861)

-0.0046(0.0757)

-0.0096(0.0731)

0.0008(0.0446)

0.7844(0.1570)

6.8677(0.0644)

-0.0160(0.1188)

-0.0033(0.0153)

0.6787(0.0163)

Panel 2: Test for diagonality of covariance matrix ΣvTest Wald Test LR Test

Value df P-value Value df P-valueTest statistic 105.4924 45 0.0000 126.9868 45 0.0000

Note: The upper panel of the table reports the estimate of covariance matrix of innovations of the transition equation. The standard errors are in parenthesis. The lower panel presents the results of the Wald-test and LR-test for the null hypothesis that the covariance matrixΣvis diagonal. Both of the test statistics are Chi-square with their respective degrees of freedom (df). P-value is the probability value of the test statistic. Bold entries denote parameters estimates are significant at the 5 percent level.

Table 3. Tests for yields-macro factors interactions

Null Hypothesis Number of restrictions

Wald test LR test

Test statistic P-value Test statistic P-value

A2=0 25 54.6882 0.0000 46.1714 0.0000A3=0 25 27.8498 0.0000 42.2961 0.0000Σ2=0 25 39.2227 0.0000 48.5376 0.0000A2=A3=0 50 80.0280 0.0000 67.8735 0.0000A2=Σ2=0 50 74.3132 0.0000 63.2359 0.0000A3=Σ2=0 50 70.6046 0.0000 84.9129 0.0000A2=A3=Σ2=0 75 127.0561 0.0000 95.7167 0.0000Note: The table presents the results of the Wald-test and LR-test for the no lagged and/or contemporaneous yields-macro factors interaction. A2, A3and Σ2refers to the relevant blocks of A and Σv matrices. A2 and A3show the extent of lagged linkage from macro-to-yields and yields-to-macro factors respectively, and Σ2 refers to the contemporaneous effect of yield curve factors on the macro variables. Both of the test statistics are Chi-square with the degrees of freedom equal to the number of restrictions. P-value is the probability value of the test statistic.

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Table 4. Descriptive statistics of the yield curve residualsMaturity Mean SD MAE RMSE ρ̂(1) ρ̂(6) ρ̂(12)

3 -0.7687 0.5291 0.7687 0.9325 0.0753 0.1050 0.01666 -0.2491 0.2654 0.3013 0.3635 0.5841 -0.0252 -0.11859 0.0032 0.4261 0.1843 0.4251 0.2756 -0.0387 -0.047112 0.1228 0.4238 0.2022 0.4403 0.2858 -0.0403 -0.050315 0.1448 0.3460 0.2121 0.3744 0.4162 -0.0534 -0.063818 0.1251 0.2665 0.1997 0.2938 0.6508 -0.0667 -0.077221 0.0866 0.2446 0.1841 0.2589 0.6714 -0.0443 -0.048024 0.0409 0.2885 0.1865 0.2908 0.3800 -0.0022 -0.014630 -0.0363 0.4299 0.2046 0.4304 0.0606 0.0178 0.013536 -0.0936 0.5434 0.2327 0.5501 -0.0305 0.0202 0.016548 -0.1322 0.6755 0.2670 0.6868 -0.0908 0.0238 0.014360 -0.1377 0.7589 0.2821 0.7695 -0.1225 0.0250 0.014172 -0.1260 0.8518 0.2872 0.8591 -0.1418 0.0201 0.008584 -0.0986 0.9731 0.2832 0.9759 -0.1526 0.0109 0.002196 -0.0653 1.1285 0.2807 1.1277 -0.1507 0.0045 -0.0023108 -0.0453 1.3130 0.2868 1.3107 -0.1433 0.0004 -0.0035120 -0.0384 1.5211 0.3013 1.5180 -0.1322 -0.0013 -0.0033180 -0.1651 2.7054 0.4012 2.7042 -0.0774 0.0032 0.0040240 -0.3130 3.7997 0.5134 3.8038 -0.0635 0.0016 0.0057300 -0.4321 4.6928 0.6122 4.7018 -0.0467 0.0056 0.0083

Note: The table presents summary statistic of the residuals for different maturity times of the measurement equation of the estimated yield-macro model, using monthly data 1996:01–2013:12. SD, MAE and RMSE are the standard deviation, mean absolute error and root mean squared errors, respectively. ρ̂ ( i ) denotes the sample autocorrelations at displacements of 1, 6 and 12 months. The number of observations is 216.

36

Table 5. VDCs of yield curve factors and macroeconomic variables

37

Period β1 t β2 t β3 t β4 t β5 t IPt EX t MS t INF t SIt

Variance decomposition of β1 t

1 92.2539 0.4437 0.6039 4.3772 1.2395 0.2393 0.5746 0.0793 0.0214 0.167312 66.4504 1.2275 2.5304 7.4665 1.4928 1.5090 10.4460 5.3105 0.1248 3.442024 53.4066 3.9667 11.9534 7.4961 1.4526 1.9062 10.6804 4.7083 0.6508 3.778840 49.9572 3.7790 12.7003 7.5388 1.7598 2.9926 11.6253 4.7282 0.7789 4.1400

Variance decomposition of β2 t

1 46.5925 47.2052 0.6716 3.2916 1.4082 0.0453 0.4857 0.1974 0.0031 0.099312 31.4838 31.1943 2.6173 3.3354 1.6885 6.2277 7.5626 6.5047 3.3928 5.993024 26.8026 28.2437 4.7735 2.8877 1.7074 7.0874 7.6495 11.2241 4.0335 5.590640 26.0621 27.9233 5.0876 2.9368 1.7359 6.9405 8.8158 11.0590 3.9350 5.5040

Variance decomposition of β3 t

1 3.1169 9.4913 72.1782 9.3765 4.8183 0.3557 0.3154 0.0091 0.3173 0.021512 5.0698 24.3624 18.3422 9.7390 8.3449 18.0732 6.1797 8.0925 0.4930 1.303324 4.8118 20.2975 14.2932 7.5762 6.8150 18.7987 5.8272 14.0288 0.5309 7.020640 4.9825 19.5553 13.1932 7.0495 6.1542 22.4193 6.3201 12.6996 0.7101 6.9162

Variance decomposition of β4 t

1 14.3355 2.5168 0.1325 73.0577 0.2901 0.1465 0.0404 0.0129 9.4274 0.040312 10.7719 5.3397 7.1135 62.3876 0.4044 0.1701 0.5669 0.0715 12.2664 0.908124 9.5563 6.2539 8.5201 60.9804 0.4128 0.1805 0.5371 0.4874 11.0838 1.987640 9.3851 6.2797 8.4298 60.6774 0.4385 0.1944 0.5366 0.6491 10.9144 2.4950

Variance decomposition of β5 t

1 69.9245 0.5143 0.4574 4.3931 14.5400 2.2158 7.4714 0.2290 0.0636 0.191012 48.4938 0.7631 11.6721 3.4136 11.6565 3.3284 18.5266 0.3527 1.2678 0.525624 40.9397 1.0188 15.3351 2.8838 16.9301 3.6865 16.9467 0.3105 1.3926 0.556140 38.4032 1.1080 15.8397 2.8857 18.1360 3.7743 16.5960 0.3242 1.9240 1.0088

Variance decomposition of IPt

1 1.0566 7.9110 12.5205 0.0249 0.4632 77.5577 0.0094 0.0712 0.0990 0.286412 1.0737 14.9873 10.6206 1.2436 0.8326 57.2633 0.7203 1.4539 4.4464 7.358324 0.9703 14.1829 8.1120 0.9798 0.7214 50.7315 3.2568 1.9818 5.3764 13.687140 1.1259 14.0017 7.8003 0.9836 0.8193 49.9997 3.4042 3.0006 5.2873 13.5774

Variance decomposition of EX t

1 4.9649 10.1458 14.5464 12.9945 5.1263 6.9886 45.1658 0.0201 0.0117 0.036012 5.5166 12.4600 17.7315 11.4962 3.3157 10.2140 38.2452 0.1363 0.1872 0.697424 5.3335 11.8281 18.2315 9.7670 3.2025 11.5039 37.4841 0.3153 0.7859 1.548140 5.1816 11.4790 18.3919 9.4799 3.1066 11.5089 36.9656 0.4049 1.1707 2.3110

Variance decomposition of MS t

1 0.1030 1.6522 1.6116 0.9372 0.1321 0.1117 4.2745 91.1270 0.0261 0.024612 1.3779 5.0740 0.5641 3.2628 2.6311 10.7918 2.7644 69.0958 1.2871 3.150924 5.0487 8.3231 2.1722 5.3701 2.8373 12.1189 4.9545 47.4819 2.9832 8.710240 10.5120 16.3864 4.9761 4.9591 2.9990 10.0728 5.5190 40.7128 3.5936 8.2692

Variance decomposition of INF t

1 0.6092 0.9853 0.0058 3.5490 0.4265 0.8891 4.8741 0.2481 88.4041 0.008912 0.5888 0.4745 0.0882 16.8837 0.6608 11.9896 4.5222 2.4321 59.0722 3.287824 1.1102 0.7554 0.1904 15.8839 0.6784 11.8463 4.5568 5.1644 49.9609 9.853240 1.3512 0.8035 0.6462 14.9554 0.6765 14.3638 6.0011 5.0148 46.1476 10.0401

Variance decomposition of SIt

1 0.0926 0.1802 0.0592 0.6531 0.0174 0.2458 6.8908 0.0374 0.0408 91.782712 0.0313 8.5675 0.2441 0.4009 0.0234 13.9336 8.4489 0.2855 0.5615 67.503224 0.1110 11.8543 0.2660 0.6518 0.1691 20.6634 8.4836 1.8517 0.7531 55.196140 0.3540 11.6073 0.3588 1.1542 0.2147 20.3435 8.2946 2.3983 1.2505 54.0241

Note: The table reports the results of the variance decompositions of all the ten variables in the system. We simulate the

38

VAR(1) model of the yield and the macro factors and compute the contribution of innovations of each explanatory variable over a series of time horizons. Each entry is the proportion of the forecast variance (at the specified forecast horizon) for a 1, 12, 24 and 40 months’ time horizons that are explained by the particular factor.

Table A1. Descriptive statistics of yields data across maturities

Maturity Mean SD Max Min Skewness Kurtosis ρ̂(1) ρ̂(6) ρ̂(12)

3 0.2094 0.2108 0.6956 0.0004 0.8717 2.2229 0.8812 0.7738 0.56736 0.2121 0.2136 0.7330 0.0041 0.8636 2.2869 0.8674 0.7508 0.58099 0.2285 0.2265 0.7699 0.0017 0.8518 2.2889 0.8614 0.7210 0.581812 0.2702 0.2408 0.8720 0.0041 0.6956 2.1064 0.8459 0.6773 0.532415 0.3000 0.2616 0.9910 0.0002 0.6922 2.1563 0.8491 0.6674 0.544418 0.3314 0.2845 1.1136 0.0130 0.7287 2.3042 0.8513 0.6620 0.546521 0.3638 0.3063 1.2377 0.0265 0.7444 2.4077 0.8535 0.6612 0.549824 0.3952 0.3276 1.3614 0.0192 0.7776 2.5691 0.8563 0.6649 0.547330 0.4673 0.3683 1.6030 0.0266 0.8743 2.9792 0.8598 0.6660 0.542536 0.5397 0.4097 1.8466 0.0505 0.9548 3.3446 0.8616 0.6693 0.541448 0.7044 0.4839 2.3083 0.0886 1.0271 3.7517 0.8659 0.6819 0.534860 0.8559 0.5458 2.6796 0.1139 1.0691 3.9729 0.8714 0.6938 0.528772 1.0030 0.5869 2.9704 0.1537 1.1181 4.1919 0.8722 0.6970 0.520684 1.1554 0.6057 3.1963 0.2364 1.1785 4.4380 0.8700 0.6925 0.505396 1.3080 0.6120 3.3739 0.3470 1.2049 4.6344 0.8663 0.6864 0.4891108 1.4432 0.6108 3.5155 0.4468 1.2537 4.8852 0.8665 0.6860 0.4809120 1.5618 0.6095 3.6304 0.5283 1.2698 5.0693 0.8663 0.6844 0.4708180 1.9339 0.5410 3.7790 0.7577 1.2324 5.2687 0.8435 0.6319 0.4063240 2.1755 0.5113 3.9802 0.9341 1.3751 6.2681 0.8358 0.6020 0.3286300 2.3484 0.4743 3.9030 1.0703 0.8599 5.1924 0.8273 0.5621 0.2757

Note: The table shows descriptive statistics for monthly yields at different maturities. The last three columns contain sample autocorrelations at displacements of 1, 6 and 12 months. The sample period is 1996:01–2013:12. The number of observations is 216.

Table A-2. Descriptive statistics of macroeconomic variables data 　 IPt EX t MS t INF t SI t

Mean 0.1354 0.4132 2.5473 -0.0951 0.3874SD 8.5073 10.7579 0.9044 0.8783 22.8919Maximum 28.8520 28.7827 4.9278 2.5573 61.4677Minimum -34.2727 -21.6024 0.4417 -2.5251 -45.2759Skewness -0.9231 0.5336 0.0608 0.7772 0.5803Kurtosis 6.6894 2.5994 2.7835 4.5665 2.7979ρ̂(1) 0.5737 0.6396 0.7209 0.6867 0.6665ρ̂(6) 0.3005 0.4105 0.5839 0.3138 0.2102ρ̂(12) -0.4450 0.1652 0.4145 0.0466 0.0043ADF-statistic -4.1761 -2.8774 -2.4473 -2.3596 -2.5350P-value (ADF-stat) 0.0000 0.0041 0.0162 0.0180 0.0112Note: The table presents summary statistics for macroeconomic variables data 1996:01–2013:12. All the five variables are measured as the last 12 months percentage growth rate. The IPt is annual growth rate in industrial production, EX t is the growth of real exchange rate,MS t is the growth of M 2 money supply,INF t is the 12-month percent change in the consumer price index and SI t is the annualized growth rate of Tokyo stock exchange index (TOPIX).ρ̂ (i ) denotes the sample autocorrelations at displacements of 1, 6 and 12 months. The last two rows contain augmented Dickey–Fuller (ADF) unit root test-statistic and its p-value.

<<Figures>>39

Figure 1. The figure presents the time series plot of estimated yield curve factors with macroeconomic variables. The estimated level and first slope factors ¿and − β̂2 t ¿ are plotted vs. annual growth of the M2 (Money Supply) in the top

left pane of figure. The top right and bottom left panes show the second slope factor ( β̂3 t )against the annual growth

rate of industrial production( IP t ) and exchange rate( EX t ), respectively. The slope factor is scaled on the left y-axis,

while IPtandEX tare measured on the right y-axis. It is worthwhile to mention that we plot β̂3 tagainst theIPt , while

− β̂3 tagainst theEX t. The lower right pane presents the first curvature factor estimate( β̂4 t )against the annual inflation

rate. Theβ̂4 tis scaled on the left y-axis, while INF tis measured on the right y-axis. Inflation rate is the 12-month percent change in the consumer price index.

40

Figure 2. The figure shows the reactions of five yield curve factors (i.e.,β1 t , β2 t , β3 t , β4 t , β5 tdenoted by level, two slopes and two curvatures factors respectively) and five macroeconomic variables (i.e.,IPt , EX t , MSt , INF t , S It) to a shock in each exogenous variables in the VAR(1) model over 40 months. We simulate the VAR(1) model of yield and macro factors and compute response of each factor to Cholesky one unit innovation. The solid blue line denotes the estimated response, while the red dashed line shows ± 2 ( SE ) (plus-minus two standard error) confidence band.

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Figure 3. The figure presents time series plot of the estimated yields [ Rt (m)EH+ ϕ̂ t (m ) ] along with the actual bond

yieldsRt (m ) for the 3, 12, 24, 36, 60 and 120 months maturities over the sample period 1996:01–2013:12. The estimated yields are depicted by dashed red line, whereas the actual yields by solid blue line. The number of observations is 216.

Figure 4. The figure presents time series plot of the estimated term premium ϕ̂t (m )under the assumption that the expectation hypothesis does not hold for the 3, 12, 24, 36, 60 and 120 months maturities over the sample period 1996:01–2013:12. The number of observations is 216.

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