Discussion Papers In Economics
And Business

The Leading Indicator Property of the Term Spreadand the Monetary Policy Factors in Japan
Hiroshi Nakaota and Yuichi Fukuta
Discussion Paper 13-09-Rev.

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANThe Leading Indicator Property of the Term Spreadand the Monetary Policy Factors in Japan
Hiroshi Nakaota and Yuichi Fukuta
Discussion Paper 13-09-Rev.

July 2013

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANThe Leading Indicator Property of the Term Spread and the Monetary Policy
Factors in Japan*
Hiroshi Nakaota† and Yuichi Fukuta‡

Abstract
Many studies have observed the leading indicator property of the term spread (LIPTS), whichindicates that the term spread —the difference between long- and short-term interest rates— has
information on future economic conditions. We examine whether this property is related tomonetary policy or not by using Japanese monthly data with consideration for structuralchanges. Results of structural change tests show that the term spread has predictive ability forthe future economic activity from 1982:4 to 1997:8. Decomposing the term spread into threeparts; one is explained by past monetary policy shocks, another is explained by expected future
call rates and the other is the remaining part, we find that all three parts are significantly related
to the future economic growth rate. Hence, we find that the monetary policy plays an importantrole for the LIPTS.
Keywords: leading indicator property of the term spread (LIPTS), term spread, future economic
activity, monetary policy
JEL classification: E32, E43, E44*

Both authors would like to thank an anonymous referee, Ryuich Nakagawa, Yuzo Honda, Shinsuke
Ikeda, Takashi Hatakeda, Kiyotaka Nakashima, and the seminar participants at the 2011 Spring Meetingof the Japanese Economic Association and Monetary Economics Workshop for their helpful comments.
Both authors are grateful to Masashi Hasegawa, Maki Nakabo and Yusuke Sumitoku for their assistancein correcting the data. The authors are also indebted to the Institute of Economic Research, Kyoto
University for their support of the joint research project. The first author is financially supported by
Grant-in-Aid for Young Scientists (B). The second author is grateful for the support of the Global Centerof Excellence Program at Osaka University.
†
Faculty of Social Relations, Kyoto Bunkyo University, 80, Senzoku, Makishima-cho, Uji-shi, Kyoto
611-0041, Japan. Tel.: +81-774-25-2965. E-mail address: h-nakaota@po.kbu.ac.jp.
‡
Graduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka, Osaka 560-0043,
Japan. E-mail: fukuta@econ.osaka-u.ac.jp.

1. Introduction
Information on future economic activity is helpful for various economic agents. If
business entrepreneurs learn more about future economic activity, they can plan betterbusiness projects. If policymakers get to know more about future economic conditions,they can adopt better policies. Researchers have long examined the predictive ability ofvarious economic variables for future business cycles. For example, Estrella and Mishkin(1998) make a comparison of the abilities for future recessions of some financial
variables. Existing studies, such as Estrella and Hardouvelis (1991), Harvey (1991) andHu (1993), find the leading indicator property of the term spread (LIPTS), which shows
the term spread—the difference between long- and short-term interest rates— has
information on future economic conditions. More concretely, the current term spread is
positively correlated with future economic activity. If the current term spread broadens,
future economic conditions tend to improve, and vice versa. Because many papers
support this property, Benati and Goodhart (2008) describe it as having become a“stylized fact”.1
Why does the term spread provide predictability for the future economic activity?
What factors produce the LIPTS? To answer these questions, a theoretical model whichis compatible with the LIPTS has to be proposed. However, in contrast to an enormousvolume of empirical studies on the LIPTS, only a few papers have presented theoreticalmodels. In terms of causes of the LIPTS, we can divide the existing theoretical studies
into two streams. The first approach proposes models where real sectors, such as
productivity, cause the LIPTS, applying the Consumption-based Capital Asset Pricing
Model (C-CAPM) in Lucas (1978).2 The second approach considers models where themonetary policy plays an important role in explaining the LIPTS.3 However, because sofar, both approaches explain the LIPTS only partially, further extensions are needed.
The comparison of the effectiveness of real sectors in the LIPTS with that of themonetary policy is useful in understanding the direction of the theoretical extensions. In
the comparison, we have to extract a factor which is related to the monetary policy orreal sectors from the term spread. If a monetary policy factor in the term spread has asignificant correlation with the future economic activity, the second approach may givea convincing explanation. In the case where the factor does not affect the future
economic condition, an extension using the first approach may be reasonable. Laurent
1

Recent studies on the relationship between term spread and future economic activity are introduced inWheelock and Wohar (2009) and the following website:
http://www.newyorkfed.org/research/capital_markets/biblio.pdf
2
See Harvey (1988) and Rendu de Lint and Stolin (2003).
3
Estrella (2005) shows that some parameters on the reaction function of the monetary authority affect the
LIPTS.

1

(1988, 1989) discusses how the term spread reflects a monetary policy stance. In
contrast, Plosser and Rouwenhorst (1994) show that the information on future economic
growth in the term spread is independent of the information on the current and futuremonetary policy. Benati and Goodhart (2008) also obtain weak evidence for the
relationship between the LIPTS and monetary policy. So far, empirical results for theeffect of the monetary policy on the future economic activity through the term spreadare not conclusive.
The purpose of this paper is to examine whether or not factors related to themonetary policy included in the term spread affect the future economic activity using
Japanese data sets. As mentioned before, the evidence in this investigation may be
useful in resolving the mechanism of the LIPTS. To extract the monetary policy factor
from the term spread, we employ the following procedure. First, estimating a VAR
model proposed by Miyao (2000) to describe the Japanese economy, we computemonetary policy shocks based on the estimated results. Because we assume that thecentral policy instrument of the Japanese monetary authority, the Bank of Japan, is a callrate, the VAR system includes a call rate.4 We regard call rate shocks as exogenous
monetary policy or monetary policy shocks.5 Next, we calculate the forecast values of
future call rates using the estimated VAR model. These values are a factor associatedwith the expected future monetary policy stance. Third, regressing the term spread on
the estimated monetary policy shocks and the future monetary policy stance factor, we
decompose the current term spread into a part related to the monetary policy shocks, apart concerned with future monetary policy stance and a remaining part. Finally, basedon the regression of the future economic growth rate on these three parts, we investigate
the explanatory power of the three factors. If we obtain a significant relationshipbetween the two monetary policy parts and the growth rate, then the monetary policy
plays an important role for the LIPTS.
Many existing empirical studies on the LIPTS in the US use spot rates computedfrom long-term bond data. Fama and Bliss (1987) present a method to calculate the spot
rates. However, some studies on the LIPTS in Japan, such as Hirata and Ueda (1998)
and Hasegawa and Fukuta (2011), use data on the yield-to-maturity of Japanese
long-term government bonds. It is well-known that the yield-to-maturity is affected by
the coupon rate. The coupon rates of Japanese government bonds have declined inrecent decades. This may cause some problems with the empirical results about the
LIPTS in Japan. To avoid this problem, we compute the spot rate data based on the
45

Miyao (2000) also uses this assumption.
This interpretation is similar to Bernanke and Blinder (1992) and Miyao (2002).

2

method proposed by Fama and Bliss (1987). By using the spot rate data, we cancompare the results with those for other countries in an unbiased way. This is one of thecontributions of this paper.
To start the above examination, we have to confirm that the LIPTS is also observedin Japan.6 Hence, we first examine whether the term spread has the leading indicator
property of future economic growth using Japanese monthly data from 1982:4 to 2007:3.
The results do not support the LIPTS for the whole data sample period. This evidence
may be affected by structural changes in the Japanese economy as pointed out by Miyao(2000) and Nakashima (2007).7 Applying the method proposed by Qu and Perron(2007) and Kurozumi and Tuvaandorj (2011), we investigate structural changes in theparameters of the VAR model in our sample period. The results show that structuralchanges happen at 1987:6, 1997:8 and 2002:10. Dividing our sample into four
subsamples based on these points, we re-examine the LIPTS in each subsample. We findthat the term spread has predictive ability for the future economic activity in the firstsubsample: from 1982:4 to 1987:6 and the second subsample: from 1987:7 to 1997:8.
Hence, we investigate whether or not the monetary policy factors in the term spread
affect the future economic activity between 1982:4 and 1997:8. Our results show thatboth monetary policy factors and other factors have explanatory power for future
economic growth. This evidence indicates that the monetary policy plays an importantrole in causing the LIPTS in Japan.
This paper is organized as follows. In Section 2, we examine the LIPTS in our
sample period and the effect of structural changes in the Japanese economy on theevidence for the LIPTS. Decomposing the term spread into parts related to the monetary
policy and other parts, we investigate whether these parts affect the future economic
activity or not in Section 3. Concluding remarks are provided in Section 46Some papers have investigated the LIPTS using Japanese data. Using the data between 1970 and 1989,
Harvey (1991) obtains mixed results for the properties which depend on the sample periods. Hu (1993)
finds the evidence for the LIPTS in the period from 1967 to 1991. Pointing out the existence ofrestrictions in the Japanese financial markets before the middle of the 1980s, Kim and Limpaphayon(1997) support the LIPTS between 1984 and 1991. Galbraith and Tkacz (2000) and Ikeno (2003) find theless evidence for the LIPTS in the sample period including the 1990s. Taking a structural change into
account, Nakaota (2005) supports the LIPTS until the middle of the 1990s. Because Wheelock and Wohar(2009) mention that after the middle of the 1980s the LIPTS is not supported in the US, the Japanese
results of the LIPTS may be similar to the US. Whereas Hirata and Ueda (1998) find the relationshipbetween the yield spread and future recessions, Bernard and Gerlach (1998) and Ikeno (2003) observe theweak relationship. Hasegawa and Fukuta (2011) find the evidence for the relationship between the current
yield spread and future recessions until the middle of the 1990s by taking the structural break into
consideration.
7
Structural breaks in the LIPTS are also observed by Nakaota (2005) and Hasegawa and Fukuta (2011).

3

2 The Leading Indicator Properties of the Term Spread (LIPTS) and Structural
Changes in the Japanese Economy
In this section, we first examine the leading indicator properties of the term spread(LIPTS) using the Japanese data between 1982:4 and 2007:3. Next, we investigate theeffects of structural changes in the Japanese economy on the evidence for the LIPTS.
2.1 An Examination of the Leading Indicator Properties of the Term Spread (LIPTS)

Based on the empirical studies by Estrella and Hardouvelis (1991), Estrella andMishkin (1997), Hamilton and Kim (2002), Nakaota (2005) and other papers, weestimate the following equation by using OLS:
y
y

α
1200

α spread
lny

k

ε ,
lny

(1)
,

spreadii,where y is the industrial production based on 2005 at t, spread means the term
spread which is given by the difference between the 9-year spot rate (i ) and 1-month
CD rate (i ) at t, ytk indicates the growth rate of the industrial production between t andt+k, denotes the forecast horizon, ε is the error term.8 ε follows a distribution
with1 th order serial correlation because of the overlapping of the forecasthorizon. We adjust the standard error by using the Newey and West (1987) method. We
use monthly data between 1982:4 and 2007:3. In the case where we set k from 2 to 10,
the estimated period is from 1982:4 to 2007:2. In the case wherek=11 to k=24, theperiod is from 1982:4 to 2007:12 k.9
Table 1 shows the estimated results. The spread coefficients,, are significant in
the case where the term spread forecasts the future economic growth rate from 2 to 4
months ahead. In other cases, we obtain no significant relationship between the current
term spread and future growth. It seems that the LIPTS is not observed in Japan.
Nakaota (2005) finds a structural change in the relationship between the Japanese term
spread and future growth rate of the industrial production. Miyao (2000) and Nakashima(2007) show evidence for a structural change in the Japanese economy by using VAR
analyses. Since the failure of the LIPTS in our sample period may result from structural
breaks, we analyze structural changes in our sample period in subsection 2.3.

8

We explain the data used in detail in the Appendix. The term spread is an annual percentage rate. To
adjust the k-month growth rate to an annual rate, we multiply the log-difference by 1200⁄k .
9Industrial production data are available up to 2007:12.

4

2.2 A VAR Model for the Japanese Economy

We have to specify the equation to test for structural breaks. The purpose of thispaper is to investigate the relationship between monetary policy factors included in theterm spread and the future economic growth. To clarify the effect of the monetary policy,
it is useful to describe the Japanese economy by a model that takes the monetary policy
effects into account. Miyao (2000) uses a VAR model to examine the stability of theJapanese monetary policy. We use the same specification as Miyao (2000) to analyze
the possibility of structural changes in our sample period.10 Following Miyao (2000),
we estimate the VAR model which contains four macroeconomic variables: the call rate(r), the industrial production based on 2005 (y), the monetary base (m) and a measure of
nominal effective exchange rates (e). We take logarithms of all variables except for thecall rate. To estimate the model, we employ monthly data from 1981:4 to 2007:12.11
First, we test the four macroeconomic variables series for a unit root using theAugmented Dickey-Fuller test. While we apply unit root tests including a constant term
and a deterministic trend to the variables in levels, we use the tests including a constantterm only for the variables in first differences. We select the optimal lag length based on
the AIC. Table 2 shows the results of the unit root tests. The null hypotheses of a unit
root against the alternative of trend-stationary process are not rejected for all variablesin levels. The hypotheses for all variables in first differences are rejected. Figure 1
presents time series plots of the first differences of the call rate presented by a solid line
and the industrial production indicated by a dotted line. Figure 2 also plots the firstdifferences of the monetary base presented by a solid line and the nominal effective
exchange rate indicated by a dotted line. From these figures, it seems that thesevariables do not have a unit root.
Based on the results of unit root tests, we characterize the Japanese economy by thefollowing structural VAR model with the first differenced four macroeconomic
variables:
B L
where

,

,

,

B L ∆X
B
B L

,
B L

(2)
B L ,

X
r ,y ,m ,e ,is pure structural shocks at ,

10

, z

r, y, m and e, is

The reason why we do not apply structural break tests to (1) directly is as follows. If the monetary
policy affects the future economic activity and the current term spread, structural breaks in the Japanesemonetary policy may also cause some changes in the LIPTS in Japan. Using a VAR model, Miyao (2000)
detects a structural break in the Japanese monetary policy. This break may also explain the weak LIPTS in
Japan. In this paper, after tests for structural changes in the VAR model proposed by Miyao (2000), we
analyze the empirical implication of the changes on the stability of the LIPTS.
11
We explain the data used in detail in the Appendix.

5the i.i.d. shock of the first difference of a variable , the covariance matrix ofis Σ(4×4 matrix), p is the number of the lag length of the VAR model, B , i 1,2, … , p ,is a (4×4) matrix andis the lag operator.12 To obtain the first differenced variables,
we multiply the log-difference of these variables by 100.13 We can rewrite the VAR
model into the following reduced VAR model:
A L

A L ∆Xu,
I A L A L

(3)
A L ,

where u is the residual vector of reduced VAR model and the covariance matrix is Σ
(4×4 matrix).
2.3 Structural Changes for the Japanese Economy

We use the methodology proposed by Qu and Perron (2007), and Kurozumi andTuvaandorj (2011) to examine structural changes.14 Qu and Perron (2007) propose
likelihood ratio type statistics to test for multiple unknown structural changes in linear
multivariate regression models. Because this test is applicable to the structural changes
in a subset of the coefficients, and the conditional mean and covariance matrix of theerrors, it is potentially useful in our investigation. However, many estimated parametersin our model cause a little difficulty when using the test statistics proposed by Qu andPerron (2007) directly. In addition, Qu and Perron (2007) assume the number of the lag
length of the VAR model a priori. In terms of this point, Kurozumi and Tuvaandorj(2011) propose modified Akaike information criterion (MAIC) to select the appropriate
model in the case of multiple unknown structural changes in linear multivariate
regression models. If we employ the MAIC for the selection of the model, we are able
to estimate the VAR model parameters, the number of structural changes and theirpoints, and the lag length of the VAR model simultaneously. More concretely, assuming
the number of lag length of the VAR model, we first apply the method of Qu and Perron(2007) to estimate the VAR model which permits multiple unknown structural changes.
Next, we employ the MAIC presented by Kurozumi and Tuvaandorj (2011) todetermine the appropriate model.
We consider

structural changes (1 regimes) in our data sample period. Then

12

The results of the unit root tests are similar to Miyao (2000). Miyao (2000) further examines whether
there are cointegrating relations in the four-variable system and finds the evidence against cointegration.
Following Miyao (2000), we characterize the Japanese economy by the VAR models with the firstdifferences of four variables.
13
Interest rates are measure in percent. We also measure the growth rate in percent.
14
Miyao (2000) and Nakashima (2007) use the methods proposed by Christiano (1986) and Cecchetti
and Karras (1994) to test for structural breaks. The test assumes a single known break point. Miyao(2000) and Nakashima (2007) find a structural change in the Japanese economy.

6

we can rewrite equation (3) as the following model:u
A L ∆X
A L
where u

I

Aj L

Aj L

(4)
A

L

(j 1, … ,1 and
1, … , )has mean 0 and covariance matrix Σ for1.15 We set

0 and. We setis the total number of observations. We denote thebreak points by , … . , .
For givenand pv , let us denote the quasi-log likelihood in (4) bylog LT , … . , | , pv . The maximum likelihood estimates (MLE) of A L and breakpoints,log LT,….,, for given
and pv , are obtained by, … . , | , pv over all possible partitions , … . ,T ,…,T
λ ,…,λ ; λ
ζ, λ
,λ
1 ζ,
Λ
λ

maximizingin the set(5)

where is the minimum sample proportion between breaks and is referred to as thetrimming parameter. A L and , … . ,are the estimated parameters and breakpoints. The estimated quasi-log likelihood is denoted by log LT, … . , | , pv . We

regard , … . ,as structural change point candidates for given
and pv . 16 We
assume that the maximum number of possible breaks, , is 4 and the minimum andmaximum possible lag lengths are 3 and 8 respectively, and the trimming parameter, ,is 0.2.17 We compute the modified Akaike information criterion (MAIC) proposed by
Kurozumi and Tuvaandorj (2011) for each pair of and pv among 0
and3 pv 8. The MAIC is given by the following form:
MAIC , pv
2 p
p
6
(6)
2log LT , … . ,where p is the total number of coefficients in the VAR model, p is thenumber of unknown variance components in all regimes.
The model with
3 and pv 3 minimizes the MAIC. 18 The selected model
implies that the estimated structural change points are 1987:6. 1997:8 and 2002:10.
Based on this result, we divide the sample period into four subsample periods; the first
period is from 1982:4 to 1987:6, the second period is from 1987:7 to 1997:8, the third
15

denotes the number of observations from the initial observation point. For example, when we use
2 implies the time period at 1981:5 in equation (4).
the sample period between 1981:4 and 2007:12,
16
We use the Gauss code provided by Qu and Perron (2007) to detect , … . , for given and pv .
17
The reason we set the maximum number of possible breaks to 4 is the restriction of the total number ofobservations. If we set it larger than 4, the smallest subsample has 50 or 60 observations which may cause
the small sample problem. The reason for 3 pv 8 is to obtain a reasonable VAR model withmonthly observations. If we employ VAR models with 1 or 2 lags, it may be quite difficult to take thequarterly cycle effect into account. In the case of VAR models with longer lag lengths, we have toestimate many parameters, which may deteriorate the degree of freedom.
18
Kurozumi and Tuvaandorj (2011) also propose a modified Bayesian information criterion (MBIC). We
3 and pv 3 andcalculate MBIC for each pair of and pv . MBIC also supports the model withthe same break points as MAIC.

7

period is from 1997:9 to 2002:10 and the fourth period is from 2002:11 to 2007:12.
2.4 A re-examination of the LIPTS in Each Subsample Period

To examine whether or not the term spread has predictive ability for the future
economic activity in each subsample period, we estimate (1) for each subsample data.
The first estimated period is from 1982:4 to 1987:6 k, where k indicates the forecast
periods. The second period is from 1987:7 to 1997:8 k. The third period is from 1997:8
to 2002:10 k. The fourth period is from 2002:11 to 2007:2 in the case where k=2 to
k=10 and from 2002:11 to 2007:3 k in the case where k=11 to k=24.
Table 3 presents the estimated results for each subsample. In the first subsample, thespread coefficients, α , are significantly positive for all forecast horizons, k, except for
k=1. The second subsample results show that α are also significantly positive in all
forecast horizon cases except for the k=1 case. In the third subsample, α aresignificantly positive only from k=1 to k=4. The fourth subsample results show that
α are not significantly positive in many forecast horizon cases. We also observe
negative significant α in both the third and fourth subsample. However, this evidence
is not compatible with the LIPTS. From these results, we find that the term spread has arobust predictive ability for the future economic activity in the first and second
subsample. In contrast, we cannot observe a significant relationship between the term
spread and the future economic activity in other subsamples. In other words, the LIPTS
is supported only in the first and second subsample. The results suggest the dwindlingpredictive power of the term spread in recent years.19 As mentioned before, to analyze
whether the monetary policy factors in the term spread are related to the LIPTS, the
LIPTS needs to be satisfied with the data. Therefore, we henceforth concentrate ourinvestigation on the first and second subsample.20
3 An Empirical Analysis of the Monetary Policy Factors and the LIPTS
In this section, we construct some monetary policy factors included in the term
spread by using the structural VAR model in section 2.2. After that, we examine whether
the factors are related to the future economic activity or not. As mentioned in theprevious section, all empirical studies in this section use the data for the first subsample
between 1982:4 and 1987:6 and the second subsample between 1987:7 and 1997:8. The
19

Wheelock and Wohar (2009) indicate that the LIPTS may not be supported by the recent US data.
Nakaota (2005) and Hasegawa and Fukuta (2011) also find the weak evidence for the LIPTS using recent
Japanese data.
20
Structural change tests indicate that a structural break occurred at 1987:7. This break may affect therelationship between monetary policy and the LIPTS. Hence, we examine the relationship for eachsubsample.

8

LIPTS is supported in these subsamples. Hence, if we observe a significant relationshipbetween the monetary policy factors included in the term spread and future economic
activity, the evidence may show that the monetary policy plays a role in the LIPTS.
3.1 A Decomposition of the Term Spread into Monetary Policy Shocks and Other Shocks

In this paper, we assume that the monetary authority controls the call rate to executemonetary policy. Estimating a structural VAR model including the call rate, Miyao(2000) identifies the shocks of the call rate as the exogenous monetary policy based on
this assumption. Following his method, we also construct the exogenous monetary
policy or monetary policy shock. The VMA (Vector Moving Average)(∞) representation
for the structural VAR model (2) is the following form:
∆X

D L

,

(7)

D L
D
D L D L ,where D is a (4×4) matrix. This representation shows that the Japanese economy isdescribed by current and past structural shocks. The first element of thematrix is theshock of the call rate at t,. Hence, we can compute the time series of the call rate
shocks . We regard a portion of the term spread correlated with the call rate shocks as amonetary policy factor in the term spread. In addition, we interpret the remaining part of
the term spread as other factors.
More concretely, we use the following steps to divide the term spread into themonetary policy factor and other factor. First, to identify structural monetary policy
shocks, we assume the structural VAR model (2) and a recursive constraint proposed by
Sims (1980).21 This requires B in (2) to be lower triangular. Concerning the order ofvariables, X
r , y , m , e , we assume that the economic variables are determinedin order of the call rate (r), the industrial production (y), the monetary base (m), and themeasure of nominal effective exchange rates (e). This implies that, whereas the current
values of the industrial production (y), the monetary base (m) and the nominal effective
exchange rate (e) do not influence the current call rate (r), the current call rate (r)influences the other three variables. As mentioned before, we suppose that the call rateshockis the monetary policy shock. We estimate the structural VAR model using
Choleski decomposition of the covariance matrix of the reduced VAR model (3), Σ .
Using the estimated results, we obtain the series of monetary policy shocks,. Next,we regress the current term spread on the estimated current and past structural monetary
policy shocks by OLS:21

See Hamilton (1994) and Enders (2010) for the Sims’s structural VAR. Miyao (2000) also identify themodel using the Sims (1980) type of recursive constraint.

9

spread

β

β

β

β

η,

(8)

where η is the residual. The lag length, , is determined by the AIC. 22 We
decompose the current term spread into a part explained by monetary policy shocks,βββ
and a remaining part of the term spread (η ). We
regard βββ
as a monetary policy factor, which is denotedby “monetary_factort ,” and η as other factor indicated by “other_factort ”. Finally, toinvestigate whether each factor has information on the future economic growth rate ornot, we apply the OLS method to regress the future economic growth rate on thecomputed monetary factor and other factor:yγγ monetary_factor
γ other_factor
ν,
(9)
23
where ν is the residual.
Table 4-1 reports the estimated results for the first subsample from 1982:4 to 1987:6.
Coefficients of the monetary policy factor γ are significant in the case where theforecast horizon k is larger than 14. The coefficients of the other factor γ aresignificantly positive in the case where the forecast horizon is from k=2 to 22. It seems
that not only the monetary policy factor but also the other factor, which may be a
combination of other factors excluding the monetary policy shock, plays an importantrole in causing the leading indicator properties of the term spread (LIPTS). We observea negative relationship between the past monetary policy shocks and the current term
spread.24 This evidence indicates that a tight monetary policy, positive monetary policy
shocks, causes a future decrease in the term spread. A positive coefficient of themonetary factor implies that the tight monetary policy results in the contraction of theeconomy 14 months or more later. This effect plays an important role for the LIPTS
especially in the long forecast horizon. Table 4-2 presents the empirical results for thesecond subsample from 1987:7 to 1997:8. All coefficient of the monetary policy factor
γ are significantly positive. Many coefficients of other factors γ are also significant.
These results show that both the monetary policy factor and the other factor contributeto the LIPTS in the second subsample. This evidence is similar to that for the first
22First, we search the optimal lag length on the assumption that the lag length is 12 or less by AIC. If the
AIC indicate that the optimal lag length is less than 12, we employ that as the lag length. Second, if the
AIC support the 12 lag length, we search for the optimal lag length on the assumption that the lag length
is between 12 and 24. If the AIC indicate that the optimal lag length is between 12 and 24, we employ thatas the lag length. Third, if the AIC support the 24 lag length, we search for the optimal lag length between
24 and 36. We continue with similar searches until the maximum lag length becomes 48.
23
To use the estimated values as explanatory variables causes a bias for the standard error of theestimates in equation (9). To overcome this problem, we adjust the standard errors by using the method
proposed by Newey and West (1997).
24
The estimated result of equation (8) shows that the estimated coefficients of past monetary policy
shocks, β , …, β , are negative. We do not present the estimated results in this paper.

10

subsample. The empirical investigation in this subsection shows that the monetary
policy plays an important role for the LIPTS in Japan.
The monetary policy factor computed in this subsection is, however, a part of theterm spread explained by the current and past monetary policy shocks. In other words,
the factor may not contain information on future expected interest rates. Hamilton andKim (2002) find that the expected future interest rate and term spread are effective inthe LIPTS by using US data. In addition, Rendu de Lint and Stolin (2003) mention thatthe term spread may reflect expectations of future interest rates. If the future interest
rates are affected by the future monetary policy stance, it may be reasonable to examine
whether or not the monetary policy factor in the term spread related to the future
expected interest rates has information on the future economic activity.
3.2 A Decomposition of the Term Spread into Monetary Policy Shocks, Expectations of
Future Monetary Policy and Other Shocks

If investors expected a future recession and a reaction to it by the monetary authority,
they would forecast a decrease in short-term interest rates. The expectation hypothesisof the term structure of interest rates implies that the average of the expected future
short-term interest rates determines the long-term interest rates. Hence, the expectationof a future recession may cause a decrease in the long-term interest rate and the term
spread. In other words, the term spread may be affected by the expectations of futuremonetary policy. If we do not take this effect into account, we may underestimate themonetary policy effect on the LIPTS. In this section, we examine the relationshipbetween the LIPTS and the monetary policy by considering not only the past monetary
policy shocks but also future expectations about the monetary policy. On the assumptionthat the monetary authority controls the short-term interest rates, the future expectedstance of the monetary policy is reflected by the future expected short-term interest
rates.
We examine whether these two monetary policy factors have any effects on the
LIPTS by the following method. First, computing the forecast values of call rates fromnext the period to future periods based on the estimated VAR model in section 2, we
subtract a current call rate from the mean values of the current call rate and the forecast
values of future call rates. We define this difference as the call spread. Second, we
regress the current term spread on the estimated current and past structural monetary
policy shocks, and the current call spread. Based on the regression results, we
decompose the term spread into three parts; one is the part explained by current and pastmonetary policy shocks, another is that explained by the current call spread and the11other is the remaining part of the term spread. Third, we regress the future economic
growth rate on these three factors and examine their predictive power. Because we
confirm that the LIPTS is satisfied by the data in this sample period, the significant
relationship between the future economic growth and monetary policy factors indicatesthat monetary policy affects the LIPTS.
We first explain the procedures to compute the forecast values of call rates and callspread. We estimate future call rates using the estimated reduced VAR model in (3). We
compute forecasts of call rates from one month ahead ı̂to 8 years and 11 months,
107 months, ahead ı̂in each month and take the simple average among thecurrent call rate and the forecasts,∑ı̂

current call rate from the simple average and definei. 25 Next, we subtract the
∑

ı̂

i

i

as thecall spread denoted by “call_spread ”. To obtain the monetary policy factor, the futuremonetary policy factor and other factor, we estimate the following formula by OLS:
spreadδδδδδ call_spread
ξ,
(10)
where
is the monetary policy shock computed in subsection 3.1 and ξ is an error
term. The lag length, p, is determined based on the AIC. 26 Using the estimatedparameters, we regard the term given by δδδas thecurrent and past monetary policy factor denoted by “monetary_factor”, the term

given by δ call_spread as the future monetary policy factor denoted by“future_monatery_factor t ” and the remaining errors, ξ , as the other factor denotedby “other_factor ”.27 We, finally, apply the OLS method to estimate the following
equation to investigate the relationship between the LIPTS and monetary policy:
monetary_factory+ future_monetary_factor tother_factor
28
where υ is the residual.
25

υ,

(11)

In this paper, the long-term interest rate is the 9-year spot rate. To match the maturity of the spot rate,
we forecast the call rates 107 months ahead.
26
First, we search the optimal lag length on the assumption that the lag length is 12 or less by AIC. If the
AIC indicate an optimal lag length less than 12, we employ that as the lag length. Second, if the AIC
support the 12 lag length, we search for the optimal lag length on the assumption that the lag length is
between 12 and 24. If the AIC indicate an optimal lag length between 12 and 24, we employ that as thelag length. Third, if the AIC support the 24 lag length, we search for the optimal lag length between 24
and 36. We continue a similar search until the maximum lag length becomes 48.
27
The method to obtain the monetary factor in this subsection is similar to that in section 3.1 with the
exception that the estimated equation in this subsection includes the call spread. Hence, we also use thesame “monetary factor” to this term.
28
We also adjust standard errors by the method proposed by Newey and West (1997) to take the problem
caused by using the estimated values as explanatory variables into account.

12

Table 5-1 presents the estimated results for the first subsample between 1982:4 and1987:6.29 Whereas the coefficients of the current and past monetary policy factor,,
are insignificant in the cases where the forecast horizons are less than 13 months except
for k=8, they are significantly positive in the case where they are 14 months or more.
This evidence shows that the part in the term spread related to the past positive call rate
shocks has information on the economic slowdown more than 14-months ahead. We
find a negative association between the past monetary policy shock and the current term
spread.30 The positive coefficients of the monetary policy factor may be reflected by
the evidence that the past tightness of the monetary policy, positive policy shocks, has
negative impact on the real economy almost 14 months later. In other words, investors
may expect that it will take more than a year until the monetary policy has an effect on
the real economy. The coefficients of the future monetary policy factor,, are positiveand significant for the forecast horizons from 2 months to 12 months. In contrast, they
are not significant in the case of the 13 months or more horizons. Positive coefficientsof the future monetary policy factor show that the increase in the yield spread caused by
the rise in the future expected short-term interest rates is followed by future higheconomic growth. It seems that the increase in the future expected short-term interest
rates raises the long-term interest rate and yield spread. Because, during a boom, theshort-term interest rates are likely to be high, this result may be reasonable.31 The
coefficients of other factor,, are positive and significant in all cases except for the 1
32month forecast horizon. The term spread between the 9-year spot rate computed fromthe Japanese government bonds and 1-month CD rate is related to not only the monetary
policy factors but also the other factor. This relation causes the predictive capability ofthe term spread for future economic growth. The contributions of these factors depend29

To compute the future call rates based on the VAR model in (3), we use the past four shocks in the
VAR model including the monetary policy shocks. Hence, the monetary factor and future monetary factorin (11) may be correlated. To control this problem, we also estimate (11) by substituting the corrected callspread for the call spread in (10). The corrected call spread is the sum of the estimated constant term anderror term based on the regression of the call spread on the current and past monetary shocks. The
empirical results for both subsamples based on the above correction are similar to those in this paper interms of the signs of the coefficients.
30
The estimated result of equation (10) shows that the estimated coefficients of past monetary policy
shocks, δ , …, δ , are negative. We do not present the estimated results in this paper.
31
Hamilton and Kim (2002) find that the expected future interest rate and term premium play a role in
the LIPTS using US data. Our results based on Japanese data may be similar to their results.
32
Singleton (2006) presents the relationship between the three factors related to the level, slope andcurvature, and maturity of bonds in terms of the expected future interest rates and the premium using the
US data. He shows that the slope factor is affected by the expected future interest rates and the curvaturefactor is related to the premium. Because both slope and curvature factors have some effect on the yieldspread, our evidence that the yield spread is influenced by not only the expected future interest rate, thefuture monetary policy factor, but also monetary policy and other factors may be compatible with his US
evidence.

13

on the forecast horizon. In short horizons, the future monetary policy factor and otherfactor play a crucial role in causing the LIPTS. The current and past monetary policy
factor and the other factor have some effects on the prediction ability of the term
spreads for future economic activity in the long horizon. Table 5-2 reports the results forthe second subsample from 1982:7 to 1997:8. The coefficients of the current and pastmonetary policy factor are significantly positive in many cases. The future monetary
policy factor also has a significant positive effect on the future economic growth. The
other factor coefficients are positive and significant especially in the case of the long
forecast horizons. These results indicate that not only monetary policy factor but also
the other factor play an important role for the LIPTS in Japan in this subsample.33
Comparing the results in the previous subsection with those in this subsection, we
confirm that the analysis which does not take future monetary policy expectations into
account in section 3.1 underestimates the effects of monetary policy on the LIPTS,
especially in the first subsample. Taking not only the current and past monetary policy
but also the future monetary policy into account, we observe differences in the effects ofthe monetary policy factors among forecast horizons in the first subsample. In the shorthorizon, a factor in the term spread related to the future expectations of the monetary
policy contains information on future economic growth rate. A factor in the term spread
concerned with the past monetary policy shocks causes the predictive ability in the long
forecast horizons.
3.3 Robustness: Other Maturities Analysis

We use the 9-year spot rate as the long-term interest rate in section 3.1 and 3.2. To
examine the robustness of our empirical results, we conduct empirical studies similar tosection 3.2 using other spot rates whose maturities range from two years to eight years.
Table 6-1 shows the estimated results for the first subsample. The coefficients ofthe current and past monetary policy factor,, are significantly positive only in thecase of the long forecast horizons. The results are similar to those for the 9-year
government spot rate. This may indicate that the effect of the current and past monetary
policy on term spread is common to all maturities. The coefficients of the future
33

In the first subsample, while the current and past monetary policy factor has a significant effect on the
future economic growth in the long forecast horizon, the future monetary policy factor affects the future
growth in the short horizon. In contrast, we do not observe such difference in the second subsample. It
might be possible to interpret this difference to mean that monetary policy effects depend on the sample
period. However, the AIC show that, whereas the lag length of equation (10) is set at 45 in the second
subsample, it is 10 in the first subsample. Hence, the current and past monetary policy factors in thesecond subsample may be more informative than that in the first subsample. Actually, if we set the lag
length of equation (10) at 10 in the second subsample, we obtain empirical results similar to the firstsubsample.

14monetary policy factor,, are positively significant in the case of the 9 months or lessforecast horizons for 6-year, 7-year and 8-year spot rates This evidence may beinterpreted to mean that the short maturity spot rates, such as 2-year and 3-year spot
rates, do not include information on the future monetary policy factor. The coefficientsof the other factor are significantly positive in the case of forecast horizons between 9
and 24 for all spot rates. On the other hand, for short term economic growth rates, thecoefficients are positive and not necessarily significant. This evidence may be a little
different from the 9-year spot rate. Table 6-2 shows similar empirical results to Table
5-2 for the second subsample except for the other factor effect in the short maturity spot
rates.34
From these results, we find that information on future economic growth in the term
spread results from the current and past monetary policy factor and the other factors inmany cases. The term spread also has information on the future monetary policy factor
in the case of the relatively long maturity and the short forecast horizon. Empiricalstudies on the LIPTS use long-term interest rates not 2 or 3 years maturity interest rates.
Hence, it may be reasonable to conclude that monetary policy plays an important role in
the LIPTS.
4. Conclusion
Many empirical studies have shown that the term spread—the difference between
long- and short-term interest rates— has information on future economic conditions.
This property of the term spread is called the “leading indicator property of the term
spread (LIPTS).” However, the reasons why we observe the LIPTS have not beenclarified. Taking structural changes in the Japanese economy into account, this paper
examines the reasons in terms of monetary policy. Tests for structural breaks in a VAR
model to characterize the Japanese economy between 1982:4 and 2007:3 showed theoccurrences of breaks at 1987:6, 1997:8 and 2002:10. Empirical analyses on the LIPTS
for the four subsamples indicated the property was supported between 1982:4 and1997:8. Using this sample period, we investigated whether the monetary policy caused
the LIPTS or not by using the following methods. First, on the assumption that thecentral policy instrument of the Japanese monetary authority is the call rate, we
regarded the call rate shocks as monetary policy shocks. Based on the estimation resultsof a structural VAR model including the call rate, we obtained the series of the monetary34

As mentioned in footnote 33, in the second subsample, the current and past monetary policy factor
may be informative because of the long lag length in the estimation of equation (10). Short maturity spot
rates are less volatile than the long maturity spot rates. Hence, the current and past monetary policy factor
may have explanatory power for the short maturity yield spreads.

15

policy shocks. Next, we computed the series of call spreads by subtracting the current
call rate from the average of the expected values of future call rates. The call spread isregarded as the future monetary policy factor. Third, regressing the term spread on theestimated monetary policy shocks and the call spread, we decomposed the current term
spread into three parts; one explained by monetary policy shocks, another explained bycall spreads and the remaining part. Finally, we examined whether these three factors
were related to future economic growth or not. From the results, we found that themonetary policy shocks, future monetary policy and the other factor are all important
for the LIPTS. This evidence shows that, for a theoretical explanation of the LIPTS, weneed to consider a model which includes monetary policy aspects. In addition, if theother factors are related to real shocks, such as production shocks, we also need topropose a model that takes real economy aspects into consideration. Theoretical studies
on the LIPTS mechanism have proposed models with real sectors and those with
monetary sectors separately. Our results may indicate that a model with both sectors isneeded to resolve the LIPTS.
Finally, we mention some restrictions of this paper and some directions for further
research. First, our empirically results depend on the VAR model proposed by Miyao(2000). Because Miyao (2000) analyzes the Japanese monetary policy by his VAR
specification, his motivation coincides with ours. However, we should examine whether
the other specifications of VAR models produce similar results or not. Second, we donot specify the source of other factors in this paper. In other words, they may include
various kinds of information, such as real shocks or specification errors. We need todecompose the other factors into more detailed factors. Third, we should provide
theoretical explanations for the reasons why we obtained our results. Based on our
results, we may need to consider a model taking both monetary sectors and real sectors
into account. Finally, we should consider the reasons for the three structural changes.
Appendix
In this appendix, we explain the data used in the paper. The sample period of the paper isfrom 1981:4 to 2007:12.35
1. Variables in VAR Model
The Call Rate (r)We construct a series of overnight call rates from 1978:1 to 2007:12 using the collateralized
overnight call rate (monthly average) and the uncollateralized overnight call rate (monthly
35

In cases where we obtain the data for the period from 1981:4 to 2007:12, we do not mention the data
period explicitly in the explanation that follows.

16

average). The uncollateralized overnight call rate is viewed as the target rate for the Bank ofJapan. However, the series is not available before 1985:6. We use the collateralized overnight
rate until 1985:6 as a proxy for the uncollateralized overnight rate by adjusting the risk premium,and use the uncollateralized overnight rate itself after 1985:7. To adjust the risk premium, wefirst compute the ratio of the mean of the uncollateralized overnight call rate to the mean of thecollateralized overnight call rate from 1985:7 to 2009:12. We then produce the quasi
uncollateralized overnight rate by multiplying the mean ratio by the collateralized overnight rateuntil 1985:6.36
the quasi uncollateralized overnight rate
the collateralized overnight rate
the mean of the uncollateralized overnight rate.
the mean of the collateralized overnight rate

A. 1

The call rate series are obtained from the Bank of Japan’s web site.
Industrial Production based on 2005 (y)The industrial production series is an index of industrial production whose base year is 2005.
A seasonally adjusted series is available from the Ministry of Economy, Trade and Industry’s
web site.
The Monetary Base (m)The monetary base series is monthly average and a seasonally adjusted series. This data is
obtained from the Bank of Japan’s web site.
A Measure of Nominal Effective Exchange Rate (e)A measure of nominal effective exchange rate is the Nominal Effective Exchange Rate. This
series is available from the Bank of Japan’s web site.
2. Spot Rates of Long-term Government Bonds
We compute the spot rate data by a method similar to the one proposed by Fama and Bliss(1987). To compute spot rates for a month, we use the data on coupon rates, bond prices at theend of that month, maturity dates and coupon payment dates for the 10-year Japanese
government bonds. Because the Japanese government bonds pay a coupon semi-annually, bonds
with a 10-year maturity have 20 coupon payments before redemption. We compute spot rates
whose maturities are 0.5-year, 1.0-year, 1.5-year, 2.0-year, …, 10.0-year on the assumption thatthe spot rates are constant for half a year. First, we use the data on bonds with less than 0.5-year
maturities. Because these bonds have only one cash payment, we can compute the discount rates
for each bond on the assumption that the rates for maturities between 0 year and 0.5 year are
constant. This assumption means that we adjust the differences in maturities by changing theinterval for the discount. The average discount rate is regarded as the 0.5-year spot rate.
36

Kitaoka et al. (2008) also produce the quasi uncollateralized overnight rate in the same way.

17

Next, we use the data on bonds with maturities between 0.5 year and 1.0 year. These bonds
have two cash payments. Applying the computed 0.5-year spot rate as a discount rate for first
coupon payment, we can compute the discount rates for the second cash payments of each bondon the assumption that the rates for maturities between 0.5 year and 1.0 year are constant. The
average discount rate is regarded as the 1.0-year spot rate. Third, the data on bonds withmaturities between 1.0 year and 1.5 year are used to compute the 1.5-year spot rate. There arethree cash payments in these bonds. Using the computed 0.5-year spot rate as a discount rate forfirst coupon payment and the 1.0-year spot rate as a discount rate for the second coupon
payment, we can compute the discount rates for the third cash payments for each bond on theassumption that the rates for maturities between 1.0 year and 1.5 year are constant. Repeating
this procedure, we can calculate spot rates from 0.5-year to 10-year at the 0.5 year interval forthat month. The application of this method to the every month from 1981:4 to 2007:12 produces
the spot rate data for these periods.37 Bond prices are collected from the Nikkei Newspaper andNikkei NEEDS FinancialQUEST. The data on coupon rates, coupon payment and maturity
dates are collected from the Tokyo Stock Exchange Monthly Statistics Report and Nikkei
NEEDS FinancialQUEST.
3. Short-term Interest Rate
The short-term interest rate series is the new issue, 1 month CD rate. This data is available
from the Nikkei NEEDS FinancialQUEST.

37

Our data set includes the bonds whose maturities are less than 9.5 year until 1986:6. Hence, we cancompute spot rates from 0.5-year to 9.5-year until 1986:6. From 1986:7, we can calculate the 10-year spot
rate.

18

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21

Figure 1: Plots of the First Differences of Call Rate ( ) and the Industrial Production ( )
5

1

4
0.5

3
2

0

1
0

-0.5

-1
-2

-1

-3
-4

-1.5
1981:05
1982:01
1982:09
1983:05
1984:01
1984:09
1985:05
1986:01
1986:09
1987:05
1988:01
1988:09
1989:05
1990:01
1990:09
1991:05
1992:01
1992:09
1993:05
1994:01
1994:09
1995:05
1996:01
1996:09
1997:05
1998:01
1998:09
1999:05
2000:01
2000:09
2001:05
2002:01
2002:09
2003:05
2004:01
2004:09
2005:05
2006:01
2006:09
2007:05-5ryNotes:The left vertical axis measures the first difference of the call rate indicated by the solid line. The right vertical axis measures
the first difference of the industrial production indicated by the dotted line. These variables are measured in percent.

Figure 2: Plots of the First Differences of the Monetary Base ( ) and Nominal Effective Exchange Rate ( )
10

5

0

-5

-10

1981:05
1982:01
1982:09
1983:05
1984:01
1984:09
1985:05
1986:01
1986:09
1987:05
1988:01
1988:09
1989:05
1990:01
1990:09
1991:05
1992:01
1992:09
1993:05
1994:01
1994:09
1995:05
1996:01
1996:09
1997:05
1998:01
1998:09
1999:05
2000:01
2000:09
2001:05
2002:01
2002:09
2003:05
2004:01
2004:09
2005:05
2006:01
2006:09
2007:05-15meNotes:
The first difference of the monetary base is indicated by the solid line. The difference of the nominal effective exchange rate isindicated by the dotted line. These variables are measured in percent.

22

Table 1: Examination of the Leading Indicator Properties of the Term Spread
Full sample Analysis 1982:4 – 2007:3
k

SE

SE

1

0.3998(1.4614)1.2839(1.0422)0.001720.6653(0.7961)

1.0439**(0.5038)

0.006930.7992(0.8024)

0.9211*(0.4841)0.008740.8951(0.8794)

0.8365*(0.5083)0.008650.8857(0.9677)

0.8475(0.5599)0.01056

1.0138(1.0253)0.7427(0.5932)

0.00847

1.0222(1.0683)

0.7478(0.6287)

0.00978

1.0196(1.1364)0.7646(0.6755)

0.01139

1.0826(1.1677)

0.7072(0.7038)0.010010

1.1156(1.2126)

0.6859(0.7427)0.010011

1.1777(1.2544)0.6283(0.7775)

0.008612

1.2130(1.2879)

0.5934(0.8080)0.008013

1.2124(1.3046)

0.5890(0.8239)0.008614

1.2427(1.3228)0.5521(0.8408)

0.008015

1.2650(1.3570)

0.5424(0.8701)

0.008016

1.2776(1.3650)0.5276(0.8752)

0.008117

1.2971(1.3751)0.4887(0.8833)

0.007218

1.3237(1.3880)0.4519(0.8945)0.006219

1.3807(1.4277)0.4044(0.9241)0.004620

1.4110(1.4540)0.3702(0.9433)

0.003621

1.4215(1.4635)

0.3480(0.9544)0.003122

1.4342(1.4872)

0.3119(0.9742)0.002123

1.4511(1.5151)

0.2918(0.9957)0.001624

1.4591(1.5364)0.2773(1.0147)0.0013

Notes:
1．We estimate the following equation for the monthly data from 1982:4 and 2007:3:
y
y

α
1200

α spread

lny ,

lny

k
spreadiε,i,where y is the index of industrial production based on 2005 at t, spread is the difference between the 9-year spot ratecomputed from the Japanese government bond data and 1-month CD rate at t, ytk indicates the growth rate of industrial
production between t and t+k,

denotes the forecast horizon, ε is the error term.

2．Standard errors corrected by the Newey and West (1987) method are in parentheses in column SE.
***, **, and * denote the statistical significance at the 1 %, 5%, and 10% levels, respectively.
3．R squared statistics adjusted for degrees of freedom are presented in column.

4. In the case where the forecast horizon k is from 2 to 10, the estimated period is from 1982:4 to 2007:2. In the case fromk=11 to k=24, the estimated period is from 1982:4 to 2007:3 k.

23

Table 2: Augmented Dickey-Fuller Tests
Variables in the Level

Variables in the First Differences

Variables

Statistics

Lags

Variables

Statistics

Lags

r

-2.9205(16)∆r-3.6344***

(24)

y

-2.1241(24)∆y-4.5424***

(24)

m

-1.9488(3)∆m-6.9527***(2)e-2.1595(11)∆e-3.9832***(10)Notes:
1. ***, **, and * denote the statistical significance at the 1 %, 5%, and 10% levels, respectively.
2. The optimal lag lengths chosen based on the AIC are in parentheses in columns Lags.
3. While the unit root tests for variables in levels includes a constant term and a deterministic trend, the tests for variables in
the first differences include a constant term only.
4. The four variables are the call rate (r), industrial production (y), the monetary base (m) and a measure of nominal effective
exchange rates (e).

24

Table 3: Re-examination of the Leading Indicator Properties of the Term Spread (LIPTS) –Subsample Analyses—
k
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24

First subsample: 1982:4-1987:6
SE
3.2723(3.1213)0.0016
3.1410***(1.1150)0.04863.0895***(0.9849)
0.1323
3.1893***(1.1023)0.13393.1758***(1.0043)
0.18382.9236***(1.0167)
0.18933.2325***(1.0304)
0.23703.3811***(0.9085)0.29373.2086***(0.9638)0.30193.1735***(0.8797)0.28893.2792***(0.7685)0.34483.0783***(0.8382)0.31763.0825***(0.7637)
0.33753.0591***(0.6318)
0.36962.9630***(0.7024)
0.34533.0245***(0.6798)
0.35632.9804***(0.5879)0.36042.9214***(0.7050)
0.31443.6814***(0.5183)
0.34664.2486***(0.3960)
0.3753
4.1653***(0.4073)
0.35334.3929***(0.7213)0.32934.4037***(0.9120)0.3226
4.4197***(0.7598)
0.3083

Second subsample: 1987:7-1997:8
SE
0.9752(1.2476)-0.0033
0.9763*(0.5590)0.0086
0.9575*(0.5426)
0.01830.9922*(0.5591)
0.02851.0890*(0.6180)
0.04281.0888*(0.6376)
0.04891.1402*(0.6673)
0.0647
1.2136*(0.7027)0.08111.2565*(0.7051)
0.09361.3168*(0.7217)0.1122
1.3288*(0.7312)0.12181.3939*(0.7382)0.14041.4324*(0.7332)
0.1562
1.4529**(0.7306)
0.1694
1.5115**(0.7330)0.1831
1.5427**(0.7151)
0.19581.5509**(0.6989)0.20701.5912**(0.6727)0.2254
1.6474**(0.6644)0.24401.6898***(0.6461)
0.25891.7522***(0.6092)0.29081.8022***(0.5877)
0.3192
1.8733***(0.5671)0.34731.9049***(0.5516)0.3647

Third subsample: 1997:9-2002:10
SE
13.5772*(7.0022)0.044012.8747***(4.5282)
0.117612.1670**(5.3987)0.126410.5989*(6.2065)
0.11509.6505(6.4213)
0.09808.2196(6.3465)
0.07387.4299(5.9388)
0.06546.8130(5.7515)0.06055.5436(5.2939)0.03863.8745(4.8776)0.01192.1929(4.2441)-0.0089
0.9844(3.9100)-0.01810.0741(3.5382)-0.0213-0.9327(3.1287)-0.0186-1.8137(2.7658)-0.0090-2.1431(2.4552)-0.0019-3.0496(2.1095)
0.0246-3.6328**(1.7405)0.0518-4.5727***(1.4240)0.1080-4.9629***(1.2098)
0.1467-5.5853***(1.0501)
0.2192-5.8219***(0.9837)
0.2724-6.2833***(1.0746)
0.3727-6.3441***(1.0354)0.4392

Fourth subsample: 2002:11-2007:12
SE
6.5959(5.1322)0.01263.2436*(1.8956)
0.00842.0700(2.1167)-0.00210.7667(2.2146)-0.0163-0.2543(2.2659)-0.0195-0.9222(1.9704)-0.0111-1.1706(1.6299)-0.0004-1.6050(1.2703)
0.0246-1.9735*(1.0005)
0.0598-2.3804***(0.7614)0.1268-2.6153***(0.7407)0.1687-2.8386***(0.8012)0.2416-2.6054***(0.8743)0.2292-2.5435***(0.9048)0.2865-2.1772**(0.8607)0.2342-1.8098**(0.8015)0.2128-1.3844**(0.6231)0.1289-1.1535**(0.5834)
0.1045-0.9594*(0.5719)0.0652-0.8789*(0.4913)0.0596-0.6566(0.5585)0.0261-0.6050(0.5500)
0.0193-0.6220(0.4648)0.0342-0.4603(0.3794)0.0071

Notes:

1. See the notes 1, 2 and 3 in Table 1.
2. The first, second and third estimated periods are from 1982:4 to 1987:6 k, from 1987:7 to 1997:8 k and from 1987:8 to 2002:10 k, respectively, where k indicates the forecast horizon. The fourth
estimated period is from 2002:11 to 2007:2 in the case where k is between 2 to 10, and from 2000:3 to 2007:3 k in the case k=11 to k=24.

25

Table 4-1: Regression Results of the Monetary Factor and Other Factor
First subsample: 1982:4-1987:6
k
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Notes:

3.7990*3.5793***3.6053***3.7353***
3.7843***3.7154***
3.8382***
3.8591***
3.8369***3.8699***3.7762***3.8182***4.0705***4.4309***4.6632***4.6853***4.5809***4.4264***4.3417***
4.1231***
3.9469***3.8090***4.1405***4.3351***SE(2.2594)(0.9619)(0.6466)(0.6721)(0.6968)(0.7770)(0.8551)(0.9250)(1.0620)(1.1319)(1.2062)(1.3455)(1.4280)(1.4864)(1.6919)(1.5715)(1.5324)(1.5938)(1.3643)(1.2439)(1.2581)(1.3793)(1.3947)(1.2818)SE(5.7576)(2.4249)(1.5810)(1.4526)(1.3446)(1.5467)(1.6190)(1.6741)(2.2040)(2.2563)(2.3373)(2.6520)(2.6317)(2.4051)(2.7854)(2.4428)(2.2525)(2.4345)(1.8765)(1.2597)(1.5580)(1.1600)(1.0380)(1.0481)-0.8168
0.09850.4766
0.93401.70981.0402
1.93382.51662.39282.40342.60622.66033.62754.8316**5.3807*5.8982**5.8923***5.6704**7.0985***8.0574***7.7451***
7.9397***
8.1980***7.8570***SE(3.9062)(1.4999)(1.0310)(1.1088)(1.0027)(1.0525)(1.0649)(0.9296)(1.0277)(1.0004)(0.9321)(1.0019)(0.8690)(0.8164)(0.8262)(0.6855)(0.6625)(0.6054)(0.5495)(0.8742)(0.6882)(1.4084)(1.5397)(1.2532)5.48455.8294***5.6583***5.7437***5.2184***5.0310***5.0058***4.7778***4.5223***4.2615***4.1282***3.7264***3.1428***2.4780***1.9578**1.6476**1.5195**1.4533**
1.9378***2.5086***2.5452***2.4388*1.69471.0275-0.00020.11640.33410.3111
0.36280.40670.3936
0.43310.42630.37420.40510.34940.3481
0.38250.35680.37090.37790.31970.37670.4282
0.39380.38840.42830.4141

1. We estimate the following equation for the first sub-sample, from 1982:4 to 1987:6:yγγ monetary_factor

γ other_factor

ν,

where ν is the residual. To obtain the monetary policy factor and other factor, we estimate the following equation:
spreadwhere ηt is the error tem and

,

β
,

β
,

β
, …

β

η,

are obtained by the estimation of the structural VAR

model using Choleski decomposition of the covariance matrix of the reduced VAR model (3). Based on the AIC, we set thelag length

at 10. We define βββterm spread̂ as the other factor using the estimated values of the above equation. The former is denoted by

as monetary policy factor and the remaining part of the“monetary_factor ” and the latter is denoted by “other_factor ” in the first equation.
2. Standard errors corrected by the Newey and West (1987) method are in parentheses in column SE.
***, **, and * denote the statistical significance at the 1 %, 5% and 10% levels, respectively.
3. R squared statistics adjusted for degrees of freedom are presented in column

26.

Table 4-2: Regression Results of the Monetary Factor and Other Factor
Second subsample: 1987:7-1997:8
k
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Notes:-7.8451*-7.1834***-6.7319***-6.3942***-6.7791***-6.3912***-6.0391***-6.1527***-5.7715***-5.6429***-5.0791***-5.0186***-4.9656***-4.5119***-4.6208***-4.3663***-4.0501***-3.7701***-3.6828***-3.6751***-3.4851***-3.4179***-3.4655***-3.3366***SE(4.4076)(2.1267)(1.7401)(1.4053)(1.1843)(0.8871)(0.6918)(0.6751)(0.6744)(0.6469)(0.7005)(0.7740)(0.7618)(0.7520)(0.7810)(0.8030)(0.7772)(0.7933)(0.7791)(0.7796)(0.6910)(0.6342)(0.5774)(0.5663)4.4246*
4.1323***3.9045***3.7709***3.9659***3.7940***3.6346***3.7448***3.5783***3.5385***3.2698***3.2775***3.2821***
3.0910***3.1918***3.0891***2.9611***2.8481***2.8693***2.8781***2.8216***2.8084***2.8406***2.7868***SE(2.2269)(1.0869)(0.9035)(0.6858)(0.5886)(0.4354)(0.3289)(0.3150)(0.2960)(0.2552)(0.2239)(0.2419)(0.2418)(0.2256)(0.2595)(0.2566)(0.2496)(0.2668)(0.2907)(0.2988)(0.2841)(0.2928)(0.2962)(0.3074)

6.04746.4969*6.1926**6.5918***6.6006***6.4247***
6.2529***6.3293***6.3768***6.3659***6.4737***
6.2123***5.7297***5.6350***5.4371***5.0847***4.8276***4.6483***4.6872***
4.0971***
3.7695***3.4617***2.8426**2.6340**SE(6.7123)(3.5488)(2.5206)(2.1827)(2.0040)(1.7905)(1.4985)(1.2016)(1.0734)(1.0470)(1.1094)(1.0719)(1.0422)(1.2012)(1.2894)(1.2494)(1.1080)(1.1684)(1.1014)(0.9350)(1.0052)(1.0992)(1.1930)(1.2309)

0.03720.15720.25720.35910.46020.47080.53170.61160.60120.66710.64760.68590.69600.68390.70080.6672
0.66470.65900.66380.65610.67610.71270.73610.7389We use the sample period from 1987:7 to 1997:8. The estimated equation and method are explained in note 1 in Table 4-1.
Based on the AIC, we set the lag length

at 48. Standard errors and R squared are also presented in note 2 and 3 in Table

4-1.

27

Table 5-1: Regression Results of the Monetary Factor, Future Monetary Factor and Other Factor
First subsample: 1982:4-1987:6
k
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24

SE
(4.5389)(1.4666)(1.0058)(1.0280)(0.9787)(1.1703)(1.0594)(1.0675)(1.1330)(1.2606)(1.2471)(1.2080)(1.2444)(1.2857)(1.3855)(1.4075)(1.3079)(1.3485)(1.2875)(1.1626)(1.2439)(1.0594)(0.9329)(1.1967)9.7142**
6.3350***6.8828***6.8837***6.3740***6.1070***5.6899***5.6559***5.6116***5.6927***5.1789***4.8668***4.5155***4.3395***4.3471***
4.1927***3.9388***3.7907***4.1343***4.4037***
4.2227***
3.9477***4.1547***4.2635***
Notes:

SE(5.2684)(1.6975)(1.0264)(0.8994)(0.8311)(0.9085)(0.8850)(0.8689)(1.1745)(1.2104)(1.2561)(1.6425)(1.5612)(1.2683)(1.4443)(1.2258)(0.9759)(1.3593)(1.1322)(1.1077)(1.4018)(1.1403)(0.9612)(1.2987)-0.6240
0.3522-0.0209
0.2613
1.33470.72401.19451.9845**1.57571.67121.83011.87092.37953.4013***3.9559***4.4685***4.5607***4.3287***5.6060***6.4356***6.0101***
6.2679***6.7217***6.4956***

7.61363.7351**4.6711***4.5981***
3.6923***3.4005***2.7226***2.5549***2.6950***2.7233***
2.1714***
1.6876*
1.00760.3250-0.0181-0.3423-0.6470-0.7019-0.16310.36910.21830.21380.52690.9275SE(5.4223)(1.5964)(0.9715)(1.0624)(0.8339)(1.0324)(0.9459)(0.8920)(0.8781)(0.8543)(0.7890)(0.9559)(0.9605)(0.7730)(0.6591)(0.6915)(0.6664)(0.6027)(0.7240)(0.7948)(0.8916)(0.7982)(0.7415)(0.7921)6.01207.3991***7.0296***7.0352***
6.7150***6.5108***7.2397***6.9326***6.5045***6.1766***6.5882***
6.0961***
5.9654***5.4360***4.6957***4.4037***4.0489***3.7150***3.8968***3.8502***3.6213***
4.1072***
3.6977***3.7439***SE(5.0339)(2.1088)(1.4326)(1.4933)(1.2208)(1.1072)(1.1021)(0.9709)(1.0359)(0.9913)(0.7156)(0.9559)(0.8361)(0.5716)(0.6192)(0.4960)(0.4622)(0.4801)(0.4355)(0.3671)(0.4483)(0.5530)(0.8882)(0.9691)0.01000.12520.40970.36460.4207
0.48210.51870.55670.52230.46150.54540.48070.51080.55500.48790.50910.52770.4521
0.49280.52160.48580.5116
0.50990.45101. We estimate the following equation for the first sub-sample, from 1982:4 to 1987:6:
ymonetary_factor*t

future_monetary_factor*tother_factor*tν,where ν is the residual. To obtain the monetary policy factor, future monetary policy factor and other factor, we estimate
the following equation:
spreadδδδwhere ξt is the error term and

,

,

,

δ
, …

δ call_spreadtξ,are obtained by the estimation of the structural VAR

model using Choleski decomposition of the covariance matrix of the reduced VAR model (3) and call_spread is the
expected future call rates for the 9-year period based on the estimated structural VAR model minus current call rate. Basedon the AIC, we set the lag length

at 10. We define δδδas the monetary policy factor,

δ call_spreadt as the future monetary policy factor and the remaining part of the term spreadt

as the other factor using

the estimated values of the above equation. The first term is denoted by “monetary_factor*t ,” the second term is indicatedby “future_monetary_factor*t ” and the third term is denoted by “other_factor*t ” in the first equation.
2. Standard errors corrected by the Newey and West (1987) method are in parentheses in column SE.
***, **, and * denote the statistical significance at the 1 %, 5% and 10% levels, respectively.
3. R squared statistics adjusted for degrees of freedom are presented in column

28.

Table 5-2: Regression Results of the Monetary Factor, Future Monetary Factor and Other Factor
Second subsample: 1982:7-1997:8
k
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24

-4.4675-4.5295**-2.5947*-3.3026**-4.4382**-3.8442***-3.5144***-4.3512***-4.2089***-4.0902***-4.0541***-4.4117***-4.2574***-3.6567***-3.7985***-3.9396***-3.5550***-3.8812***-3.7079***-3.5278***-3.0946***-3.1464***-3.1598***-3.0465***
Notes:

SE(5.1949)(2.1964)(1.5540)(1.3654)(1.8099)(1.3113)(0.9779)(0.9901)(0.6766)(0.4263)(0.4046)(0.4747)(0.3994)(0.2752)(0.3477)(0.2951)(0.2794)(0.2099)(0.2450)(0.2856)(0.3169)(0.2800)(0.2511)(0.2819)2.51282.6092**
1.7128**2.0456***2.5517***2.3153***2.2104***2.6209***2.5512***2.5234***2.4885***2.6232***2.5937***2.3608***2.4554***2.5275***2.3910***2.5501***2.5396***2.4989***2.3851***2.4421***2.5025***2.4533***SE(2.4140)(1.0510)(0.7078)(0.5801)(0.7816)(0.5646)(0.4195)(0.4324)(0.3136)(0.2598)(0.1788)(0.1852)(0.1672)(0.1568)(0.1182)(0.1264)(0.1309)(0.1300)(0.1236)(0.1368)(0.1230)(0.1077)(0.0932)(0.1201)

5.2523
7.1932**8.5621***
7.4692***5.6391***6.4362***6.8101***
5.8486***5.7053***5.9301***5.4966***4.3273***4.3177***4.6215***4.2583***3.6365***3.6909***3.0877**3.2410**3.1927**3.7128**3.4750**3.5666**3.3242**SE(6.1052)(3.0436)(2.0222)(1.8242)(1.2724)(1.2525)(1.2936)(0.9468)(0.9134)(1.0194)(0.9156)(0.6396)(0.7809)(1.0845)(0.9194)(1.0198)(1.2174)(1.3314)(1.3798)(1.5780)(1.5643)(1.4570)(1.4092)(1.4991)8.91143.94544.12885.4115*
6.2473**
5.1192*
4.11404.8794**5.7051***5.6798***6.3542***
7.5580***7.1161***
6.8965***7.4148***7.0869***6.8701***
6.4613***6.2850***5.5214***5.1124***5.2397***4.5189***3.8956***SE(9.0977)(4.6285)(3.8366)(3.0671)(3.0297)(2.8726)(2.5694)(2.2147)(1.7802)(1.3635)(1.1582)(0.9717)(0.9734)(1.2307)(1.1759)(1.4052)(1.0844)(1.0276)(0.6905)(0.6465)(0.6595)(0.5017)(0.3989)(0.4142)0.00930.14050.2516
0.35620.3956
0.43630.51640.57970.59680.67550.68300.71320.72720.73690.74060.71720.72300.73300.73390.70660.7356
0.76580.77990.7700We use the sample period from 1987:7 to 1997:8. The estimated equation and method are explained in note 1 in Table 5-1.
Based on the AIC, we set the lag length

at 45. Standard errors and R squared are also presented in note 2 and 3 in Table

5-1.

29

Table 6-1: Results of Other Maturities: First subsample 1982:4-1987:6
M k
SE
SE
2 3
0.2235(2.1290)
3.2908(2.3717)1.3304
6
0.5711(1.8685)
2.4318(2.2723)2.700991.5726(1.8122)2.3374(2.0076)
3.5443*12
2.5154(2.0257)
1.6613(1.7119)
4.2977***
15 5.5272*** (1.9621)
0.2037(0.7972)
4.0075***
18 4.8898*** (1.5644)-0.0623(0.8279)
4.0765***
21 3.4335**(1.5936)-1.1017(0.8403)5.5629***24 4.3160**(1.7147)-0.1675(0.8367)
4.9135***
3 3-0.1298(2.3941)3.0494(2.1735)
2.438660.4341(1.9853)
2.3099(2.0454)3.3741*9
1.5430(1.8079)
2.1896(1.7856)
4.2477**122.3503(1.8688)
1.6133(1.5031)4.8333***15 5.4558*** (1.9718)
0.3685(0.8099)
4.2520***18 4.8527*** (1.5403)
0.0568(0.8294)
4.2106***21
3.0737*(1.6649)-0.8835(0.9478)5.5885***24 3.9636**(1.9743)-0.0797(0.9295)
5.1861***4 3-0.1382(1.5655)
2.6161*(1.5703)4.6399***60.3025(1.1374)
2.0319(1.2678)
5.5426***9
1.1053(1.1408)
1.8520*(1.0117)5.7744***12
1.6795(1.6036)1.4017*(0.8216)
5.6364***15 4.0225**(1.8282)
0.4354(0.5398)
4.6423***18 3.8168**(1.7147)0.3548(0.6255)
4.2569***21 5.2800*** (1.6982)
0.6111(1.0791)
4.1818***24 5.9129*** (1.7445)
1.1779(1.0518)
3.8939***5 3-0.1278(1.3202)2.7302(1.7156)
4.1831***
6
0.3284(0.8598)
2.1564(1.3706)
5.0934***90.9750(0.6910)1.9717*(1.1062)5.5031***121.2107(0.9697)
1.6108**(0.8049)5.5803***15 2.7682**(1.2211)0.8596*(0.4955)
4.9364***18 2.5056**(1.2014)0.9383**(0.4340)
4.8109***21 3.8752*** (1.1355)
1.1695*(0.6932)4.5104***24 4.4249*** (1.2516)
1.7734**(0.7179)
4.4833***SE(2.5818)(2.2175)(2.0708)(1.5374)(1.1410)(0.8638)(1.0170)(1.0203)(2.2172)(1.9926)(1.9324)(1.4999)(1.0578)(0.8247)(0.7880)(1.2142)(1.6091)(1.3923)(1.3099)(1.0787)(0.7646)(0.4836)(0.6033)(1.1007)(1.3322)(1.0802)(0.8798)(0.6799)(0.4462)(0.2968)(0.3228)(0.3167)-0.0057
0.02210.07640.14040.24300.24820.40170.35150.01630.05210.11540.16670.24040.23990.37460.31460.13420.28090.36630.38630.39470.35290.37370.29380.16730.38420.54030.60660.6242
0.63400.65300.6094

M
6

7

8

k
3
6
9
12
15
18
21
24
3
6
9
12
15
18
21
24
3
6
9
12
15
18
21
24

0.06520.86971.3479**1.41282.8413***3.3104***4.7300***4.8546***
0.02650.7933
1.52801.82364.1812***4.4088***5.3901***5.8580***0.03080.95141.73722.21404.7848***5.0678***6.6175***7.0047***SE(1.0860)(0.7741)(0.6662)(1.0230)(1.0002)(1.0388)(0.8647)(1.1252)(1.1555)(0.9318)(0.9418)(1.3310)(1.1008)(1.0025)(0.9877)(1.1002)(1.1687)(1.0688)(1.4434)(2.0369)(1.5503)(1.4423)(1.5045)(1.3130)

5.2898***3.9023***3.1258***2.2015***0.8557*0.36360.87871.6189**5.2406***3.8582**
3.1291**2.05020.0348-0.6574-0.41170.2971
5.2197***3.8443***3.0716***1.8142-0.3387-1.0287-0.1160
0.4221SE(1.3002)(1.0938)(0.8513)(0.7407)(0.4517)(0.3823)(0.6185)(0.6442)(1.3698)(1.5089)(1.3311)(1.3268)(0.9159)(0.8008)(1.0086)(0.9980)(1.0491)(1.2060)(1.0537)(1.2204)(0.8511)(0.8218)(1.1969)(1.0855)

5.7067***
6.0774***6.6059***6.5912***5.5741***
4.9175***4.6457***4.9559***5.9965***5.8461***6.2823***
6.1684***4.4766***3.7511***3.5513***3.2702**
7.0214***
6.6373***
6.6084***5.9770***4.2444***3.3024***
3.1465***2.5947*SE(1.2425)(1.0690)(0.8159)(0.7811)(0.6144)(0.5669)(0.4166)(0.6812)(1.6495)(1.2621)(1.0798)(0.9261)(0.7802)(0.5261)(0.5819)(1.3827)(1.5805)(1.2756)(1.3031)(1.1820)(0.9012)(0.6010)(0.4812)(1.4120)0.37730.52970.63510.63650.63750.62330.68110.6726
0.28640.32500.38840.38080.40980.40310.44550.4246
0.38230.44870.47690.41870.43680.41020.42570.3846

Notes:
Maturity years are indicated in column M. With respect to the estimate equation, see note 1 in Table 5-1. The AIC indicate that the lag numbers are 6 for M=2, M=3, M=4 and M=5, and 9 for M=6, M=7 and M=8.
Standard errors and R squared are explained in note 2 and 3 in Table 5-1.

30

Table 6-2: Results of Other Maturities: Second subsample 1987:7-1997:8
M k
SE
SE
2 3
5.2502**(2.4167) 18.7682***(4.5836)
5.13246 5.7342*** (1.3314) 14.6609***(2.9225)
4.5993
9 4.3007*** (1.6144) 15.4796***(2.6240)
1.287812 3.8949**(1.6886) 13.2378***(2.4917)4.010715
3.5088*(1.8947) 12.0880***(2.2723)5.8457
18 3.2636**(1.5751)
9.1853***(2.8298)
5.9317*
21 3.2972**(1.3055)
9.0371**(3.7654)3.024724 4.1322*** (1.1341)
5.8424(3.6146)
1.70273 3
4.1116**(1.9979) 14.8335***(3.8505)
4.3142
6 4.3318*** (1.1584) 11.7181***(2.3175)
4.468493.3119**(1.4593) 12.2526***(1.8399)2.250612
3.0066*(1.6031) 10.4451***(1.6623)4.5019*152.6829(1.7152)
9.8607***(1.6144)5.6193*18
2.5374*(1.3722)7.5922***(2.2001)
5.1385**21 2.6053**(1.1646)
7.5167**(2.9972)
2.8036*24 3.2919*** (1.0239)
4.9733*(2.8747)1.61034 3
2.9070*(1.6249) 12.3539***(3.3098)
4.03036 3.3913*** (0.8821)
9.5302***(1.9199)4.3095
9 3.0143*** (1.0526)
9.5995***(1.4295)
2.648412 2.8070**(1.1270)
8.1013***(1.2485)
4.3282*15 2.4773**(1.1956)7.8086***(1.2757)
5.0395*18 2.7186*** (1.0327)
5.5720***(1.7868)
4.3722**21 2.7681*** (0.8808)
5.4429**(2.4212)2.3255*24 3.1179*** (0.7028)
3.6346(2.4019)1.42485 32.2813**(0.9309) 11.8341***(2.7838)
5.11626 2.7273*** (0.5100)
9.1403***(1.8357)
4.6330*9 2.8393*** (0.5217)
8.4837***(1.3876)
3.518912 3.0165*** (0.6069)
6.5085***(1.1770)
4.9552***15 2.8005*** (0.6668)
6.2371***(1.4042)5.0281**18 2.9371*** (0.5715)
4.3051**(2.0257)
4.4131***21 2.7646*** (0.4883)
4.7046*(2.5516)2.6948***24 2.8991*** (0.3724)
3.5941(2.5135)
1.8634*SE(5.8555)(4.0287)(4.8127)(3.9228)(4.1187)(3.0496)(2.1858)(2.2495)(4.8023)(3.2420)(3.4339)(2.6617)(2.9966)(2.3216)(1.5939)(1.5082)(4.1165)(2.9262)(2.9561)(2.2366)(2.6364)(1.8822)(1.3454)(1.3208)(3.4493)(2.4197)(2.4335)(1.8631)(1.9705)(1.4158)(0.9739)(1.1265)0.28400.41670.45670.4852
0.49310.42050.43820.49920.27330.39790.44640.48550.49610.41810.43490.4876
0.25700.39250.46570.51480.52480.46860.49420.54930.26430.4044
0.49680.56860.58080.55420.56570.6156

M
6

7

8

k
3
6
9
12
15
18
21
24
3
6
9
12
15
18
21
24
3
6
9
12
15
18
21
24

2.0565**2.4429***2.5940***2.7231***2.5471***2.6565***2.4680***2.5810***2.1077**2.5370***2.7138***2.8065***2.6359***2.7117***2.5015***2.5895***1.9153**2.4393***2.6413***2.7214***2.5523***2.6349***2.4432***2.5210***SE(0.8311)(0.4649)(0.3914)(0.4720)(0.5185)(0.4448)(0.3947)(0.2946)(0.8362)(0.5458)(0.3065)(0.2554)(0.2583)(0.2115)(0.2145)(0.1473)(0.7653)(0.5526)(0.2996)(0.1839)(0.1512)(0.1271)(0.1293)(0.1023)

12.2919***9.4375***8.5889***6.5113***6.2903***4.3450**4.8606*3.754010.5894***
7.9864***
7.1149***5.1998***5.0677***3.4654*4.1411*3.30159.2315***6.9206***6.1785***4.5292***4.4206***3.0441**3.6898**3.1393*SE(2.9835)(1.9918)(1.5150)(1.2850)(1.5432)(2.2012)(2.6651)(2.6477)(2.6729)(1.7167)(1.3283)(0.9830)(1.2830)(1.8803)(2.2276)(2.2164)(2.2536)(1.3900)(1.0730)(0.6535)(0.9581)(1.4707)(1.7743)(1.7258)

4.91114.8532**4.2230**5.6837***5.7866***5.1107***
3.2700***2.1851***
4.29264.7572**
4.7636**6.6250***6.6284***
5.9475***4.1860***2.9161***
3.94364.7430*4.9221**
7.1313***7.0047***
6.1575***4.6259***3.4501***SE(3.4142)(2.2961)(2.0623)(1.4271)(1.4887)(1.0389)(0.6325)(0.6879)(3.4369)(2.4145)(1.9086)(1.0767)(1.0600)(0.8117)(0.7889)(0.4684)(3.6479)(2.7776)(2.1041)(1.1553)(1.1416)(0.8438)(0.7154)(0.5163)

0.26180.40750.51310.58940.60810.57950.5766
0.61820.26360.42910.56030.66080.68850.67120.65850.69790.2566
0.43340.57770.69200.72020.71340.70950.7505

Notes:
Maturity years are indicated in columns M. With respect to the estimate equation, see note 1 in Table 5-1. The AIC indicate that the lag numbers are 48 for M=2 and M=3, 47 for M=4, and 45 for M=5, M=6, M=7 and
M=8. Standard errors and R squared are explained in note 2 and 3 in Table 5-1.

31