Marginal q and Firms’ Capital Investments: Evidence
from Time Series Data of Japanese Manufacturing
Industries∗
Masafumi KOZUKA †‡Abstract
In this paper, we verify the predictability of marginal q on firms’ capital investments. We compare Granger’s causality of four manufacturing industries with the
LA-VAR model and Vector Error Correction Model(VECM). We obtain the empiricalresults that the null hypothesis of no Granger’s causality from marginal q to investments is accepted for the chemical industry and iron-steel industry, and it is rejected
for the transportation equipment industry. For the product machinery industry, null
hypothesis is rejected with the LA-VAR model, but accepted with VECM; it is notrobust result. These results indicate that the chemical and iron-steel industry, withhigher uncertainty and irreversibility, could not adjust their capital investments in
response to the fluctuation of Tobin’s q, while the transportation equipment industry
could do so. Following the analytical implications by earlier theoretical studies, it isconsidered that uncertainty and irreversibility restrain their capital investments, or
firms with uncertainty and disposal cost do not invest in equipment because of lower
Tobin’s q than the threshold value. Thus, the role of uncertainty and irreversibility isimportant for predicting capital investments by Tobin’s q.
Keywords: marginal q; Granger’s causality; irreversibility; uncertainty
JEL Classification Numbers: C32, E22∗ The author wishes to thank Toshiki Jinushi(Kobe University) and Shingo Umino(Kochi University) for
their valuable comments. The author also thanks Masaya Ishikawa (Tokyo Keizai University) for his valuable suggestions at the 2014 Autumn Annual Meeting of the Japan Society of Monetary Economics. This
work was supported by JSPS KAKENHI Grant Number 25380417, Grant-in-Aid for Scientiﬁc Research(C).
† Faculty of Policy Studies, University of Marketing and Distribution Sciences, 3-1 Gakuen Nishi-machi,
Nishi-ku, Kobe city Hyogo, 6512188, Japan‡ Research Fellow, Graduate School of Economics, Kobe University, 2-1 Rokkodai-cho, Nada-ku, Kobecity Hyogo, 6578501, Japan1

1

Introduction

Tobin’s q, which came to light after Tobin’s publication(1969), is regarded as a major
factor in the decision-making of ﬁrms’ capital investments. Tobin’s q summerlized in several
textbooks on macroeconomics1 . Tobin’s q is calculated by ”ﬁrms’ value evaluated in thestock market” divided by ”repossession value of ﬁrms’ stock,” and this is called ”averageq.” This theory shows that the ﬁrm should increases its investments when q is larger than1, and decrease them when q is smaller than 1.
In contrast, we can obtain Tobin’s q from the Lagurange multiplier when we solve the
proﬁt maximization problem of a ﬁrm with inﬁnite horizons considering the adjustment
cost. When this multiplier is larger than 1, the ﬁrm performs investments. The Lagurange
multiplier implies a shadow price: the variation width of the objective function of thepresent discount value of the ﬁrm, with the increase of accumulation of capital stock.
Thus, this multiplier is called ”marginal q.”
Hayashi(1982) shows that average q and marginal q are equivalent assuming that production and cost are homogeniously linear and that the price of production goods andcapital stock is equal. Following Hayashi(1982), several studies have veriﬁed ﬁrms’ proﬁt
and investment behaviors considering average and marginal q.
However, ﬁrms cannot adjust their capital investments and accumulation of stock immediately even if Tobin’s q ﬂuctuates; ﬁrms adjust them after a few periods. In other words,
we can predict the ﬁrms’ future investments by observing the ﬂuctuation of q. In order toanalyze the trend of macroeconomics, it is important to forecast the investment behaviors
of ﬁrms or industries observing their qs.
Obviously, ﬁrm’s capital investments are inﬂuenced by other factors: for example, irreversibility and uncertainty. When a ﬁrm’s equipments has long periods of duarability,or when the marginal cost of investments is high, the ﬁrm faces high irreversibility. According the theoretical work by Caballero(1991), such a ﬁrm with high irreversibility tends
to reduce its investment by uncertainty considering certain conditions. And the study by
1 For example, please see Mankiw(2009), Romer(2005) and Obstfeld and Rogoﬀ(1996).

2

Dixit and Pindyck(1994) shows that threshold values of Tobin’s q will rise as uncertainty
increases. When Tobin’s q does not reach the threshold value, the ﬁrm does not carryout investments, considering disposal cost; therefore, uncertainty restrains the ﬁrms fromperforming the investment further by the ”option to wait.”
Thus, the ﬁrms’ capital investments, especially in the material industries with largesized equipments, might respond slowly when their Tobin’s q increases. The empirical
study by Ogawa and Suzuki(2000) shows that the materials industry in Japan signiﬁcantly
restrains the investments in response to the rise of uncertainty of demand, and this evidence
is consistent with the theoretical implications of previous studies such as Caballero(1991).
The empirical analysis performed by Honda and Suzuki(2000) shows that, in the sense of
Dixit and Pindyck(1994), the threshold value of q for electric machiney is higher than others
in Japan, employing a logistic curve.
Previous studies on capital investments and Tobin’s q utilize ﬁrms’ or industries’ micro data, which is a cross-section or panel with short periods. In contrast, only a few
studies perform time series analysis focusing on investment and Tobin’s q theory. Matsubayashi(1995) shows that uncertainty restrains ﬁrms from carrying out investments inboth Japan and the US, and that uncertainty tends to be caused by instability of ﬁnancial
markets and by supply shock in Japan. Matsubayashi(2011) performs time series analysis
with the structural VAR model, and states that depreciation of the Japanese Yen has positive eﬀects on expected proﬁtability, Tobin’s q, and investments in the machinery sector.
The empirical study by Hori and Ando(2002) also utilizes Japanese time series data ofsales, which is regarded as the proxy of Tobin’s q, investments, call rate and liquidity asset.
In this study, they perform empirical analysis with the Lag-Augmented VAR (LA-VAR)
model developed by Toda and Yamamoto(1995) in order to verify the eﬀects of liquidity
asset on investments and sales. This study shows that liquidity assets are Granger causedby sales, investments by liquidity asset and sales by investments; this evidence shows thatthe ﬂuctuation of liquidity asset is caused by imperfect capital asset market and that thetransmission mechanism of monetary policy does not work suﬃciently.

3

Hori and Ando(2002) and Matsubayashi(1995) are important studies in which time series
analyses of capital investments are performed, however, these studies employ aggregate
data. Matsubayashi(2011) utilizes time series data of several sectors in Japan, however, thisstudy focuses on the eﬀects of exchange rate on capital investments and Tobin’s q, and does
not discuss the diﬀerences in the eﬀects or predictability of Tobin’s q on ﬁrms’investments
in detail2 . As Ogawa and Suzuki(2000) and other studies have indicated, the responseof investment to Tobin’s q and other factors, irreversibility and uncertainty, diﬀers byindustries. Figure1 and 2 show the plots of investment-capital ratio (IK) and marginal q(MQ) of several manufacturing industries. The average values of IK and MQ are shownin Table 1. They indicate that trends of investments and marginal q diﬀer by industries.
The chemical and iron-steel (the material industries) industries tend to have lower IK
than production machinery and transportation equipments including motorvehicles (themachinery industries). In contrast, chemical and production machinery industries havehigher M Q and that of iron-steel industries are patricularly low.
Then, in this paper, we verify the predictability and inﬂuence of Tobin’s q on capital investments of the Japanese manufacturing industry using the LA-VAR model and the Vector
Error Correction Model (VECM). We employ the VECM when cointegration is detected.
In the LA-VAR model, we do not have to consider the existence of a cointegration vector
between included variables. But we have to re-examine Granger’s causality considering
cointegration because linear combination may consist of included variables in the long run
theoretically. Here, we utilize Japanese time series data of four industries: chemical, ironsteel, (material industries), production machinery and transportation equipments including
motorvehicles (machinery industries), and compare them, considering the implications of
Ogawa and Suzuki(2000).
Section 2 presents the data description and empirical analyses. Ssection 3 is the discussion, and in section 4, we draw out our conclusions.

2 According to Matsubayashi(2011), impulse response functions from marginal q to investments are
signiﬁcantly positive in manufacturing and wholesale.

4

2

Empirical Analysis

2.1

Data

In this paper, we utilize the data of four manufacturing industries: chemical, iron-steel,production machinery and transportation equipment3 .Some previous studies employ dataof manufacturing industries, and this study also does the same. We estimate the 4-variable
LA-VAR model that consists of marginal q(M qt ), investments over capital in the lastperiod(It /Kt−1 ), real eﬀective exchange rate(REERt ) and long-term interest rate(LRt )4 .
Here, we divide investments by capital stock. The sample period is 1980:Q2-2005:Q1.
Marginal q implies a ﬁrm’s present value, and it can be interpreted as the ﬁrm’s present
discount value of proﬁtover the future periods. We obtain time series data of marginal q by
calculating under certain assumptions. We show the procedure of computing the marginal
q in the Appendix.
The sample of the Company Statistics Seasonal Report is revised every 2nd quarterand thus its continuity is not maintained. Moreover, stock data is constructed by amassing
ﬂow data. And therefore, we have to adjust the data following the methods introduced by
Ogawa (2003).
First, we calculated the amount of increase from every 1st quarter and 2nd quarter.
And we assumed the number of the sample increased equally every quarter within the past
1 year. For example, when the amount that increases from the 1st and 2nd quarter in 1990
is N, we assumed the sample increased by N/4 every period in ﬁscal 1989: it increased by
N/4 in ﬁscal 1989: 2Q, 1989:3Q, 1989:4Q and 1990:1Q. Then, we multiplied the assumed
amount of increase and ﬂow per one ﬁrm, and added it to the total ﬂow of each period.

3 The electric machinery industry is considered to play an important role. However, the kinds of ﬁrms
belonging to this industry, namely the deﬁnition of this sector, altered in the sample periods we set.
And thus, time-series data of electric machinery does not have continuity. Therefore, we exclude electricmachinery here.
4 In this study, we utilize quarterly data of the depreciation rate, total depreciation, investments andcapital stock from the Company Statistics Seasonal Report published by the Ministry of Finance of Japan.
However, we acquire the data of deﬂator of investment goods from the Statistics National Account (93SNA)
and earning rate of 10-year government bond, an index of the long-term interest rate, from the International
Financial Statistics(IFS). The interest rate is deﬂated by the deﬂator of investment goods. We utilize dataof the real eﬀective exchange rate from the Bank of Japan’s ﬁnancial statistics.

5

In order to obtain the real value of capital stock, we calculated the book value in
1980:Q1, the start point of the sample5 . According to the National Wealth Survey of 1970,
the average duration (vintage) of manufacturing industries is 7 years. An economic white
paper (the Cabinet Oﬃce of the Japanese Government 1999) shows that vintage in thecurrent period (V int ) with annual data is deﬁned by the following equation:
V int = (1 − V int−1 )(Kt−1 − REt ) +

It
/Kt .
2

(1)

REt denotes removal of capital at period t. By calculating with the rate of retirementof equipment printed in the Quarterly Report on the National Account of 1980 (Economic
Planning Agency 1981), the vintage of manufacturing industries in 1980 was 8.3 years.
Then, we maintained that the book value of capital stock in 1980:Q1 is the price of 8.3
years before: in 1971:Q4.
We calculated the data series of the real value of capital stock after 1980:Q1 using theperpetual inventory method. We calculate capital stock by the following equation:
Kt = (1 − δ)Kt−1 + It .

(2)

δ denotes the depreciation rate. Here, investments are deﬂated by the current price.
This enables us to obtain data series of the real value of capital stock after 1980:Q16 .
Investments and marginal q are seasonally adjusted by X-12 ARIMA.

2.2

LA-VAR model

The LA-VAR (Lag-Augmented VAR) model was developed by Toda and Yamamoto(1995).
With this procedure, we can estimate the VAR model without considering the degree of
integration of variables in the model, and the model speciﬁcation does not depend on theexistence of cointegration relationship. Here, we show the details of this procedure.
We suppose that vector xt contains two variables x1t and x2t , and xt is written as
xt = (x1tx2t )′ .

5 The details of this method are introduced in Section 3C in Ogawa et al.(1996).
6 The data series of 93SNA is available only after 1980. And thus we calculate the vintage with 68SNA,
which is available before 1980, and connect to 93SNA at 1980:Q1.

6

Then, we set the 2-variable VAR(p) model as
xt = A0 +p∑

Ai xt−i + ut .

(3)

i=1

This ut is an error term whose expectation is 0. And p is the optimal length of lags
selected by certain criterion: for example, SBIC or AIC.
x1t and x2t obey the integrated process with order d at most. Then, we transform the
VAR model into the following equation:
xt = A0 +p+d∑

Ai xt−i + ut

(4)

i=1

When the VAR model is equation (2), estimated coeﬃcients have consistency regardlessof the order of integration and the existence of cointegration. Therefore, we can verify
Granger causality based on equation (2).

2.3

Empirical Results by LA-VAR modelFirstly, we perform a unit root test of each variable. Here, we employ the Dickey=Fuller
GLS test (Elliott, Rothenberg and Stock, 1996). The results are shown in Table 2. They
indicate that these variables are integrated order 1 at most.
Next, we estimate the VAR model. Using Equation (1) considering the time trend, theoptimal length of lags of all industries is 1 following SBIC. Therefore, the length of lags inEquation (2) is 2 for all according to the LA-VAR method.
Then, we estimate Equation (2) and verify the Granger’s causality for each industry.
Granger’s causality of each industry is shown in Table 3. In Table 3, we show how eachvariable Granger-causes only marginal q and investments. Here, we focus on the ﬁrms’
investments but not on the ﬂuctuation in the ﬁnancial markets. In line with our aims, thelong-term rate and exchange rate are regarded as exogenous. And thus we do not observe
the predictabilityon these variables. Table 3 shows that it is shown that marginal q (M qt )does not Granger-cause investments (It /Kt−1 ) in the chemical and iron-steel industries.

7

And with others, empirical results show that marginal q Granger-causes investments. The
signiﬁcance level is 10 percent here7 .

2.4

Vector Error Correction Model and Empirical Results

Here, we perform a cointegration test with the Maximum eigenvalue test by Johansen (1988)
and Johansen and Juselius (1991) ﬁrstly. We suppose that the linear trend is containedin the VAR and cointegration vector. But, following the results of unit root testshownin Table 2, for IK in the iron-steel industry, the null of unit root is rejected with a 5 %signiﬁcance level. However, KPSS test (Kwiatkowski et al. 1992) statistics considering
constant and linear trends indicate that IK in the iron-steel industry is I(1) variables with
a 5% signiﬁcance level8 . Therefore, we regard these variables as I(1).The results of thetests are shown in Table 4. It indicates that the null hypothesis of no cointegrating rank
cannot be rejected in the material industry (chemical and iron-steel). In contrast, the nullof no cointegrating rank can be rejected in non-material industries (production machineryand transportation equipment), and it is shown that these industries have one cointegration vector. The estimated cointegrating vector is shown in Table 5, and it indicates theestimated coeﬃcient of Tobin s marginal q is positive and signiﬁcant in each industry in
non-material industries9 .
Then, we verify Granger s causality of Tobin’s marginal q to investment. Considering
the results of the maximum eigenvalue test, we adopt the diﬀerence model for the material
industry and the VECM for the non-material industry.

The results of Granger’s causality

test are shown in Table 6. It is shown that the null hypothesis of no causality cannot
be rejected in the material industry. And for the transportation equipment, marginal
q Granger-causes investment-capital ratio. But for the production machinery, the null
7 In this footnote, we mention the causality between other variables. Long-term rate Granger-causes
marginal q only in production machinery, and investments cause marginal q in transportation equipments.
The exchange rate does not Granger-cause investments and marginal q in all industries. In relation to theeﬀects of exchange rate, the results we obtain are quite diﬀerent from those of Matsubayashi(2011). Modelspeciﬁcation is then considered to be the main cause of diﬀerence.
8 The KPSS test statistics are 0.171 for level and 0.088 for 1st diﬀerence. The critical values are 0.216(1%), 0.146 (5%) and 0.119 (10%) considering the constant and linear trend.
9 According to the results in Table 5, the coeﬃcient of the real long-term rate is not signiﬁcant in eachindustry. And the sign restriction of the real eﬀective exchange rate is not satisﬁed, either.

8

hypothesis cannot be rejected. Thus, only the empirical result for production machinery is
not consistent with that of the previous section10 .
Here, there seems to be a tendency that marginal q of the machinery industry havepredictability for their own investments signiﬁcantly. In the next section, we focus on thecausality from marginal q to investments and discuss them.

3

Discussion

In the previous section, we veriﬁed the predictability of Tobin’s marginal q on investments.
And in the transportation equipments industry, marginal q Granger-causes investments;
however, it does not in materials. And in the production machinery industry, it is ahown
that marginal q Granger-causes investments with the LA-VAR model, but it does not with
the VECM. In this paper, we focus on how marginal q Granger-causes investments, as we
mentioned in Section 1. Here, we discuss the causes of these diﬀerences.
As we showed in Section 1, Caballero(1991) developed the theoretical model in whichﬁrms with high irreversibility restrain their investments by uncertainty of demand. And
Dixit and Pindyck(1994) showed that a ﬁrm does not carry out investments with uncertainty
and disposal cost if Tobin’s q does not reach the threshold value.
Figure 3 shows the uncertainty of demand, standard deviation of sales, of each industry
from 1980 to 2004. In Fig.3, it is shown that the material industry, chemical industry andiron-steel industry, face higher uncertainty. And Figure 3 also shows that uncertainty ofdemand is especially low in transportation equipment.
As the study by Ogawa and Suzuki(2000) states, the material industry tends to have highirreversibility. Following Honda and Suzuki(2000), we calculate the periods of durability, aproxy of irreversibility, of each industry. The details are shown in Table 7. It shows that theperiods of durability are 12.96 years in production machinery, 11.976 years in chemical and15.55 years in iron-steel. In contrast, it is 9.448 years in transportation equipment. Thus,
transportation equipment is relatively shorter; that is, iron-steel, chemical and production
10 The exchange rate Granger-causes investments only in chemical, and marginal q only intransportationequipments. In this speciﬁcation, we can show the eﬀects of exchange rate in some induatries.

9machinery have higher irreversibility whereas transportation equipment has lower.
Considering these facts, we can infer two causes of our empirical results. The ﬁrst isthat high uncertainty and high irreversibility restrain investments in material industries,
as shown in Figure 1 and Table 1. And it is also shown that the production machinery
is a little higher than transportation equipments. The second is that high uncertainty
drives the threshold value of q higher than marginal q in two material industries withhigh disposal costs. In any case, it is diﬃcult for ﬁrms to carry out their investments
in response to ﬂuctuation of marginal q. Therefore, the marginal q does not Grangercause investments in material industries; it causes low predictability of marginal q into thecapital investments. On the other hand, following the empirical results in the previous
section, Granger’s causality from marginal q to investment might exist but it is not robustin the production machinery industry. It can be thought that a little high uncertainty andlong durable periods, high irreversibility, cause the weak evidence of causality.
The empirical results obtained in this study are consistent with Ogawa and Suzuki(2000);it shows that uncertainty caused the restraint of the material industry whose irreversibility
is high.

4

Conclusion

In this paper, we compared the Granger’s causality of four manufacturing industries utilizing the LA-VAR model and VECM. We focused on Granger’s causality of marginal q toinvestments. Considering the empirical results obtained in this study, the following points
were elucidated. Firstly, Granger’s causality from marginal q to investment does not exist
in the material industry whereas marginal q Granger-causes investment in the transportation equipment industry. Secondly, in the production machinery with high irreversibility,
Granger’s causality from marginal q to investment might exist, but it is not robust.
Following Caballero(1991) and Dixit and Pindyck(1994), we explained the backgroundof these empirical results; uncertainty and irreversibility restrain their investments, or ﬁrms
with uncertainty and high disposal cost do not invest in equipments if Tobin’s q is below

10

the threshold value. Here, we showed that the roles of uncertainty and irreversibility areimportant for predicting investments by Tobin’s q; Granger’s causality of Tobin’s q toinvestments is limited in industries with high irreversibility and high uncertainty.
However, some problems remain. The ﬁrst is the model speciﬁcation. We have to utilize
other variables related to ﬁrms’ investment behavior. Second is the empirical methods.
In this paper, we utilized LA-VAR and performed the veriﬁcation paying attention to
Granger’s causality. As a future work, performing empirical analysis based on the impulse
response function will bring other contributions.

Appendix: Tobin’s Marginal q
In the Appendix, we show the method for calculating marginal q. The model of marginalq implies a relationship between investments and their shadow price derived from theﬁrms’ proﬁt maximization problem. In this paper, we used the method introduced in
Ogawa(2003).
The marginal q (M qt ) is the discount value of marginal proﬁt additional investments,
and it is explained as follows:M qt =∞∑
1E[
βt+j (1 − δ)j πt+j .]
t
PtI
j=0

(5)

Here, PtI is the price of investment goods, πt is proﬁt rate, maximum proﬁt over capitalstock, at period t, βt+j is the discount factor at t + j ，δ is the depreciation rate and Et is
expectation operator with information set available at t. And when rt is interest rate, βt+j
is deﬁned as
βt =

1
.
1 + rt(6)Here, we assume that rt and πt obey the independent random walk process, and they
can be written as
rt+1 = rt + µt

11

and
πt+1 = πt + νt .
We can rewrite Equation (5) as follows:M qt =

πt 1 + rt.
PtI rt + δ

We assume δ is 0.0772, which is the calculated value for all industries shown in Hayashi
and Inoue(1991)．

12

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14

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15

Fig.1 InvestmentInvestment-Capital Ratio
0.100000
0.080000
0.060000
0.040000
0.020000
0.000000-0.020000-0.040000-0.060000

1980Q2
1981Q1
1981Q4
1982Q3
1983Q2
1984Q1
1984Q4
1985Q3
1986Q2
1987Q1
1987Q4
1988Q3
1989Q2
1990Q1
1990Q4
1991Q3
1992Q2
1993Q1
1993Q4
1994Q3
1995Q2
1996Q1
1996Q4
1997Q3
1998Q2
1999Q1
1999Q4
2000Q3
2001Q2
2002Q1
2002Q4
2003Q3
2004Q2
2005Q1
2005Q4-0.080000

Chemical IK

Iron-Steel IK

Production Machine IK

Transportation and Motorvehicle IK

Source: Company Statistics Seasonal Report (The Ministry of Finance, Japan)
Fig.2 Marginal q6.000000

5.000000

4.000000

3.000000

2.000000

1.000000

0.000000

1980Q1
1980Q4
1981Q3
1982Q2
1983Q1
1983Q4
1984Q3
1985Q2
1986Q1
1986Q4
1987Q3
1988Q2
1989Q1
1989Q4
1990Q3
1991Q2
1992Q1
1992Q4
1993Q3
1994Q2
1995Q1
1995Q4
1996Q3
1997Q2
1998Q1
1998Q4
1999Q3
2000Q2
2001Q1
2001Q4
2002Q3
2003Q2
2004Q1
2004Q4
2005Q3-1.000000

Chemical MQ

Iron-Steel MQ

Production Machine MQTransportation and Motorvehicle MQ

Source: Company Statistics Seasonal Report (The Ministry of Finance, Japan)

Table 1

Average values of IK
Chemical

Production Transportation
Machineand Motorvehicle
0.015
0.035
0.045

Iron-Steel

0.031

Average values of MQ
Chemical

Production Transportation
Machineand Motorvehicle
0.861
2.452
1.817

Iron-Steel

2.568

Fig.3 Uncertainty (Standard Deviation of Sales)
0.16

0.14

0.12

0.1

0.08

0.06

0.04

0.02

ChemicalIron-Steel

Production Machine

2005Q2

2004Q2

2003Q2

2002Q2

2001Q2

2000Q2

1999Q2

1998Q2

1997Q2

1996Q2

1995Q2

1994Q2

1993Q2

1992Q2

1991Q2

1990Q2

1989Q2

1988Q2

1987Q2

1986Q2

1985Q2

1984Q2

1983Q2

1982Q2

1981Q2

1980Q2

1979Q20Transportation and Motorvehicle

Source: Company Statistics Seasonal Report (The Ministry of Finance, Japan)

Table 3 Granger Causality with LALA-VAR model (F(F-test Statistics)

Chemical (Number of lags=2)
F-test stat.
X2
DF=(2,88)
I/K
MQ
MQ
0.848
142.416 ***X1(0.432)(0.000)
REEX
0.923
0.967
(0.401)(0.385)Iron and Steel (Number of lags=2)
F-test stat.
X2
DF=(2,88)
I/K
MQ
MQ
2.293
470.794 ***X1(0.107)(0.000)
REEX
0.655
0.592
(0.522)(0.556)
Production Machinery (Number of lags=2)
F-test stat.
X2
DF=(2,88)
I/K
MQ
MQ
8.973
***
59.699***X1(0.003)(0.000)
REEX
0.170
1.125
(0.844)(0.330)Transportation Equipments (Number of lags=2)
F-test stat.
X2
DF=(2,88)
I/K
MQ
MQ
6.811
***
56.353***
X1(0.002)(0.000)
REEX
0.712
2.200
(0.493)(0.117)(Note) Null hypothesis: X1 does not Granger cause X2.
When DF=(2,88) , critical values of 5% significant level is 3.1065.
Numbers in the parentheses are p-values.
*** denotes significant at 1% and ** denotes 5％.

Table 4

Cointegration test (Max eigenvalue test)<Chemical>
Null Hypothesis
Rank=0Rank=1 at most
Rank=2 at most
Rank=3 at most

Eigenvalue
0.190
0.143
0.056
0.043

Test stat.
20.6734
15.08533
5.619892
4.313582

Prob.
0.59850.62680.97
0.6964<Iron-Steel>
Null Hypothesis
Rank=0Rank=1 at most
Rank=2 at most
Rank=3 at most

Eigenvalue
0.228
0.143
0.082
0.029

Test stat.
25.31877
15.10914
8.356175
2.893646

Prob.
0.26820.6246
0.78850.8889Test stat.
31.114
16.21
7.649
3.759

Prob.
0.066*
0.526
0.852
0.777

Test stat.
31.81815.08313.8264.883

Prob.
0.054*
0.627
0.266
0.613

<Machinery>
Null Hypothesis
Eigenvalue
Rank=00.272
Rank=1 at most
0.152
Rank=2 at most
0.075
Rank=3 at most
0.038
<Tanspotation Equipments>
Null Hypothesis
Eigenvalue
Rank=00.277
Rank=1 at most
0.143
Rank=2 at most
0.132
Rank=3 at most
0.049

(Note) * denotes rejection of the hypothesis at the 10% level. We utilize

MacKinnon-Haug-Michelis (1999) p-values. These critical values of 5%
are 32.118(rank=0), 25.823(rank=1 at most), 19.387(rank=2 at most)and 12.518(rank=3 at most).

Table 5 Cointegration Vec tor<Machinery>
MQ
REEX
Estimator-0.045-0.0002
Standard error
0.008
0.00012LR-0.0001
0.0014<Tanspotation Equipments>
MQ
Estimator-0.155
Standard error
0.036

LR
0.004
0.003

REEX
-0.0009
0.0004

Table 6 Grange r Cau sality
Iron and Steel (1st difference with lag=1)
F-test stat.
X2
DF=(2,91)
IK
MQ
X1
MQ
0.169
(0.682)REEX
0.350(0.555)
0.689
Chemical (1st difference with lag=1)
F-test stat.
X2
DF=(2,91)
IK
MQ
X1
MQ
0.348
(0.556)REEX
4.340(0.040)** 0.614(Note) Null hypothesis: X1 does not Granger cause X2.
Numbers in the parentheses are p-values.
*** denotes significant at 1% .
Production Machinery (VECM with lag=1)
Chi-square test stat.
X2
DF=1
IK
MQ
X1
MQ
0.192
(0.661)
REEX
0.003(0.958)0.696
Transportation Equipments (VECM with lag=1)
Chi-square test stat.
X2
DF=1
IK
MQ
X1
MQ
5.642
(0.018)***
REEX
0.075
(0.785)
4.014(Note) Null hypothesis: X1 does not Granger cause X2.
Numbers in the parentheses are p-values.
*** denotes significant at 1% .

(0.409)(0.404)(0.404)(0.045)**

Table 7 Period of Durability

Period of Durability (Proxy of
Irreversibility)(industry)
ChemicalIron and Steel
MachineryTransportation and Motorvehicle

Industry(years)11.976
15.55
12.963
9.448

Material
NonMaterial

Source: Company Statistics Seasonal Report (The Ministry of Finance, Japan)