Exchange Rate, Marginal q and Investment Behaviorof Small and Medium-Sized Enterprises in Japan:Time Series Evidences of Manufacturing Industries

Masafumi Kozuka
March 2015
Discussion Paper No.1515

GRADUATE SCHOOL OF ECONOMICS
KOBE UNIVERSITYROKKO, KOBE, JAPANExchange Rate, Marginal q and Investment Behavior of Small andMedium-Sized Enterprises in Japan: Time Series Evidences ofManufacturing Industries
Masafumi Kozuka
Faculty of Policy Studies, University of Marketing and Distribution Sciences
3-1, Gakuen-Nishimachi, Nishi-ku, Kobe City, Hyogo, 6512188, JapanandResearch Fellow, Graduate School of Economics, Kobe University
2-1, Rokkodai-cho, Nada-ku, Kobe City, Hyogo, 6578501, JapanAbstract
In this paper, we investigate Granger’s causality among the exchange rate, Tobin’s
marginal q, and investment-capital ratio with quarterly data on firms categorized small andmedium-sized enterprises (SMEs) in Japan. We utilize the data of following industries:
chemical, iron and steel, production machinery, electric machinery and equipment,
automobile and accessories and all manufacturing. The empirical results we obtain show thatthe null hypotheses of no Granger’s causality from the exchange rate to other variables,investment and marginal q, are accepted in all industries. The reason is the lower percentageof export by SMEs. Thus, it is considered that the effects of Abenomics on SMEs are limited,
and that other kinds of reflation measures for SMEs are needed.
Keywords: marginal q; small and medium-sized enterprises; LA-VAR model;
irreversibility; exchange rate
JEL Classification Numbers: C32, F22



Any remaining errors are my responsibility. This work was supported by JSPS KAKENHI(Grant Number 25380417, Grant-in-Aid for Scientific Research (C)).
E-mail: Masafumi_Kozuka@red.umds.ac.jp.
11. Introduction
Small and medium-sized enterprises (SMEs) in Japan account for 99.7% of Japanesefirms. The share of added value produced by SMEs is 43.1%, and number of regular
employee in SMEs is 62.7% of all (Small-Medium Enterprises Agency 2014)1. Thus, it canbe supposed that SMEs in Japan play an important role in the Japanese economy, andverification of the characteristics of SMEs’ investment behavior is a significant task.
In Japan, it is said that firms’ business has recently recovered with depreciation of theJapanese Yen (JPY) as a result of Abenomics, the economic policies of the Abe cabinet. And,
if so, it can be considered that depreciation of the Japanese currency drives firms’ Tobin’s q
and investment in a positive direction. Here, as a factor which has certain effects oninvestment, we have to focus on the exchange rate. Figure 1 shows the scatter plots of realeffective exchange rate and investment or Tobin’s marginal q of manufacturing industry
categorized SMEs. And Figure 2 shows those of non-manufacturing. The sample period is
1995:Q2 - 2010:Q1. They indicate that depreciation of JPY and growths of investment ormarginal q occur simultaneously in the case of manufacturing; however, it cannot be foundwith the data of non-manufacturing. It seems that exchange rate has certain effects on
investment and marginal q, at least, in small medium-sized manufacturing firms.

On the other hand, it is pointed out that SMEs might have not been influenced byAbenomics. In which case, is there an effect of the exchange rate on investment and Tobin’s qin SMEs? And can the exchange rate forecast the trend of SMEs’ investment and Tobin’s q?
In this paper, we verify Granger’s causality with the lag-augmented VAR (LA-VAR)
model and quarterly data on small and medium-sized manufacturing enterprises: chemical,
iron and steel, production machinery, electric machinery and equipment, automobile andaccessories and all manufacturing. Here, we utilize three variables: real effective exchange
1

The English version is downloadable from following URL:

http://www.chusho.meti.go.jp/pamflet/hakusyo/H26/download/2014hakusho_eng.pdf .
2rate (REER), marginal q (hereafter, Mq) and investment-capital ratio (investment over capital,I/K).
In section 2, we perform the empirical analyses and discussion. And we present theconclusion in section 3. In Appendix, we show the data description of capital stock andinvestment.
2. Data and Empirical Analysis
2.1 Data
In this paper, we utilize marginal q (hereafter, Mq), real effective exchange rate (REER),
and investment-capital ratio (investment or I/K) to investigate Granger’s causality. The periodof the sample is from 1994:2Q to 2010:1Q.2 The data on Mq and I/K are taken from theCompany Statistics Seasonal Report by the Ministry of Finance of Japan. The data
descriptions are shown in the Appendix. The Company Statistics Seasonal Report provides
data by size of enterprise and by industrial classification. In this paper, we utilize the data on
six industries: chemical, iron and steel, production machinery, electric machinery andequipment, automobile and accessories and all manufacturing. 3 The data on REER areshown in the Monetary Statistics by the Bank of Japan.
2.2 Estimation by the LA-VAR model
In this paper, we verify Granger’s causality utilizing the LA-VAR model. The LA-VAR
model was developed by Toda and Yamamoto (1995). Following this procedure, we canestimate the VAR model with the level of variables without considering the degree ofintegration or the existence of a cointegration relationship. When the optimal lag is n and theintegrated order of included variables is at most d, we set the length of lags of the VAR model2

The data on investment and marginal q are seasonal adjusted by X11.
According to the Small and Medium Enterprises Agency, the definition of an SME is that (1) the numberof employees is not more than 300 or (2) capital is not more than three thousand million yen in the case ofmanufacturing. However, there is no category of “capital of not more than three thousand million yen,” andwe utilize the manufacturing industry’s data on “capital of not more than one thousand million yen.”33

to n+d. Here, we ignore the coefficients in last d lagged vectors in the model, because these
are regarded as zeros.
Then, we have to conduct the unit root test in order to check the degree of integration.
Here, we employ the DF-GLS test developed by Elliot, Rotenberg, and Stock (1996). Theresults of this test are shown in Table 1. It is shown that REER is I (1) and others are I (0).
Next, we check the optimal length of lags. Following SBIC, the optimal length of lags ofthe three-variable VAR model is 1 for all industries. Thus, we have to use the VAR (2) modelin order to investigate Granger’s causality.
Table 2 shows the empirical results of Granger’s causality test with the LA-VAR model.
The significance level here is 5%. Following this table, we give a brief review of theempirical results. Firstly, the null hypothesis that REER does not Granger-cause Mq isaccepted in all industries. And secondly, the null hypothesis that REER does not Granger-cause I/K is also accepted in all industries.
2.3 Effect of the Exchange Rate
In this subsection, we verify the relationship from the exchange rate to Tobin’s marginal
q and to investment-capital ratio. As we mentioned in Section 1, the exchange rate is an
important factor that influences a firm’s investment. Recently, it is said that corporate
performance in Japan has recovered by depreciation of JPY. However, the empirical results
obtained in this paper show that the exchange rate does not Granger-cause investment andmarginal q in all industries we focus on. This implies that the exchange rate cannot forecast
the marginal q and investment of major manufacturing industries categorized as SMEs.
The White Paper of the Small and Medium Enterprises 2008 (Small and Medium
Enterprises Agency 2008) mentions that manufacturing firms, especially chemical,
production machinery, and electric machinery have a high percentage of export; however, it
is also shown that a large number of manufacturing firms categorized as SMEs are not4concerned with the business of export. It shows that only 29.6% of firms with 101-300
employees are concerned with the business of export.4 This state of affairs is the main reason
for our empirical results: acceptance of the null hypothesis that the exchange rate does not
Granger-cause investment and marginal q.
As an additional verification, we perform Granger’s causality test with the data of
non-manufacturing industry. Here, we follow the same model specification as we utilized in
the previous subsection. The empirical results are shown in Table 3. It is also shown that realeffective exchange rate does not Granger-cause investment and Tobin’s marginal q in
non-manufacturing industry categorized SMEs; they are consistent with the Figure 2.
Considering the empirical results obtained in this section, the real effective exchange
rate cannot forecast the trend of SMEs’ investment and Tobin’s q. Then, our empirical results
support the opinion that a depreciation of JPY has little effects on investment and marginal qof SMEs.
3. Conclusion
In this paper, we investigate Granger’s causality among the exchange rate, Tobin’s
marginal q, and investment-capital ratio with data on Japanese manufacturing industries
categorized as SMEs in Japan. We obtain two empirical results that the null hypothesis of noGranger’s causality from the exchange rate to marginal q and investment is accepted in all
manufacturing industries. The reason is that SMEs have a low percentage of export. And withthe data of non-manufacturing, we obtain the same empirical results: acceptance of null. Thus,
it can be considered that the effects of Abenomics on SMEs are limited, and that other kindsof reflation measures for SMEs are needed.

4

The English version of this the White Paper is downloadable from following URL:
http://www.chusho.meti.go.jp/pamflet/hakusyo/h20/h20/2008hakusho_eng.pdf .
5

Appendix: Data Descriptions of Investment, Capital Stock, and Marginal q<Investment>
In the Company Statistics Seasonal Report, sample is revised every second quarter andits continuity is thus not maintained. Moreover, stock data is constructed by accumulating
flow data. And so we have to adjust the data. Here, we utilize data on individual enterprises:
variables divided by size of population. Using the data on individual enterprises, we construct
flow data and capital stock following the equations below:
I t  K tE  K tB  Dept (1) .

K tE and K tB are tangible fixed assets at the end and beginning of period t. Land isexcluded and construction-in-progress accounts are included. Dept is depreciation and I t
is the flow of investment in period t.
<Capital Stock>
We then calculate capital stock K t as follows:

K t  K t 1  Dept  I t (2) .
Here, I t and Dept are real values. We utilize the deflator of investment from 93SNA.
K t is a real value. But in order to obtain the real value of capital stock, we have tocalculate the book value in 1994:Q2, the start point of the sample, because stock data isconstructed by accumulating flow data. Following the National Wealth Survey of 1970, theaverage duration (vintage) of manufacturing industries is seven years. An economic white
paper (Cabinet Office of Japanese Government 1999) shows the way of calculating vintage inthe current period with annual data. Following this, vintage is 10.405 years at the beginningof FY 1994, 1994:Q25. Then, we maintain that the book value of capital stock in 1994:Q2 isthe price in 1984:Q4.
5

By calculating with the rate of retirement of equipment printed in the Quarterly Report on National
6

<Tobin’s Marginal q>
Next, we show the method of calculating marginal q. The model of marginal q implies arelationship between investments and their shadow price derived from firms’ profit
maximization problem. Following Ogawa and Kitasaka (1999) and other studies, marginal q(Mq) is written asMqt    j  1 1jE1t  t  j   (3) .
Pt I  j 0  i 1  1  rt i 

Here, Pt I is the price of investment goods,  t , the profit rate, is operating profit overcapital at period t,  is the depreciation rate, and E t is the expectation operator with theinformation set available at t. And rt , the discount rate, is the interest rate for borrowing.
We assume that rt (discount rate) and  t (profit rate) obey the independent random
walk process. And Mq can be explained as follows:

Mqt  t 1  rt (4)Pt I rt   We assume  is 0.0792, which is the value calculated for the manufacturing industry
shown in Masuda (2000) referring to the methods developed by Hayashi and Inoue (1991)．

Accounts of 1980 (Economic Planning Agency 1981), the vintage of manufacturing industries in 1980 is8.3 years. Then, we calculate with the rate of retirement of equipment printed in the Quarterly Report onNational Accounts of 2010.
The data series of 93SNA is available only after 1980. And we thus calculate the vintage with 68SNA,
which is available before 1980, and connect to 93SNA at 1980:Q1.
7

References

Caballero, Ricardo J. (1991) “On the Sign of Investment-Uncertainty Relationship,”
American Economic Review 81, 279-288.

Cabinet Office of the Japanese Government (1999) “Economic White Paper 1999.”

Elliott, Graham, Thomas J. Rothenberg, and James H. Stock (1996) “Efficient Tests for
an Autoregressive Unit Root,” Econometrica, 64(4), 813-36.

Hayashi, Fumio, and Tohru Inoue (1991), “The Relation between Firm Growth Q withMultiple Capital Goods: Theory and Evidence from Panel Data on Japanese Firms,”
Econometrica 59(3), 731-753.

MacKinnon, James. G. (1996) “Numerical Distribution Functions for Unit Root andCointegration Tests,” Journal of Applied Econometrics 11, 601-618.

Masuda, Kazuto, “Shihon Stock Tokei no Mikata” (Introduction to capital stock
statistics: Market value of capital stock), Research and Statistics Department Working
Paper Series 00-5, Bank of Japan, 2000 (in Japanese).

Ogawa, Kazuo and Shin-ichi Kitasaka (1999), “Market Valuation and the q Theory ofInvestment,” The Japanese Economic Review Vol.50, No.2, pp.191-211.



Small and Medium Enterprises Agency (2008) “White Paper on Small and Medium
Enterprises in Japan.”

Small and Medium Enterprises Agency (2014) “White Paper on Small and Medium
Enterprises in Japan.”8Mq and REEX(Manufacturing)

I/K and REEX(Manufacturing)
160

160

140

140
120

120

100

100

80

80

60

60

40

40

20

20
0-0.01000.010.02

0.03-10.04(1-A) Exchange Rate and Investment0123(1-B) Exchange Rate and marginal qFigure 1 Scatter Plots (Manufacturing)(Note) The vertical axis is real effective exchange rate (REER). The horizontal axis is investment-capitalratio (I/K) for 1-A and Tobin’s marginal q (Mq) for 1-B. Correlation coefficient of REER and I/K is -0.323,
and that of REER and Mq is -0.245.
I/K and REEX(Non-Manufacturing)

Mq and REEX(Non-Manufacturing)

160

160

140

140

120

120

100

100

80

80

60

60

40

40

20

20

00-0.2-0.1

00.1

0.20(2-A) Exchange Rate and Investment

0.511.52(2-B) Exchange Rate and marginal qFigure 2 Scatter Plots (Non-manufacturing)(Note) The vertical axis is REER. The horizontal axis is I/K for 2-A and Tobin’s Mq for 2-B. Correlation
coefficient of REER and I/K is -0.049, and that of REER and Mq is -0.061.
(Source of Fig.1 and 2) Mq and I/K are from the Company Statistics Seasonal Report by the Ministry ofFinance. REER is from the Monetary Statistics by the Bank of Japan.

9

Table 1 Unit Root Test (With Constant)
Elliott-Rothenberg-Stock DF-GLS test
IK(level)

MQ(level)

Chemical-3.769(1)***Iron and Steel-8.386(0)*** Iron and Steel-7.942(0)***-7.175(0)-7.886(0)-6.648(0)

Production
Machinery
Electric
Machinery
Automobile/
Accessories
NonManufacturingREEX

REEX(level)-0.904

Chemical

Production
Machinery
Electric***
Machinery
Automobile/***
Accessories
Non***
Manufacturing(0)

D(REEX)-4.910(0)***-3.680(0)***-1.997(1)**-4.834(0)***-7.049(0)***-3.026(0)***

REEX(1st difference)-7.291(0) ***＜Note> Critical values are-2.603(1% level, ***) and -1.946 (5% level, **).
The critical values are shown in MacKinnon (1996).

10Table 2 Granger Causality Test with the LA-VAR Model

ChemicalNull Hypothesis:
Wald-Statistics
REEX does not Granger-cause IK
0.133
REEX does not Granger-cause MQ
0.823
Iron and Steel
Null Hypothesis:
Wald-Statistics
REEX does not Granger-cause IK
0.313
REEX does not Granger-cause MQ
0.112
Production Machinery
Null Hypothesis:
Wald-Statistics
REEX does not Granger-cause IK
0.011
REEX does not Granger-cause MQ
0.332
Electric Machinery
Null Hypothesis:
Wald-Statistics
REEX does not Granger-cause IK
2.683
REEX does not Granger-cause MQ
1.137
Automobile and Accessories
Null Hypothesis:
Wald-Statistics
REEX does not Granger-cause IK
1.188
REEX does not Granger-cause MQ
0.657
Manufacturing (Total)
Null Hypothesis:
Wald-Statistics
REEX does not Granger-cause IK
0.024
REEX does not Granger-cause MQ
0.370<Note> The Wald test statistics obey chi-square distribution with DF=1.

Prob.
0.715
0.364
Prob.
0.576
0.738
Prob.
0.918
0.564
Prob.
0.101
0.286
Prob.
0.276
0.418
Prob.
0.876
0.543

Table 3 Granger Causality Test (Non-Manufacturing)Non-Manufacturing
Null Hypothesis:Wald-Statistics
REEX does not Granger-cause IK
0.547
REEX does not Granger-cause MQ
1.638<Note> The Wald test statistics obey chi-square distribution with DF=1.

11

Prob.
0.452
0.201