Public Capital and Asset Prices:Time-series Evidence from Japan
Kazuki Hiraga
Masafumi Kozuka
Tomomi Miyazaki

September 2016
Discussion Paper No.1625

GRADUATE SCHOOL OF ECONOMICS
KOBE UNIVERSITYROKKO, KOBE, JAPANPublic Capital and Asset Prices: Time-series Evidence from Japan
Kazuki Hiraga
Masafumi Kozuka
Tomomi Miyazaki

This research examines the effects of public infrastructure capital on asset prices
in Japan over the periods from 1983:Q1 to 2008:Q4. The empirical results show thatwhile public infrastructure capital forecasts the stock price returns and total factor
productivity by Granger’s causality test after 1991, the contribution of public
investment on stock returns is small by variance decomposition using FactorAugmented VAR model. Our empirical evidence on the post high-growth era in Japansuggest that although public capital forecasts stock price returns and TFP, public
infrastructure investment is not expected to play a key role of revitalizing capital
markets.

JEL classification: E44, G12, H54

Keywords: Public infrastructure capital in Japan; Stock price targeting; Lagaugmented VAR; Factor Augmented VAR; The authors would like to thank for Isaac Otchere for valuable comments and suggestions. This

work has been financially supported by the Japan Society for the Promotion of Science (Grant-in-Aid
for Scientific Research # 26380361) and Financial Aid by Ishii Memorial Securities Research
Promotion Foundation, Japan Securities Scholarship Foundation, and Yu-cho Foundation. Takuya
Matsuyama and Koichi Watanabe are excellent research assistants. The usual disclaimer applies.
 Associate Professor, School of Political Science and Economics, Tokai University.

E-mail: khiraga581470@gmail.com
 Associate Professor, Faculty of Economics, University of Marketing and Distribution Sciences.

Research Fellow, Graduate School of Economics, Kobe University.
E-mail: Masafumi_Kozuka@red.umds.ac.jp
 Corresponding Author: Associate Professor, Graduate School of Economics, Kobe University. 2-1,

Rokkodai-cho, Nada-ku, Kobe, Hyogo 657-8501, JAPAN. E-mail: miyazaki@econ.kobe-u.ac.jp

11. Introduction
Emerging markets and developing economies (EMDE) have played an important rolein international capital markets in recent years. For example, the IMF (2016) shows thatspillovers of EMDE shocks to equity prices and exchange rates in advanced andemerging market economies explain over 30% of the variation in asset returns in thesecountries. On the other hand, some relatively developed countries in EMDE haveinvested large amounts of money in infrastructure investment, which has contributed torevitalizing their respective stock markets. For example, the Chinese government

implemented a large economic stimulus package after the 2008 global financial crisis(GFC). About 80% of the package was spent on public infrastructure investment, andstock prices rose as a result despite the GFC. The Chinese example suggests that public

infrastructure investment is useful for revitalization of the stock market as well as

infrastructure development in EMDE.

This research examines the effects of public capital on asset prices in Japan. The

government of Japan, which has aggressively implemented public infrastructure

investment, has also implemented economic stimulus packages including public2

infrastructure investment to keep stock prices high. In other words, the policy for

attaining both the revitalization of the stock market and infrastructure development

through public infrastructure investment has been pursued in practice in Japan for along period of time even before the GFC. Therefore, our empirical evidence on Japan

may have implications for the revitalization of capital markets and public infrastructure

investment policy in relatively developed countries in EMDE.

However, to our knowledge, no previous works have examined the effect of public capitalon stock price returns in Japan. Many works such as those of Kitasaka (1998), Yoshino

and Nakajima (1999), Nemoto et al. (1999), and Annala et al. (2008) have examined themacroeconomic effects of public infrastructure capital in Japan. However, these works

have not examined the effects on stock market performance. Accordingly, our research

fills a gap in the literature on Japanese public infrastructure investment policy and stock

market revitalization.

To perform empirical investigation, we use both the standard VAR model and Toda andYamamoto (1995)’s Lag-Augmented VAR (LA-VAR) for Granger’s causality test, andimplement variance decomposition using the Factor-Augmented VAR (FAVAR) model.

3

The results show that while the null hypothesis of no Granger’s causality from public

capital to stock price returns and Total Factor Productivity (TFP) is rejected based on

the test model over the periods of 1991:Q1-2007:Q4, the movement of public investment

can only be a fraction of the movements of asset price returns using variancedecomposition. Our empirical evidence from the era of post-high growth in Japansuggests that public infrastructure investment will not necessarily be useful for

revitalization of the stock market.

This paper is organized as follows. Section 2 summarizes the public investment policy

and stock price target policy in Japan. Section 3 presents a theoretical background andtestable hypothesis. Section 4 reports the estimation results and discusses theimplications for EMDE. Section 5 presents our conclusion.

2. Background: Public infrastructure investment and stock target policy inJapan
Figure 1 shows the movement of public infrastructure investment (public capital4

formation, per GDP) among some developed countries. Public infrastructure investment

had been highest among these groups until the mid-2000s, which shows that theJapanese government implemented a large amount of public infrastructure investment.

A lot of public infrastructure was destroyed during World War II, which the government

repaired in the decades after the end of the war. Moreover, since the lack of public

infrastructure was a bottleneck for economic recovery, the government implemented

large-scale infrastructure investment such as the construction of the Tokaido

Shinkansen network and Keihin factory area. These public infrastructures, which wereconcentrated in three major metropolitan areas (Kanto, Chubu, and Kansai), supported

the tremendous growth in the mid-1950s to the early 1970s in Japan.

On the other hand, public infrastructure investment has been frequently used as a toolof macroeconomic stabilization.1 Above all, after the collapse of the asset price bubbles

in the early 1990s, the government implemented fiscal stimulus packages almost every

year, as shown in Table 1. Stimulus packages implemented in August 1992, April 1993,

1

For more details, please see Miyazaki (2010) and Asako (2012).

5

and September 1995 comprised more than half of public infrastructure investment.23

The Japanese government implemented these stimulus packages also as a tool for

supporting stock prices in these periods. Actually, Fukuda and Yamada (2011) argue thatstock prices were a target of Japanese macro stabilization policy during the 1990s. The

government implemented stimulus packages that mostly consisted of public

infrastructure investment to maintain stock prices in these periods. Following these, theJapanese case is worth investigating to examine the relationship between public

infrastructure investment and stock prices.

3. Theoretical background and our empirical strategies
3.1. Theoretical backgroundSome theories explain that public infrastructure investment affects asset prices

through two paths. One is the direct path, which means that public infrastructure

Whereas the Public Finance Act in Japan prohibits the issue of deficit bonds in principle, the Act
allows limited bond issuance in the General Account (the Japanese central government’s budget) toraise funds to finance public investments, equity investments, and loans to public corporations.
Reflecting this, the government has mainly used public infrastructure investment as an economic
stimulus by issuing construction bonds.
3 Incidentally, the Japanese government also implemented large economic stimulus packages after
the economic slowdown accompanying the 2008 global financial crisis. However, the principal items inthese packages were not public investment but subsidies or tax cuts such as lump sum transfers(teigaku-kyuhu kin), subsidies for consumer purchases of energy-conserving home appliances, and a
program of tax breaks and subsidies for purchasing “eco-friendly” cars and financial support for small
and medium-sized enterprises. For more details, see Iwaisako (2010) and Miyazaki (2016).
2

6

investment affects asset prices directly. Fiscal policy is also expected to raise asset prices,

as examined in works by Agnello and Sousa (2011) and Nutahara (2013), which showthat fiscal stimulus increases the aggregate demand and expected present value of profit(i.e. asset prices). This channel may also be applicable to public infrastructure

investment, and we define this as the short-run effect of public infrastructure investment

on stock prices.

The other is the indirect path: public capital stock increases the marginal productivityof private enterprises, and thereby, it raises asset prices. This is examined by boththeoretical and empirical models in Belo and Yu (2013). Belo and Yu (2013) assume

that public capital is one of the inputs in a firm’s production technology and they

assume that it also affects the marginal productivity of private inputs.4 Theirtheoretical model also shows that if public sector capital increases the marginal

productivity of private inputs, there is a positive relationship between the public sector

investment rate and the firm’s risk premium. This can be defined as the long-term

effect of public infrastructure capital (or stock effect) on stock prices.

4

Detailed explanation is shown in Appendix 1.

7

3.2. Our empirical strategies and the variables used in estimation
We follow two procedures to quantify the relationship between public infrastructure

capital and stock prices. Firstly, we perform Granger’s causality test to check whether

public capital can be used to forecast future stock prices. Secondly, we check thecontribution of the shocks of public investment policy on the fluctuation of stock prices

through variance decomposition based on the estimation results by VAR. We capture thedirect effect of public infrastructure investment (discussed in Section 3.1) by the short-run observations of variance decomposition, and the indirect effect of public

infrastructure capital stock (defined in Section 3.1) can be explained by the long-run

observation of variance decomposition.

To implement variance decomposition, we take differences for public infrastructure

capital data both for making the variable stationary and for capturing the shocks ofpublic investment policy in the short-run. We use the FAVAR method because thisenables us to purify the shocks of public investment policy by applying principal

component analysis for the VAR model considering potential omitted variables as slow

moving and fast moving.

8

We use three variables in estimation: stock market returns (𝑅𝑡 ), TFP (𝑇𝐹𝑃𝑡 ), andgovernment capital stock (𝐺𝑡 ). TFP is also added because public capital affects stock
prices through the increase of private firm’s productivity if indirect path shown above isalso the case.

4. Empirical Results
4.1. Dataset
Data on stock price returns came from the data of stock price earnings ratio provided

by Japan Securities Research Institute. TFP is made by us, and details are shown inAppendix 1. Public infrastructure capital data came from the data calculated by the

Cabinet Office in Japan (accessed last May 21, 2016). Incidentally, the official data by

the Cabinet Office in Japan offers only annual data. Therefore, we converted theoriginal annual capital stock data into quarterly basis (initial value) data following theprocedure employed by Kitasaka (1998); we did this using the weight for each quarter9calculated by the real seasonally-adjusted general government gross capital formation

data.5The Cabinet Office made public infrastructure capital stock data by considering fourtypes of depreciation; straight-line method, declining-balance method, and the two

types of depreciation shown in the method of the OECD (2009).6 We use all data madeby considering different types of depreciation. “G1” is the data made by the straight-

line method, “G2” is made by the declining-balance method, and the stock data named“G3a” and “G3b” follow the method of the OECD (2009).

In the straight-line method, which is employed in “G1,” a fixed value of depreciation isappropriated every year through the durable periods of fixed assets.

The decline-balance method, which is utilized in “G2,” is a way of appropriating thedepreciation amount considering a fixed rate of depreciation through the durable

periods. Here, the non-depreciated balance at the beginning of each period is multipliedby the constant depreciation rate.7

For more details, please see Kitasaka (1998).
For more details, please see http://www5.cao.go.jp/keizai2/jmcs/jmcs.html .
7 In previous studies about consumption on durable goods, they calculate the service flow of durable
goods expenditure with similar method to decline-balance method.
5

6

10

In the OECD (2009) method, used in “G3a” and G3b,” the decrease in efficiency of public

capital caused by, for example, physical depreciation and obsolescence, is considered. In

this method, firstly, the pattern of decline in value of services brought by public capitalin the future is assumed. Then, the discount rate is set up based on the assumed decline

in value, and the present discount value of services obtained by public capital iscalculated.

When the pattern of decline in value in the first step is set up, two kinds of estimation

can be utilized; estimation with linear function and with hyperbolic function. For “G3a,”linear function is utilized. And for “G3b,” hyperbolic function is employed.

We assume that public infrastructure investment is a public good in that a public

infrastructure is a non-excludable good, which potentially affects the economic

activities of all industries. Thus, we did not divide the public infrastructure into sectors

such as roads, educational facilities, and sewers.8

The sample period is from the first quarter of 1983 to the fourth quarter of 2008.

Just to make sure, we also estimate the model by limiting the category of infrastructure sock into theindustrial infrastructures such as road, port, airport, and water sewage for productions. However, theresults are not so drastically changed from our reported results. Details can be available from theauthor’s website: https://sites.google.com/site/tomomisite/research/dp .
811

4.2. Results of unit-root tests and Granger’s causality test
Firstly, we report the results of the unit-root tests. To check whether each variable isstationary, we use the Augmented Dickey-Fuller (1979) (ADF) test.

Table 2 shows the results for the variables used in the estimation. The table reportsthat the level of 𝑅𝑡 is stationary for both cases, the levels of 𝑇𝐹𝑃𝑡 and 𝐺𝑡 are
nonstationary especially in the case of a constant term with trend. Hence, we need totest the first differences of the series. All tests strongly reject the null hypothesis of

nonstationarity for the first differences. Therefore, all variables may be treated as asingle (I (1)) unit-root process.

Secondly, we check the optimal length of lags. Following the likelihood ratio test ofSims (1980), the optimal length of lags of the three-variable VAR model is 4 for allcases.

Thirdly, we explain Granger’s causality test. To implement this, we employ the LA-

VAR model as well as the VAR model taking first differences. Following LA-VAR model,

we can also estimate the VAR model with the level of variables without considering thedegree of integration or the existence of a cointegration relationship. When the optimal

12

lag is n and the integrated order of included variables is at most d, we set the length oflags of the VAR model to be n + d. Our degree of integration is at most one following

the unit-root tests, and our optimal lag length is four based on the likelihood ratio test.

Thus, we set the lag length of the VAR model taking first differences (standard VAR) as

four, and the one of LA-VAR (LA-VAR) as five, respectively.

Before we implement the VAR estimation, we check the structural change. Figure 2reports the movement of stock price returns. According to this figure, stock price returns

were volatile from the late 1980s to the early 1990s. These periods are equivalent to theasset price bubble periods in Japan. Actually, following Christiano (1986) and Cecchetti

and Karras (1994), we note a structural change in the data after this quarter. 9

Furthermore, after 2008, the volatility of stock price returns was large owing to thecollapse of Lehman. Thus, we also estimate the model using the sample periods over the

1991:Q1 to 2007:Q4. Here the lag length is set as four for standard VAR and five for LA-

VAR, respectively.

9 Detailed results can be obtained from the authors upon request.

13

Table 3 reports the results of Granger’s causality test for all our sample periods.

Although the null hypothesis that TFP does not Granger-cause R is strongly rejected,

the null that G does not Granger-cause R is accepted for all cases. In addition, we limit

the sample periods from 1991:Q1 to 2007:Q4. Here we also confirm that TFP can

forecast future stock returns. Furthermore, we can reject the null that G does not

Granger-cause R for the standard VAR model and the LA-VAR model.

The results obtained by Granger’s causality test show that public capital affected

stock price returns after the collapse of the asset price bubbles at the beginning of the

1990s. Moreover, we confirm that public capital can forecast TFP, and TFP affects

stock price returns. As shown in Section 3, public infrastructure indirectly affects stock

prices through the increase in the productivity of the private sector. Both direct andindirect effects of public infrastructure investment might be implied following theresults of Granger’s causality test.

4.3. Results of variance decomposition
We obtain the results as the variance decompositions of each stock return with respect

14

to the contribution of a public investment shock, shown in Table 5a-5d10. We estimate

factors from a dataset, which containing 28 industries quarterly macroeconomic timeseries (public capital, total factor productivity (TFP) and stock price return of aggregate

and sectoral data), for 1991:Q1 to 2007:Q4, when the null that G does not Granger-cause

R can be rejected.11 Similar to Bernanke et al. (2005), we take a logarithm difference of

TFP. In our setting, fast-moving variable is TFP and slow-moving variables areaggregate and sectoral stock price returns.12

The estimation results show that the medium- and long-term effects of public

infrastructure investment are relatively larger than the short-term effect in any industry.

This result implies that the supply-side effect may be dominant. On the other hand, theabsolute impact is not so large. That is, the contribution of public infrastructure

investment shocks can explain only a fraction of the fluctuation of stock price returns.

Following the criteria of Bai and Ng (2002), we set three factors (i.e. K=3).
There are stock returns of Aggregate, Agriculture, Mining, Construction, Food, Fiber, Pulp andPaper (Paper), Chemical, Petro-Coal (Petro), Rubber, Glass, Steel, Non-steel, Metal, Machine,
Electrical equipment, Transportation machine, Precision mechanical, Other machine, Commerce,
Finance, Real estate, Land transport, Shipping, Air transport, Warehousing, Information, Utility,
Service industries.
12 TFP is still aggregate level data even when we conduct an investigation using sectoral data.
Sectoral GDP annual data are presented because we cannot acquire such data on a quarterly basis.
Therefore, we use aggregate TFP data even for the exercises using sectoral stock price returns.
10
11

15

4.4. Implications for EMDEOur empirical results after the 1990s in Japan show that whereas public infrastructure

investment forecasts future stock price returns and TFP, the contribution of the shocksof the change in public infrastructure, or the shocks of public investment policy explain

a fraction of the stock price returns.

The level of public capital in Japan has accumulated, reflecting the large amount ofpublic investment, and Yoshino and Nakajima (1999) show that the marginal

productivity of public capital in Japan after the 1970s is lower than that before the 1970s

on a national level. Our results obtained by variance decomposition that quantitative

contributions of public investment on stock price returns are small may be related to thelow productivity of public capital.

EMDE shares a half of global infrastructure spending, according to Oxford Economics(2015). This also implies that the level of public capital in these relatively developed

countries may sufficiently accumulate in the near future as a result of huge amount of

infrastructure investment. If so, marginal productivity of public capital becomes low,

and thus the effects on stock prices may not be as substantial as in the case of our results

16

on variance decomposition. Our empirical evidence from the era of moderate growth inJapan suggests that in the near future, even if the governments in relatively developed

countries among EMDE plan the public infrastructure investment in order to pursue theinfrastructure development and the revitalization of the stock market, public

infrastructure investment will not necessarily be useful.

5. Conclusion
This research examines the effects of public infrastructure capital on stock prices inJapan using Granger’s causality test and variance decomposition calculated by FA-VAR.

Our results show that whereas public capital forecasts future stock price returns and

TFP for the periods over 1991:Q1-2007:Q4, no industry can obtain a substantial recovery

of stock price return on public investment stimulus from variance decomposition.

In future, we could also examine the effects of using firm-level data so as to compare

the effects among more disaggregate industries as in the case of Nekarda and Ramey(2011).

17

Appendix 1. Theoretical explanation of supply-side effect of public capital on
stock return

This appendix introduces public sector physical capital into the neoclassical q-theorymodel of investment following Belo and Yu (2013).

A.1. The setups

Firm technology is shown as follows:Yt  e xt GKt  Kt ,


(A.1)

where Y is output, GK is public sector physical capital, K is private capital xt is

profitability shock (or productivity shock). Seminal parameter α is the productivity(profitability) of public sector capital.

The accumulation processes of private and effective public capital are shown as Eq.

(A.2) and (A.3):

K t 1  1   K t  I t ,
18

(A.2)





GKt 1  1   GK GKt  GIKt ,(A.3)

̃ 𝑡 is the public sector investment rate, 𝐺𝐼𝑡 is the total investment
where 𝐺𝐼𝐾𝑡 ≡ 𝐺𝐼𝑡 ⁄𝐺𝐾̃ 𝑡 is the total stock of public sector capital and 𝛿 𝐺𝐾 is thein public sector capital, 𝐺𝐾
depreciation rate. The specification of Eq. (A.3) guarantees that the stock of effective

public sector capital is stationary13, the adjustment cost of private capitalg I t , K t  where IK t  I tc
IK t 2 K t ,
2

(A.4)

K t is the private sector investment rate.

A.2. The firm’s maximization problem

Suppose that the firm is all-equity financed. Dividends Dt distributed by the firm to
the shareholders are given by:

13

Assumption of stationary is necessary condition to derive the empirical predictions aseffective stock of public sector capital is equal to detrended stock of total public capital.

19Dt  e xt GK t  K t  I t The cumulative dividend market value V

V

CUM

CUM

c
IK t 2 K t .
2

(A.5)

st  is shown as follows:   
st   l max
Et  M t ,t  j Dt  j  ,t  j , K t  j 1  
  j 0



Subject to Eq. (A.2) and (A.3) for all dates t. st  K t , GKt , GIKt , xt

(A.6)

 is the vector ofstate variables and M t ,t  j is a market –determined stochastic discount factor at periodt, which is used to value the cash flows arriving in period t+j.

A.3. First-order conditions

We solve the maximization problem of Eq. (A.6). First order conditions with respect to

lt and K t 1 are as follows:qt  1  c  IK t ,

20

(A.7)


2



2
qt  Et  M t ,t 1  e xt 1 GKt 1   IK t   1   1  c  IK t .
c




(A.8)

Combining Eq. (A.2), (A.3), (A.7), (A.8) and the standard asset pricing equation

Et M t ,t 1 Rtl1  1 , in which Rt 1 is the private sector investment return, we obtain Rt 1ll

as follows:

Rtl1 

e xt 1 1   GK GKt  GIKt

  2 c  IK   1   1  c  IK .


2

t 1

1  c  IK t

t 1

(A.9)

Equation (A.9) explains the supply-side effect of public capital shown in the first term of

the numerator. If α is positive, stock return increases by a channel of positive

production externality of public capital.

Appendix 2. Calculation of potential GDP
In order to obtain the Total Factor Productivity (TFP) in Japan, we have to calculate

the Solow residual without measurement error. In this study, we employ the production

21

function approach. The Economic Planning Agency (2000) and Kamamta and Masuda(2001) calculate the Solow residual derived from Cobb=Douglas type production

functions. Here, we follow the methods shown in Kamamta and Masuda (2001). Figure

A.1. offers the source of the data.

Firstly, we set the real GDP as Yt , capital stock as K t , total labor hours (working
population×working hours) as

Lt , Solow residual as At , the operating ratio of capitalas  , and the coefficient labor input as  . The parameter 

is defined as“Compensation of employees÷total income” supposing the perfect competition. Then, theproduction function isln Yt  ln At  (1   ) ln K t   ln Lt .

(A.10)The real GDP and the capital stock are 68SNA in the Annual Report on National

Accounts. The industry consists of manufacturing and non- manufacturing sectors, andln K t can be written as22ln K t  ln( m K mt  nm K nmt )(A.11)

Here, m indicates the manufacturing and nm the non- manufacturing industry. We
must consider the nm because we cannot obtain the Japanese data. Previous studies
assumed that the operating ratio of non-manufacturing is always 100%, and themeasurement error remains in the Solow residual ( ln At ). In order to calculate TFP
correctly, Kamata and Masuda (2001) use the Business Survey Index (BSI) of non-manufacturing 14 .However, the BSI can be utilized from the second quarter of 1983

(hereafter 1983:2). On the other hand, the sample period is 1978 through 1997 in ourstudy, and we must consider another method to obtain the operating ratio of the non-manufacturing industry before 1983:2. Here, we obtain the average of two indices ofmanufacturing (operating ratio and IIP, indices of industrial production). We employ thisproxy from 1978:Q3 to 1983:Q1, BSI from 1983:Q2 and connect them.

The Solow residual ( ln At ) is calculated as follows:

In Kamata and Masuda (2001), the consumption of electric power is also considered to calculate therate of operation.
14

23

ln At  ln Yt  (1   ) ln K t   ln Lt(A.12)

Here, we regard the Solow residual as the TFP.

Appendix 3. Explanation of the FAVAR Model
Appendix 2 explains the econometric framework for the FAVAR model.15 Let Yt be an

M × 1 vector of observable economic variables, where M is small. Although Yt is used ina standard VAR, Yt alone does not easily add economic information. We therefore assume

that a K × 1 vector of unobserved factors, where K is small, summarizes this additional

information. The joint dynamics of (Ft, Yt) are given by Ft 
 Ft 1 
Y   L Y   ut , t
 t 1 (A.13)

where Φ(L) is a matrix of polynomials of finite order d and the error term ut is themean 0 with covariance matrix Σ.

There is apparently little difference between a standard VAR and the FAVAR. Yet

15This section conforms to Bernanke et al. (2005). For details, see Bernanke et al. (2005).

24

Equation (A.13), which is a FAVAR, cannot be estimated because the factors areunobservable. We must therefore assume that the factors affect a large number ofvariables to estimate Equation (A.14). This assumption allows us to infer theunobservable factors from these economic time series variables. Let Xt be an N × 1 vectorof informational economic variables, where N is large, such that K + M << N.16 Also,

assume that Xt is related to both the unobservable factors vector Ft and the observablefactors vector Yt, given as follows:

X t   f Ft  y Yt  et ,(A.14)

where  f , y are the N × K, N × M matrix of factor loadings, respectively, and et is an

N × 1 vector of error terms, which is weakly correlated with the mean 0.
For the estimation, we follow the two-step approach proposed by Bernanke et al.

(2005).17 This means we identify Ft in the first step and estimate Equation (A.13) in the16

As Bernanke et al. (2005) point out, it is acceptable for N to be greater than T.

17

Although Bernanke et al. (2005) estimate the FAVAR by the two-step approach and a Bayesian

method based on Gibbs sampling, they suggest that the two-step approach tends to produce moreplausible responses.

25

second. Specifically, we perform the following procedures in the first step. Initially, thecommon components, Ct, are estimated using the first K + M principal components of Xt.

In the second step, following Bernanke et al. (2005), variables are classified as slow

moving and fast moving. Slow-moving variables are those predetermined in the current

period, such as output and employment. Fast-moving variables are those sensitive tocontemporaneous economic news or shocks, such as asset prices. Next, a principal

component analysis is applied to the slow-moving variables to derive a vector of slowS

moving factors, Ft . Finally, the following regression is estimated:Cˆ t  bF S Fˆt S  bY Yt  et ,where the estimated factors,

estimate the VAR in(A.15)F̂t , are obtained from Cˆ t  bY Yt . In the second stage, weF̂t and Yt , and compute the impulse response function using a

Choleski decomposition.

26

References
Agnello, L., and R. M. Sousa. (2011) “Fiscal policy and asset prices.” Bulletin of

Economic Research 65:2, 154-177.
Annala, C. N., R. G. Batina, and J. P. Freehan. 2008. “Empirical Impact of Public

Infrastructure Investment on the Japanese Economy.” Japanese Economic Review 59:

419-437.

Asako, K. (2012) Studies on the Japanese Business Cycle. Tokyo: Maruzen Publishing.

Bai, J., and S. Ng. (2002) “Determining the number of factors in approximate factor

models.” Econometrica 70:1, 191-221.

Belo, F., and J. Yu. (2013) “Government investment and the stock market.” Journal of

Monetary Economics 60:3, 325-339.
Bernanke, B. S., J. Boivin., and P. Eliasz. (2005) “Measuring the effects of monetary

policy: A factor-augmented Vector Autoregressive (FAVAR) approach.” Quarterly

Journal of Economics 120:1, 387-422.

27

Brückner, M., and A. Tuladhar. (2014) “Local government spending multipliers andfinancial distress: Evidence from Japanese prefectures.” Economic Journal, 124:581,

1279-1316.

Cecchetti, S. G., and G. Karras. (1994) “Sources of output fluctuations during theinterwar period: further evidence on the causes of the Great Depression.” Review of

Economics and Statistics, 76:1, 80-102.
Christiano, L. J. (1986) “Money and the U.S. economy in the 1980s: A break from the

past?” Federal Reserve Bank of Minneapolis Quarterly Review Summer, 2-13.

Dickey, D. A., and A. Fuller. (1979) “Distribution of the estimators for autoregressive

time series with a unit root.” Journal of American Statistical Association 74:366, 427-

431.

Doi, T., and T. Ihori. (2009) The Public Sector in Japan. Cheltenham: Edward Elgar

Publishing.

Economic Planning Agency, Keizai Hakusho Fiscal 2000 (Economic Survey of Japan

Fiscal 2000: The New Era Begins), 2000 (in Japanese).

28

Fukuda, S., and J. Yamada. (2011) “Stock price targeting and fiscal deficit in Japan: Why

did the fiscal deficit increase during Japan’s lost decades?” Journal of the Japaneseand International Economies 25:4, 447-464.
IMF, 2016. Global Financial Stability Report.

http://www.imf.org/external/pubs/ft/survey/so/2016/POL040416B.htm

Iwaisako, T. (2010) “Japanese macroeconomic policy management after the global

financial crisis.” Public Policy Review 6, 795-806.

Kamada, K., and K. Masuda. (2001) “Effects of measurement error on the output gap inJapan,” Monetary and Economic Studies 19:2, 109-154.

Kisataka, S. (1999) “Optimality of Public Capital Supply: Examination by Euler

Equation,” JCER Economic Journal 39, 76-96 (in Japanese).

Miyazaki, T. (2010) “The effects of fiscal policy in the 1990s in Japan: A VAR analysis

with event studies.” Japan and the World Economy 22:2, 80-87.

Miyazaki, T. (2016) “Fiscal policy effectiveness in Japan: Evidence from recent

policies.” Applied Economics 48:27, 2506-2515.

29

Nekarda, C. J., and V. A. Ramey., (2011) “Industry evidence on the effects of government

spending.” American Economic Journal: Macroeconomics 3, pp.36-59.

Nemoto, J., K. Kamada., and K. Kawamura. (1999) “Estimates of optimal public capitalstocks in Japan: Using a public investment discount rate framework.” Empirical

Economics 24:4, 693-710.
Nutahara, K., (2013) “Asset price targeting government spending and equilibrium

indeterminacy in a sticky-price economy.” CIGS Working Paper Series No. 13-003E.

Oxford Economics. (2015) Capital Project and Infrastructure Spending Outlook to

2025. http://www.pwc.com/cpi-outlook2025
Sims, A. C. (1980) “Macroeconomics and reality.” Econometrica, 48:1, 1-48.

Toda, H. Y., and T. Yamamoto. (1995) “Statistical inference in vector autoregressions

with possibly integrated processes.” Journal of Econometrics 66 (1–2): 225–250.

Yoshino, N., and N. Nakajima eds. (1999) Economic Effects of Public Investment.

Tokyo: Nihon-hyoron-sha (in Japanese).

30

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
2006Q2
2007Q1
2007Q4
2008Q3

-5

-10

-15

31

2010

2009

2008

2007

FranceUnited Kingdom

2006

2005

2004

2003

2002

2001

2000

Canada
Japan

1999

1998

1997

1996

1995

1994

%

1993

1992

1991

Figure 1. Government gross capital formation per GDP among some developed countries
Germany
United States

10
9
8
7
6
5
4
3
2
1
0

Source: OECD Economic Outlook

Figure 2. The movement of stock price returns

%
10

5

0

Table 1. Fiscal Stimulus Packages in the 1990s (JPY trillion)

Note: This table follows Brückner and Tuladhar (2014). Other government investment includes
investment in fields such as science and technology, education and social welfare, alternative energy
and the environment, and natural disaster relief. All government investment in economic stimulus
packages in April 1995 was for natural disaster relief because this package was planned as acountermeasure for the Great Hanshin-Awaji earthquake.

Table 2. Results of unit-root tests

32

Table 3. Results of Granger’s causality test (Sample periods: 1983:Q1-2008:Q4)

33

Table 4. Results of Granger’s causality test (Sample periods: 1991:Q1-2007:Q4)

34

Table 5a. Contribution of the public investment (G1) shock to variance of each stock price in 1991:Q1-2007:Q4 (unit: %)35

Table 5b. Contribution of the public investment (G2) shock to variance of each stock price in 1991:Q1-2007:Q4 (unit: %)36

Table 5c. Contribution of the public investment (G3a) shock to variance of each stock price in 1991:Q1-2007:Q4 (unit: %)37

Table 5d. Contribution of the public investment (G3b) shock to variance of each stock price in 1991:Q1-2007:Q4 (unit: %)38

Figure A.1. Source of the data on TFP

Data

SourceReal GDP (chained),
Compensation of
Employees, and Total
IncomeNational Account (93SNA, seasonallyadjusted and reference year 2000) in
the Annual Report on the National
Account, Cabinet Office

Capital Stock on Private Sector(93SNA) with adjustment for
privatization, Cabinet Office
Labor Force Survey (for all industries),
Working Population
Ministry of Internal Affairs andCommunication
Monthly Labour Survey (All industries,
companies with more than 30
Working hours
employees), Ministry of Health, Labourand Welfare
Business Survey Index for CapitalBusiness Survey Index Investment (Large Company, Nonmanufacturing), Ministry of FinanceIndices of Operating Ratio of
Operating Ratio of
Manufacturing (1995=100), Ministry of
CapitalEconomics, Trade and Industry
We separate the population into two
categories: (1) from 15 to 64 years oldand (2) more than 65 years old. Then,
Maximum Working
we adjust the linear trend of the
Population
working population to the peak oforiginal data for each category, and we
total these two adjusted linear trends.
(In designed hours) We separate threesamples: (1)1978:1- 1987:4 (2)1988:11993:4 (3) 1994:1-1997:3. And for
Maximum Working hours
each sample, we calculate the linear
trend and adjust it to the peak of theoriginal data.
(Out of designed hours) We adjust thelinear trend of working hours to thepeak of the original data.
Then, we total these two adjusted
linear trends.

Capital Stock39