Discussion Paper No. 579

DOES AGENCY COST MODEL EXPLAIN
BUSINESS FLUCTUATIONS IN JAPAN?:
AN EMPIRICAL ATTEMPT TO ESTIMATEAGENCY COST BY FIRM SIZE

Kazuo Ogawa
andHirokuni Uchiyama

April 2003

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

March 2003

Does Agency Cost Model Explain Business Fluctuations in Japan? :An Empirical Attempt to Estimate Agency Cost by Firm Size*

Kazuo Ogawa
Institute of Social and Economic Research,
Osaka University
Hirokuni Uchiyama
Graduate School of Economics
Osaka University* This research was partially supported by Grants-in-Aid for Scientific Research
12124207 of the Ministry of Education. Any remaining errors are the sole responsibilityof the authors.

Abstract

An attempt is made to estimate a state space model of investment and borrowing ina Bayesian framework and extract the unobservable agency cost of Japanese firms byfirm size. Our estimates of the agency cost exhibited a declining trend in the late 80s
and then switched to an increasing trend in the 90s. We pin down the driving force ofagency cost to be the market value of land. Furthermore, we find that investment andborrowing behavior of small firms is very much affected by their agency cost in the late
80s and the 90s. Our evidence demonstrates that imperfection of capital market isnotable for small firms in Japan.
JEL Classification Number: C51, E22, E44, and E51
Keywords: Agency cost, Investment, Collateral, Land, Borrowing, State space model,
Kalman filter, Gibbs sampling

Kazuo Ogawa
Institute of Social and Economic Research, Osaka University,
6-1 Mihogaoka, Ibaraki, Osaka, 567-0047 JAPAN
Tel: +81- 6- 6879-8570 Fax: +81- 6-6878-2766
E-mail: ogawa@iser.osaka-u.ac.jp

Hirokuni Uchiyama
Graduate School of Economics, Osaka University,
1-7 Machikaneyama, Toyonaka, Osaka, 560-0043 JAPANE-mail: uchiyamahirokuni@srv.econ.osaka-u.ac.jp

1.Introduction
In the presence of asymmetric information between lenders and borrowers,
financial arrangements arise to prevent borrowers from acting contrary to the interestsof lenders. In addition, lenders can monitor the behavior of borrowers to enforce sucharrangements. The resulting agency cost caused by this inefficiency drives a wedge
between the cost of internal and external funds, known as external finance premium.
The agency cost or external finance premium reflects the creditor’s cost of collecting
the debtor’s information and monitoring the debtor’s behavior and the cost arising fromlemon problem or moral hazard problem. The premium for external funds influences thecost of external funds and thereby affects investment of the debtor.
It is frequently asserted that excessive fluctuations of investment by Japanesefirms in the late 1980s to the 90s are mainly caused by change in external financepremium of the corresponding period. As is well known, the external finance premiumis inversely associated with the borrower’s collateralizable net worth. In particular, realestate had played a collateral role in Japan, under the expectation that land prices would
never fall. In fact, land price soared in the late 80s when investment increased
noticeably and as land price plummeted in the 90s, investment activity became stagnant.
Plausible as this story sounds, it is quite difficult to demonstrate in a rigorous
manner that this story was indeed true. The main obstacle in conducting empirical study
along this line is unobservability of agency cost facing borrowers. Therefore in the paststudies some kind of proxy was used to represent the movement of agency cost. One
popular candidate is land asset of firms at market price. There are a number of studies toshow a positive correlation of investment with land assets. 1 However, it may bepossible to interpret the land value of firms as future profitability of investment rather
than collateral to alleviate the agency cost.
In this study we give more direct evidence for the role of the agency cost in
explaining the investment activities of Japanese firms in the late 1980s to 90s. This canbe accomplished by estimating the unobservable agency cost directly by estimating thestate space model by the Kalman filter in a Bayesian framework to extract the common
factors from the observable variables closely related to the agency cost.2 As far as theauthors know, this is a first attempt to estimate the agency cost the Japanese firms facedin the turmoil period of the late 80s to the 90s.
In the course of conducting our research, we take account of the possibility that1

Foe example, see Ogawa et al. (1996), Suzuki and Ogawa(1997), Ogawa and Suzuki(1998, 2000).
Our idea of extracting agency cost stems from Stock and Watson(1991) where an unobservable
composite index is extracted from comovement among economic variables.
2

1

the firms with different size might face different magnitude of agency cost. It is because
there exists institutional device in Japan that helps to narrow the informational
asymmetry between lenders and borrowers: industry groups known as keiretsu. Firms
within a keiretsu are able to reduce agency costs for several reasons. First, they haveclose ties with affiliated banks, which hold both debt and equity in the group’s firms.
This reduces conflicts among investors. Secondly, group firms enjoy long-term, stable
relationships with their affiliated banks. Bank employees often hold management
positions in the firms. This explains why agency costs were lower for firms withinkeiretsu groups in comparison to unaffiliated firms. Since large firms tend to beaffiliated with banks, we can compare the magnitude of agency cost and its impact on
investment activities by using the less aggregated firm data classified by firm size.
Let us preview our findings. We find that the agency cost decreased in the late
80s when the land price soared, while the agency cost increased substantially in the 90s
when the land price precipitated. This pattern of agency cost is observed irrespective offirm size and industry. Furthermore, we find that investment and borrowing are closely
associated with the agency cost, which in turn is affected negatively by the land value offirms. As for the effect of agency cost on investment and borrowings, it is noticeably
large for small firms in the 90s. Our results are consistent with the theoretical verdict of
the agency cost literature, indicating that investment activities of Japanese firms in the
turbulent period of the late 80s to the 90s are successfully explained by the changing
pattern of agency cost.
The paper is organized as follows. Section 2 briefly reviews the agency costmodel of investment and derives the fundamental equations to be estimated. Then themodel is cast into state space form. Section 3 explains the econometric procedure toestimate unobservable agency cost. Section 4 describes the data set and shows somedescriptive statistics of the variables used in the subsequent analysis. In Section 5 we
present estimated series of agency cost and discuss the association of the agency costwith investment, borrowings, land asset and interest rate premium of firms. Concluding
remarks are given in Section 6.
2. Agency Cost Model of Investment and Borrowing
We construct a model of corporate investment and borrowing with agency costor external finance premium explicitly taken into consideration. The model consists offour equations: investment equation, borrowing equation, land asset equation, andinterest rate spread equation. Agency cost is a key variable of each equation. A brief
explanation is made on each equation of the model.

2

It is well known that marginal profitability of investment or marginal q is asufficient statistics of investment under perfect capital market when a firm incurs an
extra convex cost in adjusting investment. 3 However, once we relax the assumption of
perfect capital market and incorporate the asymmetric information between lenders andborrowers into the model, marginal q is no longer sufficient statistics of investment andthe degree of asymmetry or the magnitude of agency cost matters for investment
decision.4 The upshot is that the factors to affect the agency cost enter the investment
function as an additional explanatory variable. For example, cash flow or land as
collateral can be a popular candidate besides marginal q in investment function.
Moreover, the manner in which cash flow or land affects investment differs across firms
with different agency cost structure. It has been asserted that the structure of agency
cost depends on the firms’ attributes. For example, Fazzari et al.(1988) shows that theeffect of cash flow on investment depends on the age of firm. Hoshi et al.(1991)
demonstrates that the impact of cash flow on investment hinges upon whether a firm is amember of industrial group or not. Himmelberg et al. (1999) shows that the ownershipof the firm affects the impact of cash flow on investment.
We specify investment equation as a function of marginal q and unobservableagency cost.
It= α1 + β1qt + γ 1 ACt + ε 1t(1)
K t −1
where It : real investment in period t
Kt : capital stock at the end of period t
qt : marginal q in period t
ACt : agency cost in period t
ε 1t : error term in period t.
The agency cost, defined as the difference between the cost of internal financeand external finance, affects the level of borrowing. When the agency cost is low, a firm
has more incentive to increase borrowing. Therefore we express the ratio of borrowing
to capital stock or borrowing ratio as a function of agency cost as well as marginal q.
∆Bt= α 2 + β 2 qt + γ 2 AC t + ε 2t
ptI K t −1
3
4

See Hayashi(1982).
See Hubbard(1998) for a survey of investment behavior under imperfect capital market.
3(2)

where ∆Bt : increment of borrowings in period t

ptI K t −1 : capital stock at replacement cost at the end of period t-1.

ε 2t : error term in period t.
The agency cost is inversely associated with the collateralizable net worth of the
firm. In particular land asset had long played a collateral value in Japan under the
expectation that land price would never fall. However, close association of borrowing
with land asset made loans insolvent once land price plummeted in the 90s.
Therefore we regard land asset as a proxy of collateralizable net worth and express
the agency cost as a function of the ratio of land asset to tangible asset (land asset plus
capital stock). The following equation is a relationship between the ratio of land stock totangible asset and the agency cost.

ptL Lt −1= α 3 + γ 3 ACt + ε 3t
ptI K t −1 + ptL Lt −1(3)

where ptL Lt −1 : land stock evaluated at market price at the end of period t-1.

ε 3t : error term in period t
The interest rate spread between the borrowing interest rate and the risk-free rate
directly reflects the magnitude of agency cost, so that the interest rate spread is written
as an increasing function of the agency cost.

spreadt = α 4 + γ 4 ACt + ε 4t(4)where spread t : the interest rate spread between the borrowing interest
rate and the risk-free rate in period t.
ε 4t : error term in period t
Now we have four equations relating the agency cost to investment, borrowings,
land asset and interest rate spread. To close the model, we need the equation to describe
the movement of agency cost. We assume that the agency cost is generated by a fourth4

order AR process. 5
ACt = φ1 ACt −1 + φ 2 ACt − 2 + φ3 ACt −3 + φ 4 ACt − 4 + ν t
where ν t : error term distributed as iid N (0,1)(5)

It is assumed that this transition equation is stationary.6
Now we are ready for casting our model into state space form. The state spacemodel consists of measurement equations and transition equation. The measurement
equation is defined as an equation in which unobserved variable explains observed
variables. In our model measurement equations correspond to eq.(1) to (4).
Measurement equation is summarized as follows:
I t K t −1 γ1  ε 1t  β1 

  
 
 
I
∆Bt pt K t −1 γ 2  ε 2t  β2 
 p L L ( p I K + p L L )  =  γ  AC t +  0 q t +  ε 
t
t −1
t
t −1
 t t −1  3
 3t 
 






ε 
spread t
 0
 4t 
 γ 4 (

where ε i t : iid N 0, σ i2(6))

Note that marginal q is exogenous in our model. The transition equation is the one todescribe the movement of unobservable variable. Eq.(5) is the transition equation in ourmodel. Note that the variance of innovation vt in the transition equation is normalized
to be unity in order to identify the other parameters and agency cost. In the state spacemodel we estimate an unobservable agency cost as well as the other parameters and theerror variances underlying the model. Explanations of statistical tool we use are now inorder.
3. Econometric Procedure to Estimate the State Space Model
The agency cost in eq.(1) to (5) is an unobserved variable. The main feature of
our paper is to estimate this unobservable variable by extracting the common factor
from the co-movement of four observable variables: investment rate, borrowing ratio,
ratio of land to tangible asset and interest rate spread. This common factor is identified
as the estimate of agency cost. To estimate the co-movement, the Kalman filter
technique is adopted. It is the algorithm of estimating unobserved variable or state5

The choice of lag length is partially motivated by the quarterly data set we use.
Agency cost model represented by eqs.(5) and (6) is analyzed by Uchiyama (2002), whereselection of lag order and non-stationarity test (structural change test) of eq. (5) is conducted by
Bayes factor.

65variables from Gaussian linear state space model.7
Since relatively small sample is dealt with in this study and we estimate anumber of parameters and extract the unobservable series of agency cost from the state
space model, the Bayesian approach would be appropriate. In a Bayesian framework theparameters and the agency cost are all treated as unobservable random variables to beinferred from observable data. We use the Gibbs sampler, one of the Markov Chain
Monte Carlo (MCMC) simulation techniques to obtain the parameters to characterize
the marginal distribution from conditional distribution.8
Bayesian Inference via Gibbs Sampler
In Bayesian inference the estimates such as the means and standard deviations ofparameters are derived from their marginal posterior distributions which consist of theirprior distributions and sample likelihood as follows.
p(θ | Y ) =p(θ ) L(θ | Y )p(Y )where p(θ| Y) : posterior density of parametersθ
Y: sampled datap(θ) : prior density ofθL(θ | Y ) : likelihood functionp(Y) : marginal density of Y
To find the marginal posterior distributions from the given conditional
posterior distributions, Gibbs sampler is carried out. The procedure of Gibbs sampler inthe state space model is developed by Carter and Kohn (1994).9 When their Gibbs
sampler is applied to our model, the procedure can be divided into four steps.10 In thefollowing steps we denote the j-th iteration by superscript j.
Step 1. Generate ACt(j) for t = 1, 2, 3, …, T.
( j)j)
We derive means, AC t , and variances, Σ (ACt
, of ACt for t = 1, 2, 3, …, T from7

See Hamilton (1994) for the detailed explanations of the algorithm of Kalman filter.
See Casella and George (1992) for the comprehensive survey of the Gibbs sampler
9They propose the multi-move method of Kalman filter via Gibbs sampler. Their method isefficient and the speed of convergence is faster than the single-move method.
10
See Carter and Kohn (1994) and Kim and Nelson (1999) for more detailed explanations on
this procedure.
86Kalman filter using parameters in the (j-1)-th iteration, and generate each ACt(j) from( j)j)normal distribution with means AC t and variances Σ (ACt
, i.e.,{ ACt(j ) | γ ( j −1) , β ( j −1) ,( j)

σ 2( j −1) , φ ( j −1) }～N ( AC tj), Σ (ACt)

Step 2. Generate γ ( j ) and β ( j ) in measurement equations.
We generate the coefficients, γ ( j ) , β ( j ) , of measurement equations from normal
distribution conditional on ACt and other parameters, σ 2( j −1) , φ ( j −1) , i.e.,{ γ ( j ) , β ( j ) | σ 2( j −1) , φ ( j −1) , ACt(j) }～N ( ( γ (j) , β ( j ) ) , Σ ((γj ), β ) )Step 3.

Generateφ ( j ) in the transition equation.

We generate the coefficients,φ(j), of transition equation from the truncatednormal distribution conditional on ACt and other parameters, i.e.,{ φ ( j ) | σ 2( j −1) , γ ( j ) , β ( j ) , , ACt(j) }～N ( φ ( j ) , Σ φ( j ) ) 1[ s (φ )]where 1[ s (φ )] : indicator function to return unity if the roots of φ ( L) = 0 lie
outside the unit circle, otherwise zero. 11
Step 4. Generate σ 2 ( j ) in the measurement equations.
We generate the variances, σ 2( j ) ,of measurement equations from the inverted
gamma distribution conditional on ACt and other parameters, i.e.,{ σ 2( j ) | γ ( j ) , β ( j ) , φ ( j ) , ACt(j) }～IG ( v, σ 2 ( j ) )where v : posterior degree of freedom.
By iterating these four steps, the conditional distribution of each parameter
converges to the invariant marginal distribution independent of the other parameters.
The sample extracted from converged distribution shapes the posterior marginal
distribution, and the parameter estimators are obtained from this sample. As for thepriors, we use noninformative ones for all the parameters but error variances. In thisstudy, the first 1000 iterations of Gibbs sampler is discarded for convergence, and thenext 5000 iterations are taken as our sample. A sequence of iterative steps converged
after 1000 iterations based on a diagnostic proposed by Geweke (1992). Since the11This truncated normal distribution is adopted to guarantee the stationarity of the transition
equation.
7

sample has auto-correlation, the variance formed directly from the sample tends to beoverestimated. To reduce the auto-correlation, we re-form the posterior distribution
from the means of each 10 successive elements of the original sample with 5000
elements. 12 Accordingly, 500 sample elements are obtained from this re-formed
sample, and we derive the means, standard deviations, medians and the 95% posterior
probability bands (2.5%-th and 97.5%-th values of the sample) from this new sample.
Comparison across Different Firm Groups
Since the variance of innovation of the agency cost is normalized as unity ineach firm group, comparison of the agency cost across different firm groups is notnecessarily rigorous. Therefore, we adopt the following strategy. We compute the extent
to which the agency cost affects four observable variables: investment rate, borrowing
ratio, ratio of land asset to tangible asset and interest rate spread by multiplying theestimated series of the agency cost by the corresponding coefficient ( γ 1 , γ 2 , γ 3 , γ 4 )of each measurement equation for each firm group. This exercise helps us to see how
closely each four observable variable is associated with the agency cost. As for theeffect of land asset on the agency cost, we multiply the ratio of land stock to tangible
asset, ptL Lt −1 ( ptL Lt −1 + ptI K t −1 ) , by the reciprocal of its coefficient ( γ 3 ) in eq. (3).

4. Data Construction and Descriptive Analysis
We use quarterly data reported in the Quarterly Report of Financial Statementsof Incorporated Business (QRFS) of the Ministry of Finance. The QRFS produces
quarterly reports for manufacturing and non-manufacturing firms on major items fromtheir balance sheets and profit and loss statements, disaggregated by firm size. The
virtue of this data source is the decomposition of tangible fixed assets into components
and we can construct a time series of land stock, which plays an important role in our
analysis. Our sample period includes the first quarter of 1975 through to the first quarterof 1998, covering the long booms and the severe recessions in the 1980s and the 90s.
We measure firm size by capital. Firms are categorized into three groups by theirlevel of equity capital: small, medium, and large firms. Small firms have under ¥ 100
million yen in capital, medium firms have between ¥ 100 and ¥ 1000 million yen incapital, and large firms have over ¥ 1000 million yen in capital.

12

It is referred to as batch mean.
8

Data Construction
The discontinuity of the time series is one major problem of the QRFS. This arises
from a complete renewal of the corporations in the sample every April, after which thesample is fixed for one year. It is necessary to adjust for this discontinuity in aconsistent manner. Fortunately, the survey contains the values of main balance sheet
items at the beginning and end of each period covered in the sample. This implies that
we can compute the time series of flow variables in a consistent manner. Once the flow
series is computed, the perpetual inventory method can be applied to construct the stock
series. See Ogawa(2000b) for the detailed procedures for constructing the consistent
data series.
Descriptive Analysis of Major Variables in the Firm’s Balance SheetLet us first describe the characteristics of major variables used in our analysis.
Table 1 to 4 shows the sample means of investment rate, rate of change in totalborrowing, rate of change in land stock at market price and marginal q, respectively,
over the whole sample period as well as three subperiods. They are the second quarterof 1975 to the fourth quarter of 1986, the first quarter of 1987 to the first quarter of
1991, and the second quarter of 1991 to the first quarter of 1998. The second subperiod
corresponds to the long booms (Heisei Keiki) in the late 80s when the land priceexhibited an upward trend. In the third subperiod the land price plummeted, plunging
the Japanese economy into stagnancy.
The sample average of the gross investment rate, given in Table 1, is highest in
the second subperiod and lowest in the third subperiod for manufacturing as well as
non-manufacturing industries. The volatility of fixed investment is highest among small
firms for both manufacturing and non-manufacturing industries.
The average rate of change in total borrowing, given in Table 2, is highest in thesecond subperiod except for large firms in manufacturing industries. It is highest forsmall firms of non-manufacturing industries. The average rate of change amounts to
4 % per quarter or 16 % per annum. By contrast the average rate of change is negative
for large firms in manufacturing industries except for the third subperiod. This mightreflect a shift of financing from bank loans to equity or bond for large manufacturingfirms.
Table 3 gives the sample average of the rate of change in land stock at market
price. There is no discernible difference across firm groups. The reason is as follows.
The change in land stock is decomposed into two factors: increment or decrement ofland stock in real terms and change in land price common to all firms. Close movements

9

of the change in land stock across firm size hints that the latter component dominates.
The average rate of change in land stock is highest in the second subperiod and lowest
in the third subperiod.
Finally Table 4 gives the sample average of marginal q. Marginal q is constructedby estimating a VAR model of profit rate and discount rate, as is originally developed
by Abel and Blanchard (1986).13 It should be noted that marginal q of small firms ismuch larger than that of medium or large firms.
5. Estimates of Agency Cost and Their Association with Firms’ Activities
Four measurement equations relating the agency cost to investment, borrowing,land asset and interest rate spread, along with transition equation of the agency cost, areestimated in a Bayesian context by Kalman filter technique for three firm groups (small,medium and large firms) of manufacturing as well as non-manufacturing industries.
Overall the estimation results support the theoretical supposition that agency cost isimportant especially for small firms that are likely to be constrained in capital market.14
The response of investment to agency cost is negative and significant in the sensethat the 95 % band does not include zero, irrespective of firm size and industry. The
smaller the firms are, the larger the mean response of investment to agency cost is inabsolute value. In other words, investment of small firms is more sensitive to agency
cost. The response of borrowings to agency cost is also negative and significant except
for large firms of manufacturing industries. The response of borrowing is larger inabsolute value for smaller firms, which implies that borrowings of small firms are much
more affected by agency cost. The collateral role of land in alleviating agency cost,measured by the reciprocal of γ 3 , is also successfully estimated irrespective of firm size
and industry. An increase of land value at market value reduces the agency cost. The
effect of agency cost on interest rate spread is positive and significant except for small
firms in non-manufacturing industries. The interest rate of large firms seems to reflect
the agency cost quite accurately.
As for the effect of marginal q on investment, it is significantly positive except forlarge firms in non-manufacturing industries. The marginal q has significantly positiveeffect on borrowing only for medium firms in manufacturing industries and large firms
in non-manufacturing industries. Insignificance of marginal q variable in borrowing
equation of small firms is consistent with the importance of agency cost rather than thefundamental profitability for small firms.
13
14

See Ogawa(2000a) for detailed procedure to construct marginal q series.

Details of the estimation results are given in Appendix Tables.
10

Estimates of Agency Cost
Figure 1 and 2 show the estimates of agency cost from the first quarter of 1976 to
the first quarter of 1998 for manufacturing and non-manufacturing industries,
respectively. The agency cost is normalized at 100 in the first quarter of 1976. What iscommon to all firms is an increasing trend of agency cost in the 90s when land priceplummeted. We also observe a declining trend of agency cost in the late 80s for small
and medium firms in manufacturing industries and small and large firms in
non-manufacturing industries. Note that land price soared noticeably in the late 80s. The
agency cost started to fall at the beginning of the 80s for large firms in manufacturingindustries. Development of financial markets starting from the 80s lowered agency cost
and thus enabled large manufacturing firms to finance from a variety of sources cheaply,
leading to fall of agency cost.
Association of Agency Cost with Firms’ Activities
We turn to the relationship of agency cost with firms’ attributes and activities suchas investment, borrowing, land asset, and interest rate spread. It can be seen by the
product of agency cost with the corresponding parameters.15
The effect of agency cost on investment is shown in Figure 3. It is seen that
increase of agency cost in the 90s depressed investment to a large extent. Note that theeffect is especially large for small firms. We also observe that fall of agency cost in thelate 80s is associated with vigorous investment. The effect is notably large for small
firms in non-manufacturing industries. The effect of agency cost on borrowing is shownin Figure 4. It is clear that rise of agency cost in the 90s drastically reduced borrowing
of small firms. Conversely fall of agency cost in the late 80s led to an increase ofborrowing of small firms. It should be noted that borrowing of large firms areunaffected by the agency cost. Figure 5 shows the association of interest rate spreadwith agency cost. We see that the interest rate spread of large firms is most affected by
the agency cost. In the 80s the interest rate spread tends to decline due to fall of agency
cost, while the interest rate spread exhibits an increasing trend in the 90s, reflecting arise of agency cost. Lastly Figure 6 shows the association of agency cost with land asset.
We see that agency cost is closely related to the value of land asset. In the late 80s thesoaring land price contributed to reducing agency cost, while the agency cost rose
15

The computed values in the subsequent figures are normalized by subtracting the computed value
at the first quarter of 1976 from the values in the subsequent period. Therefore, the computed values
are normalized to zero at the first quarter of 1976.
11

sharply in the 90s when the land price plummeted.
6. Concluding Remarks
In this study we made an attempt to estimate a state space model of investment andborrowing in a Bayesian framework and extract the unobservable agency cost ofJapanese firms by firm size. Our approach seems to be quite successful since we can
explain the investment and borrowing behavior of firms in the late 80s and 90s by the
movement of agency cost. We find that the agency cost exhibited a declining trend in
the late 80s and an increasing trend in the 90s irrespective of firm size. We can pin
down the driving force of agency cost to be the market value of land. Furthermore, wefind that investment and borrowing behavior of small firms is very much affected bytheir agency cost in the late 80s and 90s. In particular our results can shed light on thecause of stagnancy of business activities of small firms in the 90s. In the 90s land priceplummeted and collateral value of land fell drastically, which in turn affected severely
investment and borrowing of small firms by raising their agency cost. Our evidence
demonstrates that imperfection of capital market is notable for small firms in Japan.

12Reference

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13

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Suzuki, K. and K. Ogawa(1997).” Tochi Kakaku no Hendo to Setsubi Toshi –Nippon no Seizougyou ni kansuru Paneru Deta niyoru Bunseki – (Fluctuation in Land
Prices and Capital Investment – Evidence from Panel data of Japanese Manufacturing
Firms -,” The Economic Review (The Institute of Economic Research, Hitotsubashi
University), 48, 218-226.
Uchiyama, H. (2002). “The Index of Aggregate Agency Cost and Heisei Boom,”
mimeographed.

14

Table 1
Descriptive Statistics of Fixed Investment Rate by Firm Size(%)
75:2-86:4

87:1-91:1

91:2-98:1

75:2-98:1

Manufacturing
Industries
Small firms

4.10

4.47

2.69

Medium firms

3.72

4.03

2.69

Large firms

3.58

3.90

3.00

3.74
(0.98)
3.47(0.74)
3.46(0.63)

Non-manufacturing
Industries
Small firms

4.19

5.40

3.19

Medium firms

4.24

4.38

3.29

Large firms

4.02

4.78

3.77

4.11
(0.99)
3.98(0.69)
4.09(0.58)

Notes: The values in parentheses are standard deviation.
Table 2
Descriptive Statistics of the Rate of Change in Total Borrowing by Firm Size(%)
75:2-86:4

87:1-91:1

91:2-98:1

75:2-98:1

Manufacturing
Industries
Small firms

1.23

2.27

0.31

Medium firms

0.42

1.19

0.26

Large firms

-0.23

-0.58

0.07

1.14
(1.37)
0.51(0.91)-0.21(1.39)

Non-manufacturing
Industries
Small firms

1.92

4.02

0.49

Medium firms

1.49

2.75

0.33

Large firms

0.89

2.77

-0.15

Notes: The values in parentheses are standard deviation.

15

1.87
(1.61)
1.37(1.39)
0.92(1.48)

Table 3
Descriptive Statistics of the Rate of Change in Land Stock at Market Price by Firm Size(%)
75:2-86:4

87:1-91:1

91:2-98:1

75:2-98:1

Manufacturing
Industries
Small firms

1.14

4.56

-2.45

Medium firms

0.97

4.12

-2.50

Large firms

1.05

4.22

-2.47

0.68
(2.97)
0.52(2.85)
0.56(2.86)

Non-manufacturing
Industries
Small firms

1.23

4.67

-2.14

Medium firms

1.03

4.40

-2.29

Large firms

1.03

4.44

-2.10

0.84
(2.89)
0.64(2.86)
0.71(2.81)

Notes: The values in parentheses are standard deviation.
Table 4
Descriptive Statistics of Marginal q by Firm Size

75:4-86:4

87:1-91:1

91:2-98:1

75:4-98:1

Manufacturing
Industries
Small firms

1.66

1.92

0.93

Medium firms

1.09

1.06

0.64

Large firms

0.96

1.06

0.75

1.47
(0.47)
0.95(0.28)
0.91(0.22)

Non-manufacturing
Industries
Small firms

1.54

1.94

1.16

Medium firms

0.91

0.98

0.48

Large firms

0.80

0.93

0.57

Notes: The values in parentheses are standard deviation.

16

1.49
(0.36)
0.79(0.27)
0.75(0.17)

Figure 1. Agency Cost of Manufacturing Industries( 1976 Q1 = 100 )(a) Small Firms
115
Agency_Cost
Upper_95%_Band

Lower_95%_Band

110

105

100

95

1975

1980

1985

1990

1995

(b) Medium Firms
110

Agency_Cost
Upper_95%_Band

Lower_95%_Band

105

100

95

90

1975

1980

1985

1990

1995

(c) Large Firms
110
Agency_Cost
Upper_95%_Band

Lower_95%_Band

105

100

95

90

85

80
1975

1980

1985

1990

17

1995

Figure 2. Agency Cost of Non-Manufacturing Industries(a) Small Firms
120
Agency_Cost
Upper_95%_Band

Lower_95%_Band

115

110

105

100

95

90

1975

1980

1985

1990

1995

(b) Medium Firms
110
Agency_Cost
Upper_95%_Band

Lower_95%_Band

105

100

95

90

1975

1980

1985

1990

1995

(c) Large Firms
120
Agency_Cost
Upper_95%_Band

Lower_95%_Band

115

110

105

100

95

90

85
1975

1980

1985

1990

18

1995

( 1976 Q1 = 100 )Figure 3. Effect of Agency cost on Investment Rate
( 1976 Q1 = 0 )(a) Manufacturing Industries
%
1

Small
Large

Medium

.75
.5
.25
0
-.25
-.5
-.75
-1
-1.25
1975

1980

1985

1990

1995

(b) Non-Manufacturing Industries
%
1.5
small
large

medium

1

.5

0

-.5

-1

-1.5
1975

1980

1985

1990

19

1995

Figure 4. Effect of Agency cost on Borrowing Ratio( 1976 Q1 = 0 )(a) Manufacturing Industries
%

Small
Large

Medium

1

.5

0

-.5

-1

-1.5

1975

1980

1985

1990

1995

(b) Non-Manufacturing Industries
%

6
small
large

medium

4

2

0

-2

-4

1975

1980

1985

1990

20

1995

Figure 5. Effect of Agency cost on Interest Rate Spread( 1976 Q1 = 0 )(a) Manufacturing Industries
%
.5

0

-.5

-1

-1.5

Small
Large

Medium

-2

-2.5
1975

1980

1985

1990

1995

(b) Non-Manufacturing Industries
%

.5

0

-.5

-1

-1.5
small
large

medium

-2

-2.5
1975

1980

1985

1990

21

1995

Figure 6. Effect of Ratio of Land Asset to Tangible Asset on Agency cost
( 1976 Q1 = 0 )(a) Manufacturing Industries

10

Small
Large

Medium

5

0

-5

-10

-15
1975

1980

1985

1990

1995

(b) Non-Manufacturing Industries
small
large

medium

20

15

10

5

0

-5

1975

1980

1985

1990

22

1995

Appendix Tables
Bayesian Prior and Posterior Distribution:
Agency Cost Model of Investment and Borrowing
Table A-1 . Manufacturing Small Firms 
Prior

Posterior

Distribution

Parameters

mean

S.D.

mean

S.D.

median95%bands

CD



0

1

1.066

0.081

1.068

( 0.8931.226 )

0.006



0

1

0.023

0.074

0.025

( -0.143

0.162 )

0.001



0

1

-0.001

0.068

0.001

( -0.134

0.138 )

-0.014

01-0.1330.053-0.136( -0.224-0.030 )

0.013



0

1

-0.1410.028-0.140( -0.202-0.090 )-0.0720

1-0.2170.046-0.216( -0.317-0.141 )-0.015

0

1-1.0080.215-0.984( -1.475-0.621 )-0.073



0

1

0.039

0.013

0.037

( 0.018

0.068 )

0.034



0

1

0.983

0.176

1.005

( 0.589

1.281 )

0.016



0

1

0.366

0.280

0.397

( -0.224

0.823 )

0.051



2

4

0.206

0.020

0.205

( 0.1700.248 )

-0.009



2

4

1.290

0.096

1.287

( 1.103

1.494 )

0.032



60

20

19.8971.940

20.049( 15.82

23.83 )

-0.014



2

4

0.339

0.018

0.339

( 0.303

0.376 )

-0.026Note  The first 1000 iterations of Gibbs sampler are discarded to guarantee convergence andthe next 5000 iterations are taken as our sample. As butch mean, an average of each 10 successive
draws of the original sample is regarded as one sample of target posterior distribution.
 See eqs. (5) and (6) for the notations of parameters.
 S.D. refers to standard deviation.
 95 % bands refers to 95 % posterior probability bands.
 The convergence diagnostic (CD) statistics is derived from the i-th draw of a parameter in the recorded 5000 draws. The statistics is defined as     ,   

 



 

 ,  . Here we set 











  , and

 ¾  ¾




 

 

 

, where   ,   are standard deviation of   and   . CD of converged posterior distribution must be

asymptotically standard normal distribution. (See Geweke (1992). )23

Table A-2 . Manufacturing Medium Firms
Prior

Posterior

Distribution

parameter

mean

S.D.

mean

S.D.

median95%bands



0

1

1.063

0.075

1.068

( 0.889

1.195 )

-0.067



0

1

0.026

0.075

0.030

( -0.1200.163 )

0.015



0

1

-0.011

0.071-0.012( -0.148

0.126 )

-0.013

0

1-0.1380.049-0.140( -0.240-0.039 )

0.045



0

1

-0.1090.027-0.106( -0.169-0.059 )-0.217

01-0.1080.031-0.104( -0.184-0.055 )-0.197

01-1.117

0.195-1.114( -1.535-0.748 )-0.157



0

1

0.031

0.011

0.030

( 0.013

0.056 )

0.092



0

1

1.704

0.159

1.720

( 1.294

1.952 )

-0.093



0

1

0.642

0.175

0.662

( 0.196

0.918 )

-0.117



2

4

0.181

0.017

0.181

( 0.151

0.215 )

-0.078



2

4

0.417

0.036

0.420

( 0.3480.489 )

-0.103



60

20

19.0182.579

18.900( 14.83

24.13 )

0.110



2

4

0.256

0.014

0.256

( 0.230

0.283 )

0.051

Note: See the note of Table A-1.

24

CD

Table A-3 . Manufacturing Large Firms
Prior

Posterior

Distribution

parameter

mean

S.D.

mean

S.D.

median95%bands



0

1

1.085

0.071

1.087

( 0.936

1.217 )

0.076



0

1

0.028

0.076

0.029

( -0.117

0.177 )

-0.049



0

1

0.007

0.072

0.010

( -0.137

0.145 )

-0.0110

1-0.1570.051-0.157( -0.255-0.059 )

0.019



0

1

-0.0600.014-0.059( -0.088-0.038 )

0.109



0

1

0.021

0.009

0.021

( 0.0020.041 )

-0.004

0

1-0.9180.175-0.908( -1.290-0.608 )

0.108



0

1

0.155

0.032

0.153

( 0.097

0.223 )

-0.101



0

1

1.093

0.098

1.099

( 0.8931.275 )

0.024



0

1

-0.2290.118-0.234( -0.462

0.020 )

-0.012



2

4

0.306

0.027

0.309

( 0.247

0.353 )

-0.025



2

4

0.694

0.034

0.693

( 0.630

0.761 )

0.0415



60

20

19.4492.695

19.720( 14.41

24.27 )

0.0137



2

4

0.258

0.071

0.237

( 0.167

0.432 )

-0.001

Note: See the note of Table A-1.

25

CD

Table A-4 . Non-Manufacturing Small Firms
Prior

Posterior

Distribution

parameter

mean

S.D.

mean

S.D.

median95%bands



0

1

1.092

0.092

1.098

( 0.871

1.248 )

0.136



0

1

0.009

0.076

0.009

( -0.142

0.162 )

0.028



0

1

-0.0140.074-0.014( -0.154

0.135 )

-0.038

01-0.1140.071-0.119( -0.259

0.027 )

-0.116

01-0.1420.034-0.141( -0.217-0.080 )

0.279



0

1

-0.5500.143-0.542( -0.864-0.301 )

0.283



0

1

-0.9480.230-0.935( -1.451-0.554 )

0.262



0

1

-0.0070.006-0.007( -0.020

0.004 )

0.037



0

1

0.786

0.130

0.788

( 0.539

1.046 )

-0.030



0

1

0.156

0.316

0.178

( -0.495

0.756 )

-0.033



2

4

0.247

0.015

0.247

( 0.2180.277 )

0.025



2

4

3.201

0.253

3.208

( 2.706

3.712 )

0.071



60

20

14.47

0.83

14.48

( 12.88

16.19 )

-0.075



2

4

0.413

0.021

0.411

( 0.373

0.458 )

-0.031

Note: See the note of Table A-1.

26

CD

Table A-5 . Non-Manufacturing Medium Firms
Prior

Posterior

Distribution

parameter

mean

S.D.

mean

S.D.

median95%bands



0

1

0.980

0.120

0.994

( 0.705

1.181 )

-0.064



0

1

0.076

0.091

0.072

( -0.091

0.282 )

0.026



0

1

-0.0200.076-0.019( -0.1780.125 )

-0.0010

1-0.0750.071-0.078( -0.203

0.084 )

0.035



0

1

-0.0880.020-0.086( -0.134-0.055 )-0.146

01-0.4920.114-0.470( -0.758-0.310 )-0.160

01-0.7310.172-0.713( -1.120-0.436 )-0.115



0

1

0.070

0.024

0.066

( 0.0360.123 )

0.053



0

1

1.049

0.180

1.038

( 0.7101.429 )

-0.045



0

1

0.069

0.735

0.017

( -1.201

1.599 )

-0.045



2

4

0.220

0.012

0.220

( 0.1960.245 )

0.043



2

4

1.089

0.111

1.084

( 0.875

1.335 )

0.043



60

20

27.4301.852

27.232( 24.0731.58 )

-0.0087



2

4

0.352

0.026

0.353

( 0.2980.400 )

0.007

Note: See the note of Table A-1.

27

CD

Table A-6 . Non-Manufacturing Large Firms
Prior

Posterior

Distribution

parameter

mean

S.D.

mean

S.D.

median95%bands



0

1

1.118

0.075

1.122

( 0.9611.260 )

-0.063



0

1

0.033

0.073

0.035

( -0.1170.172 )

0.028



0

1

0.014

0.070

0.018

( -0.123

0.155 )

-0.015

01-0.1940.057-0.196( -0.302-0.077 )

0.041



0

1

-0.0820.017-0.081( -0.123-0.049 )-0.1110

1-0.0820.019-0.081( -0.124-0.048 )-0.0910

1-0.9760.217-0.962( -1.487-0.586 )-0.083



0

1

0.078

0.021

0.076

( 0.0420.122 )

0.085



0

1

0.357

0.219

0.361

( -0.089

0.747 )

-0.032



0

1

2.734

0.373

2.720

( 1.9463.456 )

-0.036



2

4

0.177

0.011

0.177

( 0.156

0.199 )

0.010



2

4

1.130

0.066

1.127

( 1.013

1.271 )

0.007



60

20

13.4670.763

13.466( 12.03

15.03 )

0.004



2

4

0.432

0.028

0.430

( 0.3810.491 )

-0.062

Note: See the note of Table A-1.

28

CD