Discussion Papers In Economics
And Business

Is Cash Flow a Proxy for Financing Constraints in the Investment Equation?
The Case of Unlisted Japanese Firms

Yuzo Honda
Kazuyuki Suzuki

Discussion Paper 06-24

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANIs Cash Flow a Proxy for Financing Constraints in the Investment Equation?
The Case of Unlisted Japanese Firms

Yuzo Honda
Kazuyuki Suzuki

Discussion Paper 06-24
August 2006

この研究は「大学院経済学研究科・経済学部記念事業」
基金より援助を受けた、記して感謝する。

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANIs Cash Flow a Proxy for Financing Constraints in the Investment Equation?
The Case of Unlisted Japanese Firms *Yuzo Honda(Osaka University)
andKazuyuki Suzuki(Meiji University)

August 16, 2006

Abstract
The literature maintains the statistical significance of cash flow in the investment
equation. One criticism against the financing constraint interpretation of cash flow isthat cash flow may be picking up information on the future profitability of a firm which
Tobin’s Q fails to capture. We confine ourselves to the investment behavior of unlisted
automobile parts suppliers, and use the sales of large automobile makers as an
exogenous instrument. Despite the various criticisms against the financing constraintinterpretation of cash flow, our statistical evidence does not disagree with the
hypothesis.
Keywords: Tobin’s Q, Investment Equation, Cash Flow, Financing Constraint, Japanese
Unlisted Firms
JEL classification: E22, G31
Correspondence: Yuzo Honda, School of Economics, Osaka University, Toyonaka
Osaka 560-0043, JAPAN1Is Cash Flow a Proxy for Financing Constraints in the Investment Equation?
The Case of Unlisted Japanese Firms

Yuzo Honda(Osaka University)
andKazuyuki Suzuki(Meiji University)

1. Introduction
Hayashi (1982) argues that average Q is a sufficient statistic for the firm’s
investment opportunities under a certain set of conditions. However, many studies havefound that cash flow variable is statistically significant in their investment equations.
Fazzari, Hubbard and Petersen (1988) divide their samples into two groups—thosefirms with a higher dividend and those with a lower dividend—and find that severely
financially constrained firms react more sensitively to cash flow. They also demonstratethat firms are not indifferent in their use of internal and external funds in theirinvestment decision. Hoshi, Kashyap and Scharfstein (1991) also divide their samples
into groups—those firms with main banks and those without—and estimate theirrespective investment equations separately. Finding that the coefficient estimate of the
cash flow variable for those firms with main banks is significantly smaller than thecorresponding estimate of those firms without main banks, Hoshi et al. (1991) argue
that main banks mitigate the asymmetric information problem and reduce the agency
cost in lending. From this viewpoint, cash flow is an important part of internal funds,
and the agency cost of internal funds is lower than that of external funds. The
investment behavior by firms is then sensitive to the volume of internal funds.

2However, there is some criticism against the above financing constraintinterpretation of cash flow variable. First, Tobin’s Q, constructed using data on stock
prices, may be a poor proxy for the future profitability of the firm, and cash flow
variable may then pick up information of the future profitability of the firm which
Tobin’s Q fails to capture. See, for example, Sims (1988), and Cummins, Hassett andOliner (2006). The latter proposes a ‘real Q’ rather than a Tobin’s Q constructed withstock prices.
Second, if we specify that the production function of a firm is subject to exogenous
technology shocks, all three variables—investment, Tobin’s Q, and cash flow—become
functions of technology shocks. Two difficult problems then emerge. The first is thatboth Tobin’s Q and the cash flow variables on the right-hand side of the investment
equation become endogenous and appropriate measures should be taken to deal withsimultaneous equations bias. The second is that since Tobin’s Q and the cash flow
variables share the same information associated with technology shocks, the statisticalsignificance of the cash flow variable does not directly imply that the firm in question isfinancially constrained. The statistical significance of the cash flow variable may thenbe simply picking up the information on technology shocks. To test whether or not thefirm is financially constrained, it is therefore necessary to divide the sample into a
supposedly financially constrained group of firms and a less financially constrainedgroup of firms, estimate their respective investment equations, and test whether or not
the coefficient estimates of cash flow variable are statistically different. See, Hayashi
and Inoue (1991), and Hayashi (2000) for details.
To absorb the information of the future profitability of a firm, which Tobin’s Q fails to
capture, Fazzari et al. (1988), Hoshi et al. (1991), and others include the sales–capital3

ratio of a firm, in addition to Tobin’s Q and the cash flow variables, in the right-handside of the investment equation, and attempt to interpret the cash flow variable as afinancing constraint. However, as Hall (1988) correctly points out, the causality between
the sales of a firm and its investment is both ways and the sales–capital ratio is
endogenous.
In this paper, we confine ourselves to the investment behavior of unlisted automobile
parts suppliers, and propose to use a better instrument—the sales of large automobile
makers—to control for the future profitability of a firm. The sales of large automakers is
exogenous to auto suppliers, and adding this exogenous demand variable to theright-hand side of the investment equation makes it easier to interpret the cash flow
variable as a financing constraint.
Indeed, we find that addition of the sales–capital ratio of large automakers to theright-hand side of the investment equation of suppliers makes the t-value of Tobin’s Q
smaller, while throughout our empirical investigation it keeps the t-value of cash flow
virtually unchanged. This finding at least suggests the cash flow variable plays the roleof a financing constraint in the investment equation.
The organization of the paper is as follows. In Section 2, we provide somepreliminary observations on our sample, and present some intuition on the issue using
our sample. In Section 3, we explain our baseline investment equation to estimate andreport our statistical results. To reconfirm our results, we extend our baseline model toswitching regression models and report our statistical evidence in Section 4. In Section
5, we summarize the contributions of this paper.

2. Some Casual Observations

4

Figure 1 shows the frequency distribution of annual data on the ratio of the amountof investment to that of cash flow for Japanese unlisted automobile parts suppliers overthe period 1975 to 2004. The total number of observations is 1,260.
[ Figure 1 around here ]If the ratio of the amount of investment to that of cash flow is less than one, wemight roughly take it as indicating that the firm in question makes investment within
the limit of internal funds. Stiglitz (1988) also points out that if the firm is facing afinancing constraint, the amount of investment is expected to cluster around thefinancing constraint. Of course, there might be cases in reality where firms just happen
to undertake investment within the limits of internal funds, not because firms facefinancing constraints, but because firms foresee the lack of future demand for theirproducts. In addition, there may be other cases where firms happen to hold other liquid
assets other than cash flow and use these for investment. Therefore, we need to becareful about interpreting the ratio of the amount of investment to that of cash flow.
However, if the ratio of a firm is far from one, we may take it as indicating that the firm
is not facing financing constraints.
Figure 1 shows that more than 60% of the sample falls within the range of 0.5 and1.5 of the investment–cash flow ratio. This suggests that many firms may be facingsome financing constraints. We now turn to the more formal analysis in the remaining
sections.

3. Baseline Investment Equation
Under the assumption of perfect competition, constant returns, and capital as the
only quasi-fixed factor, Hayashi (1982) finds that marginal Q equals average Q (the5ratio of the market value of the firm to the replacement cost of the capital stock) andthat average Q is a sufficient statistic for the firm’s investment opportunities. Whencash flow variable is added to the investment equation in empirical work, however, itscoefficient is found to be almost always significant.
There are two competing hypotheses for this empirical finding. The first hypothesisis that cash flow captures information on the future probability of each firm which
average Q fails to explain. The second hypothesis is that cash flow is a source of internalfunds, and that the price of internal funds differs from external funds due toimperfections in the capital market. Cash flow then represents the degree of tightness
in the financial constraints firms face.
Many studies, including Fazzari et al. (1988, 1996), Hoshi et al. (1991), added thesales–capital ratio to the investment equation to control for the future profitability of afirm. As Hall (1988) correctly points out, however, the sales–capital ratio is endogenous
in the investment equation, which may introduce a simultaneous equation bias inestimation. To avoid this simultaneous equation bias, we choose a sample of unlistedcompanies which supply parts of automobiles to large automobile makers, andinvestigate whether their cash flow variable represents a true financial constraint or
merely captures future profitability unexplained by Tobin’s Q. We select this particulargroup of parts suppliers in the auto industry because the sales of large automobile
makers captures information on the future profitability of parts suppliers, while thesales of large automobile makers is unaffected by the investment decisions of parts
suppliers. That is, the amount of sales for large automakers is exogenous to theinvestment decision of parts suppliers. Our base line equation is:

6

I i ,tK i ,t −1= α i + βQi ,t + γ

CFi ,t −1
K i ,t −1+δ

AS i ,t
AK i ,t −1+ u i ,t

(3.1)

Subscript i,t denotes firm i at time t. I , Q , CF , K denote investment, Tobin’s Q,
cash flow, and capital stock, respectively. (i=1,2,…,N, t=1,2,…,T). AS and AK are thesales and capital stocks of large automobile companies, respectively, to which each firm
supplies its products. Equation (3.1) is standard except for the fourth term on theright-hand side.
Most authors use the stock price of each firm to construct data on Tobin’s Q, but we
do not. We adopt a different approach. See subsection 2 of Appendix 1 for the data
construction of marginal Q.
In general, the smaller the size of the firm, the greater the probability that the firm
is financially constrained ceteris paribus, because the smaller firm is more likely tohave smaller assets and thus lower collateral. All of our samples consist of unlisted
small firms, and so are suitable for testing whether or not firms face financial
constraints. In addition, note that we cannot use stock price data, because our sample
comprises unlisted firms.
We use the one-year lagged cash flow to avoid the simultaneous equation bias
problem. Polk and Sapienza (2004) also employed the one-year lagged cash flow.
In the fixed effects model, we estimate the following equation:

I i ,tK i ,t −1
where= μ i + β Qi , t + γ

CFi ,t −1
K i ,t −1+δ

AS i ,t
AK i ,t −1+ v i + u i ,t ,μ i = E[α i other right − hand side var iables ],

(3.2)

and

vi = α i − μ iareindependently and identically distributed random variables with mean zero and7variance σ υ . vi , and u i ,t are assumed to be uncorrelated. We apply ordinary least2

squares (OLS) to equation (3.2) with N-1 individual effect dummy variables. Thisestimator is called the fixed effects estimator (FEE). It is well known that FEE
numerically equals the within-group estimator (WGE). See, for example, Arellano (2003,
pp. 14–18). We use WGE throughout the paper unless otherwise stated.1 We callequation (3.2) our baseline equation.
As for variable ( AS / AK ), we consider two alternative versions ASK and ASK 2
because of the following reasons. We use the ratio of the amount of sales of an
automaker in real terms to the book value of the total tangible assets (excluding land) at
the beginning of the period as a variable representing demand for the product. When an
automaker is reported in “Kaisha Soukan (Unlisted Firm Version)”, we simply take the
AS–AK ratio of that maker. When multiple automakers are reported, we take thesimple average of the ratios. Variable ASK denotes the averaged ratios. Variable ASK 2
denotes the ratio of the single most important automaker. When we cannot identify
which automaker is the single most important, we use the averaged ratios, even invariable ASK 2 .
In this industry, the relationship between parts suppliers and automakers issometimes that of a pyramid type with three stories. The bottommost parts suppliers
supply their products to the middlemost parts suppliers (“Denso” is one such middle
parts supplier), and the middlemost parts suppliers in turn sell their intermediate
goods to automakers (for example, “Toyota”). In such a case, we take the sales–capitalratio of automakers of final goods.
Since there are many missing data in the sample, we use an unbalanced panel
estimation method. As a result, it is difficult to include time dummy variables to capture8the typical booms and slumps of business cycles. However, recall that Within-Group
Estimation numerically equals OLS applied to data in deviations-from-time-means.
Hence, variable ASKor

ASK 2 in deviations-from-time-means picks up theinformation on the booms and slumps of business cycles, and plays a similar role to time
dummy variables.
In the estimation, we have discarded outliers with extreme values exceeding ± fivestandard deviations from the mean in any component throughout the paper, to obtainrobust estimates.
Table 1 reports the estimates of our baseline equation.
[Table 1 around here]
In Table 1, the comparison of column (5) with column (6) or column (7) shows that thet-values of cash flow CFK are virtually unchanged when the demand variable ASKor

ASK 2 is included, while the t-value of Q falls from 8.60 to 7.56 in column (6) or

7.59 in column (7). All of these results suggest that variable cash flow CFK has some
information content completely independent of the demand for the product or the future
profitability of the firm. This does not conflict with the hypothesis that the cash flow
variable represents the financial constraints of the firm.
Some may argue that the installment of newer, more efficient machines certainly
increases the profitability of a firm, and that Tobin’s Q is endogenous in equation (3.2).
To cope with this criticism, we estimated the same equation (3.2) with Tobin’s Q
replaced with the one-period-lagged Tobin’s Q. The resulting estimates are reported inTable 2.
[Table 2 around here]
Although the coefficient estimates in Table 2 are somewhat different from those in Table

9

1, the central message remains the same.2 That is, the addition of the demand variables

ASK or ASK 2 does not lower the t-value of the cash flow variable CFK , but does lower
the t-value of the lagged value of Tobin’s Q. The estimated results with the data
including lagged Tobin’s Q also suggests that cash flow works as a financing constraint.

4. Switching Regression Models
To check the robustness of the findings in the previous section, we take a different
approach. Following Hu and Schiantarelli (1998), we use switching regression models.
We take into account the possibility that those firms that are more financiallyconstrained may behave differently from those which are less constrained.
Although Hu and Schiantarelli (1998) select a set of balance sheet variables as anindicator of financial strength, these variables are not necessarily available forJapanese unlisted firms. Rather, we select two variables as an indicator of financial
strength: the lag of total assets at the beginning of the period LK (−1) , and a dummy
variable, B , indicating whether the firm in question has issued corporate bonds.
Variable B takes a value of one when the firm issued bonds in the past, and zerootherwise. Those firms which issued corporate bonds in the past, ceteris paribus, areexpected to have greater credibility and more likely to be less financially constrained.
Thirty-eight firms of a total of 82 are found to have issued corporate bonds in the past.
For variable LK (−1) , the larger total assets, ceteris paribus, the greater the credibilityof the firm.
Making use of these indicator variables, we break the sample into two groups: amore financially constrained group and a less financially constrained group. We canactually test whether or not this breakup of the sample into two groups is appropriate.

10The switching regression model is as follows.

Regime 1:

Regime 2:

I i ,tK i ,t −1
I i ,tK i ,t −1= X i ,t β c + u1,i ,tiff

y i*,t < 0 ,(4.1)= X i ,t β uc + u 2,i ,tiff

y i*,t ≥ 0 ,(4.2)

where X i ,t = [Qi ,t , (CFi ,t −1 / K i ,t −1 ), ASK t ] and ASK t = AS t / AK t −1 (version 1).
Indicator Equation: y i ,t = Z i ,tθ + ε i ,t ,

(4.3)

*

where Z i ,t = [ LK i ,t −1 ,1](4.4)

or Z i ,t = [ LK i ,t −1 , Bi ,t ] ,(4.5)

where LK i ,t −1 denotes the log of total assets of firm i at the beginning of the period t,

Bi ,t is a dummy variable which takes a value of one when firm i issued bonds in thepast, and zero otherwise, β c , β uc , θ are vectors of corresponding parameters. u1,i ,t ,u 2,i ,t , and ε i,t are error terms.
When firm i has the smaller amount of total assets, the value of LK i ,t −1 in (4.4)
becomes smaller. Assuming that the coefficient of the variable LK i ,t −1 is positive, asmaller value of LK i ,t −1 in (4.3) leads to a smaller value of y i ,t . Although y i ,t also**

depends on the random variable ε i,t , the smaller value of LK i ,t −1 tends to increase theprobability that an inequality y i ,t < 0 holds. Therefore, the smaller value of LK i ,t −1 is*associated with the tendency for the sample to fall into Regime 1 in (4.1). Parameter β cthen denotes the parameter of those firms that are more likely to be financially11constrained; β uc in equation (4.2) is the parameter of those firms that are less likely to
be constrained.
We consider two versions of the indicator equations. The first version is equation(4.4), which includes the log of total assets and a constant. The second version isequation (4.5), which includes both total assets LK and the bond dummy variable B .
Firms that issued bonds in the past are likely to have greater credibility whenborrowing, and less likely to be financially constrained.
We assume that the vector of error terms in the investment and indicator equations(u1,i ,t , u 2,i ,t , ε i ,t ) ' is jointly normally independently distributed with mean zero andcovariance matrix Σ , where:⎡σ 12 σ 12⎢
Σ = ⎢σ 21 σ 22⎢σ ε 1 σ ε 2⎣σ 1ε ⎤⎥σ 2ε ⎥ .
σ ε2 ⎥⎦

With the assumption of the joint normality of error terms, we estimate the above model(4.1) through (4.5) by maximum likelihood estimation.
The probability that sample ( I i ,t / K i ,t −1 ) falls into Regime 1 is given by:

Pr ob( y*i ,t < 0 ) = Pr ob( Z i ,tθ + ε i ,t < 0 )= Pr ob( ε i ,t < − Z i ,tθ )= Φ ( − Z i ,t θ ) .

(4.6)

The probability that ( I i ,t / K i ,t −1 ) falls into Regime 2 is given by:

Pr ob( y*i ,t ≥ 0 ) = Pr ob( Z i ,tθ + ε i ,t ≥ 0 )= Pr ob( ε i ,t ≥ − Z i ,tθ )12

= 1 − Φ ( − Z i ,tθ ) .

(4.7)

The likelihood function for each observation l i ,t is a weighted conditional density
function of u1,i ,t and u 2,i ,t with weights Pr ob( ε i ,t < − Z i ,tθ ) and Pr ob( ε i ,t ≥ − Z i ,tθ ) .

li ,t = φ ( u1,i ,t | ε i ,t < − Z i ,tθ )Φ ( − Z i ,tθ ) + φ ( u2 ,i ,t | ε i ,t ≥ − Z i ,tθ )[ 1 − Φ ( − Z i ,tθ )]⎛⎞⎜ − Z θ − σ 1ε u ⎟1,i ,t
i ,t
⎜
⎟
σ 12
= φ (u1,i ,t , σ 1 )Φ⎜
⎟
σ 12ε
⎜
⎟
1− 2
⎜
⎟
σ1
⎝
⎠

⎡
⎛
⎞⎤
⎜ − Z θ − σ 2ε u ⎟ ⎥⎢i ,t2 ,i ,t⎜⎟⎥σ 22⎢+ φ (u 2,i ,t , σ 2 ) ⎢1 − Φ⎜
⎟⎥ ,
2
σ
⎜
⎟⎥
⎢
1 − 22ε
⎜
⎟⎥
⎢
σ2
⎝
⎠⎦
⎣

(4.8)

where φ (⋅) and Φ (⋅) denote the normal density and the cumulative distributionfunctions, respectively. φ (u j ,i ,t | ⋅) for j=1,2 is the conditional density and φ (u j ,i ,t , σ j )for j=1,2 is the marginal density. The second equality sign is due to Hu and Schiantarelli(1998, pp. 470), who use bivariate normal properties and the fact that a joint density
equals the product of the conditional density and the marginal density.
For a panel of N firms with Ti observations for firm i, the log-likelihood function
for all observations is given by:NTi

L = ∑∑ log(li ,t ) .

(4.9)

i =1 t =1

We maximize equation (4.9) with respect to the parameters β c , β uc , θ , and Σ .
We may also obtain an estimate of the probability that each observation falls either
into Regime 1 or Regime 2. The ex ante probability does not take into account the
information about investment, ( I i ,t / K i ,t −1 ), and is simply given by either

13

Pr ob( yi*,t < 0 ) in (4.6) or Pr ob( yi*,t ≥ 0 ) in (4.7). Given the information of ( I i ,t / K i ,t −1 ),the ex post probability takes this information into account and updates the ex ante
probability according to Bayes’ rule. Hu and Schiantarelli show that the ex postprobability that the observation ( I i ,t / K i ,t −1 ) falls into Regime 2 is given by:

Pr ob( ε i ,t ≥ − Z i ,tθ | ( I i ,t / K i ,t −1 )) =

B
,
A+ B

(4.9)

where A = φ (u1,i ,t | ε i ,t < − Z i ,t θ )Φ ( − Z i ,tθ ) and

B = φ (u 2,i ,t | ε i ,t ≥ − Z i ,tθ )[1 − Φ(− Z i ,tθ )] .
Table 3 reports the estimates of the switching regression model (4.1), (4.2), (4.3), and(4.4), where we use the current Q variable in the right-hand side of regression equations(4.1) and (4.2), and the log of total assets of firm i, at the beginning of the period t,

LK i ,t −1 , and a constant in the right-hand side of indicator function (4.4). Panel A in
Table 3 shows the estimates in the case including only the cash flow variable, CF , with
Tobin’s Q in the right-hand side of regression equations (4.1) and (4.2), while Panel B
provides estimates in the case where the cash flow variable, CF , and the demand forthe product, ASK , are included with Tobin’s Q.
[Table 3 around here]
First, the larger the total firm assets, the more credible the firm is as a borrower,
because larger firms, ceteris paribus, tend to be older, more diversified, less prone tobankruptcy, with greater collateral, and a better known track record. Table 3 shows thatthe estimates of the coefficient of variable LK (−1) are both positive and significant,indicating that Regime 2 is more likely to occur when the total assets of a firm are large.
Hu and Schiantarelli (1998, pp. 471–473) essentially obtained a negative sign on

14

the estimates of the size of the firm, a result opposite to that found in this analysis. We
argue that this difference comes from the nature of the samples used: namely, all firms
in Hu and Schiantarelli (1998) are listed firms, while the firms in the present study are
unlisted. One reason why we obtained a positive sign on the estimate of thecoefficient LK (−1) , as against Hu and Schiantarelli (1998), is because unlisted firms are
truly small, and more likely to face severe agency and information problems.
In Table 3A, the coefficient estimate of the cash flow variable, 0.92, in Regime 1 ismuch larger than the corresponding estimate, 0.12, in Regime 2. The t-value of cash
flow variable, 5.2, in Regime 1 is also much higher than the corresponding t-value, 2.5,
in Regime 2. Firms belonging to Regime 1 are those whose total assets are smaller, andaccordingly they react more sensitively to the cash flow variable.
Second, when we add the demand variable ASK to the right-hand sides ofregression equations (4.1) and (4.2), we obtain the estimates in Table 3B. A comparisonof the respective coefficient estimates between panels A and B shows that the additionof the demand variable ASK has little effect on the t-values of the cash flow
variable CF , although it greatly reduces the t-values for Tobin’s Q. This suggests thatvariable ASK picks up information on the future profitability of the firm that variable
Tobin’s Q fails to capture, and that cash flow variable CF

has independent

information on the demand variable or information on the financing constraint. With
respect to robustness, throughout the empirical results, the t-values of the cash flow
variable are virtually unchanged by the addition of the demand variable ASK to theright-hand sides in regression equations (4.1) and (4.2).
To guard against a criticism that the Tobin’s Q variable is endogenous, we replace
Tobin’s Q variable by its one-year-lagged values, and obtain Table 4.

15

[Table 4 around here]
Although the respective coefficient estimates are affected by the replacement of
Tobin’s Q with its lagged value, our main findings remain unaffected. First, the t-valuesof the cash flow variable in Regime 1 are higher than the corresponding t-values inRegime 2, suggesting that the investment behavior of those firms that are morefinancially constrained is greatly affected by the cash flow variable. Second, theaddition of the demand variable ASK to the investment equation changes virtuallynothing in the t-values of the cash flow variable, suggesting that the cash flow variable
has an independent piece of information on the demand variable, or the information on
the financing constraint.
[Table 5 and 6 around here]
Table 5 reports the estimates of the switching regression model with the indicator
equation (4.4) replaced by (4.5). Table 6 is then the same as Table 5 except that Tobin’s
Q is replaced by its one-year lagged variable.
In Tables 5 and 6, we find that all of our estimates on the coefficient of variable B
display a positive sign, suggesting that firms that issued bonds in the past tend to havethe larger value of yi ,t in equation (4.3). Therefore, these firms are more likely to fall*

into Regime 2 in equation (4.2).
Although the estimates vary slightly depending upon the model specification, ourmain results stand solid throughout Tables 3, 4, 5, and 6. First, the investment issignificantly affected by the cash flow variable in Regime 1, where firms are morefinancially constrained, but less affected by the cash flow variable in Regime 2, wherefirms are less financially constrained. Second, the addition of the demand variable tothe investment equation does not reduce the significance of the t-values of the cash flow

16

variable, suggesting that the cash flow variable contains a piece of information
independent of the future profitability of the firm.

5. Concluding Remarks
When we include cash flow, profits, or other internal fund variables on theright-hand side of the corporate investment equation, we almost always find that thesevariables are statistically significant. Fazzari et al. (1988), among others, argue that
this statistical significance is evidence that internal funds affect investment as abinding constraint. However, there are alternative interpretations on the significance of
the internal fund variables. First, Cooper and Ejarque (2001) argue that allowing the
profit function at the firm level to be strictly concave reflecting, for example, market
power, is sufficient to replicate Q theory-based regression results where profits are asignificant variable affecting investment.
Second, as shown by Hayashi (1982), average Q equals marginal Q only under selectconditions. In addition, the market value of the firm equals its stock price only if thestock market is efficient. None of these conditions are likely to hold. There is always
then the potential for measurement error in the variable Q. See, for example, Erickson
and Whited (2000). Because of errors in measuring marginal Q, we may find thatinvestment by financially constrained firms responds strongly to cash flow.
Third, there is the possibility that our econometric specification may be incorrect,
which may wrongly lead to the statistical significance of the cash flow variable. Both
Tobin’s Q and cash flow variable in the right-hand side of the investment equation are
endogenous. Applying ordinary least squares and using the current values of thesevariables may then introduce a simultaneous equation bias to the resulting parameter17

estimates. There is also reason to believe that the investment function is nonlinear. See,for example, Abel and Eberly (1994), Barnett and Sakellaris (1998), and Honda andSuzuki (2000). The linear specification included in this analysis may then also
potentially introduce serious bias in the resulting estimates.
We do not suggest that we have presented conclusive statistical evidence that thesealternative interpretations are incorrect; rather we argue that our statistical results do
not disagree with the financial constraint hypothesis of cash flow. First, recall that wehave collected our sample only from automobile parts suppliers. Since they supply parts
to large automobile makers such as Toyota, they are unlikely to be able to exert market
power, contrary to the postulation in Cooper and Ejarque (2001). In addition, earlier
work investigates the case of listed firms. However, it is questionable whether thesestudies have appropriately addressed the question because listed firms tend to be large
and may be less likely to be financially constrained. Contrary to this literature, oursample consists of smaller unlisted firms. These should be more appropriate for testing
purposes.
Second, most empirical studies make use of stock prices as a proxy for the market
value of the firm. Since all of the firms in our sample are unlisted, stock prices are notavailable. We use a different proxy for the market value of the firm from the standard
literature, and obtain statistical evidence that does not disagree with the financial
constraint hypothesis. Our findings then add yet another piece of evidence to support
the financial constraint hypothesis. In addition, the results in this analysis are robustwith respect to changes in the proxy for Tobin’s Q. This implies that our supportive
evidence for the financial constraint hypothesis is robust, not only to changes in theproxy variables, but also against the criticism of possible simultaneous equation bias.

18

Finally, we also estimated switching regression models and found that our main
findings are robust, suggesting that our results hold even in nonlinear specifications.

19Appendix 1. Data Construction
1. Data Source
The sample data are selected from the financial statements of 82 unlisted
corporations that produce automobile parts. These data are compiled by Tokyo Shoko
Research (TSR). The Kaisha-Sokan (Corporation-List) is used to identify automobile
parts suppliers. We attempted to include all suppliers; however, the TSR database fails
to cover some firms. Our final sample comprises 82 corporations.
The potential sample period is from 1974 to 2004, or 31 years. However, there arefew firms that cover the entire sample period. Indeed there are only 28 corporations
that have more than 15-year consecutive data. Even when they have more than 15
years of data, at least some lack a few years. For example, some firms have data from1974 to 1985 and from 1987 to 2004, but lack data for 1986. Others have data from 1975
to 1996 and from 1998 to 2004, but lack data for 1997. Therefore, we are obliged to
employ an unbalanced panel of data.
The fact that most of our sample consists of data with missing observations hampers
use of the perpetual inventory method as in Hoshi and Kashyap (1990) and Hayashi
and Inoue (1991), and poses some difficulties in the construction of data on thereplacement cost of capital stock, a necessary component to obtain data on marginal Q.
Hence, we follow Kaplan and Zingales (1997), Carpenter and Petersen (2002), and Polkand Sapienza (2006) and use the book value of nominal capital stock or total assets.
2. Marginal Q
Under the assumptions of constant returns-to-scale and perfect competition, we canderive marginal Qt as:

20

Qt =

⎡∞
π t+ j ⎤1
Et ⎢∑ β t + j (1 − δ ) j⎥,
p K ,t ⎣⎢ j =0
K t + j −1 ⎦⎥(A.1)

where p K ,t , π t + j , K t + j −1 , δ , and Et denote the price of capital goods at time t, grossprofit at time t+j, real capital stock at the beginning of time t+j, depreciation rate, andthe expectation operator based on the information set at time t, respectively. β t + j isjdefined as

β t + j = ∏ (1 + rt +i ) −1 (j=1,2,･･･), β t ≡ 1 , where rt + j denotes the discounti =1

rate at time t+j. (See, for example, Ogawa(2003, pp. 97–101.)
Assuming that both the gross profit rate ( π t + j / K t + j −1 ) and the discount rate rt + jfollow independent random walks, we can rewrite (A.1) as:Qt =π t / K t −1 ⎡p K ,t⎤(1 − δ ) (1 − δ ) 2
+
+
L
⎢1 +
⎥
2
⎣ (1 + rt ) (1 + rt )⎦=π t / K t −1 ⎡ (1＋rt ) ⎤⎢⎥p K ,t ⎣ (rt＋δ ) ⎦=π t (1＋rt )/ p K ,t K t −1 .
(rt＋δ )

(A.2)

Following Hayashi (2000), we define gross profit π t as π t = (1 − τ t ) × operating
income + depreciation, where τ t denotes the corporate tax rate at time t.
Because our sample consists of unlisted firms, we calculate the cost of capital( rt + δ ) as rt + δ = (1 − τ t ) ρ t + δ , whereρ t , τ t , and δ is the rate of return on

ten-year government bonds, the corporate tax rate, and the depreciation rate,
respectively. Data on

ρ t and τ t are the same across firms, but not δ . Accordingly,

we calculate the depreciation rate as the sample average of each firm over time.
As for p K ,t K i ,t −1 , we use the book value of capital stock.

21

3. Corporate Investment
We improve the method of data construction on investment. All previous studies,including Hayashi and Inoue (1991), constructed the investment data based on thedefinition:

I HI = Current Installed Capital Investment= Tangible Fixed Assets at time t－ Tangible Fixed Assets at time (t-1)＋ Depreciation,
where Tangible Fixed Assets are defined as the sum of Building, Structures, Machineryand Equipment, Tools, Furniture and Fixtures, and Vehicles and Other Transportation
Equipment.
However, the true current capital expenditure, denoted by I , should be defined as:

I = Current Capital Expenditure= Current Capital Expenditure booked under the account of Tangible Fixed
Assets＋ Current Capital Expenditure booked under the account of Construction in
Progress.
Therefore, the true Current Capital Expenditure should be:

I = I HI－ Transfer from Construction in Progress to Tangible Fixed Assets＋ Current Capital Expenditure booked under the account of Constructionin Progress= I HI＋ Account of Construction in Progress at time t － Account ofConstruction in Progress at time (t-1).

22

In the present paper, we use I instead of I HI as the data on investment.
Finally, in this section, we keep a record on how we handled those exceptional firmsthat switched accounting periods during the sample period. For illustrative purposes,
suppose that a firm in question switched its accounting period from January 1 to
December 31, 1996 to April 1, 1996 to March 31, 1997. If data on March 1996 areavailable, Investment I at year 1996 should be defined as:

I (1996)= Tangible Fixed Assets at March 1997
＋ Account of Construction in Progress at March 1997
－ Tangible Fixed Assets at March 1996
－ Account of Construction in Progress at March 1996
＋ Depreciation for the period from April 1996 to March 1997.
However, March 1996 data are, in fact, unavailable for some firms. Therefore, we define
Investment at year 1996 as follows.

I (1996)= Tangible Fixed Assets at March 1997
＋ Account of Construction in Progress at March 1997
－ Tangible Fixed Assets at December 1995
－ Account of Construction in Progress at December 1995
＋ Depreciation for the period from April 1996 to March 1997.
For those firms whose data are available for Depreciation for the period January 1996
to March 1996, we added it to the value of Depreciation from April 1996 to March 1997.
4. Cash Flow23

We define Cash Flow as the sum of Depreciation and Net Income after Income Taxes.
The cash flow rate at time t, CFt , is the ratio of the one-year lagged Cash Flow to the
one-year lagged book value of the total tangible assets (excluding land). Our definitionof Cash Flow includes dividends because firms are assumed to make decisions on real
investment first, and then formulate dividend policy. This follows suggestions by
Fazzari et al. (1988). As in Polk and Sapienza (2006), we use the one-year lagged Cash
Flow in CFt to avoid the simultaneous equation bias problem.
5. Capital Stock
We use the book value of total tangible assets excluding land as capital stock K .
Because the absolute value of K is extremely large for large automobile makers suchas Toyota, we divide K by 106 for large auto makers, which specifies the unit ofmeasurement as a billion yen. To obtain the data LK in (4.4) or (4.5), we simply takethe natural logarithm of K .

Appendix 2. Firms Included in Samples
Corporation

Periods Included in Samples

Gunma Seiki

1992–1998

Chiyoda Seisakusho

1981–2004

Shoda Seisakusho

1986–1990

1996–2004

Sakamoto Kougyo

1974–1985

1995–1997

Kurita Arumi Kougyo

2002–2004

Mie Giken Kougyo

1974–2003

Seiken Kagaku Kougyo

1974–1984

Kiipar1974–2004

Nihon Bureki Kougyo

1987–1989

Nihon Thermostat

1980–1982

Mets

1976–1987

Nihon Wiper Bureido

1974–1992

T Estick

1977–2004

2001–2004

1998–2004

1988–1999

24

Asumo1975–2004

Ho Seimitsu Kougyo

1974–1976

Yanagawa Seiki

1974–2004

TGK

1975–1983

Oi seisakusho

1991–2002

Waizu

2000–2004

Yokohama Kikou

1980–2004

Techno Hirata

1977–1986

Central Jidousha

1975–2004

Horie Kinzoku Kougyo

1987–1989

Yajima1986–2001

Aishin Kakou

1975–2004

Matsukawa Tekkosho

1974–1989

Sango

1991–2001

Ogasawara Kougyo

1986–1988

Izumi Kougyo

1977–2004

Arakawa Kougyo

1992–2003

Chuo Seiki

1974–2004

Shimizu Kougyo

1982–1990

1994–2004

Ohashi Tekkou

1974–1994

1998–2003

Aichi Kikou

1984–1987

1990–1991

Ohara Jushi Kougyo

1975–1996

1998–2004

Ansei

1974–1985

1987–2004

Aishin Koukyu

1983–1989

Kyohô Seisakusho

1974–1987

1993–1994

Yahagi Sangyo

1975–1989

1991–2001

NT Techno

1997–2003

Kyowa Sangyo

1977–1980

Sindai1974–2004

Tsuda Kougyo

1985–1990

1999–2004

Aishin Kikou

1989–1990

1993–2003

Aichi Hikaku Kougyo

1982–1988

Fuji Press

1975–1981

Housei Bureki Kougyo

1975–1987

Kotobuki Giken Kougyo

2000–2004

GS Eletech

1982–2002

1983–1984

1987–1992

1985–1998

2002–2004

1990–1993

1998–2004

1991–1995

1997–1999

1993–1999

1998–2004

1982–2004

1991–199325

1996–2003

1995–2004

Jounan Seisakusho

1986–2004

Totsuku Seisakusho

1977–1988

Asama Giken Kougyo

2000–2004

NE

1986–1988

Shizuoka Denso

1993–1997

Usui Kokusai Sangyo

1975–1983

Biyonzu

1982–2004

1990–1994

1996–1998

2000–2002

1991–2000
1985–2003

Kanae Kougyo

1985–1987

1995–2004

Toyo Densan

1980–1992

1995–2004

Enkei

1978–1986

1988–1998

Kaneda Kougyo

1977–1982

Katsuyama Fain Tech

1977–2004

Tokai Seiko

1975–1989

Rizumu1985–1989

Pajero Seizou

1985–1995

Gifu Shatai Kougyo

1983–1985

Tokitsu Sangyo

1988–2000

Asahi Forji

1992–2003

Shinnichi Kougyo

1999–2004

Kokusan Buhin Kougyo

1981–1985

1989–1994

Aoi Kikai Kougyo

1982–1987

1993–2003

Tsukiboshi Seisakusho

1978–2003

Nisshin Seisakusho

2001–2004

Heian Seisakusho

1989–2003

Mie Kougyo

1977–1979

1981–1986

1991–1994

Takao Kinzoku Kougyo

1977 1982

1984–1995

2000–2003

Asahi Aluminium

1978–1990

1992–1999

2001–2004

Sanyo Haidorikku Kougyo 1993–1995

2001–2003

Souja Kougyo

1977–1979

1995–2004

Sanjyo Kougyo

1975–1983

1985–2004

Mizushima Kikou

1977–1979

1994–2004

Ihara Seiki

1997–2004

Yoshiwa Kougyo

1981–1988

1996–1997 1999–2004

1998–2003

1999–2004

Footnote* The authors would like to thank Takayuki Ugomori for his research assistance. They26

also gratefully acknowledge the financial support of Grant-in-Aid No. 17203016 and the
21st Century Center of Excellence Program at Osaka University, both sponsored by the
Ministry of Education, Culture, Sports, Science and Technology.
1. An obvious alternative estimator is the generalized method of moments (GMM).
However, our sample contains many missing observations, and the use of lagged data as
an instrument in GMM makes the samples too small to obtain reliable estimates. For
example, if we include a two period-lagged variable as an instrument in GMM
estimation, we cannot use the sample with observation data available at t and t-1, but
missing at t-2. The sample includes many such missing values.
2. The comparison of Table 2 with Table 1 shows that the replacement of Tobin’s Q by its
lagged value makes the t-values of cash flow variable CFK smaller. We interpret this asfollows. We use one-period lagged value of cash flow for data CFK, and the use of thelagged Tobin’s Q instead of the current Tobin’s Q makes the correlation between the twovariables higher. The higher correlation between the lagged Tobin’s Q and CFK in turnmakes the t-values of CFK smaller.

27

Figures
Figure 1 Frequency Distribution of Investment / Cash Flow Ratio

500
450
400
350
300
250
200
150
100
50

Note. This graph shows the frequency distribution of the ratio ofcorporate investment to cash flow.

28

6

5.5

5

4.5

4

3.5

3

2.5

2

1.5

1

0.5

0

.5

-0

-1

.5
-1

-2

0

Tables
Table 1 Estimates of the Investment Equation (WITHIN)
Current Q model : Dependent Variable =I i ,tK i ,t −1

(1)
Q

(5)

(6)

(7)

0.18100.14730.13030.1310(12.120)(8.597)(7.560)(7.591)

0.6316

0.32670.31650.3178(9.755)(4.595)(4.539)(4.547)

CFK

(2)

(3)

ASK

(4)

0.02900.0158(8.316)(5.080)ASK2

0.02790.0146(8.088)(4.733)AdjustedR-squared

0.17620.10700.06630.06300.19810.21530.2131parentheses

denotet-values

based

on

Observations = 1260
Note.

Numbersinheteroskedastic– consistent standard errors.

29

Table 2 Estimates of the Investment Equation (WITHIN)
I i ,tLagged Q model : Dependent Variable =K i ,t −1

(1)
Q(-1)

(5)

(6)

(7)

0.15370.11950.0976

0.0986(10.818)(5.245)(4.256)(4.313)0.61940.20750.21610.2101(8.685)(1.834)(1.953)(1.886)

CFK

(2)

(3)

ASK

(4)

0.03040.0212(8.074)(5.908)ASK2

0.02970.0203(7.983)(5.691)

AdjustedR-squared

0.12580.09770.06800.06680.12980.15980.1580parentheses

denotet-values

based

on

Observations = 1131
Note.

Numbersinheteroskedastic– consistent standard errors.

30

Table 3 Estimates of the Switching Regression Model
Current Q model : Z i ,t = [ LK ( −1), A]
A. Without Demand Variable ASK
Number of observations=1260

Log likelihood=496.372

Schwarz B.I.C.=－460.678( investment equation )regime 1

regime 2Q

0.1360(4.463)0.1466(14.055)

CF

0.9171(5.207)0.1182(2.478)σi

0.2814(21.338)

0.1331(23.194)

σ i ,ε

－0.1077 (5.428)－0.0869 (5.666)

ex post probability

0.21010.7899( switching equation )LK (−1)0.2414(3.024)A

0.6395(5.804)

B. With Demand Variable ASK
Number of observations=1260

Log likelihood=512.353

Schwarz B.I.C.=－469.520( investment equation )regime 1

regime 2Q

0.1234(4.053)0.1282(11.743)CF

0.8020(4.969)0.1175(2.431)ASK

0.0199(1.741)0.0131(4.884)σi

0.2721(23.353)0.1294(21.744)σ i ,ε

－0.1013(5.224)－0.0864(5.923)

ex post probability

0.23720.7628( switching equation )LK (−1)0.2684(3.347)

A

0.5310(4.798)Notes. A is a constant, ‘ex post probability’ refers to the estimate of theex post probability that each observation falls into Regime 1 or 2
given the information on investment value.

31

Table 4 Estimates of the Switching Regression Model
Lagged Q model : Z i ,t = [ LK (−1), A]
A. Without Demand Variable ASK
Number of observations=1131

Log likelihood=399.851

Schwarz B.I.C.=－364.697( investment equation )regime 1

regime 2Q(−1)

0.0174(0.283)0.1398(8.534)CF

0.9135(3.340)－0.0358(0.492)σi

0.3085(17.249)

0.1335σ i ,ε

－0.0940 (4.124)－0.0773 (4.671)

ex post probability

0.20970.7903(21.875)( switching equation )LK (−1)0.2509(2.910)A

0.6363(5.058)

B. With Demand Variable ASK
Number of observations=1131

Log likelihood=426.024

Schwarz B.I.C.=－383.839( investment equation )regime 1

regime 2Q(−1)

0.0113(0.215)0.1166(6.912)

CF

0.8581(3.694)－0.0358(0.479)ASK

0.0207(1.797)0.0205(6.777)σi

0.2917(19.958)

0.1262(20.833)

σ i ,ε

－0.0867(4.256)－0.0759(5.204)ex post probability

0.24750.7525( switching equation )LK (−1)0.2990(3.538)A

0.4796(3.972)

Notes. A is a constant, ‘ex post probability’ refers to the estimate of theex post probability that each observation falls into Regime 1 or 2
given information on its investment value.

32

Table 5 Estimates of the Switching Regression Model
Current Q model : Z i ,t = [ LK ( −1), BOND]
A. Without Demand Variable ASK
Number of observations=1260

Log likelihood=489.319

Schwarz B.I.C.=－453.625( investment equation )regime 1

regime 2Q

0.1584(7.742)0.1294(10.959)

CF

0.6283(5.754)0.1118(2.116)σi

0.2476(33.318)

0.1231(21.221)σ i ,ε

－0.0946(5.494)－0.0858(7.550)ex post probability

0.36000.6400( switching equation )LK (−1)0.2061(2.814)BOND

0.3566(2.836)

B. With Demand Variable ASK
Number of observations=1260

Log likelihood=508.682

Schwarz B.I.C.=－465.849( investment equation )regime 1

regime 2Q

0.1508(7.095)0.1047(8.781)CF

0.5688(5.421)0.1202(2.279)ASK

0.0161(2.109)0.0146(5.156)σi0.2436(34.684)

0.1185(20.712)σ i ,ε

－0.0925(5.611)－0.0858(8.118)ex post probability

0.37690.6231( switching equation )LK (−1)0.2152(3.154)

BOND

0.2640(2.255)

Notes. ‘BOND’ is a dummy variable indicating whether the firm has
issued bonds in the past, ‘ex post probability’ refers to theestimate of the ex post probability that each observation falls
into Regime 1 or 2 given information on its investment value.

33

Table 6 Estimates of the Switching Regression Model
Current Q model : Z i ,t = [ LK ( −1), BOND]
A. Without Demand Variable ASK
Number of observations=1131

Log likelihood=391.652

Schwarz B.I.C.=－356.498( investment equation )regime 1

regime 2Q(−1)

0.0857(2.232)0.1255(6.631)CF

0.5192(3.258)0.0043(0.049)σi

0.2690(28.169)

0.1215(20.936)σ i ,ε

－0.0737 (4.036)－0.0686(5.791)

ex post probability

0.35080.6492( switching equation )LK (−1)0.2859(3.374)BOND

0.2838(2.044)

B. With Demand Variable ASK
Number of observations=1131

Log likelihood=421.711

Schwarz B.I.C.=－379.526( investment equation )regime 1

regime 2Q(−1)

0.0540(1.419)0.1052(5.830)CF

0.6287(3.898)－0.0286(0.353)ASK

0.0177(2.139)0.0227(7.126)σi

0.2647(28.603)0.1167(21.454)

σ i ,ε

－0.0765(4.322)－0.0705(6.285)ex post probability

0.35220.6478( switching equation )LK (−1)0.3252(4.128)BOND

0.2405(1.845)

Notes. ‘BOND’ is a dummy variable indicating whether the firm has
issued bonds in the past, ‘ex post probability’ refers to theestimate of the ex post probability that each observation falls
into Regime 1 or 2 given information on its investment value.

34

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37