Silviase/jgov_v1.4_full_ann huggingface dataset:
$$ +(1-\delta)\phi=\frac{(1-z_{t})p_{t}^{I}}{(1-\tau_{t})p_{t}} $$

In eq.(9) the term of $ \left(1+r_{t+1}\right)^{-1} $ is replaced by that of $ (1-\theta_{t})(1+(1-\tau_{t+1})i_{t+1})^{-1} $ , which is interpreted as an “effective” discount factor with the borrowing constraints taken into consideration. The effective discount rate or the required rate of return is now written as $ (1-\theta_{t})^{-1}(1+(1-\tau_{t+1})i_{t+1})-1 $ and is approximated by $ (1-\tau_{t+1})i_{t+1}+\theta_{t} $ . In other words, the Lagrangian multiplier $ (\theta_{t}) $ is considered as a risk premium added on to the nominal discount rate. The tighter the borrowing constraint is for the firm, the larger the Lagrangian multiplier is, and the firm faces higher effective discount rate.

Define the forecast error $(u_{t+1})$ as follows:

$$ \begin{align*}u_{t+1}\equiv&\left(1+(1-\tau_{t+1})i_{t+1}\right)^{-1}\Biggl((1-z_{t+1})p_{t+1}^{I}+(1-\tau_{t+1})p_{t+1}\frac{\partial G}{\partial I_{t+1}}\Biggr)-\\E_{t}&\Biggl[\left(1+(1-\tau_{t+1})i_{t+1}\right)^{-1}\Biggl((1-z_{t+1})p_{t+1}^{I}+(1-\tau_{t+1})p_{t+1}\frac{\partial G}{\partial I_{t+1}}\Biggr)\Biggr]\end{align*} $$

Using eq. $ (10) $ , eq. $ (9) $ is written as

$$ \left(\frac{\partial F}{\partial K_{t}}-\frac{\partial G}{\partial I_{t}}-\frac{\partial G}{\partial K_{t}}\right)+(1-\delta)\left[\left(1+(1-\tau_{t+1})i_{t+1}\right)^{-1}\left(\frac{(1-z_{t+1})p_{t+1}^{I}}{(1-\tau_{t})p_{t}}+\frac{(1-\tau_{t+1})p_{t+1}\frac{\partial G}{\partial I_{t+1}}}{(1-\tau_{t})p_{t}}\right)\right]+ $$

$$ (1-\delta)\boldsymbol{\phi}-\frac{(1-z_{t})\boldsymbol{p}_{t}^{I}}{(1-\boldsymbol{\tau}_{t})\boldsymbol{p}_{t}}= $$

$$ (1-\delta)\boldsymbol{\Theta}_{t}\left[\left(1+(1-\boldsymbol{\tau}_{t+1})\boldsymbol{i}_{t+1}\right)^{-1}\left(\frac{(1-z_{t+1})\boldsymbol{p}_{t+1}^{I}}{(1-\boldsymbol{\tau}_{t})\boldsymbol{p}_{t}}+\frac{(1-\boldsymbol{\tau}_{t+1})\boldsymbol{p}_{t+1}\frac{\partial G}{\partial\boldsymbol{I}_{t+1}}}{(1-\boldsymbol{\tau}_{t})\boldsymbol{p}_{t}}\right)\right]+\frac{(1-\delta)(1-\boldsymbol{\Theta}_{t})}{(1-\boldsymbol{\tau}_{t})\boldsymbol{p}_{t}}\boldsymbol{u}_{t+1} $$

Specification of the marginal productivity of capital and adjustment cost function is a final step to derive the equation to be estimated. Under the assumption of linear homogeneous production function, the marginal productivity of capital is written as
$$ \frac{\partial F}{\partial K_{t}}=\frac{p_{t}F_{t}-w_{t}N_{t}}{p_{t}K_{t}} $$

As for the adjustment cost function, we assume the following type of adjustment cost function:

$$ G(I_{t},K_{t})=\left[\alpha_{0}\Biggl(\frac{I_{t}}{K_{t}}-\upmu\Biggr)+\frac{\alpha_{1}}{2}\Biggl(\frac{I_{t}}{K_{t}}-\upmu\Biggr)^{2}\right]K_{t}, $$

where $ \mu $ : normal rate of investment

$$ \alpha_{1}>0 $$

Taking account of eqs.(12) and (13), eq.(11) is expressed as

$$ \frac{p_{t}F_{t}-w_{t}N_{t}}{p_{t}K_{t}}-\alpha_{0}-\alpha_{1}\Bigg(\frac{I_{t}}{K_{t}}-\upmu\Bigg)+\frac{\alpha_{1}}{2}\Bigg(\frac{I_{t}}{K_{t}}\Bigg)^{2}+\upmu\Bigg(\alpha_{0}-\frac{\alpha_{1}\upmu}{2}\Bigg)+(1-\updelta)\upphi-\frac{(1-z_{t})p_{t}^{I}}{(1-\uptau_{t})p_{t}}+ $$

$$ (1-\delta)\Biggl[\left(1+(1-\tau_{t+1})i_{t+1}\right)^{-1}\Biggl(\frac{(1-z_{t+1})p_{t+1}^{I}}{(1-\tau_{t})p_{t}}+\frac{(1-\tau_{t+1})p_{t+1}}{(1-\tau_{t})p_{t}}\left\{\alpha_{0}+\alpha_{1}\Biggl(\frac{I_{t+1}}{K_{t+1}}-\upmu\Biggr)\right\}\Biggr)\Biggr] $$

$$ =(1-\delta)\Biggl[\Bigl(1+(1-\tau_{t+1})i_{t+1}\Bigr)^{-1}\Biggl(\frac{(1-z_{t+1})p_{t+1}^{I}}{(1-\tau_{t})p_{t}}+\frac{(1-\tau_{t+1})p_{t+1}}{(1-\tau_{t})p_{t}}\Biggl\{\alpha_{0}+\alpha_{1}\Biggl(\frac{I_{t+1}}{K_{t+1}}-\upmu\Biggr)\Biggr\}\Biggr]\theta_{t}+ $$

$$ +\frac{(1-\delta)(1-\theta_{t})}{(1-\tau_{t})p_{t}}u_{t+1} $$

Eq. $ (14) $ is a fundamental equation to be estimated in the subsequent sections.

### 2. Econometric Issues in Estimation and Testing

### A. Estimation

We employ the generalized method of moments (GMM) technique originally developed by Hansen(1982) to estimate the fundamental Euler equation (14). Under the assumption of rational expectations, candidate for the instruments should be the variables that are included in the information set dated of time t. Our list of instruments includes constant term, and once and twice lagged variables of the followings: marginal product of capital, investment-capital ratio, squared investment-capital ratio, gross interest rate on net financial liability, price of investment goods price
relative to output price, inflation rate of output price, value of land asset deflated by the output price, and cash flow (earnings plus depreciation charges) deflated by the output price. The price and interest variables are all tax-adjusted. Since our data set used for estimation is seasonally unadjusted, seasonal dummies are also added to the instruments as well as eq.(14).

### B. Testing Procedures

Two types of tests are conducted to examine the existence of the borrowing constraints. $ ^{7)} $ In the first type of test the term associated with the Lagrangian multiplier (the first term in the RHS of eq.(14)) is subsumed into the error term. Suppose that the borrowing constraints are binding and that they are affected by a certain variable. Under this situation, if those variables are included in the list of instruments, then they are correlated with the combined error term and thus the overidentifying restrictions will be violated. The natural candidate for the variables affecting the degree of borrowing constraints are the value of land asset of the firm and the firm's cash flow. It has been often asserted that the former has played an important role in borrowing contracts between creditors and debtors in Japan. It has been also reported in many studies that the latter is a significant explanatory variable in the reduced-form investment demand equations in addition to Tobin's q. That is why we incorporate these two variables in the list of instruments to see whether they are correlated with the composite error terms.

Second type of test explicitly parameterizes the Lagrangian multiplier as a function of the value of land asset or the firm's cash flow and test whether these variables are significant or not. Specifically the Lagrangian multiplier is formulated as a linear function of the value of land asset or the cash flow. $ ^{8,9)} $

$$ \boldsymbol{\theta}_{t}=\boldsymbol{\gamma}_{0}+\boldsymbol{\gamma}_{1}\boldsymbol{p}_{t-1}^{L}\boldsymbol{L}_{t-1}/(1-\boldsymbol{\tau}_{t})\boldsymbol{p}_{t} $$

$$ \boldsymbol{\theta}_{t}=\lambda_{0}+\lambda_{1}C F_{t}/(1-\boldsymbol{\tau}_{t})p_{t} $$

where $ p_{t-1}^{L} $ : price of land in period t-1

$ L_{t-1} $ : real land stock at the end of period t-1

$ CF_{t} $ : cash flow in period t

If our maintained hypothesis that an increase of the land value or the cash flow leads to mitigation of the borrowing constraints is supported, then the coefficients of $ \gamma_{1} $ and $ \lambda_{1} $ will be negative. On the other hand, when the firm faces no borrowing constraints, the parameters in eqs.(15) and (16) will be jointly zero.
### C. Data Description

Now brief explanations are in order for the data set employed. Based on the Quarterly Report of Financial Statements of Incorporated Business compiled by the Ministry of Finance, we construct the consistent quarterly series of the major items in the balance sheet of the corporations for each industry. The sample period covers from the second quarter of 1970 to the third quarter of 1990. All the data series are seasonally unadjusted. The detailed explanations on the procedures of the data construction are provided in Data Appendix. Here we describe briefly how the series of capital stock, land stock, nominal discount rate, and marginal product of capital are constructed.

## Construction of capital stock

Our basic strategy to construct a series of the physical depreciable capital stock is to follow the perpetual inventory method. Our benchmark capital stock is based on the value in the fourth quarter of 1970. Originally the benchmark figure is in terms of book value, so that it is first converted into the real value by making use of the information on the average years elapsed since installation (AGE). Specifically the book value is divided by the investment goods deflator that prevailed AGE years before.

The physical depreciation rates( $ \delta $ ) are based on those reported in Hayashi and Inoue(1991). Given the benchmark value of the depreciable stock, real investment series, and depreciation rate, we obtain the series of capital stock from the following formula.

$$ K_{t}=(1-\delta)K_{t-1}+I_{t} $$

## Construction of land stock

We also follow the perpetual inventory method in calculating the series of land stock. We choose the fourth quarter of 1970 as our benchmark period. The benchmark stock of land at the market price is computed by multiplying the book value of land stock in QRFS by the market-book ratio. This ratio is computed as 5.27, and it is adopted as a conversion factor common to every industry in order to obtain the market-priced benchmark. The net investment in land at the market price $ (NILAND_{t}) $ is computed as the increment of land, which is evaluated at current price, in the table of changes in fixed assets in QRFS minus the decrement of land at current price. The decrement of land in the table of changes in fixed assets are originally book-valued, so that it is converted into market-value under the LIFO-type assumption that the land sold in period t was purchased in the most recent period, period t-1. The net increment of land in period t is expressed as:

$$ NILAND_{t}=ILAND_{t}-DLAND_{t}\frac{p_{t}^{L}}{p_{t-1}^{L}} $$
where $ ILAND_{t} $ : increment of land in period t

DLAND_{t} : decrement of land in period t, which is priced when it was purchased

As for the land price $ (p_{t}^{L}) $ , it is constructed by taking account of the distribution of land holdings over different prefectures where different prices of land are prevailing.

Finally, the land stock at the market price is constructed by the following formula.

$$ L A N D Y_{t}=L A N D Y_{t-1}\frac{p_{t}^{L}}{p_{t-1}^{L}}+N I L A N D_{t} $$

where $ LANDY_{t}(=p_{t}^{L}L_{t}) $ : stock of land at the market price

## Discount rate

The nominal discount rate of the corporations $ (i_{t}) $ is computed as follows:

(interest and discount paid + bond interest expenses)/(short-term and long-term loans payable + bonds payable + notes receivable discounted)

## Marginal Product of Capital

Under the assumption of linear homogeneity of production function, the marginal product of capital is identical with the average one and it is calculated as the ratio of nominal operating profit to the capital stock evaluated at the output price.

### 3. Estimation Results and Interpretations

A. Estimation results of the Euler equations and test of the borrowing constraints

In the first place the basic Euler equation (14) is estimated by the GMM with the term associated with the Lagrangian multiplier $ \theta_{t} $ subsumed into the error term. The results for fourteen industries are shown in Table 1. For each industry two results are presented, depending on the choice of covariance matrix estimate. The first row uses the unrestricted covariance matrix estimate under the hypothesis that the Lagrangian multiplier is a linear function of the value of land asset while the second row uses that under the hypothesis that the Lagrangian multiplier is a linear function of the cash flow. Use of unrestricted covariance matrix enables us to test whether the land asset or the cash flow of the firm affects the degree of borrowing constraints by the $ \chi^{2} $ test developed by Newey and West (1987).

The estimation results are evaluated in terms of the sign of the adjustment cost parameter ( $ \alpha_{1} $ )
asymmetric information for several reasons. First group firms have close ties with affiliated banks and those banks are shareholders as well as bondholders, which reduces the conflicts among investors. Second group firms have a long-term stable relationship with the affiliated banks and former bank employees are often placed in management positions of the firms, which narrows the informational gaps between the bank and the firms. Therefore it is expected that the asymmetry of information is not so severe for the firms in the industry groups than unaffiliated firms. Based on the panel data of the Japanese corporations Hoshi, Kashyap, and Scharfstein(1990,1991) obtain evidence supporting this conjecture.

Most of the small-sized firms do not belong to industry groups and hence the banks have not accumulated enough information of those firms on which judgment is made as to the loan contracts. However the asset values of the land and the cash flow of the firms increased to a large extent in the middle of 80's to the early 90's, which eased the borrowing constraints of the small-sized firms, and thus boosted the investment spending during this period.

To sum up, an increase of the internal funds and the improvement of the balance sheet positions of small firms were indispensable to reduction in the effective discount rate and hence high growth of investment. The findings obtained here are consistent with the estimation results of the reduced-form type investment functions reported in the first paper, where the market value of land asset and cash flow variables exert a significant effect on the level of investment and borrowings.

### C. Related Issues

In addition to the plausible implications obtained above as to the effect of the borrowing constraints on business investment in Japan, some more evidence supporting our formulation of the investment behavior of the firms is presented here. They are the magnitude of the coefficient estimates of the adjustment cost functions. When the investment demand equation is derived as a reduced form from the value maximization of the firm, an estimate of the adjustment cost function can be retrieved as a reciprocal of the coefficient estimate of Tobin's q variable.

In most of the past studies on the investment spending the adjustment cost parameters retrieved from the reduced-form equations were somewhat overestimated from the viewpoint of the equilibrium value of Tobin's q. This is so because it is shown that the equilibrium value of Tobin's q is expressed as:

$$ \frac{1}{(1-\delta)(1-z_{t})p_{t}^{I}}\frac{\partial V_{t}}{\partial K_{t-1}}=1+\frac{(1-\tau_{t})p_{t}}{(1-z_{t})p_{t}^{I}}\alpha_{1}\delta $$

Eq. $ (20) $ is obtained under the following assumptions: $ (1) $ the coefficient of $ \alpha_{0} $ is zero $ (2) $ the
a factor to mitigate the gap between these two financial costs.

High increase rate of land price and rapid accumulation of the cash flows in the middle of 1980's to the early 90's reduced the borrowing constraints almost to zero, which induced the firms to undertake the massive amount of investment during this period. As the land price declined, the Japanese economy plunged into the deep recession. The main characteristics of the current recession is stagnancy of the business investment activities by the small-sized firms, which might be attributed to a deterioration of the land value held by the firm.

In the post-war period the Japanese banks have relied on the role of land asset as a collateral in lending decisions. Under the new circumstances where the financial liberalization has been under progress and the financial markets are interrelated internationally, new criteria should be explored in the lending decision of the banks.
## Footnotes

1) See Modigliani and Miller(1958,1963) and Miller and Modigliani(1961) for the original exposition of the Modigliani-Miller theorem.

2) There is a growing body of literature on this issue. For example, see Greenwald and Stiglitz (1988), Gertler and Hubbard (1988), and Bernanke and Gertler (1989) for theoretical developments. For empirical pieces on this issue, Fazzari, Hubbard, and Petersen (1988), Devereux and Schiantarelli (1990), Hubbard and Kashyap (1992), Whited (1992), and Hubbard, Kashyap, and Whited (1993) utilize the U.S. corporation data and examine the existence of borrowing constrains, while Hoshi, Kashyap, Scharfstein (1990, 1991), Asako, Kuninori, Inoue, and Murase (1990), Okazaki and Horiuchi (1992), Miyagawa (1993), and Mitsui and Kawachi (1993) investigate whether the investment spending is bounded by the borrowing constrains for the Japanese firms. Bond and Meghir (1994) tests the sensitivity of investment to the availability of retained earnings based on the U.K. company data.

3) See Asakura (1992) for a brief history since the Meiji era on the collateral role of the land asset in the loan contract.

4) There are not so many empirical studies accumulated along this line as those along the reduced-form approach. The studies of Hubbard and Kashyap (1992), Whited (1992), and Hubbard, Kashyap, and Whited (1993) utilize the U.S. corporation data and examine the existence of borrowing constraints by estimating the intertemporal first-order conditions of the firms. Bond and Meghir (1994) estimate dynamic investment models using GMM and tests the sensitivity of investment to the level of internal funds.

5) Among the studies based on the reduced-form type investment functions, typical are those that use the q variable. However, most of the results are not satisfactory in the sense that there remains a sizable residuals unexplained by the q variable and that the residuals exhibit positive serial correlation.

The variables such as cash flow, sales, and profit variables turn out to be significantly positive when these variables are added to the list of explanatory variables. This might hint the existence of the borrowing constraints. The studies along this line are Blundell, Bond, Devereux (1992), Devereux and
Schiantarelli (1990), Fazzari, Hubbard, and Petersen (1988), and Hoshi, Kashyap, and Scharfstein (1991). On the other hand, Abel and Blanchard (1986) and Ueda and Yoshikawa (1986) show that persistent residuals are consistent with the q theory when the delivery lags are properly taken into consideration.

Another approach to reconcile the q theory with the data is to disaggregate the capital stock into several homogeneous parts. This “multiple q” model is formulated theoretically by Wildasin (1984) and Chirinko(1986) and applied to the Japanese corporate data by Asako et al. (1989), and Hayashi and Inoue (1991).

6) Our findings are consistent with the studies of Miyagawa(1993), Mitsui and Kawachi (1993), and Kuroki(1993). They give evidence that some proxy of liquidity is a significant explanatory variable in the investment demand equations for the relatively small-sized firms.

7) Our testing strategy is on the same track as Hulberd and Kashyap (1992), Whited (1992), and Hubbard, Kashyap, and Whited (1993).

8) It is assumed here that the degree of borrowing constraints are affected by the firm-specific factors such as the land value and the cash flow. Hubbard, Kashyap, and Whited (1993) specifies the borrowing constraints as a function of not only firm-specific factors but also the overall tightness of borrowing conditions.

9) In estimation the variables of the land asset and the cash flow are divided by their sample mean, respectively.

10) For pulp, paper and paper products and electrical machinery the estimation results are not improved at all even if the borrowing constraints are explicitly taken into account. For these industries the results are somewhat improved when the seasonal dummies are removed, though the existence of borrowing constraints are not detected. The results without the seasonal dummies are given in Appendix table.

11) The conditions that the Lagrangian multipliers are between zero and unity will be a prior satisfied when the logistic function is applied to a specification of the Lagrangian multipliers. However, we did not pursue this specification since in many industries the iterations of the GMM algorithm did not converge.
## References

[1] Abel, A.B. and O. Blanchard (1986). “The Present Value of Profits and Cyclical Movements in Investment,” Econometrica, Vol. 54, No. 2, pp. 249-273.

[2] Asako, K., Kuninori, M., Inoue, T., and H. Murase (1989). “Tochi Hyoka to Tobin no q ; Multiple q no Keisoku (Land Evaluation and Tobin’s q ; A Measurement of Multiple q),” Economics Today, Vol. 10-3, Japan Development Bank, Tokyo.

[3]———(1990). “Setsubi Toshi to Shikin Chotatsu - Renritsu Houteisiki Moderu niyoru Suikei - (Capital Investment and Source of Funding - Estimation Based on a Simultaneous Model) JDB Discussion Paper No.9008, Research Institute of Capital Formation, The Japan Development Bank, Tokyo.

[4] Asakura, K. (1992). “Akusei Jibyou - Tochitanpoyushi no Kikensei (Malignant Chronic Disease Problems on Lending on the Basis of Land as a Collateral),” Economist (Japanese Edition), November 9.

[5] Bernanke, B., and M. Gertler (1989). “Agency Costs, Net Worth, and Business Fluctuations,” American Economic Review Vol. 79, No. 1, pp. 14-31.

[6] Blundell, R., Bond, S., Devereux, M., and F. Schiantarelli (1992). “Investment and Tobin’s q Evidence from Company Panel Data,” Journal of Econometrics 51, pp. 233-257.

[7] Bonds, S. and C. Meghir (1994). “Dynamic Investment Models and the Firm’s Financial Policy,” Review of Economic Studies 61, pp. 197-222.

[8] Chirinko, R. S. (1986). “Investment, Tobin’s q, and Multiple Capital Inputs,” NBER Working Paper No. 2033.

[9] Devereux, M. and F. Schiantarelli (1990). “Investment, Financial Factors and Cash Flow: Evidence from U.K. Panel Data,” in Hubbard, R. G. (ed.), Asymmetric Information, Corporate
Finance, and Investment, University of Chicago Press, Chicago, pp.279-306.

[10] Fazzari, S.M., Hubbard, R.G., and B.C. Petersen (1988). “Financing Constraints and Corporate Investment,” Brookings Papers on Economic Activity 1, pp.141-195.

[11] Gertler, M. and R.G. Hubbard (1988). “Financial Factors in Business Fluctuations, NBER Working Paper No.2758.

[12] Greenwald, B. C. and I. E. Stiglitz (1988). “Financial Market Imperfections and Business Cycles,” NBER Working Paper No. 2494.

[13] Hansen, L. P. (1982). “Large Sample Properties of Generalized Method of Moments Estimator,” Econometrica 50, pp. 1029-1054.

[14] Hayashi, F. and T. Inoue (1991). “The Relation between Firm Growth and Q with Multiple Capital Goods: Theory and Evidence from Panel Data on Japanese Firms,” Econometrica 59, pp.731-753.

[15] Hoshi, T., Kashyap, A., and D. Scharfstein (1990). “Bank Monitoring and Investment: Evidence from the Changing Structure of Japanese Corporate Banking Relationships,” in Hubbard, R. G. (ed.), Asymmetric Information, Corporate Finance, and Investment, University of Chicago Press, Chicago, pp. 105-126.

[16]———(1991). “Corporate Structure, Liquidity, and Investment: Evidence from Japanese Industrial Groups,” Quarterly Journal of Economics, Vol.CVI Issue 1, pp.33-60.

[17] Hubbard, R.G. and A.K. Kashyap (1992). "Internal Net Worth and the Investment Process: An Application to U.S. Agriculture," Journal of Political Economy, Vol. 100, No. 3, pp. 506-534.

[18] Hubbard, R.G., Kashyap, A.K., and T.M. Whited (1993). “Internal Finance and Firm Investment,” NBER Working Paper No.4392.

[19] Kuroki, Y. (1993). “Ginko Shinyou to Jitsubutsu Tousi Katsudou - nippon no Kin-yu Shihon Shijou no Fukanzensei ni kansuru Jisshou Bunseki- (Bank Credit and Real Investment Activity),” Kokumin-Keizai Zasshi (Journal of Economics & Business Administration), Vol.168, No.4,