I. The Optimal Level of Borrowing from U. S. Banks

The Japanese demand for U. S. bank credit will be explained along the lines of what has been termed the “stock adjustment” or “portfolio balance” theory of international capital movements. This theory, which has gained increasing acceptance in the empirically oriented literature in the course of the last decade,¹ is a simple application of the more general theory of portfolio selection derived by Tobin and Markowitz.² One important result of this theory is that an economic unit’s optimal holding of a risky asset (or liability) can be expressed as a function of (i) a vector of expected rates of return; (ii) a vector of the variances of (and the covariances among) these expected rates of return; and (iii) a scale variable representing the total size of portfolios. In the analysis that follows, the variances and covariances of the expected rates of return will be ignored, since this paper has nothing to add to the (very limited) stock of knowledge concerning the empirical measurement of these variables. As to the vector of expected rates of return, theory requires that it include all the rates of return that are relevant to the decision makers (and not only the difference between “the” domestic interest rate and “the” foreign interest rate, as incorrectly postulated in numerous studies). Under these assumptions, the desired stock of Japanese borrowing from U. S. banks can be expressed as

where a horizontal bar indicates the expected value of a variable; the Rs denote vectors of borrowing costs in the U. S., Euro-dollar, and Japanese markets; 5 is a vector of scale variables; and C^* is the desired level of U. S. bank credit, viewed from the standpoint of Japanese borrowers.³

The existence of assets and liabilities denominated in different currencies is a specific characteristic of portfolio selection in the international context. Under a system of fixed exchange rates—and provided expectations concerning discrete changes in parities are ruled out—this characteristic should not affect the specification of the variables in equation (1). Accordingly, Bryant and Hendershott’s (1970) identification of expected interest rates with nominal (quoted) interest rates was not unreasonable, since their analysis of U. S. short-term bank lending to Japan covered the fixed-rate period 1959–67. For the period analyzed here, this assumption would, of course, be untenable. It will, therefore, be recognized that, for any Japanese firm that considers borrowing dollars in the U. S. or Euro-dollar markets, the effective cost of borrowing will be affected, either by its subjective expectation of the future change in the yen/dollar spot rate or by the prevailing forward premium on the dollar—depending on whether the firm decides to speculate or to obtain forward cover.

This alternative can be formalized by partitioning the vector ${\overline{R}}^J$ into two subvectors, one reflecting the opportunity cost of borrowing in Japan when foreign currency liabilities are covered in the forward market $\left({\overline{R}}_1^J\right)$ and the other reflecting the opportunity cost of borrowing in Japan relative to unhedged foreign currency liabilities $\left({\overline{R}}_2^J\right)$. Let all exchange rates be defined in number of yen per dollar, and let the U. S. dollar be chosen as a numeraire.⁴ Let r denote a vector of nominal interest rates expressed in the currency in which each instrument is denominated, and assume that $\overline{r}$ = r. The expected interest rates expressed in U. S. dollar terms are then given by the following expressions:

where x is the cost of coverage (i.e., the percentage difference between the one-period forward rate and the prevailing spot rate) and z^e is the expected change in the spot rate one period ahead.⁵

The vector of scale variables (S) typically includes the net wealth of the economic units involved. Since most of Japan’s foreign borrowing is channeled through Japanese city banks, S will include the aggregate net worth of these institutions (W). Also, Japanese imports (M) will be included to represent the scale of transactions demand for U. S. funds, in view of the considerable importance of import financing in Japanese foreign borrowing. Empirical studies on capital movements generally assume that the function expressing the demand for a foreign asset or liability is homogeneous of degree one in the scale variables.⁶ This assumption has some advantages; for example, it allows for an intuitively appealing distinction between stock-adjustment effects and continued flow effects of interest rate changes.⁷ It does not, however, rest on any solid theoretical foundation. As correctly pointed out by Black (1973), this aspect of the specification of capital movements’ equations is essentially an empirical matter. Although the linear homogeneity assumption is incorporated in some of the estimated equations discussed in Section III, the following exposition assumes that the function f in equation (1) is of the simple linear-arithmetic form.

Taking into account the preceding discussion of expected interest rates and scale variables, equation (1) can be rewritten as

where the α_is are positive parameters.⁸ The dependent variable in equation (3) is the desired level of borrowing from U. S. banks by Japanese residents. If there are capital controls (or other forms of official or private interference with capital markets), the desired level C^* may, of course, diverge from the actual level C.

II. Capital Controls

Official attempts to influence capital movements may take the form of taxes (e.g., the U. S. Interest Equalization Tax of 1966) or reserve requirements (e.g., the Bundesbank’s Bardepot, or the reserve ratios specified by the Federal Reserve Board’s Regulation M). Controls of this type can be easily handled, at least in the theoretical stage of the work, by making appropriate adjustments to the relevant interest rate variables. Considerably more difficult is the case where the authorities impose a ceiling on the level of foreign claims or liabilities that domestic residents are authorized to hold at any given moment in time. In this case, the relationship between actual and desired levels of external credits is given, if the regulations are rigidly enforced, by the expression

where C^max is the maximum level of C allowed under government regulations. Unfortunately, equation (4) raises extremely difficult problems at the level of empirical implementation. First, the variable C^max is generally not publicly available in the form of a historical series.⁹ Second, even if a reasonable proxy for C^max could be constructed, it would not be possible to estimate equation (4) by ordinary least-squares methods.¹⁰

In the empirical literature on international capital flows, government controls of the “ceiling” type have been handled mainly through what might be termed the dummy technique.” The estimated equations include a variable that is given a value of one when controls are effective, and of zero otherwise.¹¹ A considerably more elaborate treatment of controls has been proposed by Bryant and Hendershott (1970). As suggested by Bryant in a later paper, this treatment assumes that “the tightening or relaxation of controls will reduce or increase, but not dampen altogether, the response of desired quantities to changes in their economic determinants.” ¹² This suggestion can be formalized by assuming that the difference between desired and actual levels of borrowing is a fraction, β, of the desired borrowing level, and that this fraction is itself a function of a vector of capital control variables, k. Actually, Hendershott and Bryant assume this function to be of the form β(k) = β₀ + β₁k, where the βs are positive parameters, thus arriving at the expression

Alternatively, the difference between desired and actual quantities can be directly related to the function β(k), leading to the linear form

Combining equations (3) and (5) yields

where α₃ = α₃₁ + α₃₂ > 0

If the linear specification of equation (6) is used, the result simplifies to

where ${{\alpha }_0}^{\prime }$ = α₀ − β₀

Finally, if the desired borrowing function f is assumed to be linear homogeneous in the scale variables, equation (1) can be written as C^* = W .f ($\overline{R}$, M/W). Linearizing the function f, multiplying its arguments through by W, and taking into account equation (6) yields¹³

III. Estimation

Equations (7), (8), and (9) were estimated for the period January 1972 to August 1975 (44 observations) and the principal results are shown in Table 2. It was initially assumed that the independent variables had no lagged effects on the level of U.S. claims on Japan (although an important exception was made in the case of the Japanese import variable M for reasons explained later). Some encouraging results obtained by experimenting with distributed lag structures for certain explanatory variables are discussed briefly in Section V.

The dependent variable in all the equations presented in Table 2 is the stock of U. S. bank claims on Japan (both short term and long term) as reported by banks in the United States, measured in billions of dollars. (Details on the construction of all variables used in the regressions are given in Appendix I, together with a list of sources.)

Table 2.

Estimated Equations for U.S. Bank Claims on Japan (C), January 1972–August 1975 ¹

¹All variables are defined in Appendix I. OLS stands for ordinary least squares, and NLLS for nonlinear least squares. Figures in parentheses are t-ratios. The mean of W over the sample period is $7.76 billion.

Table 2.

Estimated Equations for U.S. Bank Claims on Japan (C), January 1972–August 1975 ¹

Coefficient	Variable	(9–1)	(8–1)	(8–2)	(7–1)	(8–3)
		OLS	OLS	OLS	NLLS	OLS
−β	kus	–0.786	–0.745	–0.758	–0.148	–0.015
		(0.79)	(0.72)	(0.98)	(2.01)	(0.02)
Constant		2.707	–0.326	–0.399	–0.551	–1.767
		(1.95)	(0.25)	(0.31)	(0.79)	(1.81)
—α1	rus	–0.195W	–1.312	–1.314	–1.371	–1.252
		(3.87)	(3.16)	(3.37)	(3.36)	(3.93)
α2	red	0.160 W	1.030	1.033	1.125	0.954
		(3.53)	(2.75)	(3.08)	(3.16)	(3.30)
α3 :i	rj	0.061W	0.487	0.487	0.536	0.503
		(3.10)	(2.93)	(3.04)	(3.46)	(3.33)
α4	W	–0.404	–0.006	—	—	—
		(1.42)	(0.02)
α5	$\tilde{M}$	0.401	0.434	0.432	0.377	0.529
		(2.03)	(2.22)	(3.11)	(2.78)	(4.02)
–α31	x	–0.009W	–0.079	–0.079	–0.079	–0.089
		(3.78)	(3.88)	(3.95)	(3.92)	(5.10)
ζ1	p	–0.029W	–0.290	–0.292	–0.313	—
		(1.17)	(1.36)	(1.44)	(1.57)
ζ2	z	0.008W	0.066	0.066	0.052	—
		(0.76)	(0.70)	(0.75)	(0.57)
α32	z+1	—	—	—	—	–0.016
						(2.63)
${\overline{R}}^2$		0.963	0.960	0.961	0.964	0.965
D-W		1.11	0.99	0.99	1.03	1.09

¹All variables are defined in Appendix I. OLS stands for ordinary least squares, and NLLS for nonlinear least squares. Figures in parentheses are t-ratios. The mean of W over the sample period is $7.76 billion.

View Table

Table 2.

Estimated Equations for U.S. Bank Claims on Japan (C), January 1972–August 1975 ¹

Coefficient	Variable	(9–1)	(8–1)	(8–2)	(7–1)	(8–3)
		OLS	OLS	OLS	NLLS	OLS
−β	kus	–0.786	–0.745	–0.758	–0.148	–0.015
		(0.79)	(0.72)	(0.98)	(2.01)	(0.02)
Constant		2.707	–0.326	–0.399	–0.551	–1.767
		(1.95)	(0.25)	(0.31)	(0.79)	(1.81)
—α1	rus	–0.195W	–1.312	–1.314	–1.371	–1.252
		(3.87)	(3.16)	(3.37)	(3.36)	(3.93)
α2	red	0.160 W	1.030	1.033	1.125	0.954
		(3.53)	(2.75)	(3.08)	(3.16)	(3.30)
α3 :i	rj	0.061W	0.487	0.487	0.536	0.503
		(3.10)	(2.93)	(3.04)	(3.46)	(3.33)
α4	W	–0.404	–0.006	—	—	—
		(1.42)	(0.02)
α5	$\tilde{M}$	0.401	0.434	0.432	0.377	0.529
		(2.03)	(2.22)	(3.11)	(2.78)	(4.02)
–α31	x	–0.009W	–0.079	–0.079	–0.079	–0.089
		(3.78)	(3.88)	(3.95)	(3.92)	(5.10)
ζ1	p	–0.029W	–0.290	–0.292	–0.313	—
		(1.17)	(1.36)	(1.44)	(1.57)
ζ2	z	0.008W	0.066	0.066	0.052	—
		(0.76)	(0.70)	(0.75)	(0.57)
α32	z+1	—	—	—	—	–0.016
						(2.63)
${\overline{R}}^2$		0.963	0.960	0.961	0.964	0.965
D-W		1.11	0.99	0.99	1.03	1.09

¹All variables are defined in Appendix I. OLS stands for ordinary least squares, and NLLS for nonlinear least squares. Figures in parentheses are t-ratios. The mean of W over the sample period is $7.76 billion.

The theoretically important objective of including all the relevant interest rates in the estimated equations must naturally be weighted against the loss of estimation precision introduced by high levels of multicollinearity. A compromise between these two targets was achieved by including both a typical Euro-dollar lending rate, r^ed (obtained by adding the average differential charged to prime borrowers to the London rate for three-month deposits) and an average U. S. interest rate, r^us. This latter variable was generated as a weighted average of U.S. rates for the two most important types of financial instruments from the standpoint of U.S. lending to Japan: bankers’ acceptances and commercial loans.¹⁴ The Japanese rate, r^J, is the unconditional lenders’ rate in the Tokyo call money market.¹⁵

Turning to the other explanatory variables, x is the three-month forward premium on the dollar, while W is the net worth of Japanese city banks, converted into U.S. dollars using end-of-period spot rates. The expected exchange rate variable z^e, of course, cannot be observed; attempts to specify it as a function of observable variables are discussed in Section V. Finally the variable M is defined as total Japanese imports (c.i.f. basis). Most models of international capital movements include foreign trade variables, although there are few systematic discussions of the reasons for doing so. It is generally assumed that the current stock of financial liabilities (claims) to foreigners is related to the current flow of imports (exports). While this stock-flow relation is consistent with the assumption of trade finance, it also implies that all trade credits are repaid after one, period—a particularly unrealistic assumption when monthly data are used. In the equations presented in Table 2, the import variable M is defined as a three-month moving sum of total Japanese imports—a definition that is consistent with the more reasonable assumption that imports are financed on a three-month basis.¹⁶ It may be noted that M, which is based on total Japanese imports, performed substantially better than an alternative variable based on imports from the United States only, confirming that Japanese firms used U.S. financial markets to finance imports of non-U.S. goods, particularly the large increase in the value of Japanese petroleum imports since early 1974.

The results presented in the first column of Table 2 relate to equation (9), which relies on the assumption of homogeneity of the first degree in the scale variables. The results in the other four columns relate to the linear specification of the desired borrowing function assumed in equations (7) and (8). The signs of all the estimated coefficients conform to a priori expectations except for α₁ which is negative in both equations (9–1) and (8–1). Since no convincing explanation could be found for this result, the variable W was omitted from the remaining equations on which the following discussion will focus. The coefficients of all the interest rate variables are significantly different from zero at the 0.05 confidence level, and exhibit little vulnerability to changes in specification or method of estimation.

The estimated values of α₁ indicate that (other things being equal) an increase of 1 percentage point in the U. S. rate will lead to a decrease of $1.2–1.4 billion in U.S. claims on Japan. As expected, the coefficient of the Euro-dollar rate (α₂) is consistently smaller in absolute value than the coefficient of the U. S. rate (α₁), although not by a sizable margin: a one point rise in the Euro-dollar rate would, ceteris paribus, increase U. S. bank claims on Japan by about $1 billion. The ceteris paribus assumption may, however, not be very useful in the present context. It may be reasonably assumed that, following the termination of the U. S. capital control program in early 1974, arbitrage introduced a substantial degree of parallelism between U. S. and Euro-dollar rates. It may, therefore, be more interesting to note that a simultaneous increase of 1 percentage point in these two rates would, on the basis of the estimated coefficients, lead to a fall in U. S. lending to Japan of some $250–300 million. The effect of a change in the Japanese rate is roughly of the same order of magnitude: a one point increase in r^J would, other things being equal, increase Japanese borrowing from U. S. banks by some $500 million. Finally, the coefficient of the forward premium on the dollar (α₃₁) is significant in all equations and very robust with respect to minor changes in specification.

The results of experiments with capital control variables were largely disappointing. Several variables were constructed to capture the changing intensity of Japan’s complex system of capital controls, but the estimated coefficients of most of these variables were statistically insignificant and most of them had the wrong sign.¹⁷ This result cannot, of course, be construed as evidence that Japanese controls were ineffective during the sample period. However, there are reasons to believe that the type of capital flows analyzed here was not severely restricted by Japanese regulations, because of their high trade-finance content and because the Japanese authorities have traditionally encouraged the use of foreign credits to finance imports. Indeed, only in the middle of June 1975 did the Bank of Japan authorize transactions in yendenominated export and import bills with the objective of “accelerating yen-based trade.”

The only capital control variable for which the estimated coefficient turned out to have the expected sign in all equations was a variable reflecting the impact of the U.S. Voluntary Foreign Credit Restraint (VFCR) Program (k^us in Table 2). Before January 1974, this variable was given a value equal to the aggregate foreign assets subject to the VFCR ceiling divided by the aggregate ceiling for all banks subject to the Program; it was set equal to zero from January 1974 to August 1975.¹⁸ The coefficient of k^us is not significantly different from zero in the first three columns of Table 2, but it is encouraging to note that it is twice as large as its (asymptotic) standard error in equation (7–1) where the nonlinear version of the capital control equation is used.¹⁹

IV. Exchange Rate Expectations

Three hypotheses were considered in connection with the expected exchange rate variable z^e. The first is what might be termed the “naïve” hypothesis according to which expectations concerning the future change in the spot rate are based on a simple extrapolation of past changes in this rate. In symbols ²⁰

where z^e is the change that is expected to occur one period ahead, z_–i is the observed change in period t – i, and the θ_is are constant weights. This specification of z^e was used in the regressions by selecting several values for n (between 1 and 12), with and without polynominal restrictions on the θ_is. In all cases, the sum of lagged coefficients turned out to have the wrong sign.

A more general (and not so naïve) hypothesis allows for regressive as well as adaptive elements in the formation of expectations. Specifically, it is assumed that the anticipated change in the spot rate (z^e) will diverge from the current period change (z) by a fraction (γ) of the discrepancy between what speculators view as the long-run “normal” change (z^*) and the current change. Assuming that speculators relate z^* to the difference between domestic and foreign rates of inflation (p) by the simple rule z^* = δp, the expected change in the spot rate can be expressed by

which is similar to the relation used by Artus (1976, p. 4). This last expression can be incorporated into equation (7) or (8), simply by noting that

where ζ₁ = α₃₂γδ and ζ₂ = α₃₂ (1 – γ) are nonnegative parameters. This specification was used in the equations presented in the first four columns of Table 2.²¹ The relative inflation rate variable p performs according to expectations, but the coefficient ζ₂, has the wrong sign in all equations. Since this coefficient is insignificantly different from zero, the only consistent interpretation of the results is that γ = 1, that is, that market participants expect the change in the spot rate to revert to its “normal” level within one period, in this case, three months. It is interesting to note that these results differ from those obtained by Artus in his analysis of the dollar/deutsche mark rate, inasmuch as they imply that exchange rate expectations are influenced by such economic variables as relative rates of inflation, but not by current or past changes in exchange rates. Of course, the financial flows analyzed in the two studies differ in several important respects, which might account for some differences in estimation results.²²

Finally, a third hypothesis states that expectations are “rational” in the sense that they are formed by decision makers who are presumed to know the structure of the economy. These expectations—first introduced by John Muth (1961)²³—are true mathematical expectations of the anticipated variables, which in the present context implies that

where z is the change in the spot rate, the subscript +1 indicates a one-period (three-month) lead, and v is a random vector having a zero mean. This “ultrasophisticated” hypothesis implies that the expected change in the spot rate is an unbiased predictor of the actual change; and to some, this might appear to be quite extreme and unrealistic. Although a thorough discussion of these issues would go beyond the scope of the present paper, a frequent misunderstanding may be dispelled by noting that equation (13) does not imply that the difference between expected and actual exchange rate changes is small (in other words, the variance of v could well be very large) but only that the forecast errors average out to zero. The results obtained by substituting for z^e from equation (13) into equation (8) are presented in the last column of Table 2. The coefficient of the one-period-ahead change in the spot rate is negative, as expected, and significant; but it is quite small in size, particularly in relation to the coefficient of the forward premium x. The coefficients and standard errors of the other variables are not affected to any great extent by the inclusion of z₊₁.²⁴

V. Lagged Responses

Up to now, it has been assumed that the stock of trade-related credit was a function of a three-month moving sum of imports. This assumption—while less unreasonable than that which relates the stock of borrowing only to the current flow of imports—is fairly restrictive. It is shown in Appendix II that, under more general assumptions, the end-of-period stock of trade-related borrowing is a function of a weighted sum of current and past values of imports, with weights depending on the maturity structure of the credits obtained. To allow for this more general formulation, equation (8) was re-estimated by introducing a distributed lag on the import variable and constraining the lagged coefficients to lie upon a second-degree polynomial, with the restriction that the last coefficient take on a zero value. (Experiments with third-degree polynomials yielded similar results.)

The equation also allowed for lagged responses to changes in the interest rate variables. However, to keep the number of estimated coefficients within reasonable bounds, it was assumed that all foreign borrowings were covered in the forward market—that is, that α₃₂ = 0, in the notation of equation (3). The following tabulation shows, for each explanatory variable, the sum of lagged coefficients, the corresponding t-statistic, and the number of lagged coefficients.

Variable		kus	rus	red	rJ— x	M
Sum of lagged
	coefficients	–0.979	–1.196	1.144	0.061	1.949
	(t-ratio)	(1.61)	(3.52)	(3.99)	(2.40)	(7.67)
Lag (in months)		0	3	3	3	7
		${\overline{R}}^2$ = 0.989	D-W = 1.56

View Table

Variable		kus	rus	red	rJ— x	M
Sum of lagged
	coefficients	–0.979	–1.196	1.144	0.061	1.949
	(t-ratio)	(1.61)	(3.52)	(3.99)	(2.40)	(7.67)
Lag (in months)		0	3	3	3	7
		${\overline{R}}^2$ = 0.989	D-W = 1.56

The results agree with those of most previous studies, in that the estimated response to interest rate changes is virtually complete within one quarter. On the other hand, the distributed lag on the import variable extends over a period of eight months. It is interesting to note that both the Durbin-Watson statistic and the t-ratio of the import variable are substantially higher than those reported in Table 2, suggesting that the specification of capital movement equations can be considerably improved by a more accurate treatment of the role of trade variables. The sum of lagged coefficients on the import variable indicates that, in the long run, an increase of $1 billion in the monthly flow of Japanese imports leads to an increase in U. S. bank claims on Japan of approximately $2 billion. Accordingly, a rise of $1 billion in the quarterly flow of imports would increase the stock of claims by about $0.65 billion in the long run, or by somewhat more than what is implied by the estimated coefficients in Table 2.

VI. Conclusions

The character of the present study is essentially experimental and its results should, therefore, be interpreted with caution. However, strong statistical regularities emerge from the analysis, suggesting that some conclusions can be drawn with a reasonable degree of confidence. First, the problem of explaining U. S. bank lending abroad, even during the turbulent conditions of the post-1971 period, appears to be econometrically tractable. Considering that the estimated equations include neither dummy variables nor lagged dependent variables as regressors, the correspondence between actual and fitted values of the dependent variable over an estimation period including several sharp turning points, is fairly strong (Chart 1). Second, total Japanese imports (from all countries and not only from the United States) play a major role in determining the scale of U. S. bank lending to Japan. Furthermore, the explanatory power of the import variable increases noticeably when the stock of trade credit is seen to be determined by past as well as current import flows.

The effect of interest rate changes on U. S. bank lending is estimated to be virtually complete within one quarter, and no additional flows would take place in the absence of further changes in expected interest rates. Since relative credit conditions tend to follow a cyclical pattern, the impact of interest rates will generally be reversed in the long run. Within the short term to medium term, however, the magnitude of interest rate effects can be quite substantial. A change of 3 to 4 percentage points in the differential between U. S. and Japanese rates over a period of two quarters (not an uncommon occurence in the recent past) could generate capital flow of $1–2 billion; and even the generally more moderate fluctuations in the spread between U. S. and Euro-dollar rates could induce shifts amounting to as much as $1 billion.²⁵ Finally, while the important role of covered financial flows can be seen very clearly from the estimation results, there is some uncertainty about the nature of exchange rate speculation. Although it is not conclusive, the empirical evidence presented in this paper provides some support for the rational expectations hypothesis, and strongly suggests that expectations concerning future changes in spot rates are influenced by the relative price performance of the countries involved, but are unrelated to current or past exchange rate movements. There is nothing in the results to confirm the fear that exchange rate changes may feed upon themselves.