Trade Credit, Interest Rates, and the Recent Behavior of External Lending by U. S. Banks

External lending by U. S. banks has registered large increases in recent years. Following a decade of modest expansion, foreign claims reported by banks in the United States rose by $6 billion in 1973 and by almost $20 billion in 1974 (Chart 1). These changes are extraordinary by historical standards, and it is not surprising that many observers—though they recognized that the financing of petroleum imports and the evolution of relative monetary conditions had contributed to these increases—concluded that the recent behavior of U. S. external lending could not be explained by existing economic models. This paper hopes to show that if the roles of international trade financing and interest arbitrage are treated appropriately, an econometric analysis based on the modern theory of international capital movements can go a long way toward explaining this key component of the U. S. capital account.


External lending by U. S. banks has registered large increases in recent years. Following a decade of modest expansion, foreign claims reported by banks in the United States rose by $6 billion in 1973 and by almost $20 billion in 1974 (Chart 1). These changes are extraordinary by historical standards, and it is not surprising that many observers—though they recognized that the financing of petroleum imports and the evolution of relative monetary conditions had contributed to these increases—concluded that the recent behavior of U. S. external lending could not be explained by existing economic models. This paper hopes to show that if the roles of international trade financing and interest arbitrage are treated appropriately, an econometric analysis based on the modern theory of international capital movements can go a long way toward explaining this key component of the U. S. capital account.

External lending by U. S. banks has registered large increases in recent years. Following a decade of modest expansion, foreign claims reported by banks in the United States rose by $6 billion in 1973 and by almost $20 billion in 1974 (Chart 1). These changes are extraordinary by historical standards, and it is not surprising that many observers—though they recognized that the financing of petroleum imports and the evolution of relative monetary conditions had contributed to these increases—concluded that the recent behavior of U. S. external lending could not be explained by existing economic models. This paper hopes to show that if the roles of international trade financing and interest arbitrage are treated appropriately, an econometric analysis based on the modern theory of international capital movements can go a long way toward explaining this key component of the U. S. capital account.

The figures presented in Table 1 reveal two interesting facts. First, the recent increase in U. S. bank lending abroad was overwhelmingly in the form of short-term (i.e., less than one year) credits. Second, a remarkably large share of this increase went to Japan and to Eurocurrency centers in the United Kingdom, the Bahamas, and other Caribbean areas. This geographic concentration naturally suggests that outflows of U. S. bank capital might be fruitfully analyzed by focusing on a small number of countries or areas. This type of disaggregation would make it relatively easy to identify the specific variables that should be included in the model—a matter of considerable importance in the empirical analysis of international capital flows.

Chart 1.
Chart 1.

Claims on Japan Reported by Banks in the United States, 1972–75

(In billions of U.S. dollars)

Citation: IMF Staff Papers 1976, 003; 10.5089/9781451969405.024.A007

1From equation (8–2), Table 2.
Table 1.

Claims on Foreigners Reported by Banks in the United States, January 1973–August 1975

(In billions of U.S. dollars)

article image
Source: Based on data from U.S. Treasury Bulletin, Tables CM–II–2 and CM–II–5.

Mainly Bahamas and Cayman Islands.

The objective of the present paper is to take a step in the direction of this type of disaggregated analysis of U. S. foreign lending by concentrating on U. S. bank claims on Japan during the period 1972–75. Two salient characteristics of this period are the sharp increase in Japanese import-financing requirements that followed the late 1973–early 1974 increase in oil prices, and the substantial degree of flexibility in the exchange rate between the yen and the U. S. dollar. Accordingly, trade finance and the influence of exchange market conditions on the effective cost of international credit will be given particular attention.

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 R¯J into two subvectors, one reflecting the opportunity cost of borrowing in Japan when foreign currency liabilities are covered in the forward market (R¯1J) and the other reflecting the opportunity cost of borrowing in Japan relative to unhedged foreign currency liabilities (R¯2J). 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 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 ze 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 αis 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 Cmax 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 Cmax is generally not publicly available in the form of a historical series.9 Second, even if a reasonable proxy for Cmax 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 α0 = 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 (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

article image

All 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, red (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, rus. 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, rJ, 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 ze, 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 1), 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 rJ 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 (kus 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 kus 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 ze. 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 ze is the change that is expected to occur one period ahead, z–i is the observed change in period t – i, and the θis are constant weights. This specification of ze was used in the regressions by selecting several values for n (between 1 and 12), with and without polynominal restrictions on the θis. 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 (ze) 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 ze 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.

article image

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.


I. Dictionary of Symbols 26

  • C = U.S. bank claims on Japan, in billions of U.S. dollars. Includes short-term and long-term claims reported by banks. From USTB, Tables CM–II–2 and CM–II–5.

  • kus = Variable reflecting the intensity of the U.S. Voluntary Foreign Credit Restraint Program. Equal to the ratio of aggregate assets subject to ceilings to the aggregate VFCR ceilings before January 1974; and equal to zero thereafter.

  • My = Japanese merchandise imports (c.i.f. basis), in billions of yen. From IFS.

  • M = Japanese merchandise imports in billions of U.S. dollars. Obtained by dividing My by a monthly average of daily spot exchange rates. From IFS.

  • M˜ = M + M–1 + M–2.

  • p = Percentage change in the ratio of Japanese to U. S. consumer prices. Both variables from IFS.

  • red = Rate on three-month Euro-dollar deposits in London (from BEQB) plus average spread between prime Euro-dollar lending and deposit rates. From WFM.

  • rus = (rA A + rL. L)/(A + L), where rA is the rate on three-month prime bankers’ acceptances in the United States (from FRB); rL is the average prime rate on U.S. bank loans (from BCD); and A and L denote claims on Japan reported by U.S. banks in the form of acceptances and loans, respectively (from USTB, Table CM-II-3). Both A and L are fixed weights, computed as averages of end-of-quarter figures for the three-year period 1970–72.

  • rJ = Tokyo interbank call money rate (unconditional lenders’ rate). From WFM.

  • Wy = Net worth of Japanese city banks, in hundred millions of yen. Obtained by summation of reserve and capital accounts from the balance sheets of Japanese city banks published by BOJ.

  • W = Net worth of Japanese city banks, in billions of U.S. dollars, equal to Wy seasonally adjusted, divided by 10, and converted into dollars using the end-of-period spot rate given in IFS.

  • x = Three-month forward premium on the U.S. dollar. Equal to the difference between the forward rate and the spot rate, expressed as a percentage of the spot rate and multiplied by 4. Both rates are those prevailing at end of month. From IFS.

  • z = Percentage change in the spot exchange rate. Based on end-of-month exchange rates. From IFS.

  • z+1 = Three-months-ahead value of z.

II. On the Relation Between Imports and Trade Credit

Let ΔĈt denote the change in the total stock of trade-related credit over period t, and let λi, denote the proportion of imports financed during period t–i with credits due for repayment i periods later. The flow of gross borrowing during period t will be equal to (1 ‒ λ0)Mt, where Mt denotes import payments in the current period and λ0 is the proportion of these imports financed either on a cash basis or with credits maturing during the current period. The flow of amortization payments during period t will be given by the sum of past credits due for repayment in period t. Since the net change in trade-related claims equals the current flow of borrowing minus the current flow of amortization payments, we have


and it can be shown that the stock of trade-related claims at the end of period t will be


Only if λ1 = 1 will it be true that ΔĈt = ΔMt (and therefore that Ĉt = Mt) as implicitly assumed in most studies of capital movements. It can also be seen from equation (15) that λ3 = 1 implies that ΔĈt = Mt, ‒ Mt3 and therefore that


as assumed in Section III of the present paper.


  • Amano, A., “International Capital Movements: Theory and Estimation,” Ch. 9 in The International Linkage of National Economic Models, ed. by Robert J. Ball (Amsterdam, 1973), pp. 283327.

    • Search Google Scholar
    • Export Citation
  • Artus, Jacques, “Exchange Rate Stability and Managed Floating: The Experience of the Federal Republic of Germany,” Staff Papers, Vol. 23 (July 1976), pp. 31233.

    • Search Google Scholar
    • Export Citation
  • Black, Stanley W., International Money Markets and Flexible Exchange Rates, Princeton Studies in International Finance, No. 32, International Finance Section (Princeton University, 1973).

    • Search Google Scholar
    • Export Citation
  • Branson, William H. (1968), Financial Capital Flows in the U.S. Balance of Payments (Amsterdam, 1968).

  • Branson, William H. (1970), “Monetary Policy and the New View of International Capital Movements,” Brookings Papers on Economic Activity: 2 (1970), pp. 23562.

    • Search Google Scholar
    • Export Citation
  • Branson, William H., and Raymond D. Hill, Jr., Capital Movements in the OECD Area: An Econometric Analysis, Organization for Economic Cooperation and Development (Paris, 1971).

    • Search Google Scholar
    • Export Citation
  • Bryant, Ralph C., “Empirical Research on Financial Capital Flows,” Discussion Paper No. 50, Division of International Finance, Board of Governors of the Federal Reserve System (Washington, 1974).

    • Search Google Scholar
    • Export Citation
  • Bryant, Ralph C., and Patrie H. Hendershott, Financial Capital Flows in the Balance of Payments of the United States: An Exploratory Empirical Study, Princeton Studies in International Finance, No. 25, International Finance Section (Princeton University, 1970).

    • Search Google Scholar
    • Export Citation
  • Hernández-Catá, Ernesto, “International Movements of Private Financial Capital: An Econometric Analysis of the Mexican Case” (doctoral dissertation, Yale University, 1974).

    • Search Google Scholar
    • Export Citation
  • Hewson, John, and Eisuke Sakakibara, “The Impact of U. S. Controls on Capital Outflows on the U. S. Balance of Payments: An Exploratory Study,” Staff Papers, Vol. 22 (March 1975), pp. 3760.

    • Search Google Scholar
    • Export Citation
  • Hodjera, Zoran, “Short-Term Capital Movements of the United Kingdom, 1963–1967,” Journal of Political Economy, Vol. 79 (July/August 1971), pp. 73975.

    • Search Google Scholar
    • Export Citation
  • Ishiyama, Yoshihide, “Capital Account Policy in Japan” (unpublished, International Monetary Fund, September 10, 1975).

  • Lee, C. H., “A Stock Adjustment Analysis of Capital Movements; The United States-Canadian Case,” Journal of Political Economy, Vol. 77 (July/August 1969), pp. 51223.

    • Search Google Scholar
    • Export Citation
  • Muth, John F., “Rational Expectations and the Theory of Price Movements,” Econometrica, Vol. 29 (July 1961), pp. 31535.

  • Nelson, Charles R., “Rational Expectations and the Predictive Efficiency of Economic Models,” Journal of Business, Vol. 48 (July 1975), pp. 33143.

    • Search Google Scholar
    • Export Citation
  • Quandt, Richard E., and Stephen M. Goldfeld, “A Markov Model for Switching Regressions,” Journal of Econometrics, Vol. 1 (March 1973), pp. 315.

    • Search Google Scholar
    • Export Citation
  • Stevens, Guy V. G., “Two Problems in Portfolio Analysis: Conditional and Multiplicative Random Variables,” Journal of Financial and Quantitative Analysis, Vol. 6 (December 1971), pp. 123550.

    • Search Google Scholar
    • Export Citation
  • Tobin, James, “The Theory of Portfolio Selection,” Ch. 1 in The Theory of Interest Rates, ed. by F. H. Hahn and F. P. R. Brechling (London, 1965), pp. 351.

    • Search Google Scholar
    • Export Citation

Mr. Hernández-Catá, a graduate of Yale University and the Graduate Institute of International Studies in Geneva, Switzerland, was an economist in the North American Division of the Fund’s Western Hemisphere Department when this paper was prepared. He is now an economist in the Division of International Finance, Board of Governors of the Federal Reserve System.


It has been applied to the United States by Branson (1968 and 1970) and by Hewson and Sakakibara (1975); to Canada by Lee (1969); to Japan by Bryant and Hendershott (1970) and Amano (1973); to the United Kingdom by Hodjera (1971); to a group of member countries of the Organization for Economic Cooperation and Development (OECD) by Branson and Hill (1971), and to Mexico by this author (1974). This is by no means an exhaustive list, and additional references can be found in a recent survey by Bryant (1974).


For an excellent exposition of this theory, see Tobin (1965).


It is assumed that Japanese borrowers are price takers in the U.S. market; they are unable to affect the supply price of U.S. credit that is given at the prevailing U.S. bank lending rate. This implies that U.S. lenders taken as a group do not discriminate against Japanese borrowers—not an entirely realistic assumption in recent years, when Japanese banks’ agencies in the United States have sometimes borrowed in the New York interbank market at rates that exceeded prevailing market rates by a substantial margin.


A theoretically equivalent (but notationally more complicated) procedure would have been to choose the yen as a numeraire and partition each of the two vectors, R¯us and R¯ed, into two subvectors including, respectively, expected interest rates on covered dollar liabilities and expected interest rates on uncovered dollar liabilities.


The exact formulas for the domestic interest rates, expressed in U.S. dollar terms, are R1J = rJx – rJx and R2J = rJz – rJz. (See, for example, Stevens (1971), p. 1242, and Hernández-Catá (1974), pp. 37–38.) The corresponding formulas given in (2) are obtained by ignoring the cross products, taking expected values, and noting that x¯ = x (since the forward premium is known with certainty) and r¯ = r (by assumption). In the general case (where cross products are taken into consideration and r¯ ≠ r, the formula for the expected interest rate R¯2J involves the covariance between rJ and z as well as the expected values of these two variables. See Stevens (1971), particularly his equation (12).

Since the analysis focuses only on the specification of the structural equation (1), there is no need to discuss the question of how x and ze might be related. This question would, of course, have to be discussed in the context of a general equilibrium model of the foreign exchange market.


For an extensive discussion of these effects, see Branson (1970) and Hernández-Catá (1974).


It may be noted that the so-called parity condition is not assumed to hold in the present context. This condition could be derived as a polar case of equation (3) by assuming α31 = α1 dividing through by α1 and taking the limit for α1 → ∞. This, however, would imply the rather extreme assumption of perfect substitutability between Japanese and (covered) U.S. assets, an assumption that is not confirmed by inspection of the data.


An aggregate ceiling may be available, but this is not sufficient if specific ceilings are imposed on individual banks or enterprises.


The problem partly stems from the need to distinguish between periods in which the ceiling is limiting and periods in which it is not. This is the problem of “switching regressions,” tackled in a different context by Quandt and Goldfeld (1973).


See, for example, Hewson and Sakakibara (1975), particularly p. 52.


Bryant (1974), p. 11–25.


Some authors prefer to divide through by W, obtaining the borrowing to net-worth ratio C/W on the left-hand side of the equation. While this may result in reducing multicollinearity among the independent variables, it may also introduce some of the problems caused by using data in ratio form in least-squares regressions, for example, heteroscedasticity.


While borrowing by Japanese agencies in the U.S. interbank market has gained some importance in recent years, the issue of certificates of deposits by these agencies in the U.S. market was not authorized by the Japanese Ministry of Finance until June 1975.


This variable performed consistently better than its alternative, a weighted average of the call money rate and the Bank of Japan’s discount rate. When the two interest rates were included in the regressions as separate independent variables, the coefficient of the discount rate turned out to be negative and (surprisingly) larger than its standard error.


The more general specification of trade-related capital flows is considered in Appendix II.


The first variable attempted to capture the basic relaxation of Japan’s exchange control system in November 1973 (which included a liberalization of the “yen conversion control”). The second variable was defined as the marginal reserve requirement ratio on nonresidents’ “free yen” accounts. It was used not because of the importance of yen-denominated U. S. bank claims on Japan, which are quite small (at least on the basis of published U. S. figures) but because it was thought that this variable might serve as a proxy for the general stance of the Japanese authorities vis-à-vis capital inflows in general. A third variable based on the amount (per export transaction) that is freely convertible into yen without license was used for the same purpose. The construction of these variables (available from the author upon request) was based on information contained in various issues of the Japanese Ministry of Finance’s Monthly Finance Review and in Ishiyama’s (1975) description of capital account policy in Japan.


Defined in this manner, the variable exhibits a sharp decline in January 1974. Smoother versions of this variable were tried, but without any appreciable change in the results.


On the basis of equation (8–2), the VFCR Program is estimated to have reduced U.S. bank claims on Japan at the end of 1974 by about $1 billion, or some 13 per cent of what such claims would have been in the absence of restrictions. By July 1974, U.S. claims on Japan had reached $12.7 billion, but it is estimated that they would have amounted to less than $11 billion, had the VFCR Program been maintained with the same degree of restrictiveness (in terms of the variable kus) that prevailed at the end of 1973.


The so-called adaptive expectations hypothesis is no more than a special case of equation (10) for n = ∞ and geometrically declining θis. The usual formulation of this hypothesis leads to the introduction of a lagged dependent variable on the right-hand side of the equation, which may be quite bothersome in the presence of autocorrelation. Moreover, the coefficient of a lagged dependent variable in the present context could hardly be unambiguously interpreted as reflecting the magnitude of expectational adjustments only; it could very well be capturing adjustment costs, institutionally determined lags in the repayment of trade credits, or simply omitted variables.


Since the forward premium x was based on the three-month forward rate, the variables p and z were computed as average rates of change during the previous three-month period.


In his capital flow equations, Artus considers net capital flows between the Federal Republic of Germany and all other countries, while the present study focuses on gross U.S. lending to Japan only. Furthermore, trade-related capital flows receive particular attention in this paper but are excluded from Artus’ equations. Finally, this paper focuses on a single structural relationship, while Artus’ equations are estimated simultaneously as part of a complete short-run macroeconomic model of the economy of the Federal Republic of Germany.


Unfortunately, the example used by Muth in his original article was misleading because it was based on a particular model in which the “rational” expectation of a variable happened to coincide with an extrapolative expectation. In the general case, however, the rational expectation of a variable is not simply an extrapolative predictor; it must be generated from the entire history of all exogenous inputs (i.e., exogenous variables as well as disturbances). On this point, see Nelson (1975).


As can be surmised from the standard errors of these variables, z+1 is very weakly correlated with the forward premium x, which is not entirely surprising in the context of exchange controls. This illustrates a fact that has been recognized in the recent literature on fluctuating exchange rates—namely, that forward rates are sometimes poor predictors of future spot rates.


The following example may also help to illustrate the orders of magnitude involved. Of the $4½ billion increase in U. S. claims on Japan that occurred during the first two quarters of 1974, slightly more than one half is estimated to have directly resulted from the expansion of Japanese imports; some 15 per cent from the removal of U.S. foreign credit guidelines in early 1974; and as much as one third from changes in interest rate and exchange rate variables.


The following abbreviations are used: IFS: International Monetary Fund, International Financial Statistics; WFM: Morgan Guaranty Trust Co., World Financial Markets; FRB: Federal Reserve Board, Bulletin; USTB: U. S. Treasury Department, Treasury Bulletin; BEQB: Bank of England, Quarterly Bulletin; BOJ: Bank of Japan, Economic Statistics, annual and monthly; BCD: U. S. Department of Commerce, Business Conditions Digest. Series are not seasonally adjusted unless otherwise indicated. All interest rates are in per cent per annum; and all exchange rates are expressed in yen per U. S. dollar.