A Model of International Investment Income Flows
Author: Marian Bond

Although investment income flows accounted for just under 30 per cent of total receipts and payments for world services in 1971, a major proportion of these flows goes to a small number of industralized countries for whom investment income is a significant source of foreign exchange earnings. For example, the Federal Republic of Germany, the United Kingdom, and the United States—the three most important receiving countries—accounted for 64.3 per cent of world receipts from investment income in 1971, although, as might be expected, payments of investment income were much more widely spread.

Abstract

Although investment income flows accounted for just under 30 per cent of total receipts and payments for world services in 1971, a major proportion of these flows goes to a small number of industralized countries for whom investment income is a significant source of foreign exchange earnings. For example, the Federal Republic of Germany, the United Kingdom, and the United States—the three most important receiving countries—accounted for 64.3 per cent of world receipts from investment income in 1971, although, as might be expected, payments of investment income were much more widely spread.

Although investment income flows accounted for just under 30 per cent of total receipts and payments for world services in 1971, a major proportion of these flows goes to a small number of industralized countries for whom investment income is a significant source of foreign exchange earnings. For example, the Federal Republic of Germany, the United Kingdom, and the United States—the three most important receiving countries—accounted for 64.3 per cent of world receipts from investment income in 1971, although, as might be expected, payments of investment income were much more widely spread.

The purpose of this paper is to provide an analysis of the short-run determinants of international investment income flows by specifying and estimating a model that can be utilized both for short-term forecasting and to analyze the effects of policy changes on these income flows. The model is used to explain variations of income inflows and outflows for the Federal Republic of Germany, the United Kingdom, and the United States.

Flows of investment income into and out of a country arise from a variety of international transactions. These flows are defined in a balance of payments context to cover residents’ income from investment abroad and the income of foreigners in the country concerned. These investments can be broadly classified as follows:

(a) Direct foreign investment, which consists mainly of investments in a country that involve an important element of foreign control. Income on direct investments includes interest, dividends, and branch profits paid by the foreign affiliate to the parent company.

(b) Long-term financial investment. These are claims that include long-term securities, commercial credits and bank loans, equities that do not involve control, and miscellaneous other long-term claims.

(c) Short-term financial investment, which consists of deposits, commercial and financial paper, and acceptances and loans.

(d) Government investment. Government claims abroad include all government loans (long-term and short-term), the majority of which represent loans to foreign governments, and outstanding claims on international organizations. Government liabilities consist mainly of treasury bills and marketable and nonmarketable treasury bonds and notes. The vast majority of U. S. Government liabilities are to foreign official institutions.

Very few empirical studies have been carried out solely to analyze the determinants of international investment income flows. There has therefore been relatively little model building in this area. Generally, studies of these flows have been undertaken as part of a larger balance of payments model in which more attention has been devoted to the trade and capital accounts than to flows of investment income. Researchers have preferred to devote time and effort to analyzing the impact of interest rate policies and other government policies on the capital account of the balance of payments rather than on investment income flows. However, as Kwack (1972) has pointed out, interest rate policies directed toward improving the capital account of the balance of payments by reducing assets abroad relative to liabilities abroad will lead to a deterioration in the balance of payments on the investment income account. For example, raising short-term interest rates to encourage an inflow of funds from abroad can lead to a short-run improvement in a country’s balance of payments by reducing the level of financial assets abroad relative to the level of financial liabilities abroad. But the long-run effect of this policy will lead to a deterioration in the balance of payments on the investment income account. This effect is demonstrated quite well by the U. K. experience where the balance of financial investment income fell from $210 million to -$170 million over the period 1961–75.

The present study of investment income flows goes further than previous studies in the following six ways:

1. It represents an attempt to include all categories of investment income flows into a consistent methodological approach by distinguishing between different types of assets and liabilities. This has not been attempted in any other study, although Duffy and Renton (1970), in their study on the services account of the United Kingdom, disaggregate investment income flows into separate equations for (a) payments and receipts of interest and (b) payments and receipts of profits and dividends, and Kwack (1972) focuses on the separation of investment income flows into financial and government investment income flows. In the present paper, investment income is classified into three types—direct, financial, and government investment income for the United States, and direct, financial, and other investment income for the United Kingdom. The advantages of including all categories of investment income flows is that aggregated and disaggregated equations can be estimated to see whether it is advantageous to disaggregate. A priori, one might expect there to be considerable benefit from disaggregating in terms of increased accuracy of results, because separate groups of investors are involved whose behavior may be quite different. Unfortunately, owing to data limitations, no aggregation test could be performed for the Federal Republic of Germany.

2. An attempt is made to distinguish between those determinants that affect investment income flows and those that affect earnings. Earnings consist of both repatriated earnings and reinvested earnings, and investment income flows are merely repatriated earnings. Only Prachowny (1969) has made any attempt at modeling this distinction. As part of his structural model of the U. S. balance of payments, he looks at the earnings of dividends and interest and asks what portion of these earnings will be repatriated. He argues that the main determinants of repatriated earnings will be the relative profitability of investing income domestically and abroad, since if reinvestment of income abroad is more profitable than repatriation and domestic investment of the funds, less funds will be repatriated.1 The distinction, however, does not apply to U. S. Government and financial investment income flows where data are computed directly by the data-collecting agency from the asset and liability components and their assumed rates of return.

3. Both the permanent (long-run) and the transitory (short-run) components of earnings that result in quasi-rents or quasi-losses have been incorporated in the study. The distinction is important, since there is a large transitory component of earnings from international investments, related to the cyclical behavior of the economy. This factor may contribute to an explanation of the difference in results obtained by Prachowny and Kwack. Prachowny, using data for the 1950s and early 1960s, obtained a larger marginal relationship between the rate of interest and income flows than did Kwack, who used data for the 1960s. This difference might be accounted for by differences in the cyclical pattern in the two sample periods.

4. Speculative activity, involved in moving funds across frontiers, is explicitly modeled in the present study.

5. Adjustments of income flows to changes in earnings may take a few years, when changes in earnings are regarded as a permanent rather than a temporary phenomenon. These adjustments are explicitly considered in this study.

6. The homogeneity property 2 is tested. In the discussion of their results, some researchers assume that the marginal rate earned on assets is equal to the average rate (the homogeneity condition) without testing this hypothesis. From a practical point of view, it is important to know whether these returns are equal, and, hence, the homogeneity property is subjected to the appropriate tests.

The research underlying this paper has yielded the following conclusions: (a) The disaggregation of total investment income inflows and outflows into their component parts is, on the whole, justified, because the disaggregated equations tend to forecast noticeably better than the aggregate equations, (b) The distinction between earnings and income flows has proved useful from both a theoretical and an empirical point of view, (c) Our results suggest that earnings have both a permanent and a transitory component, and the transitory component is positively related to the level of economic activity in the country in which the earnings are generated, (d) Investment income inflows and outflows seem to be influenced significantly by speculative activities because they respond to expected changes in exchange rates, (e) Both income inflows and outflows tend to adjust to changes in earnings with a significant lag. (f) The homogeneity postulate is shown to hold in 13 out of the 18 equations for which the test was performed.

The empirical results that have been summarized, and which will be elaborated in the remainder of this paper, have implications for all aspects of balance of payments policies, especially borrowing and interest rate policies. Moreover, the empirical results may well improve the accuracy of balance of payments forecasts.

Although the research underlying this paper has incorporated several novel features, there is clearly room for further improvement. In particular, the following special assumptions and shortcomings of the present work should be kept in mind when evaluating the results. The factors that influence investment decisions are likely to be complex, and hence no attempt has been made to explain them. Moreover, the data have not been constrained, so that income inflows of one country are equal to income outflows of other countries weighted by shares, because (first) data are subject to errors in measurement and (second) some countries report flows of repatriated income separately while others include reinvested earnings in their balance of payments figures.

The plan of the paper is as follows: Section I provides a description of the model that explains variations of income inflows and outflows for each category of investment income; Section II describes the estimation procedures and data used; Section III evaluates the empirical results; Section IV examines the predictive properties of the model; and Section V sets forth the conclusions.

I. The Model3

This section is intended to provide the theoretical groundwork on which to base the empirical work. For ease of exposition, a two-country model is derived, first for income inflows, and then for income outflows. The resulting equations are then aggregated across n paying and n receiving countries for purposes of estimation.

INCOME INFLOWS

A country’s actual earnings (Et) during period t on each type of foreign asset is the product of the actual rate of return in the issuing country (RAt) and the value of asset holdings at the beginning of period t (At-1):

Et=RAtAt1(1)

(We assume here that the rate of return relevant to claims abroad are those set in foreign markets.)

Actual earnings on claims abroad have two components. First, the long-run or permanent component of earnings (RPt), which is related to the long-run rate of return, and, second, the transitory or short-run component of earnings (RTt), which is related to cyclical fluctuations in an economy and which results in quasi-rents or quasi-losses. The return on assets can therefore be split into two parts

RAt=RPtRTt(2)

where E(RTt) = 1, that is, in the long run, expected RTt = 1 and RAt = RPt.

The problem that we encounter here is to measure the long-run rate of return, RPt. We propose to use the long-run bond rate (rt) set by the government as a proxy for the long-run rate of return. However, this may not be an appropriate measure for the long-run rate of return earned by foreign investors, and we may need to make adjustments for this factor. Many different adjustments might be made; the one that we propose to use is the rate of invesment abroad. We postulate that if the rate of return is high, the rate of investment is likely to be high, while if it is low, the rate of investment is also likely to be low.4 The change in the level of assets can therefore be used as a proxy for this adjustment of the long-run return, and the long-run rate of return can be written as

RPt=rt(AtAt1)Ω(3)

Clearly, if Ω = 0, or if At =At-1, then RPt = rt.

The transitory component of the actual rate of return is assumed to be influenced largely by cyclical factors. These cyclical factors are related to the gross national product (GNP) and are commonly approximated by the ratio of actual real GNP (Qt) to potential real GNP (Qt)5

RTt=(QtQt)μ(4)

By combining equations (1) through (4), the earnings function can now be rewritten as

Et=[(QtQ¯t)μrt(AtAt1)Ω]At1(5)

Having specified the determinants of the flow of earnings, let us now consider the income inflows that result from these earnings. Differences between earnings and income inflows arise because some proportion of earnings is typically retained and reinvested in the host country. The proportion of earnings that is repatriated, and thus results in income inflows, will be assumed to depend upon the relative profitability of domestic and foreign investment, upon the expected foreign exchange rate, and upon the behavior of agents in adjusting income flows to earnings.6 Let us consider these three factors in turn.

First, if risks at home and abroad are the same, and reinvestment abroad is more profitable than domestic investment of the income earned, then the income earned will be reinvested abroad. We therefore hypothesize that income inflows will be smaller, the greater is the profitability of reinvesting funds abroad. A variable, GRt, representing the relative profitability of investing domestically and abroad will be used to capture this effect.

Second, income inflows involve the movement of money across national frontiers. These inflows can therefore become more or less concentrated in the current quarter, or over longer periods, depending upon speculation regarding future exchange rates.7 The expected change in the exchange rate (Xt+1*/Xt) will influence the timing of income inflows in the following way. If the exchange rate of a country is expected to appreciate, income inflows from abroad to that country may be brought forward because of expectations that any given amount of transfer into the country’s currency by foreign countries will require a greater amount of foreign currency if postponed. Similarly, if a country’s exchange rate is expected to depreciate, income inflows from abroad might be postponed because of the expectation that transfer will require less foreign currency.

Third, firms or individuals may adjust their income inflows slowly to higher or lower levels of earnings. Adjustment will be complete only when the change in earnings is accepted as a permanent, rather than a temporary, one. Therefore we can write

YIPt=Etθ(6)

where YIPt defines permanent income inflows. Since actual income inflows (YIt) do not equal permanent income inflows but adjust gradually to them over a period of time, the adjustment process can be described by a stock adjustment model of the form

YItYIt1=(YIPtYIt1)η(Xt+1*Xt)πGRtρ(7)

Substituting equation (5) into equation (6) and equation (8) into equation (7), we obtain equations (8) and (9)

YIPt={[(Qt/Q¯t)μrt(At/At1)Ω]At1}θ(8)
YIt={[(Qt/Q¯t)μrt(At/At1)Ω]At1}θη(Xt+1*Xt)πGRtρYIt1(1η)(9)

INCOME OUTFLOWS

A bilateral income flow from country i to country j represents an inflow for country j and an outflow for country i, and consequently the model presented in the previous section explains both flows. However, data on bilateral flows are not generally available, and aggregation across countries (receiving countries for outflows and paying countries for inflows) has been unavoidable in the empirical research. Hence, the following separate income outflow equation, which is quite analogous to the preceding inflow equation, has been postulated for the empirical work

YOt={[(Qt/Q¯t)μ1rt(Lt/Lt1)Ω1]Lt1}θ1η1(Xt+1*Xt)π1GRtρ1YOt1(1η1)(10)

where Lt is the receiving country’s level of liability in a particular paying country and the variables Qt/Qt, rt Xt+1*/Xt, and GRt now refer to the paying country.

HOMOGENEITY PROPERTY

It is easily seen that, according to the present definitions, the homogeneity property will be met when the average return is equal to the marginal return. For the income inflow model, we therefore differentiate equation (9) with respect to At-1, which gives the marginal return

YItAt1=K[(Qt/Q¯t)μrtAtΩ.At11Ω]θηAt11(Xt+1*Xt)πGRtρYIt1(1η)(11)

where K = ηθ(1- Ω).

And dividing equation (9) by At-1 gives the average return

YItAt1=[(Qt/Q¯t)μrtAtΩ.At11Ω]θηAt11(Xt+1*Xt)πGRtρYIt1(1η)(12)

Clearly, equating the two gives the condition that average and marginal returns are equal when K = ηθ(1-Ω) = 1.

II. The Estimating Equation

Two variables that have been used in the empirical estimation require some elaboration. They are the change in the expected exchange rate (Xt+1*/Xt) and the relative profitabilities (GRt). Let us discuss them in turn.

There are various theories of how expectations are formed with regard to future exchange rates. No one theory commands general acceptance, partly because it is felt that expectations contain predominantly stochastic elements, and all other real-world variables that affect expectations and speculative behavior cannot be included in expectations generating models.8

The model of speculative behavior that is proposed here incorporates both extrapolative and regressive expectations by specifying expectations generating functions as truncated distributed time lags that allow the data to determine the expectations pattern. In other words, apart from the truncation, no restrictions have been imposed on the parameters of the distributed lag model. One major problem is that the estimation period encompasses fixed and floating exchange rate regimes. Adjustment to equilibrium exchange rates will differ for the two periods. Under a fixed rate system, capital flows will take place to restore equilibrium, whereas under a flexible rate system, the exchange rate will change. Furthermore, the lag structures involved may be different for the two periods. These shortcomings should be kept in mind when evaluating the results.

The general truncated distributed lag function assumes that the expected change in the exchange rate (Xt+1*/Xt) will depend on past values of exchange rates (either levels, or changes, or both), thus:

Xt+1*Xt=Xtγ0Xt1γ1Xt2γ2,,Xtnγn(13)

This general distributed lag function can be reduced to represent specific expectations models. For instance, the simple extrapolative expectations model

Xt+1*Xt=(XtXt1)α00<α0<1(14)

can be obtained by postulating that 0 < α0 = γ0 < 1, γ1 = -γ0, and γ2 = γ3 = … = γn =0.

Further, a regressive expectations model of the type

Xt+1*Xt=(X¯tXt)α10<α1<1(15)

where Xt is defined as a normal exchange rate can also be interpreted as a special case of equation (13). Two cases might be distinguished here: First, if Xt = Xt-1, then in terms of equation (13), γ0 = - α1, γ1 = α1, and γ2 = γ3 = . . . γn = 0. Second, let Xt be amended in proportion to the deviation from the last period’s normal level

X¯t=X¯t1(Xt1X¯t1)1α2

which can be expanded to

X¯t=Xt1(1α2)Xt2(1α2)Xt3α22(1α2),,Xtnα2n(1α2)X¯tnα20<α2<1

or

X¯t=Πj=0nXtj1α2i(1α2)X¯tn1α2(16)

Substitution of equation (16) in equation (15) yields

Xt+1*Xt=X-a1[Πj=0nXt-j-1a2j(1-a2)X¯t-n-1a2]a1

which can be approximated to any degree of desired accuracy to equation (13) by simply assuming γ0 = -α1 and γi=α1(1α2)α2i1,i=1,,n. In the empirical estimation, the distributed lag has been truncated at n = 4, and the resulting expression for Xt+1*Xt has been used in the estimating equation.

The second variable that warrants separate discussion is the measure of the relative profitability. Several alternative proxy variables for this measure were considered, and it was decided to use the percentage rate of growth of real GNP in the foreign country compared with a similar measure of the growth rate in the domestic economy.9

As has already been mentioned, equations (9) and (10) are assumed to be adequate descriptions of the determination of bilateral income flows between any two countries. Unfortunately, however, data on bilateral flows are not generally available; hence, inflows have to be aggregated across paying countries, and outflows across receiving countries. Owing to nonlinearities, the exact aggregation of equations (9) and (10) across receiving and paying countries is possible only under highly restrictive assumptions, which are most unlikely to be satisfied in practice.10 Consequently, it will be assumed here that equations (9) and (10) can be used as adequate approximations of the aggregate relationships in which A, L, YI, and YO represent aggregate assets, liabilities, income inflows, and income outflows, respectively, and the remaining variables are appropriately weighted averages. Specifically, the two estimating equations for a particular country are as follows: 11

lnYIt=lnΣj=1mYIjt=b0+b1(Σjwilnrjt+lnAt1)+b2(lnAtlnAt1)+b3Σjwjln(Qjt/Qjt¯)+b4Στ=04(ΣjwilnXit1lnXtτ)+b5(lnGtlnGt1)Σwi(lnGijlnGit1)+b6lnΣjYIt1(17)
lnYOt=lnΣj=1mYOjt=a0+a1(lnrt+lnLt1)+a2(lnLtlnLt1)+a3ln(Qt/Qt¯)+a4Στ=04(lnXtτΣJαilnXitτ)+a5Σαij(lnGitlnGit1)(lnGtlnGt1)+a6lnΣjmYOt1(18)

(m = 1, . . ., 12)

where the js refer to paying countries in equation (17) and to receiving countries in equation (18). The weights wi, and αi are the jth country’s share of assets and liabilities, namely, wi=AiAandαi=LiL.12 The remaining variables are defined as follows:

rt = long-term interest rate on government bonds in the country, in per cent

rit = long-term interest rate on government bonds in country j, in per cent

Xt = price of the U. S. dollar in terms of the country’s currency, in index form

Xit = price of the U. S. dollar in terms of country js currency, in index form

Gt = the country’s percentage growth rate of GNP in period t

Gjt = percentage growth rate of GNP in country j in period t

All assets, liabilities, income inflows, and income outflows are expressed in U. S. dollars.

The coefficients of the estimating equations (17) and (18) are related to the underlying parameters in the following manner:

b1=θηb2=Ωθηb3=μθηb4=πb5=ρb6=(1η)(19)
a1=θ1η1a2=Ω1θ1η1a3=μ1θ1η1a4=π1a5=ρ1a6=(1η1)(20)

and these relationships imply the following sign predictions:

b1 > 0, b2 > 0, b3 > 0, b4 > 0, b5 > 0, 0 < b6 < 1

a1 > 0, a2 > 0, a3 > 0, a4 > 0, a5 > 0, 0 < a6 < 1

It can now easily be seen that the homogeneity constraint ηθ (1- Ω) = 1 is equivalent to the constraints that b1 - b2 = 1 and a1 - a2 = 1. These restrictions were imposed on equations (17) and (18) to test the validity of the homogeneity proposition.

III. The Empirical Results

Equations (17) and (18) were fitted to data for three countries for which investment income inflows and outflows are particularly important components of the balance of payments, namely, the United States, the United Kingdom, and the Federal Republic of Germany. Total investment flows have been abbreviated to TO. Moreover, total investment income flows could be, and were, disaggregated into three components, namely, direct (DI), financial (FI), and government (GI) for the United States and into direct (DI), financial (FI), and other (OI) for the United Kingdom.13 Because of the unprecedented surge of oil prices in the last quarter of 1973, oil earnings and, hence, oil investment income flows have become extremely volatile. For the United States, the oil investment income flows could be identified, and, hence, the equations for direct and total investment income flows were fitted both with and without the oil component. Thus, in total, there are 11 basic equations for income inflows and 11 for income outflows. Further, to be able to test for the validity of the homogeneity postulate, all equations apart from U. S. financial and government income flows were run both with and without the homogeneity constraint.

Two further points should be made before the empirical results are considered. First, the model presented in Sections I and II is based on the assumption that the investment flows are caused by economic decision makers whose actions are motivated primarily by self-interest. This approach seems quite appropriate for 18 of the 22 investment income flows. The exceptions are the four U. S. government and financial flows. The reason why the model may be inapplicable to these four flows is that the data for them are not obtained from a primary source but instead are computed by the data-collecting agencies from the various asset (and liability) components and their assumed rates of return. For this reason, the expected exchange rate and growth rate variables were suppressed in estimating the equations for these four investment flow categories. The resulting equations are assumed to model simply but adequately the rather complex computational formulas used by the agencies. Thus, for these equations the homogeneity test would seem to be inappropriate.

Second, a substantial proportion of U. S. financial and government assets abroad is denominated in U. S. dollars, and the returns on these assets are determined by U.S. interest rates. For this reason, U.S. interest rates were included as determinants of the U. S. financial and government investment inflows. In other words, one of the wjS. in equation (17) measures the ratio of U. S. dollar-denominated assets to total assets and one of the rjts represents the U. S. bond rate.

All equations were fitted to quarterly data by means of ordinary least squares. For the United States and the United Kingdom, the sample periods were the third quarter of 1962 to the fourth quarter of 1975 (54 observations) for income inflows and the second quarter of 1963 to the fourth quarter of 1975 (51 observations) for income outflows. The sample period for inflows and outflows for the Federal Republic of Germany was the second quarter of 1966 to the fourth quarter of 1975. Availability of data dictated this choice of sample periods. Seasonal zero-one dummy variables for the second, third, and fourth quarters, denoted by D2, Ds, and D4, were added to each equation. Other dummy variables were included to represent the effects of the oil crisis on all investment income flows (DOIL, taking the value of zero until the third quarter of 1973 and unity thereafter) and the effects of the capital restrictions on U. S. direct foreign investment income flows (DRES, taking the value of unity for the first quarter of 1965 to the fourth quarter of 1973 and zero otherwise). The detailed data sources are presented in Appendix I.

A detailed discussion of the empirical results is presented in three sections, which cover the inflow equations, the outflow equations, and the homogeneity postulate.

INFLOW EQUATIONS

The estimates of the unconstrained parameters are presented in Table 1 for the log-linear version of the model and in Table 5 in Appendix II for the linear version. The independent variables (including the seasonal, oil-crisis, and capital restriction dummies) are listed in the first row, and the 11 dependent investment inflows in the first column. The figures in parentheses are the estimated standard errors of the parameters.

Table 1.

Regression Coefficients: Investment Income Inflows, Third Quarter 1962-Fourth Quarter 1975

(All variables, except dummies, expressed in logarithms; standard errors in parentheses)

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Estimated, second quarter 1966-fourth quarter 1975.

Table 2.

Short-Run and Long-Run Investment Income Coefficients with Respect to Permanent and Cyclical Returns

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Table 3.

Regression Coefficients: Investment Income Outflows, Second Quarter 1963-Fourth Quarter 1975

(All variables, except dummies, expressed in logarithms ; standard errors in parentheses)

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Estimated, second quarter 1966-fourth quarter 1975.

Table 4.

Forecasting Errors for Individual Categories of Investment Income, 1974 and 1975

(In millions of U.S. dollars)

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Table 5.

Regression Coefficients: Investment Income Inflows, Second Quarter 1962-Fourth Quarter 1975

(All variables expressed in natural numbers; standard errors in parentheses)

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Measured in millions of U.S. dollars.

Estimated, second quarter 1966-fourth quarter 1975.

The overall explained variance, as measured by the R2s, is quite large in all 11 equations: the R2 exceeds 0.90 in 9 equations and 0.95 in 6 equations. Further, the extent of autocorrelation in the residuals, as measured by the crude Durbin-Watson statistic, also seems to be rather small. The crude Durbin-Watson statistic, however, tends to be biased (toward two) when lagged dependent variables are present. Hence, an amended Durbin-Watson statistic (h) was computed.14 If h exceeds 1.645, then, for large samples, the hypothesis of zero autocorrelation must be rejected at the 5 per cent level. The computed values of h turned out to be as follows:

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Thus, both the crude Durbin-Watson and the h-statistics suggest that, generally, autocorrelation in the residuals is not a serious problem. The other summary statistics, which are presented in the last column of Table 1, are the standard errors of the estimates (SEE) with their anti-logs in parentheses. The latter give an impression of the typical proportionate residual error.

A detailed discussion of the regression coefficients for the log-linear version of the model follows. As the omissions from Table 1 suggest, variables that had clearly insignificant coefficients in the first estimation run were omitted in the final run, so that, by design, all the remaining regression coefficients have fairly high t-ratios. In turn, five sets of coefficients are discussed, namely, those of the (a) rate-of-return variables, (b) lagged dependent variables, (c) exchange rates, (d) relative profitability, and (e) dummy variables.

(a) Table 2 contains the short-run and long-run rate-of-return coefficients. The b1 and b2 coefficients are the same as in Table 1, and the long-run coefficients are defined as θ = b1/(1 - b6) and Ω = b2/(1 - b6)—where b6 is the coefficient of the lagged dependent variable.

All rate-of-return coefficients have the predicted positive sign. Moreover, some of the coefficients are similar to those found by some previous investigators. Conceptually similar coefficients were estimated by Prachowny (1969), Duffy and Renton (1970), Kwack (1972), and Phillips (1974), although in these studies estimates of slopes rather than elasticities were obtained. Converting Kwack’s and Prachowny’s slope estimates to elasticity estimates gave elasticities of 0.49 and 0.398, respectively, for financial investment income inflows. The present figure of 0.32 is therefore rather closer to that of Prachowny than of Kwack.

According to the present theoretical framework, the b2 and Ω coefficients give an indication of the adequacy of the long-term rate of interest on government bonds as a measure of the long-run permanent rate of return. Since government lending is not subject to the same economic criteria as private investment, it is plausible that b2 = Ω = 0 for government investment flows, and the present findings support this suggestion. But in three equations for nongovernment flows, b2 and Ω are also zero, so that for these flows the bond rate may be regarded as an adequate measure of the long-run permanent rate of return. It is in only 4 of the 11 equations that it seems necessary to adjust the bond rate by a factor that is proportional (in the logarithms) to the rate of investment.

In 9 of the 11 equations, the b3 coefficient, which measures the cyclical component of the return, is significant. Moreover, the size of the coefficients suggests that investment inflows tend to be very responsive to cyclical conditions.

(b) The lagged dependent variables (Table 1) are significant in 6 of the 11 inflow equations and are omitted from the other equations. Since noneconomic factors must be expected to dominate in the determination of government inflows, the absence of lagged adjustment in the U. S. government and the U. K. other equations is not surprising. The partial adjustment coefficients of 0.66, 0.35, 0.49, 0.70, 0.62, and 1.43 in equations (1), (3), (5), (7), (10), and (11), respectively, reveal that U. S. financial income inflows are relatively inelastic in the short run with respect to changes in earnings. This agrees with the findings of Kwack that there was a partial adjustment coefficient of 0.248 for U. S. financial investment. Partial adjustment coefficients for U. S. and U. K. direct investment indicate that their income inflows are rather more elastic with respect to earnings. In one case, total inflows for the Federal Republic of Germany, the coefficient of the lagged dependent variables lies between 0 and −1, which implies an adjustment coefficient lying between 1 and 2. In terms of the stock adjustment model of equation (7), this means that the adjustment toward the long-run income inflow tends to overshoot its target in the short run but is stable in the long run.

(c) In two equations—namely, those for U. S. direct investment and U. K. other investment—lagged exchange rates do not seem to be important determinants of income inflows. For other equations (apart from U. S. financial and government equations for which the exchange rate variable was suppressed), the coefficients of the exchange rates can be rearranged, so that the effects of levels and of rates of change can be distinguished clearly:

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It is not easy to interpret these results in terms of simple, constrained models of extrapolative or regressive expectations. But in the light of the discussion in connection with equations (13) to (16) in Section II, extrapolative expectations seem to dominate in equations (1), (5), (6), and (8) and regressive expectations in equations (7), (10), and (11).

(d) It was postulated earlier that the greater the profitability of investing abroad, the less funds would be returned home. The relationship between the proxy variable for relative profitabilities and income inflows is found to be significant only in the equations for U. S. and U. K. direct investment income inflows, and consequently for the U. S. and U. K. total inflows. Moreover, the estimated elasticities for the United States seem to be quite large. For instance, an increase of 1 per cent in the relative growth rates leads to a rise of 8.94 per cent in direct investment income inflows (excluding oil flows). The perverse sign on the coefficient for the U. K. total equation is difficult to explain. In none of the other equations, however, do relative growth rates have a significant impact, so that their role must be regarded as rather limited.

(e) The coefficients of seasonal dummy variables indicate that there are substantial seasonal components in the investment income inflows, which, however, are not entirely uniform. In general, the second and fourth quarter dummies tend to be positive and the third quarter ones tend to be negative, but some of the U. K. equations have a different seasonal pattern.

The oil-crisis dummy has a positive coefficient in all but one equation, namely, the total equation for the Federal Republic of Germany; this negative coefficient may be caused by reduced foreign earnings in that country. It is interesting that U. S. direct investment income and U.K. other investment income have risen considerably as a result of the oil crisis.

The dummy representing U. S. controls on foreign direct investment has a negative coefficient for the two direct investment inflow equations but is insignificant in both total equations. These controls have given rise to a rather small reduction in U. S. direct investment income inflows.

OUTFLOW EQUATIONS

The estimates of the unconstrained parameters for the income outflow equations are presented in Table 3 and in Table 6 in Appendix II for the log-linear and linear version of the model, respectively, and the detailed discussion of the regression coefficients concentrates on the log-linear version. Again, as with income inflows, the R2s are quite large and exceed 0.90 in 9 of the 11 equations. However, the crude Durbin-Watson statistic lies in the inconclusive region for 5 of the 11 equations; this presents a problem more serious than usual because the inclusion of lagged dependent variables will bias the Durbin-Watson statistic toward two. When the amended h-statistics were computed for the relevant equations, the results were as follows:

Table 6.

Regression Coefficients: Investment Income Outflows, First Quarter 1963-Fourth Quarter 1975

(All variables expressed in natural numbers; standard errors in parentheses)

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Measured in millions of U.S. dollars.

Estimated, second quarter 1966-fourth quarter 1975.

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where the critical value of h is 1.645 at the 5 per cent level. Thus, in 7 of the 10 equations tested (1, 2, 3, 5, 8, 10, 11), the hypothesis of zero autocorrelation must be rejected at the 5 per cent level of confidence.

The results in Table 3 show that (a) rates of return, (b) lagged dependent variables, (c) exchange rates, (d) relative profitability, and (e) dummy variables are all important in determining investment income outflows, as shown by their standard errors. A discussion of each coefficient follows.

(a) The short-run and long-run rate-of-return coefficients for income outflows are itemized in columns 6 to 10 of Table 2. The long-run coefficients are θ1 = a1/(1 - a6) and Ω1 = a2/(1 - a6); and a6 is the coefficient of the lagged dependent variable. Column 6 shows the rate- of-return coefficient; all of these have the predicted positive sign and conform, in principle, to the findings of other researchers. Thus, in the short run the rate of return is quite inelastic with respect to income outflows, except for the U. K. other category. But if we consider the θ1s, which are estimates of the long-run elasticity of income outflows with respect to the rate of interest, these are uniformly larger than the short- run elasticities and close to unity in 5 of the 11 equations.

Columns 7 and 10 contain the a2 and Ω1 coefficients; these coefficients indicate that only for U. K. total and U. S. direct (excluding oil) investment outflows can the long-term government bond rate be regarded as an adequate measure of the permanent rate of return in the short run. However, in the long run, in 6 of the 11 outflow equations the long-term bond rate needs adjusting by a factor, proportional (in the logarithms) to the rate of investment.

The coefficient on the cyclical component of the return, a3, is significant in all of the equations but the one for the Federal Republic of Germany. The size of the coefficients suggests that investment outflows tend to be particularly responsive to cyclical conditions for U. S. direct investment and U. K. direct and financial investment, but less responsive for U. S. government investment.

(b) The partial adjustment coefficients, which are significant in nine of the equations, are 0.47, 0.80, 0.28, 0.29, 0.52, 0.53, 0.33, 0.68, and 1.35 in equations (1), (2), (3), (4), (5), (6), (8), (10), and (11), respectively. As in the income inflows, the U. K. other equation has no lagged adjustment; this is not surprising in view of the noneconomic factors associated with government investment. In addition, the partial adjustment coefficients reveal that income outflows are relatively inelastic in the short run with respect to changes in earnings. The coefficients are similar to those found by Kwack, of 0.225 for U. S. financial investment and 0.319 for U. S. government investment. In the total outflow equation for the Federal Republic of Germany, the adjustment to the long-run income outflow is stable but overshoots the target in the short run.

(c) Apart from the equations for which the exchange rate variable was suppressed, all other equations show lagged exchange rates to be important determinants of income outflows. The coefficients on exchange rates for the other equations are rearranged, giving the effects of levels and of rates of change on income outflows:

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It would appear that no consistent behavioral expectations model predominates for all the categories of investment income outflows, but in the light of our discussion of equations (13) to (16), extrapolative expectations appear to be influential in equations (1), (2), (6), and (9), and regressive expectations in equations (5), (7), (8), (10), and (11).

(d) The relative growth rate variable, used as a proxy for relative profitabilities, does not perform well, and this result supports our earlier conclusion that the role of relative growth rates should be regarded as rather limited. The relationship between this proxy variable and income outflows is found to be significant only in the equations for U. S. direct investment (excluding oil) income outflow and U. K. other investment income outflow. However, the coefficient on the proxy variable for U. S. direct investment (excluding oil) is negative and, therefore, perverse. We are left to conclude that either relative profitabilities are not an important explanation of income outflows for the remaining equations, or that relative growth rates are not an ideal proxy for relative profitabilities.

(e) The coefficients of seasonal dummy variables indicate that there are considerable seasonal components in investment income outflows and that these are much more uniform than those for investment income inflows. All but one of the second and fourth dummies are positive. The significance of this fourth-quarter dummy variable may be accounted for by year-end accounting (or other) practices. Its effect is particularly large for U. S. direct investment and the U. K. equations.

The oil-crisis disturbance factor had a much less important effect on outflows than on inflows and was significant and positive in only 2 of the 11 equations, namely, U. K. financial investment and, consequently, U. K. total investment. This is, in part, a reflection on the particular countries chosen for our investigation.

HOMOGENEITY PROPERTY

To test the hypothesis that the marginal rate earned on assets is equal to the average rate, we use the F-statistic.15 Thus, we test the null hypothesis that the residual sum of squares obtained from estimates of equations (17) and (18) when the equations are unconstrained are the same as the residual sum of squares when these equations are estimated with the homogeneity constraint imposed. The appropriate F-statistic is given by

F=Σi=1te^^i2Σi=1te^^i2Σi=1te^i2tkq

where the values of êi and

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are those that minimize Σi=1(yiΣj=1kβjXji), Σe^i2is the sum of squares obtained when the equation is unconstrained, and Σe^i2 the sum of squares obtained when the homogeneity constraint is imposed; q is the number of constraints (which will be 1 here); and k, the number of explanatory variables for the unconstrained equation. Thus, the degrees of freedom for the F-variable are q and tk.

The F-statistic, evaluated for each equation, is presented next. The numbers in brackets are the degrees of freedom for each equation

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where the relevant critical values of the F-statistic at the 5 per cent level of significance are as follows:

  • F(1,47) = 4.04

  • F(1,45) = 4.05

  • F(1,43) = 4.06

  • F(1,38) = 4.10

  • F(1,30) = 4.17

If the computed F does not exceed the critical value, then we do not reject the null hypothesis of common residual sum of squares. Accordingly, we cannot reject the null hypothesis in equations (1), (5), (6), (8), (9), (10), and (11) for income inflows, and in equations (1), (2), (6), (9), (10), and (11) for income outflows.

This result leads to a new interpretation of the coefficients given in Table 2. For income inflows, equation (11) indicates that, if asset levels are held constant, an increase in long-term foreign interest rates in the long run would be matched by an equiproportionate rise in income inflows. On the other hand, equations (1), (5), and (10) indicate that an increase in long-term foreign interest rates, even in the long run, would be matched by a less than equiproportionate rise in income inflows of return. Similarly for income outflows, equations (1), (3), and (6) indicate that an increase in domestic interest rates in the long run will give rise to an equiproportionate rise in income outflows, whereas equations (2) and (10) indicate that the rise in income outflows will be less than proportional to the rise in the long-term domestic interest rates. In addition, we know that for all these equations the average rate of return will equal the marginal rate of return.

IV. Predictive Power of the Model

In this section, the predictive properties of the model presented in Section I are examined and evaluated. Equations (17) and (18) for the log-linear version of the model and equations (17’) and (18’) for the linear version were re-estimated to the fourth quarter of 1973, and the known exogenous variables from the first quarter of 1974 to the fourth quarter of 1975. In Charts 1 to 22 the predicted values of inflows and income outflows beyond the sample period. Thus, we obtained two sets of forecasts—the log-linear elasticity forecasts and the linear slope forecasts—for the eight quarters from the first quarter of 1974 to the fourth quarter of 1975. In Charts 1 to 22 the predicted values of inflows and outflows obtained from the log-linear version of the model are compared with the actual values of inflows and outflows for each category of investment income; Charts 1 to 11 record inflows, and Charts 12 to 22, outflows. Although the errors in some quarters are large relative to the actual flows, for most equations it is felt that the predicted solutions reproduce the actual values reasonably well. Indeed, the test is a difficult one for the model, since the period chosen for the prediction covers the entire period since the oil crisis.

Chart 1-11.