Discussion paper No. 51

The determination of investment income in a world model

A linked approach

by

Richard Herd

Economics & Statistics Department, OECD

November 1990

Economic Research Institute

Economic Planning Agency

Tokyo, Japan

This research was done while authors were working

for Economic Research Institute, the Economic Planning

Agency in 1990. The views expressed here are author’s

and do not represent those of the Economic Planning

Agency.

The determination of investment income in a world model

A linked approach

R. Herd Economics & Statistics Department

OECD, Paris, France Page Introduction 2 An examination of the underlying investment income data 3 The reasons for the world investment income discrepancy 4 A projection of the world discrepancy from 1983 to 1988 8 Some considerations for the modelling of investment income flows 11 A model of US investment income debits 12 World investment income flows and rates of return 13 The specification of the investment income debits equations 16 The estimation results for the investment income debits equations 18 The specification of the investment income credits equations 21 The estimation results for the investment income credits equations 23 A method for removing residual fluctuations in the world discrepancy 25 Conclusions 26 Annex 28 This study was produced whilst the author was seconded to the Economic Research Institute, Tokyo - part of the Economic Planning Agency of the Japanese government. It was financed by the visiting scholar programme of the Japanese government. The author works for the OECD. The contributions of colleagues in Tokyo and Paris are gratefully acknowledged but the views expressed in this study are personal and do not necessarily reflect those of either the EPA or the OECD.

－2－

The determination of investment income in a world model:

A linked approach

R. Herd

1. A world economic model rests on the trade and financial linkages between countries

and regions. The modelling of trade linkages has been well developed. Many researchers

have studied this area using a database that is large, well-maintained and developed in great

detail. Exchange rate linkages have also been well explored. The flows of investment

income have been modelled less. The continuing imbalances in world trade have, over a

period of time, generated large imbalances in stocks of assets, increasing the significance

of investment income flows. While surpluses and deficits in trade can change quite rapidly

in response to underlying determinants, net investment income flows change much more

slowly. Changes in interest rates affect only the magnitude of net income balances. Their

sign is only changed by the longer term cumulations of stocks and so, as a result, income

imblances can perist well after the initial trade imbalances have disappeared. For this

reason, the projection of investment income has become an important element in the

medium term analysis of current accounts.

2. This study suggests a possible way of modelling investment income flows in a

consistent fashion. The proposed model should ensure that when investment income

payments change, investment income receipts change by the same amount. The paper first

looks at the quality of the underlying data and shows that it is possible both to make a

very provisional country-by-country allocation of the discrepancy and to model the way in

which the reported world discrepancy has evolved during the middle of the 1980s. The

paper then considers the linkages between world interest rates and the rates of return on

both world asset and liability portfolios. This information suggests a suitable method for

modelling investment income credits and debits in a consistent fashion. Estimates are then

－3－

presented both investment income debit and credit equations. Finally, the paper suggests

a method for allocating the remaining differences between debits and credits, so that in

simulation, a world model would not produce discrepancies in the overall balance of

investment income.

An examination of the underlying investment income data

3. In part, the lack of empirical work stems from the poor quality of the underlying

database. National authorities have found it more difficult to track financial transactions

as exchange controls have been relaxed and then, in country after country, abolished. Also,

with investment income transactions, there is a built-in incentive for one side of the

transaction not to be reported or declared. The income data for the non-bank sector tends

to be markedly under-reported in order to avoid income taxes while declaring payments on

liabilities reduces taxation. With the trade data in many countries, both an exporter and

an importer need to report their transactions. The physical movements of goods is a

further aid to obtaining trade statistics. The difference between the export and import data

for goods is less than one half percent of world trade, once allowance has been made for

the differing valuation bases of imports and exports. For investment income, the

discrepancy is much larger and amounts to almost thirteen percent of the flow of

payments. From almost being in balance the mid nineteen seventies the reported deficit

has increased rapidly, though irregularly. The negative error in world investment income

(at $65 billion) is now greater than the error for world trade in goods. The underlying

database for modelling the flows of investment income is, for this reason, poor. This may

limit the quality of the estimation results that can be obtained from a modelling exercise

and will also increase the likelihood that simulation results will be difficult to interpret.

4. One problem with the investment income data is that not all countries report

income on the same basis. Some report investment income that is not remitted to the

creditor country while other countries report only remitted profits. Such biases tend to

remain constant over time. Another important bias in the reporting of direct investment

income is that the United States has counted as profit(loss) the revaluation of its direct

－4－

Table 1

The world investment income discrepancy

Corrected for US revaluation effects

$ billion

Reported investment income United States Total

credits debits net Correction net

1980 1981 1982 1983 1984 1985 1986 1987 1988

274.4 345.1 342.7 297.4 320.0 328.1 356.4 422.8 500.3

296.0 381.9 395.3 344.0 379.5 377.9 402.4 468.2 568.8

-21.5 -36.8 -52.5 -46.6 -59.8 -49.8 -46.0 -45.4 -68.5

0.0 2.1 1.9 6.9 9.1

-7.0 -11.5 -15.8

1.0

-21.5-34.9-50.6-39.7-50.6-56.8-57.5-61.2-67.5

investments abroad when the dollar falls(rises) (Table 1). This did not conform with

standard international procedures and so the world deficit has to be corrected for this

anomaly. The US government has now changed its method of calculating investment

income and excludes capital gains. As a result, the series for the world discrepancy is

considerably smoother than the previous series (Table 1, last column).

The reasons for world investment income discrepancy

5. An understanding of the principal reasons for the large error in the world

investment income statistics may improve the prospects for modelling and should give

some basis for assessing the movement of the discrepancy in short and medium projections

of current balances. It may also give a basis for world models to correct the simulated

differences in world investment income that often occur. A joint IMF-OECD working

party reported, more generally, on the causes of the world current account discrepancy.

It focussed on the discrepancy in the world investment income accounts for the year 1983.

The report was published in 1987 ( The World current account discrepancy, IMF) and

concluded that it was possible to use data sources other than those generated by national

－5－

authorities to check the overall investment income data and to quantify the origins of the

Table 2

Estimated cross-border investment income flows

$ billion % of total

Direct investment

Bank related

Bonds

Equities

Total

38

336

39

8

421

9

80

9

2

100

Source: Report on the World Current Account Discrepancy IMF 1987,Tables 9 & 18

discrepancy.

6. Cross-border investment falls into four categories (Table 2). The working party

used data from international sources to provide estimates of the outstanding stock of cross-

border investments in the last of these three categories. International banking statistics are

collected by the BIS and the IMF while the OECD collects data for international bond

issues. No data appears to be available on the cross-border swap market. For equities,

no international data set exists but international holdings were concentrated on five markets

in 1983 (United States, Japan, UK, Germany and Switzerland) though more markets are

probably significant now than in 1983. In addition to using standard national and

international sources, the working party issued a more detailed questionnaire on investment

income and cross-border assets and liabilities to the statistical offices of member countries.

These questionnaires allowed investment income to be split into categories more detailed

than is usually the case. The categories corresponded to those of the independent stock

data. Given estimates of the interest rates on the outstanding debt, it was possible to

quantify the sources of the discrepancy both by type of income and asset and, to a limited

extent, by country (Table 3). The country-by-country estimates of the discrepancy for

－6－

Table 3

The estimated investment income discrepancy by country

Proportionate

shareAbsolute

share 1983 1988

% $b $b

United States Japan Germany

46.629 -4.322 4.822

18512.0 1720.0 1914.0

31700.0 -2946.0 3279.0

France Italy United Kingdom Canada

1.926 4.137 4.081

-2.764

764.0 1642.0 1620.0

-1097.0

1309.0 2813.0 2775.0

-1879.0

Austria Belgium Denmark Finland

0.187 4.964

-0.866 -0.191

74.0 1971.0 -344.0 -76.0

127.0 3376.0 -589.0 -130.0

Greece Ireland Netherlands Norway

1.682 -0.125 3.325

-0.272

668.0 -49.0

1320.0 -108.0

1144.0 -85.0

2261.0 -185.0

Portugal Spain Sweden Switzerland

-0.771 1.904

-0.642 10.262

-306.0 756.0

-255.0 4074.0

-524.0 1294.0 -437.0 6978.0

Australia New Zealand

-0.617 5.410

-245.0 2148.0

-419.0 3679.0

Major offshore centers Mid-East Eastern Europe Other developing countries

13.770 0.0

-17.569 25.050

5467.0 0.0

-6975.0 9945.0

9364.0 0.0

-11947.0 17034.0

income flows in the non-bank sector were made. These estimates were only partial since

a significant portion of world banking assets and liabilities are not classified by country.

In addition, it is difficult to determine which countries hold international bonds. An

approximate country-by-country breakdown of the total investment income discrepancy can

be made if it is assumed that unreported income from securities is distributed across

countries in proportion to bank deposits of the non-bank sector.

－7－

Table 4

Cross-border banking positions excluding major offshore centers

$ billion

Claims of Interbank Total non banks banks on positions on banks nonbanks claims liabilities

1979 1980 1981 1982 1983 1984 1985 1986 1987 1988

320 403 512 562 620 589 734 864

1028 1092

440 527 631 680 711 709 818 931

1115 1153

(960) 1173 1374 1446 1479 1555 1847 2348 3066 3315

(980) 1203 1359 1425 1486 1557 1856 2408 3146 3445

(2700) 3306 3876 4113 4296 4410 5255 6551 8355 9005

7. The report concluded that the principal sources of the investment income

discrepancy lay in portfolio income. It occurred because the degree of under-reporting of

the income form non-bank credits was much larger than the under-reporting of the income

form non-bank debits. More than seventy percent of non-bank deposit income was found

to be not reported. Inter-bank credits and debits were largely matched, at least for

industrial countries. For the developing countries, though, banking flows were only

reported by the major offshore banking sectors to the extent that the transactions were

linked to their domestic economies. Similarly, Switzerland did not report the income

flows from off balance sheet managed deposits taken on a trustee basis. These two

omissions accounted for over $60 billion of total income flows (17% of the total income

flow in 1983) but these flows affected almost equally both credits and debits. Income

from bonds is also under-reported but to a lesser extent than deposit income, however the

extent of the under-reporting has grown rapidly during the early 1980s.

－8－

A projection of the world discrepancy from 1983 to 1988

8. The methodology of the report can be used to provide reasonable estimates of the

evolution of the discrepancy since 1983 which was the last year fully analyzed by the

working party, despite the discrepancy having doubled since then. Three elements are

necessary for this projection. First, the movement in the outstanding stock of cross-border

assets and liabilities must be projected, then an estimate must be made of world interest

rates and finally the extent to which income is reported must be projected.

9. The first and second of these elements are relatively easy to handle. The stock of

cross-border investment portfolios can be estimated from published data and has been

growing at a faster rate than either the national income or international trade of the OECD

area: by more than twenty percent per year during the 1980s (Tables 4 and 5). The rates

of return on assets and liabilities has been estimated using the same procedures as in the

IMF-OECD report. Non-bank depositors are assumed to receive 150 basis points less than

the LIBOR while borrowers pay 100 basis points more than the LIBOR. Banks in

offshore centers are presumed to work on a spread of 60 basis points around the LIBOR.

Table 5

Cross-border asset positions Banking and bond sectors

$ billion

Excluding Offshore Offshore Bonds Total Centers Centers held by assets liabilities non-banks

1979 1980 1981 1982 1983 1984 1985 1986 1987 1988

2700 3306 3876 4113 4296 4410 5255 6551 8355 9005

293 375 482 519 546 566 622 766 973

1096

283 367 473 509 538 554 603 720 928

1024

200 220 250 310 340 408 513 738 841

1059

3476 4268 5081 5451 5720 5938 6993 8775

11097 12184

－9－

Actual banking sector interest rates are assumed to be a six month moving average of

actual interest rates. In the bond markets, new issue rates are presumed to be in line with

market rates for longer term securities while the effective rate of return on the outstanding

stock is presumed to be a seven year moving average of the rate on new issues of bonds.

This reflects the average maturity of the debt issued in this market and the fact that the

debt is cumulated at book value. Banking sector rates of return are based on a portfolio

that is ninety percent in dollars with the remainder in a spread of currencies. Bond

returns reflect the statistics for the currency of issue.

10. The projection of reporting rates is more difficult. One plausible assumption is that

reporting rates for each asset and liability have remained stable since 1983. The overall

reporting rate would then be a function of the structure of overall world asset and liability

portfolios. The reporting rates calculated by the working party for different income flows

are shown in Table 6. The bond market has expanded relative to bank deposits over the

past decade. On past performance, this should tend to reduce the world investment

income discrepancy as bond income has been better reported. However, if potential bank

deposits have been increasingly switching to bonds with the result that international bond

Table 6

Non-reported Portfolio investment income

1983

Percentage unreported

% of total income

Amount unreported

$ billion

Non-banks DepositsLoans Net

6818

32.1 13.5 18.6

Offshore Banks Assets Liabilities Net

8690

51.6 48.7 2.9

Bonds Assets Liabilities Net

4520

13.3 5.9 7.4

Equities Assets Liabilities Net

4520

3.4 1.5 1.9

－10－

holdings have become more difficult to monitor, it is possible that on the credit side, that

the reporting of income from bonds will become worse. On the liability side, though, the

increasing use of international capital markets rather than credit markets should have little

impact on measured investment income debits as the reporting rates revealed by the

working party were similar for liabilities to banks and to bond-holders.

11. For the projection two cases have been considered. In one, under-reporting of

income from internationally held bonds remains constant at 1984 rates, in the other in

under-reporting of bond income rises to the same rate as that of the income of non-banks

from bank deposits. The projection of the discrepancy based on a constant degree of

income under-reporting shows a less rapid rise in world discrepancy than the actual rise

despite the projected deficit rising more than fifty percent in five years (Table 7). The

second case (based on a rise in the under-reporting of bond income) matches the rise in

the actual discrepancy quite closely (Table 7 column 2).

Table 7

Evolution of projected investment discrepancy

Two projections compared to actual

$ billion

projected discrepancyportfolio income

total discrepancy investment income

case 1 case 2 actual

1980 1981 1982 1983 1984 1985 1986 1987 1988

-16.2 -20.0 -37.1 -30.6 -38.6 -39.1 -40.1 -44.9 -47.3

- - - - -

-41.1 -44.3 -53.2 -69.0

-21.5 -34.7 -50.6 -39.7 -50.6 -56.8 -57.5 -61.2 -67.5

－11－

Some considerations for the modelling of investment income flows

12. The analysis of the stock data and the possibility of using this stock data to

systematically model the movement of the world investment income discrepancy is

significant both for the type of investment income equation that is estimated and for the

simulation properties of the model. The IMF-OECD report illustrates that for most

international data sources, the balance sheet constraint of assets equalling liabilities does

hold. There is consequently a need to model the asset and liability side of balance sheets

simultaneously as the stock of assets should equal the stock of liabilities and the rate of

return on assets should equal the rate of return on liabilities, abstracting from the costs of

intermediation. The structure of portfolios revealed by the report, with bank deposits

dominating bond holdings, shows that short-term interest rates should predominate in the

income equations over long-term rates. The lags on the short rate of interest variable

should be small and there should only be longer lags on the bond yield. As rates of

interest fall to zero, investment income should also fall towards zero.

13. It is important for a world model that the change in the rate of return on assets

should equal the change in the rate of return on liabilities. A small difference of only 0.1

percentage points in the movement of these two rates would generate a change in the

discrepancy of $10 billion given the size of world assets and liabilities. Such a movement

would be large relative to the changes in the current accounts of any country that are

produced by typical simulations of exchange rate movements.

14. The model also needs to ensure that the growth of assets has to equal the growth

of liabilities. Normally, this would be achieved through the current account identity

provided that there is only one type of asset and liability in the model. If the model

takes into account the currency composition of world portfolios then the amounts of the

revaluations of assets and liabilities due to exchange rate movements will also have to

balance.

15. In reality, though, just as measured payments of income do not equal receipts, the

measured stock of assets does not equal the stock of liabilities. This is partially because

different countries revalue stocks on different bases and also because the capital account

of the balance of payments is measured with a considerable error. Such errors mean that

－12－

Chart 1

the change in measured assets may be different to the balance on the current account.

These factors suggest that it is unlikely that a model of investment income flows that is

modelled independently on the credit and debit side will produced balanced income flows

in simulation.

A model of United States investment income

16. The IMF-OECD report shows that reported investment income can be proxied quite

well by the product of the stock of assets and a rate of interest. An examination of

portfolio income payments of the United States confirms that a knowledge of rates of

return and stocks of labilities are sufficient to model income flows. The stock of US

portfolio liabilities can be split into six categories: bank deposits, official holdings of

government liabilities, other foreign official assets, corporate bonds, government bonds and

equities. Given a six month payment delay for interest, the appropriate stock for

calculating the income receipts of a calendar year is the stock at the end of the previous

－13－

year while the interest rates runs from the middle of the preceding year to the middle of

the year in question. Each of the six stocks can then be multiplied by the relevant rate

of return. The resulting proxy income series tracks almost exactly actual US portfolio

income debits (Chart 1).

17. A regression which uses proxy income (PROXM) to explain the movement of

actual portfolio investment income (MSIID) generates an almost unitary coefficient on

proxy income.

R**2 SEE DW

MSIID = -794 + 0.961*PROXM 0.980 3000 1.74

(1.1) (30.0)

Such a detailed approach cannot be expected to work for a world model. It would require

too much disaggregated data and would also require that countries classify asset data

according to the same criteria. Moreover, the structure of world portfolios would have to

be modelled on a consistent basis.

World investment income flows and rates of return.

18. The aggregate data for investment income debits and the stock of liabilities does

suggest, though, that there is not a need for such a detailed disaggregation. There is a

close link between average rates of returns on cross-border portfolios and world interest

rates (Chart 2). In this chart, the world rate of interest has been calculated by weighting

together the rate of interest on the liabilities of each country taking into account the

currency composition of the liabilities of each country. A regression of the rate of return

on liabilities on short and long-term interest rates shows a coefficient of about 0.85 on the

sum of the two interest rate variables (fourth column of the table below). However, free

estimation suggests a relatively high weight on long-term interest rates which conflicts with

information on the structure of international assets and liabilities. Almost all of cross-

border assets are bank related and so presumably carry interest at short rates and yet short-

term interest rates have a weight of only thirty percent in the regression shown in column

four. The regression supports the view that when rates of interest are zero, income flows

will also be zero as the constant term in the regression is zero.

－14－

Chart 2

OLS estimation of world rate of return on liabilities

Short rates Short & Long rates

Semi Annual Semi Annual

Constant 2.027 (7.7) 1.076 (2.7) 0.673 (1.9) 0.266 (0.5)

RLL . . . . 0.231 (3.8) 0.409 (3.4)

RLS 0.298 (4.7) 0.444 (7.9) 0.235 (4.6) 0.312 (5.8)

RLS(-1) 0.321 (3.4) 0.295 (5.5) 0.159 . 0.125 (2.0)

RLS(-2) 0.073 (0.8) . . . . . .

RLS(-3) 0.106 (1.7) . . . (4.8) . .

RLE(-1) . . . . 0.219 (2.4) . .

D.W./H 0.85 1.69 -0.36 2.37

SEE 0.31 0.31 0.24 0.21

R**2 0.972 0.975 0.987 0.990

－15－

where:

RLL is a world average long term interest rate constructed by a double weighting procedure. First a rate was

constructed for each country using as weights an estimate the currency structure of the external liabilities of

each country. Then the country rate of interest were weighted together using the estimates the stock of

liabilities for each country.

RLS is the same as for RLL with short rates replacing long rates

RLE is calculated as the observed rate of return on world liabilities, that is by dividing total world debits by total

word liabilities.

Chart 3

19. The rate of return on world assets and liabilities should be the same as every asset

is matched by a liability. In view of poor quality of the income data, it might be thought

that it would be extremely unlikely that such a relationship would hold for the rate of

return data. However, it would appear that the extent of under-reporting of income is

matched by the under-reporting of assets and liabilities. As a result, the world data show

that rates of return on assets and liabilities move almost exactly together (Chart 3), with

a slight difference in level in the 1970s. A regression which attempts to explain

movements in the rate of return on assets by the movements of the rate of return on

－16－

liabilities shows that the coefficient on the rate of return on liabilities is extremely close

to unity (see below for the results of a regression covering the period 1979 to 1988.

OLS estimation of the relationship between the rates

of return on world assets and liabilities 1975 - 1988 R**2 DW SEE

RAE = 0.863 + 0.934*RLE 0.972 0.58 0.303

(3.5) (29.9) 1979 - 1988

RAE = 0.196 + 0.999*RLE 0.987 1.29 0.197 ( . ) (34.5)

RAE = + 1.021*RLE 0.986 1.30 0.195

(192.5)

20. A model of world investment income flows should, then, incorporate the constraint

that world rates of return on assets and liabilities are equal. This need to ensure

consistency between investment income credits and debits means that it is necessary to

sacrifice some freedom in the specification of either the credit or the debit equations.

Either the rates of return on assets or liabilities of each country could be modelled, giving

a world rate of return on assets or liabilities. Then the world rate of return on either

assets or liabilities could be used to explain returns on liabilities or assets. As the data

for liabilities is more reliable than that for assets, it is better to model liabilities and then

to apply a constrained equation form to the credit equations. This approach does have

drawbacks. If only a world rate of return on liabilities is used to determine the rate of

return on each countries assets, then there is a failure to use all available information.

The currency composition of the assets of each country is ignored and as a result, the fit

of the regressions may be poor.

The specification of the investment income debits equations.

21. Two approaches are possible for the debit equations. Both approaches use rates of

interest weighted by the currency composition of each countries liabilities as the

explanatory variable. They differ in the way that the rate of interest enters the equation.

In the first approach, a rate of return on liabilities is calculated and then this rate of return

is made a function of rates of interest weighted according to the currency structure of

liabilities.