3. Monetary Analysis of Income and Imports and Its Statistical Application


AS THE FIRST STAGE in the development of a monetary analysis of income and imports, an earlier study 1 derived a simple theoretical model of countries’ economies in which monetary and balance of payments developments were integrated. That study led to certain general conclusions about the effects of credit expansion and of changes in exports that, it was believed, would be helpful in understanding the developments with which one is often faced in the study of individual countries. For the most part, the conclusions did not involve the use of numerical coefficients pertinent to particular countries.

AS THE FIRST STAGE in the development of a monetary analysis of income and imports, an earlier study 1 derived a simple theoretical model of countries’ economies in which monetary and balance of payments developments were integrated. That study led to certain general conclusions about the effects of credit expansion and of changes in exports that, it was believed, would be helpful in understanding the developments with which one is often faced in the study of individual countries. For the most part, the conclusions did not involve the use of numerical coefficients pertinent to particular countries.

The model can, however, be of greater use if it is given statistical content relevant to particular countries. It should then provide an explanation, in numerical terms, of the fluctuations in a country’s income, imports, money, and international reserves on the basis of data for that country’s exports, capital imports, and credit creation. Insofar as this explanation provides a satisfactory approximation of the actual development in the past of the variables explained, the same model is usable in connection with decisions of economic policy: given a country’s past exports, capital imports, and credit creation, the model can be used to compute the amount of credit creation which, together with certain estimated values for exports and capital imports, will lead to the attainment of certain desired levels of income and reserves.

To make the model suitable for the quantitative treatment of developments in individual countries requires the clarification of a number of statistical questions in order that the data may be arranged as nearly as possible in accordance with the concepts of the theory. This includes the proper definition, for our purposes, of such terms as imports, money, etc. It also requires some expansion of the theory, in order to come closer to a full explanation of the facts. To establish as firmly as possible the general elements in the theory, it is usually helpful to be able to show what specific other factors are the causes of the developments in the observed data that cannot be attributed to these general elements.

Part I of this paper is therefore concerned with the practical problems that arise in connection with this empirical work—the arrangement of the data to accord with the theory and some expansion of the theory to increase its usefulness in explaining the facts. The paper does not deal with the interpretation of the statistical results or with the qualifications that necessarily apply to this interpretation. Some of the latter were mentioned in the 1957 paper.

Part II shows the results obtained by applying the model to 39 countries, generally from 1948 or 1949 to 1958. The calculations in Part II are not intended to provide a definitive study of the application of the model to any one country. It is entirely probable that a more intensive study of the monetary structure and payments data for a particular country would lead to refinements that would improve the results. The purpose of the presentation is rather to assess the general applicability of the model by presenting the preliminary results of its application to as many countries as possible.2

Theoretical Problems Raised by Application of the Model to Country Data

1. The simple system

It may be convenient to recall the basic system in its simplest form, as shown in the 1957 paper. The central equation of that system is

in which Y indicates national income (money value), ΔM0 is the increase in the quantity of money, and t refers to an income period, i.e., the fraction of a year indicated by. the ratio of money to annual income.3 This equation may be interpreted in either of two ways:

(1) If the income velocity of money is constant, the income of the next period will equal the current period’s income plus the increase in the quantity of money.

(2) If the income velocity of money is constant, the quantity of money will increase from one income period to the next by the same amount as income.

The increase in the quantity of money is then split into its constituents, the increases in (net) foreign assets (R) and in (net) domestic assets (D):
The balance of payments equation,

states that the increase in reserves (ΔA) equals exports (X) minus imports (M) plus capital movements [C(t)].4

The combination of (2) and (3) yields an explanation of the change in money, and thereby of the change in income, in terms of three variables considered autonomous and of imports:
In what follows, the three autonomous terms will often be used in combination, for which the term Q(t) is used:

Imports are expressed as a function of income:5

From (6), (5),(4), and (1) we find
Dividing by (1 + m) and eliminating the terms with Y in the righthand side of (7) by iteration, we obtain
and the corresponding import equation,

These two equations express Y and M in terms of the autonomous determinants of the system.

To facilitate the statistical work, we make use of an alternative definition of Q(t), which follows from (4) and (5):

This relationship makes it possible to proceed in the explanation of imports and of income without first determining exports, capital movements, and credit creation separately. The relationship also makes it clear that the allocation of any transaction to one or the other of these categories will not affect the ultimate result of the income or import calculations. It might appear odd that the term Q, used in explaining imports, itself contains imports in addition to the change in money. But there is no reason to be concerned about this. The addition of M(t) to ΔM0(t) in (5’) does not make imports an explanatory factor in the fluctuations of imports. The addition is necessary in order to obtain the autonomous expansion of money, which is not fully shown by the actual increase in money. Imports have undone part of the effects of the autonomous increase in money; to get a proper measure of the autonomous expansionary factors, the money that was taken out by imports has to be added back to the observed increase in money.

2. Balance of payments data

To determine the gross expansionary factors that act through the balance of payments, and the response of the balance of payments to the gross domestic and foreign expansionary factors, the balance of payments items for any country are divided into four categories, which are here called Export Receipts, Import Payments, Capital Movements, and Reserve Movements (Table 1). All items are expressed in a country’s own currency; for countries with multiple exchange rates, entries reported in dollars have been converted at the exchange rate applicable to the transaction in question. The entries represent, therefore, the domestic currency amounts paid or received by a country’s residents in connection with the transactions concerned.

Export receipts

Export receipts cover (1) receipts from merchandise exports, including military aid exports, (2) any credit entry for nonmonetary gold, (3) net investment income (for most countries a negative item), (4) gross receipts from other services, including military aid services, and (5) private donations received.

Import payments

Import payments cover (1) payments for merchandise imports other than (a) those received under military aid, (b) nonmilitary grants of a project type, and (c) private and official project loans, (2) any debit entry for nonmonetary gold, (3) payments for services other than (a) those received under military aid and (b) investment income payments, and (4) private donations extended.

Table 1.

Systematic Classification of Balance of Payments Items

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Capital movements

These movements cover all items in the balance of payments that are not included in the two preceding categories or in reserve movements. Hence, this category includes (1) official donations with the exception of military grants and nonmilitary project grants received, (2) the net movement of private capital excluding the counterpart of imports under private project loans, and (3) the net movement of official and banking assets and liabilities other than reserve movements (mostly government capital transactions), and the counterpart of government imports under project loans.

As a rule, errors and omissions are allocated to Capital Movements. However, if it is believed that they refer either mainly to export receipts or mainly to import payments, they are allocated to the relevant one of these two categories.

Reserve movements

By the definitions used, Export Paymentsplus Capital Movements minus Import Payments equal Reserve Movements. Figures for changes in reserves are arrived at by adding balance of payments data for official and banks’ short-term assets, short-term liabilities, and monetary gold.6

Several items which involve equal debits and credits arc eliminated altogether from the analysis. These offsetting items include imports under military aid programs and under project loans and grants, and the corresponding financing.7 In determining whether such offsetting items should be eliminated, the guiding criterion is whether or not the imports can be treated as related to domestic income in the manner assumed in the model.

3. Monetary data

The monetary balance sheet implied in equation (2) contains two domestic variables: money and net credit creation. Since net credit creation is arrived at by subtracting the increase in nonmonetary liabilities from gross credit creation, the definitions of net credit creation and of money are interrelated. A narrow definition of money, which for most countries does not include time or savings deposits, is used throughout this paper; this is the definition used in the Fund’s publication, International Financial Statistics (IFS). By equation (2), net credit creation equals the increase in money less the increase in net foreign assets. To assure agreement with the balance of payments data, net credit creation is measured by subtracting the change in foreign assets based on balance of payments statistics from the change in money.8 In a few countries that have multiple currency rates, how-ever, the IFS data on foreign assets and foreign liabilities (adjusted, where necessary, in order to eliminate changes in value owing to the revaluation of these items) have been used as an indicator of the net payment or receipt of local currency on account of all other items in the balance of payments.

It should be recalled that the figure for foreign assets used in the derivation of net credit creation does not affect the value for Q; any errors in ΔR, leading to corresponding errors in ΔD, will be offset in the figure for C, which is derived as a residual.

4. The coefficients

As shown in SYSTEMATIC CLASSIFICATION OF BALANCE OF PAYMENTS ITEMS of the 1957 paper, the values over time of income, imports, money, and reserves in terms of the autonomous variables can be expressed by two coefficients, the propensity to import (m) and the income velocity of money (v).9

Velocity (v) is computed by dividing estimated end-of-year figures for Gross National Product (GNP) by the figures for money; the method followed to derive the required GNP estimates is described below (pages 364-65). Where no GNP figures are available, national income figures are used. The average velocity for the entire period studied is derived as a simple average of the end-of-year velocity figures. (Frequently the average is rounded.)

The import-income ratio is obtained by dividing import payments, as defined above, by GNP for the same year (not year-end). The average ratio is derived as a simple average of the annual ratios for the period studied. (Frequently the average is rounded.)

A derivation, for certain values of v and m, of the import and income coefficients based on annual data is given in Appendix II of the 1957 paper. The derivation becomes slightly different now that the lag in the import equation has been eliminated. A simplified presentation of the coefficients for the import equation on the old and the new basis is given in Table 2.10 To obtain the income coefficients for the new system, the term 1mv in each import coefficient given in the table is replaced by 1m2v.

Table 2.

Coefficients for the Determination ofM(0)

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s = 1 - m; r=11+m

Tables 3 and 4 provide, respectively, the import and the income coefficients for the range v = 2 to 10, m = 0.10 to 0.50. For any intermediate values, straight line interpolation is used.

The basic structure of the model, which assumes proportionality between (1) income and imports and (2) income and money, makes it plausible to suppose that the main part of the model could be described in terms of the import-money ratio alone. Analysis of the import coefficients in Table 3 shows that, in fact, for any two sets of m and v chosen in such a manner that their product mv is the same, the coefficients are approximately the same (in particular if v>2). Now mv=MY.YMO=MMO

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Thus, for instance, if mv = 1.20, the coefficients are about the same regardless of the combination of m and v from which this product arises:11

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This is of considerable practical importance: it implies that it is possible to approximate values for the coefficients without knowing v and m separately, provided one knows their product, the ratio of imports to money. Thus, while national income data are required to determine m and v separately, they are not needed to determine mv; and knowledge of mv, together with some plausible guess for m or v, makes it possible to derive, from Table 3, the coefficients needed. It also follows that we need not be greatly concerned about the quality of the national income statistics that have been used to calculate m and v. It should be added that, inasmuch as the income coefficients add up to 1m, these coefficients cannot be expected to be independent of the national income data used.

There is another important aspect in which the import coefficients differ from the income coefficients. Since any set of import coefficients adds up to unity, any error in m or v (even if it is not offset in the product w..v) produces only a shift in time of the influence of any one Q; hence the computed M;s are affected only insofar as the Q’s in two adjacent years are different. The same does not apply to the income coefficients. Any error in m (not in v) produces a nearly proportional error in the computed values for income. Thus, if m is taken as 0.40 instead of 0.41 (an error of 2½ per cent), the sum of the Y coefficients will work out at 2.50 instead of 2.44, and all computed values of Y will therefore work out as more than 2 per cent too large. The error indicated is very small in terms of our estimate of m (which may be based on an average of yearly figures fluctuating as widely as, say, from 0.35 to 0.45) ; but it is large in terms of the computed value for Y, which, if the refinements indicated in section 6 are made, should have practically no error at all.

As a result of the margin of uncertainty in respect of m, the average level of income as computed is likely to deviate somewhat from the level as observed. In the values of computed income, the discrepancy on account of this element is eliminated; its magnitude is estimated as the difference between the average actual value for Y and the average computed value for Y along the lines suggested on page 366 (first full paragraph).

Table 3.

Coefficients for Q(0), Q(-l), Q(-II), and Q(-III) in the Determination of M(0)

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Table 4.

Coefficients for Q(0), Q(-I), Q(-II), and Q(-III) in the Determination of Y(0)

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Computed imports are obtained by applying the import coefficients as shown in Table 3 to the Q’s. Any shortfall below 1.00 of the coefficients as given in the table is applied to the Q for four years back (with a rough estimate for any years for which Q is not available).12

Computed income is estimated by applying coefficients from Table 4 to the Q’s. Table 4 is limited to the coefficients for four years; their sum is given in the last column of the table. The sum of the coefficients for all years would add up to the reciprocal of the import-income ratio. Any discrepancy between the sum of the coefficients used for four years and this reciprocal is applied to the Q for four years back.12

5. Marginal propensity to import different from average propensity to import

It seemed quite likely that in many countries marginal propensities to import would differ systematically from average propensities to import.13 To investigate this point, a scatter diagram comparing imports and income was made for each country studied; where there appeared to be a systematic difference between the average and the marginal propensity, the weights in the import equation were based on the latter.

The use of a marginal propensity m’ implies the introduction of a constant term M˜ in (6):
Accordingly, (9) becomes
Since the sum of the coefficients in (9’) equals 1, this can be written as

which means a simple substitution of m’ for m.

The result is not as simple when income, rather than imports, is computed with a marginal propensity to import different from the average propensity. Using (6’), (8) becomes

income to money m’ substituted for m, but there is also a constant term, M˜m, added.

6. Expansion of the xmodel to allow for changes in velocity and autonomous imports

There are only two assumptions in our model: the constancy of the income velocity implied in equation (1) and the nature of the import equation (6) ; the other equations are definitional. What happens if the assumptions are not fulfilled?

The general answer to this question is that it then is not possible to “explain” Y, and hence M, in terms only of the autonomous factors X, ΔD, and C. To “explain” the movements of Y and M it will then be necessary to know the changes in velocity—which involves using data on Y itsel—and to know the discrepancies in the import equation—which involves using data on M itself. But even in these circumstances it will be of interest to sort out the past, even if it can no longer be claimed that we explain it; we shall, however, be able to measure the relative influence on Y of export receipts, capital movements, and credit creation, as well as the influence of changes in velocity and discrepancies in the import equation. The best that can be obtained in these circumstances is essentially a definitional relationship, but this relationship may still be of considerable interest. Alternatively, our standard explanation in terms of X, C, and AD may be considered as an approximation to this definitional relationship, which will be the more accurate, the smaller the influence of changes in velocity and of import discrepancies.

Changes in income velocity

To allow for changes in velocity, the velocity has to be brought explicitly into the equations. If we define the average ratio of annual income to money as k=1v, and the ratio in any one year as k(t) = 1v(t), then it can be shown that

Since MO is the product of income and velocity, the additive expression for ΔM0 given in (10) contains three terms: one with Δy, one with Δk, and one containing the product of the two changes. There is no unique way of attributing this product to either Δy or Δk and thus of attaining a unique additive expression for ΔM0 with only two terms, one of which can be called the income effect, and the other the velocity effect, on money. Any allocation to arrive at an expression in two terms is necessarily somewhat arbitrary. For our purposes it seems most convenient to allocate the third term entirely to the velocity effect, V(t), thus defining V(t) as the sum of the second and third terms on the right-hand side of (10), with signs reversed.14

or, defined as a residual,

Expressed in this form, V(t) can be entered directly in the calculations based on annual data. It represents (again with sign reversed) that part of the change in the quantity of money that is not explained by changes in income.

Equation (14) presents a statistical problem inasmuch as we do not have a measure of Y that refers to the same time period that is used for MO. We are using end-of-year data for MO. For most countries, there is only one figure a year indicating the rate of income; this figure refers to the year as a whole, i.e., to the average rate of income during the year. Monetary data exist generally at far more frequent intervals, and from these an average for the year could easily be compiled for MO; but the problem cannot be solved in that manner, for what we would gain here we would lose in (2) and particularly in (3), for which we would no longer be able to use annual balance of payments data. We must, therefore, try to approximate the annual rate of income at or around the end of the year. Where monthly or quarterly national income data are available, they can provide a reasonably satisfactory answer. In the absence of these, the best solution appears to be to estimate the change in income during a year as equal to one half of the change in income between the average of the preceding year and the average of the following year. This is equivalent to estimating end-ofyear income as the average of two adjacent years and using these estimated end-of-year figures to obtain the change in income during the year.15

Discrepancies in import equation

If imports are not a linear function of income, we can write a new equation that indicates, by a new variable MA (“autonomous imports”), the extent of the deviation from the income relationship:


If this equation is used instead of (6), the simple result is the appearance of one more additive term, viz., -MA, among the factors determining income.

Figures for -MA are computed by deducting actual import payments from the product of the average import-income ratio and GNP. Where a marginal propensity to import differing from the average is used, MA is measured from the regression line of imports on GNP.

Expansion of the model

The velocity effect and autonomous imports may be considered as new autonomous factors, additional to exports, capital imports, and credit creation, and thus be incorporated in the model as additions to Q(t). This is done simply by replacing Q(t) by Q’(t), defined as follows:
It follows from (5’), (14), and (15) that Q’(t) may also be written as

When the two new variables are thus incorporated in the model as additional explanatory factors, it is clear that they must be considered as playing essentially a stand-in role for the real, as yet unknown, factors that caused the discrepancies in (1) and (6). Thus MA may represent some effect of relative prices on imports that is ignored in (6), or the effect of changing intensity in import restrictions. V may represent responses to changes in interest rates. At a later stage of the analysis, it might be possible to trace to their own causes what are now residuals, and then to bring these causes into the model. For the time being, the residuals may take the place of these causes. As we proceed in replacing, step by step, our stand-in variables by more satisfactory causal variables, we shall, of course, never exhaust the residuals completely; but at some stage, the search for further causes may be stopped by the smallness of the residuals. The acceptance of the remaining residuals at that stage will necessarily mean that the definitional identity of (17) will disappear.

By applying the annual coefficients from Tables 3 and 4 to Q’(0), Q’(-I), etc., near-perfect “explanations” of M(t) and Y(t) can be found. Basically, the definitions of MA (t) and V (t) and their incorporation into Q’(t) make the whole operation one of manipulating definitional statements. Such small residual errors as still show up in the computed values for M(t) and Y(t), based on the Q’s, are attributable to certain assumptions made in the measurement of the variables. Thus it has been assumed that observed annual rates of Q(t) apply throughout the year, that changes in velocity occur gradually during the year, and that ΔY(t) may be estimated as indicated for the purpose of calculating V(t).

An alternative, more modest, interpretation of the same material is to consider the expansion of the model only as a method of allocating the residuals left by the explanations of M(t) and Y(t) on the basis of the Q’s only. According to this interpretation (which is followed in the country charts shown on pages 377 ff.), the residual in the original income equation may be considered to consist of an “MA effect on income” plus a “velocity effect on income.” The former is calculated by applying the income coefficients (Table 4) to the annual values of the MA’s (with sign reversed), and the latter by applying these same coefficients to the V’s. These two components should account substantially for the original residual; any remaining discrepancies must be due to the nonfulfillment of the assumptions of continuity just mentioned.

Not two, but three, elements are required to account for the residual in the import equation. The “MA effect on imports” and the “velocity effect on imports” are similar to the corresponding effects on income, and can be computed by applying to -MA and V the import coefficients from Table 3. In addition to these, there is MA itself, the residual in the elementary import equation (15).

II. Application to Country Data

1. Selection of countries

The charts and tables on pages 376-415 give data for 39 countries to which it was possible to apply the model. A fairly representative geographic coverage has been obtained, including 14 countries in Europe (Austria, Belgium-Luxembourg, Denmark, Finland, France, the Federal Republic of Germany, Ireland, Italy, Norway, the Netherlands, Portugal, Sweden, Switzerland, and the United Kingdom), 6 in Asia (Burma, Ceylon, India, Japan, the Philippines, and Thailand), 12 in Latin America (Colombia, Costa Rica, Cuba, the Dominican Republic, Ecuador, El Salvador, Guatemala, Honduras, Mexico, Nicaragua, Peru, and Venezuela), 3 in the Near East (Egypt, Ethiopia, and Iraq), and 4 other countries (Australia, Canada, New Zealand, and the Union of South Africa). A number of countries have been omitted either because certain essential series were missing or were not available in continuity for a sufficient number of years, or because balance of payments figures that are reported to the Fund in dollars could not, on account of exchange rate problems, be converted into local currency. The latter difficulty limited the coverage of the South American countries. The United States has been omitted because, with imports such a small proportion of national income, the coefficients would have to be applied with such a prolonged lag that no useful results would be obtained.

To reduce the bulk of the presentation, the data shown for all 39 countries are limited to the main series and the results of the import calculations. The results of the income calculations are not shown; but the coefficients necessary for that calculation, as well as the values of the Q’s to which they are to be applied, are provided in the tables.

Two charts are given for each country. The first chart shows imports and the determinants of imports, i.e., exports, capital movements, and domestic credit creation—individually and combined as Q. Also included is a curve for changes in reserves. The second chart shows computed imports against actual imports and provides an analysis of the difference between the two curves in terms of MA, MA effects, and V effects. The tables supply the information used in the computations for each country.

In compiling the figures, minor changes in the series used were ignored when they were considered insufficient in magnitude to affect the calculations significantly. Particularly for the earlier years, information for many countries is incomplete, so that MA, MA effects, and V effects for these years are based on partial or estimated data; these are shown as broken lines in the charts. Since the calculation of the V effects for 1958 requires the use of 1959 income figures, adjustments for 1958 are generally not shown.

For convenience, the symbols used in the text, the tables, and the charts are summarized below:

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2. Application to a sample country

To illustrate in detail the method developed here, full particulars of its application to one country are provided. Norway was selected for this purpose because it combines many of the problems mentioned and has satisfactory data that show important fluctuations in imports, income, and their determinants.

Table 5 gives the derivation of the four balance of payments categories from the original data. Table 6 indicates the manner in which the other time series have been compiled. Since Chart 1 showed a notable divergence between the average and the marginal propensity to import (0.44 as against 0.50), the latter has been used as the basis for the coefficients. These coefficients have been derived from Tables 3 and 4, using m = 0.50 and interpolating between v = 3 and v = 4.

In Table 7, imports are first computed on the basis of Q only. This leaves a residual, shown on line 3.4. Then the MA effect and the V effect are computed (lines 3.6 and 3.8) and a “computed residual” is built up (line 3.10) from the sum of them plus MA (line 3.9). This accounts for most of the original residual, but not all; there remains a “residual error” (line 3.11) which, as indicated above, must be attributable mainly to the approximations involved in the time units selected.

Chart 2 shows Q and M together at the top, then the three components of Q, and also ΔR. Chart 3 shows the result of the calculations: M (line 3.3) compared with computed imports M* (line 3.2), and the three components of the computed residual.

Table 8 does with respect to income what Table 7 does with respect to imports. The constant added after the Q terms equals 1,2000.50=2,400, as derived from equation (8’). Because of the adjustment for level explained at the top of page 362 and computed in line 4.13, the figure in line 4.2 is an interim figure, the final figure for income being found in line 4.5.

Computed income, Y*, which is given in line 4.5 of the table, is shown in Chart 4, together with actual income, Y (line 4.3 in the table), and the two components of the discrepancy, the MA effect (line 4.8) and the V effect (line 4.10).

Table 5.

Norway: Balance of Payments Data

(In millions of kroner)

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Source: Exports, imports, and reserves are from International Monetary Fund, Balance of Payments Yearbooks.

Includes only that part of foreign loans obtained which are considered special project loans.

Table 6.

Norway: Income and Monetary Data1

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For description of symbols, see text. Data for MO and for Y (gross national product) are from International Monetary Fund, International Financial Statistics. Except for ratios, figures are in millions of kroner.

See pp. 364-65 for description of method of estimate.

MO for 1948 and 1949, and related figures, may not be exactly comparable with figures for subsequent years.

Table 7.

Norway: Computed Imports1

(In millions of kroner)

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For description of symbols, see text.

Incomplete data.

Table 8.

Norway: Computed Income1

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For description of symbols, see text.

Incomplete data.

Chart 1.
Chart 1.

Norway: Marginal and Average Import Relationships1

Chart 2.
Chart 2.

Norway: M (Imports), Q and Its Components (X, C, and ΔD), and ΔR1

Chart 3.
Chart 3.

Norway: Actual Imports (M), Computed Imports (M*), and Components of the Residual1

1 For description of symbols, see text.
Chart 4.
Chart 4.

Norway: Actual Income (Y), Computed Income (Y*), and Components of the Residual1

1 For description of symbols, see text.


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For description of symbols, see text. The table is based on data from International Monetary Fund, Balance of Payments Yearbooks and International Financial Statistics. Except for ratios, figures are in millions of Australian pounds.

For year ended June 30.