Monetary Analysis of Income and Imports and Its Statistical Application

LORETTE BOISSONNEAULT

doi:10.5089/9781451949704.024.A003

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Monetary Analysis of Income and Imports and Its Statistical Application

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LORETTE BOISSONNEAULT

LORETTE BOISSONNEAULT
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Publication Date:: 01 Jan 1960

eISBN:: 9781451949704

Language:: English

Keywords:: SP; Canadian dollar; market; computed income; import equation; income velocity; income calculation; import-income ratio; Financial statistics; Balance of payments statistics; Africa

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AS THE FIRST STAGE in the development of a monetary analysis of income and imports, an earlier study1 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.

Abstract

AS THE FIRST STAGE in the development of a monetary analysis of income and imports, an earlier study¹ 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

I. 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

\begin{matrix} Y (t) = Y (t - 1) + Δ MO (t), & (1) \end{matrix}

in which Y indicates national income (money value), ΔMO 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):

\begin{matrix} Δ MO (t) = Δ R (t) + Δ D (t) . & (2) \end{matrix}

The balance of payments equation,

\begin{matrix} Δ R (t) = X (t) - M (t) + C (t), & (\begin{matrix} 3 \end{matrix}) \end{matrix}

states that the increase in reserves (ΔR) 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:

\begin{matrix} Δ MO (t) = X (t) + C (t) + Δ D (t) - M (t) . & (4) \end{matrix}

In what follows, the three autonomous terms will often be used in combination, for which the term Q(t) is used:

\begin{matrix} Q (t) = X (t) + C (t) + Δ D (t) . & (5) \end{matrix}

Imports are expressed as a function of income:⁵

\begin{matrix} M (t) = mY (t) . & (6) \end{matrix}

From (6), (5), (4), and (1) we find

\begin{matrix} (1 + m) Y (t) = Q (t) + Y (t - 1) . & (7) \end{matrix}

Dividing by (1 + m) and eliminating the terms with Y in the right-hand side of (7) by iteration, we obtain

\begin{matrix} Y (t) = \frac{Q (t)}{1 + m} + \frac{Q (t - 1)}{{(1 + m)}^{2}} + \frac{Q (t - 2)}{{(1 + m)}^{3}} …., & \begin{matrix} (8) \end{matrix} \end{matrix}

and the corresponding import equation,

\begin{matrix} M (t) = \frac{mQ (t)}{1 + m} + \frac{mQ (t - 1)}{{(1 + m)}^{2}} + \frac{mQ (t - 2)}{{(1 + m)}^{3}} \cdot & (9) \end{matrix}

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):

\begin{matrix} Q (t) = Δ MO (t) + M (t) . & \begin{matrix} (5^{'}) \end{matrix} \end{matrix}

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 ΔMO (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.

Table 1.

Systematic Classification of Balance of Payments Items

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.

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 Payments plus 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 are 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, however, 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 Appendix II 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 $\frac{1}{mv}$ in each import coefficient given in the table is replaced by $\frac{1}{m^{2} υ}$ .

Table 2.

Coefficients for the Determination of M(0)

^¹ $s = 1 - m; r = \frac{1}{1 + m} \cdot$

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.

Table 3.

Coefficients for Q (0), Q (–I), Q (–II), and Q (–III) in the Determination of M (0)

Table 3.

Coefficients for Q (0), Q (–I), Q (–II), and Q (–III) in the Determination of M (0)

Velocity υ	Import-Income Ratio m	Coefficients for
Velocity υ	Import-Income Ratio m	Q(0)	Q(–I)	Q(–II)	Q(–III)	Sum
	0.10	0.13	0.15	0.12	0.10	0.50
	0.15	0.19	0.20	0.15	0.11	0.65
	0.20	0.24	0.23	0.16	0.11	0.74
	0.25	0.28	0.26	0.17	0.11	0.82
2	0.30	0.32	0.28	0.16	0.10	0.86
	0.35	0.36	0.29	0.16	0.09	0.90
	0.40	0.39	0.30	0.15	0.08	0.92
	0.45	0.42	0.31	0.15	0.07	0.95
	0.50	0.44	0.31	0.14	0.06	0.95
	0.10	0.17	0.21	0.15	0.12	0.65
	0.15	0.24	0.26	0.17	0.11	0.78
	0.20	0.30	0.30	0.17	0.10	0.87
	0.25	0.35	0.32	0.16	0.08	0.91
3	0.30	0.39	0.33	0.15	0.07	0.94
	0.35	0.43	0.34	0.14	0.06	0.97
	0.40	0.47	0.34	0.12	0.04	0.97
	0.45	0.50	0.33	0.11	0.04	0.98
	0.50	0.53	0.33	0.10	0.03	0.99
	0.10	0.21	0.25	0.17	0.12	0.75
	0.15	0.29	0.31	0.17	0.10	0.87
	0.20	0.35	0.34	0.16	0.08	0.93
	0.25	0.41	0.35	0.14	0.06	0.96
4	0.30	0.46	0.35	0.12	0.04	0.97
	0.35	0.50	0.35	0.11	0.03	0.99
	0.40	0.54	0.34	0.09	0.02	0.99
	0.45	0.57	0.33	0.07	0.02	0.99
	0.50	0.60	0.32	0.06	0.01	0.99
	0.10	0.24	0.29	0.19	0.11	0.83
	0.15	0.33	0.34	0.17	0.08	0.92
	0.20	0.40	0.36	0.14	0.06	0.96
	0.25	0.46	0.36	0.12	0.04	0.98
5	0.30	0.51	0.35	0.10	0.03	0.99
	0.35	0.55	0.34	0.08	0.02	0.99
	0.40	0.59	0.33	0.06	0.01	0.99
	0.45	0.62	0.32	0.05	0.01	1.00
	0.50	0.65	0.30	0.04	0.01	1.00
	0.10	0.27	0.32	0.18	0.10	0.87
	0.15	0.37	0.36	0.15	0.07	0.95
	0.20	0.45	0.37	0.12	0.04	0.98
	0.25	0.51	0.36	0.10	0.02	0.99
6	0.30	0.56	0.35	0.07	0.01	0.99
	0.35	0.60	0.33	0.06	0.01	1.00
	0.40	0.64	0.31	0.04	0.01	1.00
	0.45	0.67	0.30	0.03	0.00	1.00
	0.50	0.70	0.28	0.02	0.00	1.00
	0.10	0.30	0.34	0.17	0.09	0.90
	0.15	0.41	0.37	0.14	0.05	0.97
	0.20	0.49	0.37	0.10	0.03	0.99
	0.25	0.55	0.36	0.07	0.02	1.00
7	0.30	0.60	0.34	0.05	0.01	1.00
	0.35	0.64	0.32	0.04	0.00	1.00
	0.40	0.68	0.29	0.03	0.00	1.00
	0.45	0.71	0.27	0.02	0.00	1.00
	0.50	0.73	0.25	0.02	0.00	1.00
	0.10	0.33	0.35	0.17	0.08	0.93
	0.15	0.44	0.38	0.12	0.04	0.98
	0.20	0.52	0.37	0.08	0.02	0.99
	0.25	0.58	0.35	0.06	0.01	1.00
8	0.30	0.63	0.32	0.04	0.01	1.00
	0.35	0.67	0.30	0.03	0.00	1.00
	0.40	0.71	0.27	0.02	0.00	1.00
	0.45	0.74	0.25	0.01	0.00	1.00
	0.50	0.76	0.23	0.01	0.00	1.00
	0.10	0.36	0.37	0.16	0.07	0.96
	0.15	0.47	0.38	0.11	0.03	0.99
	0.20	0.55	0.36	0.07	0.01	0.99
	0.25	0.62	0.33	0.04	0.01	1.00
9	0.30	0.67	0.30	0.03	0.00	1.00
	0.35	0.70	0.28	0.02	0.00	1.00
	0.40	0.74	0.25	0.01	0.00	1.00
	0.45	0.76	0.23	0.01	0.00	1.00
	0.50	0.78	0.21	0.01	0.00	1.00
	0.10	0.38	0.38	0.15	0.06	0.97
	0.15	0.50	0.38	0.09	0.02	0.99
	0.20	0.58	0.35	0.06	0.01	1.00
	0.25	0.64	0.32	0.04	0.00	1.00
10	0.30	0.69	0.29	0.02	0.00	1.00
	0.35	0.73	0.26	0.01	0.00	1.00
	0.40	0.76	0.23	0.01	0.00	1.00
	0.45	0.78	0.21	0.01	0.00	1.00
	0.50	0.80	0.20	0.00	0.00	1.00

Table 3.

Coefficients for Q (0), Q (–I), Q (–II), and Q (–III) in the Determination of M (0)

Velocity υ	Import-Income Ratio m	Coefficients for
Velocity υ	Import-Income Ratio m	Q(0)	Q(–I)	Q(–II)	Q(–III)	Sum
	0.10	0.13	0.15	0.12	0.10	0.50
	0.15	0.19	0.20	0.15	0.11	0.65
	0.20	0.24	0.23	0.16	0.11	0.74
	0.25	0.28	0.26	0.17	0.11	0.82
2	0.30	0.32	0.28	0.16	0.10	0.86
	0.35	0.36	0.29	0.16	0.09	0.90
	0.40	0.39	0.30	0.15	0.08	0.92
	0.45	0.42	0.31	0.15	0.07	0.95
	0.50	0.44	0.31	0.14	0.06	0.95
	0.10	0.17	0.21	0.15	0.12	0.65
	0.15	0.24	0.26	0.17	0.11	0.78
	0.20	0.30	0.30	0.17	0.10	0.87
	0.25	0.35	0.32	0.16	0.08	0.91
3	0.30	0.39	0.33	0.15	0.07	0.94
	0.35	0.43	0.34	0.14	0.06	0.97
	0.40	0.47	0.34	0.12	0.04	0.97
	0.45	0.50	0.33	0.11	0.04	0.98
	0.50	0.53	0.33	0.10	0.03	0.99
	0.10	0.21	0.25	0.17	0.12	0.75
	0.15	0.29	0.31	0.17	0.10	0.87
	0.20	0.35	0.34	0.16	0.08	0.93
	0.25	0.41	0.35	0.14	0.06	0.96
4	0.30	0.46	0.35	0.12	0.04	0.97
	0.35	0.50	0.35	0.11	0.03	0.99
	0.40	0.54	0.34	0.09	0.02	0.99
	0.45	0.57	0.33	0.07	0.02	0.99
	0.50	0.60	0.32	0.06	0.01	0.99
	0.10	0.24	0.29	0.19	0.11	0.83
	0.15	0.33	0.34	0.17	0.08	0.92
	0.20	0.40	0.36	0.14	0.06	0.96
	0.25	0.46	0.36	0.12	0.04	0.98
5	0.30	0.51	0.35	0.10	0.03	0.99
	0.35	0.55	0.34	0.08	0.02	0.99
	0.40	0.59	0.33	0.06	0.01	0.99
	0.45	0.62	0.32	0.05	0.01	1.00
	0.50	0.65	0.30	0.04	0.01	1.00
	0.10	0.27	0.32	0.18	0.10	0.87
	0.15	0.37	0.36	0.15	0.07	0.95
	0.20	0.45	0.37	0.12	0.04	0.98
	0.25	0.51	0.36	0.10	0.02	0.99
6	0.30	0.56	0.35	0.07	0.01	0.99
	0.35	0.60	0.33	0.06	0.01	1.00
	0.40	0.64	0.31	0.04	0.01	1.00
	0.45	0.67	0.30	0.03	0.00	1.00
	0.50	0.70	0.28	0.02	0.00	1.00
	0.10	0.30	0.34	0.17	0.09	0.90
	0.15	0.41	0.37	0.14	0.05	0.97
	0.20	0.49	0.37	0.10	0.03	0.99
	0.25	0.55	0.36	0.07	0.02	1.00
7	0.30	0.60	0.34	0.05	0.01	1.00
	0.35	0.64	0.32	0.04	0.00	1.00
	0.40	0.68	0.29	0.03	0.00	1.00
	0.45	0.71	0.27	0.02	0.00	1.00
	0.50	0.73	0.25	0.02	0.00	1.00
	0.10	0.33	0.35	0.17	0.08	0.93
	0.15	0.44	0.38	0.12	0.04	0.98
	0.20	0.52	0.37	0.08	0.02	0.99
	0.25	0.58	0.35	0.06	0.01	1.00
8	0.30	0.63	0.32	0.04	0.01	1.00
	0.35	0.67	0.30	0.03	0.00	1.00
	0.40	0.71	0.27	0.02	0.00	1.00
	0.45	0.74	0.25	0.01	0.00	1.00
	0.50	0.76	0.23	0.01	0.00	1.00
	0.10	0.36	0.37	0.16	0.07	0.96
	0.15	0.47	0.38	0.11	0.03	0.99
	0.20	0.55	0.36	0.07	0.01	0.99
	0.25	0.62	0.33	0.04	0.01	1.00
9	0.30	0.67	0.30	0.03	0.00	1.00
	0.35	0.70	0.28	0.02	0.00	1.00
	0.40	0.74	0.25	0.01	0.00	1.00
	0.45	0.76	0.23	0.01	0.00	1.00
	0.50	0.78	0.21	0.01	0.00	1.00
	0.10	0.38	0.38	0.15	0.06	0.97
	0.15	0.50	0.38	0.09	0.02	0.99
	0.20	0.58	0.35	0.06	0.01	1.00
	0.25	0.64	0.32	0.04	0.00	1.00
10	0.30	0.69	0.29	0.02	0.00	1.00
	0.35	0.73	0.26	0.01	0.00	1.00
	0.40	0.76	0.23	0.01	0.00	1.00
	0.45	0.78	0.21	0.01	0.00	1.00
	0.50	0.80	0.20	0.00	0.00	1.00

Table 4.

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

Table 4.

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

Velocity υ	Import-Income Ratio m	Coefficients for
Velocity υ	Import-Income Ratio m	Q(0)	Q(–I)	Q(–II)	Q(–III)	Sum
	0.10	1.33	1.51	1.24	1.03	5.11
	0.15	1.25	1.32	1.00	0.75	4.32
	0.20	1.18	1.17	0.81	0.56	3.72
	0.25	1.12	1.04	0.66	0.42	3.24
2	0.30	1.07	0.93	0.55	0.32	2.87
	0.35	1.02	0.83	0.46	0.25	2.56
	0.40	0.97	0.75	0.38	0.20	2.30
	0.45	0.93	0.68	0.32	0.15	2.08
	0.50	0.89	0.62	0.27	0.12	1.90
	0.10	1.71	2.06	155	1.16	6.48
	0.15	1.59	1.74	1.14	0.75	5.22
	0.20	1.49	1.48	0.86	0.50	4.33
	0.25	1.40	1.27	0.65	0.33	3.65
3	0.30	1.32	1.10	0.50	0.23	3.15
	0.35	1.24	0.96	0.39	0.16	2.75
	0.40	1.18	0.84	0.31	0.11	2.44
	0.45	1.12	0.74	0.24	0.08	2.18
	0.50	1.06	0.66	0.20	0.06	1.98
	0.10	2.08	2.51	1.72	1.17	7.48
	0.15	1.91	2.04	1.17	0.67	5.79
	0.20	1.76	1.68	0.81	0.39	4.64
	0.25	1.64	1.39	0.57	0.23	3.83
4	0.30	1.53	1.17	0.41	0.14	3.25
	0.35	1.43	1.00	0.30	0.09	2.82
	0.40	1.34	0.86	0.22	0.06	2.48
	0.45	1.27	0.74	0.17	0.04	2.22
	0.50	1.20	0.64	0.13	0.03	2.00
	0.10	2.42	2.87	1.78	1.11	8.18
	0.15	2.20	2.25	1.12	0.56	6.13
	0.20	2.01	1.79	0.72	0.29	4.81
	0.25	1.85	1.45	0.47	0.16	3.93
5	0.30	1.71	1.19	0.32	0.09	3.31
	0.35	1.59	0.99	0.22	0.05	2.85
	0.40	1.48	0.83	0.15	0.03	2.49
	0.45	1.39	0.70	0.11	0.02	2.22
	0.50	1.31	0.60	0.08	0.01	2.00
	0.10	2.74	3.16	1.78	1.01	8.69
	0.15	2.46	2.39	1.03	0.45	6.33
	0.20	2.23	1.84	0.62	0.21	4.90
	0.25	2.03	1.45	0.38	0.10	3.96
6	0.30	1.87	1.16	0.24	0.05	3.32
	0.35	1.72	0.95	0.16	0.03	2.86
	0.40	1.60	0.78	0.10	0.01	2.49
	0.45	1.49	0.65	0.07	0.01	2.22
	0.50	1.39	0.56	0.05	0.00	2.00
	0.10	3.05	3.38	1.74	0.89	9.06
	0.15	2.71	2.47	0.93	0.35	6.46
	0.20	2.42	1.86	0.52	0.14	4.94
	0.25	2.19	1.43	0.30	0.06	3.98
7	0.30	2.00	1.12	0.18	0.03	3.33
	0.35	1.83	0.90	0.11	0.01	2.86
	0.40	1.69	0.73	0.07	0.01	2.50
	0.45	1.57	0.60	0.05	0.00	2.22
	0.50	1.46	0.51	0.03	0.00	2.00
	0.10	3.33	3.56	1.66	0.77	9.32
	0.15	2.93	2.52	0.82	0.27	6.54
	0.20	2.60	1.84	0.43	0.10	4.97
	0.25	2.34	1.38	0.23	0.04	3.99
8	0.30	2.11	1.07	0.13	0.02	3.33
	0.35	1.93	0.84	0.08	0.01	2.86
	0.40	1.77	0.68	0.05	0.00	2.50
	0.45	1.64	0.55	0.03	0.00	2.22
	0.50	1.52	0.46	0.02	0.00	2.00
	0.10	3.60	3.68	1.56	0.66	9.50
	0.15	3.13	2.53	0.72	0.20	6.58
	0.20	2.76	1.81	0.35	0.07	4.99
	0.25	2.46	1.33	0.18	0.02	3.99
9	0.30	2.21	1.01	0.10	0.01	3.33
	0.35	2.01	0.79	0.05	0.00	2.85
	0.40	1.84	0.63	0.03	0.00	2.50
	0.45	1.69	0.51	0.02	0.00	2.22
	0.50	1.57	0.42	0.01	0.00	2.00
	0.10	3.86	3.78	1.46	0.56	9.66
	0.15	3.32	2.52	0.62	0.15	6.61
	0.20	2.90	1.76	0.28	0.05	4.99
	0.25	2.57	1.27	0.14	0.02	4.00
10	0.30	2.30	0.95	0.07	0.01	3.33
	0.35	2.08	0.74	0.04	0.00	2.86
	0.40	1.90	0.58	0.02	0.00	2.50
	0.45	1.74	0.47	0.01	0.00	2.22
	0.50	1.61	0.38	0.01	0.00	2.00

Table 4.

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

Velocity υ	Import-Income Ratio m	Coefficients for
Velocity υ	Import-Income Ratio m	Q(0)	Q(–I)	Q(–II)	Q(–III)	Sum
	0.10	1.33	1.51	1.24	1.03	5.11
	0.15	1.25	1.32	1.00	0.75	4.32
	0.20	1.18	1.17	0.81	0.56	3.72
	0.25	1.12	1.04	0.66	0.42	3.24
2	0.30	1.07	0.93	0.55	0.32	2.87
	0.35	1.02	0.83	0.46	0.25	2.56
	0.40	0.97	0.75	0.38	0.20	2.30
	0.45	0.93	0.68	0.32	0.15	2.08
	0.50	0.89	0.62	0.27	0.12	1.90
	0.10	1.71	2.06	155	1.16	6.48
	0.15	1.59	1.74	1.14	0.75	5.22
	0.20	1.49	1.48	0.86	0.50	4.33
	0.25	1.40	1.27	0.65	0.33	3.65
3	0.30	1.32	1.10	0.50	0.23	3.15
	0.35	1.24	0.96	0.39	0.16	2.75
	0.40	1.18	0.84	0.31	0.11	2.44
	0.45	1.12	0.74	0.24	0.08	2.18
	0.50	1.06	0.66	0.20	0.06	1.98
	0.10	2.08	2.51	1.72	1.17	7.48
	0.15	1.91	2.04	1.17	0.67	5.79
	0.20	1.76	1.68	0.81	0.39	4.64
	0.25	1.64	1.39	0.57	0.23	3.83
4	0.30	1.53	1.17	0.41	0.14	3.25
	0.35	1.43	1.00	0.30	0.09	2.82
	0.40	1.34	0.86	0.22	0.06	2.48
	0.45	1.27	0.74	0.17	0.04	2.22
	0.50	1.20	0.64	0.13	0.03	2.00
	0.10	2.42	2.87	1.78	1.11	8.18
	0.15	2.20	2.25	1.12	0.56	6.13
	0.20	2.01	1.79	0.72	0.29	4.81
	0.25	1.85	1.45	0.47	0.16	3.93
5	0.30	1.71	1.19	0.32	0.09	3.31
	0.35	1.59	0.99	0.22	0.05	2.85
	0.40	1.48	0.83	0.15	0.03	2.49
	0.45	1.39	0.70	0.11	0.02	2.22
	0.50	1.31	0.60	0.08	0.01	2.00
	0.10	2.74	3.16	1.78	1.01	8.69
	0.15	2.46	2.39	1.03	0.45	6.33
	0.20	2.23	1.84	0.62	0.21	4.90
	0.25	2.03	1.45	0.38	0.10	3.96
6	0.30	1.87	1.16	0.24	0.05	3.32
	0.35	1.72	0.95	0.16	0.03	2.86
	0.40	1.60	0.78	0.10	0.01	2.49
	0.45	1.49	0.65	0.07	0.01	2.22
	0.50	1.39	0.56	0.05	0.00	2.00
	0.10	3.05	3.38	1.74	0.89	9.06
	0.15	2.71	2.47	0.93	0.35	6.46
	0.20	2.42	1.86	0.52	0.14	4.94
	0.25	2.19	1.43	0.30	0.06	3.98
7	0.30	2.00	1.12	0.18	0.03	3.33
	0.35	1.83	0.90	0.11	0.01	2.86
	0.40	1.69	0.73	0.07	0.01	2.50
	0.45	1.57	0.60	0.05	0.00	2.22
	0.50	1.46	0.51	0.03	0.00	2.00
	0.10	3.33	3.56	1.66	0.77	9.32
	0.15	2.93	2.52	0.82	0.27	6.54
	0.20	2.60	1.84	0.43	0.10	4.97
	0.25	2.34	1.38	0.23	0.04	3.99
8	0.30	2.11	1.07	0.13	0.02	3.33
	0.35	1.93	0.84	0.08	0.01	2.86
	0.40	1.77	0.68	0.05	0.00	2.50
	0.45	1.64	0.55	0.03	0.00	2.22
	0.50	1.52	0.46	0.02	0.00	2.00
	0.10	3.60	3.68	1.56	0.66	9.50
	0.15	3.13	2.53	0.72	0.20	6.58
	0.20	2.76	1.81	0.35	0.07	4.99
	0.25	2.46	1.33	0.18	0.02	3.99
9	0.30	2.21	1.01	0.10	0.01	3.33
	0.35	2.01	0.79	0.05	0.00	2.85
	0.40	1.84	0.63	0.03	0.00	2.50
	0.45	1.69	0.51	0.02	0.00	2.22
	0.50	1.57	0.42	0.01	0.00	2.00
	0.10	3.86	3.78	1.46	0.56	9.66
	0.15	3.32	2.52	0.62	0.15	6.61
	0.20	2.90	1.76	0.28	0.05	4.99
	0.25	2.57	1.27	0.14	0.02	4.00
10	0.30	2.30	0.95	0.07	0.01	3.33
	0.35	2.08	0.74	0.04	0.00	2.86
	0.40	1.90	0.58	0.02	0.00	2.50
	0.45	1.74	0.47	0.01	0.00	2.22
	0.50	1.61	0.38	0.01	0.00	2.00

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 $mυ = \frac{M}{Y} \cdot \frac{Y}{MO} = \frac{M}{MO}$ . 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

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 $\frac{1}{m}$ , 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 mv) 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 2 $\frac{1}{2}$ 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).

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 $\tilde{M}$ in (6):

\begin{matrix} M (t) = m^{'} Y (t) + \tilde{M} . & (6^{'}) \end{matrix}

Accordingly, (9) becomes

\begin{matrix} M (t) = \frac{m^{'}}{1 + m^{'}} [Q (t) - \tilde{M}] + \frac{m^{'}}{{(1 + m^{'})}^{2}} [Q (t - 1) - \tilde{M}] + \cdot \cdot \cdot \cdot + \tilde{M} . & (9^{'}) \end{matrix}

Since the sum of the coefficients in (9’) equals 1, this can be written as

\begin{matrix} M (t) = \frac{m^{'}}{1 + m^{'}} Q (t) + \frac{m^{'}}{{(1 + m^{'})}^{2}} Q (t - 1) …., & (9^{"}) \end{matrix}

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

Y (t) = \frac{Q (t) - \tilde{M}}{1 + m^{'}} + \frac{Q (t - 1) - \tilde{M}}{{(1 + m^{'})}^{2}} \cdot \cdot \cdot \cdot;

hence

\begin{matrix} Y (t) = \frac{Q (t)}{1 + m^{'}} + \frac{Q (t - 1)}{{(1 + m^{'})}^{2}} \cdot \cdot \cdot \cdot - \frac{\tilde{M}}{m^{'}} . & (8^{'}) \end{matrix}

Thus, not only is m’ substituted for m, but there is also a constant term, $- \frac{\tilde{M}}{m^{'}}$ , added.

6. Expansion of the model 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 itself—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 ΔD 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 $k = \frac{1}{ν}$ , and the ratio in any one year as $k (t) = \frac{1}{ν (t)}$ , then it can be shown that

\begin{matrix} Δ MO (t) = kΔY (t) + Δ k (t) Y (t - 1) + Δ^{'} k (t) Δ Y (t), & (10) \end{matrix}

Where

\begin{matrix} Δ k (t) = k (t) - k (t - 1) & (11) \end{matrix}

and

\begin{matrix} Δ^{'} k (t) = k (t) - k . & (12) \end{matrix}

Since MO is the product of income and velocity, the additive expression for ΔMO 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 ΔMO 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

Thus

\begin{matrix} V (t) = - [Δ k (t) Y (t - 1) + Δ^{'} k (t) Δ Y (t)] & \begin{matrix} (13) \end{matrix} \end{matrix}

or, defined as a residual,

\begin{matrix} V (t) = kΔY (t) - Δ MO (t) & (14) \end{matrix}

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-of-year 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 M_A (“autonomous imports”), the extent of the deviation from the income relationship:

\begin{matrix} M (t) = mY (t) + M_{A} (t) . & (15) \end{matrix}

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

Figures for –M_A 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, M_A 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:

\begin{matrix} Q^{'} (t) = Q (t) + M_{A} (t) + V (t) . & (16) \end{matrix}

It follows from (5’), (14), and (15) that Q’(t) may also be written as

\begin{matrix} Q^{'} (t) = mY (t) + kΔY (t) . & \begin{matrix} (17) \end{matrix} \end{matrix}

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 M_A 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 M_A (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 377ff.), the residual in the original income equation may be considered to consist of an “M_A 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 M_A’s (with sign reversed), and the latter by applying these same coefficients to the Vs. 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 “M_A effect on imports” and the “velocity effect on imports” are similar to the corresponding effects on income, and can be computed by applying to –M_A and V the import coefficients from Table 3. In addition to these, there is M_A 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 M_A, M_A 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 M_A, M_A 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:

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.

Table 5.

Norway: Balance of Payments Data

(In millions of kroner)

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

^¹Includes only that part of foreign loans obtained which are considered special project loans.

Table 5.

Norway: Balance of Payments Data

(In millions of kroner)

		1948	1949	1950	1951	1952	1953	1954	1955	1956	1957	1958
Import Payments (M)
	1.1 Merchandise, nonmonetary gold	3,521	3,982	4,618	5578	5,959	6,242	7,031	7,496	8,282	8,729	9,038
	1.2 Service payments	1,675	1,911	2,001	2,591	2,785	2,620	2,679	3,127	3,395	3,947	3,695
	1.3 Private donations	34	30	34	39	44	42	45	45	54	62	63
	1.4 Drawings on project loans¹	0	0	0	0	0	0	0	0	7	38	70
	1.5 Reparations	15	0	21	0	0	0	0	0	0	0	0
	1.6 M (1.1+1.2+1.3–1.4–1.5)	5,215	5,923	6,632	8,508	8,788	8,904	9,755	10,668	11,724	12,700	12,726
Export Receipts (X)
	1.7 Merchandise, nonmonetary gold	2,186	2,191	2,950	4,618	4,230	3,806	4,316	4,709	5,711	5,935	5,370
	1.8 Private donations	62	50	56	69	65	81	81	105	102	108	128
	1.9 Investment income, net	–63	–59	–62	–78	–64	–73	–97	–134	–179	–187	–222
	1.10 Other service receipts	2,250	2,506	2,816	4,094	4,471	4,117	4,216	5,062	6,047	7,021	6,303
	1.11 X (1.7+1.8+1.9+1.10)	4,435	4,688	5,760	8,703	8,702	7,931	8,516	9,742	11,681	12,877	11,579
Change in Reserves (ΔR)
	1.12 Short-term assets	+47	–73	+147	+276	–33	–37	–36	+214	+308	+246	+490
	1.13 Gold	–100	–1	–10	–1	+1	+12	–52	+6	+35	–38	–14
	1.14 Short-term liabilities	–55	–184	+303	+35	+226	–366	–266	–23	+208	+43	–188
	1.15 ΔR (1.12+1.13+1.14)	–108	–258	+440	+310	+194	–391	–354	+197	+551	+251	+288
Capital Movements (C)
	1.16 C (1.6–1.11+1.15)	672	977	1,312	115	278	582	885	1,123	594	74	1,435

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

^¹Includes only that part of foreign loans obtained which are considered special project loans.

Table 5.

Norway: Balance of Payments Data

(In millions of kroner)

		1948	1949	1950	1951	1952	1953	1954	1955	1956	1957	1958
Import Payments (M)
	1.1 Merchandise, nonmonetary gold	3,521	3,982	4,618	5578	5,959	6,242	7,031	7,496	8,282	8,729	9,038
	1.2 Service payments	1,675	1,911	2,001	2,591	2,785	2,620	2,679	3,127	3,395	3,947	3,695
	1.3 Private donations	34	30	34	39	44	42	45	45	54	62	63
	1.4 Drawings on project loans¹	0	0	0	0	0	0	0	0	7	38	70
	1.5 Reparations	15	0	21	0	0	0	0	0	0	0	0
	1.6 M (1.1+1.2+1.3–1.4–1.5)	5,215	5,923	6,632	8,508	8,788	8,904	9,755	10,668	11,724	12,700	12,726
Export Receipts (X)
	1.7 Merchandise, nonmonetary gold	2,186	2,191	2,950	4,618	4,230	3,806	4,316	4,709	5,711	5,935	5,370
	1.8 Private donations	62	50	56	69	65	81	81	105	102	108	128
	1.9 Investment income, net	–63	–59	–62	–78	–64	–73	–97	–134	–179	–187	–222
	1.10 Other service receipts	2,250	2,506	2,816	4,094	4,471	4,117	4,216	5,062	6,047	7,021	6,303
	1.11 X (1.7+1.8+1.9+1.10)	4,435	4,688	5,760	8,703	8,702	7,931	8,516	9,742	11,681	12,877	11,579
Change in Reserves (ΔR)
	1.12 Short-term assets	+47	–73	+147	+276	–33	–37	–36	+214	+308	+246	+490
	1.13 Gold	–100	–1	–10	–1	+1	+12	–52	+6	+35	–38	–14
	1.14 Short-term liabilities	–55	–184	+303	+35	+226	–366	–266	–23	+208	+43	–188
	1.15 ΔR (1.12+1.13+1.14)	–108	–258	+440	+310	+194	–391	–354	+197	+551	+251	+288
Capital Movements (C)
	1.16 C (1.6–1.11+1.15)	672	977	1,312	115	278	582	885	1,123	594	74	1,435

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

^¹Includes only that part of foreign loans obtained which are considered special project loans.

Table 6.

Norway: Income and Monetary Data¹

^¹For 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.

^²See pp. 364–65 for description of method of estimate.

^³MO for 1948 and 1949, and related figures, may not be exactly comparable with figures for subsequent years.

Table 6.

Norway: Income and Monetary Data¹

		1948	1949	1950	1951	1952	1953	1954	1955	1956	1957	1958
2.1	Y, average for year	13,870	14,790	14,880	18,480	20,380	20,580	22,250	23,620	26,610	28,210	27,810
2.2	Y, estimate for year end ²	14,300	14,835	16,680	19,430	20,480	21,415	22,935	25,115	27,410	28,010	….
2.3	M ÷Y (1.6÷2.1)	37.6	40.0	44.6	46.0	43.1	43.3	43.8	45.2	44.0	45.0	45.8
2.4	m (average of 2.3)	Average for 1949–57: m=0.44
2.5	MO	4,988³	4,995³	4,823	5,604	6,001	6,263	6,506	6,688	6,880	6,864	7,050
2.6	ΔMO	261	–33	–132	781	397	262	243	182	192	–16	186
2.7	Y÷MO (2.2÷2.5)	2.87	2.99	3.46	3.47	3.41	3.42	3.53	3.76	3.98	4.08	….
2.8	v (average of 2.7)	Average for 1949–57: v=3.57; k=0.28
2.9	ΔY (from 2.2)	970	505	1,845	2,750	1,050	935	1,520	2,180	2,295	600	….
2.10	kΔY	272	141	517	770	294	262	426	610	643	168	….
2.11	V (kΔY-ΔMO)	11	174	649	–18	–103	0	183	428	451	184	….
2.12	Marginal import equation	M =0.50F–1,200 (see Chart 1)
2.13	M computed on basis of 2.12	5,735	6,195	6,240	8,040	8,990	9,090	9,925	10,610	12,105	12,905	12,705
2.14	Minus M_A (2.13–1.6)	520	272	–392	–468	202	186	170	–58	381	205	–21
2.15	ΔD (2.6–1.15)	369	225	–572	471	203	653	597	–15	–359	–267	–102
2.16	Q (1.11+1.16+2.15) (also equals 1.6+2.6)	5,476	5,890	6,500	9,289	9,183	9,166	9,998	10,850	11,916	12,684	12.912

^²See pp. 364–65 for description of method of estimate.

^³MO for 1948 and 1949, and related figures, may not be exactly comparable with figures for subsequent years.

Table 6.

Norway: Income and Monetary Data¹

		1948	1949	1950	1951	1952	1953	1954	1955	1956	1957	1958
2.1	Y, average for year	13,870	14,790	14,880	18,480	20,380	20,580	22,250	23,620	26,610	28,210	27,810
2.2	Y, estimate for year end ²	14,300	14,835	16,680	19,430	20,480	21,415	22,935	25,115	27,410	28,010	….
2.3	M ÷Y (1.6÷2.1)	37.6	40.0	44.6	46.0	43.1	43.3	43.8	45.2	44.0	45.0	45.8
2.4	m (average of 2.3)	Average for 1949–57: m=0.44
2.5	MO	4,988³	4,995³	4,823	5,604	6,001	6,263	6,506	6,688	6,880	6,864	7,050
2.6	ΔMO	261	–33	–132	781	397	262	243	182	192	–16	186
2.7	Y÷MO (2.2÷2.5)	2.87	2.99	3.46	3.47	3.41	3.42	3.53	3.76	3.98	4.08	….
2.8	v (average of 2.7)	Average for 1949–57: v=3.57; k=0.28
2.9	ΔY (from 2.2)	970	505	1,845	2,750	1,050	935	1,520	2,180	2,295	600	….
2.10	kΔY	272	141	517	770	294	262	426	610	643	168	….
2.11	V (kΔY-ΔMO)	11	174	649	–18	–103	0	183	428	451	184	….
2.12	Marginal import equation	M =0.50F–1,200 (see Chart 1)
2.13	M computed on basis of 2.12	5,735	6,195	6,240	8,040	8,990	9,090	9,925	10,610	12,105	12,905	12,705
2.14	Minus M_A (2.13–1.6)	520	272	–392	–468	202	186	170	–58	381	205	–21
2.15	ΔD (2.6–1.15)	369	225	–572	471	203	653	597	–15	–359	–267	–102
2.16	Q (1.11+1.16+2.15) (also equals 1.6+2.6)	5,476	5,890	6,500	9,289	9,183	9,166	9,998	10,850	11,916	12,684	12.912

^²See pp. 364–65 for description of method of estimate.

^³MO for 1948 and 1949, and related figures, may not be exactly comparable with figures for subsequent years.

Chart 1.

Norway: Marginal and Average Import Relationships ¹

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

¹ For description of symbols, see text.

In Table 7, imports are first computed on the basis of Q only. This leaves a residual, shown on line 3.4. Then the M_A 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 M_A (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.

Table 7.

Norway: Computed Imports ¹

(In millions of kroner)

^¹For description of symbols, see text.

^²Incomplete data.

Table 7.

Norway: Computed Imports ¹

(In millions of kroner)

		1948	1949	1950	1951	1952	1953	1954	1955	1956	1957	1958
		Marginal Import-Income Ratio: 0.50; Velocity: 3.57
3.1	Q (2.16)	5,476	5,890	6,500	9,289	9,183	9,166	9,998	10,850	11,916	12,684	12,912
	0.57Q(0)		3,357	3,705	5,295	5,234	5,225	5,699	6,184	6,792	7,230	7,350
	0.33Q(–I)		1,807	1,944	2,145	3,065	3,030	3,025	3,299	3581	3,932	4,186
	0.08Q(–II)		400²	438	471	520	743	735	733	800	868	953
	0.02Q(–III)		90²	100²	110	118	130	186	184	183	200	217
3.2	M ^*, computed imports		5,654²	6,187²	8,021	8,937	9,128	9,645	10,400	11,356	12,230	12,706
3.3	M (1.6)		5,923	6,632	8,508	8,788	8,904	9,755	10,668	11,724	12,700	12,726
3.4	Residual (3.3–3.2)		269	445	487	–149	–224	110	268	368	470	20
3.5	Minus M_A	520	272	–392	–468	202	186	170	–58	881	206	–21
	057[–M_A (0)]		155	–223	–267	115	106	97	–33	217	117	–12
	0.33[–M_A (–I)]		172	90	–129	–154	67	61	56	–19	126	68
	0.08[–M_A (–II)]			42	22	–31	–37	16	15	14	–5	30
	0.02[–M_A (–III)]		—	—	10	5	–8	–16	4	4	3	–1
3.6	M_A effect on imports		327²	–91²	–364	–65	128	165	42	216	241	85
3.7	V (2.11)	11	174	649	–18	–103	0	183	428	451	184	….
	0.57V(0)		99	370	–10	–59	0	104	244	257	105	….
	0.33V(–I)		4	57	214	–6	–34	0	60	141	149	61
	0.08V(–II)		1	14	52	–1	–8	0	15	34	36
	0.02V(–III)		—	—	0	3	13	0	–2	0	4	9
3.8	V effect on imports		103²	428²	218	–10	–22	96	302	413	292	106²
3.9	M_A		–272	392	468	–202	–186	–170	58	–381	–205	21
3.10	Computed residual (3.6+3.8+3.9)		158²	729²	322	–283	–S2	90	402	248	328	212²
3.11	Residual error (3.4–3.10)		111²	–284²	165	134	–142	20	–134	120	142	–192²

^¹For description of symbols, see text.

^²Incomplete data.

Table 7.

Norway: Computed Imports ¹

(In millions of kroner)

		1948	1949	1950	1951	1952	1953	1954	1955	1956	1957	1958
		Marginal Import-Income Ratio: 0.50; Velocity: 3.57
3.1	Q (2.16)	5,476	5,890	6,500	9,289	9,183	9,166	9,998	10,850	11,916	12,684	12,912
	0.57Q(0)		3,357	3,705	5,295	5,234	5,225	5,699	6,184	6,792	7,230	7,350
	0.33Q(–I)		1,807	1,944	2,145	3,065	3,030	3,025	3,299	3581	3,932	4,186
	0.08Q(–II)		400²	438	471	520	743	735	733	800	868	953
	0.02Q(–III)		90²	100²	110	118	130	186	184	183	200	217
3.2	M ^*, computed imports		5,654²	6,187²	8,021	8,937	9,128	9,645	10,400	11,356	12,230	12,706
3.3	M (1.6)		5,923	6,632	8,508	8,788	8,904	9,755	10,668	11,724	12,700	12,726
3.4	Residual (3.3–3.2)		269	445	487	–149	–224	110	268	368	470	20
3.5	Minus M_A	520	272	–392	–468	202	186	170	–58	881	206	–21
	057[–M_A (0)]		155	–223	–267	115	106	97	–33	217	117	–12
	0.33[–M_A (–I)]		172	90	–129	–154	67	61	56	–19	126	68
	0.08[–M_A (–II)]			42	22	–31	–37	16	15	14	–5	30
	0.02[–M_A (–III)]		—	—	10	5	–8	–16	4	4	3	–1
3.6	M_A effect on imports		327²	–91²	–364	–65	128	165	42	216	241	85
3.7	V (2.11)	11	174	649	–18	–103	0	183	428	451	184	….
	0.57V(0)		99	370	–10	–59	0	104	244	257	105	….
	0.33V(–I)		4	57	214	–6	–34	0	60	141	149	61
	0.08V(–II)		1	14	52	–1	–8	0	15	34	36
	0.02V(–III)		—	—	0	3	13	0	–2	0	4	9
3.8	V effect on imports		103²	428²	218	–10	–22	96	302	413	292	106²
3.9	M_A		–272	392	468	–202	–186	–170	58	–381	–205	21
3.10	Computed residual (3.6+3.8+3.9)		158²	729²	322	–283	–S2	90	402	248	328	212²
3.11	Residual error (3.4–3.10)		111²	–284²	165	134	–142	20	–134	120	142	–192²

^¹For description of symbols, see text.

^²Incomplete data.

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.

Chart 2.

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

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

¹ For description of symbols, see text.

Chart 3.

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

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

¹ For description of symbols, see text.

Table 8 does with respect to income what Table 7 does with respect to imports. The constant added after the Q terms equals $- \frac{- 1, 200}{0.50} = 2, 400,$ 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.

Table 8.

Norway: Computed Income¹

(In millions of kroner)

^¹For description of symbols, see text.

^²Incomplete data.

Table 8.

Norway: Computed Income¹

(In millions of kroner)

		1948	1949	1950	1951	1952	1953	1954	1955	1956	1957	1958
		Marginal Import-Income Ratio: 0.50; Velocity: 3.57; M= –1,200
4.1	Q (2.16)	5,476	5,890	6,500	9,289	9,183	9,199	9,998	10,850	11,916	12,684	12,912
	1.14Q(0)			7,410	10,589	10,468	10,449	11,398	12,369	13,584	14,460	14,720
	0.65Q(–I)			3,828	4,225	6,038	5,969	5,959	6,499	7,052	7,745	8,245
	0.16Q(–II)			876	942	1,040	1,486	1,469	1,467	1,600	1,736	1,907
	0.05O(–III)			250²	274	295	325	464	459	458	500	542
	$- \frac{\tilde{M}}{m^{2}}$			2,400	2,400	2,400	2,400	2,400	2,400	2,400	2,400	2,400
4.2	Computed income, interim figure			14.764²	18,430	20,241	20,629	21,690	23,194	25,094	26,841	27,814
4.3	Y (2.1)			14,880	18,480	20,380	20,580	22,250	23,620	26,610	28,210	27,810
4.4	Residual, interim figure (4.3–4.2)			116²	50	139	–49	560	426	1,516	1,369	–4
4.5	Y^* computed income (4.2+4.13)			14,871²	18,537	20,348	20,736	21,797	23,301	25,201	26,948	27,921
4.6	Residual (4.3–4.5)			9²	–57	32	–156	453	319	1,409	1,262	–111
4.7	Minus M_A (2.14)	520	272	–392	–468	202	186	170	–58	381	205	–21
	1.14[–M_A (0)]			–447	–534	230	212	194	–66	434	234	–24
	0.65[–M_A (–I)]			177	–255	–304	131	121	111	–38	248	133
	0.16[M_A (–II)]			83	44	–63	–75	32	30	27	–9	61
	0.05[M_A (–III)]			—	26	14	–20	–23	10	9	8	–3
4.8	M_A effect on income			–187²	–719	–123	248	324	85	432	481	167
4.9	V (2.11)	11	174	649	–18	–103	0	183	428	451	184	….
	1.14V (–0)			740	–21	–117	0	209	488	514	210	….
	0.65V (–I)			113	422	–12	–67	0	119	278	293	120
	0.16V (–II)			2	28	104	–3	–16	0	29	68	72
	0.05V (–III)			—	1	9	32	–1	–5	0	9	21
4.10	V effect on income			855²	430	–16	–38	192	602	821	580	213²
4.11	Computed residual (4.8+4.10)			668²	–289	–151	207	515	687	1,253	1,061	380²
4.12	(4.4–4.11)			–552²	339	290	–256	45	–261	263	308	–384²
4.13	Average of 4.12			Average for 1951–57: 107
4.14	Residual error (4.6–4.11)			–659²	232	183	–363	–62	–368	156	201	–491²

^¹For description of symbols, see text.

^²Incomplete data.

Table 8.

Norway: Computed Income¹

(In millions of kroner)

		1948	1949	1950	1951	1952	1953	1954	1955	1956	1957	1958
		Marginal Import-Income Ratio: 0.50; Velocity: 3.57; M= –1,200
4.1	Q (2.16)	5,476	5,890	6,500	9,289	9,183	9,199	9,998	10,850	11,916	12,684	12,912
	1.14Q(0)			7,410	10,589	10,468	10,449	11,398	12,369	13,584	14,460	14,720
	0.65Q(–I)			3,828	4,225	6,038	5,969	5,959	6,499	7,052	7,745	8,245
	0.16Q(–II)			876	942	1,040	1,486	1,469	1,467	1,600	1,736	1,907
	0.05O(–III)			250²	274	295	325	464	459	458	500	542
	$- \frac{\tilde{M}}{m^{2}}$			2,400	2,400	2,400	2,400	2,400	2,400	2,400	2,400	2,400
4.2	Computed income, interim figure			14.764²	18,430	20,241	20,629	21,690	23,194	25,094	26,841	27,814
4.3	Y (2.1)			14,880	18,480	20,380	20,580	22,250	23,620	26,610	28,210	27,810
4.4	Residual, interim figure (4.3–4.2)			116²	50	139	–49	560	426	1,516	1,369	–4
4.5	Y^* computed income (4.2+4.13)			14,871²	18,537	20,348	20,736	21,797	23,301	25,201	26,948	27,921
4.6	Residual (4.3–4.5)			9²	–57	32	–156	453	319	1,409	1,262	–111
4.7	Minus M_A (2.14)	520	272	–392	–468	202	186	170	–58	381	205	–21
	1.14[–M_A (0)]			–447	–534	230	212	194	–66	434	234	–24
	0.65[–M_A (–I)]			177	–255	–304	131	121	111	–38	248	133
	0.16[M_A (–II)]			83	44	–63	–75	32	30	27	–9	61
	0.05[M_A (–III)]			—	26	14	–20	–23	10	9	8	–3
4.8	M_A effect on income			–187²	–719	–123	248	324	85	432	481	167
4.9	V (2.11)	11	174	649	–18	–103	0	183	428	451	184	….
	1.14V (–0)			740	–21	–117	0	209	488	514	210	….
	0.65V (–I)			113	422	–12	–67	0	119	278	293	120
	0.16V (–II)			2	28	104	–3	–16	0	29	68	72
	0.05V (–III)			—	1	9	32	–1	–5	0	9	21
4.10	V effect on income			855²	430	–16	–38	192	602	821	580	213²
4.11	Computed residual (4.8+4.10)			668²	–289	–151	207	515	687	1,253	1,061	380²
4.12	(4.4–4.11)			–552²	339	290	–256	45	–261	263	308	–384²
4.13	Average of 4.12			Average for 1951–57: 107
4.14	Residual error (4.6–4.11)			–659²	232	183	–363	–62	–368	156	201	–491²

^¹For description of symbols, see text.

^²Incomplete data.

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 M_A effect (line 4.8) and the V effect (line 4.10).

Chart 4.

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

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

¹ For description of symbols, see text.

Australia ¹

^²For year ended June 80.

^³Y for 1949, and related figures, may not be exactly comparable with figures for subsequent years.

^⁴For calculating M/Y and M_A, average income for the calendar year is estimated from the June 30 data by interpolation. For calculating Y/MO and V, income for the end of a calendar year is assumed to be the same as the annual rate for the year ended the following June.

Austria ¹

^²MO and Y prior to 1950, and related figures, may not be exactly comparable with figures for subsequent years.

AUSTRALIA

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

AUSTRIA

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

Belgium-Luxembourg ¹

^²Money for Belgium plus Sight Deposits and Post Office Checking Deposits for Luxembourg, as published in International Financial Statistics.

^³MO for 1948 and 1949, and related figures, may not be exactly comparable with figures for subsequent years.

^⁴Based on estimated ONP for 1958 of 547.3 billion francs.

Burma ¹

^²Deduction has been made on account of reparations (32 million kyats for 1956; 181 million kyats for 1957; 133 million kyats for 1958).

^³For year ended September 30.

^⁴For calculating M/Y, Y/MO, M_A, and V, income for the calendar year is estimated from the data for the year ended September 30.

BELGIUM - LUXEMBOURG

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

BURMA

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

Canada ¹

^¹For description of symbols, see text. With the exception of Y, the table is based on data from International Monetary Fund, Balance of Payments Yearbooks and International Financial Statistics. Y is taken from Dominion Bureau of Statistics, National Accounts, Income and Expenditure, which gives quarterly income data; this permitted year-end income to be estimated from last and first quarters instead of from annual rates. A check revealed that there was no substantial difference in the results obtained from the two methods. Except for ratios, figures are in millions of Canadian dollars.

Ceylon ¹

^²Includes changes in government and central bank holdings of long-term securities.

^³MO for 1948, and related figures, may not be exactly comparable with figures for subsequent years.

CANADA

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

CEYLON

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

Colombia ¹

^¹For description of symbols, see text. The table is based on data from International Monetary Fund, Balance of Payment) Yearbooks and International Financial Statistics. Except for ratios, figures are in millions of pesos. Balance of payments data were reported to the Fund in U.S. dollars. X and M have been converted at the following rates (in pesos per dollar, 1949 through 1958, respectively)—X: 1.95, 1.95, 2.13, 2.29, 2.37, 2.40, 2.58, 2.77, 3.60, 5.04; M: 1.95, 2.17, 2.46, 2.60, 2.65, 2.64, 2.87, 3.49, 4.36, 7.03. Afi has been converted at 2.50 pesos per dollar for the entire period.

^²Y for 1949, and related figures, may not be exactly comparable with figures for subsequent years.

Costa Rica ¹

^²National income.

COLOMBIA

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

COSTA RICA

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

Cuba ¹

^²Includes the amount shown in the Balance of Payments Yearbooks as errors and omissions (58 million pesos for 1965; 88 million pesos for 1956; 57 million pesos for 1957).

^³MO for 1950, and related figures, may not be exactly comparable with figures for subsequent years.

^⁴National income.

Denmark ¹

^²Based on estimated GKP for 1958 of 33,770 million kroner.

CUBA

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

DENMARK

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

Dominican Republic ¹

^¹For description oi symbols, see text. The table is based on data bom International Monetary Fund, Balance of Payments Yearbooks and International Financial Statistics. Except for ratios, figures are in millions of pesos.

Ecuador ¹

^¹For 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 sucres. Balance of payments data, which were reported to the Fund in U.S. dollars, have been converted at official rates.

^²M and ΔR for 1950, and related figures, may not be exactly comparable with figures for subsequent years.

DOMINICAN REPUBLIC

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

ECUADOR

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

Egypt ¹

^²MO for 1950 and 1951, and related figures, may not be exactly comparable with figures for subsequent years.

^³Through 1956, MO includes Egyptian currency in circulation in both Egypt and the Sudan. In 1957, Egyptian currency was withdrawn from the Sudan; the amount withdrawn (23.8 million Egyptian pounds) has been added to ΔMO for 1957.

El Salvador¹

EGYPT

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

EL SALVADOR

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

Ethiopia ¹

^²Includes changes in long-term assets.

^³Includes time and savings deposits.

^⁴No income figures are available for Ethiopia. On the basis of the ratio of imports to money (1.1), the two ratios, imports to income and income to imports, have been estimated: m = 0.22; i = 5 (see text, p. 356).

Finland ¹

^²MO prior to 1948, and related figures, may not be exactly comparable with figures for subsequent years.

^³National income.

ETHIOPIA

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

FINLAND

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

France ¹

^²X and M include merchandise transactions with, but not services to or from, overseas territories.

Federal Republic of Germany ¹

^²MO prior to 1950, and related figures, may not be exactly comparable with figures for subsequent years.

^³Based on year-end income estimated from last quarter 1958 and first quarter 1959.

Federal Republic of Germany ¹

	1950	1951	1952	1953	1954	1955	1956	1957	1958
X	9,305	16,296	19,747	22,065	26,107	30,819	37,437	44,454	47,971
C	2,162	1,211	222	–663	–1,380	–908	–761	–370	–4,095
M	11,771	15,487	17,875	17,982	22,271	28,066	32,209	37,049	39,282
ΔR	–304	2,020	2,590	3,420	2,456	1,845	4,477	7,035	4,594
MO ²	17,000	19,500	21,700	23,900	26,900	29,700	31,900	35,800	40,600
ΔMO	2,400	2,500	2,200	2,200	8,000	2,800	2,200	3,900	4,800
ΔD	2,704	480	–390	–1,220	544	955	–2,277	–3,225	206
Y	97,200	119,600	134,200	148,800	154,000	175,600	193,400	209,600	222,300
Q	14,171	17,987	19,575	20,222	25,271	30,866	34,409	40,949	44,082
M/Y	12.1	12.9	12.9	12.5	14.5	16.0	16.7	17.7	17.7
Y/MO	6.38	6.51	6.41	6.23	6.13	6.21	6.32	6.03	5.57 ³
−M_A	–2,457	–685	1,004	2,749	959	456	674	–197	682
V	271	442	–276	–626	–472	332	503	–1,602	–3,138 ³
	(1) M = 0.245Y — 14,500 (2) Y = 6.3MO (1950–56)
		Q(O)	Q(–I)	Q(–II)	Q(–III)	Q(–IV)
Import coefficients		0.61	0.36	0.09	0.02	0.02
Income coefficients		2.08	1.44	0.36	0.09	0.11

^²MO prior to 1950, and related figures, may not be exactly comparable with figures for subsequent years.

^³Based on year-end income estimated from last quarter 1958 and first quarter 1959.

Federal Republic of Germany ¹

	1950	1951	1952	1953	1954	1955	1956	1957	1958
X	9,305	16,296	19,747	22,065	26,107	30,819	37,437	44,454	47,971
C	2,162	1,211	222	–663	–1,380	–908	–761	–370	–4,095
M	11,771	15,487	17,875	17,982	22,271	28,066	32,209	37,049	39,282
ΔR	–304	2,020	2,590	3,420	2,456	1,845	4,477	7,035	4,594
MO ²	17,000	19,500	21,700	23,900	26,900	29,700	31,900	35,800	40,600
ΔMO	2,400	2,500	2,200	2,200	8,000	2,800	2,200	3,900	4,800
ΔD	2,704	480	–390	–1,220	544	955	–2,277	–3,225	206
Y	97,200	119,600	134,200	148,800	154,000	175,600	193,400	209,600	222,300
Q	14,171	17,987	19,575	20,222	25,271	30,866	34,409	40,949	44,082
M/Y	12.1	12.9	12.9	12.5	14.5	16.0	16.7	17.7	17.7
Y/MO	6.38	6.51	6.41	6.23	6.13	6.21	6.32	6.03	5.57 ³
−M_A	–2,457	–685	1,004	2,749	959	456	674	–197	682
V	271	442	–276	–626	–472	332	503	–1,602	–3,138 ³
	(1) M = 0.245Y — 14,500 (2) Y = 6.3MO (1950–56)
		Q(O)	Q(–I)	Q(–II)	Q(–III)	Q(–IV)
Import coefficients		0.61	0.36	0.09	0.02	0.02
Income coefficients		2.08	1.44	0.36	0.09	0.11

^²MO prior to 1950, and related figures, may not be exactly comparable with figures for subsequent years.

^³Based on year-end income estimated from last quarter 1958 and first quarter 1959.

FRANCE

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

FEDERAL REPUBLIC OF GERMANY

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

Guatemala ¹

^²MO prior to 1948, and related figures, may not be exactly comparable with figures for subsequent years.

Hondtjbas ¹

^²Y for 1949, and related figures, may not be exactly comparable with figures for subsequent years.

GUATEMALA

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

HONDURAS

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

India¹

^¹For description of symbols, see text. The table is based on data from International Monetary Fund, Balance of Payments Yearbooks andInternational Financial Statistics. Except for ratios, figures are in millions of rupees.

^²National income for year beginning April 1.

^³For calculating M/Y and M_A, average income for the calendar year is estimated from the April 1 data by interpolation. For calculating Y/MO and V, income for the end of a calendar year is assumed to be the same as the annual rate for the year beginning the previous April.

Iraq ¹

^¹For 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 dinars.

^²Includes changes in official long-term assets.

^³Includes quasi-money.

INDIA

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

IRAQ

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

Ireland ¹

^²Includes changes in foreign assets of the Central Bank, the commercial banks, and the Post Office Savings Bank.

^³MO prior to 1948, Y for 1948 and 1949, and related figures, may not be exactly comparable with figures for subsequent years.

Italy¹

^¹For 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 billions of lire. Balance of payments data, which were reported to the Fund in U.S. dollars, have been converted at 625 lire per dollar.

IRELAND

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

ITALY

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

Japan ¹

^¹For 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 billions of yen. Balance of payments data, which were reported to the Fund in U.S. dollars, have been converted at 860 yen per dollar.

^²MO for 1949–62, Y for 1949–50, and related figures, may not be exactly comparable with figures for subsequent years.

Mexico ¹

^¹For description of symbols, see text. The table is based on data from International Monetary Fund. Balance of Payments Yearbooks and International Financial Statistics (IFS). Except for ratios, figures are in millions of pesos. Balance of payments data, which were reported to the Fund in U.S. dollars, have been converted at the conversion rates shown in IFS.

^²National income.

JAPAN

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

MEXICO

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

Netherlands ¹

^²Deduction has been made for reparations received (3 million guilders for 1949; 8 million guilders for 1950).

^³MO for 1949, and related figures, may not be exactly comparable with figures for subsequent years.

^⁴Based on estimated GNP for 1958 of 36,070 million guilders.

Netherlands ¹

	1949	1950	1951	1952	1953	1954	1955	1956	1957	1958
X	5,141	6,732	9,016	10,643	10,556	11,538	13,173	13,842	15,017	15,580
C	180	1,243	231	–499	–619	–169	–1,015	–433	713	339
M	5,364²	7,772²	9,112	8,170	8,996	11,159	12,177	14,428	15,542	13,932
M_o	0	11	7	20	16	0	0	0	0	0
ΔR	–43	203	135	1,974	941	210	–19	–1,019	188	1,987
MO	7,627³	6,850	7,028	7,745	8,270	8,829	9,584	9,227	9,026	10,103
ΔMO	242	–471	178	717	525	559	755	–357	–201	1,077
ΔD	285	–674	43	–1,257	–416	349	774	662	–389	–910
Y	17,590	19,040	21,730	22,770	24,270	27,170	29,920	32,170	35,020
Q	5,606	7,301	9,290	8,887	9,521	11,718	12,932	14,071	15,341	15,009
M/Y	30.5	40.8	41.9	35.9	38.1	41.1	40.7	44.8	44.4	38.6⁴
Y/MO	2.31	2.98	3.17	3.06	3.11	3.23	3.24	3.64	3.94	….
−M_A	290	–1,248	–974	592	666	243	875	–26	670	2,810⁴
V	294	1,154	437	–298	201	373	70	1,199	845	….
	(1) M = 0.60Y — 4,900				(2) Y = 3.0MO (1948–55)
			Q(0)		Q(–I)	Q(–II)	Q(–III)
Import coefficients			0.58		0.32	0.08	0.02
Income coefficients			0.97		0.53	0.13	0.04

^²Deduction has been made for reparations received (3 million guilders for 1949; 8 million guilders for 1950).

^³MO for 1949, and related figures, may not be exactly comparable with figures for subsequent years.

^⁴Based on estimated GNP for 1958 of 36,070 million guilders.

Netherlands ¹

	1949	1950	1951	1952	1953	1954	1955	1956	1957	1958
X	5,141	6,732	9,016	10,643	10,556	11,538	13,173	13,842	15,017	15,580
C	180	1,243	231	–499	–619	–169	–1,015	–433	713	339
M	5,364²	7,772²	9,112	8,170	8,996	11,159	12,177	14,428	15,542	13,932
M_o	0	11	7	20	16	0	0	0	0	0
ΔR	–43	203	135	1,974	941	210	–19	–1,019	188	1,987
MO	7,627³	6,850	7,028	7,745	8,270	8,829	9,584	9,227	9,026	10,103
ΔMO	242	–471	178	717	525	559	755	–357	–201	1,077
ΔD	285	–674	43	–1,257	–416	349	774	662	–389	–910
Y	17,590	19,040	21,730	22,770	24,270	27,170	29,920	32,170	35,020
Q	5,606	7,301	9,290	8,887	9,521	11,718	12,932	14,071	15,341	15,009
M/Y	30.5	40.8	41.9	35.9	38.1	41.1	40.7	44.8	44.4	38.6⁴
Y/MO	2.31	2.98	3.17	3.06	3.11	3.23	3.24	3.64	3.94	….
−M_A	290	–1,248	–974	592	666	243	875	–26	670	2,810⁴
V	294	1,154	437	–298	201	373	70	1,199	845	….
	(1) M = 0.60Y — 4,900				(2) Y = 3.0MO (1948–55)
			Q(0)		Q(–I)	Q(–II)	Q(–III)
Import coefficients			0.58		0.32	0.08	0.02
Income coefficients			0.97		0.53	0.13	0.04

^²Deduction has been made for reparations received (3 million guilders for 1949; 8 million guilders for 1950).

^³MO for 1949, and related figures, may not be exactly comparable with figures for subsequent years.

^⁴Based on estimated GNP for 1958 of 36,070 million guilders.

New Zealand ¹

^²For year beginning April 1.

^³Y for 1948 and 1949, and related figures, may not be exactly comparable with figures for subsequent years.

^⁴For calculating M/Y and M_A, average income for the calendar year is estimated from the April 1 data by interpolation. For calculating Y/MO and V, income for the end of a calendar year is assumed to be the same as the annual rate for the year beginning the previous April.

^⁵Based on estimated Y for 1958 of 1,118 million New Zealand pounds.

NETHERLANDS

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

NEW ZEALAND

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

Nicaragua ¹

^¹For description of symbols, see text. The table is based on data from International Monetary Fund, Balance of Payments Yearbooks and International Financial Statistics (IFS). Except for ratios, figures are in millions of cordobas. Balance of payments data, which were reported to the Fund in U.S. dollars, have been converted at the following rates (in cordobas per dollar): 1949, 5.04; 1950, 6.20 for commodity imports, 5.00 for net foreign loans, and 7.00 for services; 1951, 7.20 for commodity imports, 5.00 for drawings on loans, and 7.00 for services; 1952–54, 5.00 for government imports and drawings on foreign loans, and 7.00 for other imports (including imports by foreign companies) and service payments; 1955, 7.20 for commodity imports (excluding imports by foreign companies) from January to June and 7.00 for commodity imports from July to December, and 7.00 for imports by foreign companies, drawings on foreign loans, and services for the entire year; 1956–58, 7.00. ΔR is derived from IFS: foreign assets (line 20) minus prepayment for foreign exchange (line 25a) minus the 1955 revaluation profit of 30 million cftrdobae.

Norway¹

^²Deduction has been made for reparations received (15 million kroner for 1948; 21 million kroner for 1950).

^³MO for 1948 and 1949, and related figures, may not be exactly comparable with figures for subsequent years.

NICARAGUA

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

NORWAY

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

Peru ¹

^²MO for 1949, and related figures, may not be exactly comparable with figures for subsequent years.

Philippines ¹

PERU

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

PHILLIPINES

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

Portugal ¹

^¹For 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 escudos. Exports and imports are those of the metropolitan area only, including exports to and imports from the overseas territories. All services are counted as applying to the metropolitan area except those specified in the balance of payments as applying to the overseas territories. Services rendered to or paid for from the overseas territories are not included, no figures being available. All movements of official short-term assets and gold are applied to the metropolitan area. Insofar as any of these should be applied to overseas territories, results will be incorrect.

^²MO for 1949, and related figures, may not be exactly comparable with figures for subsequent years.

Sweden ¹

PORTUGAL

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

SWEDEN

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

Switzerland ¹

^²The balance of payments statements for 1949–54 give only net amounts for services; therefore, in computing X and M, net data have been used for the entire period, 1949–58, and X and M are accordingly understated.

^³National income.

Thailand ¹

SWITZERLAND

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

THAILAND

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

Union of South Africa ¹

^¹For description oi 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 South African pounds.

^²MO for 1948 and 1949, and related figures, may not be exactly comparable with figures for subsequent years.

^³National income for year ended June 30.

United Kingdom ¹

UNION OF SOUTH AFRICA

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

UNITED KINGDOM

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

Venezuela ¹

^¹For 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 bolivares. Balance of payments data were reported to the Fund in U.S. dollars; X and M have been converted at 3.35 bolívares per dollar, and ΔR at 3.06 bolívares per dollar for 1948–55 and 3.35 bolivares per dollar for 1956–58.

^²Y for 1949, and related figures, may not be exactly comparable with figures for subsequent years.

Venenzula

Citation: IMF Staff Papers 1960, 001; 10.5089/9781451949704.024.A003

Mr. Polak, Director of the Department of Research and Statistics, is a graduate of the University of Amsterdam. He was formerly a member of the League of Nations Secretariat, Economist at the Netherlands Embassy in Washington, and Economic Adviser at UNRRA. He is the author of An International Economic System and of several other books and numerous articles in economic journals.

Miss Boissonneault, economist in the Special Studies Division, is a graduate of George Washington University.

J. J. Polak, “Monetary Analysis of Income Formation and Payments Problems,” Staff Papers, Vol. VI (1957–58), pp. 1–50, hereinafter referred to as the 1957 paper.

The authors acknowledge assistance and suggestions received from their colleagues in the Research and Statistics Department of the Fund, in particular from Hang-Sheng Cheng, Graeme Dorrance, J. Marcus Fleming, Poul Høst-Madsen, and John S. Smith.

Polak, op. cit., p. 18.

Capital movements were not allowed for separately in the 1957 paper.

In the 1957 paper, a lag of one income period of imports behind income was assumed. On reconsideration, there appears to be little justification for such an assumption. It is more plausible to suppose that expenditure on imports moves concurrently with expenditure on home production, which, in its receipts aspect, constitutes income.

Changes in a country’s net position vis-à-vis the International Monetary Fund (IMF) are not treated here as reserve movements. Rather, IMF drawings are considered as a capital inflow, offset, in its effect on income and money, by an equal contraction of domestic credit to the government.

In the country tables in Part II, the amount involved is indicated as M_c. Consideration has been given to a similar treatment of direct investment capital inflows and the corresponding imports of capital goods. In practice, information is rarely available to permit any distinction between the capital and the consumer goods imports of foreign companies; the figures that are available seem to indicate that, in most cases, consumer goods form the largest part of such imports. Consequently, except where the necessary figures are available, no deduction is made here for the imports of direct investment companies.

It should be noted that the distinction between capital movements and net domestic credit creation is often vague, or at least ambiguous, where the government is the borrower abroad and uses the proceeds of the sale of the foreign exchange to reduce its indebtedness at home. In such instances it may be useful, in future work, to present the data with a subdivision between private and government, as follows:

This coefficient was labeled “x” in the original paper, but on reconsideration the symbol “ν” seems simpler.

In Table 2, Q (0), Q (–I), etc., refer to the annual values of the Q’s, as in the 1957 paper.

This particular property of the coefficients can be derived from the simplified mathematical expression for them given in Table 2. The coefficients contain only two elements: mν and ${(\frac{1}{1 + m})}^{ν}$ . It is obvious that the first of these two is invariant to changes in m and ν that keep mν constant. The second element may be written as ${(1 + m)}^{- ν} \equiv {(\frac{1}{1 + m})}^{- nν}$ when n = 1. The limiting value of this expression for n → ∞ is e^–mv, which again contains only the product of m and ν. For a wide range of values of m and ν, the difference between the expression for n = 1 and n → ∞ is small, as shown by the following tabulation for extreme values. The effect of moderate increases in n is of course even smaller.

In a few cases where the residual was large, the coefficients for earlier years were calculated and the whole calculation was pushed one or two years further back. The short formula indicated in the 1957 paper (p. 50) was not used.

It is also conceivable that in some countries a proportion of the total stock of money is, in one way or another, immobilized in the hands of a group of the population that does not actively participate in the fluctuations in income, so that the marginal adjustment of money to income is systematically smaller than the average ratio; however, no clear evidence of this was found.

Defined in this way, a positive value for V(t) indicates that it is an expansionary factor.

It will readily be seen that the two versions,

$Δ Y (t) = \frac{1}{2} [Y (t + 1) - Y (t - 1)]$

and

$Δ Y (t) = \frac{1}{2} [Y (t + 1) + Y (t)] - \frac{1}{2} [Y (t) + Y (t - 1)]$

are identical.

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IMF Staff papers: Volume 7 No. 3

Author:

International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1960: Issue 001

Publisher:: International Monetary Fund

ISBN:: 9781451949704

ISSN:: 1020-7635

Pages:: 145

DOI:: https://doi.org/10.5089/9781451949704.024

Keywords
I. Theoretical Problems Raised by Application of the Model to Country Data
II. Application to Country Data
- 1. Selection of countries
- 2. Application to a sample country

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Chart 1.

Norway: Marginal and Average Import Relationships ¹

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Chart 2.

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

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Chart 3.

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

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Chart 4.

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

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AUSTRALIA

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AUSTRIA

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BELGIUM - LUXEMBOURG

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BURMA

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CANADA

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CEYLON

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COLOMBIA

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COSTA RICA

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CUBA

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DENMARK

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DOMINICAN REPUBLIC

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ECUADOR

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EGYPT

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EL SALVADOR

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ETHIOPIA

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FINLAND

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FRANCE

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FEDERAL REPUBLIC OF GERMANY

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GUATEMALA

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HONDURAS

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INDIA

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IRAQ

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IRELAND

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ITALY

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JAPAN

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MEXICO

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NETHERLANDS

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NEW ZEALAND

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NICARAGUA

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NORWAY

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PERU

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PHILLIPINES

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PORTUGAL

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SWEDEN

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SWITZERLAND

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THAILAND

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UNION OF SOUTH AFRICA

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UNITED KINGDOM

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Venenzula

		X = Export Receipts	C = Capital Movements
		M = Import Payments	ΔR = Change in Reserves
				Credit	Debit
Merchandise				X	M
Nonmonetary gold				X	M
Investment income				X	–X
Freight and insurance on imports recorded c.i.f.				–M	(no entry)
Other services plus private donations				X	M
Government donations
	Reparations			–M	–X
	Project			–M	C
	Other			C	C
Net errors and omissions				C or X	C or M
Private capital
	Project loan liabilities financing imports			–M	C
	Assets and other liabilities			C	C
Official and banking capital plus monetary gold
	Project loan liabilities financing imports			–M	C
	Long-term assets and other long-term liabilities			C	C
	Gold payments and short-term liabilities to IMF			C	C
	Short-term assets and other monetary gold and short-term liabilities			ΔR	ΔR

		X = Export Receipts	C = Capital Movements
		M = Import Payments	ΔR = Change in Reserves
				Credit	Debit
Merchandise				X	M
Nonmonetary gold				X	M
Investment income				X	–X
Freight and insurance on imports recorded c.i.f.				–M	(no entry)
Other services plus private donations				X	M
Government donations
	Reparations			–M	–X
	Project			–M	C
	Other			C	C
Net errors and omissions				C or X	C or M
Private capital
	Project loan liabilities financing imports			–M	C
	Assets and other liabilities			C	C
Official and banking capital plus monetary gold
	Project loan liabilities financing imports			–M	C
	Long-term assets and other long-term liabilities			C	C
	Gold payments and short-term liabilities to IMF			C	C
	Short-term assets and other monetary gold and short-term liabilities			ΔR	ΔR

Coefficient for	One Period Lag in Import Equation¹	No Lag in Import Equation¹
Q(0)	$\frac{1}{mυ} [mυ - (1 - s^{υ})]$	$\frac{1}{mυ} [mυ - (1 - r^{υ})]$
Q(–I)	$\frac{1}{mυ} \cdot {(1 - s^{υ})}^{2}$	$\frac{1}{mυ} \cdot {(1 - r^{υ})}^{2}$
Q(–II)	$\frac{1}{mυ} \cdot s^{υ} {(1 - s^{υ})}^{2}$	$\frac{1}{mυ} \cdot r^{υ} {(1 - r^{υ})}^{2}$
Q(–III)	$\frac{1}{mυ} \cdot s^{2 υ} {(1 - s^{υ})}^{2}$	$\frac{1}{mυ} \cdot r^{2 υ} {(1 - r^{υ})}^{2}$

Coefficient for	One Period Lag in Import Equation¹	No Lag in Import Equation¹
Q(0)	$\frac{1}{mυ} [mυ - (1 - s^{υ})]$	$\frac{1}{mυ} [mυ - (1 - r^{υ})]$
Q(–I)	$\frac{1}{mυ} \cdot {(1 - s^{υ})}^{2}$	$\frac{1}{mυ} \cdot {(1 - r^{υ})}^{2}$
Q(–II)	$\frac{1}{mυ} \cdot s^{υ} {(1 - s^{υ})}^{2}$	$\frac{1}{mυ} \cdot r^{υ} {(1 - r^{υ})}^{2}$
Q(–III)	$\frac{1}{mυ} \cdot s^{2 υ} {(1 - s^{υ})}^{2}$	$\frac{1}{mυ} \cdot r^{2 υ} {(1 - r^{υ})}^{2}$

X	Export receipts
C	Capital movements (net capital imports)
M	Import payments
M_o	Deductions from imports for “project loan” drawings (includes generally loans by the International Bank for Reconstruction and Development and the Export-Import Bank of Washington, but only those parts of the loans which are estimated to have financed imports that would not otherwise have taken place)
ΔR	Net changes in foreign assets of the banking system
MO	Money
ΔD	Changes in domestic assets of the banking system (domestic credit expansion)
Y	Income—GNP where available, national income in other cases
Q	X+C +ΔD
M/Y	Ratio of imports to income, expressed as a percentage
Y/MO	Ratio of income (estimated, end of year) to money
m	Average propensity to import
m’	Marginal propensity to import
ν	Average income velocity
k	$\frac{1}{ν}$
$\tilde{M}$	Constant in the import equation
M_A	Autonomous imports
V	The effect of velocity changes on money
M^*	The result of applying the import coefficients to the Q’s (Computed Imports)
Y^*	The result of applying the income coefficients to the Q’s (Computed Income)
M_A effect (on income, imports)
	The result of applying the (income, import) coefficients to the M_A series (with signs reversed)
V effect (on income, imports)
	The result of applying the (income, import) coefficients to the V series

	m =0.1		m =0.5
	ν=2	ν=8	ν=2	ν=8
(1+m)^–ν	0.827	0.467	0.444	0.039
e^-mν	0.819	0.449	0.368	0.018

	1949	1950	1951	1952	1953	1954	1955	1956	1957	1958
X	540	717	918	777	922	772	819	882	1,043	801
C	130	124	125	179	–27	65	135	156	113	181
M	581	764	1,184	968	751	942	1,091	985	990	1,055
ΔR	119	77	–91	–12	144	–105	–137	53	166	–73
MO	1,000	1,254	1,422	1,374	1,538	1,582	1,620	1,603	1,677	1,633
ΔMO	156	254	168	–48	164	44	38	–17	74	–44
ΔD	37	177	259	–36	20	149	175	–70	–92	29
Y ²	2,200³	2,670	3,575	3,809	4,167	4,487	4,842	5,235	5,667	5,770
Q	707	1,018	1,302	920	915	986	1,129	968	1,064	1,011
M/Y ⁴	22.6	24.5	30.7	24.3	17.4	20.2	21.7	18.1	17.3	17.8
Y/MO ⁴	2.67	2.85	2.68	3.03	2.92	3.06	3.23	3.54	3.44	3.74
–M_A ⁴	–32	–99	–348	–120	170	51	–18	176	228	210
V ⁴	–86	–105	118	122	–54	60	74	141	63	77
	(1) M = 0.213Y (1950–58)				(2) Y = 3.2MO (1950–57)
		Q(0)		Q(–I)	Q(–II)	Q(–III)		Q(–IV)
Income coefficients		0.32		0.31	0.17	0.10		0.10
Import coefficients		1.51		1.41	0.80	0.44		0.53

	1949	1950	1951	1952	1953	1954	1955	1956	1957	1958
X	540	717	918	777	922	772	819	882	1,043	801
C	130	124	125	179	–27	65	135	156	113	181
M	581	764	1,184	968	751	942	1,091	985	990	1,055
ΔR	119	77	–91	–12	144	–105	–137	53	166	–73
MO	1,000	1,254	1,422	1,374	1,538	1,582	1,620	1,603	1,677	1,633
ΔMO	156	254	168	–48	164	44	38	–17	74	–44
ΔD	37	177	259	–36	20	149	175	–70	–92	29
Y ²	2,200³	2,670	3,575	3,809	4,167	4,487	4,842	5,235	5,667	5,770
Q	707	1,018	1,302	920	915	986	1,129	968	1,064	1,011
M/Y ⁴	22.6	24.5	30.7	24.3	17.4	20.2	21.7	18.1	17.3	17.8
Y/MO ⁴	2.67	2.85	2.68	3.03	2.92	3.06	3.23	3.54	3.44	3.74
–M_A ⁴	–32	–99	–348	–120	170	51	–18	176	228	210
V ⁴	–86	–105	118	122	–54	60	74	141	63	77
	(1) M = 0.213Y (1950–58)				(2) Y = 3.2MO (1950–57)
		Q(0)		Q(–I)	Q(–II)	Q(–III)		Q(–IV)
Income coefficients		0.32		0.31	0.17	0.10		0.10
Import coefficients		1.51		1.41	0.80	0.44		0.53

	1950	1951	1952	1953	1954	1955	1956	1957	1958
X	7,776	11,829	12,953	16,591	20,517	22,630	28,176	32,926	32,139
C	2,587	4,427	3,637	689	925	1,509	374	1,345	2,664
M	10,090	15,046	15,074	14,599	18,712	25,522	27,280	81,793	30,521
M_o	0	0	0	0	0	192	673	869	273
ΔR	273	710	1,516	2,681	2,730	–1,383	1,321	2,478	4,282
MO ²	13,940	16,720	18,260	22,340	28,260	28,610	29,710	32,100	35,560
ΔMO	1,660	2,780	1,540	4,080	6,920	350	1,100	2,390	3,460
ΔD	1,377	2,070	24	1,399	3,190	1,733	–220	–88	–822
Y ²	49,600	66,400	76,800	77,600	87,500	100,400 ]	110,600	121,800	128,900
Q	11,740	17,826	16,614	18,679	24,632	25,872	28,330	34,183	33,981
M/Y	20.8	22.7	19.6	18.8	21.4	25.4	24.6	26.1	23.7
Y/MO	4.16	4.28	4.23	3.70	3.32	3.69	3.91	3.90	….
–M_A	–202	–454	2,430	8,129	1,788	–1,410	–262	–1,652	1,571
V	1,716	702	–106	–2,710	–3,002	2,607	1,639	–48	….
	(1) M = 0.28Y — 4,000		(2) Y = 3.90MO (1950–56)
	Q(0)	Q(–I)	Q(–II)		Q(–III)	Q(–IV)	Q(–V)
Import coefficients	0.43	0.35	0.13		0.05	0.02	0.02
Income coefficients	1.55	1.25	0.46		0.18	0.07	0.06

	1950	1951	1952	1953	1954	1955	1956	1957	1958
X	7,776	11,829	12,953	16,591	20,517	22,630	28,176	32,926	32,139
C	2,587	4,427	3,637	689	925	1,509	374	1,345	2,664
M	10,090	15,046	15,074	14,599	18,712	25,522	27,280	81,793	30,521
M_o	0	0	0	0	0	192	673	869	273
ΔR	273	710	1,516	2,681	2,730	–1,383	1,321	2,478	4,282
MO ²	13,940	16,720	18,260	22,340	28,260	28,610	29,710	32,100	35,560
ΔMO	1,660	2,780	1,540	4,080	6,920	350	1,100	2,390	3,460
ΔD	1,377	2,070	24	1,399	3,190	1,733	–220	–88	–822
Y ²	49,600	66,400	76,800	77,600	87,500	100,400 ]	110,600	121,800	128,900
Q	11,740	17,826	16,614	18,679	24,632	25,872	28,330	34,183	33,981
M/Y	20.8	22.7	19.6	18.8	21.4	25.4	24.6	26.1	23.7
Y/MO	4.16	4.28	4.23	3.70	3.32	3.69	3.91	3.90	….
–M_A	–202	–454	2,430	8,129	1,788	–1,410	–262	–1,652	1,571
V	1,716	702	–106	–2,710	–3,002	2,607	1,639	–48	….
	(1) M = 0.28Y — 4,000		(2) Y = 3.90MO (1950–56)
	Q(0)	Q(–I)	Q(–II)		Q(–III)	Q(–IV)	Q(–V)
Import coefficients	0.43	0.35	0.13		0.05	0.02	0.02
Income coefficients	1.55	1.25	0.46		0.18	0.07	0.06

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Abstract

I. Theoretical Problems Raised by Application of the Model to Country Data

1. The simple system

2. Balance of payments data

Export receipts

Import payments

Capital movements

Reserve movements

3. Monetary data

4. The coefficients

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

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

Changes in income velocity

Discrepancies in import equation

Expansion of the model

II. Application to Country Data

1. Selection of countries

2. Application to a sample country

Same Series

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