2. Monetary Analysis of Income Formation and Payments Problems
Author: J. J. Polak1
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund


THE PURPOSE OF THIS PAPER is to bring monetary events, monetary data, and monetary problems within the framework of income analysis, and thereby to bridge the gap between (1) the views widely held on the relation between financial policies and payments questions and (2) the analytical tools used to explain payments developments. Broadly, payments problems are associated with inflationary causes; and moderation in credit expansion is generally prescribed as a preventive or a curative of payments difficulties. But since existing analytical studies rarely succeed in integrating monetary and credit factors in the explanation of income or of payments developments, an adequate theoretical basis—in particular, a quantitative basis—for these conclusions seems to be lacking.

THE PURPOSE OF THIS PAPER is to bring monetary events, monetary data, and monetary problems within the framework of income analysis, and thereby to bridge the gap between (1) the views widely held on the relation between financial policies and payments questions and (2) the analytical tools used to explain payments developments. Broadly, payments problems are associated with inflationary causes; and moderation in credit expansion is generally prescribed as a preventive or a curative of payments difficulties. But since existing analytical studies rarely succeed in integrating monetary and credit factors in the explanation of income or of payments developments, an adequate theoretical basis—in particular, a quantitative basis—for these conclusions seems to be lacking.

The failure to accommodate monetary factors in the analysis probably becomes most evident when questions are raised concerning the effects of specified monetary changes on income or on the balance of payments. Questions like the following will typically go begging, not merely an answer, but even a method to arrive at an answer. What would be the effect of a credit expansion of 10 million pesos in country A? The money supply in country B has increased by x per cent during the last year; is this, or is it not, too much from the point of view of the balance of payments or from that of internal balance? Country C prescribes that bank credit may not expand by more than 2 per cent per month; what is the relevance of such a percentage?

The embarrassing inability to handle such questions contrasts strikingly with the ease with which nonmonetary problems are approached in income analysis. Every graduate in economics knows how to compute the effect of a given increase in investment on income, imports, etc. Allow him a few hours to estimate the required propensities—to save, to import, to pay taxes, etc.—and he can provide the answer.

But the customary income analysis cannot handle monetary questions. Even where it is pushed to a considerable degree of refinement, it not infrequently omits monetary factors altogether. Thus the system of equations underlying the Central Economic Plan for the Netherlands1—supposedly a tool of economic analysis to guide economic policy in a country relying importantly on monetary instruments—does not refer to money or any similar variable in any of its 27 equations with 55 economic variables.

The tools used in the economic analysis of particular situations are necessarily simplifications of a more general economic theory—simplifications which bring into focus the factors that seem most important in the classes of situation studied. The multiplier analysis was a simplification that seemed particularly appropriate to the developed countries in the depression conditions of the 1930’s when the demand for money was highly elastic. This particular simplification is much less useful in dealing with developed economies that are on the verge of inflation; or with economies, such as those of most of the less developed countries, where money is kept almost exclusively for transactions purposes and its demand is not very elastic; or with countries, developed or less developed, which rely to a considerable extent on monetary policy to guide their economies.

To find a more suitable simplification it is necessary to go back to a more general body of theory and make it serviceable for the situations now being considered. Keynes’ General Theory2 provides an adequately integrated theory of income (employment) and money. But while the part of the theory dealing with income has been given a form suitable for economic analysis, the monetary part has seemed to be less tractable to such treatment and—the excess liquidity of the 1930’s helping—has stayed in the limbo of classroom and journal discussions.

Perhaps the failure to develop empirical monetary analysis on the basis of the General Theory is less surprising than the fact that an empirical income analysis was developed from it. Surely, anyone who took seriously all of Keynes’ objective (six) and subjective (eight plus four) factors affecting the propensity to consume, together with their variability over time, would shrink from thinking of this propensity as something even approaching a statistical constant (which, of course, Keynes never suggested it was).3 But empirical economics, taking its cue from Kahn’s4 earlier dynamic multiplier approach, has tended to sweep away doubts and fears of this nature, at least “as a first approximation,” and has managed to turn Keynes’ formal multiplier into a usable tool of analysis and policy. It has gone one step further and substituted for his marginal efficiency of capital—that ragbag of psychology, uncertainties, and expectations—the elegance of a “marginal propensity to invest.”5

A somewhat similar streamlining of the monetary side of the analysis is attempted here. Our starting point is that income equals the quantity of money times the income velocity of money. This is nothing but an identity, like the statement that income equals consumption plus investment. But if meaningful propositions about money and about the velocity of money can be found, it may be possible, via this definition, to come to meaningful propositions about income.

Far too little work has been done on the factors that explain changes in the velocity of circulation of money to permit here a treatment of this subject that could be considered at all satisfactory. Readily available statistics for a large number of countries are presented in Appendix I, Table 3. They are based on end-of-year figures for money supply divided by national income for the corresponding year; a more refined analysis would probably be based on monthly or quarterly data for money supply. The annual data show considerable evidence of year-to-year stability or of a tendency for movements in one year to be subsequently reversed.

As shown in Chart 1, the ratio of money to income in 1954 was very close to that in 1950 in a number of countries where there were large changes in the money supply—such as Brazil, Burma, Chile, Ecuador, Japan, New Zealand, Thailand (1953). The chart also shows that the changes in the ratio of money to income are usually much smaller than those in the money supply itself. In the years covered, the most notable exceptions were Canada, the Philippines, and the United Kingdom—where the money supply itself changed very little—and Israel, where a large rise in the money supply was supported by an even larger increase in its velocity.

Chart 1.
Chart 1.
Chart 1.
Chart 1.
Chart 1.

Fluctuations in Money Supply(MO)and in the Ratio of Money to Income(MO/Y)in 44 Countries, 1950-54

(Logarithmic vertical scale)

These crude empirical observations on the money-income ratio could not support the proposition that the income velocity of money is a constant under all circumstances, a proposition that would in any case be meaningless; but they are sufficient to suggest that the assumption of a constant ratio of money to income may be a worthwhile step in a monetary theory of income formation, and that it might be profitable to investigate the full consequences of this assumption. That is what is done in Parts I-IV of this paper.

There are further grounds for the separate treatment of the quantity of money and its velocity. In the first place, it is quite plausible to assume that people adjust their holdings of money in proportion to changes in monetary transactions,6 of which, in the relatively short run, national income (or gross national product) is a suitable indicator.7 Secondly, it is relevant to note that the monetary authorities in many countries base their policy on the assumption that the income velocity is approximately constant. Lastly, it is probably possible to isolate at least some of the factors that determine such fluctuations in velocity as occur. A very provisional discussion of these factors is given below in Part V.

Two general points should be made at this stage. First, it might be thought that piling a “propensity to hold money” on top of all sorts of other propensities would result in compounding one set of dubious assumptions with another. But, as will be shown, this turns out not to be so. The introduction of the constant ratio of money to income means eo ipso the discarding of the propensities to save, consume, and invest. There is, in this respect, a real and perhaps unexpected gain in simplicity. Secondly, it might be asked whether, in the assumptions made about money, the Quantity Theory of Money does not rear its barely disguised head? That question will be considered later. Suffice it to say at this stage, first, that the monster was never really slain;8 and, second, that once it has been properly tied to income analysis it appears to be not only harmless but indeed quite useful.

It will be found that the analysis that deals with monetary factors also has to incorporate, as autonomous causes, changes in exports and in import restrictions. The conclusions of this paper deal, therefore, with these subjects as well as with the effects of credit expansion by the monetary system. This credit expansion is distinguished sharply from that by other institutions whose liabilities are of a nonmonetary character. The conclusions may be summarized as follows:

On the assumption of a constant velocity of circulation and a number of other simplifications specified in the text:

  • I A. A lasting increase in exports9 will, by itself, i.e., without credit expansion or relaxation of import restrictions, gradually bring about

    • (1) the same percentage increase in the rate of money national income;

    • (2) an increase in the rate of imports equal to the increase in the rate of exports;

    • (3) an increase in the quantity of money and in foreign assets of the order—depending on the country concerned—of 50 to 300 per cent of the increase in the annual rate of exports.

  • B. A lasting increase in the rate of credit expansion by the monetary system will, by itself, gradually bring about

    • (1) the same increase in the rate of money income and of the stock of money as would be produced by a lasting increase in exports of the same size;

    • (2) an increase in the rate of imports equal to the increase in the rate of credit expansion;

    • (3) a rate of loss in reserves that will approach the rate of credit expansion;

    • (4) a total loss in reserves equal to the cumulative credit expansion minus the increase in the quantity of money indicated in I A (3).

  • II A. A temporary increase in exports will, by itself, bring about

    • (1) a temporary increase in money income which, aggregated over all periods, will be of the same proportional size as the increase in exports;

    • (2) a temporary increase in imports which, aggregated over all periods, will be of the same absolute size as the increase in exports;

    • (3) a temporary increase in money and reserves.

  • B. A temporary expansion of credit (terminated, but not reversed, after the end of, say, one year) will, by itself, bring about

    • (1) a temporary increase in money income and the stock of money;

    • (2) a temporary increase in imports and a permanent reduction of reserves equal in size to the credit expansion.

The same relationships determine the size of the expansion of credit by the monetary system that can safely be permitted on the basis of a permanent increase in exports. This varies from virtually none for some small countries with a low ratio of money to imports to four or five times the increase in exports for large countries with a high ratio of money to imports.

Changes in velocity attributable to two sets of causes are discussed in Part V. First, the velocity of circulation may oscillate in response to a sudden large influx or efflux of money. Temporary fluctuations in velocity that are due to such causes do not affect the conclusions, except as far as their timing is concerned. The conclusions are affected, however, by changes in velocity in response to changes in the rate of interest, which occur primarily in the more developed countries. The variability of money holdings in these countries in response to changes in the rate of interest implies the necessity of greater intensity of credit policy than would be needed in most of the less developed countries in order to obtain a given change in money income.

I. Income and Money

The circular flow of income

On the assumption of a constant ratio of income to money, the income process may be pictured as a circular flow in which the stock of money and the flow of income are uniquely related by proportionality, in much the same way as the quantity of water in a closed set of circuits would be related to the recordings on a flow meter set anywhere in these circuits.

The circular character of the income stream implies that the stream feeds on itself. There are qualifications to this, but they do not destroy the main proposition, viz., that income in one period is the main determinant of income in the next period. The process from income in period 1 to income in period 2 may run through different channels. Most income will accrue to consumer households, be spent on consumption goods, and reappear as new income in the form of payments to the factors of production in the consumption goods industry. Other income may find its way to reincarnation through taxes and government purchases of goods and services. A third section of income may run through the capital market, or through savings banks; or it may not change owners at all, as when business profits are ploughed back into selffinanced investment.

Rather than concentrating on the circular character of the income flow, the multiplier analysis has put its main emphasis on the lapses from circularity, in particular for new additions to the stream. It has stressed that, on its way around, some income may get lost, never to show its face again as new income. Some savings by consumers may never be invested by anyone else. Some of the tax money paid to the government may be saved by it forever—e.g., in the form of repayment of the public debt—or at least for a long time. Corporations may withhold profits from shareholders without having any short-run plans to use the money for expansion of capacity. The various propensities in the multiplier analysis are designed to account for these “leakages” from the main stream. Since the multiplier analysis is typically non-monetary (or perhaps we should say a-monetary) in character, it is of no consequence to it whether any shrinkage recorded in the income flow is due to a reduction in the velocity of circulation of a given quantity of money or to a reduction in the quantity of money at unchanged velocity.

By focusing on the monetary side of the same circular process, we can approach the problem from another angle, which makes it more tractable in many situations. The assumption of a constant ratio of income to money obviously implies that the income stream cannot change except as the quantity of money changes. If, therefore, we can explain changes in the quantity of money, we would have a satisfactory explanation of income by means of a monetary analysis.

In contemporary economic analysis, as distinguished from economic theory, there is no lack of “explanations” of changes in the quantity of money. “Money” is an entry, or a combination of entries, on the liability side of the balance sheets of the banking system. Since balance sheets are constructed on the principle that the sum of all assets equals the sum of all liabilities, it is always possible to “explain” the changes in one balance sheet item by adding together (with appropriate signs) the changes in all other balance sheet items. Since the item called “money” represents in many countries a very large proportion of all liabilities of the banking system, one can usually come close to an “explanation” of the changes in money by adding the changes in the asset items in the balance sheet.

In the studies of the “origin of the money supply” that are prevalent in Latin America,10 this process of “explanation” is formalized to the point of designating the quantity of money that is equal to the (net) foreign assets of the banking system as “money of external origin” and the quantity of money that is equal to the domestic assets of the system as “money of internal origin.”11

We shall follow this analysis in its simplification, viz., that changes in the quantity of money equal changes in (net) foreign assets of the banking system plus changes in domestic credits of the banking system. Thus, for reasons discussed in more detail below,12 the changes in other liabilities of the banking system are disregarded. But accepting then the statistical identity, what explanatory value does it have?

The assumption of a constant ratio of income to money constitutes in itself an economic explanation of changes in the quantity of money; it implies that money changes proportionally to changes in income. There is no general presumption that the “explanations” based on balance sheet identities contribute any meaningful additional information to the explanation of money and income. Whether they do or not depends on whether they reduce the changes in money to other variables that may themselves usefully be considered as autonomous variables—variables beyond which economic explanations do not in the particular situation want to probe. This question will be considered separately for (1) the purchase of domestic assets and (2) the purchase of foreign assets; and it will be found that, both from an analytical and from a policy point of view, (1) is a useful stopping point of the analysis, while (2) is not.

Domestic credit creation

The decision to treat domestic credit expansion as an autonomous variable is dictated by the purposes of our analysis. To be able to integrate monetary analysis into income analysis, to study the effects of credit policy on income and the payments situation, credit creation must be accepted as an ultimate variable, not to be explained away further in terms of such variables as the desire to invest or the willingness to save.

This treatment of domestic credit expansion might not be reasonable in a purely descriptive, historical study which could, and perhaps Such a study might, for instance, find that in a certain country bank credit tended to be expanded particularly rapidly after export income or exchange reserves had increased. But from the vantage point of the monetary authorities—and the same holds for the International Monetary Fund—a different approach is the more reasonable one. Credit expansion is subject to the responsibility of the banking system. It may be difficult, perhaps in some circumstances humanly impossible, for the system to withstand demands for credit from the government or from other insistent borrowers; and in such circumstances, the desire to make public development expenditure, or to construct private factories, may be considered, from many points of view, the cause of the expansion in the economy. But for purposes of monetary analysis and monetary policy there is a clear gain in clarity if the responsibility is pinpointed on the credit expansion. The economic development could also have been financed by higher taxes or by a foreign loan. The factories might have been built by restriction of consumption or by the repatriation of capital. In all these situations, the desire to spend for a particular purpose would not have led to a payments problem. In a real sense, the credit expansion is the cause of the payments problem.13

As statistically measured, credit expansion is a net concept, the difference between credit outstanding at the end and at the beginning of a period. Part of the repayments that occur during a period may be caused by new loans granted during this or a preceding period. To what extent, then, can the net credit extension be considered as autonomous?

The answer is that credit policy over any but the shortest period of time is essentially a net operation. Some of the bank loans are repaid every day, and new ones are granted every day. The effect of a particular credit policy can therefore be measured correctly on a net basis only. The use of net credit expansion as an exogenous factor makes it necessary to distinguish between the credit granted for one particular large project and net credit expansion during a period. The distinction is particularly important in those cases where the increase in income that results from credit expansion will lead to substantially higher tax receipts by the government and, as a result, a reduction of government borrowing from the banking system. This does not affect the analysis insofar as it deals with an interpretation of the past; credit expansion to business will be found to be offset by a reduction in net credit to the government. But with respect to policy for the future, any “leak” of purchasing power owing to increased tax receipts will have to be taken into account.

Foreign trade

The suitability of the foreign balance as an autonomous factor has been discussed considerably in the framework of multiplier theory; and, insofar as economic questions ever get resolved, this one appears to have been resolved rather definitely in the negative.14 The foreign balance has been ruled out as a suitable multiplicand, primarily because it fails to use the worthwhile empirical observation that fluctuations in imports are to a large extent determined by fluctuations in income. Accordingly, a useful model should include the various elements of the balance of payments—especially exports and imports—separately, rather than only their net effects on reserves.

Next to credit creation, exports are the main source—and normally much larger in size—of continuous injections of new income into the circular flow. The sale of goods or services abroad continually captures income from abroad and naturalizes it as income of the factors of production engaged in the export industry. Broadly speaking, this stream of new income tends, of course, to be offset by an outgoing income stream reflecting imports, where incomes are paid out to become the incomes of foreigners and, thereafter, to circulate mostly in their income streams. In a situation of balance of payments equilibrium (on goods and services account, to be precise), the income additions from exports will match exactly the income subtractions from imports and the circular flow of income is not changed—from the point of view of static analysis—by the fact that, through exports and imports, it is linked to a wider set of national flows.

A dynamic analysis has to make allowance, however, for the changes in the income stream that may arise from the export and import sides. On both sides, there may be either autonomous or induced changes. Autonomous changes find their origin outside the domestic income stream itself but the causes may be foreign or domestic. Thus a country’s exports may change because foreign income changes, or foreign import restrictions are adjusted, or a new export industry is established in the country. Imports may change because of changes in the country’s own tariff policy or consumer preferences. All these would be autonomous changes. They could be either stabilizing or destabilizing with respect to domestic income, depending on the rate of income with which they happen to coincide. An autonomous fall in exports would be stabilizing in a period of inflation, destabilizing in a period of internal deflation.

Induced changes in exports or imports respond to changes in the domestic income stream and are always stabilizing. When internal demand falls, the resulting decline in prices may produce some offsetting increase in exports. When income rises, imports will tend to increase too, thus channeling some of the higher income abroad and bringing the level of income in the next period closer to normal. Conversely, when there is an autonomous contraction of income, imports are likely to fall, thus transmitting some of the contraction abroad and mitigating, correspondingly, the contraction of income at home. Imports perform the income-stabilizing function most strongly when the income elasticity of demand is high, so that a relatively large proportion of a high national income flows off abroad, while a large proportion of smaller income is kept within the domestic income flow.

Empirically, for most countries at most times, autonomous changes tend to dominate exports, while induced changes account for most of the variations in imports. The following analysis will for simplicity assume that these observations hold not merely as empirical generalizations, but rigidly. This simplification is justified also because—if one does not forget its nature—it does not entail a loss in generality of the conclusions. For at the level of abstraction at which we operate, an autonomous increase in imports is equivalent in effect to an autonomous decline in exports; and any marginal effect of income (or domestic prices) on exports may be allowed for, in numerical calculations, by a corresponding increase in the coefficient indicating the marginal effect of income (or domestic prices) on imports.15

In the simplified model used in this paper, it is assumed that exports minus imports equals changes in reserves. The whole array of other items—invisibles, capital items, transfers, and, most importantly, errors and omissions—which lie between the trade and the reserve items in the balance of payments is disregarded. For any practical application of the analysis it would, of course, be necessary to find a suitable way of assimilating each of these items with exports, imports, or reserve movements.

Credit, exports, and the income stream

When we speak of credit as an addition to the income stream, we pass over an intermediate stage, the purchase by the borrower of goods. If these goods are totally domestic goods, the increase in domestic income will be as large as the credit expansion. If they have an import component, the domestic income creation will be proportionally smaller. And if, as the marginal case, the import component is 100 per cent—if the investment financed by credit expansion is wholly in imported commodities or foreign exchange balances—the domestic income component vanishes and the credit expansion is fully absorbed by increased imports. In that case, we might say that potential income is lost fully by an autonomous increase in imports of equal size.

The same qualification holds with respect to exports. They, too, create domestic income only insofar as they do not represent imports. Where exports have a high import component, the income creation per dollar of exports is small; and where exports are merely re-exports, the domestic income component vanishes. An increase in exports would be matched by an autonomous increase in imports.

The assumption of a constant velocity of circulation eliminates another complication, viz., the extension of credit or the purchase by the banking system of existing domestic assets which does not lead to expenditures on goods and services by the borrower or seller of the assets. An operation of this nature would be equivalent to an increase in the quantity of money without an increase in income, i.e., a reduction in the velocity of circulation. So would a purchase by the banking system of existing foreign exchange holdings from the private sector. This is not to suggest that either of these transactions cannot occur, but that in our simplified system they have no place and, for that reason, may provisionally be left out of account.

II. The System

The economic model described in the previous section is extraordinarily simple. Its central relationship is that of the circular flow, with additions and subtractions as specified:

income of this period = income of the previous period

  • ⁺ new income resulting from internal credit creation

  • ⁺ new income resulting from exports

  • —income lost through imports.

Of the four variables in this equation, two—credit creation and exports—are considered exogenous in character. Only one more equation is needed (and possible), therefore, to tie the whole system into a complete package. That equation is the one explaining imports. The money value of imports is explained here in terms of the money value of income. This form of the import equation implies the assumption of a unit elasticity of demand for imports.16

The two equations together determine the development of the two endogenous variables, income and imports, as functions of the two autonomous variables, exports and credit creation.

The equations may be put in a slightly more rigorous mathematical form, by the use of the following symbols:

article image

The equations then read:


The expressions (t) and (t-1) indicate the timing of the variables in terms of unit periods that are equal to the income period of circulation of money. Imports in equation (2) are assumed to be lagged by one period.

Underlying the first relationship is the assumption of a constant velocity of circulation of money which links money to income by proportionality, as expressed by equation (3):


If this equation is combined with the definition of changes in the balance sheet


equation (1) is obtained.

This is another way of stating that the determination of income by a continuous circular flow, and the constancy of the velocity of circulation, are one and the same assumption. If the former is given up, e.g., by putting a coefficient (a marginal propensity to spend) that is different from unity before Y(t-1) on the right side of (1), then (3) can no longer be true. This does not mean that, in a system in which a true Keynesian spending equation is assumed to be present, the quantity of money cannot depend on the rate of income. It only means that in such a system there must be another variable, such as the rate of interest, entering in (1), in (3), or in both, to make separate spending and money holding equations possible.

If the marginal propensity to spend is written as c, the dependence of Y(t) on the rate of interest, r(t), as gr(t), and the dependence of money on the rate of interest as hr(t), then (1), (3), and (4) combine to


This determines the current rate of interest in terms of last period’s income and rate of interest. Either one of the interest terms can be omitted; but if both are absent, as in (1) and (3), it follows that, unless c equals 1, the velocity of circulation cannot be a constant.

While this model may seem so obvious as to be trite, it is not common property of economists. Nor do the conclusions that follow from the model appear to be common property.

III. The Effects of Changes in Exports and Credit Expansion

In our system there are two main autonomous variables—exports (which also do double duty for autonomous changes in imports) and credit expansion. In this part of the study, the effect of changes in these variables on income, imports, and the monetary system is analyzed.

First a lasting change, i.e., from one level of exports to a continued higher level, and from one annual rate of credit creation to a continued higher rate of credit creation, is studied. The results found are summarized in Chart 2 and Table 1.


For some reason outside the country, e.g., a rise in world market prices, exports increase by, say, 20 million at an annual rate. Income increases by the same amount. As a result, the demand for money increases. If the income velocity of circulation in this country is 4 times per year, the desired increase in the quantity of money will be 5 million. The additional exports provide the required additional money approximately at the rate at which it is required. There may be a temporary shortage of money if the exporters have to lay out money before they receive payment—e.g., to collect crops at higher prices or to hire additional workers. That situation will clear up soon, however; at the end of one income period of exports, enough money will have been received to continue business at the higher level. From here on, the extra earnings of the export industry can be spent and, under our assumptions, will be spent.

Chart 2.
Chart 2.

Effects of Lastino Increase in Exports (A) and in Credit Creation (B)

(Assumptions: m= H 0.20, a = 0.25)

Table 1.

Effect on Current Value of the Dependent Variables of Current and Past Values of the Independent Variable

article image
NOTE: For description of table, see pages 28-29.

Representing effect on dependent variable of a lasting increase in independent variable.

All coefficients carry the factor a on the assumption that exports and credit creation are expressed as annual rates.

Most of the additional expenditure is likely to be directed toward domestic goods and services, thus increasing money income in the country. If there is sufficient excess capacity and demand is directed toward the output of the industries that have excess capacity, the increase in money income may represent mainly, or even entirely, an increase in real income, prices rising little or not at all; if, on the other hand, there is no spare capacity, the rise in money income will merely represent a rise in prices. Part of the additional spending will be directed toward imports, stimulated by the higher real income (if production could expand), or by the rise in prices in the country as against the price level abroad (if there is no possibility of expansion of production), or by some combination of the two. It will be recalled that the effect on imports of a 1 per cent rise in real income has been assumed to be about the same as the effect of a 1 per cent rise in the domestic price level (on the assumption that prices abroad remain constant) ; hence, the fraction of an increase in income that is spent abroad may be taken to be independent of the extent to which the expansion in money income was a “real” or a “price” phenomenon.

Assume that under the particular circumstances the fraction spent abroad (the marginal propensity to import) is one fifth; then income in the second quarter will run at the quarterly rate of 9 million above the original level: 5 million exports plus 4 million induced home expenditure.

In order to have the required money to handle the extra business of 4 million a quarter, the economy as a whole will have to save 4 million during the quarter. Either the recipients of the 4 million additional income will have to wait before they increase their spending, or others will have to save money to the extent that the first group does increase its spending.

In the third quarter, however, income can rise another step, as the necessary savings of money to handle the second quarter rate of income have been made. Thus in the third quarter, assuming again one fifth of the new increase to be spent abroad, income will go to 12.2 million (5 + 4 + 3.2), where it will have to remain for another quarter.

This process continues until income approaches its equilibrium level of 25 million per quarter (100 million per year) higher than before. The final increase is related to the initial increase by a multiplier of 5, which is the inverse of the figure assumed for the marginal propensity to import (0.2). At the final rate of income, imports will be 20 million per year above their original level: they will have increased as much as exports. There will no longer be a balance of payments surplus, and the quantity of money will be constant. It can be constant only at its equilibrium level, where it equals one quarter’s income, or 25 million above its original level. Since no change in the domestic assets of the banking system has been assumed, the increase in the money supply must have been accompanied by an equally large accumulation of foreign exchange reserves.

Thus the 20 million increase in exports has had the following effects:

  • A. Income has gradually increased to a level 100 million higher. This level is determined by the increase in exports (20) and the assumed marginal propensity to import (0.20), viz., 200.20=100. If (a) the marginal propensity to import equals the average ratio of imports to income,19 and (b), initially, exports equal imports, then income in the new equilibrium position will have increased in the same proportion as exports.

  • B. Imports have gradually increased to a level that is higher by the same absolute amount as exports, i.e., 20 million. This finding does not depend on any numerical assumption; it follows from the qualitative assumption that, apart from the need for increased money, all additional income received is respent. Thus income will continue to rise until the export surplus is eliminated.

  • C. The quantity of money has gradually increased by 25 million. This increase is determined by the increase in income, as derived in A above, and the assumed ratio of money to annual income (0.25). If the increase in money is related to the increase in exports, it is found—again on the two assumptions suggested in A—that
  • D. Although there is no lasting improvement in the balance of payments, the fact that the adjustment of imports to the increase in exports is lagged does produce an increase in reserves. This increase must be equal to the increase in the quantity of money, since there is assumed to be no change in the third item in the balance sheets, domestic credit.

These findings give particular importance to a “new” ratio in economics, that between money and imports. This empirical ratio is used here as an indicator of the order of magnitude of the ratio of the (marginal) desire to hold money to the marginal propensity to import. This new ratio for 48 countries, together with the component ratios for 44 countries, is given in Table 2.

It is found that the ratio varies from about one half to three (leaving out of consideration the ratio of eleven for the United States). Both the component ratios show some tendency to rise with a country’s income level; but, for the ratio of money to imports itself, such a tendency, if it does exist, is not very obvious (see Appendix I).

The magnitude of the ratio makes a large difference in the reserves that a country will tend to accumulate as exports rise and also, as will be shown later, in the amount of credit it can safely create. For countries at the lower range of the scale of this ratio, an autonomous increase in exports would, by itself (i.e., if it were not accompanied by internal credit expansion), lead to an increase in money and reserves equal to something like one-half year’s additional exports; for countries at the other end, the increase would be closer to two or three years’ additional exports. For many countries with a ratio rather close to unity, the increase would be in the order of one year’s additional exports.

Lasting autonomous reduction in imports

As suggested above, the effects of an autonomous reduction in imports can be considered, on the level of abstraction on which we operate here, as equivalent to an increase in exports. This is true independently of the character of the measures that produce the reduction in imports: increased tariff, quantitative restrictions, or exchange depreciation. Given the immediate effects of these measures on imports, the ultimate effects may be expected to be the same as those derived in the preceding section for an increase in exports of the same size. There will be the same increases in income, money, and reserves over time. The resulting increase in induced imports—approaching in magnitude the autonomous reduction in imports—implies that measures to reduce imports do not have a lasting effect on the balance of payments. They do, however, have a lasting effect on the level of income; and their temporary effect on the balance of payments during the transition period may be of great importance in restoring a country’s reserve position.

Table 2.

Median Values, 1950-54, of Ratios of Money to Income (MO/Y), Imports to Income (M/Y), and Money to Imports (MO/M), by Countries1

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Figures have been derived from data in Appendix I, Table 3. For each country, the median of the 1950-54 values was selected for the ratio of money to imports; for the two other ratios, the figures were then taken for the same year.


Assume that credit expansion by the banking system, which in previous years had been zero, is brought to 5 million a year. It is assumed20 that the full 5 million is spent by the borrowers to pay out as income, e.g., in connection with investment activities or government deficit spending. The initial and the ultimate income effect is here the same as that of an increase in exports of the same magnitude. The effects on imports and money—both being related to income—are also the same. The effects on reserves, however, are totally different, as the negative effect of additional imports is not offset by a positive effect of increased exports. There will be a continuous loss of reserves, which will gradually build up to an annual rate equaling the injection of credit—the quantity of money approaching a constant.

In the transitional period while this equilibrium rate is being approached, however, the loss of reserves will be smaller than the total credit expansion by an amount which, on the basis of the figures for the money-import ratio used above,21 would be somewhere between six months’ and three years’ credit expansion, depending on the country. To that extent the additional income injected by credit expansion will have been saved in the form of money to handle the higher level of income; for the remainder of the credit expansion, the increase in domestic assets has been offset by a loss in foreign assets.

It follows from our system that, as income approaches the new equilibrium level, the quantity of money also approaches its corresponding equilibrium level, based on the specified ratio of money to income; no further condition is necessary to bring income and money in line. This also entails that no further additional condition on income and money is possible without disrupting the assumption of a constant velocity of money. On this account, the assumption made earlier that all credit expansion is spent is a necessary assumption.

Suppose, for a moment, that this assumption would not be fulfilled, and that those who borrow 5 a year systematically spend only 3, keeping the remainder as additional cash balances in anticipation of the needs of larger business. The multiplier process would then start with 3 instead of 5 as the multiplicand, and income would build up to 15 rather than 25. Money corresponding to an income of 15 would be added to the public’s holdings, but in addition borrowers would be putting aside an extra 2 every year. Thus after, say, five years, income would have risen by approximately 15, and money not by about 3.75, but by 3.75+ (5x2) =13.75. The marginal velocity of circulation over the five-year period would appear as slightly over 1, against a previous average of 4.

Thus the assumption of full spending of credit creation is a necessary corollary of the assumption of constancy of the velocity of circulation. This does not mean, of course, that it must be assumed that individual borrowers spend all their borrowings. But deviations of individuals in one direction must be offset by deviations of other individuals in the opposite direction if the basic assumption of a constant income-money ratio is to remain valid.

Discontinuous changes in autonomous variables

In view of the similarities found for the effects of lasting changes in different autonomous variables, the effects of a discontinuous change in these variables may be discussed briefly.

The effects follow simply from well-known multiplier propositions.22 A discontinuous autonomous increase in income (from exports, import restrictions, or credit expansion) will lead to a temporary expansion in income that will gradually subside. The aggregate increase in income, over time, will equal the autonomous increase divided by the marginal propensity to import. The quantity of money will first increase along with income, then decline to its original level. Aggregate imports over time will equal the value of the autonomous increase. If the autonomous factor is an increase in exports, or import reduction, reserves will first increase and then return to their original level; if it is credit expansion, reserves will decline over time by an amount equal to the credit expansion.

In arriving at this last conclusion, no account has been taken of the effect of an increase in one country’s imports on the income of the rest of the world and thereby on its own exports. It will easily be seen that the omission of this further refinement is of negligible significance for all countries except the United States. It is true that, if we adhere strictly to our assumptions, not all the money created by credit expansion in country A can flow out through additional imports. The outflow will stop when a new equilibrium situation is reached, in which the money supply of the rest of the world will have increased in the same proportion as in A. Country A will then have a slightly higher income than before the credit expansion and correspondingly higher imports, which will be offset by an equal increase in exports as income abroad is also slightly higher. Thus A would, in the end, not lose all of its credit creation in reserves, but a fraction less. The magnitude of this fraction would be the ratio of its money supply to the money supply of the whole world. For the United States, which has about 60 per cent of the world’s money supply, this correction is important. But next in order are the United Kingdom, which has only about 7 per cent of the world’s money supply, and France, which has 5 per cent. There are only a few other countries for which the correction would be as much as 2 per cent.23

Pattern of income, money, and imports over time

As shown in the preceding sections, the effect of each of the three autonomous factors on income, money, and imports is the same. Changes in each of these variables may therefore be understood as a function of the sum of changes in exports, in import restrictions (measured numerically as the amount of imports kept out by price, exchange rate, or prohibitive measures), and in credit expansion.

The effects of these autonomous variables are most conveniently derived from the findings on discontinuous changes. The patterns of exports, import restrictions, and credit expansion may be seen as a set of autonomous causes that vary discontinuously over time and whose fluctuations determine the rate of income and imports, stocks of money, and reserves at any moment of time. Income, money, and imports depend positively on the sum of the three variables, exports, import restrictions, and credit expansion.

Since the process of adjustment takes time, the fluctuations in income, imports, money, and reserves will lag behind those of the autonomous variables. Income during any period is thus a weighted average of the current and past values of the sums of the autonomous variables, with the sum of the weights equaling 1marginalpropensitytoimport. The value of imports is a weighted average of the current and past values of the sums of the autonomous variables, with the sum of the weights equal to 1. The magnitude in terms of years of the average lag of income and imports depends on the marginal propensity to import and on the velocity of circulation of money. The greater these two parameters, the smaller the lag. A method for computing this lag is derived in Appendix II. Application of this method shows that, for plausible values of the two parameters, the lag may run from half a year to well over a year. This theoretical finding is well in accordance with empirical observations frequently made in dealing with problems of financial policy:

1. An expansion of exports during a substantial period tends to produce a rate of reserve increase that is not maintained thereafter; if actions are taken on the assumption that the export surplus will persist (e.g., in the form of credit expansion), serious balance of payments difficulties may arise.

2. Credit creation will have its full effects on a country’s reserves only over a considerable time; in the early stages, the effects may appear both minor and harmless.

3. Measures to combat payments problems by means of restriction of credit expansion will normally become effective only slowly and gradually.

The change in reserves equals current exports minus the weighted sum of past values of the autonomous variables, with the sum of the weights equaling 1. The stock of money depends on the weighted average of the sum of the autonomous variables, with the sum of the weights equal to am (equals the ratio of money to imports if the marginal propensity to import equals the average propensity). Reserves are equal to the stock of money minus the total credit expansion. These relationships are summarized in Table 1.

Discussion of some of the conclusions reached

It may be useful to check the conclusions reached against some of the literature on the subject. The first observation is that the balance of payments conclusions are substantially those of the classical economists. The existence of an equilibrating mechanism by which an increase in exports produced its own offset, and the proposition that an increase in money beyond the proper quantity would be drained off through purchases of gold and silver, were, indeed, among the most essential of their findings.

But the classical economists did not typically study the details of these processes over time, through variations in income, imports, money, and reserves. Nor did they have the equipment to arrive at numerical magnitudes—or, more modestly, orders of magnitude—for the changes that could be expected in the course of these processes. For these reasons alone, a somewhat more precise restatement of the classical tenets, in a more modern form, may be appropriate.24

Another justification may be found in the alarming naivete so often found in analytical studies of particular countries. When such studies deal with past events, they all too often show surprise that an increased flow of exports, which produced a large balance of payments surplus the first year that it occurred, does not continue to produce such a surplus in later years. When a country is running a balance of payments deficit, it is far too often believed that any measure or event that will increase exports or decrease imports (oil discoveries, higher world market prices, the entry into production of some import-replacing industry, etc., etc.) will by itself relieve the deficit. The correct view, according to our conclusions, is that these events will by themselves produce a temporary, but not a lasting, improvement in the balance of payments. They will, of course, produce a lasting increase in the country’s income. This increase will, at least in part, be an increase in real income, depending on the elasticity of supply; to that extent, it may facilitate taking the additional measures necessary to eliminate the deficit permanently. If, for example, the deficit was due to an unbalanced government budget, a higher national income may make it easier to raise taxes and thus to eliminate the payments deficit via the elimination of the budget deficit.

The same line of reasoning will indicate that the belief that import restrictions can correct a balance of payments deficit is inaccurate, unless there is evidence that these restrictions will lead to a specific increase in saving, e.g., if the restrictions are known to be temporary. As shown above, such restrictions will have an initially favorable effect on the payments situation, which will disappear reasonably soon as the effects through the expansion of income make themselves felt. If restrictions were to have the same effective restrictive effect in terms of the value of the commodities kept out, they would have to be continually made more severe as the effectiveness of earlier restrictions wore off.

With respect to the effects of credit creation on the balance of payments, the classical views are not commonly heard at present. The opinion recently expressed by E. M. Bernstein that for “a country like the Philippines, which constitutes a very small part of the world monetary economy,… it can be said with approximate accuracy that an inflation of 100 million pesos [1 peso = US$0.50] will result in a balance of payments deficit equivalent to US$50 million,”25 does not, it is believed, reflect a point of view commonly held in the profession. According to the above analysis, this opinion is correct even without the conditions specified in the text, viz., that there is full employment and that the rise in prices is proportional to the increase in the quantity of money.26

Two prevailing schools of thought will, however, come up with different answers: both those who discuss expansion in terms of the multiplier and those who put their faith in an approach through the income velocity of money. The former group tends to take it for granted that there is, in any system, some marginal nonspending, i.e., marginal saving in forms other than money that does not lead to expenditure by someone else, as a result of which, obviously, not the whole credit expansion would eventually find its way into imports. But the question is whether there is indeed such marginal nonspending; as we have seen, there can be none, after the adjustment period, if the velocity of circulation is a constant.

It is perhaps a little more surprising that most approaches based on the quantity theory also manage to come to conclusions that are wrong or at least without applicability. The error—not a logical but a practical error—is due to the tendency to base these analyses implicitly or explicitly on a closed economy. This simplification is far more serious in velocity analysis than in multiplier analysis. In the latter, it is equivalent to disregarding one out of a number of “leaks” which are a function of income; the others, such as savings and taxes, are being allowed for. The numerical results are thus in the right direction, although they are too large. But to ignore imports in velocity analysis is to overlook the one and only leak there is in the system. Hence the conclusions are not only quantitatively, but also qualitatively, wrong. It is inferred that a single injection of credit leads to a lasting increase in income,27 and that continuous injection of the same amount of credit per period leads to an ever increasing rate of income.28 Both types of conclusions are based on a monetary multiplier equal to the inverse of the velocity of circulation. They fail to see that for open economies the income velocity approach cannot lead to conclusions that are even in the qualitative sense correct without being spliced on to income analysis; and that, when this is done, the ultimate value to which income approaches does not depend on the velocity of circulation at all, but only on the marginal propensity to import.

It is true that, by basing the analysis not on a given expansion of credit but on the assumption of a fixed increase in the quantity of money, velocity conclusions can be recast in a form that is formally correct. But since imports subtract from this quantity of money, the assumption implies, for an open economy, a continual offsetting of imports by new credit expansion.29

This brings us to the applicability of the quantity theory of money. Its weakness is not so much the assumption of a constant V, an assumption which, at least for the less developed countries, is probably as good as that of the constancy of any other coefficient. Nor do difficulties arise from the side of P and T; for the purpose of studying payments problems, the extent to which credit expansion leads to an increase in prices and the extent to which it leads to a rise in real income may not make too much difference. The basic difficulty, it would seem, is with M itself.30 For an open economy, an increase in M, unlike credit expansion, is not a useful autonomous variable to take as the multiplicand, because through the multiplier process an autonomous increase in M leads to a subsequent reduction of the same magnitude in M.

IV. Conclusions on Financial Policy

Long-run expansion of internal credit by monetary system

The analysis in Part III can be used to derive an estimate of the amount of internal credit expansion by the monetary system which an economy can afford. It should be stressed that the estimate refers not to credit expansion in general but only to credit expansion by the monetary system. The total new credit that can be extended in an economy depends on (1) the amount of income saved and (2) the extent to which saving is channeled into investment through credit institutions. The amount of new credit extended per year can be enlarged by increased saving or by an increased use of credit intermediaries. Accordingly, there is no narrow limit beyond which total credit cannot expand; and, on the whole, an increase in credit indicating increased saving, or even an increased use of intermediaries of a given amount of saving, is likely to be a healthy sign.

The situation is different, however, for saving through the monetary system, insofar as this saving takes the form of increased holdings of money. Since, with a constant velocity of circulation, money cannot increase faster than output without a rise in prices, and since price increases are generally not desired, more than a moderate amount of saving in the form of money is, on the whole, an unhealthy sign.31

The distinction between an unhealthy expansion of credit that leads to too large an increase in money and a healthy one that is indicative of an increased flow of savings into financial intermediaries is necessarily somewhat tenuous. The difficulty arises from the inevitable arbitrariness of any definition of money which draws a sharp line between money and what is called quasi-money in International Financial Statistics—assets which, unlike money, are used primarily as a store of value but, because of the ease with which they can be turned into money, perform some of the functions of precautionary balances, and perhaps even of the less active part of transactions balances. There is no satisfactory way to avoid this difficulty.

But it is made serious both in substance and in the treatment of the problem at hand if the same institutions that have large monetary liabilities also owe large quasi-monetary liabilities. It complicates the problem of substance, because the possibility of having both money and quasi-money (e.g., a checking account and a savings account, or a sight deposit account and a time deposit account) in the same bank tends to increase the ease of transfer from money to quasi-money and thus to blur further the line of distinction between the two.

At the same time, the distinction between the monetary system and other financial intermediaries becomes blurred. Where, as in France, the deposit banks have virtually no nonmonetary deposits, that distinction is easy. But where, as in Germany, the deposit banks have time deposits twice the size of their sight deposits and bonds outstanding in an amount equal to their sight deposits, the distinction between the monetary system and other intermediaries cannot be made on an institutional basis.

The fact that a community holds, in addition to money, large amounts of quasi-money is an important economic factor, both as to its causes and as to its effects. But whether the public holds these quasi-monetary assets in the commercial banks or in other institutions is primarily an institutional question, which is of a much lower order of importance. In the theoretical approach that is used in this paper it seems proper, therefore, to make a distinction by economic categories rather than on an institutional basis. Accordingly, we discuss the ability to expand internal credit not of the empirical banking system of each country, but of its monetary system. The latter is defined, in balance sheet terms, as all the liabilities of the central bank plus the monetary liabilities of the commercial banks and any other institutions that may have such liabilities (e.g., the postal checking system in some European countries). The asset side of the balance sheet is represented by all the net foreign assets of the institutions covered plus the amount of their domestic assets that is required to add up to the total of monetary liabilities. The remaining domestic assets are notionally split off as if they were held by some savings banks which also owe the corresponding amount of nonmonetary liabilities.

With respect to the monetary system, it was found in Part III that every credit expansion leads ultimately to a corresponding loss in reserves. From this, it might seem to follow that a country could not afford any permanent expansion of internal credit without endangering its balance of payments. To prevent a lasting deterioration in the balance of payments, any credit expansion in one period would, it might seem, have to be offset by a credit contraction in a later period. On closer analysis it will be clear, however, that this conclusion is not generally correct. We have seen that a lasting expansion in the rate of exports will lead to an’ increase in reserves. If the country is willing to forego part of this increase in reserves, it can afford a secular expansion of credit for every secular expansion in exports.

But should not reserves also increase secularly as exports and imports go up? Yes, they should; but the reserve increase that comes about automatically without credit expansion as exports increase is normally larger than the country would require in relation to that expansion of its trade. The automatic increase in reserves associated with any increase in exports would be equal to that increase times quantityofmoneyimports. For most countries this ratio is in the order of 1 or more. Countries do not, however, typically hold reserves equal to 1 or more. Countries do not, however, typically hold reserves equal to a year’s exports (or imports) ; as exports increase, they do not need to add a full year’s increase to their reserves. On the basis of a very cursory inspection of the ratios of reserves to imports of many countries of the world, it would seem that reserve ratios of the order of 50 per cent were found to be adequate by many countries, and smaller ratios by some. Where, then, export increases would by themselves tend to build up reserves by more than this, the country could afford to exchange part of its increase in reserves for domestic capital goods by means of credit expansion.

For some countries, however, where imports are a very large proportion of domestic variables (e.g., national income and the quantity of money), the ratio of money to imports may approach the desired ratio of reserves to imports. In a few countries shown in Table 2, the ratio of money to imports approaches 0.5; if these countries wanted to hold reserves of the order of 50 per cent of imports, they would not be able to afford any significant internal cerdit expansion, however much their exports might increase.

In general terms, the ratio of domestic assets to foreign assets of the banking system that an economy can afford, as a long-run proposition, is indicated by the formula


where a= ratio of money to income

m= ratio of imports to income

k = the desired ratio of reserves to imports.32

Thus a country where am=3 can, on this basis, have adequate reserves and yet an internal credit expansion five times its foreign exchange reserves, if k is taken at 0.5. With the same numerical degree of “reserve adequacy,” a small underdeveloped country with a large import ratio and a high velocity of circulation can afford much less credit expansion. For m = 0.3, a = 0.2 (velocity = 5), and k = 0.5, the ratio becomes ⅓, or the ratio of domestic credit to money becomes ¼. This agrees with the finding of E.A. Birnbaum that, for small underdeveloped countries with reserves that seemed adequate, the reserves were in the order of two thirds of the money supply, so that only one third of the money supply was matched by domestic credit.33

Cyclical variation of credit expansion

The preceding section set the limits for credit expansion in the long run. In the shorter run, in response to fluctuations in exports, the measure of the proper expansion of credit is more ambiguous, since the objectives of internal and external stability are likely to come in conflict. When export proceeds are cyclically high, considerations of internal stability and the prevention of inflation might require a reduction in credit expansion below the long-run normal; but balance of payments considerations would permit a larger than normal credit expansion. Similarly, in a depression, internal considerations would lead to an offsetting policy, while balance of payments reasons might necessitate a reduction in internal credit expansion.

There is, therefore, no single objective short-run test for a proper credit policy in response to cyclical variations, even on the assumption that cyclical variations in exports can be distinguished from long-run changes. To the extent to which they consider offsetting policies possible or desirable, countries can reasonably have different attitudes. Some may be willing to have external fluctuations permeate their economies, riding high on high tides—hoping perhaps that these may prove to be a lasting rise in level rather than a mere cyclical wave—and, if disappointed by a return of low tides, go through a period of restriction. Other countries may prefer to put primary emphasis on the stabilization of the internal economy, accumulating reserves in good years and running them down in bad years.

The maximum extent to which a policy of riding with the tide could reasonably be pursued would be to expand credit on the assumptions that (1) the increased level of exports would persist, but (2) the increase in reserves corresponding to a higher level of trade should be accumulated. The total credit expansion permissible on this basis is (am=k) times the increase in exports; for am. Δ exports is the reserve increase that will take place in the absence ot credit expansion, and k is the desired reserve ratio (in terms of exports or imports) that should remain after credit expansion.

V. Changes in Ratio of Money to Income


The preceding analysis has been based entirely on the assumption of a constant ratio of income to money. The analysis should now be broadened by allowing explicitly for other factors that may also play a role in determining the holdings of money, and whose changes will therefore be reflected in changes in the ratio of money to income.

Changes in this ratio may be attributable to two sets of causes: (1) changes in factors, other than income, which affect the desirability of holding money; (2) changes in the (opportunity) cost of holding money, i.e., in the rate of interest. The first might be considered shifts of a demand curve for money (at constant levels of income) ; the second, movements along such a demand curve in response to changes in interest rates.

Other demand factors

Changes of the type listed in the first group appear to occur frequently in the short run, particularly in response to sudden large purchases or sales of assets by the banking system. A large increase in exports or a large government deficit may increase the quantity of money more than in relation to income, as decisions to spend the larger income, either at home or for imports, are delayed. A large reduction of money, e.g., through an increase in inventories of imports or through capital flight, may lead to an increase in velocity as the economy continues its normal rate of current expenditure in spite of the inadequacy, by normal standards, of its cash balances. For some of the countries, the data in Chart 1 and Appendix I, Table 3, show changes in velocity that are probably due to such causes. Thus the very large export in-creases related to the Korean war produced high ratios of money to income at the end of 1951 in Australia and Pakistan. A large import of short-term capital brought about a high ratio in Mexico in 1950. A speculative wave of importing in the same period explains the declines in the ratios in Germany and the Netherlands at the end of 1951. But these deviations from a more normal relation between income and money apparently do not last.34 As the figures for the countries mentioned indicate, velocity returned to normal in a relatively short period.

Insofar as these demand factors are of a temporary character, the conclusions reached earlier in this paper would continue to be valid except with respect to their timing. Thus, if a large increase in exports leads to a temporary increase in the willingness to hold money (compared with income), income and imports will initially rise less, and money and reserves more, than would have been expected. But when the relationship of money to income returns to normal, these discrepancies will disappear.

It would seem that, generally, these other demand factors operate as a moderating force on both expansionary and contractionary processes. Even without changes in velocity there are difficulties of analysis and economic policy owing to the fact that the effects of these processes tend in any case to be lagged. Insofar as fluctuations in the velocity of money increase this lag, they may make proper analysis and proper policy even more difficult. Credit expansion may then proceed even longer, without much effect on the balance of payments. High export prices may lead to an even more impressive accumulation of reserves. Thus policies may be continued in the first case, or initiated in the second case, that are more inflationary than the economy will be able to stand when the normal velocity returns. Similar difficulties of interpretation may lead to excessively deflationary policies in other situations. Thus an import boom may temporarily continue even though cash balances have been reduced well below normal. In such a situation, additional deflationary measures to protect the reserves may seem necessary (in particular when the reserves have been decreased to a very low level and no secondary reserves are available), although it may be expected that the process may, reverse itself as cash balances are restored to normal.

The policy issues involved are made more difficult in both inflationary and deflationary situations by the ever present possibility that the ratio of money to income may have changed permanently. After all, these ratios are, as we have seen, quite different for different countries; and they have changed for individual countries over time,35 although usually only slowly.

Changes in response to rate of interest

In most of the less developed countries, the transition from money to other assets is fairly abrupt. On the one hand there is money; on the other hand there are real assets—land, buildings, stocks of international goods, perhaps gold and foreign balances. There is little in between. Treasury bills, government bonds, prime industrial bonds, readily marketable shares—all these assets that form the transition between money and real assets in countries with fully developed financial systems play a minor role in the asset structure of most of the less developed countries. Money is held for one purpose, transactions; real assets are held as the store of value. There may be occasional fluctuations in the holdings of money for the reasons discussed in the preceding section. But there is little room for short-run changes between money and real assets on the basis of changes in the rate of interest. In fact, in such countries there usually is no true market—neither a money market nor a capital market—in which a rate of interest is formed by the interplay of demand and supply forces.

The situation is different in the developed countries, where there is a continuous range of other assets yielding interest at the expense of liquidity. Here, moreover, money holdings are normally rather large, compared with income, giving more room for adjustments in response to the opportunity cost of holding money. In these circumstances, it seems logical to expect a reasonably clear influence of the interest rate factor on cash holdings in addition to the influence of income. In a recent unpublished study by William H. White, strong evidence that the velocity of circulation responds to changes in interest rates was found for six developed countries: Canada, Denmark, Sweden, Switzerland, the United Kingdom, and the United States. The relationship was found to be less close, but still present, for eight other countries: Australia, Belgium, Brazil, India, Mexico, the Netherlands, Norway, and Uruguay. Some of these, it will be noted, are less developed countries. Of the countries for which data are available, three—Chile, France, and Peru—did not show a relationship between interest and velocity.36

Changes in velocity are equivalent in their effect to injections into or subtractions from the income stream. Therefore, in circumstances where the velocity depends on the rate of interest, it is necessary to take changes in interest rates into account both for analytical and for policy purposes.

In studying the interest rate mechanism it is necessary to distinguish between the central bank and the commercial banks. The creation of credit by the central bank depends on its own decision (sometimes, to be true, taken under pressure); the size of the creation of credit by the commercial banks is normally left to their discretion, the central bank influencing the degree of ease or stringency of the commercial banks by means of its net purchases of exchange, its own credit expansion, its open market operations, and changes in reserve requirements. While these supply conditions affect the willingness of the banks to lend at different interest rates, demand conditions, such as business activity and profit expectations, affect the desire to borrow at different interest rates. The interplay of these demand and supply factors determines, at the same time, the amount of credit creation and the rate of interest.

If the central bank desires to change the amount of credit expansion by the whole banking system, this will normally lead to a change in the rate of interest (unless the supply and demand factors adjust themselves or are adjusted in such a manner as to make this unnecessary). By itself, a contractionary policy will lead to a rise in the rate of interest, an expansionary policy to a fall in the rate. But these changes in the rate will tend to induce changes in money holdings that will in part neutralize the initial policy.

Assume that in a particular situation it is felt necessary to reduce the additions to the income stream originating in the monetary system from 600 last year to 200 this year. To bring this about in the face of a constant or rising demand for credit, the reserve positions of the banks are tightened and the rate of interest rises. Now, insofar as businesses and consumers reduce their ratio of cash balances to turnover because of the high cost of money, the intent of the monetary authorities is frustrated. Assume, for instance, that, in response to the increase in the rate of interest for the total quantity of money of 2,000 million, the velocity of circulation is increased by 10 per cent. This is equivalent in its effect on income to a credit injection of 200 million. Thus the net effect on income achieved by the authorities is only half what was intended, and also only half the amount that the figures on credit expansion and the money supply might lead one to believe had, in fact, been achieved. In the face of the interest elasticity of demand for money in this imaginary country, the authorities would have had to tighten the reserve position of the commercial banks considerably more to achieve the desired net effect on income creation.

Changes in the velocity of circulation, whether resulting from changes in demand factors or from changes in the rate of interest, will have to be taken into account in the explanation of income and imports. For this purpose, they will have to be treated as equivalent to an increase in the quantity of money at constant velocity. But there is room for a certain difference in expectation when the change in velocity is due to a variation in interest rates, compared with the situation in which it is attributable to a change in demand factors. For when velocity has risen in response to an increase in the rate of interest, the change may be expected to be lasting as long as the rate remains high, while changes in velocity not attributable to changes in interest seem to have a tendency to reverse themselves.


I. Note on the Ratio of Money to Imports

As indicated in the text, the ratio of money to imports plays an important role in our conclusions. This ratio is itself composed of two ratios: that between money and income and that between imports and income. The three ratios for 44 countries in the period 1950-54 are given in Table 3. For 4 more countries for which suitable national income data were lacking, only the ratio of money to income is entered.

For the majority of countries, the ratio of money to imports shows a considerable measure of stability from year to year. But the differences between countries are very large—from about 0.5 at the one extreme (Costa Rica, Finland, Honduras, Iceland) to 2.5 to 3 at the other (Brazil, France, India, Italy), not counting the ratio of 11 for the United States. These differences are obviously not due to arbitrary factors, and it would seem tempting to look for an explanation that would reduce them to some typical characteristics of the countries in question. That much cannot be achieved in this paper, but a few observations on the data may be helpful for future research.

Any explanation should go back to the two component ratios—money to income and imports to income. Both are well-known ratios, each with a name of its own in economics: the “income velocity of money” (the name applies to the inverse of our first ratio) and the “average propensity to. import.” But surprisingly little has been done to explain the international differences in these structural coefficients. Two studies may be mentioned: one by E. M. Doblin on the ratio of money to income 37 and one by Tse Chun Chang on the ratio of imports to income.38 Each adduces evidence that the particular ratio under study increases as one moves from countries with low real income to countries with higher real income.39

Table 3.

Ratios of Money to Income (MO/Y), Imports to Income (M/Y), and Money to Imports (MO/M) for 48 Countries, 1950-541

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Sources: International Monetary Fund, International Financial Statistics (IFS) (Washington), October 1956, and, for some national income figures, United Nations, Monthly Bulletin of Statistics (New York), October 1956.

Figures for money pertain to end of year, and those for income and imports to calendar years, except as otherwise indicated in sources. Imports are c.i.f. When the import data on a country page in IFS are on f.o.b. basis, c.i.f. figures in national currency have been estimated on the basis of the adjustments in the World Trade Table (IFS, pp. 31-32).

For countries for which no national income data are available, the income data have been roughly estimated as follows: about 85 per cent of gross national product (GNP) for Ceylon, Guatemala, and Iceland, and 80 per cent of GNP for the United Kingdom and Sweden.

The figures in italics indicate the median value for MO/M. These figures, and the corresponding ratios of MO/Y and M/Y, have been used in Table 2.

High income country; see text.

Rough extrapolation from 1952 data.

These propositions have been tested on the ratios at hand. In order to eliminate as far as possible abnormal years, especially in the import ratio, one figure has been selected for each country, the median for the five years. It was selected on the basis of the ratio of money to imports; the corresponding two other ratios were then used for the same year. But it is clear for many countries that even if the figures do not change much from year to year, they may still be subject to error, or be untypical for the country in more normal conditions. The figures on money, especially for some of the more developed countries, suffer from the difficulty of definition. The income figures for some of the countries may be very inadequate, thus leading to unexplainable ratios for money to income, and imports to income, but not, of course, for money to imports. The import figures may be unduly low in terms of national currency in those cases where the currency is seriously overvalued and payments are balanced by severe restrictions. For these reasons, no attempt has been made, for purposes of this paper, to explain the ratios for individual countries.40 Only one division has been made. All countries were distributed into two nearly equal groups on the basis of their per capita income in dollars in 1952-54. Countries with income of $300 or more per capita are listed in the first group as “high income countries,” those with less than $300 per capita as “low income countries.”41 This is roughly a division between developed and less developed countries. That there were interesting differences in the ratios between the two sets of countries is indicated by Table 4. and Chart 3.

The median for the ratio of money to income (MO/Y) for the developed countries is nearly twice that for the low income countries. The difference between the two groups for the money-imports ratio (M/Y), though somewhat smaller, is also pronounced. As a result, there seems to be some difference remaining between the ratios of money to imports (MO/M). But the difference is not pronounced, nor is it large compared with the range within each group. There are, in fact, high and low income countries among those quoted at both ends of the range.

Table 4.

Medians of Ratios, 1950-54, of Money to Income (MO/Y), Imports to Income (M/Y), and Money to Imports (MO/M), by Groups of Countries1

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Based on data in Table 3. For method of grouping countries, see text.

II. Lag of Imports Behind Changes in Exports and Credit Expansion

The formulas in Part II of the main section of this paper and the data in Table 1 are expressed in terms of income periods. For practical purposes, it is desirable to have them expressed in terms of years. This would also be required for any statistical testing of the formulas. Even when quarterly data on exports, income, imports, etc., might be available, it frequently might be best not to use them, in order to avoid seasonal and random fluctuations.

We shall therefore derive a formula linking M to exports and credit expansion, with all variables expressed as annual figures. Since the two autonomous variables affect imports in the same manner, we have to deal with only their sum, which we call Q(t):

Chart 3.
Chart 3.

Frequency Distribution of Ratios of Money to Income (MO/Y), Imports to Income (M/Y), and Money to Imports (MO/M) for High Income and Low Income Countries

1 Ratio for United States omitted.

Table 1 gives the formula for M(t) as a function of past Q’s, which may be written in summary form

i = ∞


i = 1

in terms of income periods. Writing r = 1—m, we find the matrix of coefficients, still in terms of income periods, as given in Table 5.

Let the annual data be indicated by roman numerals:


where x is the velocity of circulation per year.

If the income period is, say, one quarter, we find from the matrix, mostly by adding terms but in part by use of the assumption that Q(1)=14Q(I), that


Note that the coefficient for Q(—II) is found as (1 + r + r2 + r3), reading vertically, times (1 + r + r2 + r3), reading horizontally. The coefficient for Q(—III) is r4 times that of Q(—II) in every place; etc. More generally, if the income period is l/x, the formula for M(0) is


Since the sum of the coefficients for Q(0), Q(—I), etc., equals 1, we may also consider the coefficients as weights that form part of a distributed lag. Numerical values for these weights are given in Table 6, which covers a fairly wide range of assumptions for m (from 0.10 to 0.35) and x (from 3 to 8).

This table shows that, if m is 0.20 or higher, a very large proportion of the total influence of Q is exhausted in four, and indeed in three, years. However, even for rather high values of x and m (e.g., x = 6, m = 0.30; x = 7, m = 0.25), only about half of the import effect of an increase in Q falls in the same year. The weighted average lag of imports behind the initial expansionary factor that can be computed from these data runs from about one third for the very highest values of x and m to well over a year for low values.42

Table 5.

Matrix of Coefficients forQin the Determination ofM, in Terms of Income Periods

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Table 6.

Coefficients forQ(0), Q(—I), Q(—II), andQ(—III) in the Determination ofM(O)1

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See discussion in text.

Table 5 may pose difficulties in empirical work, especially if it covers only relatively short periods. In the form in which it is presented it requires data on Q

for three or four years back to explain the current M. Thus any empirical explanation of M could go back only three or four years less than the period for which data on Q are available. However, if it is assumed that last year’s M reflects reasonably well the Q’s of the years before last year, the formula can be simplified so as to eliminate long lags.

If the coefficient for Q(0) is indicated by k0 and that for Q(—I) by k1, etc., the formula for M(0) can be compared with that for M(—I) as follows:


Hence: M(0)=k0Q(0)+[k1k0rz]Q(I)+M(I)rz

which eliminates the need for all data more than one year back.


Central Planning Bureau, Central Economic Plan for 1955 (The Hague, 1955).


J. M. Keynes, The General Theory of Employment, Interest and Money (London and New York, 1936).


Even in Keynes’ own early application of the multiplier to policy problems, the marginal propensity to consume is handled almost purely on an illustrative basis, as is evident from the following quotation from his The Means to Prosperity (New York, 1933), p. 10: “What proportion of this additional income will be disbursed as additional expenditure? Insofar as it accrues to the wage-earning classes, one can safely assume that most of it will be spent; insofar as it increases profits and salaries and professional earnings, the proportion saved will be larger. We have to strike a rough average. In present circumstances, for example, we might assume that at least 70 per cent of the increased income will be spent and not more than 30 per cent saved.”


R. F. Kahn, “The Relation of Home Investment to Unemployment,” Economic Journal (London), Vol. 41 (1931), pp. 173-98.


Professor Meade was, I believe, the first to make investment endogenous by linking expected profits to current profits and thus being able to introduce an “incentive to invest” with respect to income. See J. E. Meade, “A Simplified Model of Mr. Keynes’ System,” Review of Economic Studies (London), Vol. 4, No. 2, February 1937, pp. 98-107.


Professor Baumol has put forward an alternative theoretical suggestion, viz., that cash balances should vary in proportion to the square root of the value of transactions. This alternative does not, however, seem to have general validity. See J. J. Polak and William H. White, “The Effect of Income Expansion on the Quantity of Money.” Staff Papers, Vol. IV (1954-55), p. 416, footnote 15.


A valuable business cycle theory has been built on the comparable assumption that holdings of another category of circulating capital, inventories, would be proportional to sales.


In “Keynesian Economics and the Quantity Theory,” Don Patinkin shows that, under plausible assumptions, from “the analytical framework … of the modern income-expenditure approach … emerges … [the voice] of the traditional quantity theory.” (Kenneth K. Kurihara, ed., Post Keynesian Economics, New Brunswick, N.J., 1954, p. 139.)


The effects of import restrictions correspond to those of equivalent increases in exports.


See Earl Hicks, Graeme S. Dorrance, and Gerard R. Aubanel, “Monetary Analyses,” in “Recent Developments in Monetary Analysis,” Staff Papers, Vol. V (1956-57), pp. 342 ff.


Domestic nonmonetary liabilities are either netted out against domestic assets or, in the annual Economic Survey of the Economic Commission for Latin America, treated separately in a residual category called “money supply absorbed.”


A similar point of view on the subject of a proper choice of models has been expressed by Dr. Holtrop: “It is clear that such a model [i.e., a multiplier model] cannot fit the purposes of a central bank. If one analyzes monetary phenomena with the purpose of getting some guidance for monetary policy, one must necessarily use a model in which monetary policy can find its place. If we believe that by monetary policy we can exert an influence on the creation of money, and maybe also on the propensity of the business community to hoard or to dishoard, and if we further believe that the exertion of such influence will affect the course of the inflationary or deflationary process, then, for the exposition of our ideas, we must choose a model in which the creation and cancellation of money and the acts of hoarding and dishoarding are treated as autonomous factors.” See M. W. Holtrop, “Method of Monetary Analysis Used by De Nederlandsche Bank,” in “Recent Developments in Monetary Analysis,” Staff Papers, Vol. V (1956-57), pp. 305-6.


J. J. Polak, “The Foreign Trade Multiplier,” American Economic Review (Menasha, Wisc.), Vol. 37 (1947), pp. 889-97; Gottfried Haberler, “Comment,” ibid., pp. 898-906; J. J. Polak and G. Haberler, “A Restatement,” ibid., pp. 906-7.

Assume that both exports and imports have an autonomous componem (Xa and Ma) and an induced component Xt and Mt, the latter being linearly dependent on income:

In general, x would be small compared with m, and normally the fluctuations of Xa would be large compared with those of Xi. Also, unless import restrictions were varied frequently with a large effect on the effective restriction of imports, fluctuations of Ma would tend to be small compared with those of Mi.

To simplify the analysis, the autonomous parts of both variables are combined under the name of one that is mostly autonomous
and the induced parts of both under the name of the one that is mostly induced

Similarly, one coefficient indicated for simplicity as the price elasticity of demand for imports could, at the same time, represent the effect of a change in relative prices on the balance of payments through imports and through exports.

Assume that the true structural import equation is in real terms, linking the volume of imports (m) to the volume of real income (y), while it also contains a substitution term:

Here,μ is the marginal propensity to import in real terms, ε is the elasticity of substitution of foreign goods for home goods, ρd is the domestic price level, pm the import price level. The substitution term is defined to include both the substitution effect in the narrow sense and the income effect of price changes; and real income is accordingly defined as the volume of domestic output not adjusted for changes in the terms of trade. The treatment differs in these points from that in my International Economic System (Chicago, 1953).

Taking pd and pm as indices with base = 1, we can substitute
Hence (i) becomes
If the marginal propensity to import equals the average propensity, so that μy = m, (iv) becomes

This is equivalent to an equation in terms of M and Y only, as used in the text, for any and all values of pd and pm, provided ε = 1.

Admittedly, the specific assumption that ε = 1 has been made for reasons of sim-plicity of the system. This is not to admit, however, that it is an unreasonable assumption. Insofar as our empirical evidence goes, e is probably somewhat smaller than unity for most countries. We must not forget, however, that the relative price term in the import equation also does double duty for the effect of changes in relative prices on exports (see footnote 15). The implicit assumption is, therefore, that a rise in domestic prices by 1 per cent would of itself worsen the country’s balance of payments by 1 per cent of the value of imports through import substitution plus loss on exports. Wherever, in a particular case, better specific knowledge about the magnitude of e is available, it could, of course, be used. But this would then necessitate building into the system separately a price and a quantity component of the change of national income, while in the present model the extent to which a given change in money income is due to quantity or to price changes may be ignored.


Note that the special notations used in footnote 16 do not apply in the rest of the paper.


This coefficient is not used until later.


The validity of this assumption is discussed in Polak and White, op. cit., p. 411


This is a necessary assumption; see below.


Assuming marginal propensity to import equals average propensity to import.


See, for example, Fritz Machlup, International Trade and the National Income Multiplier (Philadelphia, 1943).


Based on 1952 figures taken from “The Dollar Value of the World’s Money Supply,” International Financial Statistics (Washington), July 1953, pp.


A nonnumerical discussion of the process that follows an expansion of exports is given by E. M. Bernstein in “El Precio del Café y la Politica Monetaria” (“The Price of Coffee and Monetary Policy”), El Trimestre Económico (Mexico, D.F.), Vol. 17 (1950), pp. 416-38. The conclusions reached there are the same as those of this paper.


E. M. Bernstein, “Strategic Factors in Balance of Payments Adjustment,” Staff Papers, Vol. V (1956-57), pp. 153-54.


The additional condition of a fixed rate of exchange is necessary in the sense that any regime under which the balance of payments adjusts itself automatically through changes in the rate excludes the possibility of a balance of payments deficit by assumption.


A recent example is found in De Nederlandsche Bank, Report for the Year 1964 (Amsterdam, 1955), p. 65: “If as the result of inflationary impulses economic activity increases, or prices and incomes rise, or if in a word such impulses enlarge the national income, then the cash requirements of the households taking part in transactions will inevitably also become greater. This greater need for cash will be met through a part of the income received not being spent. … In the conditions existing in the Netherlands, the extent to which money becomes ‘fixed’ in cash holdings is of the order of 30 per cent of the increase in the annual national income. From another point of view this means that an inflationary impulse, provided that it does not lead to a balance of payments deficit—in which case newly created or activated money would disappear from circulation and cease to produce any stimulating effect on the domestic economy—and provided that the impulse is not offset by a deflationary impulse elsewhere, will continue to produce its inflationary effect until such time as increased activity or price rises have produced an ‘income effect’ amounting to roughly three times as much as the impulse. The point is that each addition to income tends when it is spent to cause fresh additional income to arise; and only the fact that a part of each fresh addition to income is left unspent so as to meet the greater need for cash due to the rise in income prevents the inflationary impulses from producing a constantly extending cumulative effect. In any inflationary process therefore we should always find an increase in cash holdings, expressed in the form of an accumulation of primary liquid resources.” Although one of the two reservations made envisages the possibility of an induced balance of payments deficit, this complication is not pursued, and a quantitative conclusion for the Netherlands is reached on the basis of the quantity theory. In a journal article, however, Dr. Holtrop indicates explicitly that the “monetary multiplier” (i.e., the inverse of the velocity of money) applies only in a closed economy. In an open economy one also has to take account of the import leak, “as a result of which the remaining income effect would become smaller and smaller, ultimately vanishing when the cumulative balance of payments effect will have equaled the value of the initial inflationary impulse.” (M. W. Holtrop, “The Interpretation of Monetary Phenomena” [in Dutch], Economisch- Statistviche Berichten (Rotterdam), Vol. 39 (1954), p. 994.


S. C. Tsiang, “Liquidity Preference and Loanable Fund Theories, Multiplier and Velocity Analyses: A Synthesis,” American Economic Review (Menasha, Wisc.), Vol. 46 (1956), p. 563. After reaching this conclusion, the author recommends velocity analysis for the study of development problems in underdeveloped countries—which surely are not typically closed economies—while sounding a warning against the use in such cases of the multiplier method whose conclusions are considered to be “dangerously misleading.”


The validity in this form is equivalent to that meaningless way in which the multiplier can always be shown to be exactly equal to the ratio of income to investment.


In this paragraph, M stands for money, which elsewhere in this paper is indicated as MO.


An important exception is a period of currency stabilization when the velocity of circulation is suddenly reduced and the economy can absorb a large quantity of money without inflationary effects.

If R represents reserves, desired reserves are R = kmY. Since

Eugene A. Birnbaum, “The Cost of a Foreign Exchange Standard or of the Use of a Foreign Currency as the Circulating Medium,” Staff Papers, Vol. V (1956-57), pp. 477-91, in particular, Group III in his Table 2. The same paper also shows that, for countries in this position, the ratio of foreign exchange to currency alone exceeded 100 per cent so that there was, in the long run and in retrospect, no economy for them in using a currency of their own.


M. W. Holtrop, “Method of Monetary Analysis Used by De Nederlandsche Bank,” Staff Papers, Vol. V (1956-57), p. 307.


In Germany, for instance, the velocity declined sharply in the pre-1914 period. See Ernest M. Doblin, “The Ratio of Income to Money Supply: An International Survey,” Review of Economics and Statistics (Cambridge, Mass.), Vol. 33 (1951- 52), pp. 201-13, and International Financial Statistics (Washington), November 1951.


Clear evidence of the relationship for South Africa has been brought forward in a recent article by Dr. G. de Kock, “Die Verhouding van die Volksinkome tot die Geldvoorraad in Suid-Afrika, 1917-54,” South African Journal of Economics (Johannesburg), Vol. 23 (1955), chart on page 201. See also “Money Supply and National Income: The Income Velocity of Money and the Rate of Interest,” International Financial Statistics (Washington), November 1951, pp. iii-v.


Ernest M. Doblin. op. cit.


Tse Chun Chang, “International Comparison of Demand for Imports,” Review of Economic Studies (London), Vol. 13 (1945-46), No. 34, pp. 53-67.


Doblin also shows that the ratio of money to income in the same country increases over time, presumably because income rises. However, the ratio of imports to income has more generally been held to decline over time, although the evidence on this is by no means clear: cf. United Nations, World Economic Survey, 1955 (New York, 1956), pp. 51-53.

Neither Chang nor Doblin has been able to give a statistically satisfactory explanation that would fit the data for all countries. Doblin limited his explanation to 13 countries, after eliminating both the Scandinavian and the Anglo-Saxon countries for special reasons. His main correlation was, moreover, based on the ratio of currency to income; with the ratio of currency plus demand deposits to income, the regularity was said to be less good. Chang stratified his countries in three groups, within which the propensity to import is related to real income. The differences between the groups are attributed to different degrees of specialization, but the evidence on this seems inconclusive. The result of a somewhat more refined correlation calculation made with the data should be reported here. For 43 countries (all those in Table 3 except Costa Rica, El Salvador, Indonesia, Iran, and Iraq), an attempt was made to explain the average propensity to import (m) on the basis of per capita income (y) and population (p), using logarithms of the three variables. The result was:
Population, and not real income, accounted for almost all of the variance explained; omitting y, the finding was

Based on data from Statistical Office of the United Nations, Per Capita National Product of Fifty-Five Countries, 1952-1954 (New York, 1957).

The weighted average lag is found to be as follows:

where k1 is the coefficient of Q(—I), k2 that of Q(—II), etc.

A Collection of Research Papers by Members of the Staff of the International Monetary Fund