absorption approach

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A Note on Some Mechanics of the Absorption Approach Author(s): William R. Allen Source: Weltwirtschaftliches Archiv, Bd. 86 (1961), pp. 69-85Published by: SpringerStable URL: http://www.jstor.org/stable/40434796Accessed: 14-09-2015 14:34 UTC

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A Note on Some Mechanics of the Absorption Approach

By

Professor William R. Allen Los Angeles, Calif.

Contents: I. The Model. - II. Alternative Adjustment Patterns. - III. The Case of Import Restriction. - IV. Income Changes Further Considered. - V. Balances in Domestic and Foreign Currencies.

recent years, the "absorption/* or "aggregate-spending/' approach to balance of payments analysis has received considerable attention1. Perhaps contrary to the impression which one might gain from some

of the literature, the absorption approach relates to balance of payments analysis generally; it is not confined either to some specific policy alternative, such as devaluation or severe deflation, or to some inherent, automatic adjustment mechanism. The underlying framework of the approach is a national income model including foreign trade components. 1 'Exports' ' and "imports" can thus be segregated, stating the trade

Remark: This is a considerable elaboration of editorial material in : Foreign Trade and Finance: Essays in International Economic Equilibrium and Adjustment, Ed. by William R. Allen and Clark Lee Allen, New York, 1959, pp. 387sqq., 397sq. I appreciate the comments of several persons, including Harmon Alexander and the late Ragnar Nurkse. The paper was completed during a fellowship granted by the Ford Foundation; the analysis does not necessarily represent the view of the Foundation.

1 On an abstract level, one may consult Sidney S. Alexander, "Effects of a Devaluation on a Trade Balance", International Monetary Fund, Staff Papers, Washington, D.C., April 1952, pp. 23sqq. - Fritz Machlup, "Relative Prices and Aggregate Spending in the Analysis of Devaluation", The American Economic Review, Vol. XLV, Evanston, 111., 1955, pp. 255 sqq. - Franz Gehrels, "Multipliers and Elasticities in Foreign-Trade Adjustments", The Journal of Political Economy, Vol. LXV, Chicago, 111., 1957, pp. 76sqq. - Hans Brems, "Devaluation, A Marriage of the Elasticity and the Absorption Approaches", The Economic Journal, Vol. LXVII, London, 1957, pp. 49sqq. - Sidney S. Alexander, "Effects of a Devaluation: A Simplified Synthesis of Elasticities and Absorption Approaches", The American Economic Review, Vol. XLIX, 1959, pp. 22 sqq. - More empirically oriented are Ragnar Nurkse, "The Relation Between Home Investment and External Balance in the Light of British Experience, 1945- 1955", The Review of Economics and Statistics, Vol. XXXVIII, Cambridge, Mass., 1956, pp. i37sqq. - Robert Triffin, Europe and the Money Muddle, From Bilateralism to Near-Convertibility, 1947 - 1956, Yale Studies in Economics, 7, New Haven and London, 1957, Chapter 2. - J. Black, "A Savings and Investment Approach to Devaluation", The Economic Journal, Vol. LXIX, 1959, pp. 267sqq.


yo William R. Allen

balance in terms of the other income variables. A major objective of the approach is, then, to make explicit the connection between the foreign trade balance and the domestic variables in national income, thereby presumably enhancing appreciation, and facilitating analysis, of the "domestic" conditions of "externar* balance1.

On the basis of an income model presented in Section I, Section II reviews alternative changes of exports and imports yielding in each case a given change in the trade balance and the necessary concomitant adjustments of domestic variables. Section III takes up in additional detail the case of improving the trade balance solely by curtailing imports. Most of Sections II and III are based on the assumption of constant national income. Section IV considers the effects of an initial (autonomous) change of the trade balance on income and the subsequent repercussions on the balance. Section V demonstrates the relationship between changes in the trade balance expressed in domestic currency and in a foreign currency when the exchange rate has been altered.

I. The Model

Letting Y = national income, C = consumption expenditure on domestic output, I = investment expenditure on domestic output, G = government expenditure on domestic output, S = saving, T = tax collections, X = exports, i.e., current account credits, M = imports, i.e., current account debits, E = total expenditure on (absorption of) domestic and foreign

output, we may set up a national income model. 1 "Balance of payments statistics record a country's deficit in terms of its external

transactions alone. A current account deficit thus represents the excess of a country's imports of goods and services over its exports. In national accounts statistics, the same deficit is alternatively recorded as an excess of over-all expenditure above overall production. This necessary identity is, of course, obvious: If a country buys more abroad than it sells abroad, its citizens taken as a group must spend more money currently than they currently earn. Its merit is to draw attention to another commonplace truth, sometimes obscured in learned balance of payments discussions: In down-to-earth terms, a country's deficit - like an individual's deficit - can always be brought back to its failure to live within its income." Triffin, op. cit.t pp. 42 sq. This is not to say that correction of a balance of payments deficit must entail an absolute curtailment of "over-all expenditure." Rather it is required that there be a reduction of expenditure relative to "over-all production." And in Europe, from the immediate post-World War II period into the 1950's, "the elimination of the foreign deficits was not achieved through a curtailment of consumption, investment, and imports [all of which rose impressively], but through the persistent growth of production and exports" {ibid., p. 45).


A Note on Some Mechanics of the Absorption Approach Jl

(1) Y = C + I + G + X, with respect to income-creation, (2) Y = C + S + T + M, with respect to income-disposal.

Therefore: (3) I + G + X = S + T + M,

and: (4) S + T - I - G=X - M.

Since by definition : (5) E = C + I + G + M,

then: (6) Y=E + X - M, (7) Y-E = X-1P,

or: (8) Y - C - I - G - M=X - M2.

Between them, equations (4) and (8) state X - M in terms of C, S, T, I, and G. But it would be helpful to have C, S, and T in one equation, as we have C, I, and G in equation (8). We could thereby express the trade balance in terms of the domestic income-disposal variables as well as in terms of the domestic income-creation variables.

Rewriting equation (2) as: (2') Y - C - S - T - M = O,

1 Not only may the trade balance be expressed as the difference between national income and national absorption, it is equal to the difference between total "leakages" and total "injections." Substituting from equations (2) and (5) for Y and E, we have:

C + S + T + M - C - I - G - M = X - M, S + T - (I + G) = X - M.

Cf. M. F. W. Hemming and W. M. Corden, "Import Restriction as an Instrument of Balance- of-Payments Policy", The Economic Journal, Vol. LXVIII, 1958, p. 483 n.

2 Some would prefer a model based on national income accounting data, in which "sources" of income include net exports (X - M). C, I, G, and X are then "gross," inclusive of imports, and thus M must be explicitly subtracted. If we assume, unrealistically but conveniently, that all imports are "consumption" imports, i.e., C + M = C, we have the following model :

Y = C' + I + G + X - M, Y = C + S + T.

Since: E = C + I + G,

then: Y = E + X - M,

and: Y - E = X - M.

In either this model or the one in the text, Y - E = X - M, i.e., the current account balance equals the difference between income and absorption. However, for purely abstract, as compared to empirical work, there is some gain in conceptual clarity in using the model in the text.


72 William R. Allen

and adding X - M to both sides, we have: (9) y - C - S - T - 2M + X=X - M.

We may now assume the following numerical values1: Y=C+I+G+X 160 = ioo + 15 + 25 + 20 Y=C+S+T+M 160 = 100 +10 + 20 + 30

The following discussion is in terms of equations (8) and (9). Inserting the foregoing values in these equations, we have :

Y - C - I- G- M = X- M 160 - 100 - 15 - 25 - 30 = 20 - 30 = - 10 Y - C - S- T- 2M+X = X - M 160 - 100 - 10 - 20 - 60 + 20 = 20 - 30 = - 10

II. Alternative Adjustment Patterns Assume now that we wish somehow to increase X - M to zero, i.e.,

eliminate the deficit, while holding money national income unchanged (on the assumption of full employment initially and with inflation to be avoided). We can (a) increase X to 30, (b) reduce M to 20, or (c) alter both X and M so that the combined change is + 10, where increases (decreases) in exports and decreases (increases) in imports are considered plus (minus) variables.

(a) Y- C - I - G- M = X - M 160 - (130) - 30 = 30 - 30 = o Y - C - S - T- 2M + X =X - M 160 - (130) - 60 + 30 = 30 - 30 = o

With Y and M unchanged, when X = 30, the aggregate of C + I + G must fall from 140 to 130: an increase in exports with unchanged income necessitates a reduction of equal value in absorption, and in this case the reduction is confined to the "domestic" components of absorption. If the decrease in C + I + G falls to any extent on C, to that degree S + T must rise, f or C + S + T remains constant at 130; if the entire decrease falls on I and G, then S and T (as well as C) remain constant2. As in all cases to follow in which income is constant, the total "dis-

1 In the model of p. 71, footnote 2, we would have: Y = C' + I+G+X - M 160 = 130 + 15 + 25 + 20 - 30 Y = C + S + T 160 = 130 + 10 + 20

Nurkse (op. cit., pp. i44sqq.) offers reasons why "the brunt of adjustment is likely to fall on domestic investment."


A Note on Some Mechanics of the Absorption Approach 73

absorption," i.e., the reduction in C + I + G + M, equals the improvement in the trade balance.

(b) y- C - I - G- M=X - M 160 - (140) - 20 = 20 - 20 = 0 Y - C - S - T - 2M + X =X - M 160 - (140) - 40 + 20 = 20 - 20 = o

When M = 20, with Y and X constant, the sum of C -f I + G remains unchanged at 140. But C + S + T must increase from 130 to 140. The reduction in the expenditure on imports out of a constant income may or may not be directed wholly or in part to consumption. If some of the increase in C + S + T takes the form of consumption, to that extent I + G must fall; if C does not rise, S + T must increase by 10.

(C) Y - C - I - G- M = X- M 160 - (134) - 26 = 26 - 26 = o Y - C - S - T- 2M+ X = X- M 160 - (134) - 52 + 26 = 26 - 26 = o

The fall in M requires that C + S + T rise from 130 to 134; the increase in X requires that C + I + G fall from 140 to 134. If C is unaffected, the changes take place entirely in S + T and I + G. If C rises, S + T rises by that much less, and I + G falls by that much more; if C falls, S + T rises by that much more, and I + G falls by that much less.

(d) As an elaboration of case (c), we may suppose that M increases, thus necessitating an increase in X greater than the initial deficit.

Y - C - I - G- M = X - M 160 - (125) - 35 = 35 - 35 = o Y - C - S - T- 2M+ X = X - M 160 - (125) - 70 + 35 = 35 - 35 = o

The rise in M requires that C + S + T fall by 5 ; the increase in X requires that C + I + G fall by 15. If C rises, both S + T and I + G fall by that much more; if C falls, S + T and I + G fall by that much less. In any case, I + G falls by 10 (the amount of the initial deficit) more than the decrease in S + T.

(e) Finally, as an alternative elaboration of case (c), assume a fall in X and thus a fall in M greater than the initial deficit.

Y - C - I - G- M = X- M 160 - (145) - 15 = 15 - 15 = o Y - C - S - T- 2M+ X = X - M 160 - (145) - 30 + 15 = 15 - 15 = 0


74 William R. Allen

Here C + I + G and C + S + T must rise to 145, with S + T increasing more than I + G by 10.

III. The Case of Import Restriction For a more detailed review of the foregoing relationships, consider

again case (b), in which the entire trade balance adjustment takes the form of reduced imports. The initial situation, it is to be recalled, is:

(i) Y- C- I- G - M = X- M 160 - 100 - 15 - 25 - 30 = 20 - 30 = - 10.

(ii) Y - C - S - T- 2M+ X = X- M 160 - 100 - 10 - 20 - 60 + 20 = 20 - 30 = - 10

To take only the limiting cases, the reduction in expenditure on imports by 10 may be saved and/or drained o in taxes or (b) spent on domestic consumption; and if consumption rises, we may specify that national income either (a) remains the same, as assumed in Section II, or (b) rises.

In the first of the income-disposal alternatives, equation (ii) becomes: (') Y - C - S - T - 2M + X = X- M

160 - 100 - (40) - 40 + 20 = 20 - 20 = 0 Equation (i) is not affected.

In the second alternative, equation (ii) becomes : (ii") Y - C - S - T- 2M + X = X - M

160 - no - 10 - 20 - 40 + 20 = 20 - 20 = o But if now C = no, equation (i) also is affected. If national income is to be held constant, the increase in C must be offset by an equal fall in I + G:

(i') y - C - I - G- M = X - M 160 - no - (30) - 20 = 20 - 20 = 0

If, however, money income is allowed to rise, equation (i) could - with a consumption multiplier of unity - be:

(i") Y- C - I- G- M=X- M 170 - no - 15 - 25 - 20 = 20 - 20 = o

And, correspondingly, equation (ii) would then look as follows: (ii'") Y - C - S - T - 2M+ X = X - M

170 - no - (40) - 40 + 20 = 20 - 20 = o Here, with a rise in income equal to the correction of the trade balance, total absorption is not reduced, although its composition is altered.

Which of these alternatives is fulfilled is scarcely a matter of in- difference. Assuming that Y is to be held constant when M is reduced,



the remaining absorption in the form of C + I + G must not be allowed to rise. If the money not now spent on imports is saved or taxed away, the fall in imports has no further repercussions in the model. But if the cut in imports leads to an increase in consumption, income can be held constant only by an equal reduction in investment plus government expenditure: the import ' 'belt-tightening/' regardless of what particular types of imports are curtailed, would eventuate in a restriction of domestic investment and/or government spending.

We may allow C to rise without a concomitant restriction of I + G, but only by allowing Y to rise. If idle resources exist, this rise in money income will tend to induce a rise in real income, thus permitting total real absorption to remain unchanged while imports are restricted. But if the increase in Y is a manifestation of inflation, real absorption is reduced: with or without inflation, absorption remains at 170; if real absorption is deemed to remain constant in the absence of inflation (the increase in C offsetting the fall in M), it falls when domestic prices rise. Furthermore, exports, which heretofore we have assumed to remain constant, will tend to fall, at least in volume, as exportable production is shifted toward the inflating domestic market. It may be added that, whether or not inflation occurs, the reduction in imports may well discourage exports through induced income effects abroad, i.e., "foreign repercussions."

IV. Income Changes Further Considered

An initial improvement in the trade balance may not be accompanied by adjustments in domestic variables required to keep Y constant. And, in contrast to the case illustrated by equations (i") and (ii'") in the preceding section, if Y increases, we may expect that induced changes in imports and probably also in exports will reduce the improvement in the trade balance - but presumably will not eliminate it.

The equation for the change in the equilibrium level of income of the country pursuing the balance of payments policy (AYa) can be derived by algebra which is conceptually simple but a bit cumbersome. It is assumed in the following that an autonomous change in imports (AM) is accompanied by a corresponding and opposite change in consumption (AC), i.e., the propensity to spend on consumption plus imports is constant. It is assumed, further, that there are no changes, autonomous or induced, in government spending or in investment.

First, we derive an equation for AYb in terms of AYa and marginal variables. With c, s, and m being the marginal propensities to consume, to save, and to import out of disposable income (AY'); t being the


76 William R. Allen

marginal tax rate; and thus AY' = AY (1 - t); and with AC and AX being the total changes of induced and autonomous consumption and exports, respectively; we have the following income model for country B:

AYb = ACb + AXb, ACb = cbAYb (1 - tb) - AMb,

= cbAYb(l-tb)-AXa, AXb = maAYa(l-ta) + AXb(

= maAYa(l - ta) + AMa. Therefore :

AYb = cbAYb (1 - tb) + niaAYa (1 - ta) + AMa - AXa, _ HlaAYa (1

- ta) + AMa - AXa 1 - Cb(l - tb)

Similarly for country A: AYa = Ca AYa (1 - ta) + mbAYb (1 - th) + AXa - AMa.

Substituting the equation for AYb and rearranging, we have: a^ A^n *v , AYamb (l-tb) ma (1-ta) AYa a^ = CaAYa(l-ta) A^n *v + , ^ (^

~

mb(l-tb)(AXa-AMa) - i-cb(iz;tb)-

+^-^Ma

AYa Av [, ,. . . mb (1- tb) ma(l- ta)] AYa Av [, [1-Ca (l-ta)- ,. . . mb (1-

j_^ tb)

^ ta)]

j =

.AY A ut 1~Cb (1~tb) -m" (1"tb) - .AY (AXa-AMa) A ut i_c^(h_^ '

AXa-AMa [l-ca (l-ta)] [l-cb (l-tb)] -ma (1- ta) mb (1- tb)

1- Cb (1- tb) - mb (1- tb) This can be rewritten :

AY = AXa-AMa _ a 1-Ca d-ta) + mb (l-tb) J^-t^J 1- Cb (1- tb) - -^|~ mb (1- tb) ai 1- Cb (1- tb) - mb (1- tb)

or reduced to :

AYa= AX*-AM*

-_ u

1-Ca (1-0 + mb (l-tb) -Ja4r4 -_

I1 - tb) "+ t3 tb Sb I1 - tb) "+ tb 1 We may drop the assumption that consumption rises (falls) autonomously by the

full amount of the autonomous fall (rise) in imports. Suppose that for country A the ratio of autonomous consumption change to autonomous import change is designated f; in country B, the ratio is g. Then :

( AXa - f AMa ) [1 - cb (1 - tb)_] - mb (1 - tbMgAXa - AMa )

[1 - ca (1 - ta jj [1 - cb (1 - tb)] ~ mb (f- tb") ma (1 - ta) '

If f = g = 1, this equation is the same as that in the text.



The equation for AYb in analogous terms is the same as for AYa, with subscripts reserved.

Table 1 illustrates the first several periods of the adjustment process and the final equilibrium values, with the assumed marginal propensities and marginal tax rates as indicated and assuming that country A has an autonomous rise in exports of 6 and an autonomous fall in imports of 4, as in case (c) of Section II. But here, in contrast to case (c), income is allowed to change, giving rise to induced changes in imports and in exports which substantially reduce, but do not eliminate, the initial trade balance. (It will be noted that AYa = - AYb. This is not a general result and obtains only when, as in this illustration, sa = tb and ta = sb.)

Table 1

Aut Ind ! Ind ; Ind ' Ind Aut : Aut ! Net AC . AC I AS ; AM I AX AX j AM A(X-M)|

^Y Ai AY

Country A: c = .5; s = .3; m = .2; t = .1 4 6 -4 10 10 1 9 4 4.5 ! 2.7 , 1.8 - .7 i 6 -4 7.5 13.8 1.38 ; 12.42 4 ; 6.21 3.7261 2.484J- .966 6-4 6.55 15.244 1.524 13.72 4 6.86 4. 116! 2.7441 -1.067 6 -4 6.189: 15.793! 1-579! 14.214 4 7.258J 4.3551 2.9031 -1. 129 6 -4 5.968 16.129 1.613 14.516

Country B:c= .8; s = .i;m= .1; t = .3 -6 : -46 -10 -10 -3 ;- 7 -6 -5.6 |- .7 - .7 ! 1.8 -4 6

- 7.5 -13.8 -4.14 !- 9-66 -6 I -7.728- .966- .966J

! 2.484^ -4 , 6 - 6.55 -15.244 -4.573 -10.671

~6 I -8.537 -1.067! -1 .067I 2-744 -4 ,

6 - 189! -15.793! -4.738 -11.055 -6 [-9-032 -1.129j-1.129j 2.903! -4 6 I - 5.968 -16.1291-4.8391-11. 290

AX, AM, and AC are here composed of two elements, one autonomous and one induced. In the schema of Sections II and III, the final equilibrium situation of country A can be presented thus:

AY - AC - AI - AG + AM = AX - AM 16.129 - 11.258 - o - o + 1.097 = 4.871 + 1.097 = 5.968

AY - AC - AS - AT + 2 AM + AX = AX - AM 16.129- 11.258- 4.355 - 1.613 + 2-I94 + 4-871 =4-871 + 1.097 = 5.968

In terms of the same marginal variables, we may express the "final- balance ratio" of country A, i.e., the ratio of the final trade balance when the multiplier process is completed (B2) to the initial trade balance determined by the autonomous changes in imports and exports (Bj)1.

1 Cf. my "A Note on the Money Income Effects of Devaluation", Kyklos, Vol. IX, Basel, 1956, pp. 378 sqq.


78 William R. Allen

Since the final balance equals the initial balance plus induced exports and minus induced imports:

B2 AX - AM + mb AY'b- ma AY'a Bi

= """ X~-^M

'

AYa[l-ca(l-ta) + mb(l-tb);^^] ~ AX - AM + mbAYb (l-tb) - maAYa (l-ta) + '"~ " AX- AM

l-ca (l-ta) -ma (l-ta) = 1-0.(1^ + ^ (^1^^

In this illustration, the final balance is three-fifths (.597) of the initial balance. Under what conditions would the entire initial improvement be eliminated by induced changes in trade? From the equation for B^B^ it is apparent that B2 = 0 if:

l-Ca(l-ta)-ma(l-ta)=O, 1= (l-ta) (ca + ma),

1 ca + ma= - 1 - xa

If ta = 0, B2 = 0 if ca + ma = 1. But if ta > 0 (say, .1, as in Table 1), then it is necessary that ca + ma > 1 (viz., 1.111) - which implies a negative marginal propensity to save ( - .111). One would scarcely expect, therefore, that the entire effect of the autonomous trade changes would be dissipated through opposite induced changes if ta > 0. And if ca + ma < 1 (e.g., .7, as in Table 1), in order that B2 = 0, it is necessary to have a negative marginal tax rate (viz., - .429). A negative t seems even less likely than a negative s - if t is interpreted as the slope of a given tax schedule relating tax collections and income1. However, we may more reasonably assume two tax schedules, one pertaining to the initial equilibrium and one to the new equilibrium after the autonomous trade changes. AY and AT, which previous derivations allow us to calculate, would then define not a movement along one tax schedule, but rather a jump from one schedule to another, with each schedule presumably having the usual characteristic of a positive slope. When thus interpreted, t = AT/ AY may better be termed the marginal tax ratio rather than the marginal tax rate.

1 Comments of S. C. Tsiang were helpful on this general matter.



To indicate the magnitude of the tax policy which would make B2 equal to zero, we can refer to the change in the average tax rate (t). Initially F0 = T/Y; after the autonomous trade changes, we can shift the tax schedule in such fashion that

_ T + AT _ . *i=Y+ _

AY' _ Therefore:

.

_ t T + AT At=Y-YTY'

_ TAY - Y AT _ "~~Y(Y + AY)

*

Assuming the marginal propensities and value of autonomous A(X - M) in Table 1, it follows that AY = 35 and AT = - 15 (and thus t = - .429) in order that B2 = o. With these values, Table 2 is prepared, showing magnitudes of tx and of At at alternative initial income levels when the initial average tax rate is always .25. The higher the initial level of income, ceteris paribus, the smaller the reduction in t is required to offset completely the autonomous changes in trade. However, if t is not reduced or is reduced less than the critical amount, in the new income equilibrium there will remain some improvement in the trade balance.

Table 2 Y AY I T i AT I tp tt At

I : ' : ! 5,000 ; 35 ! 1,250 ; -15 .25 .245 '- .005 1,000 ! 35 i 250 I

- 15 .25 I .227 I - .023 500 ! 35 I 125 I

- 15 .25 .206 -.044 60

j 35

j 15 I -15 25

S - -.250

We may pose a second problem as follows: what is the necessary value of ta, given all other relevant values, which will leave the final balance equal to the initial balance ? We may set Bg/Bj = 1, in which case:

ma (t-1) = mb (l-tb) ^"Ht *- - and solve for ta :

t ~ = ma (sb- sbtb + tb) + mbsa (1- tb) a = ~ ma (sb- sbtb + tb) + mbsa (1- tb) + mb

(tb- 1 j Assuming that tb < 1, it follows that ta > 1. Specifically, if we

assume the same values as were employed in Table 1 for all variables


8o William R. Allen

except ta, then ta = 3.8. This specifies another unusual tax schedule if t is looked upon as a marginal tax rate, and it is preferable again to consider it instead as the marginal tax ratio. In this case, in which induced imports are to be precluded, the average tax rate must rise. The necessary size of the increase will be smaller, the greater is the initial income level.

V. Balances in Domestic and Foreign Currencies The figures we have been using presumably are in terms of the

domestic currency, say, pounds. But the export and import figures relevant for balance of payments (in contrast to national income) analysis are in terms of foreign money, say, dollars. If the exchange rate is not altered, i.e., the balance of payments policy is implemented

Table 3

Case I XrMrB j X,-M$

= B$

(a) * 3 = 1 30-3 = 90-90 = o $ 2 = 1 40-25 = 15 : 80-50 = 30

(b) $ 3 = 1 20 - 30 = - 10 I 60 - 90 = - 30 $ 2 = I 30 30 = O 60 60 = O

(c) $ 3 = / i 20 - 30 = - io , 60 - 90 = - 30 $2 = i 37-32 = 5 ! 74- 64 = IO

(d) $ 3 = 1 20 - 30 = - 10 ; 60 - 90 = - 30 $ 2 = 1 21-29 = - 8 i 42-58 = -16

(e) $ 3 = 1 20-30 = -10 j 60-90 = -30 $ 2 = 1 28-38 = -10 56 - 76 = -20

(f) $ 3 = 1 20-30 = -10 I 60-90 = -30 $2 = i 25-40 = -15 ! 50-80 = -30

(g) $ 3 = i 20 - 30 = - 10 I 60 - 90 = - 30 $ 2 = I 23-41 = -18 46-82 = -36

(h) $ 3 = i 30 - 20 = io 90 - 60 = 30 $2 = i 31 - 21 = io ! 62 - 42 = 20

(i) $ 3 = i 30 20 = IO I 90 60 = 30 $2 = i 31-26= 5 i 62-52= 10

(j) $ 3 = i 30-20 = 10 I 90-60 = 30 $ 2 = I 4O-15 = 25 I 80-30 = 50

(k) $ 3 = 1 30-20 = 10 I 90-60 = 30 $ 2 = I 34-I9 = IS I 68-38

= 30 (1) $ 3 = 1 20 - 30 = IO 60 - 90 = 30

$ 2 = 1 21-34 = - T3 42-68 = -26

(m) $ 3 = 1 30 - 20 = 10 90 - 60 = 30 $2 = i 31-18 = 13 62-36 = 26


A Note on Some Mechanics of the Absorption Approach 8 1

by means other than devaluation, the trade balance will change in the same direction and in the same proportion in terms of both currencies. But with a policy of devaluation, an improvement of the trade balance expressed in pounds may or may not be an improvement in dollar value1; and even if the balance improves in both currencies, it will not improve by the same proportion in both.

This is illustrated in Table 3, which presents alternative cases when the pound is devalued from $ 3 to $ 22. As in case (a), if X = M in terms of one currency, it holds true also in terms of the other currency; and if, through devaluation, a surplus is created in one currency, there will be a surplus in the other. As in case (b), a deficit in one currency is also a deficit in the other; and if the deficit is completely eliminated in one currency, it will be eliminated also in the other. And as in case (c), an "over-correction" of a deficit in one currency will mean the creation of a surplus in the other.

The other ten cases, which are somewhat more complex, in addition to cases (b) and (c), can be summarized thus:

(ia) If a deficit is not increased, the $ deficit falls (cases b, c, d, e). (ib) If a deficit is increased, the effect on the $ deficit is indeterminate

(cases f, g, I)8. (2a) If a $ deficit is not reduced, the deficit rises (cases f, g). (2b) If a $ deficit is reduced, the effect on the deficit is indeterminate

(cases b, c, d, e, 1). (3a) If a surplus is not increased, the $ surplus falls (cases h, i). (3b) If a surplus is increased, the effect on the % surplus is indeter-

minate (cases j, k, m). (4a) If a $ surplus is not reduced, the surplus rises (cases j, k). (4b) If a $ surplus is reduced, the effect on the surplus is indeterminate

(cases h, i, m). Of the four determinate cases, (ia) and (2a) are contrapositive state-

ments, as are (3a) and (4a). 1 Cf. Machlup, op, cit., p. 270, where the issue is raised but only briefly discussed. 1 An aspect incidental to our discussion is that the figures are chosen so that at the new

exchange rate the dollar value of imports is smaller than at the original rate, and the pound value of exports is greater. The changes in the dollar value of exports and in the pound value of imports are indeterminate. These are the results to be expected from the direct price effects of devaluation. See G. Haberler, "The Market for Foreign Exchange and the Stability of the Balance of Payments, A Theoretical Analysis", Kyklos, Vol. Ill, 1949, pp. I97sqq.

The devaluation lowers the dollar price of the pound by 50 per cent. If the pound deficit increases by 50 per cent, the net effect on the initial dollar deficit is zero (case f) ; if the pound deficit increases more than 50 per cent, the dollar deficit rises (case g) ; and if the pound deficit increases less than 50 per cent, the dollar deficit falls (case 1).

Weltwirtschaftliches Archiv Bd. LXXXVI. 6


82 William R.Allen

These relationships can be easily noted algebraically. Let B^ and B|2 be the initial and the new (post-devaluation) dollar balances, B1 and B2 the pound balances, and {$l)i and ($/)2 the exchange rates (dollar prices of the pound). It follows that:

Bf ,($/)! =B$1, B2($/)2 = B$2.

Thus:

B^__B? ($/)2

B$1 ~B~ ~(%)i or:

B$2 _B2 B

"" B ($/)2(/$)i*

Since .


Zahlungsbilanz durch Begriffe der anderen Einkommensvariablen erklrt, empfiehlt es sich, die inlndischen Bedingungen der Auen-bilanz zu analysieren.

Es kann leicht gezeigt werden, da dann, wenn das inlndische Volkseinkommen konstant gehalten wird, die Ausschaltung eines laufenden Zahlungsbilanzdefizits eine quivalente Nichtauf saugung (disabsorption) erfordert, d. h. eine Verringerung des Verbrauchs plus Investitionen plus Regierungsausgaben plus Einfuhren. Jedoch werden die Konsumausgaben steigen, wenn das Defizit durch Krzung der Ein- fuhren beseitigt wird, sofern nicht eine Erhhung der Ersparnisse und der Steuern eintritt, die den gleichen Umfang hat wie der Rckgang der Importe. Wenn das Einkommen unverndert gehalten werden soll, mu ein Ansteigen des Verbrauchs durch eine Verringerung der Investitionen und der Regierungsausgaben wettgemacht werden. Wenn man das Geldeinkommen steigen lt, wird die reale Absorption verringert, wenn gleichzeitig auch die Preise steigen. Ferner wird eine Ausweitung des Geldeinkommens dazu fhren, da Einfuhrsteigerungen ausgelst werden, wo- durch die Zahlungsbilanzverbesserung wieder verringert wird, die man auf Grund der anfnglichen (autonomen) Einfuhrdrosselungen erwartet hatte. Der durchschnittliche Steuersatz mu auf ein bestimmtes Niveau fallen, um die Verbesserung voll- stndig auszuschalten, er mu erhht werden, um die ganze Verbesserung beizu- behalten.

Die vorstehende Analyse wird unter Zugrundelegung inlndischer Wechselkurse durchgefhrt. Wenn die Zahlungsbilanzpolitik mit Hilfe einer Abwertung betrieben wird, wird eine Verbesserung der Zahlungsbilanz oder eine Beibehaltung der be- stehenden Zahlungsbilanzsituation, berechnet auf Grund der inlndischen Whrung, zu einer Verbesserung der Situation, ausgedrckt in auslndischer Whrung, fhren. Ein Anwachsen des Defizits in heimischer Whrung mag oder mag nicht eine Ver- besserung der Devisenbilanz herbeifhren. Dies hngt davon ab, ob das Defizit an auslndischen Zahlungsmitteln mehr oder weniger proportional zunimmt als der Grad der Abwertung.

*

Rsum: Au sujet de certains mcanismes de la thorie de l'absorption. - L'ide d'expliquer la balance des paiements en l'approchant du ct absorption se base sur un modle du revenu national, qui comprend des composants de commerce extrieur. Si l'on exprime la balance des paiements par les autres variables du revenu, il sera utile d'analyser les conditions nationales de la balance extrieure.

On peut facilement dmontrer que, si le revenu national montaire reste constant, on ne saurait liminer un dficit courant qu'au moyen d'une non-absorption (disabsorption) quivalente, c'est dire, d'une rduction de consommation plus investissements plus dpenses du gouvernement plus importations. Toutefois, si le dficit est limin par la rduction des importations, les dpenses de consommation monteront, s'il n'y a pas d'augmentation correspondante aux pargnes et impts. Si l'on veut garder le revenu inchang, toute augmentation de la consommation doit tre balance par une diminution des investissements plus dpenses du gouvernement. Si l'on permet au revenu montaire de monter, l'absorption relle est rduite au cas que les prix montent eux aussi. En plus, l'expansion du revenu dclenchera l'augmentation des importations, ce qui diminuera de nouveau l'amlioration de la balance des paiements, qu'on pouvait esprer la suite du retranchement initial (autonome) des importations. Le taux moyen d'imposition devrait tomber un certain niveau, pour que l'amlioration soit compltement limine; il devrait monter, pour que l'amlioration soit prserve intacte.

6*


84 William R. Allen

Cette analyse est faite sur la base des cours de changes nationaux. Si la politique de la balance des paiements comprend une dvaluation, et qu'on arrive amliorer la balance des paiements, ou bien la garder inchange, calcule en monnaie nationale, ceci amnera une amlioration de la situation, calcule en monnaie trangre. L'augmentation du dficit en monnaie national pourra, ou ne pourra pas entraner une amlioration de la balance en monnaie trangre. Ceci dpendra de l'augmentation du dficit en monnaie nationale proportionnellement plus ou moins grande que celle du degr de dvaluation.

Resumen: Notas sobre algunos mecanismos de la teora de absorcin. - La prueba de explicar la balanza de pagos por una consideracin de absorcin (ab Sorption approach) se basa en un modelo de la renta nacional incluyendo compo- nentes de comercio exterior. Si se explica la balanza de pagos por conceptos de las dems variables de la renta, ser conveniente analizar las condiciones interiores de la balanza exterior.

Puede fcilmente mostrarse que, si la renta nacional interior es mantenida constante, la eliminacin de un dficit corriente de la balanza de pagos requiere una no-absorcin (disabsorption) equivalente, es decir una reduccin del consumo ms de inversiones ms de gastos gubernamentales ms de importaciones. Pero los gastos de consumo aumentarn, a no ser que ahorros e impuestos elevados igualen las importaciones reducidas. Si se quiere, que la renta sea mantenida sin cambiar, un aumento del consumo debe ser compensado por una disminucin de las inversiones y de los gastos gubernamentales. Si se hace subir la renta monetaria, es reducida la absorcin real, si los precios aumentan al mismo tiempo. Adems una expansin de la renta monetaria causar un aumento de las importaciones y de tal manera es reducido el mejoramiento de la balanza de pagos, esperado a base de la reduccin inicial (autnoma) de las importaciones. El tipo medio de impuesto debe bajar a cierto nivel para eliminar completamente el mejoramiento y debe subir para preservar el mejoramiento entero.

El anlisis precedente es ejecutado a base de los cambios interiores. Si la poltica de la balanza de pagos es practicada mediante una devaluacin, de un mejoramiento de la balanza de pagos o de un mantenimiento de la situacin de la balanza, calcolada a base de los cambios interiores, resultar un mejoramiento de la situacin expresada en moneda extranjera. Un aumento del dficit en moneda interior puede o no puede significar un mejoramiento de la balanza de las divisas. Esto depende de la circun- stancia, si el dficit de medios de pago extranjeros aumenta ms o menos proporcio- nalmente que el grado de la devaluacin.

*

Riassunto: Note su alcuni meccanismi della teoria dell'assorbimento. - II tentativo di esplicare la bilancia dei pagamenti mediante una considerazione deas- sorbimento (absorption approach) si basa su un modello del reddito nazionale che rinchiude anche componenti di commercio estero. Se la bilancia dei pagamenti esplicata per concetti delle altre variabili di reddito, sar raccomandabile di analizzare le condizioni interne della bilancia estera.

Pu facilmente essere mostrato che, se il reddito nazionale interno mantenuto costante, l'eliminazione di un dficit corrente della bilancia dei pagamenti richiede un non-assorbimento (disabsorption) equivalente, cio una riduzione del consumo



pi d'investimenti pi di spese di governo pi d' importazioni. Per le spese di consumo aumenteranno a meno che risparmi ed imposte elevati non adeguino le importazioni ridotte. Se si vuole che il reddito sia mantenuto inalterato, un aumento del consumo dev'essere compensato per mezzo d'una diminuzione degli investimenti e delle spese di governo. Se si fa crescere il reddito monetario, l'assorbimento reale ridotto, se i prezzi aumentano allo stesso tempo. Di pi un'espansione del reddito monetario causer un aumento delle importazioni e con ci ridotto il miglioramento della bilancia dei pagamenti, aspettato in base alla riduzione iniziale (autonoma) delle importazioni. Il tasso medio dell'imposta deve cadere a un certo livello onde eliminare completamente il miglioramento, e deve crescere onde pre- servare l'intiero miglioramento.

La precedente analisi eseguita in base ai cambi intcriori. Se la politica della bilancia dei pagamenti fatta per mezzo d'una devalutazione, da un miglioramento della bilancia dei pagamenti o da un mantenimento della situazione della bilancia, calcolata in base ai cambi intcriori, risultar un miglioramento della situazione espressa in moneta estera. Un aumento del deficit in moneta interiore pu o non pu significare un miglioramento della bilancia delle divise. Questo dipende dalla cir- costanza, se il deficit dei mezzi di pagamento aumenta pi o meno proporzionalmente che il grado della devalutazione.


Article Contentsp. [69]p. 70p. 71p. 72p. 73p. 74p. 75p. 76p. 77p. 78p. 79p. 80p. 81p. 82p. 83p. 84p. 85

Issue Table of ContentsWeltwirtschaftliches Archiv, Vol. 86 (1961) pp. I-XII, 1-377, 1-96Front MatterZur Interpretation des Artikels 65 des Montanvertrages [pp. 1-45]Some Income and Wage Distribution Theories. Summary and Comments [pp. 46-68]A Note on Some Mechanics of the Absorption Approach [pp. 69-85]Zur Produktivittsfunktion der finnischen Industrie [pp. 86-102]Recent Developments in American Business Administration and Their Conceptualization [pp. 103-130]BerichteRelative Production Levels of Industrial Countries and Their Growth Potentials [pp. 131-143]Die britische Einkommensteuerreform als evolutorischer Proze. Zum Final Report der Royal Commission on the Taxation of Profits and Income [pp. 144-193]

An unsere Leser [pp. 195-195]A Theory of Unbalanced Growth in the World Economy [pp. 196-217]The Cost-Push Theory of Inflation and Tight-Money Policy [pp. 218-231]Das konomisch rationale Steuersystem [pp. 232-285]The Inventory Problem: A New Model with Uncertainty [pp. 286-302]Zur Rentabilitts- und Liquidittsplanuug von Kreditinstituten [pp. 303-351]BerichteDie wirtschaftswissenschaftliche Ausbildung in der Schweiz [pp. 353-362]Das wirtschaftswissenschaftliche Studium an den niederlndischen Hochschulen [pp. 363-377]

SchrifttumBesprechungsaufstzeZentralplanung in Ungarn [pp. 1-7]

Einzelbesprechungen und AnzeigenReview: untitled [pp. 8-9]Review: untitled [pp. 9-10]Review: untitled [pp. 10-12]Review: untitled [pp. 12-13]Review: untitled [pp. 13-14][Anzeigen] [pp. 14-15]Review: untitled [pp. 15-17][Anzeigen] [pp. 17-17]Review: untitled [pp. 18-20]Review: untitled [pp. 20-23]Review: untitled [pp. 23-24]Review: untitled [pp. 24-26][Anzeigen] [pp. 26-26]Review: untitled [pp. 26-27][Anzeigen] [pp. 27-28]Review: untitled [pp. 28-30][Anzeigen] [pp. 30-31]Review: untitled [pp. 31-33]Review: untitled [pp. 33-35][Anzeigen] [pp. 35-35]Review: untitled [pp. 35-36]Review: untitled [pp. 36-42]Review: untitled [pp. 42-42][Anzeigen] [pp. 42-42]

BesprechungsaufstzeNeuberechnung einiger Schtzwerte fr deutsche Konsumfunktionen [pp. 51-61]

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absorption approach

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