Domestic Financial Policies under Fixed and under Floating Exchange Rates (Politiques

finacièrieures intérieures avec un système de taux de change fixe et avec un système de

taux de change fluctuant) (Política financiera interna bajo sistemas de tipos de cambio fijos
o de tipos de cambio fluctuantes)
Author(s): J. Marcus Fleming
Source: Staff Papers (International Monetary Fund), Vol. 9, No. 3 (Nov., 1962), pp. 369-380
Published by: Palgrave Macmillan Journals on behalf of the International Monetary Fund
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 Domestic Financial Policies Under Fixed
and Under Floating Exchange Rates
J. Marcus Fleming*
T HE BEARING of exchange rate systems on the relative effective-
ness of monetary policy on the one hand, and of budgetary policy
on the other, as techniques for influencing the level of monetary de-
mand for domestic output, is not always kept in mind when such
systems are compared. In this paper it is shown that the expansionary
effect of a given increase in money supply will always be greater if
the country has a floating exchange rate than if it has a fixed rate.
By contrast, it is uncertain whether the expansionary effect on the
demand for domestic output of a given increase in budgetary expendi
ture or a given reduction in tax rates will be larger or smaller with
a floating than with a fixed rate. In all but extreme cases, the
stimulus to monetary demand arising from an increase in mone
supply will be greater, relative to that arising from an expansionary
change in budgetary policy, with a floating than with a fixed rate of
exchange.

The Model

Let us assume a simple Keynesian model' in which (a) taxati

and private income after tax both vary directly with national inco
(b) private expenditure (on consumption and investment) varies d
rectly with income after taxation,2 and inversely with the intere
rate, (c) the interest rate varies directly with the income-velocity
circulation of money (the ratio of national income to the stock
money), (d) the balance of trade (exports less imports of goods
services) varies inversely with domestic expenditure3 and dire
with the domestic currency value of foreign exchange, and (e)
*Mr. Fleming, Advisor in the Department of Research and Statistics, i
graduate of Edinburgh University. He was formerly a member of the Leagu
Nations Secretariat, Deputy-Director of the Economic Section of the U.K
Cabinet Offices, U.K. representative on the Economic and Employment Co
mission of the United Nations, and Visiting Professor of Economics at Colu
University. He is the author of numerous articles in economic journals.
1 See Appendix (pp. 377-79) for a mathematical formulation.
2 It is assumed that the private marginal propensity to spend will alway
less than unity with respect to income before tax.
3 It is assumed that the marginal propensity for the balance of trade to dec
as expenditure increases is less than unity.
369

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370 INTERNATIONAL MONETARY FUND STAFF PAPERS

balance of payments on capital account varies directly with

of interest. All magnitudes are expressed in domestic wage
wages are assumed to remain constant in domestic currency
count is taken of any changes in the propensity to spend f
income changes that result from changes in the terms of t
account is taken, initially, of the effect of exchange specu
capital movements.

Effects of an Expansionary Shift in Budgetary P

Let us first compare the effects of an expansionary shift

etary policy brought about by an increase in public expenditure,
without any change in tax rates, under (a) a fixed exchange rate
system and (b) a floating exchange rate system, respectively. (A
decline in taxation, resulting from a reduction in tax rates, would
have effects on expenditure, income, and the balance of payments
similar to, though less powerful than, those resulting from an equal
increase in public expenditure. No essential feature of the ensuing
analysis would be altered if it had been concerned with the former
rather than the latter type of budgetary expansion.)
Under fixed exchange rates, an increase in public expenditure will
give rise to an increase in income which will be associated-if the
economy was previously underemployed-with increases in employ-
ment and output.4 The increase in expenditure will lead to a deteri-
oration in the balance of payments on current account, owing, nota-
bly, to a rise in imports. The increase in expenditure and income will
also enhance tax revenues, though not to such an extent as to equal
the initial increase in public expenditure.5
In order to isolate the effect of a change in budgetary policy, it is
necessary to assume that monetary policy remains, in some sense, un-
changed. In this paper, that is taken to mean that the stock of money
is held constant.6 To keep the money stock constant while the in-
crease in government expenditure is pushing up incomes will necessi-
tate economy in the use of money which is possible only if the interest
4 Since the marginal propensity to spend out of income is less than unity and
since a fraction of each round of expenditure leaks abroad in additional net im-
ports, the increase in income and expenditure will be limited, though possibly
large. See Appendix, paragraphs 3 and 4.
5 The rise in tax revenue could exceed the initial rise in government expendi-
ture only if the marginal propensity to spend out of private income after tax
were substantially greater than unity. See Appendix, paragraph 5.
6 The only clear-cut alternative would appear to be that of defining constancy
of monetary policy as the maintenance of a constant rate of interest. In "Flexi-
ble Exchange Rates and Employment Policy," Canadian Journal of Economics

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 DOMESTIC FINANCIAL POLICIES 371

rate is raised or allowed to rise. The rise in interest in turn will

result in (a) a check to the increase in expenditure and income,
though some increase will remain,7 and (b) a favorable shift in the
balance of payments on capital account, i.e., a decline in capital
exports and/or an increase in capital imports.
Since the increase in public expenditure provokes an unfavorable
shift in the current balance and a favorable shift in the capital bal-
ance, it is uncertain whether the balance of payments as a whole will
deteriorate or improve. It is the more likely to deteriorate, and the
less likely to improve, the higher is the marginal propensity to import
and the greater the adverse effect on the value of exports as domestic
expenditure increases, the less sensitive is the rate of interest to
changes in money income and hence in the velocity of circulation,
and the less sensitive are capital movements to changes in the rate of
interest.8
To the extent that the increase in public expenditure gives rise to
an improvement or a deterioration, respectively, in the balance of
payments, the maintenance of a constant stock of money will call for
a decline or an increase, respectively, in the rate of expansion of bank
credit. More important is the fact that, if the policy of budgetary
expansion results in a deterioration of the balance of payments, short-
age of reserves may ultimately compel the authorities to abandon the
policy and to renounce the associated expansion in income and em-
ployment.9
Suppose, now, that the increase in public expenditure takes place
in a country where the balance of payments is kept in equilibrium
through exchange rate adjustments. Then, if the parameters of our
model-notably the sensitivity of capital movements to changes in
the rate of interest-are such that a rise in public expenditure would
have resulted, with a fixed exchange rate system, in a deterioration
in the balance of payments, it will result, with a floating rate system,
in a depreciation of the exchange rate, which will bring about a
partial restoration of the trade balance. (This restoration will, in

and Political Science (November 1961), Mr. R. A. Mundell has compared the
effects of monetary policy (defined as interest policy), fiscal policy, and com-
mercial policy in a flexible exchange rate system and a fixed exchange rate
system, respectively.
7 It is uncertain whether private expenditure, stimulated by the rise in income
and depressed by the rise in interest, will increase or decrease. But expenditure
as a whole, like income, will increase, except where income velocity is entirely
inelastic. See Appendix, paragraphs 6 and 7. In this extreme case, not only ex-
penditure but also income and the balance of trade will remain unchanged.
8 See Appendix, paragraph 8.
9It is assumed not only that the exchange rate will remain fixed but that
there will be no resort to restrictions on international transactions,

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372 INTERNATIONAL MONETARY FUND STAFF PAPERS

general, be only partial since some net deterioration of the

ance, compared with the situation before the rise in publ
ture, must remain to offset the improvement in the capi
To the extent that the current balance is restored, there
increase-over and above that discussed above-in expen
come, and output. In other words, the stimulus to income
and employment resulting from a given increase in public
will be greater with a floating exchange rate than with a
change rate.10 If capital movements were entirely insensi
rise in the rate of interest, the exchange rate would d
whatever extent was necessary completely to restore the
ance, and the stimulus to income and output would be
order as would have occurred in a closed economy.
On the other hand, if a rise in public expenditure wo
fixed exchange rate, have effected an improvement in th
payments, it will, with a floating rate, lead to an exchang
tion; and, to the extent that appreciation intensifies the d
in the trade balance, the net stimulus to income, output, a
ment will be less than in an open economy with a fixed rat
sight, the case in which a rise in government expenditur
an exchange appreciation would appear to be an academ
without practical significance. However, as is shown in a
pared by Mr. R. R. Rhomberg, expounding an econometri
the Canadian economy, the responsiveness of internati
movements to changes in interest rates, and the respon
interest rates to changes in money national income, ha
been sufficiently great in that country over a large part of
period, relative to the marginal propensity to import, fo
government expenditure at a constant money stock to ha
to produce just such a result.
It is of interest to note that, if the flow of capital b
country and the outside world were infinitely elastic wit
the interest rate, the appreciation of the exchange rate res
the inflow of capital would bring about a net deterior
current balance of payments large enough to offset comp
stimulating effect of the budget deterioration on natio
National income would not increase at all, and the interest
remain at the original level.12

10 See Appendix, paragraph 10.

11 Ibid.
12 See Appendix, paragraph 11.
A high sensitivity of the interest rate to changes in velocity of cir
a low elasticity of velocity with respect to the interest rate, while

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 DOMESTIC FINANCIAL POLICIES 373

Effects of an Increase in the Stock of Mon

Now, let us compare the effects on income, output, and

of increasing the stock of money (a) with fixed exchange
(b) with floating exchange rates, respectively.
An increase in the stock of money will entail a dec
velocity of circulation and lead to a reduction in the rate
which will stimulate an increase in private expenditure on
and consumption, both directly and via the Keynesian
The rise in expenditure will be associated, as before, with
increase in income and output13 and a deterioration in th
payments on current account.14 The rise in income will m
decline in the rate of interest but not to the point of eli
otherwise, neither investment nor income could increase.1
monetary expansion, even after the rise in expenditure a
lowers the interest rate, some deterioration will tend to
balance of payments on capital account. In the case of
expansion, therefore, by contrast with that of an increas
expenditure, a deterioration in the balance of payment
is bound to occur in all circumstances. It follows that the
expansion, and the associated expansion of income and ou
only be sustained indefinitely to the extent that in their
balance of payments would have been favorable.
It is easy to see that a monetary expansion must alw
a more powerful effect on income and output when ther
floating rate of exchange than when the exchange rate is
initial tendency toward an adverse shift in the balance of
will cause a depreciation of the exchange rate to whatever
be necessary to keep external transactions as a whole in b
favorable influence of the exchange depreciation on the t
must come to outweigh the adverse influence of the incr
come to whatever extent may be necessary to produce a ne
ment in that balance equal to the deterioration in the cap
The stimulus afforded by the depreciation to the trade b

favorable balance of payments response to government spending

therefore tends to make the income response smaller under floatin
fixed exchange rates, also tends to reduce the magnitude of that re
both exchange systems. If the velocity of circulation were compl
a change in government expenditure would have no net effect on
either exchange system.
13 See Appendix, paragraph 12.
14 See Appendix, paragraph 13.
15 See Appendix, paragraph 14.

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374 INTERNATIONAL MONETARY FUND STAFF PAPERS

also act, both directly and via the multiplier, as a stimulus

raising it above the level which would have prevailed w
exchange rate.16
The expansive effect of a given increase in the stock
under the floating exchange rate system will be the gr
greater the responsiveness of the international capital flow
ments in the rate of interest. If there were no responsive
ever, the exchange rate would depreciate to the point at wh
the monetary expansion, no change occurred in the current
payments. Income would expand to the same extent as
economy. On the other hand, if the capital flow were infin
with respect to the interest rate, the exchange rate would
to the point at which the balance of trade became so favor
income increased so much, that the rate of interest remai
original level. This implies that money income would incre
same percentage as the stock of money.17

Relative Effects of the Two Kinds of Financial P

It remains to show that the effect on income and output

monetary expansion relative to that of a given budgetary
will never be less, and will generally be greater, under a f
change rate than under a fixed rate, even where budgetar
has a tendency to cause a depreciation of the exchange valu
currency.18 The simplest way to demonstrate this is to co
increase in the monetary stock (Policy A) and an increas
expenditure (Policy B) such that, under a fixed exchang
two policies have equal effects in the aggregate on income
and employment, and to show that, under a floating rate,
of Policy A will never be less, and will in general be gr
that of Policy B.
Since we have supposed that under a fixed exchange rate
policies have the same aggregate effect on income and out
will bring about approximately the same adverse shift in t

16 See Appendix, paragraphs 15 and 16. However, in the extrem

velocity of circulation is completely inelastic, money income will
tionately to the money stock under either exchange system. See App
graph 17.
17 See Appendix, paragraph 18.
18 To put the same thing in other words, the effect under a floating rate relative
to the effect under a fixed rate will never be greater, and will generally be less,
in the case of budgetary expansion than in the case of monetary expansion.

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 DOMESTIC FINANCIAL POLICIES 375

of trade.19 Since, with incomes the same under the two poli
money stock will be greater and the velocity of circulation le
Policy A than under Policy B, the rate of interest will be les
the former than under the latter policy. If capital movemen
totally insensitive to changes in the interest rate, the tw
would, under a fixed exchange rate, have the same effects on
ance of payments as a whole; and under a floating rate, they
require an equal exchange depreciation to restore external equ
The consequent restoration of the trade balance and the a
further stimulus to income would be the same for the two p
However, if capital movements respond in any degree to
changes, the two policies will have different effects. Since P
reduces, and Policy B raises, the rate of interest, Policy A
fixed exchange rate will occasion a more unfavorable capital
than Policy B. It follows that under a floating rate, Polic
require, to restore payments equilibrium, a deeper exchange
tion, and will consequently bring about a greater improvemen
trade balance, and a greater stimulus to income and outp
Policy B.20 The superiority of Policy A over Policy B as a me
increasing income and output depends notably, as we have
the sensitivity of international capital movements to change
rate of interest. At zero sensitivity, there is nothing to choos
the two policies. If the sensitivity is infinite, the level of in
sulting from Policy A will exceed that resulting from Po
much the same proportion as the money stock under A exce
under B.
The nature of the exchange regime has an important bearing not
only on the relative effectiveness in influencing income and output of
the two types of financial policy-monetary policy and budgetary
policy-but also on their relative practicability or sustainability.
Thus, under a fixed exchange rate-except to the extent that the ex-
ternal accounts were originally in surplus-monetary expansion can
be sustained only as long as reserves hold out, while budgetary ex-
pansion, if capital movements are sufficiently sensitive to interest
rates, may be sustained indefinitely.21 Under a floating exchange
rate, on the other hand, not only is monetary expansion, while it lasts,
likely to generate more additional income than budgetary expansion,
19 We have to neglect, as unknown, any effects on trade of the difference in
the composition of expenditure under the two policies.
20 See Appendix, paragraph 19.
21 It should be noted, however, that the responsiveness of capital movements
to interest rate changes is made up of two components: a relocation of existing
capital and a shift in the location of the placement of new savings. Since the
former component is nonrecurrent and the latter recurrent in character, it is

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376 INTERNATIONAL MONETARY FUND STAFF PAPERS

relative to what would happen under a fixed exchange rate

types of policies can be sustained indefinitely, so far as th
of payments situation is concerned.

The Exchange Speculative Element in Capital Mo

The foregoing argument has generally assumed the absen
change speculation. Under a floating exchange rate, the inf
exchange speculation varies according to whether it is equilib
disequilibrating. If it is equilibrating-as was generally the c
example, in Canada in the 1950's-it will tend to mitigat
change rate variations resulting from variations in interna
policy, whether that policy is budgetary or monetary in ch
However, since the greater relative effectiveness which a flo
gives to monetary policy, compared with budgetary pol
tributable to the stronger influence that the former exerc
change rates, it is to be expected that equilibrating specu
damping down exchange rate effects, will tend to reduce the
in effectiveness between the two kinds of policy. Disequ
speculation on the other hand, by exaggerating exchange r
tions, tends to accentuate this difference in effectiveness.22

probable that the sensitivity of capital movements to interest cha

greater in the short run than in the long run. Consequently, the diff
tween the two policies with respect to effectiveness and sustainability is also
likely to be less in the long run than in the short.
22 Exchange speculation has a bearing not only on the relative effectiveness,
but also on the practicability and sustainability, of the two policies. Under ex-
change rates that are fixed and are expected to remain so, exchange speculation
would be absent. But if confidence in the fixed rate were less than complete,
the fear of arousing disequilibrating movements of capital would tend to limit
the magnitude and duration of the expansionary financial policies, particularly
of monetary policy, the effect of which on the balance of payments is in any
case the more adverse than that of budgetary policy.

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 DOMESTIC FINANCIAL POLICIES 377

APPENDIX

1. Let Y stand for national income,

T for taxation,
N for private income,
X for private expenditure,
S for public expenditure,
Z for total expenditure,
B for exports less imports,
M for stock of money,
V for income velocity,
R for rate of interest,
C for net capital import, and
F for domestic currency value of foreign currency.
2. Then
Y=X + S + B.
z = x + S.
y

N = Y - T.
T=T(Y). 1 > Ty > 0.
X X(NIR). Xr < 02 1 > X,,(l - Ty) > 0.
R =R(V). R, > 0.
B =B(Z,F). 1 > - B, > O. Bf > 0.
C = C(R).

3 Let (dY)00 signify dunder fixed exchange rates whe

Let d I dTI IdC idB dC -IdB be analogou

\dS/o' \dS/s' \dS '\ dS /0'0\dR/ a' \dR/s
Then dY 1 1 +B
d ' (11+B,z)X,(1 - Ty)+
4. Since 1 > - B, > 0,
1 > X. (1 - Ty) > 0,
and X,< O,
> 0.

5. For the same reasons,

(dT) Ty (1 + B,)

6(dX\
dS55 1
> 0
-1

(1 +B.) ~X.(1 - Ty)

as X,(1- Tv)
2M <
+ XR>

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378 INTERNATIONAL MONETARY FUND STAFF PAPERS

7. (dZ 1 >0.
\dS/oo M
1 -(1 + B,
8.(dR\ R, dY\
8. dSoo M dS)oo > .
(dC) +dB) (dR)\ (dC) (dB)
Tds}w \dS}w \dSw I \dR}w 1 \dR 0
MB, > O
= Rv(1 + Bz) <
CrR, > -Bz
as M < 1 + B,
as

9. Let(dY) s ignify dY
9. Let d(-i signify
\ dS10 -dS under floating exchange rates, when
lo dS
dB + dC = 0 and dM = 0.

Then(d o 1 > 0.
o X(1 -Ty) X _ X C)

10.dY > dY as\ -B > R,as

10 dS / < \dS-oo 1 +B, < M
(dC\ + (dB\ <-
i.e., as )oo + (doo>
11. As Cr-> oo,
(dY\ 1

->0.

(dY\ dY
12. Let -dM = dM at fixed exchange rates when

Let (dRM)o (d-M)l (d)l be analogously defined

/dY\ -XrR,Y - 1
\dM)olB M2 1 XrR
dM- l1 1
_B, -
) M Xn(l - Ty) -
(dB\
M13 -+ 0Mo1
(dC B,
dM(dY +B
~ 1 + C \dMa
(dR <r + M <dM

14 dR = -RY 1 -X(B, + 1) (1 -T) -

15. Let (dM) = dM under floating exchange rates, when dB +

dS = 0.

dYTh\dM}
TLen _ - R,Y(C,
~= M2 -Rd(Cr1
X,) - 1, - X) 0
1 - -

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 DOMESTIC FINANCIAL POLICIES 379

(16 (dY\ (dY\

16 dM)n dM)ol
R,Y - Cr - X Xr
M2 X,(l
M2 -Xn(-TV)+j (Ty) +
> (Cr-X,)
B. B, +1Mm
+1 )-
> 0.

17. AsR,- oo,

(dY\ Y
dM oi M

and dY y
\dM/11 M
18. As C,- oo,
/dY\ CrR,Y Y
kdM n MCrRv M

(dY\
19. Letf = M2
(dY\ -X,R,Y
\dM)01
(dY
Then dS l- M <
/ dY (C - Xr)RvY
\dMjll
unless Xr = -oo
or R, = ?o.

Politiques financieres int6rieures avec un systeme de taux de

change fixe et avec un systkme de taux de change fluctuant

Resume

Les comparaisons entre les systemes de taux de change ne tiennent

pas toujours compte des incidences de ces systemes sur l'efficacit6
comparee de la politique monetaire d'une part, et de la politique budge-
taire d'autre part, en tant que moyens techniques d'influencer le niveau
de la demande monetaire de la production interieure. Le present article
montre que l'expansion resultant d'une augmentation donnee de la
masse monetaire sera toujours plus forte si le pays a un taux de change
fluctuant que s'il a un taux fixe. Au contraire, il n'est pas certain que
l'accroissement de la demande de production interieure resultant d'une
augmentation donnee des depenses budgetaires ou d'une reduction

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380 INTERNATIONAL MONETARY FUND STAFF PAPERS

donnee des taux d'imposition soit plus fort ou plus faible a

fluctuant qu'avec un taux fixe. A l'exception des cas extremes,
stimulante exerc6e par l'augmentation de la masse mon
toujours plus grande, en comparaison avec celle qui re
politique budgetaire a caractere expansionniste, lorsque
change est fluctuant que lorsqu'il est fixe.

Politica financiera interna bajo sistemas de tipo

de cambio fijos o de tipos de cambio fluctuantes

Resumen

Al establecer una comparaci6n entre los sistemas cambiarios, no

siempre se toma en consideracion la influencia que estos ejercen sobre
la eficacia relativa de la politica monetaria y la politica presupuestaria
como medios de influir en el nivel de la demanda monetaria de la
producci6n interna. En este estudio se demuestra que cuando un pais
emplea un tipo de cambio fluctuante, el efecto expansionista de u
aumento dado del medio circulante sera siempre mayor que cuand
emplea un tipo de cambio fijo. Por otra parte, no se sabe si el efecto
expansionista que ejerceria sobre la demanda de la producci6n intern
un aumento dado de los gastos presupuestarios, o una disminuci6
dada de las tasas tributarias, habria de ser mayor o menor con u
tipo de cambio fluctuante que con un tipo de cambio fijo. Salvo e
casos extremos, cuando el tipo de cambio es fluctuante, el estimu
que ejerce sobre la demanda monetaria un aumento del medio cir
culante sera siempre mayor, en relacion con el que provoca una mod
ficacion de caracter expansionista de la politica presupuestaria, qu
cuando el tipo de cambio es fijo.

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