DE ECONOMIST 130, NR. 2, 1982
M O N E T A R Y P O L I C Y IN A N O P E N E C O N O M Y W I T H PRIVATE DEBT: ANOTHER VARIATION ON THE IS/LM T H E M E BY H. VISSER*
1
INTRODUCTION
Nonmonetary financial instruments, such as bonds and shares, lead a somewhat uneasy and shadowy life in 1S/LM-type analyses. The liquidity preference theory which underlies the LM-curve assumes the existence of bonds of course. Usually, however, no curve or equation for the bond market is included in the model. Noninclusion of the bond market is based upon the validity of Walras's Law, which is mostly taken for granted in this connection, and is only occasionally explicitly assumed (e.g., Bailey, 1962, p. 119). Walras's Law says that in an n-equation system n - 1 equations are sufficient to establish the equilibrium values of the dependent variables. So why not delete the equation or curve for the bond market? Even if we follow the conventions of our science and accept the validity of Walras's Law and the Walrasian framework with its clearly defind excess demands and excess supplies (which are not as self-evident as may be thougt, cf. Kornai, 1980, especially pp. 319-322, 476-479), it nevertheless seems advisable to include an equation for the bond market or more generally the capital market in the system and not to delete any equation. There are two reasons for this. Firstly, if we leave out one equation, the remaining equations may well be sufficient to establish the equilibrium values of the system, but the dynamics of the system may become obscured. When, for instance, Harry Johnson added a curve for the bond market to the IS/LM-diagram, it turned out that the loanable funds theory and the liquidity preference theory of interest rate * Professor of Monetary Economics, Free University, Amsterdam. I am indebted to Dr. W.J.B. Stairs, Prof. F.C. Palm and Mr. S.C.W. Eijffinger for helpful comments. Mrs. Brummel-Meeke kindly corrected m y English. Unfortunately they cannot b e held responsible for any mistakes or faulty reasoning.
M O N E T A R Y POLICY IN AN OPEN E C O N O M Y
265
determination might conflict in this framework also (Johnson did not know how to solve this conflict, el. Johnson, 1971, pp. 12-14, but subsequently A.G. Hines provided an elegant and simple solution by abandoning the timeless nature of the Walrasian system in which bonds can be directly exchanged against goods; he resolved the conflict between the loanable funds theory and the liquidity preference theory by making bonds only exchange against money and replacing current income by planned expenditure as an argument in the money demand function, see Hines, 1971). Secondly, if we do not include the bond market in our system, developments which influence the equilibrium solution of the system may be hidden from view. If, for instance, a government f'mances an expansion of its expenditures by borrowing on the capital market, the resulting increase in the volume of bonds and the consequent adjustment of the private sector's portfolio, which will in most cases push the rate of interest upward independently of income changes, will easily be neglected. Fortunately, IS/LM-type models which explicitly take account of the demand for and supply of government bonds are becoming more and more commonplace. The general run of models with a government budget constraint (in which a public sector borrowing requirement is financed either by creating money or by selling bonds) do not, however, contain a separate equation or curve for the bond market. In these models, government bonds are a part of private sector wealth and in this guise appear in the money demand and the expenditure functions (el Blinder and Solow, 1973 and 1974, Havrilesky and Boorman, 1978, Ch. 12; Infante and Stein, 1976; Silber, 1970; Choudry, 1976; in general the literature concerned with the 'crowding out' of private expenditure by government expenditure). Models with separate demand functions for bonds are less widespread (examples are Argy and Kouri, 1974; Steinherr, 1975). Compared with the growing attention that government bonds are receiving, private sector bonds still suffer from neglect. Though Patinkin showed the way in his Money, Interest, andPriees (Patinkin, 1965, pp. 2 1 3 221), the followers were few (el Crouch, 1972, especially Chs.5 and 6 curiously, in Ch. 13 on the Hicksian IS/LM analysis it is assumed that the bond market clears when the money market clears and the bond market is therefore excluded from the discussion - Bhaskar and Murray, 1976, Ch. 8). In the model developed in the next section and which is then used to study the impact of monetary policy on the balance of payments, the demand for and supply of private sector bonds play a crucial role. The distinguishing feature of this model is that all private sector borrowing is by selling bonds, which are either taken up by the private nonbank sector itself or by
266
H. VISSER
the banks. The distribution of these bonds, that is the distribution of the supply of credit over the banks and the private sector, is exclusively determined by the public's demand for money, domestic bonds and foreign bonds, respectively. Banks passively adjust to the wishes of the public. In this model the LM-curve is not supplemented by a curve for the bond market, either, but the LM-curve is transformed into a curve showing the equilibrium conditions for the financial markets, both the Walrasian money market and the bond market. The emphasis in this article is on monetary policy. The introduction of fiscal policy would imply the necessity to introduce government bonds also, which would unduly complicate the analysis. We follow the great majority of models for an open economy by restricting ourselves to a small economy which has to take the foreign rate of interest, the foreign price level and the foreign level of income as given. After the model has been developed, monetary policy will first be analysed for the fixed exchange rate case, and then for the flexible exchange rate case. 2
THE MODEL
Our model is an elaboration of the standard IS/LM-model for an open economy. In order not to burden the analysis with nonessentials, we neglect wealth effects throughout. The model will be developed for the general case with the possibility of price level changes built in, but the analysis will be restricted to the fixed price level case (apart from a brief discussion of the consequences of changes in the price level at the end of the article). The equilibrium condition for the goods market is
y =z(y,r) + ex(e/P,y*) -e/P. ira(y, e/P)
(1)
where y = real national income, z = real domestic expenditure, r = the rate of interest, e = the domestic price of foreign commodities, P = the price level, im= real imports. An asterisk refers to the rest of the world. It should be noted that e/P is the reciprocal of the (commodity) terms of trade and that e/P. irn is the real volume of imports, measured in terms of the domestic good. e reflects both the foreign price level and the rate of exchange. Using subscripts for partial derivatives, we assume that
1 >Zy >O,z r O, exy, >O, imy >O, ime/p
M O N E T A R Y POLICY IN AN OPEN E C O N O M Y
267
restriction 1 > Zy implies that the /S-curve is downward-sloping. A higher value Of Zy is indeed conceivable if not only consumption but also investment is a positive function of the level of income. We abstract, however, from the case of Zy ~> 1, which would imply a horizontal or upward-sloping/S-curve. We next introduce the equilibrium condition for the Walrasian money market: Md(y,P,r) = NFA_ 1 + Q + NDA + H
(2)
where M d = nominal demand for money, N F A = net foreign assets of the banking system and N F A _ 1 = net foreign assets one period back, Q = the surplus of the balance of payments (surplus on the balance of nonmonetary transactions) during the current period, N D A = net domestic assets of the banking system, i.e., private sector bonds taken up by the banks, H = the monetary policy parameter. Net foreign assets consist of both the official reserves held by the monetary authorities and the net foreign assets of the commercial banks. Q therefore refers to the transactions of the nonmonetary sectors. If these transactions do not balance, the net foreign assets of the banking system (monetary authorities and commercial banks) act as a buffer stock. Surpluses are sold to the banking system and increase the domestic money supply. Deficits are covered by sales of foreign exchange by the banking system to the nonmonetary sectors (the public), which pay with domestic currency. Deficits therefore make the money supply contract. The money supply grows, of course, when the banks grant credit to the nonbank private sector, that is, when they buy bonds from the public. These bonds are the net domestic assets of the banking system. H measures the impact of the policy conducted by the monetary authorities on the money supply. It is assumed that the monetary authorities act on the money supply and do not wish to fix the rate of interest. We will return to H later on. The usual values for the partial derivatives are assumed:
> o,
> o, Me < o.
The equilibrium condition for the bond market is B d (y,P,r) = B s (y,P,r) - N D A + Bf(y,P,r,e,y*,r*)
(3)
where B d = the demand for bonds by the private (nonbank) sector, B s = the supply of bonds by the private sector, B f = the private sector's demand for
268
H. VISSER
foreign bonds. From the total supply of domestic and foreign bonds the bonds which are sold to the banks in exchange for money (NDA) are subtracted. In order to avoid the necessity of taking into account changes in the market price of bonds when interest rates change, we assume that bonds pay t h e market rate of interest. They are variable rate bonds and their market price is invariant as to the rate of interest. For the sake of simplicity, international capital flows can only occur through the domestic private sector buying or selling foreign bonds. The small country assumption implies that at the given foreign rate of interest the amount of foreign bonds in the domestic public's portfolios is entirely demand-determined: any amount can be supplied by foreigners at that rate of interest. For the partial derivatives we have :
:
?,g
The public demands more bonds when national income, real or nominal, rises and when the rate of interest rises. With higher interest rates, it becomes more attractive to grant credit. The domestic supply of bonds also rises with the increase of income, for more credit is then needed, especially for investments. The domestic bond supply falls when interest rates rise, because it then becomes more expensive to borrow. When the domestic rate of interest rises, domestic bonds become more attractive compared with foreign bonds. Foreign bonds are sold off and capital imports occur. A rise in the foreign rate of interest evidently elicits capital exports, that is, purchases of foreign bonds. Domestic and foreign income increases can work either way. A domestic income increase, for example, may induce people to buy more domestic bonds, because prospects are bright and risks are thought to be lower than before. On the other hand, a higher income may induce people to buy more foreign bonds, because they have more savings available and want to spread their risks. There is empirical evidence for both effects (see Makin, 1976, p. 4). It will be seen that equations (2) and (3) can be combined, by eliminating NDA. We then find
Md(y,P,r) + Bd(v,P,r)=NFA_ 1 + Q+H+BS(y,P,r)+Bf(y,P,r,e,y*,r *)
(4)
Equation (4) gives the equilibrium condition for the financial markets, both the money and bond markets. The curious thing is that, with only one rate
M O N E T A R Y P O L I C Y IN A N O P E N E C O N O M Y
269
of interest and given the public's money demand, bond demand and bond supply functions, there is no place in the model for an independent loan supply function (or bond demand function) of the banks. If the demand f o r bonds and money minus the demand for foreign bonds is equal to the supply of money from the balance of payments (past and present, i.e. N F A _ 1 + Q) and monetary policy (H) plus the domestic bond supply, the public can always attain the desired portfolio composition by selling bonds to the banks in exchange for money or buying bonds back from the banks for money. Within a given total, the public can, in this way, vary the distribution of this total over money and bonds at will. Now, we come to the equation for the balance of payments. In a system with fixed exchange rates, the goods and financial markets may both be in equilibrium without balance of payments equilibrium. We do not, therefore, include an equilibrium condition for the balance of payments in our system, but an equation which defines the balance of payments surplus Q: P.ex(e/P,y*) - P.e/P.im(v, e/P) + Bf_ 1 - B f (v,P,r,e,y*,r *) = Q or
P.ex(e/P,y*) - e.im(y, e/P) + B~-1 - B f (v,P,r,e,y*,r *) = Q
(5)
For the flexible exchange rate case, where neither the monetary authorities nor the commercial banks intervene and the balance of the nonmonetary sectors is therefore = 0 by definition, we get instead of eq. (5) P.ex(e/P,y*) - e.im (y,e/P) + Bf_l - Bf(y,P,r,e,y*,r *) = 0
(6)
In this case, the endogenous variable is the rate of exchange, e. As B f 1 is the volume of foreign bonds one period back, B f 1 - B f is the decrease in the volume of foreign bonds, i.e. capital imports. The receipt of interest on foreign bonds could be accounted for by adding r*.Bf to equations (5) and (6). This would complicate the analysis. Instead, we could add r * . B ( 1 . This is defensible, because interest is received with a lag after credit has been granted. After total differentiation, the term r*.BY_ 1 vanishes. Finally, we add an equation explaining the price level: P = P(e,y) with Pe ~ O,Py >10.
(7)
270
H. VlSSER
Domestic prices may rise when the domestic price of foreign commodities increases because foreign commodities are inputs in domestic production and because competition may make the prices of domestic goods move in step with the prices of foreign goods. Py reflects the aggregate supply function. Py = 0 results when both the marginal physical product of labour and the money wage rate are constant (cf.. Takayama, 1972, pp. 335-336; Visser, 1980, p. 219). In the context of this model, we want to study the impact of monetary measures. Our model does have some peculiarities. It does not seem possible to increase the money supply by way of open market policies or by manipulating cash or liquidity ratios of the banks. The banks are entirely passive and if the authorities buy bonds from the public or sell bonds to the public, the public will correct any resulting deviation from its desired portfolio composition via transactions with the banking system. The way out is to assume that monetary policy is conducted by means of a kind of open market policy, whereby the monetary authorities deal in nonfinancial assets, trading directly with the public. 3 M O N E T A R Y POLICY A N D THE B A L A N C E O F P A Y M E N T S WHEN DOMESTIC PRICES A N D THE R A T E O F E X C H A N G E A R E F I X E D
In order to get a clear picture of the functioning of our system, we assume that domestic prices are fixed. We start with the fixed exchange rate case, The generality of our approach is not affected if our units are chosen in such a way that P = 1 and e = 1. Our system then reduces to
y =z(y,r) § exO'*) - i m ( y )
(8)
Md (y,r)+ Bd (y,r) = NFA_ 1 + Q + H + BS O~,r) + B f O~,r,y*,r*)
(9)
ex(y*) - imO, ) + Bf_1 - B f (y,r,y*,r *) = Q
(10)
We assume that Q = 0 initially. A change in the net volume of foreign assets of the banking system is then equal to dQ. H = 0 initially, too. In order to find the influence of monetary policy on the balance of payments, system (8)-(10) is totally differentiated. We get, in matrix notation;
MONETARY
1
-Zy+imy
POLICY
IN AN OPEN
271
ECONOMY
-Z r
Mdy + Bdy -B~ -B; M d +Bdr+BSr-BYr
rexy. dy*
1
dH +B; .dy*
\
+gfr*dr* imy +
B(
h (11)
(exy.-Bfy.)dy* -] Bfr.dr * I
The Jacobian of this system (the determinant of the matrix of first derivatives) is +
-
+
-
_
+
Jx = ( l ~ y ) ( M d + B d r - B r S ) + z r ( M d
+
+
+
+Bdy-Bf +imy)
(12)
With the help of Cramer's Rule we find for the impact of monetary policy on national income, the rate of exchange and the balance of payments, respectively:
dy
zr
dH ~1
dr
1- Zy + imy
~=
9'1 -
dr
(13)
+
(14) ?
-
+
-Zr (imy + B ; ) - B f r (1 -Zy +~"-'-~my)
d//=
Jx
(15)
In order to interpret these results, we depict system (8)-(10) in the r-y plane, calculate the slopes of the various curves and trace the shift of the FMcurve resulting from the impulse ~ The FM-curve replaces the LM-curve in our model. Holding the exogenous variable y* constant, after total differentiation of equation (8) we find the slope of the/S-curve:
dr 1 - Zy + imy dy zr
(16)
Under our assumptions, the/S-curve has a negative slope. From equation (9) we can derive the FM-curve. This curve shows the interest-income pairs at which the financial markets are in equilibrium.
272
H. VISSER
Holding y * and r* constant and with Q and curve is:
H = 0
the slope of the FM-
(17)
dy
Mdr + Bdr _ BSr _ B[r
Apparently, the FM-curve may have a negative slope. If, for instance, bond supply and demand are relatively insensitive to interest rate changes, and the denominator in the right-hand side of equation (17) is negative, the numerator may well be positive because of a high income sensitivity of bond supply. An increase in income at unchanged interest rate would produce an excess supply of financial assets, which has to be neutralized by a fall in the rate of interest. A negatively sloping FM-curve is also possible with a relatively low value of B~ and relatively high absolute values of Brd and BrS.An increase in income with unchanged rate of interest would, in this case, produce an excess demand for financial assets and a fall in the rate of interest would in itself cause an excess supply of financial assets. In general,and now also taking the demand for foreign bonds into account, the FM-curve has a negative slope if
- ~ - ~ +~,~ + B ; > o and
Mr + Sar - 8 ~ - B~ < O or if
-My~- ~ + ~ + B~ < o and Mrd + Brd -
Brs - Brf > 0
Finally, from equation (10) an equilibrium curve for the balance of payments the EE-curve (for External Equilibrium), can be derived, holding y * and r* constant and putting Q = 0. The slope of this curve is
dr dy
imy + B ; _ ~(
(18)
273
MONETARY POLICY IN AN OPEN ECONOMY
The EE-curve has a positive slope, unless ~B f < -imy. In that case an increase in income would, with an unchanged rate of interest, lead to a balance of payments surplus because of capital imports, i.e., sales of foreign bonds. A lower rate of interest is necessary then in order to diminish capital imports. Because of space limitations, we cannot go into all the possible results that this model allows. We could, of course, list all the possible outcomes of dH on national income, the rate of interest and the balance of payments with the ranges of the various variables which combine to reach these outcomes, but that would not shed much light upon the working of the system. It seems more useful to single out a limited number of interesting cases and trace what happens when the money supply is increased by the authorities. In a conventional 1S/LM-model for an open economy, an increase in the money supply makes national income grow larger, pushes the rate of interest down and causes a balance of payments deficit. Exceptions are: the case of infinite interest elasticity of international capital flows, where both the LM-curve and the EE-curve run horizontal and a monetary impulse given by the monetary authorities is immediately compensated by a capital outflow, and the case where the EE-curve has a larger ~negative slope than the IScurve. In the latter case the increase in the level of national income and the fall in the rate of interest produce a balance of payments surplus (Fig. 1)
Eft -
-I-
/M
is
0
LM
J
y
Figure 1 - Expansionary monetary policy and the balance of payments when the curve has a larger negative slope than the/S-curve, conventional 1S/LM-case
EE-
274
H. VISSER
( c f Levin, 1974, p. 284; Visser, 1980, pp. 270-271). We always have an LM-curve with a non-negative slope that shifts to the right. But in the present model we have an FM-curve that may have a negative slope and that, moreover, may shift to the left. Under what conditions will the FM-curve shift to the left when dH > 0? When the monetary authorities increase the money supply, an excess supply of financial assets arises. If we hold the rate of interest constant, national income then has to be varied in such a way that the demand for money, Myd, and the demand for domestic bonds Byd - B f , increase more or decrease less than the domestic bond supply, B],. The FMcurve will shift to the left, therefore, if Myd + Byd - B ~ - Byf < 0. Let us now assume that F M has a positive slope and that M d + R d - FIs - Byf < 0. This implies that Mrd + Brd - Brs - Brf > 0. Generallyy, in -this y case -y J1 will be positive, national income will fall (see equation (13))and the rate of interest will rise (equation (14)). The balance of payments will show a surplus, except when By f has a large negative value relative to Brf, such that the negative slope of the EE-curve is absolutely larger than the slope of the /S-curve. From equations (16) and (18) it follows that in that case
imy + -Be
1 --
-Zy §
<
and - z r ( i m y + Bf)-Brf(1 - Zy + i m y ) < O. With
Zr
J1 > 0 and Q = 0 initially, this means that a balance of payments deficit resuits, even if national income falls and the rate of interest rises (see Fig. 2 and
IS
EE
0
y
Figure 2 - Expansionary monetary policy and the balance of payments when the E E curve has a larger negative slope than t h e / S - c u r v e and the FM-curve shifts inwards
275
MONETARY POLICY IN AN OPEN ECONOMY
equation (15)). It should be noted that with Myd + Bd - B~ - 8 ; < 0 a large negative value of B ; implies low income sensitivities of the demand for financial assets and a very high income sensitivity of bond supply. In other words, the demand for credit has to react very strongly to income changes. Even though J1 is generally positive, it may be negative. Under our assumptions, ( 1 - Zy + imy) (Mdr + B ff - BSr - Bfr) + z r (Mdy + ff~ - B~ - B ; ) is positive. The difference between this expression and J1, - Br(1 - Zy + imy) -zr(Bfy + imy), has to be strongly positive in this case. This condition implies that
1-zy
+ imy < Bly + imy
Zr
- Bf
and from equations (16) and (18) we see that the EE-curve either has a positive slope or a smaller negative slope than the/S-curve. A leftward shift of the FM-curve would apparently cause such a large balance of payments surplus that the FM-curve has to shift to the right in order to restore equilibrium on the financial markets. The resulting balance of payments deficit is sufficiently strong to compensate both the increase in the volume of money caused by the open market purchases of the monetary authorities and the excess of domestic bond supply over the demand for money and domestic bonds that occurs when national income increases. A positive slope of the FM-curve will also result from
Md+Bg_B~_B
f > OandMra+ B~-Br'-B~ d s < O.
Generally, J1 will be negative, the rate of interest will fall and national income will increase. The balance of payments will show a deficit, unless the EE-curve has a steeper negative slope than the/S-curve. J1 may, however, be positive. As
(1 - Zy - im,)(g~ + B e - ~ -
8~) + zr(M~ + ~
- B~ - Bi) < O,
a necessary condition f o r J 1 to be positive is that - Brf(I - Zy + imy ) - zr(B; + imy) be strongly negative. This implies that
1- ~y + imy zr
>
B~ + imy - B fr
276
H. VISSER
or, verbally, that the EE-curve has a negative slope which is steeper than the slope of the IS-curve. National income falls and the rate of interest rises, because the FM-curve has to shift to the left in order to avoid a too-large balance of payments surplus. Such a surplus would continue increasing if the FM-curve were to shift to the right in order to create a gap between the demand for money and domestic bonds on the one hand and the supply of domestic bonds on the other hand. (This gap would have to absorb the monetary impulse from the authorities and the impulse from the balance of payments.) With the FM-curve shifting to the left in order to avoid cumulative disequilibria, the balance of payments moves into a deficit. To conclude this section on the fixed exchange rate case, we analyse the situation with a negatively sloping FM-curve that runs steeper than the IScurve. From equations (16) and (17) it follows that in this case
1-Zy + imy
-Mdy - Bd + B~ +By M e + B dr _ B ss _ B fr
<
(19) zr
Let us assume that the FM-curve has a negative slope because the numerator of the fraction on the left-hand side is positive and the denominator is negative. We have seen that the FM-curve will shift to the left in these circumstances. With a flatter/S-curve, we would expect a rise in the rate of interest and a fall in the level of national income, while the balance of payments may develop either way (see Fig. 3). ,r
FM
\
FM
IS
0
y
Figure 3 - A leftward shift o f the FM-curve when this curve has a larger negative slope than t h e / S - c u r v e
M O N E T A R Y P O L I C Y IN A N O P E N E C O N O M Y
277
From inequality (19) it follows that
(1-Zy +imy)(Md+Bd-BSr-Bf)+zr(Md+Bd-B~'-B;)
> 0
(20)
By subtracting - Brf(1 - Zy + imy) ~fZr(imy + B ; ) we find J1, which may be either positive or negative. With - B r ( 1 - Z y + i m y ) - Z r ( i m y + Bfv) < 0 the EE-curve has a steeper negative slope than the/S-curve. National income falls, the rate of interest rises and the balance of payments moves into a deficit. With-Brf(1 - Z y + i m y ) - Z r ( i m y + B ; ) > 0 and J 1 still positive, the balance of payments will show a surplus. The EE-curve either has a positive slope or a smaller negative slope than the IS-curve. With this configuration J1 may become negative. A leftward shift of the FM-curve would then cause a balance of payments surplus and a consequent increase in the money supply of such a magnitude, that a further leftward shift of the FM-curve would only aggravate the imbalance. The FM-curve therefore has to shift to the right. National income rises, the rate of interest falls and the balance of payments shows a dificit. It is left to the reader to work out other cases. Meanwhile, it should be noted that a balance of payments surplus will in subsequent periods make the FM-curve move further in the direction in which it has shifted, and a deficit will make it move back to the starting point. 4 MONETARY POLICY AND THE BALANCE OF PAYMENTS WHEN THE RATE OF E X C H A N G E IS F L E X I B L E A N D D O M E S T I C PRICES A R E F I X E D .
For the case of flexible exchange rates, our system of equations is
y = z(y,r) + ex(e,y*) - e.im(y,e)
(21)
M e O',r) + B d (y,r) = NFA 1 + H + B s (y,r) + Bf(y,r,e,y*#*)
(22)
ex (e,y*) - e. im (y,e) + Bf__1 - B f (v,r,e,y*,r *) = 0
(23)
For simplicity's sake we retain the assumption of fixed domestic prices. This is quite a usual procedure (cf Tumovsky, 1977, p. 206), but it is, of course, a bit difficult to imagine if domestic prices of foreign commodities fluctuate. But then, flexible prices would make our system even less transparant. Differentiating totally, and putting Bfede = 0 for simplicity, we get, in matrix notation, the following system:
278
H. VISSER
1 -zy +e.imy
-z r
Mdy + B d - B~, - B ;
xy.dy*
e.im e + i m - e x e t
Mdr + Brd- B~-Bfr
IdH+
0
=lBrf*dr*
-e.im -
-8r
-e.ime -im
24) te
t "exy * d y ~
1§ The Jacobian J2 of the matrix of first derivatives is (ex e - e.im e - i m ) [(Myd + Bdy - B~ - B ; ) ( B f r + Zr) + ( 1 - Zy - B ; ) .
(Mrd+ Brd - Brs - Brf)] .
(25)
For e x e - e. im e - On we may write eXe
ex ._-ira-ira. eX/e e
ime = -~7 irn/e
ex ex im . _ _ - im - im. rl e
(26)
where ~7e x = the elasticity of foreign imports with regard to the rate of exchange (viewed from the foreign country) and 77im = the elasticity of domestic imports with regard to the rate of exchange. If we make the simplifying assumption that e x = e.im initially, for expression (26) we may write: - i m ( ~ ex + Him + 1)
(27)
If the Marshall-Lerner condition is satisfied, the expression between brackets is negative and expression (27), as a whole, is positive, ex e - e. im e - im therefore is positive. BrZl+ Zr is negative. The other expressions between brackets in J2 may be either positive or negative (or zero). Applying Cramer's Rule, we find dy _ zr (exe - e'ime - ira)
a/t
(28)
s2
with the numerator < 0; dr dH"
(e.ime+im-exe)(Zy-1 J2
+B;)
(29)
M O N E T A R Y POLICY IN AN OPEN E C O N O M Y
279
with the numerator > 0, unless B f > 1 -Zy; _
+
9
_
:
+
Zr(e.imy + Bfy) + BJr(1 - zy + e.imy)
de dH
J2
(30)
with the numerator < 0, unless By f has a large negative value, such that not only Byf < -e.imy, but Zr(e.imy + Byf ) > -Brf(1 - Zy + e.imy). For the slope of the IS-curv~ we find
dr_
1 - zy + e.imy
dy
zr
(31)
which only differs from the fixed exchange rate case in that imports are multiplied by e, while e is not restricted to unity (cf. equation (16)). The slope of the FM-curve again is dr_
+
dy
M d + B d _ B rs_Brf
(32)
In order not to tax the reader's patience too much we will illustrate the working of the system by analysing one case only. Let us assume that - M d - Bdy + B~ + Bfy > O and Md + B d - BSr - Bfr > 0. TheFM-curvewillthen have a positive slope and a positive impulse from the side of the monetary authorities will make the FM-curve shift to the left. J2 is generally positive. With Bfvj < 1 - Z y J2 cannot but be positive. An expansionary monetary policy will lead to a fall in national income and a rise in the rate of interest. The rate of exchange may either rise or fall. From equation .(30) it follows that with
'
<
e.imy.Z r + Be(1 - Zy + e.imy) -
Zr
the rate of exchange will rise. Byf is negative and J2 is, therefore, positive. The /S-curve shifts to the right, because a rise in the rate of exchange produces a surplus of exports over imports (cf equation (21)), but not enough to nullify the impact of the leftward shift of the FM-curve on national income. A shift to the right of the/S-curve will give an extra boost to the rise in the rate of interest caused by the shift to the left of the FM-curve. We may imagine that the leftward shift of the FM-curve exerts an upward pressure on the rate of
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H. VISSER
interest and a downward pressure on the income level. A rise in the rate of interest induces capital imports, but a fall in the level of income induces, with Byf highly negative, capital exports that overcompensate the interest-induced capital imports plus the improvement in the current account of the balance of payments (exports minus imports) that results form the fall in income. Consequently, the rate of exchange rises and the fall in the level of income is mitigated. Income-induced capital exports are reduced again and the rate of interest rises to induce further capital imports. With J2 > 0 and Byf > 1 - Zy not only national income, but the rate of interest will fall. In this case the /S-curve shifts more to the left than the FM-curve. From equation (30) we see that there is a substantial fall in the rate o f exchange, which of course is what makes the/S-curve shift to the left. If J2 < 0, it follows from expression (25) and our assumptions that Byf > 1 - Zy. A higher level of income is attained and the rate of interest rises. From equation (30) we see that there is a substantial rise in the rate of exchange. The/S-curve shifts to the right, apparently over a greater distance than the FM-curve shifts to the left. 5 CONCLUDING R E M A R K S
We have not paid any attention to government expenditures and taxes. It is, in principle, quite simple to analyse their influence. In a graphical representation, an increase of government expenditures makes the/S-curve shift to the right and an increase of taxes makes the/S-curve shift to the left. If expenditures and taxes change by the same amount, there is still a rightward shift of the/S-curve, by virtue of the Haavelmo effect. However, if a government deficit or surplus appears, we would have to take account of the increase in the volume of money and/or bonds which results from the financing of a deficit or the decrease which results from the financing of a surplus. With Myd + Byd - B)~- Byf < 0, the FM-curve will shift to the left in the case of a deficit, because national income has to fall in order to take up the resulting excess supply of financial assets. In the case of a surplus the FM-curve will shift to the right, of course, and with Myd + Byd - By - B f > 0 it is the other way round. Introducing a variable price level would complicate our analysis enormously. One would have to differentiate totally the equations (1), (4), (5) or (6), and (7) and proceed in the same way as we have done in the case of fixed prices. Working through the equations would be more tedious and timeconsuming, but not more difficult. Interpreting the results would, however, not be an easy task. We will confine ourselves to giving an indication of the
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281
direction in which the various curves move as a consequence o f price level changes. A domestic price increase means that the (commodity) terms o f trade improve, that is, the fraction e/P gets a lower value. The IS-curve will shift to the left, as a result of this price increase, in the case o f a fixed exchange rate. In the flexible exchange rate case the increase o f the domestic price level may be fully compensated by an increase in the rate o f exchange, i.e., in the domestic value o f a unit o f foreign currency; the IS-curve would then remain in the same position. As for the FM-curve, price level changes have the same influence on its position as changes in the level o f income if the partial derivatives of money and bond demand (including the demand for foreign bonds) and bond supply with regard to the price level all have the same (positive) value. Balance o f payments surpluses or deficits will have a larger nominal value if prices move in step with real national income. We may, in general, conclude that our way o f adding private sector demand and supply o f bonds completely upsets the results of conventional 1S/LM-analysis. This is because the FM-curve, which replaces the LM-curve, may have a negative slope instead of a positive slope, and, moreover, may shift to the left instead of to the right after an increase o f the m o n e y supply. It is left to the reader to trace the consequences o f changes in exogenous variables other than H, sc. y*, r* and, in the case of fixed, or rather pegged, exchange rates, e. REFERENCES Argy, V. and P.J.K. Kouri, 'Sterilization Policies and the Volatility in International Reserves,' in: R.Z. Aliber (ed.), National Monetary Policies and the International Financial System, Chicago, 1974. Bailey, M.J., National Income and the Price Level, New York, 1962. Blinder, A.S. and R.M. Solow, 'Does Fiscal Policy Matter?,' Journal of public Economics, 2, (1973). Blinder, A.S. and R.M. Solow, 'Analytical Foundations of Fiscal Policy,' in: A.S. Blinder, R.M. Solow a.o., The Economics of Public Finance, Washington, D.C., 1974. Choudry, N.N., 'Integration of Fiscal and Monetary Sectors in Econometric Models: A Survey of Theoretical Issues and Empirical Findings,' IMF Staff Papers, (23) 1976. Crouch, R.L., Macroeconomics, New York, 1972. Havrilesky, Th.N. and J.T. Boorman, Monetary Macroeconomics, Arlington Heights, 1978. Hines, A.G., On the Reappraisal of Keynesian Economics, London, 1971. Infante, E.F. and J.L. Stein, 'Does Fiscal Policy Matter?,'JournalofMonetary Economics, 2, (1976). Johnson, H.G., Macroeconomics and Monetary Theory, London, 1971. Kornai, J., Economics of Shortage, Amsterdam, 1980.
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Levin, J.H., 'IS, LM, and External Equilibrium: Some Extensions,' Economia Internazionale, 27 (1974). Makin, J.H., 'Introduction and Summary,' in: C.H. Stem, J.H. Makin and D.E. Logue (eds.), Eurocurrencies and the International Monetary System, Washington, D.C., 1976. Patinkin, D., Money, Interest, and Prices, 2nd ed., New York, 1965. Sibler, W.L., 'Fiscal Policy in IS-LM Analysis: A Correction,' Journal of Money, Credit and Banking, 2 (1970). Steinherr, A., 'Economic Policy in an Open Economy under Alternative Exchange Rate Systems: Effectiveness and Stability in the Short and Long Run,' WeltwirtschaftlichesArchiv, 111 (1975). Takayama, A., International Trade, New York, 1972. Turnovsky, S.J., Macroeconomic Analysis and Stabilization Policies, Cambridge, 1977. Visser, H., Monetaire theorie, 2nd ed., Leiden, 1980.
Summary MONETARY POLICY IN AN OPEN ECONOMY WITH PRIVATE DEBT: ANOTHER VARIATION ON THE IS/LM THEME I n this article an a m e n d e d version o f t h e t r a d i t i o n a l 1S/LM-model for an o p e n e c o n o m y is developed. The L M - c u r v e is r e p l a c e d b y an F M - c u r v e , w h i c h represents e q u i l i b r i u m b e t w e e n the d e m a n d f o r and s u p p l y o f m o n e y and bonds. The b a n k s passively satisfy the wishes o f t h e p u b l i c as to t h e comp o s i t i o n o f its p o r t f o l i o o f m o n e y and b o n d s , creating or d e s t r o y i n g m o n e y in the process. It t u r n s o u t t h a t n o t m u c h is left o f t h e w e l l - o r d e r e d I S / L M world.