Homepage International Economics
International Economics, Robert A. Mundell, New York: Macmillan, 1968, pp. 250-271.
Capital Mobility and Stabilization Policy under
Fixed and Flexible Exchange Rates1
Robert A.
Mundell |
The world is still a closed economy, but its regions and countries are becoming increasingly open. The trend, manifested in both freer movement of goods and increased mobility of capital, has been stimulated by the dismantling of trade and exchange controls in Europe, the gradual erosion of the real burden of tariff protection, and the stability, unparalleled since 1914, of the exchange rates. The international economic climate has changed in the direction of financial integration2 and this has important implications for economic policy.
My paper concerns the theoretical and practical implications of the increased mobility of capital. To present my conclusions in the simplest possible way, and to bring the implications for policy into sharpest relief, I assume the extreme degree of mobility that prevails when a country cannot maintain an interest rate different from the general level prevailing abroad. This assumption will overstate the case, but it has the merit of posing a stereotype toward which international financial relations seem to be heading. At the same time it might be argued that the assumption is not far from the truth in those financial centers of which Zurich, Amsterdam, and Brussels may be taken as examples, where the authorities already recognize their lessening ability to dominate money market conditions and insulate them from foreign influences. It should also have a high degree of relevance to a country like Canada, whose financial markets are dominated to a great degree by the vast New York market.
The assumption of perfect capital mobility can be taken to mean that all securities in the system are perfect substitutes. Because different currencies are involved, this implies that existing exchange rates are expected to persist indefinitely (even when the exchange rate is not pegged) and that spot and forward exchange rates are identical. All the complications associated with speculation, the forward market, and exchange-rate margins are thereby assumed not to exist.
To focus attention on policies affecting the level of employment, we assume unemployed resources, constant returns to scale, and fixed money wage rates; this means that the supply of domestic output is elastic and its price level constant. We assume further that saving and taxes rise with income, that the balance of trade depends only on income and the exchange rate, that investment depends on the rate of interest, and that the demand for money depends only on income and the rate of interest. Our last assumption is that the country under consideration is too small to influence foreign incomes or the world level of interest rates.
Monetary policy will be assumed to take the form of open market purchases of securities, and fiscal policy the form of an increase in government spending (on home goods) financed by an increase in the public debt. Floating exchange rates result when the monetary authorities do not intervene in the exchange market, and fixed exchange rates when they intervene to buy and sell international reserves at a fixed price.
It will be helpful, in the following discussion, to bear in mind the distinction between conditions of sectoral and market equilibria (illustrated in Table 18-1). There is a set of sectoral restraints (described by the rows in the table) that show how expenditure in each sector of the open-economy is financed: A budget deficit (G - T) in the government sector is financed by an increase in the public debt or a reduction in government cash balances (dishoarding); an excess of investment over saving (I - S) in the private sector is financed by net private borrowing or a reduction in privately held money balances; a trade balance deficit (M - X) in the foreign sector3 is financed by capital imports or a reduction in international reserves; and, finally, an excess of purchases over sales of domestic assets of the banking sector is financed by an increase in the monetary liabilities of the banking system (the money supply) or by a reduction in foreign exchange reserves. For simplicity of exposition, we shall assume that there is, initially, no lending between the sectors.
|
Table 18-1
| ||||||||
|
Market | ||||||||
| Sector | Goods | Securities | Money | International Reserves |
||||
| Government |
T - G |
+ | Government borrowing |
+ | Government dishoarding |
+ |
*1 |
= 0 |
|
+ |
+ |
+ |
+ |
+ | ||||
| Private |
S - I |
+ | Private borrowing |
+ | Private dishoarding |
+ |
*2 |
= 0 |
|
+ |
+ |
+ |
+ |
+ | ||||
| Foreign |
M - X |
+ | Capital outflow |
+ |
*3 |
+ | Increase in reserves |
= 0 |
|
+ |
+ |
+ |
+ |
+ | ||||
| Banking |
*4 |
+ | Open market sales |
+ | Monetary expansion |
+ | Foreign exchange sales |
= 0 |
|
|| |
|| |
|| |
|| |
|| | ||||
|
0 |
+ |
0 |
+ |
0 |
+ |
0 |
= 0 | |
|
| ||||||||
| * Negligible or ignored items: (1) would refer to Treasury
holdings of foreign exchange; (2) to the nonbank public's holdings of
foreign exchange; (3) to foreigners' holdings of domestic money (domestic
currency is not a "key" currency); and (4) to the net contribution of the
banking system to goods account. In the analysis, government dishoarding
will also he assumed zero.
Note that if the entries are defined as ex ante or planned magnitudes both the horizontal and vertical sums to zero are equilibrium conditions, but if they are defined as ex post or realized magnitudes the sums to zero are identities. Note also that the rows could be disaggregated, making special distinctions between households and firms, commercial and central banks, etc., down to each individual spending unit, just as the columns could be multiplied to distinguish between different classes of goods, money, and securities.
| ||||||||
There is also a set of market restraints (described by columns in the table) that refer to the condition that demand and supply of each object of exchange be equal. The goods-and-services market is in equilibrium when the difference between investment and saving is equal to the sum of the budget surplus and the trade balance deficit. The capital market is in equilibrium when foreigners and domestic banks are willing to accumulate the increase in net debt of the government and the public. The foreign exchange market is in equilibrium when the actual increase in reserves is equal to the rate (which may be positive or negative) at which the central bank wants to buy reserves.4 And the money market is in equilibrium when the community is willing to accumulate the increase in the money supply offered by the banking system. We shall assume also that, initially, each market is in equilibrium.
Under flexible exchange rates the central bank does not intervene to fix a given exchange rate, although this need not preclude autonomous purchases and sales of foreign exchange.
MONETARY POLICY
Consider the effect of an open market purchase of domestic securities in the context of a flexible-exchange-rate system. This results in an increase in bank reserves, a multiple expansion of money and credit, and downward pressure on the rate of interest. But the interest rate is prevented from falling by an outflow of capital, which causes a deficit in the balance of payments, and a depreciation of the exchange rate. In turn, the exchange-rate depreciation (normally) improves the balance of trade and stimulates, by the multiplier process, income and employment. A new equilibrium is established when income has risen sufficiently to induce the domestic community to hold the increased stock of money created by the banking system. Because interest rates are unaltered, this means that income must rise in proportion to the increase in the money supply, the factor of proportionality being the given ratio of income and money (income velocity).
In the new equilibrium private saving and taxes will have increased as a consequence of the increase in income, and this implies both net private lending and retirement of government debt. Equilibrium in the capital market then requires equality between the sum of the net private lending plus debt retirement, and the rate of capital exports, which in conjunction with the requirement of balance-of-payments equilibrium, implies a balance of trade surplus. Monetary policy therefore has a strong effect on the level of income and employment, not because it alters the rate of interest, but because it induces a capital outflow, depreciates the exchange rate, and causes an export surplus.5
It will now be shown that central bank operations in the foreign exchange market ("open market operations" in foreign exchange) can be considered an alternative form of monetary policy. Suppose the central bank buys foreign reserves (gold or foreign currency) with domestic money. This increases bank reserves, causing a multiple expansion of the money supply. The monetary expansion puts downward pressure on the interest rate and induces a capital outflow, further depreciating the exchange rate and creating an export surplus, which in turn increases, through the multiplier effect, income, and employment. Eventually, when income has increased sufficiently to induce the community to hold the increased stock of money, the income-generating process ceases and all sectors are again in equilibrium, with the increased saving and taxes financing the capital outflow. This conclusion is virtually the same as the conclusion earlier reached regarding monetary policy, with the single important difference that foreign assets of the banks are increased in the case of foreign exchange policy while domestic assets are increased in the case of monetary policy. Foreign exchange policy, like monetary policy, becomes a forceful tool of stabilization policy under flexible exchange rates.
FISCAL POLICY
Assume an increase in government spending financed by government borrowing. The increased spending creates an excess demand for goods and tends to raise income. But this would increase the demand for money, raise interest rates, attract a capital inflow, and appreciate the exchange rate, which in turn would have a depressing effect on income. In fact, therefore, the negative effect on income of exchange-rate appreciation has to offset exactly the positive multiplier effect on income of the original increase in government spending. Income cannot change unless the money supply or interest rates change, and because the former is constant in the absence of central bank action and the latter is fixed by the world level of interest rates, income remains fixed. Since income is constant, saving and taxes are unchanged, which means, because of the condition that the goods market be in equilibrium, that the change in government spending is equal to the import surplus. In turn, the flexible exchange rate implies balance-of-payments equilibrium and therefore a capital inflow equal to the import surplus. Thus, both capital and goods market equilibria are assured by equality between the rate of increase in the public debt and the rate of capital imports, and between the budget deficit and the import surplus. Fiscal policy thus completely loses its force as a domestic stabilizer when the exchange rate is allowed to fluctuate and the money supply is held constant. Just as monetary policy derives its importance as a domestic stabilizer from its influence on capital flows and the exchange rate, so fiscal policy is frustrated in its effects by these same considerations.
Under fixed exchange rates the central bank intervenes in the exchange market by buying and selling reserves at the exchange parity; as already noted the exchange margins are assumed to be zero.
MONETARY POLICY
A central bank purchase of securities creates excess reserves and puts downward pressure on the interest rate. But a fall in the interest rate is prevented by a capital outflow, and this worsens the balance of payments. To prevent the exchange rate from falling, the central bank intervenes in the market, selling foreign exchange and buying domestic money. The process continues until the accumulated foreign exchange deficit is equal to the open market purchase and the money supply is restored to its original level.
This shows that monetary policy under fixed exchange rates has no sustainable effect on the level of income. The increase in the money supply arising from open market purchases is returned to the central bank through its exchange stabilization operations. What the central bank has in fact done is to purchase securities initially for money, and then buy money with foreign exchange, the monetary effects of the combined operations canceling. The only final effect of the open market purchase is an equivalent fall in foreign exchange reserves: The central bank has simply traded domestic assets for foreign assets.
FISCAL POLICY
Assume an increase in government spending superimposed on the foreign exchange policy of pegging the exchange rate. The increased spending has a multiplier effect upon income, increasing saving, taxes, and imports. Taxes increase by less than the increase in government spending, so the government supplies securities at a rate equal to the budget deficit, whereas the private sector absorbs securities at a rate equal to the increase in saving.
After the new equilibrium is established, both the goods and capital markets must be in balance. In the goods market the budget deficit has as its counterpart the sum of the excess private saving over investment and the balance-of-trade deficit, which implies that the induced balance-of-trade deficit is less than the budget deficit. In the capital market the private and foreign sectors must be willing to accumulate the new flow of government issues. But, because the excess private saving is equal to the flow of private lending, and because the budget deficit equals the flow of new government issues, capital market equilibrium requires that the import deficit be exactly balanced by a capital inflow, so that there is balance-of-payments equilibrium after all adjustments have taken place.
There will nevertheless be a change in foreign exchange reserves. Before the flow equilibrium is established the demand for money will increase, at a constant interest rate, in proportion to the increase in income. To acquire the needed liquidity the private sector sells securities and this puts upward pressure on the interest rate and attracts foreign capital. This improves the balance of payments temporarily, forcing the central bank to intervene by buying foreign reserves and increasing the money supply. The money supply is therefore increased indirectly through the back door of exchange rate policy. Foreign exchange reserves accumulate by the full amount of the increased cash reserves needed by the banking system to supply the increased money demanded by the public as a consequence of the increase in income.
Other cases deserve attention in view of their prominence in policy discussion. In the following cases it is assumed that exchange rates are fixed.
DEFICIT FINANCE
An important special case of combined operations of monetary, fiscal, and exchange policies is central bank financing of budget deficits (deficit finance) under fixed exchange rates. As before, the increase in government spending yields a multiplier effect on income. In the new equilibrium there is a budget deficit, an excess of saving over investment, and a balance-of-trade deficit. The government issues securities at a rate equal to the budget deficit and these are (by assumption) taken up by the central bank. Capital market equilibrium therefore requires that the net flow demand for securities on the part of the private sector be equal to the net capital outflow.
It is easy to see that in the new equilibrium the balance-of-payments deficit and the consequent rate at which reserves are falling is exactly equal to the budget deficit and to the rate at which the central bank is buying government securities. Because the capital outflow is equal to the excess of saving over investment, and the loss of reserves is equal to the balance-of-payments deficit, which is the sum of the trade deficit and the capital outflow, reserves fall at a rate equal to the sum of the import deficit and the excess of saving over investment. Then because this sum equals the budget deficit, by the condition of equilibrium in the goods market, it follows that reserves fall at a rate equal to the budget deficit. The budget is entirely at the expense of reserves.
There is, however, in this instance, too, an initial stock-adjustment process. As income increases the demand for money grows, and the private sector dispenses with stocks of securities, causing a capital inflow and an increase in reserves. This increase in reserves is a once-and-for-all inflow equal to the increase in cash reserves necessary for the banks to satisfy the increased demand for money. The rate of fall in reserves takes place, therefore, from a higher initial level.
THE NONVIABILITY OF STERILIZATION OPERATIONS
Sterilization (or neutralization) policy is a specific combination of monetary and exchange policy. When the central bank buys or sells foreign exchange the money supply increases or decreases. The purpose of sterilization policy is to offset this effect. The mechanism is for the central bank to sell securities at the same rate that it is buying foreign exchange, and to buy securities at the same rate that it is selling foreign exchange. In reality, therefore, neutralization policy involves an exchange of foreign reserves and bonds. The exchange rate is stabilized by buying and selling reserves in exchange for securities.
Suppose the government increases spending during a time when neutralization policy is being followed. The increase in spending would normally have a multiplier effect on income. But this would increase the demand for money and put upward pressure on interest rates as the private sector dispenses with holdings of securities; this would cause a capital inflow and induce a balance-of-payments surplus. But now the authorities, in their rate-pegging operation, buy foreign exchange and simultaneously sell securities, thus putting added pressure on interest rates and accelerating the inflow of capital without satisfying the increased demand for money. The system has now become inconsistent, for goods market equilibrium requires an increase in income, but an increase in income can take place only if either the money supply expands or interest rates rise. The capital inflow prevents interest rates from rising and the neutralization policy inhibits the money supply from expanding. Something has to give, and it must either be the money supply or the exchange rate. If the central bank sells securities at the same rate as it is buying reserves, it cannot buy reserves at a rate fast enough to keep the exchange rate from appreciating. And if the central bank buys reserves at a rate fast enough to stabilize the exchange rate, it cannot sell securities fast enough to keep the money supply constant. Either the exchange rate appreciates or money income rises.
In a similar way it can be shown that, from an initial position of equilibrium, open market operations (monetary policy) lead to an inconsistent and overdetermined result. A purchase of securities by the central bank would cause a capital outflow, balance-of-payments deficit, and sales of foreign exchange by the central bank. The restrictive monetary impact of the foreign exchange sales are then offset by further open market purchases that induce further sales of foreign exchange. The process repeats itself at an accelerating speed. There is no new equilibrium because the public wants to hold just so much money, and the central bank's attempt to alter this equilibrium simply results in a fall in reserves. The sterilization procedures merely perpetuate the self-generating process until exchange reserves are exhausted, or until the world level of interest rates falls.
Figure 18-1. Monetary Policy.
Figure 18-2. Fiscal Policy.
These results can be illustrated by diagrams similar to those I have used for analysis of related problems.6 In the top quadrant of both Figures 18-1 and 18-2, XX plots the relation between the interest rate and income (given the exchange rate) along which there is no excess demand in the goods-and-services market (internal balance); LL describes a similar relation for the money market; and FF gives the external-balance condition that is dominated by the world level of interest rates. Analogously in the bottom quadrants, XX plots internal balance and FF external balance as functions of income and the exchange rate. The internal-balance line in the top quadrant applies only for the given exchange rate represented by pi0 in the bottom quadrant, and the external-balance schedule in the bottom quadrant applies only for the initial rate of capital imports (assumed to be zero).
Consider the effects of monetary policy (Figure 18-1). From Q an increase in the money supply shifts LL in the upper quadrant to L'L', implying at the original interest rate and income level (at Q) excess liquidity; this causes a capital outflow. Under flexible exchange rates FF in the lower quadrant shifts downward to F'F', and the improvement in the trade balance increases income and employment as XX in the top quadrant is pushed by the devaluation toward X'X'. The new equilibrium is at P, with an improved trade balance and greater capital outflow (or lessened inflow).
With the exchange rate fixed at pi0, however, the increase in the money supply merely creates excess liquidity, an export of capital, a balance-of-payments deficit, and a reduction in the money supply with no shift in XX in the top quadrant. The line L'L' returns to its original position and Q is restored as equilibrium at a lower level of reserves; Q is the only possible equilibrium consistent with both FF and XX, so the money supply will adapt to it if it is allowed to. But if the increase in the money supply is accompanied by sterilization operations, that is, if L'L' is maintained, there can be no equilibrium. The central bank buys securities, gold flows out, and the central bank buys more securities. Because the exchange rate is maintained at pi0, XX in the top quadrant is unaffected, as is FF. The attempt of the central bank to maintain L'L' cannot satisfy both the conditions that the interest rate remain at the world level and that the new equilibrium be on XX. Either the exchange rate must change (shifting XX to X'X') or the attempt to maintain L'L' by sterilization operations must be abandoned.
Consider next the case of fiscal policy (Figure 18-2). An increase in government spending shifts XX to X'X' in both quadrants. At the fixed exchange rate pi0 this increases income and increases the demand for money. Interest rates tend to rise, capital is attracted from abroad, the balance of payments improves, and the money supply increases, eventually establishing L'L' as the new money curve. After this instantaneous "stock adjustment," process capital is attracted from abroad sufficiently to establish F'F' as the new foreign balance line, with the equilibrium P in both quadrants.
Under flexible rates, however, the money supply remains constant. The increased spending puts upward pressure on interest rates and appreciates the exchange rate. FF therefore shifts to F"F", establishing R as the new equilibrium. At R the price of foreign exchange is lower but output and employment are unchanged.
Again, if the exchange rate is fixed and the authorities attempt to sterilize the initial gold inflow, one of the policies must fail, because the new equilibrium (P) on FF and X'X' in the upper quadrant is consistent only if the money supply is allowed to expand. Obviously, the points J and P cannot be maintained simultaneously.
Certain qualifications or extensions to the analysis should be mentioned. The demand for money is likely to depend upon the exchange rate in addition to the interest rate and the level of income; this would reduce the effectiveness of a given change in the quantity of money, and increase the effectiveness of fiscal policy on income and employment under flexible exchange rates, while, of course, it has no significance in the case of fixed exchange rates.
Another possible influence is the real balance effect, but this cannot alter in any essential way the final result: Income rises, under flexible exchange rates, in proportion to the increase in the money supply, whereas income remains unchanged, in the case of fixed exchange rates, because the quantity of money does not increase.
A further factor that might be considered is the negative effect of changes in the exchange rate upon the level of saving. Again there is no important alteration in the results: Although the budget deficit arising from increased government spending under flexible exchange rates is then partly financed by an increase in saving of the private sector, the conclusions regarding changes in the level of output and employment are unaltered.
The conclusions, of course, have not made any allowance for growth. Because of growth, the money supply will normally be increased at a rate more or less commensurate with the growth of the economy; my conclusions are, so to speak, superimposed on the growth situation. Moreover, many of our actual observations about the economic world are observations of disequilibrium positions; it is clearly possible to alter the money supply (under fixed exchange rates) if there is excess or deficient liquidity, although even this is in practice unnecessary since we can be assured, as we were as long ago as the days of Ricardo, that the money supply will automatically settle down to its equilibrium level. In any case these observations do not vitiate the principles we have been trying to elucidate.
We have demonstrated that perfect capital mobility implies different concepts of stabilization policy from those to which we have become accustomed in the post-World War II period. Monetary policy has no impact on employment under fixed exchange rates, whereas fiscal policy has no effect on employment under flexible exchange rates. On the other hand, fiscal policy can have an effect on employment under fixed exchange rates (if the Keynesian model is valid), whereas monetary policy has a strong effect on employment under flexible exchange rates (classical quantity theory conclusions hold).
Another implication of the analysis is that monetary policy under fixed exchange rates becomes a device for altering the levels of reserves, whereas fiscal policy under flexible exchange rates becomes a device for altering the balance of trade, both policies leaving unaffected the level of output and employment. Under fixed exchange rates, open market operations by the central bank result in equal changes in the gold stock, open market purchases causing it to decline and open market sales causing it to increase. And under flexible exchange rates, budget deficits or surpluses induced by changes in taxes or government spending cause corresponding changes in the trade balance.
Gold sterilization policies make no sense in a world of fixed exchange rates and perfect capital mobility and will ultimately lead to the breakdown of the fixed exchange system. In the absence of gold sterilization, as we have seen, an attempt of the central bank to alter the money supply is frustrated by capital outflows and automatically offsetting monetary changes through the exchange equalization operations; this is running water into a sink that is filled to the brim, causing the water to spill over the edges at the same rate that it is coming out of the tap.7 But sterilization operations are analogous to trying to prevent the water from spilling out, even though the sink is full and water is still pouring out of the tap.
If my assumptions about capital mobility were valid in Canada,8 it would mean that expansive fiscal policy under flexible exchange rates was of little help in increasing employment because of the ensuing inflow of capital, which kept the exchange rate high and induced a balance of trade deficit: We should have observed a zero or very small multiplier. By the same token, now that Canada has adopted a fixed exchange system, we should not reason from earlier negative experience about the size of the multiplier and conclude that the multiplier is now low: Although a reduction in the budget deficit under flexible rates would have helped the trade balance without too much damage to employment, a reduction in the budget deficit today could be expected to have a sizable impact on excess demand and unemployment.
Of course, the assumption of perfect capital mobility is not literally valid; my conclusions are black and white rather than dark and light grey. To the extent that Canada can maintain an interest-rate equilibrium different from that of the United States, without strong capital inflows, fiscal expansion can be expected to play some role in employment policy under flexible exchange rates, and monetary policy can have some influence on employment and output under fixed exchange rates. But if this possibility exists for us today, we can conjecture that it will exist to a lesser extent in the future.
______________________________________
The World Economy9
This chapter has analyzed the effect of stabilization policies on employment and income in an economy that is assumed to be small in relation to the rest of the world. The purpose of this appendix is to generalize the results by taking into account repercussion effects and altering the assumption that the country pursuing the policy is small. The primary complication this involves is that world interest rates may no longer be taken as given. This complication can best be introduced in the context of a mathematical model of the world economy.
For simplicity we assume that the level of external reserves in the world as a whole is constant. We shall also include government spending and taxing under "investment" and "saving." The last simplification of course entails no important loss of generality, whereas the first is readily modified.
The following notation is used:
y = income
I = investment
S = saving
B = balance of trade
M = money supply
D = domestic assets of
the banking systemL = demand for money
R = foreign exchange reserves
r = interest rate
pi = foreign exchange rate
W = world reserves
This notation will be used both for the home country, represented without superscript, and, for the rest of the world, denoted by a superscript. (The exchange rate pi is defined as the price of a unit of the home currency in terms of foreign currency with pi = 1 initially by appropriate choice of units.)
We can now write seven equations expressing the system in a world context. First, we have two equations specifying that the flow market for goods and services in each country is in equilibrium [Transcription note: a tilde is used in lieu of bar above parameters]:
I(r) + I~ - S(y) + B(y, y', pi) = 0. (1)
This condition ensures that the current supply of goods and services equals the current demand, where I~ is a parameter representing an autonomous element in the investment schedule, separated for purposes of analysis:
I'(r) - S'(y') - B(y, y', pi) = 0. (2)
This equation is analogous to (1) except that it refers to equilibrium in the market for current production in the rest of the world, its balance of trade being equal, but opposite in sign, to the balance of trade of the home country. Note that the interest rates at home and abroad are assumed to be equal because of our assumption that capital markets are integrated.
The next two equations ensure that the demand for money is equal to the supply of money in each country:
M = L(r, y). (3)
M' = L'(r, y'). (4)
where the demand for money, L, is assumed to depend upon the interest rate and domestic income.
The next two equations specify the identity between assets and liabilities of the monetary sector [assets are distinguished as between foreign (R) and domestic (D) claims]:
M = D~ + R. (5)
D~ is taken as a policy-determined parameter:
M' = D~' + R'. (6)
This equation is analogous to (5).
The last equation fixes the level of reserves in the world:
R + R' = W. (7)
W is the level of world reserves, assumed to be constant.
These seven equations contain eight unknowns: r, y, y', pi, R, R', M, and M'; and four parameters I~, D~, D~', and W~. When pi is specified, as in the fixed-exchange-rate system, or when one of the R's is known, as in the flexible-exchange-rate system, the results become determinate.
Let us first analyze the fixed-exchange-rate system. M, M', and R' can be eliminated from the system and equations (5 to 7) dropped. Differentiation of the remaining four equations with d pi = 0 (because the exchange rate is fixed) results in
where s, s', m, and m' are the marginal propensities to save and import at home and abroad, and Ir, I'r, Ly, L'y, Lr, and L'r are the partial derivatives of investment and the demand for money with respect to the variable appearing in the subscript. We can assume dI~' = dD~' = 0.
Our primary interest is in the effect of a change in investment (or government spending) (dI~) and an open market operation (dD~) on the equilibrium levels of income at home and abroad. The solutions for dy/dI, dy'/dI, dy/dD~ and dy'/dD~ are as follows:
where
assuming the usual signs of the partial derivations: s > 0, m > 0, Ly > 0, Lr < 0. etc. It then follows that
In other words, an increase in investment or government spending increases income at home, but may increase or decrease income abroad; whereas an open market purchase at home necessarily increases both income at home and income abroad.
The results are, perhaps, surprising. According to traditional theory a boom in one country is normally transmitted abroad, under fixed exchange rates, through the international multiplier. But the above result shows that an increase in investment or government spending at home increases income at home but may either increase or decrease income abroad.10
The difference in results is due to capital mobility and allowance for the income-specie-flow international-adjustment mechanism. Expansion at home causes higher income, increased imports, tighter money-market conditions, and a capital inflow. The exports of the rest of the world rise with an expansionary effect. but there is an offset because of higher interest rates and reduced investment spending; the final result depends upon which effect is greater. In general, it can be said that the more money that is released from idle balances due to the higher interest rates, the less money that is demanded at home as income expands, the smaller is the effect of higher interest rates on investment; and the lower is the home propensity to import, the less likely it is that income in the rest of the world will fall. But it cannot be asserted that expansionary fiscal policies at home tend to raise income in the rest of the world under fixed exchange rates when capital is mobile, or that booms and depressions are necessarily transmitted from one country to another.
The analysis of open market operations appears to conflict with the results of the previous discussion. But here the question of size becomes important. An expansionary monetary policy at home brings about some reduction in interest rates throughout the world. But, if the country is very small, the only important effect of the monetary policy on domestic income is through its prior effect upon foreign income. In the expression for dy/dD~ the term Ir becomes negligible in relation to I'r as the home country becomes insignificant in size in relation to the rest of the world. Monetary policy quickly becomes generalized in its effect: A $1 open market purchase in a small country has the same effect on the world money supply and world investment as a $1 open market purchase in a large country. This means that the stabilization effect of monetary policy in a small country depends upon its impact on income in the rest of the world; and if the marginal propensity to import abroad is proportionately slight, such a policy would quickly run into the practical limitation that exchange reserves are not inexhaustible.
Let us now analyze the flexible exchange system. If we eliminate M and M' from the system of equations (1) to (7) and hold D~', R~, and R~' constant, we get, after differentiation, the following expression:
where Bpi is the change in the home country's balance of trade due to an appreciation of its currency; with the sum of the import demand elasticities exceeding unity this terms is negative.
The solutions of concern to us are the following:
where
It follows that
In other words, expansive fiscal policy (or investment) increases income both at home and abroad, whereas monetary expansion increases it at home and decreases it abroad.
Once again these conclusions contain surprises. According to traditional theory, an investment boom in one country is not transmitted abroad under flexible exchange rates. My results show that there is a transmission mechanism at work when capital is mobile. The traditional theory, that expansion in one country causes an increase in imports, currency depreciation, and no change in the trade balance, is crucially dependent upon the assumption of capital immobility. But when capital is mobile, and account is taken of the monetary system, an expansion of investment will put pressure on the money and capital markets, increase interest rates, attract foreign capital, and appreciate (or ameliorate the depreciation of) the domestic currency. It cannot, therefore, be asserted that a country is automatically immunized by its flexible exchange rate from business cycle disturbances originating abroad.
These results can be related to the conclusion of my previous discussion. I argued that fiscal policy would have no effect upon domestic income when capital is mobile and the exchange rate is flexible. The conclusion is valid if the country is a small one; for in that case, the term Lr in the expression for dy/dI~ is negligible in relation to the other terms. This may also be seen by converting the expression dy/dI~ (which is dimensionless) into one based entirely on magnitudes which are dimensionless:
with primed terms denoting similar relations in the rest of the world. As the home country (hypothetically) becomes smaller in relation to the rest of the world alpha -> 0; and as alpha -> 0, dy/dI~ -> 0. This verifies our conclusion that a very small country will find fiscal policy useless for income-stabilization purposes under flexible rates and capital mobility.
There is an interesting counterpart to this, however, in the impact of a small country's domestic fiscal policy upon the rest of the world. Putting the expression for dy'/dI~ into a dimensionless form we have
As alpha -> 0,
the closed economy multiplier (with a monetary constraint) in the rest of the world. The major employment-creating effects of fiscal policy in a small country accrue to the rest of the world!
Fiscal policy in a large country, however, can be effective for a domestic stabilization. This is seen by making a progressively larger. As alpha -> infinity,
In other words, if a large country engages in fiscal policy the bulk of the expansionary effects accrue to it and very little spills over to benefit the rest of the world, the exact opposite of the situation for a small country.
The combined results may be conveniently summarized by noting that the ratio of the two multipliers, dy/dI and dy'/dI, is simply
If it is assumed that income and interest elasticities of demand for money are similar in magnitude (and there is no reason to expect them to be affected in any important way by size per se), the ratio of the multipliers reduces to the ratio of incomes.
Turning to monetary policy, it may be noted that an open market purchase raises income at home and lowers income abroad, and for this reason it is sometimes assailed as a beggar-my-neighbor policy. However, unless there is a substantial difference between the marginal propensities to save in the two countries, the additional income created in the expanding country exceeds the loss of income to the rest of the world.
Further insight into the effect of monetary policy is given by a consideration of the size of the home country relative to the rest of the world. In the previous discussion we concluded that an open market purchase in a small country results in a proportionate increase in income, the factor of proportionality being income velocity. That this is true when the rest of the world is taken into account is seen by rewriting the expression for dy/dD in the following form:
It follows that when alpha, the ratio of the outputs, approaches zero, the expression for dy/dD~ approaches 1/Ly, the "marginal" income velocity. When the country is small it gets the maximum benefit from monetary policy, and the depressing effect on the rest of the world is correspondingly greatest. The analogous expression for the rest of the world is
and it is easy to see that a reduction in a raises the absolute value of dy'/dD~.
The corollary of this is that as the home country becomes large relative to the foreign country, monetary policy has a smaller influence on home income and a correspondingly weaker depressing effect upon foreign income. From the above expressions it is clear that as a becomes very large, the negative effect upon foreign income approaches zero, while the positive effect upon domestic income is reduced from 1/Ly to
as alpha -> infinity.
The conclusions of this chapter must be interpreted as special cases of the present results. Specifically:
1. When a country is small and repercussion effects are ignored, fiscal policy under fixed exchange rates has a normal Keynesian effect upon employment. When the rest of the world is taken into account, the results hold except that allowance must be made for a dampening effect of an increase in the world level of interest rates, which could have the effect of lowering income abroad. A corollary of this is that business cycles at home may or may not be transmitted abroad when full account is taken of the monetary mechanism of balance-of-payments adjustment.2. Monetary policy in a small country would have no impact upon employment when repercussion effects are ignored because of the automatic and equal loss of foreign exchange reserves; open market operations would not alter the domestic money supply. However, when account is taken of behavior in the rest of the world, some influence on domestic income must remain, because the world level of interest rates falls. But even for a small country the major effect of the monetary policy on employment will come about through interactions with the rest of the world. Monetary expansion gets quickly generalized and a small country only gets a proportionately small share in the benefits from world monetary expansion.
3. Fiscal policy in a small country has no effect upon employment when the exchange rate is flexible; this conclusion remains valid when interactions with the rest of the world are brought into account. It does not hold, however, for large countries. An interesting conclusion is that fiscal policy in a small country has no effect upon income at home, but it has an ordinary multiplier effect on income in the rest of the world. Conversely, fiscal policy in a large country has a large effect upon employment at home but a negligible influence upon employment in the rest of the world. The ratio of the multipliers, in fact, conforms closely to the ratio of the incomes, unless considerable disparities exist between income and interest elasticities of demand for money in the two countries.
4. Under flexible exchange rates monetary policy in a small country would have a " classical " effect upon income in the sense that income increases in proportion to the open market operation. A corollary of this is that it also has a considerable influence in the opposite direction on foreign income. But as the size of the country is made (hypothetically) large relative to the rest of the world, the high degree of effectiveness of monetary policy is diminished, and so is its opposite impact on the rest of the world.
It is hardly necessary to say that the conclusions of this chapter and appendix are subject, as always, to the limitations of the model from which they have been derived. I trust the logic is correct and that the assumption set implies the solution set. But applicability of the model to practical policy is a jump, and can only be made, responsibly, after due account is taken of the host of details that apply in any actual situation. I have already mentioned above the importance of the polar assumption of capital mobility. It should also be apparent that the analysis is short-run in character and this neglects long-run consideration of changes in the capital stock and the level of indebtedness. There is another consideration, however, that deserves more explicit mention.
This consideration refers to the definition of income used in the savings and import functions of each country. A capital flow from one country to another reduces "disposable" income in one country and increases it in the other country, giving rise to expenditure effects of the Ohlin-type discussed in Chapter 2 of this book.
These direct expenditure effects mean that the rate of lending will directly affect the balance of trade, thereby reducing the initial disequilibrium created by a capital flow and limiting the need for residual corrective adjustments in the money supplies and employment levels or exchange rates of the two countries.
The theoretical implication of taking account of these direct expenditure effects is to reduce the impact on employment of fiscal policy under fixed exchange rates as compared to the situation applying when these effects are absent. The conclusion that monetary policy is relatively ineffective under fixed exchange rates, as compared to flexible exchange rates, remains valid, but fiscal policy under both fixed and flexible exchange rates, for a small country, becomes a weaker means of achieving alterations in the level of output.
The incorporation of these expenditure effects into the Keynesian international trade model is important theoretically because it illustrates, more powerfully than is implied by my original 1963 article, the similarity between the conclusions reached by classical and Keynesian methods, when all relevant effects have been incorporated. For a small country fiscal policy, under either fixed or flexible exchange rates, alters the balance of trade but does not necessarily improve the level of output and employment. Monetary policy under a system of fixed exchange rates becomes a means of altering the level of reserves of a (small) country, whereas monetary policy under a system of flexible exchange rates becomes a means of adjusting the price level and, therefore, if money wage rates are rigid, the level of employment and output.
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1 Adapted from: Can. Jour. Econ. Pol. Sci., 29, 475-485 (Nov. 1963).
2 See Ingram [27] for a valuable analysis of financial integration under fixed exchange rates, Johnson [37] for a discussion of some of the advantages of closing the exchange rate margins, Kindleberger [39], for a discussion of competition among financial centers as integration proceeds, and McLeod [53] for a theoretical discussion of related topics.
3 The foreign sector refers to all the transactions of the country as a whole with respect to the outside world.
4 For certain purposes it would be more elegant to define a separate market for foreign goods as distinct from domestic goods, but the present approach is satisfactory for the purpose on hand.
5 Caves has arrived at essentially the same result [6].
6 See the preceding chapters. In Chapter 17 the main purpose was to show that commercial policy -- import restriction or export promotion -- was ineffective under flexible exchange rates. It was also argued that both monetary and fiscal policies are more effective under flexible exchange rates than under fixed exchange rates. The apparent conflict with the present analysis lies in the different definition of monetary and fiscal policy and in the extreme assumption in the present paper of perfect capital mobility. In Chapters 16 and 17 fiscal policy was taken to be an increase in government spending with interest rates maintained constant by the central bank, while capital inflows were assumed to be a function of the rate of interest alone; in other words, no capital inflow takes place (because the domestic interest rate is constant) while the money supply is allowed to expand in proportion to the increase in income induced by the more expansive fiscal policy. In the present chapter we have defined fiscal policy as an increase in government spending financed by government bond issues with no change in the money supply. In both cases the underlying model is (in essence) the same and would yield the same results if the same assumptions were made about capital mobility and the same definitions were used.
It may puzzle the reader why I went to some length to alter the definitions of monetary and fiscal policy and thus to bring about a seemingly artificial difference between the conclusions based purely upon different definitions. The reason is that monetary policy cannot in any meaningful sense be defined as an alteration in the interest rate when capital is perfectly mobile, because the authorities cannot change the market rate of interest. Nor can monetary policy be defined, under conditions of perfect capital mobility, as an increase in the money supply, since the central bank has no power over the money supply either (except in transitory positions of disequilibrium) when the exchange rate is fixed. The central bank has, on the other hand, the ability to conduct an open market operation (which only temporarily changes the money supply) and that is the basis of my choice of this definition of monetary policy for the present analysis.
7 John Exter has used a reservoir simile [13].
8 See the accounts of the Canadian experience by Barber [3] and Johnson [36].
9 Adapted from: Can. Jour. Econ. Pol. Sci. 30, 421-431 (Aug. 1964).
10 The reader can verify that this possibility is not ruled out by the conditions of dynamic stability under the postulates that incomes move in proportion to excess demands and that world interest rates rise in proportion to the excess world demand for money.
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[6] R. E. CAVES, "Flexible Exchange Rates," Amer. Econ. Rev., 53, 120-129 (May 1963).
[27] J. C. INGRAM, "A Proposal for Financial Integration in the Atlantic Community," U.S. Congress, Joint Economic Committee, November 1962.
[37] H. G. JOHNSON, "Equilibrium under Fixed Exchange Rates," Amer. Econ. Rev., 53, 112-119 (May 1963).
[39] C. P. KINDLEBERGER, "European Economic Integration and the Development of a Single Financial Center for Long-Term Capital," Weltwirtschaft. Arch., 90, 189-210 (1963).
[53] A. N. MCLEOD, "Credit Expansion in an Open Economy," Econ. Jour., 62, 611-640 (Sept. 1962).
© Copyright, Robert A. Mundell 1968