9. Mundell-Fleming Model with a Fixed Exchange Rate

(See handout no.8; chapter 14)

Fixed versus floating: a warning

The previous lecture looked at an open economy with a floating exchange rate. This lecture examines an open economy with a fixed exchange rate.

In the Mundell-Fleming framework, the two versions (fixed and float) produce diametrically opposed results concerning the effectiveness of fiscal and monetary policies. As we recall, under a floating rate, fiscal policy was ineffective and monetary policy was very effective. Under a fixed rate, monetary policy is ineffective and fiscal policy is very effective.

This is a bit disturbing since in reality the exchange rate is neither freely floating nor completely fixed for most countries. In such arrangements as adjustable peg, crawling, managed float, currency basket, etc., flexibility and stability are combined. The Mundell-Fleming model cannot provide any clear-cut answers on policy effectiveness for these cases.

To make the matter even more complicated, what the government declares and what is actually practiced often diverge. Each IMF member country is obliged to report its exchange rate system, and their reported exchange arrangements are published by IMF (for example, in the International Financial Statistics). One such table is listed on pages 374-375 of the Rivera-Batiz book. In this table, China says it has a managed floating system, but their actual management was very close to a fixed rate, with a big change in 1994 (in level and system). Before 1997, Thailand reported to IMF that the baht was pegged to a currency basket with undisclosed weights but, actually, it was tied to the US dollar. Moreover, some "floaters" are actually more stable than "fixers" depending on how the system is managed in reality.

A Move to More Flexibility?

Percentage of countries adopting alternative exchange regimes

Source: Monzur Hossain (GRIPS PhD student), 2004. De jure shows how countries report to IMF; de facto shows how IMF evaluates the members' actual exchange management.

Thus, it is very difficult to cleanly distinguish fixed exchange rates from flexible ones. The IMF even has another list of exchange arrangements evaluated by IMF economists (de facto regimes), which is different from the officially reported one (de jure regimes--see graph). Whichever definition we may use, we detected a general trend from fixed exchange rates to floating in the 1990s. But there are also important exceptions to this trend. The most notable is EU, which unified their currencies (the most extreme form of fixed rates). Also, currency boards and "dollarization" (use of US dollar as a legal tender) are recommended by some economists.

These alternative exchange rate arrangements will be discussed more in detail in lecture 14.

Endogeneity of money under a fixed exchange rate

The key point to remember here is: under a fixed exchange rate, money supply is endogenous. The term "endogenous" means that its magnitude is determined as a result of the working of the entire model and, therefore, cannot be pre-determined by outside forces (including by the policy authority). In plain English, we can say as follows: "When the exchange rate is fixed, money supply must be used to keep the exchange rate stable, so the government cannot determine money supply freely." In other words, a fixed exchange rate ties the hands of the monetary authority.

This idea is crucial in understanding the merits and demerits of the fixed exchange rate regime.

According to the principle of money multiplier, a country's money supply (M) is a certain multiple of "high-powered money" (H). High-powered money is also called "base money" or "monetary base." Below, m is called the money multiplier (assumed stable in the short run).

M = mH

In the balance sheet of the central bank, H is the central bank's liabilities. It is also equal to its assets, which are the sum of international reserves (IR) and domestic credit (DC). DC includes government bonds and bills, loans to the public sector, and loans to commercial banks (the central bank does not lend directly to the private business or household sectors).

H = IR + DC

By controlling H, the central bank controls money supply. There are two ways for the central bank to increase or decrease H:

(1) Open market operation: the central bank purchases domestic assets (typically government bonds). DC increases and the payment for it (in cash or in credit to bank deposits) increases H by the same amount. The reverse happens when the central bank sells domestic assets.

(2) Foreign exchange market intervention: the central bank purchases foreign assets (typically US dollar assets including dollar deposits, US government securities, etc). IR increases and the payment for it also increases H. The reverse happens when the central bank sells foreign assets.

However, under a fixed exchange rate system, the central bank has the obligation to keep the exchange rate fixed by passive foreign exchange intervention. This means that it must continue to sell or buy IR so that the nominal exchange can remain stable. Therefore, IR is uncontrollable while DC is controllable (at least for the moment) under a fixed rate regime.

What does the balance of payments equilibrium look like under this circumstance? Remember the BOP equation in the previous lecture:

B = T (q, Y) + K (i - i*) - [increase in IR] = 0              T1 >0,  T2 <0;   K1 > 0

where T is the trade balance and K is the capital account. We have added -[increase in IR] to represent the central bank intervention. This is because the central bank must now ensure that there is no pressure in the foreign exchange market to either appreciate or depreciate the home currency (B=0). If the overall balance is in surplus (T+K>0), the central bank must buy dollars and sell domestic currency. This increases IR, H and ultimately M. If the overall balance is in deficit, it must do the opposite. The overall balance must always be offset by such an operation.

But complications arise depending on the degree of capital mobility.

If capital is not mobile internationally, then K=0, always. The balance of payments is now the same as the trade balance, plus intervention. The balance of payments equilibrium (B=0 without intervention) is achieved only when T=0. But there is only one Y (GDP) that makes that happen, because q (real exchange rate) cannot be changed--remember, P is constant and E is also fixed by the central bank, by assumption. The balance of payments line becomes vertical in the (i, Y) plane.

To the right of this line, the trade balance is in deficit (T<0) so the central bank must sell dollars, and IR and M are decreasing. To the left of this line, we have T>0, and IR and M are increasing.

See also p.384 in Rivera-Batiz

If, by contrast, there is perfect capital mobility, we must have i = i* for the reason explained in the previous lecture. If not, there is a massive capital inflow or outflow so B=0 cannot be maintained. Thus, the balance of payments line is horizontal at i = i*. Above it, we have a big capital inflow; below it, a big capital outflow.

If capital mobility is imperfect (between zero and perfect), we have a middle situation. We ignore this case.

Sterilization

Let us ask the question: even with a fixed exchange rate, can the central bank still control money supply through open market operation (changes in DC) to offset the effect of passive foreign exchange intervention (changes in IR)?

Even though IR is uncontrollable, we can still use DC to keep H (=IR+DC) constant at some desirable level. Then we can insulate money supply from external effects and regain monetary independence. For example, even if T+K<0, money supply need not shrink. More generally, the central bank can set H and M independently, regardless of the balance of payments situation.

This idea of offsetting the change in IR by manipulating DC is called "sterilization." It means sterilizing (=killing, cutting off) the effect of foreign exchange intervention on domestic money supply.

Again, whether this is possible depends on the degree of capital mobility.

If capital movement is controlled, sterilization may be possible for a considerable time. Suppose the economy is to the right of the T=0 line above, and the central bank is losing IR. But it can sustain the situation by increasing DC, until finally IR is depleted (when IR reaches zero, that is the end of the game). You can also remain to the left of T=0 and gain IR.

But if capital is perfectly mobile, i (=i*), Y and Ms are all given by IS, LM and BOP conditions. In particular, money supply Ms is determined by money demand LD. Any attempt to increase DC will be immediately offset by a loss of IR of the same amount. The central bank cannot change money supply at all; it can only change its composition (relative shares of IR and DC). In this case, sterilization is not possible.

Equilibrium with no capital mobility

With a fixed exchange rate and no capital mobility, how does the equilibrium look? Our three equations are as follows:

Y = f (i, q; G)              f1 <0,  f2 >0,  f3 >0            <IS>

Ms/P = LD (i, Y)            LD1 <0,  LD2 >0             <LM>

T (q, Y) = 0                  T1 >0,  T2 <0                <BOP>

But since the real exchange rate q is given and unchanged by assumption, we can ignore it for now. q will matter only when the government devalues or revalues the exchange rate.

Since the trade balance must be zero, output Y and the interest rate i are determined by IS and LM as if in a purely domestic macro model. IS is downward sloping and LM is upward sloping in the (i, Y) plane. The economy goes to the intersection of IS and LM. This is the short-run equilibrium.

But this is not the final outcome. This short-run equilibrium may be off the BOP line (T=0). If it is to the right of T=0, there is a trade deficit because Y is too large. To keep the exchange rate fixed, the central bank is obliged to sell dollars, lose IR and reduce H. Gradually, money supply Ms falls and the LM curve shifts up and to the left--until the three lines (IS, LM, T=0) intersect at the same point. After that, there is no more movement; we have reached the long-run equilibrium.

See also p.390 in Rivera-Batiz

As we said before, the government can resist the shift of LM by sterilization. But eventually, it will run out of international reserves. Then the process above must continue.

Equilibrium under perfect capital mobility

With a fixed exchange rate and perfect capital mobility, what is the equilibrium situation? Consider the following set of equations.

Y = f (i, q; G)          f1 <0,  f2 >0,  f3 >0              <IS>

Ms/P = LD (i, Y)            LD1 <0,  LD2 >0            <LM>

i = i*                                                           <BOP>

The only difference from the case of no capital mobility is the BOP condition. Instead of trade balance, we have interest rate equalization.

Let us do comparative statics with this model. Are monetary and fiscal policies effective (can they change Y)?

We already said that money is endogenous under a fixed exchange rate, and any attempt for sterilization is futile when capital is perfectly mobile. So we know monetary policy can do nothing.

To be more precise, consider an attempt at monetary expansion by increasing DC (open market purchase of domestic government bonds). The LM curve wants to shift down and to the right, but this movement is immediately countered by a massive capital outflow and a loss of IR, at the slightest fall of the domestic interest rate. So the total high-powered money H (=DC+IR) remains constant. LM cannot shift. The conclusion is that under a fixed exchange rate and perfect capital mobility, monetary policy is ineffective.

In the previous lecture with a floating exchange rate, a massive capital outflow prompted currency depreciation and an export boom. Here, with a fixed exchange rate, it simply leads to the loss of international reserves.

See also p.395 in Rivera-Batiz

How about fiscal policy?

If government spending G is increased, the IS curve is pushed up and to the right. But this tends to raise i and generate a massive capital inflow. To prevent an appreciation of the domestic currency, the central bank must buy up dollars, which will increase IR and H. Money supply Ms jumps up and the LM curve shifts out as a consequence. Note that this occurs instantaneously. Unlike the case of no capital mobility, there is no distinction between short-run and long-run. Everything takes place at once.

Since both IS and LM shifts to the right, Y is doubly increased. The conclusion is that under a fixed exchange rate and perfect capital mobility, fiscal policy is very effective.

See also p.397 in Rivera-Batiz

Please see handout no.8 for the summary of the Mundell-Fleming model outcome.

Devaluation: does it work?

Suppose your country has a trade deficit and the IMF wants you to devalue. Does this really work? We have already raised this question in the previous lectures where the ever-higher yen hypothesis and the elasticities approach were discussed. But it may be useful to summarize the argument again.

It is assumed that the monetary authority has some control over the exchange rate. Typically, it is under an adjustable peg, a crawling peg, a currency basket, or a substantially managed float. (If the currency is freely floating under capital mobility, the exchange rate is not a policy variable and the central bank cannot devalue it at will.)

Here is a list of possible effects of currency devaluation.

<Positive or intended effect>

(1) Relative-price effect: When the domestic currency is devalued, domestic products become relatively cheap compared with foreign products. The improvement in price competitiveness should improve the trade balance as long as the Marshall-Lerner condition is satisfied (i.e., trade volumes respond sufficiently to the change in price competitiveness). Consumers switch from foreign products to domestic products (this is called the expenditure-switching effect).

<Negative or ambiguous effects>

(2) Laursen-Metzler effect: This says that devaluation worsens the terms of trade, which lowers real income.

Note: the terms of trade (TOT) generally means the price ratio of (what you sell)/(what you buy). In the context of countries, it means the ratio of (export price)/(import price). For farmers, it is the ratio of (farm product price)/(input price), and so on. Devaluation usually worsens (lowers) the country's terms of trade, and reduces its real income as well; exports become relatively cheaper and imports become relatively more expensive, and you must work harder and produce more to buy the same amount of imports.

As real income declines, Prof. Laursen and Prof. Metzler argue that the saving propensity (S/Y) goes down as people try to maintain the previous living standard (spend a larger share of income). Absorption rises relative to income (A>Y), so the trade deficit worsens (see p.401 of Rivera-Batiz).

(3) J-curve effect: This effect, already explained in Lecture 7, suggests that quantity responses of both exports and imports may be quite weak immediately after the devaluation. If so, the initial impact of devaluation is to temporarily increase the trade deficit. In the long run, if the Marshall-Lerner condition holds, the positive effect will dominate (also see p.403 of Rivera-Batiz).

(4) Reverse absorption effect: This effect may also be called the "investment effect." After a devaluation, investment (both domestic and FDI) may be stimulated because the country now is a low cost producer. But since investment is part of absorption, an investment boom means the trade deficit worsens, rather than improves.

(5) Pass-through effect: The pass-through of exchange rate changes to domestic prices may be high. This is particularly true in the case of a small open economy with a high degree of dollarization or wage and price indexation to the exchange rate (prices and transactions are often quoted and invoiced in USD). Higher the pass-through, the smaller is the change in the real exchange rate (i.e., competitiveness), and the intended relative-price effect is offset accordingly.

(6) Expansionary monetary policy: Unless the exchange rate is determined by decrees, its change must be indirectly generated by monetary expansion and lower interest rates. But this change in monetary policy will shift the LM curve and upset the entire macroeconomic balance. Normally, higher inflation or output will result, both of which contribute to the worsening of the trade deficit.

(7) FDI and the hollowing-out effect: In Japan, a higher yen (intended to reduce the trade surplus) causes an exodus of manufacturing firms to China and Southeast Asia, because it now is too costly to produce at home. In Japan, this phenomenon is called the "hollowing-out" of the manufacturing base. How such FDI changes the trade flow is uncertain. At first, FDI-related exports of machines and components may increase Japan's surplus. When FDI firms start to operate, the products may be sold to Japan (or the US). Whether and how the Japanese surplus (or the US deficit) is affected is too complex to tell.

The relative strength of each effect is different in each country, and the overall effect must be evaluated for each case. But we can say that, unless the first effect dominates all the rest, it is difficult to say anything definite about whether a devaluation improves or worsen the trade balance. This is not to suggest that the IMF is always wrong (sometimes they are right). But we must be guarded against the dogmatic understanding of the benefits of devaluation.


<References>

Edwards, Sebastian, Real Exchange Rates, Devaluation, and Adjustment: Exchange Rate Policy in Developing Countries, MIT Press, 1989.

Edwards, Sebastian, and Liaquat Ahamed, eds, Economic Adjustment and Exchange Rates in Developing Countries, NBER/University of Chicago Press, 1986.

Hossain, Monzur, "Exchange Rate Regime Choice: Verifying Some Stylized Facts," a work in progress, GRIPS, May 2004.