The simple monetary model of a fixed exchange rate

Now consider a situation where the exchange rate is not allowed to move. The analy- sis here is slightly more complicated, so it will help if we start by clarifying which variables are being taken as exogenous and which endogenous.

Real income, y, is assumed to be given by factors outside the scope of our model, as before, and the foreign price level, P*, is determined by foreign money supply, income and so on, and hence is also taken as given.

Recall the discussion of the money supply in Section 4.1.2 (Equation 4.10). Under a fixed exchange rate regime, we concluded that the money supply was not an exogen- ous variable. Instead, the policy variable was domestic credit, DC, and we could write:

FX+ DC ≡ Ms

so that the burden of adjustment to changes in the exogenous variables fell on the foreign currency reserves, FX.

The only remaining exogenous variable is the exchange rate itself, which is fixed by the decision of the authorities at some level, Q.3

5.2.1

Money supply increase under fixed exchange rates

Now look at Figure 5.5, which shows the effect of an expansionary monetary policy, in other words, an increase in domestic credit, from an initial level of DC0to a higher

level, DC₁.

Figure 5.5 Domestic credit increase under fixed rates (Ms

5.2 The simple monetary model of a fixed exchange rate 155

Start with Figure 5.5(c), which plots levels of the money stock (vertical axis) against levels of the foreign exchange reserves, FX (horizontally). Measure off the quantity DC0on the vertical axis, and from that point, extend a 45° line. That ray

then shows how the money stock increases with additions to the reserves, given the initial quantity of domestic credit, DC₀. For example, if the reserves were nil, the whole money stock would be credit. As we move to the right, each additional pound of reserves increases the money stock by one pound exactly.

If we start with reserves of FX₀, the money stock must be:

Ms

0= FX0+ DC0 (5.9)

so that the starting point in that diagram is at H.

Now let us set the initial value of the money supply and the price level at unity. In other words, assume we happen to have: ky₀= 1. This device is for purposes of illus- tration only. It has the advantage that it allows us to translate the money stock value on the vertical axis of Figure 5.5(c) directly into the implied price level in Figures 5.5(a) and (b).

Exploiting this fact, the initial price level given a money stock of Ms

0must be P0.

Hence the economy starts off at point a in Figure 5.5(b). Notice that as far as aggre- gate demand and supply are concerned, the diagram is unchanged, since at this stage we have no reason to believe that the private sector’s behaviour will be any different under fixed rather than under floating exchange rates.

As with Figure 5.4, the left-hand diagram (Figure 5.5(a)) plots the PPP line. How- ever, with the exchange rate pegged at Q0, the economy must at all times be restricted

to points that lie along the vertical line. Since, as before, equilibrium requires that the domestic price level be at purchasing power parity, it follows that the system must start off at A, at the intersection of the PPP line with the fixed exchange rate line. Put formally, we must have:

P= Q₀O* (5.10)

where the bars over the right-hand side variables remind us that both S and P* are fixed exogenously.

The economy is in full equilibrium initially, because the PPP price level defined in Equation 5.10 is precisely the one consistent with the (endogenous) money stock and hence with equality of aggregate supply and demand at the point a in Figure 5.5(b). Now suppose the initial equilibrium illustrated by points A, a and H is disturbed by a monetary expansion.

With the expansion of domestic credit, the 45° line in the money supply diagram Figure 5.5(c) shifts upward by the amount of the expansion, so that, with the foreign exchange reserves still at their previous level (of FX0), the money stock has now

swelled to Ms

1, as we can see at the point J.

Following the line across from J, we see that the new money stock implies a price level of P1(at b), thanks to an upward shift in the aggregate demand schedule. From

the PPP line in Figure 5.5(a), it is clear that the higher price level has made the domestic economy uncompetitive, since, given unchanged foreign prices and the fixed exchange rate, it amounts to a real appreciation. At C, there is an incentive for domestic entrepreneurs to import from abroad and none for foreigners to buy locally produced goods.

156 Chapter 5 · Flexible prices: the monetary model

The obvious outcome must be a deficit on the balance of payments4 _{as the}

economy responds to the changed terms of trade. The situation is unsustainable. It would cause an immediate depreciation if the authorities permitted one. However, by assumption, they avoid that outcome by using the foreign exchange reserves to buy the domestic currency or, to put it differently, to finance the ongoing payments deficit. The result is that the reserves start to fall.

Each successive reduction in the reserves tends to reduce the money supply, push- ing the economy along the arrowed paths in the three quadrants, so that the system moves from J to K, from b back to a and from C down to A. The process ends with competitiveness restored and the balance of payments deficit reduced to zero, back at A on the PPP line, with the price level restored to its old level of P0 (at the

point a). The reinstatement of the original equilibrium is possible because the money supply has contracted, to the point where it is once more at its initial level, Ms

0.

To understand why we get this result, recall from Equation 4.7 that our demand for money, given PPP, must equal:

Md_{= kPy = k(QO*)J (5.11)}

The final term is the demand for money. Notice that all its components are exogen- ously given variables. It follows that, under our assumptions, nothing the domestic monetary authority does can affect the demand for money. If the market is to clear, then it follows equally that the money supply must automatically find its way back to its pre-expansion level.

Equating demand and supply:

Md_{= kQO*J = M}s_{= FX + DC (5.12)}

so that, solving for FX gives us:

FX= kQO*J − DC (5.13)

Equation 5.13 tells us that the foreign currency reserves, FX, must be exactly equal to the gap between the given demand for domestic money and the supply generated by the local banking system, through the process of domestic credit expansion. It fol- lows that the more sparing the domestic authorities are in their credit creation, the greater will be the shortfall that has to be made up by the reserves.

In terms of changes, we can state that:

Proposition 5.4.Under fixed exchange rates in the monetary model, starting from a position of equilibrium, domestic credit creation will be neutralized, other things being equal, by a fall in the reserves as a result of a temporary balance of pay- ments deficit. Conversely, domestic credit contraction will cause a temporary balance of payments surplus and a consequent offsetting rise in the reserves.

Notice that, as always in the monetary model, the mechanism involved here could be expressed purely in terms of the excess demand for money.

The right-hand side of Equation 5.13 is the excess demand for money balances. It is this excess demand that is satisfied by the supply of international currency. An increase in domestic credit from an initial equilibrium generates an excess supply of money balances in the local market. As in the closed economy context (see

5.2 The simple monetary model of a fixed exchange rate 157

Section 4.1.2), the effect is to cause domestic residents to run down their excess money balances by spending. With real income fixed, however, the consequent inflation makes foreign products relatively cheaper and the home country’s exports more expensive. The external deficit is a by-product of the private sector’s attempt to sub- stitute goods for excess money balances. As reserves flow out, the foreign component of the money stock falls along with domestic prices until equilibrium is reinstated.

Notice that since it is stocks of money that count in this model, the flow of reserves in or out of a country can only be a temporary phenomenon, as the money stock adjusts over time to the demand. In other words, balance of payments deficits or sur- pluses are viewed as inherently transient by-products of the adjustment mechanism. Once that process is complete and the money market is back in equilibrium, the deficit or surplus will have evaporated.

If the money supply, price level and balance of payments all return to their previ- ous level, what has changed in the new equilibrium?

Compare the points K and H in Figure 5.5(c). Although the money supply is unchanged at K, its composition has altered as a result of the cumulative impact of the balance of payments deficit that persisted throughout the period of adjustment. The new money supply is made up as follows:

Ms

0= FX1+ DC1 (5.14)

In other words, the net outcome is that the money stock now consists of more domestic credit and less foreign exchange than previously. What has occurred is a kind of debasement of the currency – a dilution of the international asset backing of the domestic money supply. Obviously, the process has a well-defined limit – at the point when the reserves have fallen to zero and the entire money stock is composed of domestic credit.

Sterilization of reserve changes

Notice that the process described here amounts to a type of automatic stabilization. In fact, this is broadly the mechanism relied on to guarantee the stability both of the pre-World War I Gold Standard and the Bretton Woods system (see Section 1.5.1). With a fixed exchange rate, flows of reserves act automatically to adjust the money stock so as to reinstate equilibrium. Government monetary policy is not only imposs- ible, it is also unnecessary.

In particular, viewed from this standpoint, balance of payments deficits (or sur- pluses), far from requiring remedial macroeconomic policy, are actually the channels through which disequilibria are spontaneously rectified.

Nonetheless, a government that wishes for whatever reason to resist these stabil- izing forces might in principle be able to do so, temporarily at least. To see how this can be achieved, go back to the situation facing domestic policymakers at the start of what has been called here the adjustment phase, in the aftermath of the initial destabilizing domestic credit expansion, when the economy is at points C, b and J respectively in Figures 5.5(a) to (c).

At that juncture, the UK is running a balance of payments deficit and is therefore losing reserves (as first seen in Equation 4.11). In other words, the UK money stock is falling because, in the identity:

158 Chapter 5 · Flexible prices: the monetary model

∆FX + ∆DC ≡ ∆Ms

the first term is negative. Since the second term is constant (the once and for all increase is assumed to have already taken place), the money supply is falling. Hence, it is only a matter of time until the cumulative effect of the continuing deficits reduces the money supply to its pre-disturbance level.

Now suppose the authorities decided to try to prevent the money stock falling by further expanding domestic credit. It would appear that, in so doing, they could pre- empt the fall in the money supply. If they increased credit enough to offset the fall in the foreign currency reserves in each period, it looks as though they could neutralize the deficits completely.

The following piece of jargon is commonly used:

Sterilization is the process of neutralizing the effect of a balance of payments deficit (surplus) by creating (retiring) enough domestic credit to offset the fall in the foreign exchange reserves.

There has been a great deal of debate, among both researchers and policymakers, about how far sterilization is actually feasible. Even its most enthusiastic advocates would not claim it can work for very long. Whether it can work at all in today’s cur- rency markets is extremely dubious.5

To see why its usefulness is likely to be limited, we need to follow through the implication of the second stage increase in domestic credit. Obviously, the effect of an increase in domestic credit starting from the situation at J in Figure 5.5(c) will be to move the money supply line even further up the vertical axis. The result will be to further dilute the foreign currency backing of the UK money stock.

Neither is that all. We have already established that, as long as the money stock is above its equilibrium level, the UK will be haemorrhaging reserves. Clearly, any- thing that prolongs that situation will reduce the reserves below what they otherwise would be in the absence of any attempt at sterilization.

It follows that sterilization is likely to prove a treadmill. Each expansion of domestic credit will prolong the reserve loss and hence generate the need for further credit creation. At each stage, the domestic credit component of the money stock gets larger and the reserve component smaller.

In theory, at least, there will come a stage when the reserves are exhausted and the game will be over. In reality, the limit to this process is likely to come some time before the country’s reserves are actually exhausted, simply because currency markets will anticipate the evil day and thereby hasten its arrival by rushing to sell pounds at the current exchange rate while they still can,6_{as we shall see in Chapter 17.}

5.2.2

Income increase under fixed exchange rates

As far as changes in real income and the world price level are concerned, the analysis involves a straightforward application of the results from the floating rate case.

With the price level unchanged, an increase in real income amounts to a rise in the demand for real money balances, other things being equal. Starting from a position

5.2 The simple monetary model of a fixed exchange rate 159

of equilibrium, then, the impact will cause domestic residents to spend less, so as to raise their balances to a level commensurate with their new, higher volume of trans- actions. In doing so, they force the price level down, which with a fixed exchange rate makes the home country’s output overcompetitive on world markets, leading to a balance of payments surplus and consequent rise in the reserves. This process will come to an end only when the domestic money stock has grown sufficiently to match the new, larger demand.

So, as the reader may confirm by redrawing Figure 5.5 and shifting the aggregate supply line to the right, we can state the following:

Proposition 5.5.Under fixed exchange rates in the monetary model, starting from a position of equilibrium, the result of a rise in (the domestic country’s) real income will be to cause an increase in the reserves as a result of a temporary balance of payments surplus, other things being equal. In the new equilibrium, the domestic money stock will have risen and the home price level will have returned to its PPP level.

Again, note the contrast with the DIY model (Section 1.4).

5.2.3

Foreign price increase under fixed exchange rates

As for a rise in the world price level, the effect under a fixed exchange rate is directly to increase the home country’s competitiveness, causing a payments surplus and consequent rise in the reserves. (In terms of Figure 5.5, the impact effect is to cause the PPP line to become steeper.) This in turn brings about a rise in the money stock, pushing up the home country price level until it reaches parity with that of the outside world, at which point PPP and external balance are restored. So, for completeness:

Proposition 5.6.Under fixed exchange rates in the monetary model, starting from a position of equilibrium, the result of a rise in the rest of the world’s price level will be to cause an increase in the reserves as the result of a temporary balance of payments surplus, other things being equal. In the new equilibrium, the domestic money stock will be greater and the home price level will have risen to its PPP level.

Note the implication: a country that pegs its exchange rate has ultimately to accept the world price level. In the common jargon of the 1960s and 1970s, it is forced to import inflation from the rest of the world. The fact that it cannot control its own money supply means it cannot choose its price level or inflation rate inde- pendently of developments beyond its borders.

Hence, an important conclusion of the monetary model is that, subject to one qualification we shall deal with in a moment, a country cannot follow an independent monetary policy under fixed exchange rates – neither, as a consequence, can it choose a price level or inflation rate different from that of the rest of the world.

To see the qualification that needs to be added to this statement, ask yourself the following question: what determines the world price level, P*? What causes world inflation – at any rate, in this simple model?

The answer must be that world prices rise when the world’s money stock increases faster than world demand. Also, world money supply and demand are simply the sum of the supply and demand in all of the countries in the world. It follows that, when we analyse the effect of, say, an increase in the home country’s money stock,

we can only treat the world price level as exogenous if the additional money creation is of negligible significance to the world as a whole. In other words, we have to be able

safely to ignore the impact of the home country’s money supply increase on the rest of the world’s money markets and hence on world prices. Obviously, this assumption only makes sense if the domestic country is small enough in economic terms relat- ive to the world economy for us to be able to ignore the repercussions of its policy measures on the world economy.7

5.2.4

Devaluation under fixed exchange rates

Before leaving the analysis of fixed exchange rates, there is one special case that merits attention, because it provides a particularly clear insight into the nature of the monetary model.

No fixed exchange rate is fixed forever. Sooner or later the authorities find them- selves forced to move the rate to a new level, higher or lower. That is why a fixed exchange rate regime is sometimes referred to as an adjustable peg. What happens when the peg is adjusted?

Figure 5.6 shows the effect of a devaluation, an announced, once-and-for-all rise in the price of foreign currency. It must be emphasized that the analysis is only applicable to a devaluation that is an isolated event, and perceived as such, not one that generates the expectation of further devaluation (or revaluation) to come.