David O. Cushman - March 2001

THE PORTFOLIO BALANCE APPROACH TO EXCHANGE RATES We will utilize the following assumptions, which provide one simple version of the portfolio balance approach. The availability of foreign bonds and lack of uncovered interest parity are the essential core. 1. Three assets are available to home residents: Home money (M), home bonds (B), and foreign bonds (F). 2. The home country is small relative to the foreign country (rest of the world). Foreign residents are assumed not to hold either home asset. The foreign interest rate, i*, is exogenous to the home country. 3. Uncovered interest parity does not hold: home and foreign bonds have different risk characteristics and both, along with money, are part of a portfolio diversified to balance risk and expected return. One can say that the two bonds are not perfect substitutes, contrary to the monetary approach. 4. Purchasing power parity does not hold; home and foreign goods are not perfect substitutes either, again contrary to the monetary approach. 5. Exchange rate expectations are static (no change is expected).

Method of Analysis: We will determine a curve for each asset that shows the combinations of the exchange rate (S) and home interest rate (i) that maintain equilibrium in its supply and demand, holding all other factors constant. Any other factor that affects the market will shift the curve. We can then see what happens to the exchange rate and interest rate. From Walras Law, we know that equilibrium in two of these markets ensures equilibrium in the third. Therefore, when convenient, we need consider only two curves at a time. Remember, we are dealing with demands and supplies for “stocks”, not “flows”. Variables: W = wealth, P = home price level, M = home money, B = nominal value of home bonds (usually considered to be government bonds because there is no direct offsetting liability - unless Ricardian equivalence holds), F = foreign currency value of foreign bonds held by home residents, S = domestic currency price of foreign currency, i = home interest rate, i* = foreign interest rate, Y = home real income, E = expected value. Wealth Constraint in Real Terms: W/P = M/P + B/P + SF/P Supply = Demand for Each Asset: (-) (-) . (+) (+) (M/P)s = L( i, i* + E(S), W/P, Y ) s

(B/P)

(+) (-) . (+) (-) = h( i, i* + E(S), W/P, Y )

(-) (+) . (+) (-) (SF/P)s = j( i, i* + E(S), W/P, Y )

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David O. Cushman - March 2001

The demand for each asset (the right side of the equality) is positively related to its own return, and negatively related to the return on the other assets. For example, if the home interest rate rises, the demand for home bonds goes up. Given wealth, the demand for the other two assets must fall (both fall under the assumption that there are no complementary assets). Further, since this fall in demand is divided among two assets, the decline in demand for either must be less than the increase in demand for home bonds. Similarly, an increase in the foreign interest rate increase the demand for foreign bonds more than it reduces the demand for home bonds. Money pays no explicit return, but has an implicit return from its value as the medium of exchange (transactions demand from Y). An increase in wealth is assumed to increase the demand for all assets, though not necessarily proportionately. A reasonable assumption is that it increases demand for home bonds more than for foreign bonds. We are assuming static exchange rate expectations. Therefore, E( S& ) is always zero in this version of the portfolio balance approach. It is left in the above equations just to remind us that in a more general treatment, this source of return on foreign assets must not be forgotten.

Deriving the Curves: Graph: i is on the horizontal axis and S is on the vertical axis. The money market, MM curve: Raise S. Higher real wealth (from higher foreign bond value in terms of domestic currency) increases demand for real money. Demand can be restored equal to the given real money supply by an increase in i, the return on an alternative asset to money. For a given bond coupon payment, higher i also reduces wealth because it implies lower home bond price. This wealth effect from interest rate changes will also lower money demand and help to restore equilibrium. The MM curve is thus upward sloping. The home bond market, BB curve: Raise S. Higher real wealth (from higher foreign bond value in terms of domestic currency) increases the demand for real home bonds. This demand can be restored to the supply with a lower i, the return on these bonds. Lower i also increases B’s price. This wealth effect from the interest rate change increases the value of B by more than it increases the demand to hold B. This net supply increase also helps to restore equilibrium. The BB curve is thus downward sloping. The foreign bond market, FF curve: Raise S. This increases foreign bond supply (valued in home currency) by the same amount that real wealth rises, but since any increase in wealth is desired to be spread among all three assets, there will be excess supply of foreign bonds. Demand for them can be restored by a fall in i which makes one of the alternative assets (home bonds) less attractive and also increases wealth (and thus the demand for foreign assets) through the wealth effect from the i change. The FF curve is thus downward sloping. Since i, through both its effect as a rate of return and its wealth effect, is assumed to have less impact on demand for F than on demand for B, it takes a greater change in i to restore the F market, so the FF curve must be flatter than the BB curve. S| | | | | |

BB

MM

FF i

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David O. Cushman - March 2001

The Impact Period We now consider the effects of several forms of monetary policy, of an increase in the foreign interest rate, and of expansionary fiscal policy. Each shifts two, or possibly three of the curves, leading to a new equilibrium for S and i. We first consider an “impact period,” where only S and i can adjust to maintain equilibrium, and real output Y and the aggregate price level P are constant. The exchange rate and the interest rate can certainly adjust almost instantaneously, but we assume for now that Y and P cannot. A money supply increase through domestic open market operations: The central bank buys home bonds in return for money balances. Total wealth is unchanged by this action (though the adjustment can then affect wealth through the S and i changes). The excess supply of money would be willingly demanded if the interest rate were lower (given S), so MM must shift left. Alternatively, it would be demanded if S were higher (given i) because this would increase wealth through the domestic currency value of F, so MM could also be said to shift up. The FF curve is unaffected because supply and demand for F is unaffected directly by the bank’s action (it is subsequently affected as S and i adjust, a movement along the given FF curve). We can infer from Walras Law that BB must shift left. Indeed, this reflects the lower supply of home bonds (with fewer available, they do not need to pay as high an interest rate i). The effect of the policy is therefore to lower i and raise S (or depreciate home currency). This can be contrasted with the situation under static expectations if home and foreign bonds are perfect substitutes and uncovered interest parity (UIP) holds. The BB and FF curves collapse to a vertical line where i = i*. In this situation, the monetary expansion would have its effect entirely through the exchange rate, not the interest rate. (This conclusion is modified if exchange rate expectations are not static, a case we shall not consider here.) A money supply increase through foreign exchange operations: We now hypothesize that the central bank increases the money supply by buying foreign assets. Again, total wealth is unchanged by this, but now it is F supply (not B supply) which is reduced. The BB curve remains unchanged and FF shifts right and up (the smaller supply of foreign bonds F would be willingly held if home bonds were more attractive from a higher i, or if the country were wealthier from the valuation effect of a higher S). Once again, the effect of monetary policy is to lower i and raise S, but the relative magnitudes of these changes are different: the exchange rate effect is relatively stronger. Under UIP, however, the two ways of increasing the money supply have exactly the same effect. MM shifts along the horizontal interest rate line regardless of which type of bond the central bank acquires. Sterilized foreign currency operations: In general, the term “sterilize” means that the central bank tries to keep certain factors from changing the money supply. For example, an official settlements balance deficit from the sale of foreign exchange reserves by the central bank tends to reduce the money supply. The central bank could attempt to sterilize this by buying home bonds. According to the monetary approach, the attempt would not be successful unless the underlying source of the deficit was removed. But in the portfolio balance approach, it could be. The application we shall consider here is that the central bank buys foreign bonds (for money balances) and simultaneously sells home bonds (getting the money balances back). If real-life central banks try this, it is probably because they wish to affect S without changing the money supply. The reduced supply of foreign bonds shifts FF right (or up) because a higher i would be needed to reduce the demand for them (or higher S to restore the supply by increasing their domestic currency value) . The increased supply of home bonds shifts BB right, but not by as much (horizontally) as the FF shift because the demand for home bonds is

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David O. Cushman - March 2001

more sensitive to the home interest rate than is the demand for foreign bonds (and thus smaller shifts in BB can still restore equilibrium with respect to the home bond market). The MM curve remains constant because the money supply was not changed. The net effect is therefore to raise both S and i. Compared to the first two monetary operations, this third one moves S and i in the same direction, and depreciating home currency is associated with higher home interest rates. A general observation: If the portfolio balance approach has validity (a subject of empirical debate in economics) then the central bank has more power than if UIP holds. It has more power over both exchange rates and interest rates, which are the avenues by which monetary policy is usually thought to affect the rest of the economy. One way we can see this is that by some mix of the above three operations, any combination of S and i can be achieved. A rise in the foreign interest rate “i*”: Canada has periodically been subjected to this sort of external influence, e.g., in 1994-95 and 1999-2000 as U.S. interest rates were raised by the Federal Reserve System. The rise in i* increases the demand for foreign bonds, so FF shifts right because an even larger rise in i (the return on one alternative asset to F) would be necessary to offset this increased demand in the F market. The demand for home bonds is reduced, so BB also shifts right, but not by as much, because a rise in i is more effective at restoring the home bond market equilibrium. Finally, the demand for home money is also reduced. A fall in the home interest rate could restore it, so MM shifts left. The net effect of the three shifts clearly must increase S, so the home currency depreciates. If B demand and M demand are equally sensitive to i*, then BB shifts right less than MM shifts left (because for a given shock it takes less of an i change to restore the B market than the M market), and i falls. But if home bond demand is more sensitive to i* because B and F are close (though not perfect) substitutes, i could rise. The question of relative interest elasticities is an empirical question. Over 1994-95, for example, rising S and i occurred. But other factors may not have remained constant. For example, the Bank of Canada may have simultaneously reduced Ms (or its growth). Under UIP (B and F are perfect substitutes), a rising i* definitely increases i (and depreciates home currency as with the portfolio balance approach). Fiscal Expansion financed by bonds: We shall now examine the possible effects of a fiscal expansion financed by bonds. Such a policy can have an effect in this model if it upsets asset market equilibrium. Its effect (in the impact period) is not directly through any spending changes, unlike the Keynesian model for example. But when the government spends more, it must acquire the required money balances somehow. We assume it obtains them by selling bonds to the public. We wish to examine “pure” fiscal policy, so we shall assume these bonds are not sold to the central bank. If they were, we would have fiscal expansion plus monetary expansion mixed together. The sequence of events would be this: The treasury sells bonds to the public in return for bank balances (money). Now the public has bonds instead of the equivalent money balances. Then the treasury spends the money on goods and services bought from the public, and the public once again has the money balances, and it still has the bonds. This raises the question of whether the public treats the new bonds it now owns as an increase in its net wealth. In other words, in our model has the supply of B really risen? A completely rational and fully informed public would realize that the government now has a corresponding liability. The government’s ability to support this lies in its ability to tax, so the liability really falls to the taxpayers, who are members of the general public. So while the public does have a new bond asset, it also has a new future tax liability of equal value in present value terms. If the public does realize all this, “Ricardian equivalence” holds, and in our model the value of B including tax liability does not rise. But it is quite possible that this rational tax

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David O. Cushman - March 2001

calculation does not hold completely. (How many people calculate their portion of the national debt when figuring their net worth or making financial decisions? Probably not many. How many people include the value of any government bonds they own either directly or indirectly as parts of mutual funds and retirement accounts? Probably most.) Let us assume Ricardian equivalence does not hold and that the fiscal policy increases the supply of B. Real wealth also rises as a consequence. Since people wish to diversify their wealth, the increase in bond supply is greater than the increase in bond demand (from the wealth effect), and the BB curve shifts right (an increase in the home interest rate on these bonds is necessary for the extra ones to be willingly held). The increase in wealth also increases the demand for money, so MM shifts right (a higher home interest rate would be required to offset this, given the money supply). Finally, the increased wealth increases the demand for foreign bonds, so FF must also shift right. The interest rate definitely rises, while the effect on the exchange rate is indeterminate. However, if F and B are not particularly close substitutes, then F demand is relatively less responsive than M demand to i than otherwise, and so FF will tend to shift more than MM from the wealth effect (more change in i is required to restore the F market). Then S rises (home currency depreciation). Also, if M demand is not very wealth elastic, then the MM curve will be steep vertical (recall that its slope derived from a wealth effect) as well as shifting little. This would lead to an even greater rise in S, and a smaller rise in i. In contrast, under UIP (where F and B are perfect substitutes), the home interest rate cannot change relative to i*. Portfolio equilibrium can only be restored by a fall (not a rise) in S, which reduces the value of the foreign portion of bond holdings to restore total wealth to its original value. This must happen because there would otherwise be an increase in the demand for money with no increase in its supply.

The Long Run The impact period changes in S or i brought about by any of the above shocks can have further effects through time. Thus, the longer-run equilibria will differ from the above results. This section sketches briefly a plausible long-run response to the first monetary expansion discussed above. This was the money supply expansion through domestic open market operations. The major effects above were that i fell and S rose. The fall in home interest rates would stimulate investment and thus spending on domestic output. The depreciation of home currency creates a current account surplus that also increases spending on domestic output.1 The current account surplus also gradually increases the economy’s F supply. The increased demand for home goods and the rise in the price of imported goods will tend to increase the price level P, and real output Y may rise temporarily beyond the full employment point. This gets rather complex, so we shall simplify. Let us assume that real output remains unchanged and that the current account balance is a function of the real exchange rate only. The current account surplus results in the acquisition of foreign assets, increasing the F supply and nominal wealth. The demand for F rises, but not enough to match the increased supply, because some of the increased wealth raises the demand for the other two assets. Thus, FF shifts left, BB shifts left, and MM shifts right. From these effects, S clearly falls from its impact-period point, while the interest rate change from its impact-period value is indeterminate. If we ignore the positive impact of higher interest receipts from abroad on the current account, the long-run equilibrium is reached when the real exchange rate is restored to its original level. This is so because at that point, the rate of acquisition of foreign assets has returned to zero.2 Since prices are rising, S does not fall back to its original value.3 Therefore, the impact-period value for S was an overshoot.

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David O. Cushman - March 2001

Of course, the rise in P during the long-run adjustment could also shift the three curves. However, starting from the impact-period equilibrium point, the price rise affects all asset values the same, and thus plays no role in the adjustment other than its role in restoring the real exchange rate to its original value. Although the change in the interest rate is indeterminate starting from the impact-period equilibrium point, we can show that it does end up lower than its value before the monetary expansion. This is from two effects that both require a lower i to restore long-run portfolio equilibrium. First, the real value of foreign bonds, SF/P, ends up higher from the temporary current account surplus (given P*, the real exchange rate, which is ultimately unchanged, is S/P). Second, the real value of home bonds, B/P, ends up lower from higher P and lower B (the latter from the open market operations). The relative scarcity of home bonds is what leads to the lower interest rate on these bonds. The long-run equilibrium also entails greater wealth for the home economy. This and the lower interest rate mean there is a net increase in real money demand, which requires P to rise less than M. We see that, although no change in Y has been allowed by assumption, the money supply change has nevertheless not been neutral. This is in contrast with effects when UIP is assumed.

1

This discussion will not make the distinction between trade and non-traded goods that is in Hallwood and MacDonald, pp. 230-242. Furthermore, the role of the desired rate of saving will not be explicitly considered. 2

Instead of zero, this could be some steady non-zero rate, consistent with overall growth in the economy, which we are ignoring by holding real output constant. 3

In Hallwood and MacDonald’s Fig. 11.5, p. 236, point Z is higher than point X.

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