The Role of the Current Account in Exchange Rate Determination: A Comment on Rodriguez

International Finance Discussion Papers Number 191

October 1981

THE ROLE OF THE CURRENT ACCOUNT IN EXCHANGE RATE DETERMINATION: A COMMENT ON RODRIGUEZ

by

Michael P. Dooley and Peter Isard

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment by a writer that he has had access to unpublished material) should be cleared with the author or authors.

Revised, October 1981 Michael P. Dooley* and Peter Isard

The Role of the Current Account in Exchange Rate Determination:

A Comment on Rodriguez

In a recent contribution to the JPE, Rodriguez (1980) analyses the role of trade flows in exchange rate determination based on a rational expectations formulation of the portfolio balance framework. The purpose of this comment is to extend the Rodriguez analysis by relaxing the restrictive assumption that domestic holdings of foreign currency can only accumulate or decumulate through trade surpluses or deficits, or more generally, through current account imbalances. We derive a modified version of the Rodriguez solution form using assumptions that better reflect: the high degree of development of international credit markets, under which current account imbalances transfer wealth between domestic and foreign portfolios but may have little to do with changing the stocks and currency mix of the (outside) assets that public sectors impose (at market clearing prices) upon private portfolios. In addition, we interpret a key parameter in the Rodriguez solution form which raises an important issue about the role of the current account in the limiting case of perfect: asset substitutability.

" %7 Woard of Governors of the Federal Reserve System. The first author _ is on leave at the International Monetary Fund. This paper represents the views of the authors and should not be interpreted as reflecting

the views of the Board of Governors of the Federal Reserve Systen, the International Monetary Fund, or other members of their staffs.

Qur extension of the Rodriguez model focusses on the monetary bases (MB, MB*) and the stocks of outside interest-bearing bonds (B,B*), dJenominated in domestic and foreign currencies. Private domestic and foreign residents hold money~plus-bond portfolios of size Wp and Wr, which we refer to as "wealth" levels.1/ It is assumed that MB and MB* are eatirely held, respectively, in domestic and foreign portfolios. R and R* denote own rates of interest on domestic and foreign bonds. S, F and S© denote the spot, forward and expected future spot exchange rates, as domestic currency prices of one unit of foreign currency.

By combining market clearing conditions and portfolio demand assumptions we can analyze the relative yields on assets that are expected under conditions of portfolio balance. 2/ The market~clearing condition for foreign bonds can be expressed as:

(1) SB* = xp(Wp - MB) + xp S(Wp - MB*): where xp and xp denote the shares of their bond portfolios that domestic and foreign residents choose to hold as foreign bonds. These portfolio shares are assumed to reflect constant elasticities of demand with respect to the ratio of the expected future prices of foreign and domestic bonds (per unit of domestic currency invested).

"17 We assume that current account imbalances are settled by payments in ~ money or bonds (direct international equity investments are suppressed), and that public budget deficits are financed with money or bond issues. © Beyond this, our conclusions are not affected by ignoring the equity and future-

tax-liability components of financial wealth.

2/ We have previously analyzed this framework in Dooley and Isard (1979 a and b). .

(2) xp = ape

(3) Xp = ap of where

(4) o =[(1/S)(14R*)S®&] /(14R) Under the condition of covered interest rate parity

(5) S = F (1+R*)/(1+4R) The expected future price ratio is seen to represent the ratio of the expected future spot rate to the forward rate.

(6) o = S&/F It is common to refer to o as the exchange risk factor, or 1 plus the premium for bearing exchange risk, or (as an approximation) 1 plus the expected differential yield in favor of foreign bond holdings.

As a notational convenience, denote the global size of bond portfolios as

(7) W = (Wp - MB) + S (Wr — MB*) and derote the division of the global portfolio, by ownership, as

(&) wp

(S) we

(Wp - MB)/W

S(Wp - MB*)/W

Conditions (1)-(3) and (8)-(9) accordingly combine into (10) S = Gob

where

(11) G

(ap Wp + ap wr)W/B*

We focus on the logarithmic form of (10) using an approximation, based on (4), that the logarithm of o equals the interest differential plus the expected change in the logarithm of the exchange rate. Thus,

the logarithmic form of (10), evaluated at time t, can be expressed as

(12) s(t) = g(t) + B [s(ttl) - s(t) + R*¥(t)-R(t)] where s=log S, g=log G, the interest rates apply to the holding period between t and t+l, and variables with time arguments beyond t--in particular, s(t+l)--are understood to represent expectations held at time t. It is readily seen that § corresponds to the reciprocal of Rodriguez's “b" parameter and that the continuous time version of (12) is analogous to Rodriguez's condition (7) with the solution form 1/

(13) s(t) = s(t+T)e 7/8 + s2rRe(ttr) -R(t+r)

+(1/g)g(t+t)] e7 T/B dr

Note that conditions (2) and (3) provide an economic interpretation of 6 -namely the elasticity of demand with respect to the expected relative price of bonds denominated in different currencies.

The thrust of the Rodriguez model is that the current account ‘influences the exchange rate through wealth and portfolio balance effects. Our extension of the Rodriguez framework refines and qualifies this conclusion by recogniz—ing that with highly developed international credit markets, current: account imbalances can be settled via transfers of claims denominated in either the domestic or the foreign currency unit. Under the assumption that the global stocks and currency mix of public debts are independent of the current account, condition (11) captures the influence of the current account on G via its role in transferring wealth between domestic and foreign residents (reflecting its equal and opposite effects on wp and Wp), and in condition (13) the effects on g=log G feed through to the exchange rate. An important refinement of the Rodriguez result, however, is that the effects of the current account on the exchange rate depend on dif-

ferences in the portfolio preferences of domestic and foreign residents.

1/7 The solution form abstracts from the valuation effects of the

exchange rate on g via the wealth variables wp, wp and W.

-5-

In the limiting case of identical preferences (ap= af), G is inde-

pendent of the distribution of private wealth between domestic and foreign residents, and hence the current account has no wealth or portfolio balance effects on the exchange rate.

The evaluation of the role played by the current account in exchange rate determination can be further extended by considering the limiting case of perfect asset substitutablity. In this case — = ~, the solution form reduces to a condition of open interest rate parity and the current account has no wealth or portfolio balance effects on the exchange rate. It is noteworthy that in this case the rational expectations solution cannot close the model since the coefficient on the expected future exchange rate does not have a limiting value of zero.

The fact that the portfolio~balance framework, as traditionally modeled, does not provide a role for the current account under neutrality toward exchange risk is a serious and unnecessary limitation. One of the oldest conjectures in international economics is that residents of one country will not willingly lend forever to residents of another due to political or default risk. A portfolio balance framework in which claims on non-residents are assumed to be imperfect substitutes for claims on residents, even when the currency denomination of such claims is identical, would represent a sensible extension of the framework developed in this note. Such a framework would retain portfolio considerations as central to the explanation for why exchange market pressures arise in response to unexpected current account imbalances, even for coun-

tries that denominate their debt to nonresidents in foreign currencies. 1/

1/ Dooley and Isard (1979b), Hooper and Morton (1980) and Mussa (1980)

discuss the influence of the current account on expected future exchange rates but do not explicitly link the influence to political risk.

References

Dooley, Michael P. and Isard, Peter. “A Portfolio-Balance Rational- Expectations Model of the Dollar-Mark Rate: May 1973-June 1977." Revised manuscript, Federal Reserve Board, Washington, 1979a.

- “The Portfolio-Balance Model of Exchange Rates." Internat:ional

Finance Discussion Paper No. 141, Federal Reserve Board, Washingt:on,

1979b.

Hooper, Peter and Morton, John. "Fluctuations in the Dollar: A Model of Nominal and Real Exchange Rate Determination." International Finance Discussion Paper No. 168, Federal Reserve Board, Washingt:on, 1980.

Mussa, Michael. "The Role of the Current Account in Exchange Rate Dynamics." Center for Mathematical Studies in Business and Economics, report 8033, University of Chicago, Chicago, 1980.

Rodriguez, Carlos Alfredo. "The Role of Trade Flows in Exchange Rate Determination: A Rational Expectations Approach." JPE, 88, No.6 (December 1980): 1148-1158.