APPENDIX List of Symbols
A = assets held by domestic residents
BOT = balance of trade
CAP = capital account balance
CUR = current account balance
c = constant term
C = consumption (in real terms)
D = demand for domestic output
E =real domestic expenditure
F = forward rate
G = government expenditure (in real terms)
i = nominal interest rate
I = imports (in real terms)
M = money supply
NFA = net foreign assets of the domestic central bank
O = nominal output
P = domestic price level
S = domestic currency price of foreign exchange on the spot market
T = tax receipts of the government
W = domestic real wealth
X = exports (in real terms)
Y = national income (in real terms)
Yd = nominal disposable income
π = expected rate of depreciation of the domestic exchange rate
An e (superscript) denotes the expected future values of a variable.
A d (subscript) denotes the domestic value of a variable.
An f (subscript) denotes the foreign value of a variable.
The expression E ( ) denotes an expected value operator.
An* denotes the desired or target level of a variable.
An N (subscript) denotes nontraded goods.
A T (subscript) denotes traded goods.
Variables symbolized by small letters denote logarithms.
A bar over a variable denotes the long-run or fixed value of the variable.
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Poole, William (1967), “Speculative Prices as Random Walks: An Analysis of Ten Time Series of Flexible Exchange Rates,” Southern Economic Journal, Vol. 33 (April 1967), pp. 468–78.
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Ms. Schadler, economist in the Special Studies Division of the Research Department, holds degrees from Mount Holyoke College and the London School of Economics and Political Science.
Mundell (1968) actually analyzed situations of less than full employment. The following analysis is conceptually identical to his, although the price level, rather than income, adjusts.
Throughout this paper, the exchange rate is defined as the domestic currency price of foreign exchange.
Frenkel (1976) provides evidence that this was true for the Federal Republic of Germany during an earlier floating exchange rate period as well. He finds that during the hyperinflation in that country (1920-23), the elasticity of the current exchange rate with respect to the money supply over the preceding five years exceeds unity.
See Aliber (1976) for a lucid explanation of the costs of exchange rate variability and basic empirical evidence on the importance of these costs.
The terminology in the early part of this debate was, at best, poorly defined. “Speculation” was usually used synonymously with “private short-term capital flows”; more formally, it can be assumed that speculation is the deliberate assumption of a net open position in foreign currency reflecting a judgment on the part of the transactor as to future exchange rate movements. Destabilizing speculation in Nurkse’s context appears to apply to those speculative capital movements that tend to prevent the rate from stabilizing at a unique level. In Friedman’s context, destabilizing speculation refers to speculative capital movements that are not based on judgments about the long-run equilibrium level of the exchange rate as determined by the relative stance of economic policy in the countries concerned.
See, for example, Kindleberger (1976), who attributes large swings in the current floating regime to “destabilizing and profitable” speculation.
Polak (1943) comes to similar conclusions about exchange rate behavior during the hyperinflation in the Federal Republic of Germany (1920-23). Using a small structural model of the foreign exchange market, Polak concludes that in the initial postwar period speculators expected a return to prewar par values. When depreciation continued, speculators “lost all confidence in an eventual recovery” and instead “projected the rate of depreciation into the future.”
Tsiang (1959) offers another interpretation of the franc’s behavior during the 1920s. He analyzes exchange rate developments vis-à-vis both the relative purchasing power of the franc and France’s policy during the period of letting the money supply vary to maintain a fixed interest rate. He argues (p. 271) that the “almost infinitely elastic supply of money and credit” required to hold interest rates constant was primarily responsible for periods of heavy speculation against the franc. Yeager (1966) presents a similar view. For empirical tests of the period, see Aliber (1962).
Kemp’s counterexample is rather academic, however, since the type of nonlinearities required in demand functions for foreign exchange are unlikely to exist in reality.
where Q = supply of currency
S = domestic currency price of foreign exchange
D = nonspeculative demand
c1, c2, b1, and b2 are constants
One, two, and three dots represent, respectively, the first, second, and third derivatives of the variable with respect to time.
which implies constant sinusoidal exchange rate movements.
where c3, a, and w are constants.
where K = c2 + c3a, e = b2 + c3
which must have at least one positive real root, since complex roots come in pairs and a negative root cannot satisfy an equation with alternating positive and negative terms.
Actually, this proof has been the focus of considerable controversy. Under certain conditions, the sinusoidal component of the time path of the exchange rate could be dominated by an exponential component, so that speculators behaving as postulated would have to acquire stocks of foreign exchange indefinitely and never be able to cash them in to realize profits. For more on this problem, see Telser (1959), Baumol (1959), and Kemp (1964).
Baumol (1957, p. 270) himself notes that “there is little reason to expect any consistent pattern of cyclical price movement on [foreign] exchanges. Rather, the time path can plausibly be expected to be erratic, responding to the political developments in the countries involved.” He holds, however, that any of the cycles in his examples could be a “never-to-be-repeated erratic individual movement” and that the type of profitable destabilizing speculation he envisions could exist.
Barro (1976) and Bilson (1976 a) have arrived at much the same conclusions via a similar monetarist model with explicit assumptions of perfect efficiency in all markets. Bilson, however, has a more extensive discussion of the connection between innovations in the money supply and income and of their possible offsetting effect on the exchange rate.
Mussa’s reduced-form equation for the exchange rate acually comes from a model by Sargent and Wallace (1973).
See the Appendix for definitions of variables used throughout this paper but not identified in the text.
This can be shown by substituting equations (8) and (9) in equation (7') and equation (7') in equation (7) to get st = 1/λ[mt-k+(η/λ) · E(αt)]. A disturbance to εt affects only mt, while through δt it affects E(αt) and mt.
Tests (only some of which relate random exchange rate behavior to market efficiency) of time series properties of exchange rates during the recent float were made by Giddy and Duffy (1975), Levich (1976), Dooley and Shafer (1976), Cummins and others (1976), and Logue and Sweeney (1976). See Poole (1967) for similar tests on earlier floating rate periods.
Tests are generally run on the forward rate or the spot rate corrected for interest differentials, the two being equivalent if interest parity holds as expected.
One problem with relating interest rate differentials to the speculative influence alone is that the effect of changes in interest differentials on the valuation of domestic and foreign assets in the portfolios of wealth holders, which is likely to influence the exchange rate quite apart from speculative pressures, is ignored.
See Foley (1975) for a detailed discussion of the stock versus flow approaches and the appropriateness of each for certain applications.
This point is developed further in the following section.
where w ≡ Af + M/P
which, holding M, Y, and π constant, gives FF in Figure 2. DD is given by a version of equation (10) with desired wealth held constant and actual wealth substituted in BOT = Y - C(Y - T, Af + M/P) - G.
The implications of this assumption are developed further in the following section.
Rational expectations in this context imply that θ is determined by the model.
Since λ and θ are positive parameters, ds/dp evaluated at equilibrium is negative. This result is perfectly intuitive, since an increase in prices relative to their long-run equilibrium level, when money market equilibrium and interest rate parity hold continuously, decreases money balances and increases the interest rate. Given a constant foreign interest rate and long-run exchange rate expectations, the current spot exchange rate must change sufficiently to fulfill equation (27). The upward-sloping Ṗ = 0 schedule is derived by setting Ṗ =0 in equation (26) to fulfill goods market equilibrium, and substituting from equation (22) for id to get P = [δλ/(δλ+σ)]s + [σ(δλ+σ)]m + [λ/(δλ+σ)] (u + (1-γ)y - φσy/λ).
Actually, Dornbusch describes two influences that tend to worsen the trade balance initially after a monetary expansion. First, a fall in the domestic interest rate stimulates expenditure and therefore reduces the gap between income and absorption. Second, if quantities traded depend on the expected exchange rate but trade is effected at the current rate, a monetary expansion that produces a smaller depreciation of the expected rate than of the actual rate worsens the trade balance. Several empirical studies of the effect of exchange rate changes on current balances have indicated initial perverse effects. See Branson (1972) for several member countries of the Organization for Economic Cooperation and Development (OECD), Artus (1975) for the United Kingdom, and Clark (1977) for the United States.
More formally, bb and cc are possible equilibrium loci, each expected with a 50 per cent probability to be realized loci of combinations of p and s consistent with equilibrium in the money market. The expected equilibrium locus, before accounting for risk, is B'B''.