Exchange-Rate Regimes in Transition: Italy 1974

International Finance Discussion Papers Number 193

November 1981

EXCHANGE-RATE KEGIMES IN TRANSITION: ITALY 1974

by

Robert P. Flood and Nancy Peregrim Marion”

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. fhe research reported here was accomplished in part while N. Marion was a Visiting Scholar at the Board of Governors. The research is also part of the NBER's research program in International Studies.

It was partially supported by the NBER Summer Institute in International Studies and by National Science Foundation Grant SES-7926807. Any opinions expressed are those of the authors and not those of the National Bureau of Economic Research or the Board of Governors of the Federal Reserve System or other members of its staff. The authors wish to thank Julie Withers for research assistance.

I. Introduction

From August, 1971, when the U.S. suspended dollar convertibility, ur.til February, 1973, when the dollar was devalued another 10 per cent, the Bretton Woods System was in the final stage of collapse. During the transition period from fixed but adjustable exchange rates to managed floating, some major European countries adopted a middle-ground position, instituting some sort of two-tier exchange market, with separate exchange rates for current-account and capital-account transactions. The authorities generally pegged the commercial exchange rate and allowed the financial exchange rate to be determined by market forces. It: was hoped that the two-tier exchange market would relieve pressure on official reserves caused by massive shifts in capital flows. At the same time, it would insulate commercial transactions from exchange-rate fluctuations and eliminate the need for discretionary restrictions on capital transactions. Insulation of foreign trade from exchange-rate fluctuations seems to have been a less pressing objective for some countries during this period, since they pursued a two-tier float where the commercial rate was allowed to float in its own tier.

Italy, France, the Belgium-Luxembourg Economic Union (BLEU), the U.K. and the Netherlands were the major European practitioners of twotier exchange markets in the early 1970s, although the BLEU has operated such a system continuously since 1957 and France adopted a modified version again in the spring of 1981.

Existing studies of two-tier exchange markets (e.g., Fleming (1971,

1.974), Barattieri and Ragazzi (1971), Argy and Porter (1972), Lanyi (1975),

Decaluwe and Steinherr (1976), Flood (1978), Marion (1981), and Flood and Marion (1981)) have focussed on the operation of a two-tier exchange market, with special emphasis on such topics as the ability of the system to insulate an economy from foreign disturbances and

the formulation of expectations under such a regime. Neglected in all these studies is the fact that the two-tier markets of the early 1970s represented an intermediate step in the transition from fixed (but adjustable) exchange rates to flexible (but managed) exchange rates. The transitional nature of these regimes -- their perceived temporariness -may help to explain the behavior of exchange rates under such regimes which cannot be otherwise explained by standard market fundamentals.

A case in point is the strange behavior of Italian exchange rates during the transition from a two-tier float to a uniform flexible exchange rate on March 22, 1974. Table I illustrates the behavior of Italian exchange rates during the December 1973-March 1974 period.

It also includes data for France, which made a similar transition ‘rom a two-tier float to a uniform flexible exchange rate on March 21, 1974. The table shows the percentage premia of the financial lira over the commercial lira and the financial franc over the commercial franc.

Note that the spread between the financial and commercial franc narrowed steadily as the March 21 transition date approached. The French data exhibit exactly the pattern predicted by a simple rational expectations model of a two-tier float. If agents expect that the exchange markets will be unified on a fixed future date, then the bidding away of expected speculative profits will drive the financial and

commercial exchange rates together, with any gap between the two rates

vanishing the instant before market unification.

The Italian data, on the other hand, pose an interesting puzzle. The spread between the financial and commercial lira did not narrow steadily. In fact, it grew from around 2% at the. beginning of 1974 to

9% on March 4, 1974. The two rates then moved together somewhat during

eee

the period March 4-21, but on March 21, the final day of the Italian

pt nee -

two-tier float, a 2.7% discount in the financial lira remained. Chart I shows that Italian exchange rates were also quite volatile prior to the March 22 transition date.

The purpose of this paper is to present a model of an exchange-rate regime in transition which is consistent with the Italian data. We hypothesize that forward-looking agents believed the Italian two-tier

float to be temporary, but they were uncertain about the type of exchange-

ens me omcines nmtan at egcenmnemree femme FO neces

rate regime the authorities would next adopt. Our model shows that

Netter erie yananrcecreratenaramnmaar mn ere NS

expectations of a transition in regime, combined with uncertainty about the nature of the post-transition regime, can cause a jump in the exchange rates at the moment of transition as well as extreme volatility in exchange rates prior to the transition. Moreover, the presence of

a discrete jump in the exchange rates at the time of transition implies only that speculative profits were made ex-post, not that they were expected ex-ante.

Several items illustrate the nature of the confusion surrounding Italy's exchange-rate regime transition. First, agents in the lira markets had seen the French abandon their two-tier float and move to a unified flexible rate. Undoubtedly agents believed the same sort

of move could take place in Italy. Second, agents apparently

believed that a return to a standard two-tier exchange market with a pegged commercial rate was possible. Rushing (1974), for example, wrote at the time: "In February, 1973, Italy adopted a two-tier exchange-rate structure... Currently (March, 1974), both rates are floating against all currencies. Presumably, the rationale for maintaining the two-tier structure even though both rates are floating is the expectation of an eventual return to a fixed rate for noncapital (i.e., currentaccount) transactions."

Confusion was also generated by the Italian authorities.

For example, in a March, 1974, letter of intent backing an Italian request for a $1.2B International Monetary Fund stand-by credit, the Italian Treasury Ministry reaffirmed its intention to maintain controls on capital movements "for a certain period," and this included keeping some sort of two-tier exchange market mechanism.

With agents confused about the nature of the post-transition regime, political events in early 1974 could only heighten their confusion. OPEC's fourfold increase in oil prices in early 1974 was expected to cause severe balance-of-payments difficulties for Italy, and agents were unsure of how the authorities would respond. Then in March, 1974,

+

a new center-left coajition government was established in Italy whose ere ve

specific foréign-exchange market policies could hardly have been known to agents in the foreign-exchange markets.

Our strategy in modeling Italy's exchange-rate regime transition is first to develop a general model capable of describing the relevant exchange-rate regime alternatives for Italy. This general model is

presented in Section II. In Section III we provide exchange-rate

solutions for each type of exchange-rate regime. In Section IV we parameterize the "confusion" surrounding the Italian transition. We then examine Italy's actual transition from a two-tier float to a unified flexible exchange rate given that agents thought a transition to either a two-tier regime with a fixed commercial rate or to a uniform float was possible. Section V provides some concluding remarks ani highlights an important conclusion of the analysis: the "temporariness" of an exchange-rate regime should be treated as a market fundamental, and agents' subjective probabilities about the nature of a transition may be a key explanatory variable of exchange-rate movements

prior to the transition.

Il. The General Model

Italy adopted a two-tier exchange market with a fixed commercial rate in January, 1973, after substantial outflows of private capital, coupled with expectations of a devaluation of the lira, led to mounting pressure onofficial reserves. From February, 1973 until March, 1974, when the two-tier regime was abolished, the commercial rate was allowed to float in its own tier. In this section, we present a macro model general enough to incorporate the three exchange-rate

regime alternatives for Italy:

(1) the two-tier float (TTF), which was the regime in effect prior to the transition,

(2) the two-tier exchange market with a fixed commercial rate (TT), which the Italians operated in January, 1973, and which agents believed could become the post-transition regime,

(3) the uniform flexible exchange-rate regime (FLEX), which agents believed was a possible post-transition regime and which, in fact, was adopted on March 22, 1974.

Because of turmoil in the foreign-exchange markets, including the pressures of massive interest-sensitive and speculative capital flows, the uniform fixed exchange-rate regime was never a viable option for Italy during this period.

In the model presented below, the domestic economy is assumed to be small both in commodity markets and in the market for internationally-

traded financial assets.

Notation

Lower case letters generally denote logarithms of variables; a dot over a variable indicates the time derivative; a bar over a variable

indicates that it is held constant; an asterisk indicates "foreign."

d Domestic component of monetary base

g International reserve component of monetary base i Domestic interest rate (level)

k Domestic stock of traded securities

m Monetary base

p Domestic price level

€ Uniform flexible exchange rate (home currency/foreign currency) Ss Commercial exchange rate

x Financial exchange rate

Ww Domestic real financial wealth

y Domestic real output

t Time

The Model

Monetary Sector

(1) m(t)-p(t) = Og ~ 2 (4) + Oy (t) i Oy? Ay >9

(2) a(t) = i*(t) +y(s(t)-x(t)) +x(t); Y>o

(3) m(t) = Og(t)+(1-8) a(t); O<O<1

i} Lo}

(4a) m(t) = d(t) = G(t) (FLEX, TTF)

(4b) m(t) = O9(t); A(t)

i [o>]

(TT)

Saving

Yi >O0

(5) w(t) = Hy + Fly Ce) -w(t)) + FCG (t) p(t) ); Be 2

(6) w(t) = nm(t)+(1-n) (x(t) +k(t))-p(t); O<n<l

Foreign-Exchange Market

(Ja) s(t) = x(t) = E(t) (FLEX)

(7b) s(t) = Ss (TT)

Prices

it

(8) p(t) p*¥(t) + s(t)

Exogenous Variables

(9) y(t) = y

(10) d(t) = 4

(11) p*(t)

i} Ze) *

(12) i*(t) = i*

(13) k(t) =k (TT, TTF)

Eguation (1) depicts money-market equilibrium. It equates the real monetary base, m(t)-p(t), to money demand, which depends negatively on the opportunity cost of holding money and positively on real output. Equation (2) specifies the opportunity cost of holding money. It is general enough.to encompass the three alternative exchange-rate regimes. In the case of two-tier exchange rates, the principal on foreign bonds must be acquired and repatriated at the financial rate, X (level), but interest income, a current-account item, must be repatriated at the commercial rate S (level). To derive Equation (2), we consider the opportunity cost of holding money for a time period of length h and then let h>0O to obtain our continuous-time expression. At the beginning of a period of length h, one unit of domestic money will buy 1/X(t) units of financial foreign exchange which may be repatriated at the end of the period at the rate X(tth). During the period, the 1/xX(t) units of foreign exchange earn hi*(t)/X(t) in interest income which may be repatriated into domestic money in amount S(t+h)hi*(t)/X(t). These two elements of return can be combined to give X(t+h) S (t+h) hi*(t)

—_—__ . <A th tunit an overall return of x(t) (1 X(t+h) ) ence, e opportunity

cost of holding domestic money from time t to time (tth) is hi(t) in

10

the expression

; _ X(tth) S(t+h) hi* (t) (14) 1+hi(t) = xt) (1+ Xten)

A logarithmic approximation to (14) is

S(t+h)hi*(t)

(15) hi(t) = x(tth) - x(t) + X(t+h)

Dividing each side of (15) by h and letting h°*0, we obtain

S(t) i*(t)

(16) i(t) = x(t) + x(t)

Finally, we approximate S(t)i*(t)/X(t) in (16) by i*(t)+y[s(t)-x(t)] to get Equation (2) 2/

When we analyze the two-tier float, s(t) and x(t) in Equation (2) are simultaneously determined endogenous variables. When we examine a two-tier market with a fixed commercial rate, s(t) is held fixec at s by the domestic monetary authorities. Under unified flexible exchange rates, s(t)=x(t)=e(t) and Equation (2) becomes the familiar uncovered interest arbitrage condition with risk neutrality.

Equation (3) states that the nominal domestic monetary base, m(t), is a weighted average of the book value of an international reserve component, g(t), and a domestic component, d(t). Throughout the enalysis we hold d(t) constant at a. We also assume that under the TTF and

FLEX regimes, the government does not intervene in the foreign-exchange

market, so g(t) is constant at g. Consequently, Equation (4a) holds

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for these two regimes. Under the TT regime, the government must intervene in the foreign-exchange market to peg the commercial rate, so g(t) will not be constant. Equation (4b) holds for this regime. Since the foreign-exchange markets are partitioned under the TT regime,

the accumulation of reserves, g(t), is determined solely by the current-account surplus. Consequently, g(t) is a continuous

variable and does not make discrete jumps as it might under a uniform fixed exchange rate.

Equation (5) equates real wealth accumulation to planned saving. Planned saving depends positively on the output-wealth ratio, y(t)-w(t), and positively on the real rate of interest, i(t)-p(t).

Equation (6) specifies the logarithmic linearization of real wealth, with nominal wealth being a weighted average of nominal money, m(t), and the nominal domestic-currency value of traded securities, x(t)+k(t). Net domestic holdings of traded securities are assumed to be nonnegative.

The exchange-rate regime in effect dictates the channels through which the economy alters its real stock of wealth. Indeed, the way in which wealth is acquired is the most significant difference

between the TTF, TT, and FLEX regimes.

Under the TTF regime, the flexible commercial rate keeps the current-account in balance while the flexible financial rate prevents net capital flows. Since we have also assumed that there is no change in the domestic component of the money base, equations (4a), (10) and

(13) are relevant and real wealth accumulation under the TIF regime is

12 (17) w(t) = (l-n) k(t) - Bit). Under the TT regime, real wealth accumulation becomes (18) w(t) = n6g(t) + (1-n) x(t) - p(t).

Equation (18) differs from (17) by the term nOg(t), which gives the wealth effect of a current-account surplus or deficit and the extent of

current-account intervention to peg s(t) at Ss. Under the FLEX regime, we have (19) w(t) = (1-n) (x(t) +K(t)) - p(t),

where K(t) need not equal zero.

Equations (7a) and (7b) describe exchange-rate relationships under the various regimes. Equation (7a) states that for the FLEX regime, there is one uniform exchange rate; (7b) states that for the TT regime the commercial rate is pegged. ‘Under the TTF regime, no set relation between the commercial and financial rates exists independently of private behavior. “under the TT regime, the financial rate is flexible and the model determines the relationship between S and x.

Equation (8) is the goods arbitrage condition. In logs, the price of domestic output, p(t), equals the foreign output price plus the commercial exchange rate. Since commodity trade is a current-account transaction, it is appropriate to specify the arbitrage condition using the commercial exchange rate. |

Equations (9)-(12) list the model's exogenous variables.

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This completes the exposition of the general model. Our aim is to use the model to study the expected transition from a temporary TIF regime to either the TT or the FLEX regime. To accomplish our aim, we find in the next section the exchange-rate solutions of our model for the various regimes. In Section IV we model the expected transition by taking the general exchange-rate solutions of the TTF regime (s(t) and x(t)) and using a weighted average of the TT and FLEX exchange-rate solutions as our terminal conditions. Further, since our motivation for this study comes from the Italian experience in 1974, we will indicate in our analysis any additional assumptions which Limit the generality of our model in order to make it more directly applicable to

the Italian case.

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III. Exchange-Rate Solutions In this section we use the general model to derive exchange-rate solutions for the three regimes, TTF, TT and FLEX. We do so by solving a system of linear differential equations for each regime. In Section

IV we model the expected regime transition.

III.1 The TTF Solution Equations (1)-(3), (4a), (5)-(6), (8)-(13) of the general model are used to derive the two primary equations of the TIF regime. These two equations represent semi- reduced forms of money-market equilibrium and

planned saving behavior:

(20) m-p*-s(t) = O,-O, La +¥ (s(t) ~ x(t)) +%(t)] +O,5y

(21) (l-n)x(t)-s(t) = ¥o

+¥, (yonm- (1-n) (x(t) #k) +p #48 (t) )

+¥, (itty (s (€)-x(t)) +%(t)-8 (t))

Equations (20) and (21) are a pair of simultaneous linear differential equations in the exchange rates s(t) and x(t).

In our investigation of conditions actually prevailing in It:aly in late 1973 and early 1974, we discovered that Branson and Haltizunen (1979) had constructed a time series on the level of Italian net foreign assets which encompassed the late 1973- early 1974 period. Their data indicate that during this period, Italian net foreign assets were approximately zero. Since we are interested in the Italian case, it seems

reasonable to specialize our solutions to account for the Branson-

15

Haltttunen data. Hence, we specialize our solutions by reporting the 4/ lim:.ting case of the solutions with (1-n)*0.7~

The exchange-rate solutions for the TTF regime are:

(l-a,y) (22) x(t) = c.evé + ~—t— cebt ig 1 ay Gury) 2 t A (23) s(t) =C eH’ 4g, where , (Y. +—) _ 1 Oy wary

3 (1-0, Y) B, - BL you y

You m2 s=—

u B = {a -o, i#-m+p*+a,y] 1 Oy 0 ol 2

D*-m+v is . _ tot mty) +¥, (i +B) 20 Y-1 2

and we assume (¥,-1) #0. In Equations (22) and (23), % and § are the steady-state values of x(t! and s(t), respectively, ) and Y are the two distinct roots of the

sysem, and C_, and C

1 2 are as yet undetermined coefficients.

Since x(t) and s(t) are both simultaneously-determined, "forward-

16

looking" variables, the model of the TTF regime does not in genexal have the now familiar saddle point property which often occurs when

one endogenous variable is predetermined and the other is "forwardlooking." Note that if U is positive, then the system contains t:wo positive roots, and the TTF model is formally an unstable node. Under these circumstances, non-zero values for Cc) and cy will prevent the financial and commercial exchange rates from ever reaching their steadystate values. Instead, they will both ride a speculative bubble indefinitely.

If the TTF regime were expected to be permanent, then the condition of no speculative bubbles would require agents to set C,=0 and =o set C,=0 when u>0. However, since agents expect the TTF regime to be temporary, the coefficients C, and C, need not be set at zero. AS we

1 2

shall see in Section IV, agents will set Cy) and Cy at values where a transition to some more permanent regime -- either the TT or FLEX --

can be made without expected speculative profits.

III.2 The TT Solution Equations: (1)-(3), (4b), (5)-(6), (7b), (8)-(13) from the general model are used to derive the semi-reduced forms of the money-market

equilibrium condition and planned saving behavior for the TT regime:

(24) (1-9) d+6g(t)-p*-s =

Oo, (L*+y (S-x (t) ) +k(t)) 40,9

17

(25) nOg(t)+(1-n) x(t) = ¥ tty lyn [(1-6) d+6g(t) ] -(1-n) [x (t) +k] +p*+s}

+¥, (iY (s-x(t)) +x(t)).

Recall that under the TT regime, the financial exchange rate is flexible but the government pegs the commercial exchange rate. The government's foreign-exchange market intervention to peg s(t) at Ss alters the international reserve component of the monetary base over time. Consequently, Equations (24) and (25) represent a pair of simultaneous linear differential equations in g(t) and x(t).

The exchange-rate and reserves solutions for the TT regime are:

y

2 (26) g(t) = (g(t) -He 1a) 4g; tor (27) x(t) = Ag(t) +R-AG; t>T where A= 6 ¥o a, +g7 ty) 1 B _ a. 3 s g=——~y_*6 2 Yi ty 1 a OB, Pale x= ¥ Y Ss a. (Y. + 2) Y 11 a

18

1 - c 5 re B, = pity * ¥y ly + Pt (1-8) a) + ¥, G*+B,)]

1 BA = a, |%o ~ Oy

i*+ any - (1-6)d+ p*] and where T is defined as the transition date. The terms g and & are the steady-state values of g(t) and x(t), respectively.

Unlike the TTF regime, the TT regime exhibits saddle-point stability. The value of g(t), which represents the book value of international reserves, is given by history at an instant in time. The financial exchange rate, x(t), is not predetermined; rather, it is a currently determined "forward-looking" variable.

Since T represents the transition date -- the initial instant of the TT regime -- g(T) is the initial condition for our solution of the time path of g(t), tT.

The initial condition for our solution of the time path of x(t) is found by invoking the requirement that the model place itself on the stable branch leading to the steady state. Equation (27) is the stable branch of the equation system (24), (25). Equation (26) traces the motion of g(t). The motion of x(t) is obtained by substituting (26) into (27).

The final component in our solution of the TT model is the setting of commercial rate at s. If agents believe during the operation of a TTF regime that the authorities will switch to a TT regime, then they must form beliefs about the level at which s will be set under the TT regime. These beliefs are subjective, but

some guidance can be obtained from public policy announcements just

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prior to the transition. For example, in Italy's March, 1974, letter of intent to the IMF, it firmly undertook to eliminate its non-oil “current-account deficit. Hence, agents may reasonably have believed that the commercial exchange rate would be set at a level designed

to achieve some current-account target, Z, at time T. Let ¥9 (28) Z=g(T) =-(¥) +o) (g(T)-9),

where the final equality in (28) follows from differentiating (26). To find the value of ‘Ss which will yield current-account target Z,

substitute the definition of g into (28) to obtain

¥ - (29a) Ze= (CY) +g) (-g (T) + * * y+) 1a,

Din!

Rearranging (29a), we get

6(Z-B,) ¥

2

(YY, +>) 1 ay

(29b) § = 6g(T) +

Equation (29b) has the sensible property that a larger currentaccount surplus target (a smaller current-account deficit target)

requires a higher price for commercial foreign exchange, since

das 9 dz Y (¥. +—)

1 oO,

20

The complete solution of the TT model is obtained in the following

manner. First, substitute (29b) into the definitions of g and &. This

gives: B Z-B (30a) gG = 3 + g(T) + 3 ¥5 ¥5 (¥ +) (+o) Oy 1 6B B 8 (Z-B.) (30b) = a - + ogi) + —— . 2 2) yo, (¥, +—) (Y, +— 131 Oy 1 Oy

Next, substitute (30a) and (30b) into the solutions for g(t) and x(t) in Equations (26) and (27). We now have a complete solution to tire TT regime conditional on the current-account target Z and the model placing

itself on the stable branch leading to the steady state.2/

III.3 The FLEX Solution

Under the FLEX regime, the general model of Section II decomooses, and we need only know the money-market equilibrium condition to determine the value of the exchange rate. Equations (1)-(3), (4a), (7a) and (9)~(12) of the general model can be combined to derive the semi-reduced

form of the money-market equilibrium for the FLEX regime: (31) m- pt - €(t) =a, - a, (*+E(t)) + ay, t>T.

Equation (31) is a linear differential equation in €(t). In the absence

of speculative bubbles, the solution to (31) is

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(32a) e(t) =m- p* +a i* - Qoy — 5s t>T.

Since e€(t) in (32a) is a constant, it will be the exchange rate in

effect at the initial instant the authorities switch to a FLEX regime.

Hence,

=™m-ov* i* - y= (32h) e€(T) m- p* + O42 O5¥ Oy .

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IV. The Transition from a TTF Regime

In this section we will study the expected transition from a TIF regime to either a FLEX regime or a TT regime. Prior to the transition, the market will set exchange rates at levels such that speculatoxs could not anticipate making speculative profits by entering the market the instant before the transition.

As an example of what is meant by the absence of expected s)eculative profits, suppose that at the instant after the regime switch financial foreign exchange would be worth 700 lire per dollar if the switch were made to the FLEX regime or 800 lire per dollar if the switch were made to the TT regime. The absence of expected speculative

profits requires

x(T_) = 71700 + (1 - 1)800 ,

where T_ represents the instant before the transition and 7 is the subjective probability attached by speculators to an actual transition to the FLEX regime. The above expression states that financial foreign exchange just prior to the transition will be a weighted average of the price of foreign exchange under a FLEX regime at time T and the price of foreign financial exchange under the TT regime at time T.

Figure 1 depicts one possible time path for the value of financial foreign exchange given our example. As seen in figure 1, x(T_) is set at a level between 700 lire per dollar and 800 lire per dollar such that speculators do not expect to profit from the transition. Cf course,

once the actual regime switch is announced and instituted on date T,

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the value of financial foreign exchange will make a discrete jump. If the switch is made to a TT regime, then financial foreign exchange will jump up in value, if the switch is made to a FLEX regime, financial foreign exchange will jump down in value. Consequently, when agents are uncertain about the nature of the post-transition regime, the requirement that there be no expected speculative profits just prior to a regime switch leads to a discrete jump in exchange rates on the transition date.

The condition that speculators bid away expected profits prior to the transition date is the terminal condition which allows us to set Cy and Cy in our solution to the TTF regime. In particular, suppose that at time t < T agents attach probability T(t) to the event "transition to FLEX" and probability (1 - 1(t)) to the event "transition

to TT." The terminal conditions for the TTF model at time t are

(33) x. For)

mt)e(T) + (L = nlt))x 2 (r)

(34) gs TF or)

n(t)e(Z) + (1 - m(t))s-

where oF refers to the financial exchange rate of the TTF regime, etc. The variable m(t) is the subjective probability attached by agents at time t to an actual transition to the FLEX regime at time T.

Given the terminal conditions (33) and (34), we can now solve for the undetermined coefficients Cy and C, in Equations (22) and (23) and

obtain complete exchange-rate solutions for the TTF regime prior to the

trensition.

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Combining (22), (23) with (33), (34), we know that at time t < T,

the absence of expected speculative profits at time T implies

(35) W(tye(T) + (1 - T(t))x T(r) =

(1-0, Y) UT <ATTF

yt + ———~e +x a, (u-Y)

C, (tie

(36) m(t)e(T) + (1 - m(t))s =

aATTF s

UT C, (tle +

Solving these equations for C, (t) and C,(t) yields

(37) cyt) = tm(tyecr) + G2 - T(t))x) (nr) - 27

(1 - a, Y)

-TT ATTF) -YT - ———1_ - - sf a=W [ M(t) e(T) + (1 - Mt))s g Ve (38) Cy (t) = {m(t)e(r) + (L - mts - 3 Wer

Because our terminal conditions depend on T(t), which may vary

with time, we have allowed C, and Cy also to depend on time. Note that

1 at any time t, n(t) refers to an event in the future. Agents set T(t) at time t at the level which optimally uses all information available. Hence, agents expect T(t) to be constant and thus expect C, (t) and C, (t) to be constant. However, as new information becomes available, agents

may alter 1 through time.

It is through these possibly time-varying subjective probabilities

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that we capture another aspect of the confusion in Italy's foreignexchange market in early 1974. Typical exchange-rate models yield exchange-rate solutions where exchange rates change only when standard market fundamentals such as money supplies, foreign interest rates, foreign prices, output or wealth change, or when agents perceive such market fundamentals will change. Our model stresses a previously neglected source of volatility in exchange rates -- changes in agents' subjective probabilities about the nature of an exchange-rate regime transition. Our model recognizes the inherently temporary nature of the Italian TTF regime in 1973-74, and it demonstrates that changes in agents' subjective probabilities of a transition to either a TT or a FLEX regime may account for erratic exchange-rate movements under the TTF regime not otherwise explained by standard market fundamentals.’ During early 1974, the political situation in Italy was quite unsettled, and agents must have been forming beliefs about exchange-rate regime transition based on relatively little information. This situation is exactly the one where rumors and announcements can have dramatic effects on agents' probabilities over a transition. According to the complete solution of our TTF model for t < T, dramatic movements in m(t) may cause dramatic movements in C, (t) and Cot), and dramatic movemants in C, (t) and Cy (t), according to Equations (22) and (23), may. cause dramatic movements in exchange rates. Thus, through movements in T(t), our model is consistent with the erratic fluctuations in Italian exchange rates just prior to the transition, and because of uncertainty about which regime would be

adopted after the transition, our model is consistent with the discrete

26

jump observed in the Italian financial rate at the time of the transition.

In our discussion of the Italian case, we have focussed on just one source of uncertainty -- the nature of the transition. We have assumed that agents know with certainty both the transition date, T, and the government's current-account target, 2.

It turns out that our results are completely unaffected by assuming that agents do not know the transition date. Neither the state variables nor the terminal conditions (33) and (34) depend on the transition date T; consequently the exchange-rate solutions for the TTF regime will not depend on the transition date a!

However, our solutions will be altered if agents did not know for certain the government's current-account target, Z. Therefore,

a more complete treatment of uncertainty in the Italian case would require more general terminal conditions than (33) and (34).

These new terminal conditions could be developed by recognizing that at any date t <T, agents must have formed some subjective probability density function £(z|t) over the random variable Z. The more general terminal conditions would then be obtained by integrating the terminal conditions (33) and (34) over Z. The undetermined coefficients C, (t) and Cy (t) of our TTF solutions could then be calculated by applying these more general terminal conditions.

We have not pursued this extension because it merely reinforces our point that volatility in agents' subjective probabilities about the nature of a transition can result in exchange-rate volatility prior

to the transition.

27

V. Concluding Remarks

The two-tier exchange markets of the early 1970s represented an intermediate step in the transition from fixed but adjustable exchange rates to flexible but managed exchange rates. Our attempt to explain the behavior of the lira during the operation of the Italian two-tier exchange market in 1973-74 has led us to develop a model of exchangerate :xegimes in transition.

Qn the assumption that the market will set exchange rates so as to eliminate expected speculative profits at the time of transition, our model indicates that expectations of a transition, combined with uncertainty about the nature of the post-transition regime, can cause a jumo in exchange rates at the moment of transition as well as volatile exchange-rate movements prior to the transition. The model suggests that the perceived temporariness of an exchange-rate regime should be treated as a market fundamental. Moreover, agents' time-varying subjective probabilities about the nature of a transition can account for exchange-

rate movements not explained by standard market fundamentals.

1 Dates

731203 731204 731205 731206 731207 731210 731211 731212 731213 731214 731217 731218 731219 731220 731221 731226 731227 731228 740102 740103 740104 740107 740108 740109 740110 740111 740114 740115 740116 740117 740118 740121 740122 740123 740124 740125 740128 740129

Notes:

Bw HY

mr

2 _S_ 4.5133 4.5457 4.5417 4.5196 4.5416 4.5596 4.5508 4.5366 4.5572 4.5632 4.5815 4.6209 4.6023 4.6142 4.6286 4.6965 4.6956 4.7565 4.8442 4.8183 4.8875 5.0113 4.8945 4.8802 4.8766 4.9153 4.9991 4.9767 4.9691 4.9736 5.22 5.2125 5.2313 5.2275 5.2275 5.195 5.2225

3 X

4.697

4.7114 4.717 4.6849 4.6904 4.7048 4.7026 4.6893 4.6893 4.7148 4.5777 4.8031 4.7858 4.795 4.7608 4.8614 4.8924 4.931 4.9801 4.9813 5.0403 5.1813 5.1203 5.08 5.0761 5.1086 5.1733 5.1573 5.148 5.1653 5.3763 5.3362 5.3276 5.3404 5.3562 5.2875 5.3

Year, month, day

Commercial exchange rate, Financial exchange rate,

Table I

FRANCE 4

&n(S/X) | Dates - .0399 740130 -.0358 740131 -.0379 740201 -.0359 740204 -.0322 740205 ~.0313 740206 - .0328 740207 -.0331 740208 -.0286 740211 -.0327 740212 -0008 740213 -.0387 740214 -.0391 740215 - .0384 740219 -.0282 740220 — 740221 -.0345 740222 ~.0411 740225 - .0360 740226 -.0277 740227 -.0333 740228 -.0308 740301 - .0334 740304 -.0451 740305 -.0401 740306 -.0401 740 307 - .0386 740308 -.0343 740311 -.0356 740312 -.0354 740313 -.0378 740314 -.0295 740315 ~.0235 740318 -.0183 740319 -.0214 740320 - .0243 740321 ~.0176 740322

-.0147 francs/dollar

francs/dollar

S)

5.1638

5.1075 5.035 5.005 4.9755 5.0467 5.0364 5.01 5.0174 4.9854 5.0046 5.0064 4.9949 4.9494 4.9351 4.9201 4.8164 4.8996 4.8824 4.8103 4.8111 4.8819 4.8811 4.8504 4.8258 4.8413 4.8561 4.8375 4.8013 4.7938 4.82 4.8363 4.8519 4.8515 4.849

x

5.26 5.1975 5.06 5.0725 5.035 5.15 5.1325 5.1086 5.1151 5.08 5.0852 5.08 5.0761 5.005 4.9913 4.9591 4.7847 4.92 4.8769 4.7966 4.8146 4.9035 4.896 4.8461 4.8485 4.8426 4.8414 4.9068 4.8065 4.8008 4.8263 4.835 4.8757 4.8685 4.8555

_&n(S/X)

-.0185 -.0175 -.0050 -.0134 -.0119 -.0203 -.0189 -.0195 -.0193 -.0188 -.0160 -.0146 -.0161 -.0112 -.0113 -.0079

-0066 -.0042

-0011

-0029 ~- .0007 -.0044 - .0030

-0009 -.0047 - .0003

-0030 -.0142 -.0011 -.0015 ~.0013

-0003 -.0049. -.0035 -.0013

Qn(S/X) is approximately equal to the percentage difference between

S and X.

Data Source:

IMF Desk Sheets

Table I

(continued) ITALY Dates i Ss 2 x 3 _&n(S/X) 4 Dates Ss xX Qn (S/X) 731203 606.75 628.75 -.0356 740130 663 694.69 -.0467 731204 610.8 633.73 - .0369 740131 662.5 694.2 -.0467 731205 611.75 630.72 - .0305 740201 658.5 691.56 -.0490 731206 608.5 630.72 -.0359 740204 657 691.56 -.0513 731207 608 628.73 -.0335 740205 654 689 .66 -.0531 731210 610 628.73 -.0302 740206 659.5 693.48 -.0502 731211 608 627.35 -.0313 740207 661.25 698 .08 -.0542 731212 605.2 624.22 -.0309 740208 660.5 697.59 -.0546 731213 605.125 624 .02 -.0307 740211 660.5 696 .86 -.0536 731214 606.125 618.43 -.0201 740212 657.25 695 -.0558 731217 605.85 623.05 -.0280 740213 657.75 697.11 -.0581 731218 606.75 616.33 -.0157 740214 657.5 698 .08 -.0599 731219 605.25 608.83 -.0059 740215 656 696.86 -.0604 721220 604.5 604.41 .o0o01 740219 650 691.56 © -.0620 731221 604.38 605.69 -.0022 740220 649.88 690.85 -.0611 731226 - - - 740221, 650.25 690.85 -.0606 731227 606 610.87 -.0080 740222 649.05 687.29 -.0572 731228 608 616.14 -.0133 740225 649.5 693.24 -.0652 .. 740102 612.5 623.05 -.0171 740226 648 694.69 -.0696 740103 619.5 632.91 -.0214 740227 648.25 696.14 -.0713 740104 620 630.12 -.0162 740228 647.75 700.04 -.0776 740107 630 636.54 -.0103 740301 654.5 708.72 -.0796 740108 636.5 642.67 -.0096 740304 652.75 715.82 -.0922 740109 626.75 636.74 -.0126 740305 650 710.48 - .0890 740110 630 636.54 -.0103 740306 648.125 703.23 -.0816 740111 628.5 - - 740307 650 701.51 -.0763 740114 630.75 637.15 -.0101 740308 648 681.43 -.0503 740115 637.5 643.09 -.0087 740311 645 670.02 -.0381. 740116 639.5 644 .12 -.0072 740312 641 660.72 -.0303 740117 641.5 652.1 -.0164 740313 640.75 668 -.0416 740118 650 663.35 -.0203 740314 640.75 673.63 -.0500 740121 653 677.51 -.0368 740315 639.75 674 .08 -.0523 740122 671 694 .68 -.0347 740318 639 674.54 -.0541 740123 675 696.62 -.0315 740319 635 670.47 -.0544 740124 674.5 702.49 -.0407 740320 633.375 670.69 -.0572 740125 673.5 708.47 -.0506 740321 625.5 642.67 -.0271 740128 664.5 702.99 -.0563 740322 623.75 - - 74012¢ 668.25 698.81 ~.0447 Notes:

1. Year, month, day

2 Commercial exchange rate, lire/dollar

3, Financial exchange rate, lire/dollar

4 Qn(S/X) is approximately equal to the percentage difference between S and X.

5. Data Source: IMF Desk Sheets

: cL bl hE -It-€ ht-1-€ htbl ie hL-t-1 . tu EL EU!

4 » hy @ & iS) 0t4 ob? yoI Prrowers o> 94rd PPHugwwo? —————+ OL

Jvyyor /2si|

Value of financial foreign exchange (lira/dollar)

800

1700 + (1-1) 800

700

time

Figure l

Fl

Footnotes * Board of Governors of the Federal Reserve System and the University

of Virginia, and Dartmouth College, respectively.

Te have used two logarithmic approximations in obtaining Equation (2). First, for small hi(t), &n(1 + hi(t)) Whi(t). Second, S(t)i*(t)/X(t) Y i*(t) + i*(t) (s(t) - x(t)]. We have used i*(t)[s(t) - x(t)] VV yis(t) - x(t)] + xi*(t) + YX, where Y is the mean value of i*(t) and x is the mean value of [s(t) - x(t)]. For simplicity,

we have chosen the normalization xX = 0.

2 We recognize that during the 1973-early 1974 period, the domestic component of the Italian money supply was growing rapidly. Inco:poration into the model of a constant money growth path or a nonconstant but exogenous money growth path would be no more difficult than assuming the domestic component is fixed at da; however, it would not subst:antially change any of our results. Incorporation of a nonconstant, endogenous money growth path would be much more difficult to handle, since :t would

require solving a higher order linear differential equation system.

3 see the evidence cited in Section III.1 on the Italian net foreign

asset position during this period.

Aone solutions for the general case where (1 - n) #0 are available from the authors on request. The solutions reported in the text are

simpler and not substantively different from the more general sclutions.

F2

We realize that it is unreasonable for agents to have had precise knowledge of the government's target current-account, Z. In the next

section, we will not require agents to know 2 exactly prior to the

transition.

6 >In fact, our model of the TTF regime treats standard market

fundamentals as constant (Equations (4a), (9)-(13)), highlighting

the role of volatile subjective probabilities about a transition in

generating volatile exchange-rate movements.

‘t¢ we had not assumed our exogenous variables to be constant

prior to the transition, then the exchange-rate solutions for the TIF regime would depend on the time of transition, and T would be an

additional source of uncertainty.

References

Argy, V. and M. Porter (1972). "The Forward Exchange Market and tne Effects of Domestic and External Disturbances Under Alternative Exchange-Rate Systems," IMF Staff Papers, Volume 19, No. 3.

Barattieri, V. and G. Ragazzi (1971). "An Analysis of the Two-Tier

Foreign Exchange Market," Banca Nazionale del Lavoro Quarterly

Review, 24.

Branson, W. H. and H. Halttunen (1979). "Asset-Market Determination of

Exchange Rates: Initial Empirical and Policy Results," in

J. P. Martin and A. Smith, eds., Trade and Payments Adjustment

under Flexible Exchange Rates, Macmillan: London.

Decaluwe, B. and A. Steinherr (1976). "A Portfolio Balance Model for

a Two-Tier Exchange Market," Economica, 43.

Fleming, J. M. (1971). "Dual Exchange Rates for Current and Capital

Transactions: A Theoretical Examination," in his Essays in

International Economics, Allen and Unwin: London.

(1974). “Dual Exchange Markets and Other Remedies for Disruptive

Capital Flows," IMF Staff Papers, 21.

Flood, R. (1978). "Exchange-Rate Expectations in Dual Exchange Markets,"

Journal of International Economics, 8.

and N. Marion (1981). "The Transmission of Disturbances Under

Alternative Exchange-Rate Regimes with Optimal Indexing," Qua:cterly Journal of Economics, forthcoming.

Lanyi, A. (1975). "Separate Exchange Markets for Capital and Current

Transactions,” IMF Staff Papers, 22.

R2

Marion, N. (1981). “Insulation Properties of Two-Tier Exchange Rates in a Portfolio-Balance Model," Economica, 48. Rushing, P. (1974). "The Two-Tier Exchange-Rate System," New England

Economic Review, March-April.