dt L&e&y, Na&vi~le, TN 37235, USA

Received November 1987, final version received April 1988

In a stochastic cash in advance model of an open economy, a rat is dynamically inconsistent (and hence economically infeasible) in a eq if there are no exogenous constraints imposed on ent behaviour and nominal interest rates are strictly positive. On the other hand, a perfectly floating exchange rate regime is feasible but it cannot sustain any international asset trade. However, a noncooperative equilibrium with nonem asset trade and a fixed exchange rate regime may become feasible when we allow policymakers to employ trigger (retaliation) strategies.

veral issues in the analysis of foreign exchange rate regimes that in the recent international finance litera-

, a fundamental one is the comparison of th s and subsequently 1) showed that in a representa-

sh-in-advance, distortion free world, con- fare levels are identical under a floating

exchange rate regime. Lucas (1982) reached the same co complete asset mar

of economic distortions. ts by allowing for various types

rateful to r ve

sevier

462 H. Della, Alternative exchange rate regimes

but not as a m urn of exchange; but it can also arise a money-in-the- utifity-fun&on mq&l when the two currencies enter t additively; or in a cash-in-advance

currencies for specific ating regime in overlap models is the lack of

turn dominance of one of the two dominance is simply as an make a currency valuable may not be time-consistent.

aviour of alternative exchange regimes with cash-in-advance model is employed. Two ns is the standard Coumot-Nash in which to account the effect of their actions on

their opponents’ behavior. It is shown that in the absence of government precommitment and/or operative in tional control on exchange rate management (a) if nominal interest rat strictly positive, a fixed exchange rate regime is not ~nomically feasible because it is dynamically inconsistent; (b) a flexible regime leads to a determinate equilibrium (because of the currency controls imposed in the form of cash-in-advance-constraints); it cannot, however, sustain any international asset trade.

e intuition behind these results is simple. Since domestic goods can only

oreover, a government

tion can be brought about by unanticipated changes in the real assets. The fact that a fixed exchange rate rule s incentive for ‘surprises’, and people endowed

lly understand the nature of the policymaker’s ion rules, implies that promise to kc the exchange rate - at

any level - will ever be credible. reover, since optimality of domestic

H. Delhs, Alternative

strategies to support a nonzero asset trade equilibrium and + fked

t any wide disparities in the denomination of in

e

consists of two countries, the home and the fo is by an infinitely-lived representative individual. is endowed with a single good x and the foreign munt&ry Y- omestic agent’s goal is to maxim& his/her expected l&time utility

where q and c,* are his/her period t consumption of the home country’s output and the foreign country’s output, respectively, and 6 is the discount

utility function u is assumed to be strictly concave and twice

e domestic economy’s resource constraint is

ct + m, S x,, (2)

where m, is exports of the domestic good.

H. Dellas, Alternative exchange rate regimes

graphs of this section).

country’s liabilities and assets denominated in one currency should

he domestic indivi ‘s lifetime budget constraints are3

00

a+& -p,q) + (N,- f=O

2 Pf% t=O,l,..., (4

where qr is the domestic currency price (present value) at date 0 of a dollar t; pI is the current domestic money price at date t of a unit

of a unit of the foreign t of foreign currency at date

paper is to compare

A tiwe ex rate regimes

8’24; = ~Pt?lt+ let+ 1 + YtPh ow

4?t+1- qt) + Bt = 0,

4?t+1et+1- q&t) + Yt =o, (64

where uct and u,*, are the marginal utilities of consumption of the domestic od, respectively, and date t.

and (5) are in the com-

n multiplying (3) throu by it and using the rem

00

isu, x, + ( +4X (4 t+l

t==O

466 H. Dellas, Alternative exchange rate regimes

wealth effects from ho1 ng money. Consequently, (7) can be written as

s a similar m tion problem rent utility function and a different wealth constr

optimal solution satisfies an expression similar to (7’). The home country’s total consumption would increase if the real value of

payments due to her outstanding credit (debt), OB, and OF,, increased (de- creased). Since p: is determined in the rest of the world by the condition & = p,*y, where F is the foreign stock of money, the second term in (7’) cannot be influenced by the actions of the domestic government. However, the first term depends on the domestic price level, p. Under a flexible exchange rate regime mcney supply is exogenous and a change in the money stock will result in a change in the general price level and the exchange rate. If people at date zero had not anticipated a date t price change when they decided on the expected real interest rates will differ from the realized ones. In such a case the real value of domestic currency denominated assets can be influenced by monetary policy. Now suppose that the current domestic government cannot force future governments to follow any prespecified policy. Also assume that a government, in choosing a policy, ignores the effect of her actions on the behavior of the foreign policymaker, that is, she assumes that no reaction will occur (the standard Coumot-Nash approach). It follows that the domestic gove ent will always find it optimal to generate a monetary surprise at date t, for any given rice expectations. The domestic monetary authority’s objec-

ate t is to choose the that m aximizes (1) subject to (7’). The solution to this maximization p em dictates setting ;, = 0 if oB, > 0 and

< 0. Under the assumption of rational expectations foreigners perceive this incentive and refuse to pay this infinite ‘capital

ic currency denominated assets. A similar ehaviour of the foreign government. The only

brium is characterized by dynamic inconsistency

er these circumstances, no e rate corre-

H. Delias, Alreraative excha rate

e Py is the relative price of good y X. nominal interest rates are not restrict tive there is no

need to hold any foreign reserves to maintain a fixed exchange rate. To see this, assume that the expected realization of yt is such that the equilibrium exchange rate will have to depreciate. In order to offset this eKect so that the fixed rate is maintained, the domestic m _.-onc*G~y authority will have to contract the domestic money sunk (say, via lump-sum taxation). If the resulting expected deflation exceeds the real interest rate, the current nominal interest rate will have to be zero. In this situation, flexible and fixed exchange rate regimes lead to identical real allocations.

In this paper, we have followed Lucas and Stokey (1983) and 981) in assuming strictly positive nominal interest B i- 43. This

contractions in the money supply cannot be arbitrarily large (for any red interest rate). Consequently, maintenance of a tied exch holding of sufEcient reserves of the foreign currency.4 earlier, reserves are subject to an unanticipated capital (inflation) tax and this leads to dynamic inconsistency. Under these circumstances, a fixed exchange ra regime is not feasible.

efore concluding this section it is worthwhile to compare the characteris- tics of the zero asset trade, flexible exchange rate equilibrium discussed above

by Lucas (1982). Both equilibria are time-consistent, but they rent properties. Lucas employs a mmplete asset market set-up

that supports a perfectly pooled equilibrium. y the constmtion of the equilibrium, agents residing in difI’erent countries are identical and face identical budget constraints; this amounts to essentially having a representative agent. Consequently international net asset trade is still have national governments, but from an e@o ‘c point of view we cannot distinguish domestic from foreign residents. librium - monetary policy, precommitted or not, can never i

distribution of income across countries b asset menu makes the inflation tax exac

OV hi!

terest rates via monetary su

4 e redred forei reserves

468 Deks, Alternative exchange rate regimes

consistency problem. ne might say that a perfectly pooled equilibrium a market solution to dynamic inconsistency and it

o focus on the dynamic inconsistency issue, we restrict ttention to an tup. In general, our results carry to other asset

as we exclude perfectly pooled equilibria or indexed debt In any such model the zero net asset trade equilibrium is the result sence of dynamic inconsistency problems and is to-inferior if

(relative to either the perfectly pooled com- urn or to the incomplete asset market with policy

lability of policy precommitment technology properties of equilibrium in Lucas, it is important in this

ode1 because it determines the size of asset trade and welfare.

he equilibrium discussed in section 2 is a t-Nash equilibrium in which each government assumes that the other mment will not react to an attempt to redistribute world wealth. It is t to consider whether different formulations of the policy game that incorporate more ‘realistic’

lusions on asset this section we very popular in

o and Gordon (1983)]. pose that both policymakers understand that as long as each one sticks

s/her preannounced contingent policy, the other one honors his/her ses. If, however, a country uses monetary policy to affect its intema-

tional wealth position, the other country retaliates by doing the same. e will postulate the following trigger (retaliation) strategy for the foreign policy-

estic one acts symmetrically). Choose

H. Dehs, A~~er~a~iv~ ex

strategy equilibrium iff they are credible and the lo

mental parameters of the model. To gain valuable insights on the effectiveness of trigger strategies as a deterrent, we have chosen to work with a simplified but sufficiently rich version of the model of section 2.

t us assume [following Lucas (1982)] that agents are given the opportunity e in assets before they are randomly assigned to a country of residence.

Since countries differ with regard to wealth (output endowments), ris individuals will attempt to insure themselves against the likelihood assigned to the ‘poor’ country. To allow for time inconsistency, we will restrict t menu of possible asset trades by requiring that claims on monetary t sfers cannot be issued? Since we are mainly concerned with savings decisions, we will assume that the stochastically arriving commodities are perfect substitutes in consumption.

For comparison purposes, let us consider first the case with exogenous monetary policies. For simplicity, we will assume that the money stock is constant in both countries.

he representative domestic agent chooses current consumption and asset holdings to m aximize the following value function:

=max(u(c,+cp)+iS

subject to constraints (4), (5), and

1

P, 1 -1- PI-&_1 + (N,_, - P* *

’ Such conditions have been possible to on’s (1983) because those models ha -one asset-one gove

ith as se of

other macroecon

470 H. Dellas, Alternative exchange rate rq$mes

a two-element vector of asset

output (both asset supplies are n

($,$> and c,+c,*=(X,+ X)/2. Now let us assume that monetary policy, rather than being

is a choice variable. Since the cash in advance constraints are bin reduces to

7 Lx,-, p+: +t

e,pt*_ A- 1

4 4 = c, + c,*,

t

or equivalently, noting that q = = P,X,, and Pt = e, l Pr*, to

l y,_,=c,+q?. (12)

in section 2, the optimal Coumot monetary policy is to set Pt = ca. will now postulate the following trigger strategy for the foreign country.

Choose

i= 1,2,...,

t of the domestic

counterpart are satisfied,

The first two terms in (14) give the current gain from a s rise move. The third term is the discounted value of future losses (gains) both countries repudiate their own currency denominated liabilities.

amination of (1 reveals that a country wiII be more likely to abstain from using inflation to cheat when:

0 a

(W

0 C

03

e value of assets denominated in the domestic currency is not sign.& cantly greater than the value of the foreign currency denominated assets.

our example, this requires that the X and Y processes are of compara- e value, so that u(( X + Y)/2) 2 u(X). In the limiting case of a single

currency of denomination, the trigger strategy in condition (13) is not ve in restraining the behavior of monetary authorities. trade is important from a welfare point of view either because the

utility function is sufficiently concave (individuals have a strong preference h consumption stream) or the volatility of future

tors have a positive efkct on u(( X + Y)/2) - u(X)

e discount factor is low, so future utility losses from having a more stream are substantial. with exceptionally high levels of outstanding assets

(liabilitiesk this limits the size of potential art-term ation. In the context of our model we

gains of a suq+fise t need to retrict the probabil-

istribution of output (dividends) to rule ou tions.

412 H. De/as, Alternative exchange rate regimes

It has been wry common in the existing literature of the optimal choice of the exchange rate regime to proceed to regimes withou the conditions under meaningful. In librium cash-in-advan exercise so long as no dynamic inconsi because of government precommitment). I was undertaken by explicitly incorporating the game theoretic aspects of international monetary arrangements when discretionary policy is allowed and governments attempt to maximize domestic welfare. Ihe main conclusion reached was that, if nominal interet rates are strictly positive, a fixed exchange rate regime is dynamically inconsistent when policy-makers ignore the effect of their actions on the behavior of their opponents (the Coumot-Nash equi-

the context of our model, this implies that the fixed regime is infeasible. On other hand, a flexible regime is always eco- sible, but it is acterized by a zero level of asset trade. Both

results are due to the fact that national governments without prekommitment power attempt to extract resources from the rest of the world by revaluing (devaluing) their outstanding stock of assets (liabilities) via une change rate changes. ch behaviour precludes the holding of forei

s a fixed exchange rate unsupportable. owever, if the possibility of retaliation is taken into accc YIP, a

asset trade bzome feasible (the trigger strategy equi- e success of a trigger strategy in deterring policymakers from

unexpectedly inflatkg depends among other things on the value attached to consumption smoothing, the rai< of time preference, the currency composition

al assets, and t e entire asset profile of the economies.

ere

Barro, R. and D.E. Gordon, 1983, Rules, discretion and reputation in a model of monetary policy, Journal of Monetary Economics 12, lW421.

fiscal and monetary policy in an economy without