Week-10

Econ Theory (2013) 53:357–382 DOI 10.1007/s00199-012-0694-2

R E S E A R C H A RT I C L E

On the relevance of floating exchange rate policies

Alexandre B. Cunha

Received: 1 July 2009 / Accepted: 17 February 2012 / Published online: 4 March 2012 © Springer-Verlag 2012

Abstract I study the relevance of the composition of the public debt between domes- tic and foreign liabilities in a standard stochastic small open-economy framework. The government issues nominal bonds of several maturities with noncontingent face value at redemption. Intervening in the exchange market to implement an adequate state- contingent path for the nominal exchange rate is an effective way for the government to prevent the economy from reaching any competitive equilibrium it wishes to rule out. Most sterilized interventions are not neutral; however, few of them are. As a con- sequence, the composition in question is undetermined. Hence, a floating regime may decentralize every competitive outcome, even one induced by a pegging policy. Con- versely, outcomes brought forth by a floating regime can also be induced by a policy that prescribes active government intervention in the foreign currency market. More- over, an open-market operation can be replaced by an equivalent combination of an exchange intervention plus a restructuring of the domestic debt maturity. Introducing in the model strategic behavior by the government combined with asymmetric infor- mation or lack of commitment can remove that indeterminacy. Hence, these factors seem to be the major determinants of a possible relation between floating exchange rate policies and economic outcomes.

The comments and suggestions of two anonymous referees greatly improved this paper. I also thank Eurilton Araújo, Hector Calvo Pardo, Luciane Carpena, Timothy Kehoe, Emanuel Ornelas, Harald Uhlig and participants of several conferences and seminars for their comments. Financial support from the Brazilian Council of Science and Technology (CNPq) is gratefully acknowledged. Of course, the usual disclaimer applies.

A. B. Cunha (B) Instituto de Economia, Universidade Federal do Rio de Janeiro, Av. Pasteur 250, Rio de Janeiro, RJ 22290-240, Brazil e-mail: research@alexbcunha.com

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Keywords Floating exchange rate regime · Equilibrium indeterminacy · Equilibrium implementation · Maturity structure of public debt

JEL Classification E42 · E58 · F31 · F41

1 Introduction

I show in this paper that, under not far-fetched assumptions on the availability of debt instruments, a floating exchange rate policy can support any competitive equilibrium allocations and prices of a dynamic stochastic economy, even those induced by a fixed exchange rate regime. Conversely, an exchange rate policy that requires the govern- ment to buy or sell foreign exchange in every period can decentralize any allocations and prices that are brought forth by a floating regime. These results are a consequence of the indeterminacy of the currency denomination and maturity structure of the public debt in a competitive equilibrium.

I obtain these conclusions in a model in which the nominal exchange rate is well determined. Moreover, it is an effective policy tool, in the sense that if the government selects a state-contingent trajectory for that variable and intervenes in the exchange market by trading foreign assets at the specified exchange rates, then those interven- tions will definitively prevent the economy from coordinating on any competitive outcome the government wishes to rule out.

Besides being the forefather of the results of this paper, the Modigliani–Miller Theorem also helps to establish their relevance. That seminal proposition is important not because its hypotheses or conclusions provide an accurate description of the real world. Its relevance comes from the fact it establishes a set of sufficient assumptions for a firm’s financing choices not to matter. Therefore, anyone who wants to under- stand why the composition of a firm’s capital is relevant has to consider models in which some of its assumptions do not hold.

The importance of the results of this paper is justified on the same grounds. They provide sufficient conditions for the implementation of a floating exchange rate regime to be irrelevant. Comprehending why such a policy can indeed have any impact on economic outcomes requires the adoption of models with features not present in mine here, and most important, in many other popular macroeconomic models as well.

The findings of this paper are related to several well-known indeterminacy results in the macroeconomic literature. For instance, Barro (1974) showed that if the gov- ernment has access to lump-sum taxes, then the time path and initial value of the public debt are irrelevant. Wallace (1981), Chamley and Polemarchakis (1984), and Bassetto and Kocherlakota (2004) obtained similar results in many different contexts. As Sargent (1987) pointed out, results of this type can be interpreted as an equiva- lent of the Modigliani–Miller Theorem for government funding. Jeanne (2009) also pointed out that the study of the structure of countries’ external debt and the analysis of the composition of firms’ liabilities are closely related problems.

Sargent and Smith (1988) derived some competitive equilibrium indeterminacy results in an open-economy setup. They considered a two-country stochastic over- lapping generation model with a single storable consumption good. Each country

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On the relevance of floating exchange rate policies 359

issued its own currency. Governments had access to lump-sum taxes. People and governments traded state-contingent claims on the consumption good. Markets were complete. They showed that if both currencies were dominated in rate of return by storage, then a government could change its holdings of foreign currency without affecting prices and quantities. The same result was obtained when just one currency was dominated in rate of return. However, in this last case, the government could be required to use its lump-sum instruments to rebate earning differentials associated with distinct portfolios.

Backus and Kehoe (1989) (BK from now on) adopted a many-country stochastic model with a single infinitely lived household in each nation. Each country issued its own currency. Cash-in-advance constraints induced people to hold their country’s money. Lump-sum taxes were not available. Each government issued a set of bonds with state-contingent returns denominated in its own currency as well as other nations’ currencies. If markets were complete, then the composition of a government portfolio was not determined in a competitive equilibrium. Concerning incomplete markets, the same result could hold, provided that the securities satisfied some spanning condition.

Duffie and Huang (1985) established that a set of long-lived securities could rep- licate the returns of state-contingent assets. Later, Angeletos (2002) and Buera and Nicolini (2004) also showed that noncontingent public debt of several maturities can complete the markets. For this to happen, two conditions have to be satisfied at each date: (i) the number of distinct maturities must be equal to or greater than the number of possible states of nature at the next date and (ii) the term structure of the price of the government bonds must be linearly independent across the future states of nature.

I apply the findings of these authors to obtain results similar to those of Sargent and Smith (1988) and BK in a environment in which the government issues bonds, of all maturities, that pay one unit of the domestic currency.1 The model adopted in this paper is a small open-economy variant of the models of Lucas and Stokey (1983) and BK. It has a single consumption good, which can be traded abroad. People face a cash-in-advance constraint on a fraction of their purchases of that good. Labor is the only input. There are exogenous distorting taxes on labor income. Government consumption is a random variable. No lump-sum tax or subsidy is available. There is free financial capital mobility so that people and the government can purchase and sell abroad, at an exogenous price, a security that pays one unit of a foreign currency.

I show that a competitive equilibrium pins down only the total government debt and not its composition between domestic and foreign bonds whenever the term structure of the discount rates is linearly independent across the states of nature. As a conse- quence, contrary to the conventional wisdom on exchange rate regimes, competitive equilibrium prices and allocations can be consistent with any path for the govern- ment’s foreign assets. Hence, a competitive equilibrium does not uniquely pin down the government’s interventions in the foreign exchange market—despite the fact that the government can use these interventions to rule out many outcomes.

1 The assumption about the available public bonds plays a crucial role in this paper. I discuss this issue fur- ther in Sect. 6.1. For now, it is enough to say that it was not a straightforward task to conceive of a complete set of financial instruments that had clear real-world counterparts and allowed deriving this paper’s results.

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360 A. B. Cunha

Bloise (2006) and Dubey and Geanakoplos (2006) pointed out that the price level is undetermined in many monetary models. For the specific case of open economies, Kareken and Wallace (1981) showed, in a two-country model, that if the two currencies are perfect substitutes, then the exchange rate path is undetermined. The indeterminacy results of this paper are of a very different nature.

In the model economy of this paper, most sterilized interventions are not neu- tral. However, some of them are. As a consequence, any path of government foreign assets and liabilities can decentralize every competitive equilibrium outcome. Hence, a competitive exchange rate sequence is consistent with any trajectory for those policy instruments.

This does not imply that government intervention in the foreign exchange market is ineffective or that the exchange rate path is irrelevant. In fact, if the government wishes to prevent the economy from coordinating on some specific competitive outcome, then implementing an adequate exchange rate path suffices to achieve that goal. However, there are uncountably many combinations of open-market and foreign currency oper- ations that implement any exchange rate path.2 Therefore, the concept of competitive equilibrium is not sufficient to bring into existence a well-defined map from foreign assets to exchange rates or allocations.

Since a floating exchange rate regime can lead to any competitive outcome, it is not relevant whether the exchange rate floats or not in a purely competitive environment. This conclusion is also a consequence of the fact that in such a framework, the govern- ment does not behave in a strategic way. It simply picks a policy and lets markets clear. The irrelevance in question is unlikely to arise when that agent behaves strategically.

The findings of this paper have theoretical, empirical, and policy implications. On the theory side, they suggest that a model in which the government does not behave in a strategic manner can miss some crucial features of the relation between exchange rate policies and other economic variables.

Concerning the empirical implications, BK argued that since the currency denom- ination of the public debt is undetermined in a competitive equilibrium, interpreting the results of regressions of exchange rate or interest rate differentials against the former variable is not a straightforward exercise. It is possible to take their reasoning a little further and conclude that unless there are data on variables that shed light on the strategic interactions between government and private agents, an empirical anal- ysis of exchange rate policies can miss some crucial feature of the possible relation between these policies and other macroeconomic variables. In other words, empirical studies of exchange rate policies should manage to control for the strategy space of the underlying game that generated the sample being studied.

These theoretical and empirical consequences have some repercussions in the policy arena. More specifically, accounting for the strategic interactions between government and other players is necessary when assessing and designing exchange rate policies.

2 I also show that an open-market operation is equivalent to a combination of two alternative operations: (i) another open-market operation that restructures the maturity of the domestic debt without affecting its level (that is, its discounted present value) and (ii) a foreign exchange intervention that exactly matches the change in the level of the domestic debt prescribed by the original open-market operation.

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On the relevance of floating exchange rate policies 361

This paper is organized as follows. Section 2 describes the model adopted. The definition of competitive equilibrium and the relevance of the exchange rate are dis- cussed in Sect. 3. Section 4 provides a general result on the indeterminacy of govern- ment foreign assets in a competitive equilibrium. Section 5 applies that result to obtain another one specific to exchange rate regimes. Section 6 provides a detailed assessment of the findings. Section 7 presents the concluding remarks. The “Appendix” explains how to decompose an open-market operation into an equivalent combination of an exchange intervention with a change in the maturity structure of the domestic public debt.

2 The economy

The model economy of this paper is very similar to those of Lucas and Stokey (1983) and BK. There is a small country populated by a single infinitely lived household and a government. The household is composed of a shopper and a worker. The latter is endowed with one unit of time.

This country produces a single good. The household and the government consume that good. The respective amounts they consume are denoted by c and g. The country also exports or imports this good; x denotes the amount exported. A negative value for x means that the country is importing the good. A single competitive firm produces the consumption good. Technology is described by 0 ≤ y ≤ l, where y is the output and l is the amount of time allocated to production.

Markets operate in a particular way. At a first stage of each date t , a spot market for the consumption good and labor services operates. At a second stage, after that market closes, a securities and currency market operate.3

A domestic currency M circulates in this economy. Two types of securities are traded: a claim Bk , which matures at date k, to one unit of M and a claim A, with the maturity of one period, to one unit of some foreign currency. The government and household can purchase and/or sell the claims A at a price of q∗t units of the foreign currency. Foreigners do not sell or buy claims to the domestic currency.4

The worker cannot sell her services outside the country. The shopper faces a cash- in-advance constraint. A fraction of his purchases of the consumption good must be paid for with the domestic currency. Except for these cash purchases, all other trans- actions are settled during the securities and currency trading session. The date t price, in terms of the foreign currency, of the consumption good is constant and equal to 1.

Denote the government consumption at date t by gt . The sequence {gt }∞t =0 is random and each gt has a finite support G = {γ1,γ2, ...,γn } ⊂ [0, 1). I denote the t -fold Carte- sian product of G by Gt . The realization of gt is known at the beginning of date t . This formulation implicitly assumes that at t = 0 all agents already know g0. The variable gt denotes the history of realizations (g1, g2, ..., gt). By convention, g

0 = g0 and

3 See Nicolini (1998) and Svensson (1985) for further details on this timing convention. The results pre- sented in this paper do not depend on that particular assumption. 4 The last assumption has the benefit of simplifying the notation. As discussed in Sect. 6, by no means is it necessary for the results presented in this paper.

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362 A. B. Cunha

G 0 = {g0}. For a given gt , μ(gt) denotes the probability that the particular history gt

will happen. Let c1(g

t) and c2(g t) denote the shopper’s respective cash and credit purchases

of the consumption good at date t . These variables are conditioned on the history gt

(other variables indexed by gt will have analogous meaning). Feasibility requires

c1(g t ) + c2(gt) + gt + x(gt) = y(gt). (1)

The government finances the sequence {gt }∞t =0 by issuing and withdrawing domes- tic currency; by issuing and redeeming claims Bk ; by purchasing and selling A; and by taxing labor income at a proportional rate τ. The sequence {τt, q∗t }∞t =0 is exogenous.

The government budget constraint, expressed in units of the domestic currency, is

S(gt)gt + M(gt −1) + S(gt)q∗t AG(gt) + ∞∑

k=t qk(g

t )Bk(g

t −1 )

= τtw(gt)l(gt) + M(gt) + S(gt)AG(gt −1) + ∞∑

k=t +1 qk(g

t )Bk(g

t ), (2)

where M(gt) is the amount of money that people hold at the end of date t ; Bk(g t) is

the amount of public debt that matures at date k > t that people hold at the end of date t ; AG(g

t) stands for the foreign assets the government holds at the end of date t ; w(gt) is the date t nominal wage; S(gt) is the date t nominal exchange rate; and qk(g

t) is the monetary price of Bk(g t). Of course, qt(g

t) = 1. A negative value for AG(g

t) means the government is borrowing abroad, while a negative value for Bk(g t)

means the government is lending to the household. At t = 0, the government holds an initial amount ĀG of foreign assets.

Let A H(g t) stand for the foreign assets the household carries at the end of date t .

To avoid Ponzi schemes, I impose the borrowing constraints

∣∣ A H(gt) ∣∣ ,

∣∣ AG(gt) ∣∣ ,

∣∣∣∣

∑∞ k=t +1 qk(g

t, gt +1)Bk(gt) S(gt, gt +1)

∣∣∣∣ ≤ K < ∞ (3)

on asset holdings. As usual, K is some real number large enough so that these con- straints never bind in equilibrium.

The function u : R2+ × [0, 1] → R ∪ {−∞}, u = u(c1, c2, 1 − l), is the house- hold period utility function. This function displays local nonsatiability. Intertemporal preferences are described by

∞∑

t =0

∑

gt ∈Gt β

t μ(gt)u

( c1(g

t ), c2(g

t ), 1 − l(gt)) , (4)

where β ∈ (0, 1). The household’s date t budget constraint is

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On the relevance of floating exchange rate policies 363

S(gt)[c1(gt) + c2(gt)] + M(gt)

+S(gt)q∗t A H(gt) + ∞∑

k=t +1 qk(g

t )Bk(g

t ) ≤ (1 − τt)w(gt)l(gt)

+M(gt −1) + S(gt)A H(gt −1) + ∞∑

k=t qk(g

t )Bk(g

t −1 ), (5)

while the cash-in-advance constraint is

S(gt)c1(g t ) ≤ M(gt −1). (6)

I denote a list of prices (S(gt),w(gt), {qk(gt)}∞k=t +1) by ψ(gt) and a bundle (c1(g

t), c2(g t), l(gt)) by χ(gt), while ϕ(gt) stands for the household’s asset holdings

(M(gt), A H(g t), {Bk(gt)}∞k=t +1). Additionally, I denote the contingent sequences

{[ψ(gt)]gt ∈Gt }∞t =0, {[χ(gt)]gt ∈Gt }∞t =0 and {[ϕ(gt)]gt ∈Gt }∞t =0 by, respectively, ψ, χ and ϕ.

At date zero, given initial asset holdings M̄ , Ā H and {B̄k }∞k=0, the household chooses χ and ϕ to maximize (4) subject to the constraints (3), (5), (6), and l(gt) ≤ 1. Except for Bk(g

t) and A H(g t), all these variables must be nonnegative. Additionally,

the sequences {[c1(gt)]gt ∈Gt }∞t =0, {[c2(gt)]gt ∈Gt }∞t =0 and {[M(gt −1)/S(gt)]gt ∈Gt }∞t =1 have to be bounded.

Concerning the firm, recall that the production function displays constant returns to scale. Hence, in equilibrium, it will have zero profits. Thus, without loss of generality, I assume that for every history gt , given an output level y(gt), the firm chooses l(gt) to minimize its total cost w(gt)l(gt) subject to y(gt) ≤ l(gt). That trivially implies that y(gt) = l(gt). From now on, I will use this equality to substitute l for y without further comment.

3 Equilibrium and exchange rate relevance

In this section, I first define a competitive equilibrium. Then, I establish that the nom- inal exchange rate is not undetermined and is a strong tool for the policymakers of my artificial economy.

An array [ψ,χ,ϕ, {[ AG(gt)]gt ∈Gt }∞t =0, {[x(gt)]gt ∈Gt }∞t =0] is a competitive equi- librium if it satisfies: (i) given ψ, (χ,ϕ) solves the household’s problem; (ii) w(gt) = S(gt); and (iii) (1) and (2) hold. An array [ψ,χ, {[x(gt)]gt ∈Gt }∞t =0] is a competitive outcome if there exists another array [ϕ, {[ AG(gt)]gt ∈Gt }∞t =0] such that the combina- tion of the two constitutes a competitive equilibrium.

It is not necessary to spell out a balance-of-payment condition when defining com- petitive equilibrium. The zero-profit condition is w(gt)l(gt) = S(gt)[c1(gt)+c2(gt)+ gt + x(gt)]. Add it to (2) and (5), taken as equality, to obtain

x(gt) + AG(gt −1) + A H(gt −1) − q∗t [ AG(gt) + A H(gt)] = 0, (7)

which is the balance-of-payments identity of this model economy.

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364 A. B. Cunha

I now turn to the task of establishing that the exchange rate indeterminacy found in Kareken and Wallace (1981) does not arise in the model economy of this paper. For now, suppose that the initial nominal exchange rate S(g0) is given. In this cash-credit economy, inflation is a distorting tax. Hence, as BK pointed out, the inflation rate cannot be neutral. Given that the nominal exchange rate is equal to the price level, the same conclusion holds for the devaluation rate.

A possible irrelevance of S(g0) remains to be discussed. This variable defines the real value of the government’s initial domestic liabilities M̄ +∑∞k=0 qk(g0)B̄k . Hence, unless that sum equals zero, S(g0) cannot be neutral, since a change in that variable affects people’s and the government’s budget constraints. Therefore, only under very particular conditions will the date zero nominal exchange rate be irrelevant, while devaluation rates are certainly not neutral.5

It is now possible to show that the policymakers of this economy can use the exchange rate to rule out any competitive outcome. Let [ψ,χ, {[x(gt)]gt ∈Gt }∞t =0] be such an outcome and {[S(gt)]gt ∈Gt }∞t =0 be the underlying exchange rate path. Suppose that the government follows a policy of trading foreign currency at the rate S(gt) for every gt . That policy will prevent the economy from coordinating on any outcome that does not have {[S(gt)]gt ∈Gt }∞t =0 as one of its components. Moreover, since exchange rate devaluations are distorting taxes, the number of competitive outcomes being ruled out is large. And if {[S(gt)]gt ∈Gt }∞t =0 is not a member of any other competitive out- come, then the policy in question suffices to ensure that the economy will coordinate on [ψ,χ, {[x(gt)]gt ∈Gt }∞t =0].6 For this reason, I say that the exchange rate is an effective policy instrument.7

4 Foreign assets indeterminacy

Let [ψ,χ,ϕ, {[ AG(gt)]gt ∈Gt }∞t =0, {[x(gt)]gt ∈Gt }∞t =0] be a competitive equilibrium. The goal is to investigate under which conditions the government can carry out open- market and foreign exchange operations without breaking down the corresponding outcome. More specifically, let {[ A′G(gt)]gt ∈Gt }∞t =0 be a bounded sequence of foreign assets. I wish to identify sufficient conditions for the existence of an alternative port- folio ϕ′ with the property that ψ, χ, ϕ′, {[ A′G(gt)]gt ∈Gt }∞t =0, {[x(gt)]gt ∈Gt }∞t =0 also constitute a competitive equilibrium.

No matter how I construct ϕ′, [ψ,χ,ϕ′, {[ A′G(gt)]gt ∈Gt }∞t =0, {[x(gt)]gt ∈Gt }∞t =0] will satisfy (1) and condition (ii) of the competitive equilibrium definition. Moreover,

5 A different question is whether the pair (ψ,χ) is undetermined or not. For the type of economy consid- ered in this paper, it is not possible to ensure that (ψ,χ) is determined in a competitive equilibrium. For a detailed discussion of this issue, see Woodford (1994). 6 The reader may wonder whether it is possible to ensure that the implementation of an exchange rate path is a sufficient policy action for the government to attain a specific outcome. This is definitively possible in a deterministic setup and, in general, not possible in a stochastic context. 7 The notion of exchange rate effectiveness clearly relies on the competitive equilibrium concept. I make no claim about the effectiveness of the exchange rate in other games that can be played in the environment described in Sect. 2, much less in other economic models.

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On the relevance of floating exchange rate policies 365

it will yield the same lifetime expected utility to the household. Thus, it remains to show that ϕ′ satisfies the budget constraints of both the household and government.

Given A′G(g t) and ϕ(gt), define M ′(gt) and A′H(g

t) according to

M ′(gt) = M(gt) (8) A′H(g

t ) = AG(gt) + A H(gt) − A′G(gt). (9)

Observe that (9) ensures that (7) holds. The definition of the alternative debt holdings {B′k(gt)}∞k=t +1 is a little more

demanding. Consider the equality

S(gt, gt +1)A′H(g t ) +

∞∑

k=t +1 qk(g

t , gt +1)B′k(g

t )

= S(gt, gt +1)A H(gt) + ∞∑

k=t +1 qk(g

t , gt +1)Bk(gt). (10)

This constraint ensures that, for every history (gt, gt +1), the household’s wealth at the beginning of each date t + 1 is the same regardless of whether it selected the portfolios ϕ(gt) or ϕ′(gt) at the end of the previous period. The reader will be able to verify that if there exists an array {B′k(gt)}∞k=t +1 satisfying (10), then ϕ′ will respect both the household and government budget constraints.

I now discuss some sufficient conditions for the existence of {B′k(gt)}∞k=t +1. Recall that G = {γ1,γ2, ...,γn }. For each gt , define the matrix Q(gt) according to

Q(gt) =

⎡

⎢⎢⎢ ⎣

1 qt +2(gt,γ1) qt +3(gt,γ1) . . . 1 qt +2(gt,γ2) qt +3(gt,γ2) . . . ...

... ...

...

1 qt +2(gt,γn) qt +3(gt,γn) . . .

⎤

⎥⎥⎥ ⎦ .

Denote its rank by ρ(gt). To obtain the results I am after, ρ(gt) must equal n. That is, the term structure of the discount rates must be linearly independent across gt +1.

As Angeletos (2002) and Buera and Nicolini (2004) pointed out, the requirement that ρ(gt) = n has an obvious analogy with the definition of complete markets. These authors also showed that this requirement is not a very restrictive one. I should emphasize that the assumption that the government issues debt of all maturities can be replaced by the weaker requirement that it issues bonds of n distinct maturities.

If ρ(gt) = n, then there exists a set T = {t1, t2, . . . , tn } (which may depend on gt ) of n dates such that the matrix

QT(g t ) =

⎡

⎢⎢⎢ ⎣

qt1(g t,γ1) qt2(g

t,γ1) . . . qtn(g t,γ1)

qt1(g t,γ2) qt2(g

t,γ2) . . . qtn(g t,γn)

... ...

... ...

qt1(g t,γn) qt2(g

t,γn) . . . qtn(g t,γn)

⎤

⎥⎥⎥ ⎦

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366 A. B. Cunha

has an inverse. Define the auxiliary variables B̃t1(g t), B̃t2(g

t),…, B̃tn(g t) according

to

⎡

⎢ ⎣

B̃t1(g t)

...

B̃tn(g t)

⎤

⎥ ⎦ =

[ QT(g

t ) ]−1

⎡

⎢ ⎣

b1(g t)

...

bn(g t)

⎤

⎥ ⎦ , (11)

where

bi(g t ) = S(gt,γi)[ A H(gt) − A′H(gt)] +

∑

k∈T qk(g

t ,γi)Bk(g

t ).

Then, define the debt holdings {B′k(gt)}∞k=t +1 as

B′k(g t ) =

{ Bk(g

t) if k /∈ T B̃k(g

t) if k ∈ T . (12)

This definition and (11) imply that

∑

k∈T qk(g

t , gt +1)B′k(g

t ) = S(gt, gt +1)[ A H(gt) − A′H(gt)] +

∑

k∈T qk(g

t , gt +1)Bk(gt).

Finally, use the fact that B′k(g t) = Bk(gt) for every k /∈ T to conclude that

{B′k(gt)}∞k=t +1 satisfies (10).8 Proposition 1 Let [ψ,χ,ϕ, {[ AG(gt)]gt ∈Gt }∞t =0, {[x(gt)]gt ∈Gt }∞t =0] be a competi- tive equilibrium and {[ A′G(gt)]gt ∈Gt }∞t =0 be any bounded array of foreign assets. If Q(gt) is of full rank for every gt , then there exists a portfolio ϕ′ such that [ψ,χ,ϕ′, {[ A′G(gt)]gt ∈Gt }∞t =0, {[x(gt)]gt ∈Gt }∞t =0] is a competitive equilibrium. Proof Define ϕ′ as specified in (8), (9) and (12). I need to show that ψ, χ, ϕ′, {[ A′G(gt)]gt ∈Gt }∞t =0 and {[x(gt)]gt ∈Gt }∞t =0] constitute a competitive equilibrium. The first step in this process consists of showing that ϕ′ satisfies the borrowing bounds in (3). The sequence {[ A′G(gt)]gt ∈Gt }∞t =0 respects that constraint by assumption. The boundedness of {[ A′H(gt)]gt ∈Gt }∞t =0 follows from the inequalities | A′H(gt)| ≤ | A H(gt)| + | AG(gt)| + | A′G(gt)| ≤ 3K . Recall that ϕ′ satisfies (10). From that equa- tion I obtain ∣∣∣∣

∑∞ k=t +1qk(g

t, gt +1)B′k(g t)

S(gt, gt +1)

∣∣∣∣ ≤ | A H(gt)|

+ ∣∣∣∣

∑∞ k=t +1qk(g

t, gt +1)Bk(gt) S(gt, gt +1)

∣∣∣∣ + | A′H(gt)| ≤ 3K .

8 Regardless of the uniqueness of the set T, there are uncountably many ways of constructing {B′k(gt )}∞k=t +1. The procedure adopted here has the intuitive advantage of setting B′k(gt ) = Bk(gt ) when- ever A′G(g

t ) = AG(gt ).

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On the relevance of floating exchange rate policies 367

Let me now show that (χ,ϕ′) satisfies the household’s budget constraint (5). The first-order conditions for A H(g

t) and Bk(g t) are

λ(gt)qk(g t ) =

∑

gt +1∈G λ(gt, gt +1)qk(gt, gt +1) (13)

and

λ(gt)S(gt)q∗t = ∑

gt +1∈G λ(gt, gt +1)S(gt, gt +1), (14)

where λ(gt) is a Lagrange multiplier for (5). Multiply both sides of (10) by λ(gt, gt +1), add over gt +1 and combine the resulting equality with (13) and (14) to obtain

S(gt)q∗t A ′ H(g

t ) + ∑∞k=t +1qk(gt)B′k(gt)

= S(gt)q∗t A H(gt) + ∑∞

k=t +1qk(g t )Bk(g

t ). (15)

Now lag (10) by one period. Thus,

S(gt)A′H(g t −1 ) +

∞∑

k=t qk(g

t )B′k(g

t −1 ) = S(gt)A H(gt −1) +

∞∑

k=t qk(g

t )Bk(g

t −1 ).

Combine these last two equalities with the fact that (χ,ϕ) satisfies (5) with equality to conclude that so does (χ,ϕ′).

I am now able to conclude the proof. Concerning item (i) of the definition of com- petitive equilibrium, the pair (χ,ϕ′) yields the same expected lifetime utility as (χ,ϕ). So, (χ,ϕ′) is an optimal choice for the household when the prevailing price system is ψ. Clearly, ψ satisfies (ii). With respect to item (iii), χ and {[x(gt)]gt ∈Gt }∞t =0 obvi- ously satisfy (1). Moreover, I constructed ϕ′ so that (9) holds. Thus, {[x(gt)]gt ∈Gt }∞t =0, {[ A′G(gt)]gt ∈Gt }∞t =0 and {[ A′H(gt)]gt ∈Gt }∞t =0 satisfy (7). Combine that condition with (1) and (5) with equality to conclude that (2) holds. �

I established that if the government uses {[ AG(gt)]gt ∈Gt }∞t =0 to induce the out- come composed by {[S(gt),w(gt), {qk(gt)}∞k=t +1]gt ∈Gt }∞t =0, {[x(gt)]gt ∈Gt }∞t =0 and {[c1(gt), c2(gt), l(gt)]gt ∈Gt }∞t =0, then it can use any other foreign asset policy {[ A′G(gt)]gt ∈Gt }∞t =0 to decentralize exactly the same prices and allocations. I did not claim that the nominal exchange rate path {[S(gt)]gt ∈Gt }∞t =0 is irrelevant. In fact, I showed in Sect. 3 that the exchange rate does not display such an indeterminacy and is an effective policy tool.

Despite the exchange rate relevance, Proposition 1 establishes that the govern- ment can use many distinct foreign exchange and open-market strategies to pursue its goals. For this reason, the concept of competitive equilibrium is not enough to construct a function (or some meaningful correspondence) from the space of foreign assets {[ AG(gt)]gt ∈Gt }∞t =0 to the set of exchange rate paths {[S(gt)]gt ∈Gt }∞t =0.

Proposition 1 clearly has a Modigliani–Miller like flavor. In a perfectly competitive environment with full information and complete markets, whether a firm finances its

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368 A. B. Cunha

investment projects with equity or debt is irrelevant. On the other hand, whenever Q(gt) is of full rank, the public debt perfectly mimics the returns of a one-period state-contingent asset. Thus, in such a context, whether the government finances its transitory deficits by issuing domestic or foreign bonds is irrelevant.

Proposition 1 relies on the fact, that although most sterilized interventions are not neutral, some few specific ones are. Indeed, such an intervention is any combination of an open-market operation with a purchase or sale of foreign assets that satisfies (15). The discussion following Eq. (10) makes clear that not every sterilized intervention will satisfy this last constraint, which is a necessary condition for such an intervention to be neutral.

As I have previously mentioned, Proposition 1 is closely related to the results of Sargent and Smith (1988) and BK. Therefore, I must clearly compare my contribution to the results of those authors.

Let me first consider the findings of Sargent and Smith. Equalities (10) and (15) are constraints that a sterilized intervention has to fulfill so that it does not impact equilibrium prices and real variables. The traders in such an operation are the govern- ment and its nationals. As I detail next, this is an important departure from Sargent and Smith’s conclusions.

They considered a two-country overlapping generation model with two moneys. They only studied equilibria in which at least one currency was dominated in rate of return. A subtle consequence of their assumptions regarding traders, assets and markets is that a sterilized intervention as described in the previous paragraph could not take place. If both currencies were dominated in rate of return, a sterilized inter- vention that did not affect equilibrium prices and allocations would require the two governments to cooperate. If just one currency was dominated in rate of return, such an intervention would require some fiscal adjustment to compensate for earnings or losses resulting from changes in agents’ portfolios.

The key difference between Proposition 1 and BK’s conclusions lies in the assump- tions about the available debt instruments. They considered a many-country model in which each government could issue bonds denominated in several currencies, while I only allow the government to issue bonds denominated in its own currency. This difference is of great relevance in Sect. 5, where I establish that a floating exchange rate regime is consistent with any competitive outcome.

Let [ψ,χ,ϕ, {[ AG(gt)]gt ∈Gt }∞t =0, {[x(gt)]gt ∈Gt }∞t =0] be a competitive equilib- rium. The array {[ AG(gt)]gt ∈Gt }∞t =0 is the unique inducer of the outcome [ψ,χ, {[x(gt)]gt ∈Gt }∞t =0] if there is a history gt such that ρ(gt) < n.

When an array {[ AG(gt)]gt ∈Gt }∞t =0 is the unique inducer of some competitive out- come, the indeterminacy result of Proposition 1 does not hold. In such a context, there is an obvious sense in which the implementation of a sequence of foreign assets has clear-cut implications on prices and real variables. However, the concept of unique implementation is not easily falsifiable.

To show that an array {[ AG(gt)]gt ∈Gt }∞t =0 is the unique inducer, it is necessary to find a history gt such that the rank of Q(gt) is smaller than n. Since any sample from an actual economy will contain just part of a single row of each member of that family of matrices, one could at the very best test whether the government’s foreign assets constitute the unique inducer of some outcome. Of course, estimating the rank of an

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On the relevance of floating exchange rate policies 369

infinite dimension matrix based on an observation of some components of just one of its rows is not a trivial problem.

There is another obstacle that makes the task of inferring whether a sequence of foreign assets uniquely implements an outcome a difficult one. Angeletos (2002) and Buera and Nicolini (2004) pointed out that small changes in the tax rates may have small effects on the discount factors {[{qk(gt)}∞k=t +1]gt ∈Gt }∞t =0. Hence, for each com- petitive equilibrium in which ρ(gt) < n for some gt , there may exist an arbitrarily close equilibrium in which ρ(gt) = n for every gt . Hence, to distinguish between the two equilibria is not a straightforward task.

5 Regime indeterminacy

Usually, the exchange rate is said to float if the government does not intervene in the foreign exchange market. That is, the government carries a constant amount of foreign assets. The next definition follows this tradition.

Definition 2 Given a history g∞, the exchange rate floats at t if AG(gt −1) = AG(gt) and it permanently floats if AG(g

t) = ĀG for every t . The exchange rate uniformly floats if it permanently floats for every g∞ and it never floats if AG(gt −1) �= AG(gt) for every t and every g∞.

A uniform float is a stronger requirement than a permanent one, which in turn is stronger than a transitory float. This poses an additional challenge to the study of floating regimes. If the adoption of this type of policy is to have some real effects, they are unlikely to be the same for transitory, permanent and uniform floats. However, for any sample, a researcher obtains from an actual economy, she will not be able to distinguish with certainty among the three regimes. Therefore, she may be compelled to treat in a homogenous way data generated by distinct policies.

Define A FG(g t) = ĀG for all histories. Clearly, {[ A FG(gt)]gt ∈Gt }∞t =0 calls for a

uniform float. Then, let {[ A NG(gt)]gt ∈Gt }∞t =0 be a bounded sequence of foreign assets in which the exchange rate never floats. For instance, it is possible to define A NG (g

t) = ĀG + (−1)t +1a, where a ∈ R − {0}. It is now possible to connect the findings of Proposition 1 to floating policies.

Proposition 3 Let [ψ,χ,ϕ, {[ AG(gt)]gt ∈Gt }∞t =0, {[x(gt)]gt ∈Gt }∞t =0] be a competitive equilibrium in which Q(gt) is of full rank for every gt . Then there exist portfolios ϕF and ϕN such that both [ψ,χ,ϕF, {[ A FG(gt)]gt ∈Gt }∞t =0, {[x(gt)]gt ∈Gt }∞t =0] and [ψ,χ,ϕN , {[ A NG(gt)]gt ∈Gt }∞t =0, {[x(gt)]gt ∈Gt }∞t =0] are also competitive equilibria. Proof Since both {[ A FG(gt)]gt ∈Gt }∞t =0 and {[ A NG(gt)]gt ∈Gt }∞t =0 are bounded, an appeal to Proposition 1 establishes the desired result. �

That is the main result of this paper. Hence, before proceeding, it is advisable to fur- ther discuss its contents. Let {[ AG(gt)]gt ∈Gt }∞t =0 be any generic contingent sequence of foreign assets. Proposition 3 established that if {[ AG(gt)]gt ∈Gt }∞t =0 can decentralize a competitive outcome [ψ,χ, {[x(gt)]gt ∈Gt }∞t =0], then so can {[ A FG(gt)]gt ∈Gt }∞t =0 and

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{[ A NG(gt)]gt ∈Gt }∞t =0. In other words, if the government can lead the economy to the outcome [ψ,χ, {[x(gt)]gt ∈Gt }∞t =0], then it can attain the same outcome with a floating regime as well as by daily purchasing or selling foreign currency.

I emphasize again that this does not imply any type of indeterminacy for the nom- inal exchange rate. Nor does it imply that the exchange rate is irrelevant. In fact, I showed in Sect. 3 that if the government can conceivably rule out some outcome, then the nominal exchange rate is an effective instrument to do so.

One can easily particularize Propositions 1 and 3 to a deterministic environment.9

In such a context, the rank condition will be automatically satisfied even if the gov- ernment issues bonds of a single maturity.

Observe that Proposition 3 established that every competitive outcome can be imple- mented by a policy that prescribes a uniform float. It also established that every com- petitive outcome can be induced by a policy in which the exchange rate never floats. As a corollary of this last conclusion, competitive outcomes induced by a uniform (or any other type of) floating policy can also be induced by active central bank intervention in the foreign currency market.

Proposition 3 has some implications for the study of fixed exchange rate policies. Assume that the government of my artificial economy sets up a currency board to implement such a policy. Needless to say, to avoid a speculative attack, the fiscal policy must be consistent with the pegged exchange rate. Suppose that the govern- ment often purchases or sells foreign currency to its nationals, so that AG(g

t) is never constant. One can apply Proposition 3 to conclude that the same exchange rate path is fully consistent with a uniform float. In this alternative equilibrium, open-market operations induce the currency stability. Under the currency board arrangement, the pegged exchange rate seems to be mostly a consequence of direct government inter- ventions in the exchange market. Under the alternative policy, the currency stability appears to be an unintended consequence of sound monetary and fiscal fundamentals. However, the two policy regimes are equivalent.

Exchange rate crises are not the focus of this paper. However, it does shed some light on this subject. Consider a deterministic version of my artificial economy. Sup- pose that the government fixes the exchange rate at some level S̄. Suppose also that the fiscal variables are given by τt = 0 and gt = g > 0 for every date t , while ĀG > 0. Finally, suppose that the government finances its fiscal deficit by gradually selling its foreign assets. That combination of fiscal deficit and fixed exchange rate cannot last indefinitely. Moreover, as in Krugman (1979), the collapse of the pegging policy and the ensuing devaluation will entail a speculative attack at some date T < ∞.10

One can apply Proposition 3 to conclude that the currency crisis is fully consis- tent with a permanent float. In a such an alternative competitive equilibrium, the government will finance its deficit by gradually issuing domestic debt. After date T the government will fail to place any newly issued debt. Hence, the exchange rate

9 See Cunha (2005) for a didactical exposition of deterministic versions of many indeterminacy results on the composition of the public debt, including some similar to those of Proposition 3. 10 In this paper, time is a discrete variable. Therefore, as Obstfeld (1986) pointed out, the collapse of the currency peg may require two consecutive speculative attacks.

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On the relevance of floating exchange rate policies 371

depreciation will appear to be a side effect of a confidence crisis that worsened the government’s ability to manage the public debt.

I deliberately used the expressions “ devaluation” for the first competitive equilib- rium and “depreciation” for the second one. The former concept is usually associated with an increase in the nominal exchange rate induced by government actions, while the latter is used to denote a similar increment in a floating regime. However, there is hardly any distinction between the two concepts in this context.

I have just established that a currency crisis can take place under a floating regime in a first-generation model of exchange rate devaluations. The same conclusion applies to third-generation models. For this reason, Aghion et al. (2001) concluded that a crisis could happen under a floating regime in their model. Only second-generation models can display a link between exchange rate crisis and the composition and maturity of the public debt.

Lahiri and Végh (2003) and Obstfeld (1994) listed some episodes in which gov- ernments resorted to increases in the nominal interest rate when facing speculative attacks. Given that an open-market sale is a standard tool to induce such a raise, one can see this type of operation as a policy instrument to defend the domestic currency. Indeed, I show in the “Appendix” that if the discount rates are linearly independent across the states of nature, then every open-market operation has a component that is equivalent to an exchange intervention.

6 Assessing the results

The main goal of this section is to spell out the implications of Propositions 1 and 3. However, a full appreciation of these results requires a sound understanding of the subtle relation between market completeness, exchange rate interventions and the assumptions concerning the availability of financial instruments. Moreover, identify- ing the factors that can or cannot lead to the breakdown of these results will facilitate the analysis of their implications. Therefore, Sect. 6.1 dissects the aforementioned relation, while Sect. 6.2 discusses the robustness of Propositions 1 and 3. Finally, Sect. 6.3 assesses their implications.

6.1 The role of the chosen financial instruments

If the matrix Q(gt) is of full rank for every gt , then the domestic bonds constitute a complete set of financial instruments. As a consequence, it is possible to construct a portfolio of those bonds that perfectly mimics the return of the foreign claims A. There- fore, one can understand Proposition 1 as a consequence of the well-known fact that once markets are complete, any additional financial instrument will be redundant.11

11 Since foreigners do not hold domestic bonds, it is not exactly true that foreign bonds are redundant. However, as discussed in Sect. 6.2, relaxing that assumption has no effects on the results of this paper. Hence, one can safely assume that the domestic bonds suffice to implement any competitive outcome whenever ρ(gt ) = n for every gt .

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The preceding paragraph makes clear that the findings presented in Proposition 1 are not specific to the asset instruments considered in this paper. However, it is not a straightforward task to identify a set of securities that allows one to obtain a result with the flavor of Proposition 3. The clarification of this crucial point is the focus of the remainder of this subsection.

Proposition 3 establishes that if a government can implement some outcome, then it can implement the same outcome without ever intervening in the foreign currency market, as well as by means of daily interventions in that market. As a consequence, an outcome induced by a policy that prescribes active intervention can also be induced by a floating policy. Conversely, if such a policy induces some outcome, then it can be decentralized by a policy that requires frequent foreign exchange interventions.

Suppose that the domestic government issues dollar-denominated bonds of sev- eral maturities instead of {[{Bk(gt)}∞k=t +1]gt ∈Gt }∞t =0. A result similar to Proposition 1 holds in such a context. However, the same cannot be said about Proposition 3. Many economists say that a government that issues bonds denominated in a foreign cur- rency is intervening in the exchange market. For instance, Calvo and Reinhart (2002, p. 388) stated that a central bank that issues that type of debt is carrying out a “hidden foreign exchange reserves transaction.” Roubini and Setser (2004) developed similar reasoning on page 52 of their book. Moreover, they argued at page 39 that governments often issue “debt denominated in a foreign currency” to defend a pegged exchange rate “that comes under pressure.”

If one allows the government to issue only dollar-denominated bonds of several maturities, then it becomes necessary to change Definition 2 to take into consideration the popular understanding expressed by Calvo and Reinhart and Roubini and Setser. And after such an adjustment, it will be impossible to establish a result equivalent to Proposition 3.12

It is well known that options can complete markets. Hence, if the only assets in my model economy were the bonds A and some set of options, futures and other foreign currency derivatives, then it could be possible to establish a counterpart to Proposition 1. However, economists tend to connect government trading of currency derivatives to exchange rate interventions. For instance, Calvo and Reinhart (2002, p. 388) argued that a central bank that trades foreign currency derivatives is changing its foreign reserves balance. Obstfeld (1994, p. 197) explicitly considered the Swedish central bank “forward position in foreign currencies” when assessing its exchange interventions during the krona crisis of 1992. Canales-Kriljenko et al. (2003) also pointed out that a central bank can carry out foreign currency interventions in the forward and other derivatives markets. For this reason, the replacement of domestic bonds by foreign currency derivatives requires changing Definition 2 and, as in the case of dollar-denominated bonds, it will not be possible to establish a result equivalent to Proposition 3.

12 The reason for such impossibility is very simple. The proof of Proposition 3 will break down if the government cannot trade a complete set of assets that is unrelated to foreign exchange interventions. This is so because that argument requires simultaneous changes in the government balance of foreign assets (which is associated with foreign exchange interventions) and in its debt denominated in domestic currency (which is not connected to those type of interventions).

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On the relevance of floating exchange rate policies 373

Suppose that instead of issuing the bonds {[{Bk(gt)}∞k=t +1]gt ∈Gt }∞t =0, the govern- ment issues n (recall that is exactly the cardinality of G) bonds that mature in one period. Define their returns so that for each state, there is a bond that pays one unit of the domestic currency in that state and zero in the others. In such a context, it is defi- nitely possible to obtain a counterpart to Proposition 3. However, actual governments do not issue this class of security, while bonds of several maturities are widely found in the real world.

It is worth discussing whether bonds indexed to the domestic price level with matu- rity of one period can replace the bonds {[{Bk(gt)}∞k=t +1]gt ∈Gt }∞t =0 without breaking Propositions 1 and 3 down. Since the returns of indexed bonds depend on the price level, which in turn depends on gt , these claims may constitute a complete set of finan- cial assets. Hence, it is clearly feasible to establish a result similar to Proposition 1. However, the same cannot be said of Proposition 3. The economy of this paper has just a single good. Therefore, the nominal exchange rate and the domestic price level are identical and the indexed bonds will be equivalent to dollar-denominated claims. Nev- ertheless, in a model with nontradable goods, there will be no such direct equivalence. As a consequence, it is possible to obtain a result with the flavor of Proposition 3 in this more complex environment.

It should now be clear to the reader that not every set of financial instruments is con- sistent with the essence of Proposition 3. To have that consistency property, an array of assets must satisfy three attributes: (i) completeness; (ii) realism (i.e., the bonds must have clear real-world counterparts); and (iii) no association by economists of the trading of those assets by the government with interventions in the foreign exchange market. Finding financial instruments that meet these requirements was an important step of this research project.

6.2 Robustness

Propositions 1 and 3 have a common set of assumptions and the latter is a direct con- sequence of the former. Hence, there is no loss of generality in focussing the present analysis only in the first result.

Two features of the competitive environment are essential in Proposition 1: (i) the government is not an active player and (ii) people have no arbitrage opportunities in the securities market. Provided that these two features are preserved, it is possi- ble to introduce many frictions in the model economy of this paper and still obtain the same indeterminacy result. Particularly, the finding will survive the introduction of features such as monopolistic competition, price stickiness, price discrimination, price-to-market and so on.

Proposition 1 is robust to some variations in the hypotheses concerning the way international financial markets operate. For instance, one can let the interest rate at which the country borrows abroad be a function of its total external debt −[ AG(gt −1)+ A H(g

t −1)] without affecting the conclusion in question. Exactly the same reasoning used in the proof of that proposition works in such a context.

In the model economy of this paper, foreigners are not allowed to purchase domes- tic bonds. A loosening of this assumption has no impact on Proposition 1. Its proof

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relied on the ability of the government to trade securities with its nationals—recall that such trading is subjacent in Eqs. (10) and (15). Therefore, the composition of the portfolio that international investors hold is not relevant for that proof. The same argument establishes that Proposition 1 holds in a many-country model. An appeal to BK provides another way of verifying the robustness in those dimensions, since it is possible to replace the financial instruments they considered by securities identical to those of this paper without affecting their main findings.

The indeterminacy presented in Proposition 1 will also arise if one focuses on optimal policies with commitment, as in Chari and Kehoe (1999). In fact, it is not even necessary to assume that the government wishes to maximize people’s expected lifetime utility (4). The government’s payoff can be any function that does not depend on the portfolio ϕ.

The reasoning underlying the proof of Proposition 1 can be applied even if equilib- rium prices and allocations are undetermined—provided that, in the case of sunspots, the coordination of agents’ expectations does not depend on ϕ. Thus, the findings of this paper can hold in economies that display the types of indeterminacy found in the models of Kareken and Wallace (1981), Russell (2003), Antinolfi and Huybens (2004), Salto and Pietra (2011), and Woodford (1994).

I now turn to the task of identifying factors that can break down the equilibrium indeterminacy of Proposition 1. Borrowing constraints are the first one I consider. Buera and Nicolini (2004) pointed out that the matrix Q(gt) may be close to singular. Hence, the alternative debt holdings defined in (11) may turn out to be quite large. Clearly, if government or people are constrained by relatively tight borrowing bounds, the proof fails. However, assuming that a fraction of the people face borrowing bounds or credit constraints does not suffice to break Proposition 1 down, since the government would still be able to trade with the unconstrained households.

Since Modigliani and Miller (1958) seminal essay, many papers have addressed the relevance of firms’ capital structure. Myers (2001) competently surveyed this literature. He pointed out that there are several reasons for capital structure to be relevant. Given the close relation between my results and the Modigliani–Miller Theorem, it is natural to check whether any of those reasons can also help to under- stand why the time path of a government’s foreign assets should matter. Among the factors that Myers listed, informational factors have been considered in many interna- tional macroeconomics papers, as in Herrendorf (1997, 1999) and Atkeson and Kehoe (2006).

Time consistency and sovereign debt can eliminate the equilibrium indeterminacy. Lucas and Stokey (1983), Alvarez et al. (2004), and Persson et al. (2006) pointed out that the composition and maturity of government debt matters for the time consistency of monetary policy. On the other hand, Giavazzi and Pagano (1990), Obstfeld (1994), and Obstfeld and Rogoff (1995) pointed out the relevance of time consistency factors for several exchange rate crises. BK also mentioned that the set of implementable pol- icies depends on the composition of the government debt. Clearly, if the government selects policies in a sequential fashion, then the composition and the denomination of its total debt will be relevant. Moreover, it is unlikely that a result such as Proposition 1 will hold if the government and currency speculators behave strategically, as in Pastine (2000).

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On the relevance of floating exchange rate policies 375

Concerning sovereign debt, observe that the construction of ϕ′ entails a modifica- tion (relative to the original competitive equilibrium) in people’s and government’s shares of the total external debt −[ AG(gt −1) + A H(gt −1)]. Although this variable does not change, the foreign public debt does. As Cole and Kehoe (2000) pointed out, such a variation can affect the government’s incentives to default. Hence, the portfolio change underlying Proposition 1 may fail to be neutral.

6.3 Implications

For ease of exposition, I divide this subsection into three parts. In each of them I discuss, in this respective order, their theoretical, empirical and policy implications.

6.3.1 Theoretical implications

Section 6.2 provides an outline of a class of economies that satisfy conditions that pre- vent Propositions 1 and 3 from holding. For the equilibrium outcomes of a game not to display that type of indeterminacy, that game must have at least one of the following two features: (i) borrowing bounds are tight enough to preclude the government from carrying out sterilized interventions as specified in (15); (ii) the government behaves in a strategic fashion and (a) it lacks commitment or (b) there is asymmetric information. Henceforward, I will refer to (i) and (ii) as floating relevance conditions.

I illustrate the importance of the floating relevance conditions to the study of exchange rate policies by briefly discussing two major issues in international macro- economics. The first is the classic fixed-versus-floating debate. Several authors com- pare these regimes and discuss the implications of each option. They often rely on models that satisfy none of the floating relevance conditions to carry out their theo- retical analyses. However, in such a context, a floating policy is consistent with any conceivable equilibrium. As a consequence, the comparison in question is pointless.13

The second issue is the ability of calibrated dynamic general equilibrium mod- els to replicate the distinct empirical regularities associated with floating and fixed exchange rate regimes—for instance, real exchange rate volatility is known for being lower under the latter. Duarte (2003) and Sopraseuth (2003) are typical examples of papers in that field. It should be clear that using models that display some floating relevance condition in exercises of this type can contribute to our understanding of the behavior of macroeconomic variables under each regime.

6.3.2 Empirical implications

There are at least three major lines of empirical research on exchange rate poli- cies. A large body of literature has focused on identifying the empirical regularities

13 Proposition 3 differs from other authors’ conclusions because they often combine the floating regime with some additional hypotheses about the monetary policy. For instance, Calvo (1999) and Lahiri et al. (2007) considered a combination of floating with a constant money supply, while Hernandez-Verme (2004) assumed that this variable grew at a constant rate. Hence, the implications of these authors attributed to the floating regime were, at least partially, induced by other features of the macroeconomic policy.

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associated with floating and fixed exchange rate regimes. Baxter and Stockman (1989) and Levy-Yeyati and Sturzenegger (2003) are typical examples of this class of research. Another important agenda is the one focused on classifying exchange rate policies, as the works of Gosh et al. (2002, chap. 4), Levy-Yeyati and Sturzenegger (2005), and Reinhart and Rogoff (2004). The third one aims at assessing the efficacy and impacts of government intervention in the foreign exchange market. Beine et al. (2007) and Kearns and Rigobon (2005) constitute a representative sample of this last line.

As in the analysis of theoretical consequences of Propositions 1 and 3, I will use the floating relevance conditions to establish their empirical implications. I start by introducing a useful stylized example.

Example 4 Consider three countries (A, B, and C) that are identical to the artificial economy described in Sect. 2. Parameter values and stochastic process do not vary across countries. In each of them the government selects a policy aimed at maximizing the expected lifetime utility (4). Governments A and B have commitment, whereas C does not. Government A implements the optimal policy by means of a floating regime, while B allows its foreign assets to change every period. The lack of com- mitment prevents C from implementing the same outcome as A. Hence, the expected lifetime utility is higher in A than in C. In addition, suppose that the lower welfare in country C is reflected in a consumption volatility higher than its counterpart in A. Moreover, as discussed in the previous subsection, the maturity and the denomination of the liabilities of government C are likely to be well-defined. Hence, its foreign assets change as gt evolves over the time. Therefore, country C is not pursuing a floating policy.

Suppose that a researcher collects data from economies A and B and applies the classification procedures discussed by Gosh et al. (2002, chap. 4) and Levy-Yeyati and Sturzenegger (2005). These two nations are likely to fall into distinct categories. However, in such a context, that separation should not happen, since the two countries are pursuing equivalent policies. On the other hand, if the researcher compares A with C, then she/he may conclude that consumption is less volatile under floating exchange rates. Of course, that assessment is not correct. The factor that really matters here is commitment.

Concerning the literature about government interventions in foreign currency mar- kets, Proposition 3 implies that measuring these interventions is a more complex task than usually assumed. The next example provides a useful illustration of this fact.

Example 5 There exist two nations (D and E ) that are identical to the artificial econ- omy described in Sect.2. As in the previous example, they have the same parameter values and stochastic processes. Each government has commitment and has pegged its currency to the U.S. dollar. As shocks on public expenditures hit country D, its central bank buys or sells foreign assets to keep the nominal exchange rate at the desired target. Concerning country E , at every period, its monetary authority buys or sells exactly 10% of the amount of foreign assets traded by its counterpart in D; any further policy action that is required to keep the exchange rate on target is carried out by trading domestic bonds.

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On the relevance of floating exchange rate policies 377

Assume that a researcher wants to compare the effectiveness of foreign exchange interventions of governments D and E . The fact that the latter uses much less foreign assets than the former to achieve the same target may lead the researcher to conclude that these interventions are more effective in E than in D. Such an assessment is misleading, because countries D and E are pursuing equivalent policies.

As discussed in Sect. 6.1, the above analysis relies on the assumption that the trad- ing of domestic bonds is not seen as an exchange rate intervention. Indeed, that point of view is not stated in the related literature. For instance, that equivalent avenue was not mentioned by Neely (2001) in his list of the types of exchange intervention; neither was it considered in the construction of the intervention index proposed by Weymark (1997).

The above analysis illustrates the importance of controlling for commitment when carrying out an empirical study of exchange rates. Of course, all other floating rele- vance conditions are equally important. Thus, in an ideal situation, empirical research on exchange rate policies should take into consideration borrowing bounds, asymmet- ric information, commitment, and strategic behavior by the government.

These factors are not easily measured or appraised. Hence, controlling for them in an empirical exercise is not an obvious task. It is beyond the scope of this paper to tackle this problem. Nevertheless, I wish to mention that some of the political variables that Persson and Tabellini (2003) used to quantify the forms of government, electoral rules, and the quality of democracies may be useful in empirical studies of exchange rate regimes. For instance, if those political proxies are related to a government’s abil- ity to commit to a policy and the strategy space of the game it plays with other agents, then they can help to explain the evidence that exchange rate policies are relevant for growth and volatility of GPD in nonindustrial economies but are not in industrial ones, as Levy-Yeyati and Sturzenegger (2003) documented.

The above discussion is clearly grounded on an offspring of the theoretical impli- cations of Proposition 3. That is to say, an empirical investigation into exchange rate regimes that does not account for the floating relevance conditions is likely to provide an incomplete picture of the question being studied.

6.3.3 Policy implications

Propositions 1 and 3 have important policy repercussions, which are related to (i) the characterization, (ii) the secrecy, and (iii) the evaluation and prescription of exchange rate policies. I discuss these three items in that order.

As argued in the last part of this paper, a major consequence of Propositions 1 and 3 is the fact that the classification of exchange rate regimes is a more challenging task than usually assumed. Moreover, the same applies to the assessment of govern- ment interventions aimed at affecting the path of nominal exchange rates. I elaborate on this issue in the next pair of paragraphs.

Canales-Kriljenko et al. (2003) mentioned that countries that benefit from an IMF- supported adjustment program often are advised to “confine their interventions to smoothing exchange rate volatility.” On the other hand, Proposition 3 establishes that a government does not need to intervene in the foreign exchange market to implement a competitive outcome. To further complicate the matter, I show in the “Appendix”

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378 A. B. Cunha

that an open-market operation can be equivalent to a combination of two other policy actions, one of them being an exchange intervention. It should be clear that a country may be able to affect the exchange rate in a manner opposed to the IMF’s expectations.

As Sarno and Taylor (2002) pointed out, there are occasions in which governments carry out coordinated exchange rate interventions. A consequence of Proposition 3 is that a plain purchase or sale of foreign assets by a government does not suffice to establish that it indeed contributed to a change in the nominal exchange rates or that it effectively abided by a joint intervention agreement.

Concerning secrecy, Sarno and Taylor (2002) mentioned that “most of the actual interventions in the foreign exchange market have been, at least partially, not publicly announced by the monetary authorities.” Neely (2001) made an equivalent statement. These authors also pointed out that the role played by secrecy is not well compre- hended. In any case, it is worth mentioning that the indeterminacy results of this paper may provide the monetary authorities additional ways to covertly influence the exchange rate.

To illustrate the implications of Propositions 1 and 3 to policy evaluation and pre- scription, I will again rely on Example 4. As previously mentioned, one can compare countries A and C and wrongly conclude that the difference in outcomes is due to the fact that A follows a floating policy, while C often intervenes in the exchange market. A policy recommendation that the latter nation should implement a floating regime to improve its performance is unsound. Adopting a floating policy entails placing a constraint on the foreign assets of country C and imposing such a constraint does not necessarily lead to a better outcome—in fact it may lead to a worse one.

The result presented in the last paragraph directly follows from the analysis carried in the previous two parts of this paper. Namely, as theoretical and empirical studies on the matter, the evaluation and prescription of exchange rate policies should pay attention to the floating relevance conditions.

7 Conclusion

Many authors have derived results establishing that a competitive equilibrium may fail to pin down the maturity structure and the currency denomination of the public debt. In this paper, I investigated the possible implications of that class of indeterminacy to the study of exchange rate regimes.

I considered a stochastic small open-monetary economy in which the government issues nominal bonds of several maturities with noncontingent face value at redemp- tion. In such an environment, the structure of government liabilities can be undeter- mined in a competitive equilibrium. Thus, competitive allocations and prices may be decentralized by a floating regime, as well as by a policy of daily government intervention in the foreign exchange market.

The competitive equilibrium concept requires optimizing behavior of firms and households, but only demands a balanced budget from the government. In games in which this agent acts strategically, the aforementioned indeterminacy is unlikely to arise. Therefore, associating—at either the theoretical or empirical level—float- ing policies with macrovariables such as GDP growth, consumption volatility and

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On the relevance of floating exchange rate policies 379

unemployment rate requires taking into consideration the strategic interaction between governments and the other economic agents.

Appendix

I established in Proposition 3 that if ρ(gt) = n for every gt , then any exchange intervention can be replaced by an equivalent open-market operation. I am concerned in this appendix with a converse question. Namely, I investigate to what extent an open-market operation can be replaced by an exchange intervention.

It turns out that if Q(gt) is of full rank, then an open-market operation that takes place at gt is equivalent to a combination of: (i) an exchange intervention that decreases (increases) the government’s foreign assets exactly by the increase (decrease) in the level (i.e., the discounted present value) of the domestic debt embedded in the original operation plus and (ii) another open-market operation that holds constant the level of the domestic debt and changes its maturity structure. I formalize this result in the forthcoming Proposition 6.

Let [ψ,χ,ϕ, {[ AG(gt)]gt ∈Gt }∞t =0, {[x(gt)]gt ∈Gt }∞t =0] be a competitive equilibrium. An open-market operation takes place at gT if Bk(g

T ) �= Bk(gT −1) for some k ≥ T + 1. This condition entails that the amount of domestic debt to be redeemed at some future date changes at gT . Additionally, I say that an open-market operation is a pure maturity restructuring if

∞∑

k=T +1 qk(g

T )Bk(g

T ) =

∞∑

k=T qk(g

T )Bk(g

T −1 ). (16)

That is, a pure maturity restructuring operation changes the maturity structure of the domestic debt without affecting its level.

Now, let ĝT be a history in which an open-market operation happens at date T . Define A G(g

t) according to

A G(g t ) =

{ AG(g

t) − if gt = ĝT AG(g

t) if gt �= ĝT ,

where

= ∑∞

k=T +1 qk(ĝ T )Bk(ĝ

T ) − ∑∞k=T qk(ĝT )Bk(ĝT −1) q∗T S(ĝT )

. (17)

Observe that I constructed the array {[ A G(gt)]gt ∈Gt }∞t =0 by changing the value q∗T S(ĝ

T )AG(ĝ T ) of the government’s foreign assets only at ĝT and exactly by the

opposite variation in the level of the domestic debt specified by the open-market oper- ation in question.

Proposition 6 Let [ψ,χ,ϕ, {[ AG(gt)]gt ∈Gt }∞t =0, {[x(gt)]gt ∈Gt }∞t =0] be a competitive equilibrium in which an open-market operation takes place at ĝT . If ρ(ĝT ) = n, then

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380 A. B. Cunha

there exists a portfolio ϕ with the following properties: (i) ϕ (gt) = ϕ(gt) for every gt �= ĝT ; (ii) [ψ,χ,ϕ , {[ A G(gt)]gt ∈Gt }∞t =0, {[x(gt)]gt ∈Gt }∞t =0] is a competi- tive equilibrium in which a pure maturity restructuring open-market operation takes place at ĝT .

Proof I start by constructing the portfolio ϕ . Define M (gt) and A H(g t) as in (8)

and (9). Concerning {B k (gt)}∞k=t +1, set B k (gt) = Bk(gt) for gt �= ĝT , while B k (ĝT ) is defined as in (12). The reasoning applied in the proof of Proposition 1 establishes that [ψ,χ,ϕ , {[ A G(gt)]gt ∈Gt }∞t =0, {[x(gt)]gt ∈Gt }∞t =0] is a competitive equilibrium. It remains to show that the open-market operation at ĝT is a pure maturity restructur- ing. Observe that A H(ĝ

T ) − A H(ĝT ) = . Combine this equality with (15) and (17) to conclude that

∑∞ k=T qk(ĝ

T )Bk(ĝ T −1) = ∑∞k=T +1 qk(ĝT )B k (ĝT ). The fact that

B k (ĝ T −1) = Bk(ĝT −1) implies that {B k (ĝT −1)}∞k=T and {B k (ĝT )}∞k=T +1 satisfy

(16). �

In response to the financial crisis that started in 2007, the Federal Reserve (Fed) implemented a quantitative easing program. Under such a program, a central bank purchases medium- and long-term bonds instead of the short-term ones usually traded in most open-market operations. On that occasion, the Bank of England, the European Central Bank, and the Bank of Japan also adopted similar policies. Moreover, the last institution pursued a similar policy during the earlier 2000s.

The quantitative easing policy provides an enlightening illustration of the princi- ples of Proposition 6 at work.14 Assume that at date zero, the central bank of my model economy implements a quantitative easing policy by purchasing long-term bonds whose discounted present value is V . According to Proposition 6, there is an equivalent competitive equilibrium in which at date zero the central bank increases, in a once-and-for-all fashion, its foreign assets exactly by V/[q∗0 S(g0)] and simulta- neously carries out a pure maturity restructuring open-market operation.

The reasoning developed in the last paragraph makes clear that a quantitative easing policy can induce a depreciation of the nominal exchange rate. Many authors argue exactly in this direction. For instance, Feldstein clearly stated that view in (2010a) and (2010b). Joyce et al. (2010) mentioned that the Bank of England’s quantitative easing program led to the depreciation of the British pound, while Spiegel (2001) made sim- ilar comments when analyzing the monetary policy of the Bank of Japan during the earlier 2000s.

Interestingly enough, Cline and Willianson (2010) mentioned that governments of several emerging nations believed that their currencies should appreciate (i.e., the U.S. dollar would depreciate) as a consequence of an additional round of quantitative easing by the Fed. Thus, policymakers seem to be aware, at least to some extent, of the mechanics underlying Proposition 6.

14 I thank one of the referees for pointing out the possible links between the quantitative easing policy and Propositions 1 and 3. The formalization of these connections led to Proposition 6.

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On the relevance of floating exchange rate policies 381

References

Aghion, P., Bacchetta, P., Banerjee, A.: Currency crises and monetary policy in an economy with credit constraints. Eur Econ Rev 45, 1121–1150 (2001)

Alvarez, F., Kehoe, P.J., Neumeyer, P.A.: The time consistency of optimal monetary and fiscal policies. Eco- nometrica 72, 541–567 (2004)

Angeletos, G.M.: Fiscal policy with noncontingent debt and the optimal maturity structure. Q J Econ 117, 1105–1131 (2002)

Antinolfi, G., Huybens, E.: Domestic financial market frictions, unrestricted international capital flows, and crises in small open economies. Econ Theory 24, 811–837 (2004)

Atkeson, A., Kehoe, P.J.: The advantage of transparency in monetary policy instruments. Staff report 297, Federal Reserve Bank of Minneapolis (2006)

Backus, D.K., Kehoe, P.J.: On the denomination of government debt: a critique of the portfolio balance approach. J Monet Econ 23, 359–376 (1989)

Barro, R.J.: Are government bonds net wealth? J Polit Econ 82, 1095–1117 (1974) Bassetto, M., Kocherlakota, N.: On the irrelevance of government debt when taxes are distortionary.

J Monet Econ 51, 399–436 (2004) Baxter, M., Stockman, A.C.: Business cycles and the exchange-rate regime: some international evidence.

J Monet Econ 23, 377–400 (1989) Beine, M., Lahaye, J., Laurent, S., Neely, C.J., Palm, F.C.: Central bank intervention and exchange rate

volatility, its continuous and jump components. Int J Financ Econ 12, 201–223 (2007) Bloise, G.: A note on the existence of monetary equilibrium over an infinite horizon. Econ Theory 27, 59–

77 (2006) Buera, F., Nicolini, J.P.: Optimal maturity of government debt without state contingent bonds. J Monet

Econ 51, 531–554 (2004) Calvo, G.A.: Fixed versus flexible exchange rates: preliminaries of a turn-of-millennium rematch. Unpub-

lished manuscript. http://hdl.handle.net/1903/4295 (1999). Accessed 23 Dec 2011 Calvo, G.A., Reinhart, C.M.: Fear of floating. Q J Econ 117, 379–408 (2002) Canales-Kriljenko, J.I., Guimarães, R., Karacadağ, C.: Official intervention in the foreign exchange market:

elements of best practice. Working paper 03/152, International Monetary Fund (2003) Chamley, C., Polemarchakis, H.: Assets, general equilibrium and the neutrality of money. Rev Econ

Stud 51, 129–138 (1984) Chari, V.V., Kehoe, P.J.: Optimal fiscal and monetary policy. In: Taylor, J.B., Woodford, M. (eds.) Handbook

of Macroeconomics—volume 1C, Amsterdam: North-Holland (1999) Cole, H.L., Kehoe, T.: Self-fulfilling debt crises. Rev Econ Stud 67, 91–116 (2000) Cline, W.R., Willianson, J.: Currency wars? Policy brief 10-26, Peterson Institute for International Eco-

nomics (2010) Cunha, A.B.: Managing public debt, money supply and foreign assets: some indeterminacy results. Revista

Brasileira Econ 59, 427–444 (2005) Duarte, M.: Why don’t macroeconomic quantities respond to exchange rate variability? J Monet

Econ 50, 889–913 (2003) Dubey, P., Geanakoplos, J.: Determinacy with nominal assets and outside money. Econ Theory 27, 79–

106 (2006) Duffie, D., Huang, C.-F.: Implementing Arrow-Debreu equilibria by continuous trading of few long-lived

securities. Econometrica 53, 1337–1356 (1985) Feldstein, M.: QE2 is risky and should be limited. Financial Times, 3 Nov, p. 11 (2010a) Feldstein, M.: Quantitative easing and the renminbi. Project syndicate. http://www.project-syndicate.org/

commentary/feldstein30/English (2010b). Accessed 27 June 2011 Giavazzi, F., Pagano, M.: Confidence crises and public debt management. In: Dornbusch, R., Draghi, M.

(eds.) Public Debt Management: Theory and History, Cambridge: Cambridge University Press (1990) Gosh, A.R., Gulde, A.-M., Wolf, H.C.: Exchange Rate Regimes: Choices and Consequences. Cambridge:

MIT Press (2002) Hernandez-Verme, P.L.: Inflation, growth and exchange rate regimes in small open economies. Econ The-

ory 24, 839–856 (2004) Herrendorf, B.: Importing credibility through exchange rate pegging. Econ J 107, 687–694 (1997) Herrendorf, B.: Transparency, reputation, and credibility under floating and pegged exchange rates. J Int

Econ 49, 31–50 (1999)

123

382 A. B. Cunha

Jeanne, O.: Debt maturity and the international financial architecture. Am Econ Rev 99, 2135–2148 (2009) Joyce, M., Lasaosa, A., Stevens, I., Tong, M.: The financial market impact of quantitative easing. Working

paper 393, Bank of England (2010) Kareken, J., Wallace, N.: On the indeterminacy of equilibrium exchange rates. Q J Econ 96, 207–222 (1981) Kearns, J., Rigobon, R.: Identifying the efficacy of central bank interventions: evidence from Australia and

Japan. J Int Econ 66, 31–48 (2005) Krugman, P.: A model of balance-of-payment crises. J Money Credit Bank 11, 311–325 (1979) Lahiri, A., Végh, C.: Delaying the inevitable: interest rate defense and balance of payments crises. J Polit

Econ 111, 404–424 (2003) Lahiri, A., Singh, R., Végh, C.: Segmented asset markets and optimal exchange rate regimes. J Int Econ 72,

1–21 (2007) Levy-Yeyati, E., Sturzenegger, F.: To float or to fix: evidence on the impact of exchange rate regimes on

growth. Am Econ Rev 93, 1173–1193 (2003) Levy-Yeyati, E., Sturzenegger, F.: Classifying exchange rate regimes: deeds vs. words. Eur Econ

Rev 93, 1603–1635 (2005) Lucas, R.E. Jr., Stokey, N.L.: Optimal fiscal and monetary policy in an economy without capital. J Monet

Econ 12, 55–93 (1983) Modigliani, F., Miller, M.H.: The cost of capital, corporation finance and the theory of investment. Am

Econ Rev 58, 261–297 (1958) Myers, S.C.: Capital structure. J Econ Perspect 15, 81–102 (2001) Neely, C.J.: The practice of central bank intervention: looking under the hood. Fed Reserve Bank St Louis

Rev 83, 1–10 (2001) Nicolini, J.P.: More on the time consistency of the monetary policy. J Monet Econ 41, 333–350 (1998) Obstfeld, M.: Speculative attack and the external constraint in a maximizing model of the balance of

payments. Can J Econ 29, 1–20 (1986) Obstfeld, M.: The logic of currency crises. Cah Econ Monetaires 43, 189–213 (1994) Obstfeld, M., Rogoff, K.: The mirage of fixed exchange rates. J Econ Perspect 9, 73–96 (1995) Pastine, I.: Devaluation of fixed exchange rates: optimal strategy in the presence of speculation. Econ

Theory 15, 631–661 (2000) Persson, M., Persson, T., Svensson, L.E.O.: Time consistency of fiscal and monetary policy: a solution. Eco-

nometrica 74, 193–212 (2006) Persson, T., Tabellini, G.: The economic effects of constitutions. Cambridge: MIT Press (2003) Reinhart, C.M., Rogoff, K.: The modern history of exchange rate arrangements: a reinterpretation. Q J

Econ 119, 1–48 (2004) Roubini, N., Setser, B.: Bailouts or Bail-ins? Responding to Financial Crises in Emerging Economies. Wash-

ington: Peterson Institute for International Economics (2004) Russell, S.: Quasi-fundamental exchange rate variation. Econ Theory 22, 111–140 (2003) Salto, M., Pietra, T.: Welfare and excess volatility of exchange rates. Econ Theory (2011). doi:10.1007/

s00199-011-0654-2 Sargent, T.J.: Dynamic Macroeconomic Theory. Cambridge: Harvard University Press (1987) Sargent, T.J., Smith, B.D.: The irrelevance of government foreign exchange operations. In: Helpman, E.,

Razin, A., Sadka, E. (eds.) Economic Effects of the Government Budget, Cambridge: MIT Press (1988) Sarno, L., Taylor, M.P.: The Economics of Exchange Rates. Cambridge: Cambridge University Press (2002) Sopraseuth, T.: Exchange rate regimes and international business cycles. Rev Econ Dyn 6, 339–361 (2003) Spiegel, M.: Quantitative easing by the Bank of Japan. Economic Letter 2001–31, Federal Reserve Bank

of San Francisco (2001) Svensson, L.E.O.: Money and asset prices in a cash-in-advance economy. J Polit Econ 93, 914–944 (1985) Wallace, N.: A Modigliani–Miller Theorem for open-market operations. Am Econ Rev 71, 267–274 (1981) Weymark, D.N.: Measuring the degree of exchange market intervention in a small open economy. J Int

Money Financ 16, 55–79 (1997) Woodford, M.: Monetary Policy and price level determinacy in a cash-in-advance economy. Econ The-

ory 4, 345–380 (1994)

123

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