NBER WORKING PAPER SERIESEXCHANGE CONTROLS AS A FISCAL INSTRUMENT
Stephanie Schmitt-Grohé
Martín Uribe
Working Paper 31294
http://www.nber.org/papers/w31294

NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
June 2023, Revised October 2024

We thank for comments and suggestions Javier Bianchi, Guillermo Calvo, Francisco Ciocchini,
Eduardo Davila, Andy Neumeyer, Nikhil Patel, Alessandro Rebucci, Federico Sturzenegger, andseminar participants at the 2024 ASSA meetings, Brown, Columbia, UCEMA, Rutgers, theMinneapolis FED, the Federal Reserve Board, the IMF, the NBER IFM Spring 2024 meeting, andthe Macroeconometric Caribbean Conference (Bahamas, February We thank for comments andsuggestions Javier Bianchi, Guillermo Calvo, Francisco Ciocchini, Eduardo Davila, Andy
Neumeyer, Nikhil Patel, Alessandro Rebucci, Federico Sturzenegger, and seminar participants atthe 2024 ASSA meetings, Brown, Columbia, UCEMA, Rutgers, the Minneapolis FED, the Federal
Reserve Board, the IMF, the NBER IFM Spring 2024 meeting, and the Macroeconometric
Caribbean Conference (Bahamas, February 2023). Giovanni Bonfanti, Emilio Zaratiegui, andPatricio Goldstein provided excellent research assistance. 2023). Giovanni Bonfanti, Emilio
Zaratiegui, and Patricio Goldstein provided excellent research assistance. The views expressedherein are those of the authors and do not necessarily reflect the views of the National Bureau of
Economic Research.
NBER working papers are circulated for discussion and comment purposes. They have not been
peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies
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© 2023 by Stephanie Schmitt-Grohé and Martín Uribe. All rights reserved. Short sections of text,
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Exchange Controls As A Fiscal Instrument
Stephanie Schmitt-Grohé and Martín Uribe
NBER Working Paper No. 31294
June 2023, Revised October 2024
JEL No. E5, E63, F41
ABSTRACT
About 20 percent of countries employ multiple exchange rates. An important rationale for thispractice is the creation of fiscal revenue. This paper develops a general equilibrium model withexchange controls. It shows that such controls can mobilize significant fiscal resources, but also
cause dollar shortages, misallocation, and smuggling. The paper studies an optimal taxation
problem where chronic fiscal deficits must be financed with money creation and exchange controls.
Under plausible calibrations, the optimal policy favors multiple exchange rates, with stronger
controls on exports than on imports. Both exchange controls and inflation finance significant
portions of the deficit.

Stephanie Schmitt-Grohé
Department of Economics
Columbia University
420 West 118th Street, MC 3308
New York, NY 10027
and NBER
stephanie.schmittgrohe@columbia.edu
Martín Uribe
Department of Economics
Columbia University
International Affairs Building
New York, NY 10027
and NBER
martin.uribe@columbia.edu

1Introduction

About 20 percent of all countries, especially in poor and emerging areas of the world, have inplace dual, multiple, or parallel exchange rates (Ilzetzki, Reinhart, and Rogoff, 2019). This
paper investigates the fiscal implications of exchange controls for countries that experiencechronic fiscal deficits financed with money creation. Exchange controls are akin to a tax oninternational trade (Bhagwati, 1978). Therefore, they compete with the inflation tax as analternative source of fiscal revenue. The question we pose is what is the optimal monetaryand exchange control policy for a government that faces an exogenous stream of fiscal deficits.
To address this question we embed exchange controls in a general equilibrium model of anopen economy with a tradable and a nontradable sector. Both sectors use imported materials
as inputs of production. A demand for money is motivated by a transactions cost that isincreasing in money velocity. The government runs an exogenous stream of primary fiscal
deficits. In addition, the economy is financially isolated from the rest of the world but the
government owes an external debt denominated in foreign currency on which it pays interest.
We have in mind a situation in which regular taxes are already high, and the government
has lost its political ability to raise them further to close the fiscal gap. As a result, thegovernment must finance fiscal imbalances with revenues generated by money creation andexchange controls.
In the model economy, exchange controls work as follows. The government obliges exporters to surrender their foreign exchange earnings at the central bank in exchange fordomestic currency at an exchange rate (the official exchange rate) that is disadvantageous
relative to the market exchange rate. Thus, exchange rate controls act as a tax on exports
with the tax rate being the gap between the market and the official exchange rate. The government also supplies foreign exchange to importers at the official exchange rate. Therefore,
exchange-rate controls also represent a subsidy on imports. However, we show that to guarantee positive revenue from exchange controls, it can be in the interest of the government tolimit the amount of foreign exchange it makes available to importers at the official exchange
rate. When this limit becomes binding, exchange controls turn from an import subsidy to an
import quota. This novel result is relevant for two reasons. First, it rationalizes the notionof “dollar shortage” characteristic of economies with exchange controls. Second, we find thatdollar shortages induced by exchange controls are a major source of resource misallocationin all sectors of the economy.
Analyzing exchange controls in the context of a general equilibrium framework reveals
an additional channel through which they can mobilize fiscal resources. Because government
obligations have a nontradable and a tradable component, total government obligations

1

measured in units of consumption depend on the real exchange rate. Thus, exchange controls
can generate fiscal space by altering the real exchange rate. This effect implies that exchange
controls can also create fiscal space through a reduction in the government’s external debt
burden. This channel has not been discussed in the related literature and turns out to bequantitatively relevant under certain forms of exchange controls.
Due to the arbitrage opportunities created by the difference between the market andthe official exchange rates, exporters and importers have incentives to circumvent exchange
controls by smuggling goods in and out of the country and by under invoicing exports andover invoicing imports. Engaging in smuggling, however, entails a cost, which limits theability of firms to make arbitrage profits from the exchange-rate gap. We show analyticallythat if exchange controls are to affect fiscal revenue both legal and illegal trade must takeplace in equilibrium. In other words, when smuggling costs are so high that illegal tradeis zero or when smuggling costs are so low that legal trade is zero, fiscal revenue ceases tobe affected by the exchange rate gap. Thus, a government wishing to alter its fiscal space
through variations in exchange controls must tolerate some contraband.
In the model, the government faces a tradeoff between financing the fiscal deficit with
inflation or with exchange controls. We consider a benevolent government that maximizes
the welfare of domestic households by choosing paths for inflation and exchange controls.
We compare the outcome of the optimal policy with those of two alternative policy regimes.
In one of these alternative regimes the government does not resort to exchange controls
and finances the fiscal deficit entirely through inflation. In the other alternative regime,
the government minimizes inflation and therefore maximizes fiscal revenues from exchange
controls.
We calibrate the model to the Argentine economy. Over the past two decades, thiscountry has experienced high inflation, persistent fiscal deficits and exchange controls. We
find that under the welfare maximizing policy the government finances two thirds of the
deficit with exchange controls and one third with seignorage revenue. The optimal exchange
control policy favors multiple official exchange rates, with stronger controls on exports thanon imports. If the government is constrained to set the same official exchange rate onexports and imports—perhaps with the intention to comply with the International Monetary
Fund’s (IMF) position against multiple currency practices—the optimal policy finances the
majority of the fiscal deficit through money creation. In this regard, exchange-control regimesthat do not permit the use of different official exchange rates on imports and exports are
inflationary. The reason why the government makes less use of exchange controls in his caseis that exchange controls on imports are highly distorting, as they create a dollar shortage
that forces the economy to operate with an inefficiently low level of imported inputs of2

production.
The paper motivates the use of exchange controls as a way to raise fiscal revenue. It
is therefore natural to discuss empirical evidence supporting this assumption. Dornbusch(1986) reviews macroeconomic aspects of exchange controls and lists their ability to generatefiscal revenue as the first motivation. Kamin (1994), in a case study of exchange controls inArgentina (the economy to which we calibrate the model), points out that governments—
especially those with net foreign currency obligations to the rest of the world (an assumption
maintained in our paper)—gain implicit tax revenues through exchange controls. The IMF
has a “Policy on Multiple Currency Practices (MCPs)”—the official IMF term for exchange
controls—according to which IMF program countries have to ask for approval from the IMF
when implementing exchange controls. The 2022 report on Multiple Currency Practices(IMF, 2022) discusses conditions under which MCPs should be approved. In this context
the report states that countries maintain MCPs to avoid balance of payments problems andto raise revenue by taxing exchange transactions. Both of these motivations concord withthe role that exchange controls play in the present study. And when discussing reasons
why countries are slow to remove exchange controls, the report states “...countries have
faced difficulties in removing such MCPs, reflecting a lack of progress on domestic revenue
mobilization and other fiscal reforms.” Further, the 2019 IMF report on Multiple Currency
Practices (IMF, 2019) contains a discussion of why countries impose exchange controls. The
report cites expansionary fiscal policies, unsustainable macroeconomic policies, and revenue
mobilization. Moreover, it discusses why exchange controls may be adopted instead of moreconventional types of taxation. In this regard the report states that “The use of multiple
rates is preferred over taxation for two main reasons. First, the administration of multiple
rates is easier when compared to the administrative difficulties of direct taxation (export
and import taxes) particularly when state capacity is weak... Second, revenue collection
through multiple rates can be sizable, especially in the near term.” Taken together these
discussions in academic and official IMF policy papers provide compelling evidence that inpractise countries are motivated to use exchange controls for fiscal reasons. Finally, theuse of exchange controls as a fiscal instrument is not a recent phenomenon but goes backa long way. For example, Sherwood (1956) presents empirical evidence of fiscal aspects ofmultiple exchange rate systems for three developing countries, Cuba, the Philippines, andVenezuela, over the period 1951 to 1954 and finds that the fiscal revenue obtained fromexchange controls ranged from 5 percent to 20 percent of total revenue.
To the best of our knowledge the present paper is the first attempt to frame the determination of exchange controls as the outcome of an optimal monetary and fiscal policy problem.
The paper is related to several strands of literature. An early formulation of the functioning3

of a dual exchange-rate system using a non-optimizing framework and adaptive expectations
is Argy and Porter (1972). Flood and Marion (1982) introduce rational expectations into
the framework of Argy and Porter. These papers are primarily concerned with the abilityof a dual exchange rate system vis-à-vis a single exchange rate arrangement to isolate thecountry from domestic and external disturbances.
Closer to the present analysis is Adams and Greenwood (1985) who incorporate a dual
exchange-rate system in a two-period optimizing model with rational expectations. Theseauthors show that the Ramsey optimal policy calls for the Friedman rule (i.e., a zero nominalinterest rate and average inflation equal to minus the real interest rate) and no exchange
rate controls. A key difference with the present study is that these authors assume that the
government can set lump sum taxes endogenously to ensure fiscal solvency independentlyof the monetary or the exchange rate arrangement. In other words, unlike in the present
study, these authors assume that the government need not rely on seignorage revenue or onrevenues from exchange controls to balance the budget. It can be readily shown that theirconclusion would also obtain in our framework were we to add lump-sum taxation as a policy
instrument.
More recently, Mosquera and Sturzenegger (2021) analyze an optimizing model in which
exchange controls act as a tax on exports. They show that because these types of taxes are
distorting, exchange rate controls are welfare reducing. However, Mosquera and Sturzenegger
do not explore the fiscal consequences of exchange controls nor their optimal determination,
both of which are at the core of the present investigation. Espino, Gauna, and Neumeyer(2023) augment a Krugman-style balance of payment crisis model with dual exchange rates
and capital controls to study how these frictions affect the timing of the balance of payments
crisis and the transitional dynamics of expenditure, the exchange rate gap, and interest
rates. Recently, there is work investigating the ability of exchange rate manipulation toachieve goals other than the collection of fiscal revenue. For example, Ottonello, Perez, andWitheridge (2024) present a model in which real exchange rate management can alter acountry’s speed of convergence to the technological frontier. Itskhoki and Mukhin (2023)
show that different sanctions that give rise to the same real allocation can have different
effects on the real exchange rate, so that the exchange rate is not always an appropriate
gauge of the effectiveness of sanctions.
Another body of work to which this paper is related is one that studies optimal monetaryand fiscal policy when the government has access to distortionary taxation in the form oflabor or capital income taxes. One of the questions studied in this literature is under what
conditions the Friedman rule is optimal (Lucas and Stokey, 1983; Chari, Christiano, andKehoe, 1991; Correia, Nicolini, and Teles, 2008; Schmitt-Grohé and Uribe, 2004a,b). In the4present paper, the fiscal instrument available to the government—exchange controls—is also
distortionary, so the problem of the benevolent government can be framed in similar terms
as in this literature. Thus, we contribute to this body of work by characterizing a realistic
environment in which the Friedman rule is not supported as an optimal outcome.
Finally, there are a number of empirical studies that document episodes of dual andmultiple exchange rate practices. Reinhart and Rogoff (2004) present empirical evidence
on observed exchange rate gaps in monthly data for 153 countries from 1946 to 2001. In
addition, they estimate the degree of underinvoicing of exports over this period and findthat underinvoicing was sizeable in countries with dual and parallel exchange rates. Ilzetzki,
Reinhart, and Rogoff (2019) provide the history of multiple exchange rate regimes for 194
countries from 1946 to 2016. Kiguel, Lizondo, and O’Connell (1997) contains a collection ofcase studies of exchange controls in developing countries.
The remainder of the paper proceeds as follows. Section 2 presents the model. Section 3
discusses the calibration and characterizes the equilibrium effects of changes in the exchangerate gap on key macroeconomic indicators of interest. Section 4 analyzes optimal monetaryand exchange control policy. Section 5 concludes.

2

The Model

We study a small economy open to international trade but isolated from international financial markets. The economy produces a nontradable good and an export good. Nontradables
are produced with labor and imported materials, and export goods are produced with imported materials. Money is motivated by a transactions cost on consumption purchases. The
government has a chronic fiscal deficit and owes an external debt on which it pays interest.
It finances these outlays with a combination of seignorage revenue (money creation) andrevenue from exchange controls.

2.1

Households

The economy is populated by a large number of identical households with preferences givenby∞X

β t U(ct , ht),

(1)

t=0

where ct denotes consumption in period t, ht denotes labor supplied in period t, β ∈ (0, 1) isthe subjective discount factor, and U is the period utility function. Labor income is Wt ht,
where Wt denotes the nominal wage rate. The household also receives in a lump-sum fashion5

a government transfer denoted τt and profits from the ownership of firms denoted φt , bothmeasured in units of consumption. Consumption purchases are subject to a proportionaltransactions cost, denoted s(vt), that is increasing in money velocity, vt = Pt ct /Mt , whereMt denotes nominal money holdings and Pt is the price level. Households can trade a purediscount bond denominated in domestic currency, denoted Bt , that pays the interest rate it.
Their sequential budget constraint is then given by[1 + s(vt)]Pt ct + Mt +Bt
= Wtht + Pt (τt + φt) + Mt−1 + Bt−1 .
1 + itLetting at ≡ (Mt + Bt )/Pt denote real private asset holdings, mt ≡ Mt /Pt denote real money
balances, and wt ≡ Wt /Pt the real wage, the budget constraint of the household expressedin units of consumption is given by[1 + s(vt)]ct +

it
at
at−1
mt +
= wt ht + τt + φt +,1 + it1 + it1 + πt(2)where πt ≡ Pt /Pt−1 − 1 denotes price inflation.
The household chooses paths of consumption, labor, money holdings, and asset holdings to maximize the lifetime utility function (1) subject to the budget constraint (2), thedefinition of money velocity
vt =

ct
,
mt

(3)

and to some no-Ponzi-game constraint. The first-order conditions associated with this maximization problem give rise to a money demand function of the form
vt2 s0(vt ) =it,
1 + it(4)

to the labor supply schedule−

U2(ct , ht )wt=,
U1(ct , ht )1 + s(vt) + vt s0(vt )and to the Euler equation
λt = β(1 + it )
where
λt =

λt+1
,
1 + πt+1(5)(6)

U1 (ct, ht )1 + s(vt ) + vts0 (vt)denotes the marginal utility of wealth. Under the assumption that v 2s0(v) is increasing inv, the optimality condition (4) implies that the demand for real money holdings, mt , is6

decreasing in the interest rate and proportional to consumption. In addition to generating
resource losses (shoe leather costs), the transactions cost distorts the marginal rate of substitution between consumption and leisure in favor of the latter (optimality condition (5)).
This distortion is increasing in the nominal interest rate it. Changes in the interest rate also
distort the intertemporal allocation of consumption (optimality condition (6)).

2.2

Firms

Suppose that there is a representative firm that produces a nontradable consumption good
and an exportable good. Output of the nontradable consumption good is produced using
as inputs labor, ht , and imported materials, qtn. The production technology is of the form
F (ht, qtn ). The exportable good is produced with imported materials, denoted qtx, using thetechnology X(qtx ). Both production functions, F (·, ·) and X(·), are assumed to be positive,
increasing, and concave.
The world price of imported materials is assumed to be constant and equal to one unitof the foreign currency, and the world price of the exported good in terms of imported
materials (the external terms of trade), denoted pxt , is assumed to be exogenously given. Let
Et denote the market nominal exchange rate and Eto the official nominal exchange rate set by
the government. Both exchange rates are defined as the domestic-currency price of one unitof foreign currency, so that an increase in Et or Eto represents a depreciation of the domestic
currency.
Firms are required to sell to the government the foreign currency generated by exports
in exchange for domestic currency at the official exchange rate Eto . We refer to this typeof exports as official exports and denote them xot . Similarly, firms are obliged to acquirefrom the government the foreign currency needed to buy imported materials. We refer tothis type of imports as official imports and denote them qto. The government sells foreign
currency at the official exchange rate Eto to firms that wish to import. This exchange rateis in general cheaper than the market rate, Et , so the government rations its quantity at thelevel q̄to , which the firm takes as given. Here we focus on the case in which exchange controls
are applied equally to imports and exports, that is, the case in which there is a single official
exchange rate. Section 4.3 considers the case in which the government can apply different
official exchange rates on imports and exports.
It is illegal to export or import goods outside of the official channel. However, firms
can circumvent exchange rate controls by smuggling. This assumption is motivated by thefact that in countries with exchange controls contraband is typically observed. Section 3.1
provides some evidence from the economy to which the model is calibrated. Let xst and qts

7denote the amount of smuggled exports and imports. Smuggling carries a cost C(xst , κx) andC(qts, κq ) measured in units of consumption, where κx and κq are parameters representing
the strength of barriers to smuggling such as the degree of enforcement of contraband laws.
The function C(·, ·) is assumed to be positive, convex in its first argument, and to satisfy
C(0, ·) = 0 and C2 > 0.
Then, letting φt denote profits of the firm expressed in units of the consumption good,
we have thatEto x oEtnφt = F (ht, qt ) + (pt xt − qto ) + (pxt xst − qts) − wt ht − C(qts, κq ) − C(xst, κx ).
Pt
Pt

(7)

A positive value of xst can be interpreted as under invoicing of exports to customs authorities.
A negative value of xst represents over invoicing of exports. Clearly, as long as Eto < Et , itwill not pay for the firm to over invoice exports as it would result in an avoidable loss. A
positive value of qts represents under invoicing of imports and a negative value represents overinvoicing of imports. As we will see, both under and over invoicing of imports are possible
in equilibrium. In particular, under invoicing of imports may arise in equilibrium even if
Eto < Et because of rationing of foreign exchange at the official rate.
The firm chooses xst , xot , qts , qto, qtn , qtx, and ht to maximize (7), subject to
qtn + qtx = qto + qts,

(8)

xot + xst = X(qtx),(9)

qto ≤ q̄to ,(10)

xot ≥ 0.

(11)

and

The firm takes the upper bound q̄to on official imports as given, but, as will be clear shortly,q̄to is endogenously determined in equilibrium, which introduces an externality. The nonnegativity constraint (11) states that the government does not allow firms to import theexportable good at the subsidized official exchange rate Eto . Let
γt ≡

Et
−1
Eto

denote the gap between the market exchange rate and the official exchange rate. We will

8

refer to γt as the exchange rate gap.1 Let
Et
.
Pt

et =

Absent exchange controls, et represents the real exchange rate, that is, the relative price of
the imported good in terms of the nontraded good. However, as we will discuss in section 2.5,in the presence of exchange controls firms perceive a different real exchange rate.
Using these definitions to eliminate Et and Eto and equations (8) and (9) to eliminate qtn
and xot from (7) and (11), the firm’s problem consists in choosing ht , qtx, qts, xst , and qto to
maximize
F (ht, qto +qts −qtx)+et[px (X(qtx )−xst)−qto]+et(pxt xst −qts )−wtht −C(qts, κq )−C(xst, κx) (12)
1 + γt t

subject to (10) andX(qtx ) − xst ≥ 0.

(13)

Letting µqt and µxt denote the Lagrange multipliers associated with (10) and (13), the firstorder conditions with respect to ht , qtx, qts , qto, and xst , respectively, are
F1 (ht, qto + qts − qtx) = wt,
F2(ht , qto + qts − qtx ) =




etpxt
x
+ µt X 0 (qtx),
1 + γt(14)(15)

F2(ht , qto + qts − qtx ) = et + C 0(qts , κq ),

(16)

et
+ µqt ,
1 + γt(17)

et pxt+ µxt = etpxt − C 0(xst , κx),
1 + γt(18)

F2(ht , qto + qts − qtx) =and the nonnegativity and complementary slackness conditionsµqt ≥ 0,(19)µxt ≥ 0,(20)

µqt (q̄to − qto) = 0,(21)µxt [X(qtx) − xst ] = 0.

(22)

and
1

In the related literature, the exchange rate gap is also referred to as the “parallel market premium.”9

Optimality condition (14) is a demand for labor. Equation (15) says that the value of themarginal product of imported materials must be the same in the nontraded sector and theexport sector. Optimality condition (16) says that in producing nontradable goods the firm
equates the marginal product of the imported input to the marginal cost of smuggling it,
which is the sum of the market real exchange rate, et, and the marginal smuggling cost,
C 0(qts , κq ). Condition (17) says that if the import constraint is not binding (µqt = 0), thenthe firm equates the marginal product of imported materials in producing nontradables tothe marginal cost of imported materials through the legal market. When the firm’s legal
imports are rationed (µqt > 0), the shadow marginal cost of importing materials throughthe legal market is larger than the official marginal cost. Finally, when the nonnegativity
constraint on official exports is not binding (µxt = 0), condition (18) says that at the margin,
the firm is indifferent between exporting through the official market or through contraband.

2.3

The Government

The government prints money, Mt , issues discount bonds denominated in domestic currency,
Bt , and in foreign currency, Bt∗, and makes transfers, τt . It also collects resources from theimposition of exchange controls. Its sequential budget constraint is then given byBt
Et Bt∗∗Mt +++ (Et − Eto )(pxt xot − qto ) = Pt τt + Mt−1 + Bt−1 + Et Bt−1,∗
1 + it 1 + it
where i∗t denotes the interest rate paid by the government on its external debt and is assumed
to be exogenously determined. The left-hand side represents the government’s sources offunds and includes revenues from exchange rate controls. The right-hand side represents thegovernment’s uses of funds. Dividing the above expression through by the price level, Pt ,and recalling the definition at ≡ (Mt + Bt)/Pt , the sequential budget constraint expressed inunits of consumption is given byitat
et Bt∗
etγt x o
at−1
∗
mt +
+
+
(pt xt − qto) = τt ++ et Bt−1.
∗
1 + it1 + it 1 + it
1 + γt1 + πt(23)

The last term on the left-hand side represents the fiscal surplus generated by taxing theofficial trade balance with the exchange-rate gap. We denote this source of fiscal revenue by
st ,
st ≡

γt
et(pxt xot − qto ).
1 + γt(24)

Given our focus on the case of a positive exchange-rate gap, γt > 0, it is clear from thisexpression that if the government is to generate any direct fiscal revenue from exchange
10controls, it must ensure a positive official trade balance, pxt xot − qto > 0. In equilibrium,
exchange controls can also affect the government’s finances indirectly through their effects
on endogenous variables such as the external real exchange rate, et, and real balances, mt.
For simplicity, we assume that the bond denominated in domestic currency trades onlyin the domestic market and that the bond denominated in foreign currency trades only in
the international market. Furthermore, we have in mind a government that is financially
isolated from the international capital market. The government makes interest payments
to the rest of the world, but cannot change its external debt position endogenously—tosmooth transitory disturbances, say. Specifically, we set Bt∗ = B ∗ , where B ∗ is a positive
constant. Thus, net international interest payments expressed in units of the imported good,i∗t B ∗ /(1 + i∗t ), are exogenously given.
Iterating the government’s budget constraint (23) forward, using (24) to replace et γt /(1+γt )(pxt xot − qto ), and using the household’s transversality condition, we can write
it B
it
∞
X
mt + st − τt − et 1+i
∗
a−1
1+it
t
=
.
Qt−1 1+is
1 + π0s=0 1+π
t=0
∗

∗

(25)

s+1

In the numerator on the right-hand side, the first term is seignorage revenue. The second
term is the amount of resources the government extracts from the private sector throughexchange controls. The third term is the primary fiscal deficit, and the last term is net
international interest payments in units of consumption goods. Thus, equation (25) says thatthe government’s initial domestic real liabilities, a−1 /(1 + π0), must be backed by the present
discounted value of primary fiscal surpluses plus seignorage revenue and resources fromexchange controls, net of international interest payments. We assume that the government
starts with a liability position, a−1 > 0.
As explained earlier, we assume that the government provides foreign exchange to importers at the official exchange rate Eto . However, the government limits the amount offoreign exchange importers can buy at the official exchange rate, which may necessitate rationing. We make this assumption because rationing is an ubiquitous feature of exchange
control regimes in general (Dornbusch, 1986) and in particular of the existing arrangementin Argentina, the economy on which we base the calibration of the model. Since direct fiscal
revenue from a positive exchange-rate gap, st , is positive only if the official trade balance,
pxt xot −qto , is in surplus, we assume that the amount of foreign exchange the government offers
to importers must be smaller than official exports. Specifically, we assume that the government imposes the following upper bound on purchases of foreign exchange at the official

11

rate:q̄to = (1 − ρt )pxt xot ,(26)

with 0 < 1 − ρt < 1. The higher ρt is, the more restricted legal imports will be. Absent
restriction (26), there are no guarantees that the official trade balance, pxt xot − qto , will bepositive. In other words, constraint (26) ensures that the government, if it wishes, will
be able to collect resources from taxing official net exports when the exchange-rate gap ispositive.
The government uses ρt as a policy instrument. Note that firms take q̄to as exogenously
given, but that in equilibrium it is endogenously determined. This feature introduces anexternality into the model because firms do not internalize that by exporting more they
could relax the import restrictions and buy more foreign exchange at the subsidized rate
Eto . Firms understand that their collective exports raise the import limit q̄to , but they also
understand that individually they are too small to affect it.
Finally, we have in mind a situation of a country that is unable or unwilling to eliminate
chronic primary fiscal deficits. Thus, we will assume that the path of primary fiscal deficits,
τt , is exogenously given. It follows that the government has three policy instruments at hand:the domestic interest rate it, the exchange rate gap γt , and import restrictions ρt . Becauseof its intertemporal budget constraint, the government can pick freely the paths of only twoof these three instruments.

2.4

Equilibrium

In equilibrium the market for nontradable goods must clear. Formally,[1 + s(vt )]ct + C(qts, κq ) + C(xst , κx ) = F (ht, qtn ).

(27)

Combining the budget constraint of the household (equation (2)), the budget constraintof the government (equation (23)), the definition of profits (equation (12)), and the market
clearing condition in the nontraded sector (equation (27)) yields
pxt (xot + xst ) − (qto + qts ) −i∗t B ∗
= 0,
1 + i∗t(28)

which says that because the country is financially isolated from the rest of the world, its
current account is nil up to changes in the external interest rate i∗t .2
Conditions (3)-(5), (8)-(11), (14)-(22), (24), and (26)-(28) represent a static system of 16
2

The current account is given by [1/(1 + i∗t−1 ) − 1/(1 + i∗t )]B ∗ , which vanishes only when i∗t = i∗t−1 .

12equations and 4 inequalities in the 16 endogenous variables vt , ct , mt, ht , wt , qtn , qtx, qto , qts,
xot , xst , q̄to , st, µqt , µxt , and et, given policy variables γt , ρt , and it, and exogenous variables pxt ,i∗t , and τt . This static system can be solved for the equilibrium values of the 16 endogenous
variables as functions of the policy variables and the exogenous shocks. We summarize thisresult in the following proposition:
Proposition 1 (Partial Equilibrium) Letting
ηt =hγt ρt it

i

ηt∗ =

h

pxt i∗t τtibe the policy vector andthe vector of exogenous shocks, then in equilibrium the 16 endogenous variables vt, ct , mt,
ht , wt, qtn , qtx, qto, qts , xot , xst , q̄to, st , µqt , µxt , and et are the solution to the static system of 16
equations and 4 inequalities given by (3)-(5), (8)-(11), (14)-(22), (24), and (26)-(28) and canbe expressed as functions of ηt and ηt∗ . Thus, if xt is any of the aforementioned endogenous
variables, then one can write
xt = x(ηt , ηt∗).
The policy variables γt , ρt , and it in the policy vector ηt are not independent of one anotherin equilibrium because the intertemporal equilibrium conditions of the model must also besatisfied. Specifically, the intertemporal budget constraint of the government (equation (25))
and the Euler equation (6) introduce a restriction on the equilibrium path of the policy vector
ηt . Combining these two equations and letting θt ≡ 1 + s(vt) + vts0 (vt) denote the distortionin the consumption leisure decision of the household introduced by inflation, a competitive
equilibrium can be defined as follows:
Definition 1 (Competitive Equilibrium) A competitive equilibrium is a scalar π0 and asequence of policy variables ηt ≡ [γt ρt it ]0 for t ≥ 0 satisfying


∞
∗
∗
∗
∗
∗ ∗
X
a−1
t U1 (c(ηt , ηt ), h(ηt , ηt ))θ(η0 , η0 ) it m(ηt , ηt )∗∗ it B=β+ s(ηt , ηt ) − τt − e(ηt, ηt )
,
∗
∗
∗
∗
1 + π0
U
(c(η
,
η
),
h(η
,
η
))θ(η
,
η
)
1
+
i
1
+
i
1
0
0
t
t
t
t
0
0
t=0
(29)
and
it ≥ 0,given the initial stock of real government liabilities a−1 > 0 and the sequence of exogenous
shocks ηt∗ ≡ [pxt i∗t τt ]0 , for t ≥ 0.
13

2.5

Exchange Controls and Competitiveness: Internal and External Relative Prices

In the presence of exchange controls, there are two real exchange rates, an external one andan internal one. The external real exchange rate, et ≡ Et /Pt , is the relative price of theimported good in terms of the nontraded good using the market exchange rate to convert
foreign currency prices into domestic currency prices (recall that the foreign currency priceof the imported good is assumed to be one). The external real exchange rate is economically
relevant because it affects the cost of servicing the government’s external debt in terms of
nontradables, eti∗t B ∗/(1 + i∗t ), see equilibrium condition (29). However, the external realexchange rate is not economically relevant for domestic firms in the presence of exchange
controls. The reason is that firms cannot purchase the imported good at the price Et without
having to pay a smuggling cost. The internal real exchange rate takes this distortion into
account. It is defined as the relative price of the import good in terms of the nontraded goodin the domestic market. The price of imports inside the country is Et +Pt C 0(qts , κq ). This is so
because the imported good is not always available for purchase at the official exchange rate
(Eto ), but is always available through smuggling, which requires paying the market exchange
rate (Et ) plus the marginal cost of smuggling (Pt C 0(qts , κq )). Thus the internal real exchange
rate is given by [Et + Pt C 0 (qts, κq )]/Pt , which can be written as
internal real exchange rate = et + C 0(qts , κq ).

(30)

In words, the internal real exchange rate equals the external real exchange rate adjusted by
the marginal contraband cost. The economic relevance of the internal real exchange rate forthe firm is reflected in optimality condition (16), which says that firms equate the marginal
product of imported materials in the production of nontradable goods to the internal realexchange rate.
Exchange rate controls distort not only the real exchange rate but also the terms of trade.
The external terms of trade, pxt , is the relative price of the exported good in terms of theimported good in world markets. The small open economy takes the external terms of trade
as exogenously given. However, internally, producers of export goods perceive a different
relative price. The internal nominal price of the exported good is Eto pxt and the internal
nominal price of the imported good is Et + Pt C 0(qts , κq ). Taking the ratio of these two prices,
the internal terms of trade can be written as
internal terms of trade = pxt

14

et
.
(1 + γt )(et + C 0 (qts, κq ))In the absence of exchange controls (γt = ρt = 0) the internal terms of trade are equal tothe external terms of trade because smuggling and hence marginal smuggling costs are zero
(qts = C 0 (qts, κq ) = 0). Consider now the case of exchange controls (γt > 0). Using optimality
conditions (16) and (17) to eliminate et + C 0(qts , κq ) from the definition of the internal termsof trade given above, we can writeinternal terms of trade = pxt

et
1+γt

.
et
+ µqt
1+γt

It is clear from this expression that the internal and external terms of trade are equal toeach other if the import constraint (10) is slack (µqt = 0). On the other hand, when thisconstraint binds (µqt > 0), exchange controls deteriorate the internal terms of trade.
We conclude that exchange controls worsen the perceived competitiveness of the economy
from the point of view of both the producers of nontradable goods (the internal real exchange
rate depreciates) and the producers of export goods (the internal terms of trade deteriorate).

2.6

The Necessity of Legal and Illegal Trade

In this section we show that for exchange-rate controls to matter as a fiscal instrument (i.e.,
to be a useful vehicle to generate income for the government) it is essential that smuggling
be costly but not prohibitively so. In other words, if the government is to affect the fiscal
space through changes in the exchange-rate gap, contraband laws must be strict enoughto guarantee some legal trade but also weak enough to guarantee some illegal trade. To
show that both legal and illegal trade are necessary for the exchange-rate gap to be fiscally
relevant, we consider two polar cases. In one case, contraband laws are so strict that allinternational trade occurs through the legal channel. In the other case, contraband laws are
so lax that all international trade occurs through the illegal channel. We show that in bothcases changes in the exchange-rate gap do not affect the fiscal space in equilibrium.
2.6.1

The Necessity of Illegal Trade

Consider first the case of strict enforcement of contraband laws. Specifically, assume that
C(x, κ) = ∞, ∀x 6= 0. In this case, the firm chooses not to smuggle goods in or out of thecountry, that is,xst = qts = 0.

15

The resource constraint for tradable goods (28) then implies that the official trade balance,
which now equals the overall trade balance, must satisfy
pxt xot − qto =i∗t B ∗.
1 + i∗tUsing this expression and the definition of st given in (24) to eliminate the official tradebalance from the equilibrium intertemporal budget constraint of the government (29) yields



∞
X
U1(c(ηt , ηt∗ ), h(ηt, ηt∗ ))θ(η0 , η0∗) it m(ηt, ηt∗)e(ηt , ηt∗) i∗t B ∗
a−1
t
=
β
− τt −.
1 + π0U1 (c(η0 , η0∗), h(η0 , η0∗))θ(ηt , ηt∗ )1 + it1 + γt 1 + i∗tt=0This expression says that the exchange-rate gap, γt , has fiscal consequences only if it affects
the equilibrium values of et/(1 + γt ), mt, ct, ht , or vt . However, it turns out that, when
exchange controls are strictly enforced, these variables are independent of γt . To see this,note that in this case the objective function of the firm, given in (12), becomes
F (ht, qto − qtx ) +et[px X(qtx ) − qto] − wt ht,
1 + γt t(31)

which depends on et/(1 + γt ) but not on γt or et separately. The constraints of the firm—
which under strict enforcement of contraband laws become qto ≤ q̄to and X(qtx ) ≥ 0—featureneither et nor γt . Thus, the optimality conditions of the firm depend on et/(1 + γt ), wt, andq̄to , but, again, not on et or γt separately. Further, neither et nor γt appear in the resource
constraint for tradables (28), the resource constraint for nontradables (27), the demand formoney (4), the supply of labor (5), or the definition of q̄to given in (26). It follows that theequilibrium values of vt , ct , mt, ht, wt, qtn , qtx , xot , q̄to , and et/(1 + γt ) are independent of
the exchange-rate gap γt . This implies that when exchange controls are strictly enforced,changes in the exchange-rate gap, γt , do not affect the fiscal space. We summarize this resultin the following proposition:
Proposition 2 (Necessity of Illegal Trade) If anti-contraband laws are strictly enforced(C(x, κ) = ∞ for all x 6= 0), then in equilibrium government revenue, it /(1+ it )mt + st − τt −eti∗t B ∗/(1 + i∗t ), and the real allocation, ct , ht , and vt, are independent of the exchange-rate
gap γt .
The intuition behind Proposition 2 is that if contraband costs are prohibitively high, thenthere is no black market in which the government could sell the foreign currency it confiscatesfrom exporters. As a result, the government cannot profit from exchange controls.

16

2.6.2The Necessity of Legal Trade

Suppose that C(x, κ) = 0 for all x. Then, if γt > 0, no exports will be channeled throughthe legal market,
xot = 0.
On the other hand, the firm will desire to channel all imports through the official market, where the exchange rate is subsidized. However, because the upper bound on official
imports imposed by the government, q̄to = (1 − ρt )pxt xot, is proportional to official exports(equation (26)), we have that official imports must be nonpositive, qto ≤ 0. But official imports can never be negative when γt > 0, because it would imply that the firm buys imported
materials in the illegal market at et and sells them in the legal market at et/(1 + γt ) < et,making an avoidable loss. Formally, this can be seen by combining optimality conditions (16)and (17), which implies that µqt > 0 when γt ≥ 0 and C 0(·, ·) = 0. In turn, by the slackness
condition (21), µqt > 0 and the fact that q̄to = 0 imply that
qto = 0.
Since the official trade balance, pxt xot − qto , is zero, so is the amount of direct revenue fromexchange controls collected by the government, st (see equation (24)). It remains to show thatby changing γt the government cannot collect resources indirectly by altering the equilibrium
values of the variables that enter in its equilibrium intertemporal budget constraint (29),namely, ct , ht , vt, mt, and et . By optimality conditions (15), (16), and (18), we have that
pxt X 0 (qtx ) = 1, which pins down qtx independently of γt . In turn, the resource constraint for
tradables (28) determines qtn also independently of γt . Now, by (4), vt depends only on thepolicy variable it . Then, equilibrium conditions (5), (14), and (27) represent a system of threeequations in three unknowns, ct , ht , and wt , that is independent of γt . Finally, optimality
condition (16) determines et , again, independently of γt . This completes the demonstrationthat if the government fails to enforce contraband laws, then exchange-rate controls do notserve as a fiscal instrument. We summarize this result in the following proposition:
Proposition 3 (Necessity of Legal Trade) If anti-contraband laws are not enforced (C(x, κ) =0 for all x), then in equilibrium government revenue, it/(1 + it )mt + st − τt − et i∗t B ∗/(1 + i∗t ),and the real allocation, ct , ht , and vt, are independent of the exchange-rate gap γt .
The intuition behind Proposition 3 is that if smuggling is costless, then no trade occurs
at the official exchange rate, so, the government cannot confiscate any foreign currency.

17

3

Quantitative Analysis

Section 2.6 shows that in the extreme cases of strict enforcement of contraband laws and noenforcement of such laws, changes in the exchange-rate gap γt do not affect fiscal revenue.
In fact, in those extreme cases the entire real allocation is independent of γt . In this section,
we consider the intermediate case in which there is some enforcement of contraband lawsthat results in an equilibrium in which international trade occurs both through the legal andillegal markets. We discipline the cost of smuggling by requiring that the model replicate
aspects of international trade observed in an actual economy with exchange controls.

3.1

Calibration

Table 1 displays the calibrated parameters. The time unit is a quarter. Variables without atime subscript denote steady-state values.
We calibrate the policy parameters of the model to the Argentine economy during theperiod 2007 to 2021. This period includes two episodes of exchange controls, known as
cepos cambiarios. The first cepo cambiario lasted from October 2011 to December 2015and had an average exchange rate gap of 45 percent. The second cepo cambiario started in
September 2019 and was still in effect at the end of the sample, with an average exchangerate gap of 72 percent. We start the calibration period in 2007 because this year marks the
beginning of the administration during which the first spell of exchange rate controls was
implemented. During much of the calibration sample, the cepos cambiarios specified a single
official exchange rate for imports and exports, which coexisted with a market-determined
parallel exchange rate. The domestic currency was always more depreciated in the parallelmarket than in the official market, Et > Eto , implying a non-zero exchange-rate gap, γt > 0.
We set the steady-state value of the exchange-rate gap at 23 percent, γ = 0.23. Thisvalue is the average exchange rate gap observed in Argentina during the calibration period(January 2007 to December 2021). Drawing on the empirical estimate of the interest rate
faced by Argentina in international capital markets presented in Schmitt-Grohé and Uribe(2016), we set i∗ to 13 percent per year (i∗ = 1.131/4 − 1).
We assume that the production technologies of nontradable and exportable goods are of
the form
F (h, q n) = An hαh (q n )αnandX(q x) = Ax(q x )αx .
We normalize An and Ax to unity. Following Uribe (1997), we set αh to 0.75. This value
18

Table 1: Calibration
Calibrated Parameters
γ0.23
β1.04−1/4
Ax , An1αx , αn
0.15
αh
0.75
σ
2
χ1
0.5
i∗
1.131/4 − 1px
1
Estimated Parameters
A
0.80
B
1.95
D
1.77
Implied Parametersρ
0.088
κq , κx
0.71
χ0
0.82
∗
B
3.29
a
1.81
τ
0.0183δ
0.03
Targeted Moments
epx xo0.17
yeB ∗ /(1+i∗ )0.22
4ye(px xo −q o )
0.015
y
τ
0.02
y
π
1.311/4 − 1b0.38
4y(1+i)h
1Exchange-rate gap, γ = E/E o − 1
Subjective discount factor
Level of technology in the nontraded and export sectors
Import elasticity of output in the nontradable and export sectors
Labor elasticity of nontraded output
Inverse of the intertemporal elasticity of substitution
Inverse of the Frisch elasticity of labor supply
External interest rate
External terms of trade
Parameter of transactions cost function
Parameter of transactions cost function
Parameter of transactions cost function
Import limit at the official exchange rate, q o ≤ (1 − ρ)px xo
Parameter of the smuggling cost function, C(x, κ) = (κ/2)x2
Preference parameter
External public debt
Total domestic government liabilities, a = m + b
Primary fiscal deficit
Off-the-books government revenue
Recorded exports to output ratio
Share of foreign government liabilities in output
Recorded trade balance to output ratio
Fiscal deficit to output ratio
CPI inflation rate
Ratio of domestic government debt to annual output
Steady state value of hours

Notes. The time unit is a quarter. The variable y ≡ (1 + s(v))c + e(px xo − q o ) denotes steady-state
recorded real output.

19implies a share of labor in nontraded gross output of 75 percent. Based on the crosscountry evidence on the average share of imported inputs in domestic production presented
in Gopinath, Itskhoki, and Rigobon (2007), we set αn = αx = 0.15. We normalize the steadystate of the external terms of trade to one, px = 1.
We assume a period utility function of the formU(c, h) =c1−σ − 1
h1+χ1
− χ0
.
1−σ
1 + χ1

We set σ = 2, which is a standard value for the inverse of the intertemporal elasticity of
consumption substitution in business-cycle analysis. We set χ1 equal to 1/2. This value
implies a Frisch elasticity of labor supply of 2, which is commonly used in the calibration of
open-economy business-cycle models (Mendoza, 1991). The parameter χ0 is a scaler, which
determines the steady-state value of hours worked. As explained below, we set it to ensurethat in the steady state hours are normalized to 1. The implied value is 0.82. The subjective
discount rate is assumed to be 4 percent per year, β = 1.04−1/4 .
We propose a transactions cost function of the form
1+B
A − Dv.
s(v) =
1+B(32)

This functional form ensures that the demand for money has the following three properties:(i) a satiation point (i.e., a finite demand for money at a zero nominal interest rate); (ii) a
Laffer curve for the inflation tax (i.e., an inverse-U shape for the relationship between inflation and seignorage income); and (iii) a unit income elasticity. These features are desirable
because we estimate the demand for money over a period in which Argentina experienced
wildly different inflation outcomes ranging from hyperinflation (1989 to 1991) to deflation(1998 to 2001). If the demand for money does not satisfy (i), then seignorage revenue couldigrow unboundedly as the interest rate approaches zero ( 1+im → ∞ as i → 0). Similarly, if
the demand for money does not satisfy (ii), then seignorage revenue could become arbitrarilyim → ∞ as i → ∞).
large as the interest rate becomes large ( 1+i

The transactions cost function (32) implies a demand for money of the form
"

A
1
m=c
−
D D



i
D(1 + i) B1 #,(33)

which is essentially a power function with an intercept. This demand for money gives rise
AB B
to a Laffer curve for seignorage revenue, i/(1 + i)m, with a peak at i/(1 + i) = D 1+B.

At the Friedman rule, i = 0, the demand for money is finite and equal to cA/D.
20

We estimate the parameters A, B, and D on Argentine data over the period 1960 to
2021 using nonlinear least squares. The estimation includes a dummy for the period 1991
to 2001 during which the Argentine peso was convertible to dollars at a one-to-one rate.
During the convertibility period the money-to-output ratio experienced a significant discrete
fall of about 45 percent in spite of the inflation rate being at the lowest level in the sample.3
The reason why real balances were low during this period is that the government lifted
restrictions on the use of the dollar as a medium of exchange, as a store of value, and as aunit of account, which led to widespread currency substitution. These restrictions were later
reinstituted.
There is no reliable quarterly data on consumption and nominal interest rates for Argentina over long time spans. For this reason, we use annual data, GDP as a proxy for
consumption, and CPI inflation as a proxy for the nominal interest rate. Specifically, theproxy for the nominal interest rate is inflation plus a constant riskless annual real interest
rate of 4 percent. Data on the money base is taken from the Central Bank of Argentina.
The source for nominal GDP is Kehoe and Nicolini (2021) for the period 1960 to 2017 andthe Ministry of the Economy of Argentina for the period 2017 to 2021. The source for CPI
inflation is the price index produced by Instituto Nacional de Estadı́stica y Censos (INDEC),
the government statistical office in charge of producing the Argentine consumer price index,
except for the period 2007 to 2016, for which the source is Cavallo and Bertolotto (2016).
The Cavallo-Bertolotto CPI index controls for the fact that for much of the period 2007
to 2016 INDEC underreported inflation figures.4 The parameter estimates are A = 0.80,
B = 1.95, and D = 1.77.5
Figure 1 displays the implied money demand function and the associated Laffer curvefor seignorage income. At the average inflation rate of 31 percent per year observed overthe calibration period, the money demand function implies a money-to-output ratio of 8.6
percent per year. The peak of the Laffer curve occurs at a quarterly interest rate of 106
percent. Given the assumed discount rate of 4 percent per annum, at the peak of the Laffer
curve the monthly inflation rate is 27 percent. With this inflation rate, the government
collects 7.9 percent of GDP in seignorage revenue.
We assume that in the steady state the inflation rate is 31 percent per year, π = 1.311/4 −1.
This value corresponds to average CPI inflation observed in Argentina over the calibration
period for policy variables, 2007 to 2021. By the Euler equation (6), the steady-state domestic
nominal interest rate, i, satisfies i = (1 + π)/β − 1. Given the assumed values of β and π,
3

Controlling for inflation, the fall in real money holdings during the convertibility period was 72 percent.
We thank Emilio Zaratiegui for sharing this data.
5
These parameter values are expressed in a form compatible with a demand for money observed at aquarterly frequency, so they can be used directly in the calibration of the model.
421Figure 1: Estimated Money Demand Function and Laffer Curve: Argentina 1960 to 2021

0.8
10
0.6
0.4

5

0.2
0

0
0

0.1

0.2

0.3

0.4

0

0.2

0.4

0.6

0.8

1

Notes. The notation is m = real money balances, y = real quarterly GDP, and i = quarterly nominalinterest rate. Dots and stars represent, respectively, data outside and during the convertibility
period (1991 to 2001). Solid lines represent the estimated money demand function (left) and the
Laffer curve (right). Seignorage is defined as i/(1 + i)m/y. The money demand function has theform given in equation (33). The estimated parameter values are shown in Table 1.

the implied steady-state nominal interest rate is 36 percent per year, or i = 0.08.
We assume that the smuggling cost function is the same in the export and import sectors,
κq = κx = κ, and adopt a quadratic functional formC(z, κ) =

κ 2
z ,
2

(34)

for z = q s, xs . Government detection and sanctioning of smuggling activity is regularly
reported in the press during spells of exchange controls.6 We adopt an indirect inference
approach to estimate the parameter κ. In essence, the strategy to identify κ consists incomparing the recorded trade balance and the country’s observed interest payments on ex6

For example, on February 12, 2023, Cları́n, one of the main newspapers of Argentina, reported thegovernment’s uncovering of an export under invoicing scheme involving 20 slaughterhouses. The strategy
consisted in channeling meat exports through traders located in a third country (Cyprus, Uruguay, and theUnited States). These middlemen added no value added, but would simply buy meat from the slaughterhouses at a below-market price and then re-export it to other countries (including China, Chile, and Brazil)
with a markup of about 30 percent. The profit, denominated in hard currency, would then be depositedin banks outside Argentina in accounts owned by the involved slaughterhouses, thereby avoiding having torender the foreign exchange at the central bank. In the same article, Cları́n reports another under invoicing
strategy consisting in exporting regular beef (class C) as canner beef (class D or E). The price difference isagain deposited outside Argentina, avoiding conversion to domestic currency at the official exchange rate by
the central bank.

22

ternal debt. The difference between these two figures is the smuggling trade balance. The
value of κ is picked to induce the required smuggling trade balance as an equilibrium outcome. Formally, we jointly calibrate κ, B ∗, ρ, and χ0 by simulated method of moments.
The targeted moments are: (a) An official trade balance to output ratio of 1.5 percent,e(px xo − q o )/y = 0.015, where y ≡ c[1 + s(v)] + e[px xo − q o ] denotes output. This matches
the recorded average value observed in Argentina over the calibration period. The data
source is the IMF’s International Financial Statistics (IFS). (b) A net external debt of thegovernment of 22 percent of annual GDP, eB ∗/(1 + i∗)/(4y) = 0.22. This figure represents
the average value of the Argentine government’s debt with external creditors as a fractionof GDP over the calibration period. The data source is the Argentine Ministry of the Economy. (c) Official exports equal 17 percent of output, epx xo /y = 0.17. This figure matches
the corresponding observed value in Argentina over the calibration period. The source is
IFS. And (d) an average level of hours of 1, h = 1.
Over the calibration period, the average primary fiscal deficit in Argentina was 2 percent
of GDP, τ /y = 0.02, and the average domestic government debt was 38 percent of GDP,[(a − m)/(1 + i)]/(4y) = 0.38. The data sources are IMF Fiscal Monitor and Argentine
Ministry of the Economy, respectively.
The above calibration of the model provides values for all components of the government’s
budget constraint (29) in the steady state: seignorage (i/(1 + i)m), revenue from exchange
controls (s), the primary fiscal deficit (τ ), interest payments on external debt (ei∗B ∗ /(1+i∗ )),and total domestic government liabilities (a). As discussed in Kehoe, Nicolini, and Sargent(2021), in general, these numbers need not exactly satisfy the government budget constraint.
The reasons why in general the government budget constraint will not be satisfied at thecalibrated values include: (a) Argentina may not have been at exactly a steady state during
the calibration period; (b) the different components of the budget constraint were takenfrom independent sources; and (c) the model does not allow for default or confiscation offinancial assets, which is a recurrent phenomenon in Argentina. To circumvent this issue,
we follow Kehoe, Nicolini, and Sargent and introduce a residual, denoted δ, to ensure thatthe government budget constraint is satisfied in the steady state. Thus, the steady-state
government budget constraint becomesaβ −1 − 1ii∗ B ∗=m(η, η ∗) + s(η, η ∗) − τ − e(η, η ∗)
+ δ,
1+i
1+i
1 + i∗(35)

where we used the Euler equation (6) evaluated at the steady state to replace π0 by β(1+i)−1.
The resulting value of δ is 0.03. We keep this value constant for the remainder of the paper.

23

Table 2: Exchange Controls and Changes in the Fiscal Space

γ
0
1
2
3
4
5

0
0
0.3
0.4
0.4
0.4
0.3

ρ
0.5
1.4
3.1
3.2
3.2
3.0
2.8

1
2.3
3.9
4.5
4.8
4.9
4.8

Notes. Changes in the fiscal space are measured in percent of GDP and relative to the caseγ = ρ = 0. The interest rate is kept constant at its baseline value.

3.2

Fiscal Effects of Exchange Controls

Exchange controls affect the fiscal deficit through two channels. First, the exchange-rate
gap γ represents a tax on official net exports px xo − q o. Second, if the government has
obligations denominated in units of tradables and in units of nontradables, then by affecting
the real exchange rate e, exchange controls can alter the real value of the fiscal deficit. In thepresent model the primary deficit τ is a stream of nontradable goods, whereas interest on
the external debt i∗B ∗ /(1 + i∗ ) and revenues from the exchange rate gap γ/(1 + γ)(px xo − q o)are streams of tradable goods. Movements in the real exchange rate change the relative
importance of these components of the fiscal deficit. Thus, exchange controls are not just a
tax on net exports but may also create fiscal space if they reduce the government’s external
debt burden measured in units of consumption.
To gauge the ability of exchange controls to generate fiscal revenue, Table 2 displays thechange in the fiscal space,fiscal space = s(η, η ∗) − e(η, η ∗)i∗ B ∗− τ,
1 + i∗

as a fraction of output for selected values of γ and ρ, holding the nominal interest rate it andthe exogenous shock vector ηt∗ constant at their baseline values. Changes in the fiscal space
are measured relative to a situation with no exchange controls (γ = ρ = 0). The analysis
is in partial equilibrium because the fact that the nominal interest rate i is kept constant
implies that the intertemporal government budget constraint (29) need not be satisfied.
Table 2 shows that exchange controls can raise significant revenue for the government.
The maximum revenue is close to 5 percentage points of GDP. This is a big number. It is
two and a half times as large as the primary fiscal deficit observed in Argentina over the24calibration period (2007 to 2021). The government generates this outcome by setting theexchange rate gap at 400 percent and by not providing any foreign exchange to importers
at the official exchange rate (ρ = 1). The table further shows that a government that seeks
to maximize fiscal revenue from exchange controls does not sell any foreign currency toimporters at the official exchange rate regardless of the value of the exchange rate gap γ.
Finally, given ρ, there is an exchange-rate gap Laffer curve, in the sense that there is a valueof γ below which fiscal revenue is increasing in γ and above which fiscal revenue is decreasing
in γ.
Having established that exchange controls can be a powerful fiscal tool, a natural questionthat arises is what are the macroeconomic effects and welfare costs of using exchange controls
to generate fiscal revenue. This will be the focus of the discussion that follows. For theremainder of the paper, the analysis will be performed in general equilibrium, that is, thepath of the policy triplet ηt = [γt ρt it] will always be required to ensure the satisfaction of
the equilibrium intertemporal budget constraint (29).

3.3

Macroeconomic Effects of Exchange Controls

In this section we study the general equilibrium effects of varying the exchange-rate gap γt .
To this end, we consider equilibria in which the policy vector ηt = [γt ρt it] is constant overtime. We keep the import restriction ρt fixed at its baseline value (ρt = ρ = 0.088). We also
keep fixed at their baseline values the vector of exogenous shocks and the real value of total
government liabilities (ηt∗ = η ∗ and at = a). The assumption that at is fixed implies thatthe government does not use a one-time jump in the price level to inflate away part of its
domestic liabilities to cover changes in the present discounted value of fiscal revenues inducedby changes in the exchange-rate gap γ. Instead, the government finances these imbalancesby adjusting the flow of seignorage revenue. Thus, although the nominal interest rate isconstant across time, it is different for different values of γ. Specifically, for every value of γ,i adjusts to satisfy the intertemporal budget constraint of the government, equation (35).
Figure 2 displays the general equilibrium effects of changing the exchange rate gap γ onexports and imports. The exchange rate gap is akin to a tax on legal exports. Consequently,
when γ increases, firms move away from legal exports and toward smuggling or under invoicing of exports (xo falls and xs increases). The figure shows, however, that the increasein illegal exports does not fully offset the fall in legal exports. As a result, total exports,
xo + xs , decline.
At the same time, the exchange rate gap γ represents a subsidy on legal imports. The
larger the exchange rate gap is, the larger the incentive to over invoice legal imports will be

25

Figure 2: Exports and Imports as Functions of the Exchange Rate Gap

0.15

0.7

0.7
0.68

0.1

0.6

0.66
0.64

0.05
0.5
0

0.62
0.5

1

0.6
0.55
0.5
0.45
0

0.5

1

0

0

0.5

1

0

0.08

0.6

0.06

0.58

0.04

0.56

0.02

0.54

0

0.52
0

0.5

1

0

0.5

1

0.5

1

Notes. The vertical dotted lines mark the average value of γ during each of the two spells of
exchange-rate controls that took place during the calibration period, 45 percent in the first episodeand 72 percent in the second. The economy is in steady state. The policy variable ρ, the exogenous
variables τ , i∗ and px , and total domestic government liabilities, a, take their baseline steady-statevalues shown in Table 1. The nominal interest rate, i, adjusts with γ to guarantee that the economy
is in general equilibrium, that is, to guarantee that equation (35) is satisfied.

26

(q o > q n + q x or, equivalently, q s < 0). Firms have an incentive to over invoice imports, thatis, to exaggerate their foreign exchange needs to the central bank to profit from the difference
between the official and the market exchange rates. The positive relation between γ and q ooccurs for values of γ below 5 percent. For values of γ greater than 5 percent, the relation
between γ and q o turns negative (bottom left panel of Figure 2). This is because the incentive
to import through the official channel and the disincentive to export through the official
channel are so large that the import constraint becomes binding, q o = q̄ o = (1 − ρ)px xo.
That is, the government starts to ration the provision of foreign exchange at the official
exchange rate to importers. At this point, exchange controls turn from an import subsidy
to an import quota. The larger is the exchange rate gap γ, the smaller legal exports will be
and therefore the more stringent the import quota (1 − ρ)px xo will be. Thus, paradoxically,as the subsidy on official imports increases (i.e., as γ increases), official imports decline. In
the mainstream press, this effect is sometimes described as a “shortage of dollars.” Deriving
the shortage-of-dollar effect as an equilibrium outcome is a contribution of this paper. The
figure suggests that dollar shortage begins to plague the economy at relatively low values ofthe exchange-rate gap (γ > 0.05), and, in particular, that it was a feature of the two spellsof exchange controls observed in Argentina during the calibration period (vertical brokenlines).
For exchange rate gaps larger than 12 percent (γ > 0.12), the supply of foreign exchange
at the official rate is so scarce that importers stop over invoicing (q s ceases to be negative)
and begin to smuggle intermediate materials into the country (q s becomes positive). In
other words, for γ > 0.12 the amount of imported materials used in production exceeds theamount of official imports (q n + q x > q o), or illegal imports are positive. The larger γ is, thelarger the amount of smuggled imports will be. However, as the figure shows, the increasein illegal imports as γ goes up is not large enough to offset the fall in legal imports. As aresult, as γ increases, total imports, q o + q s , fall.
In sum, Figure 2 shows that both total imports and total exports are decreasing functions of γ.7 Thus, as the exchange rate gap widens, the economy becomes more closed tointernational trade.8 Both the traded and nontraded sectors are forced to operate with less7

For values of the exchange-rate gap 0 < γ < 0.05, total exports, X(q x ), and total imports, q x + q n ,are independent of γ. For this range of values of γ, both the import restriction and the nonnegativity
constraint on official exports are slack (q o < (1 − ρ)px xo and xo > 0). The production of export goods isefficient and determined by the condition px X 0 (q x ) = 1, so q x is independent of γ. The amount of imports
used in the production of nontradables, q n , is also independent of γ and determined by the conditionpx X(q x ) = q x + q n + i∗ B ∗ /(1 + i∗ ).
8
The intuitive discussion of Figure 2 abstracts from the fact that the interest rate, i, which changes
with γ because the analysis is in general equilibrium, does affect imports and exports. Changes in thenominal interest rate distort the labor-consumption decision (optimality condition (5)). In turn, changes in
employment affect the production of tradable and nontradable goods, and thus also exports and imports.

27

imported inputs of production, which represents a misallocation of resources.
The appendix analyzes the effects of changes in the exchange rate gap on other macroeconomic indicators of interest. It shows that as the exchange rate gap increases, the economy
becomes less competitive (firms face an increase in the cost of imported materials, which
deteriorates their terms of trade) and more reliant on domestic factors of production (employment becomes inefficiently high). This misallocation of imports and employment drives
consumption down. The appendix also shows that an increase in the exchange rate gap
generates fiscal space, which allows the government to curb money creation and thus reduce
inflation. The increase of fiscal space originates from two sources: first, a higher exchangerate gap represents a higher tax on the official trade balance. Second, a higher exchange-rate
gap appreciates the external real exchange rate (et falls), which reduces the cost of servicing
the foreign debt in terms of domestic consumption.
Next, we characterize optimal policy when a benevolent government chooses the exchangerate gap γ, the nominal interest rate i, and the degree of import restrictions ρ.

4Optimal Exchange Controls

This section presents the optimization problem of a benevolent government and characterizes
its solution. It considers two exchange-rate arrangements: In the first one, the Ramsey
planner is constrained to set the same official exchange rate on imports and exports, so
there are two possible exchange rates, the official exchange rate and the parallel marketdetermined exchange rate. In the second regime, the Ramsey planner can choose different
official exchange rates on imports and exports. Under this regime, there are three exchange
rates, the official exchange rate on imports, the official exchange rate on exports, and theparallel market-determined exchange rate. Both arrangements are frequently observed inpractice (Ilzetzki, Reinhart, and Rogoff, 2019).

4.1

The Ramsey Problem

We present the Ramsey problem for the case of a single official exchange rate. The Ramsey
problem for the case of multiple official exchange rates is similar.
We assume that the government chooses the path of the policy instruments it , γt , and ρtin a benevolent fashion, that is, aiming to maximize the lifetime welfare of the representative
household. We also assume that the government can commit to its policy announcements.
However, these effects happen to be small, so that movements in exports and imports are dominated bychanges in γ.

28

Further, we assume that policy is optimal from the timeless perspective in the following
sense. We assume that the fundamentals pxt , i∗t and τt are constant over time. Then, we
define optimality from the timeless perspective as a policy that supports a steady state inwhich the stock of real domestic government liabilities, at , is constant over time at a value,a, determined in the indefinite past. Thus, the Ramsey optimal equilibrium is defined asfollows:
Definition 2 (Ramsey Policy from the Timeless Perspective) A Ramsey optimal equilibrium from the timeless perspective is a policy triplet (γ, ρ, i) that maximizes
U(c(η, η ∗ ), h(η, η ∗))subject to the intertemporal restriction (35) and the nonnegativity constraint on nominal
rates
i ≥ 0,(36)

given a, where η ≡ [γ ρ i] and η ∗ ≡ [px i∗ τ ].
The Ramsey problem does not admit a closed form solution. It is a complex maximization
problem because both the objective function and the constraints feature functions of thepolicy triplet (γ, ρ, i) that are themselves the solution to a system of a relatively large numberof equalities and inequalities (see Proposition 1). Accordingly, we solve the Ramsey problem
numerically. All structural parameters as well as the real value of domestic government
liabilities a and the exogenous fundamentals px , i∗, and τ take the values shown in Table 1.
We compare the Ramsey optimal policy with two alternative policies. One is a policy
without exchange-rate controls or import restrictions (γ = ρ = 0).9 Under this policy, thegovernment collects no revenue from exchange controls, and fiscal solvency is attained solely
through seignorage revenue. The second alternative policy we consider is one in which theobjective of the government is to minimize inflation instead of to maximize the welfare of
the representative household. This policy seeks to gauge the ability of exchange controls togenerate fiscal revenue in general equilibrium (recall that the analysis around Table 2 is inpartial equilibrium). This policy regime is formally defined as follows:
Definition 3 (Minimum-Inflation Equilibrium from the Timeless Perspective) The
minimum-inflation equilibrium from the timeless perspective is a policy triplet (γ, ρ, i) thatsolves the problem
min π
9Strictly speaking, the regime without exchange-rate controls or import restrictions is γ = 0 and ρ = −∞.
However, because in equilibrium the economy must generate a trade surplus to service the interest on theexternal debt, i∗ B ∗ /(1 + i∗ ), the policy γ = ρ = 0 delivers the same equilibrium.

29

Table 3: Optimal Policy with a Single Official Exchange Rate

Variableexchange-rate gap γ
import restrictions ρinterest rate (%/yr)
inflation (%/yr)
seignorage (% GDP)
revenue from FX controls (% GDP)
welfare cost (% consumption)

No Exchange Optimal Exchange MinimumControls
Controls
Inflation
0
0.03
0.87
–
0.15
0.52
45.2
41.1
0
39.6
35.6
-3.8
2.9
2.7
0
0
0.2
3.0
0.02
0
4.57

Notes. FX controls stands for exchange controls. Revenue from FX controls is defined as follows.
Let z ≡ s − ei∗ B ∗ /(1 + i∗ ) and z 0 be the value of z in the absence of FX controls (γ = ρ = 0).
Similarly, let y 0 be the value of y in the absence of FX controls. Then revenue from FX controls asa percent of GDP is defined as 100(z − z 0 )/y 0 . The welfare cost of a given policy is computed as
the percentage increase in consumption each period required to make households as well off under
the given policy as under the optimal one.

subject to the intertemporal restriction (35), the nonnegativity constraint on nominal rates (36),
and the Fisher equation
1 + π = β(1 + i),(37)

given a, where η ≡ [γ ρ i] and η ∗ ≡ [px i∗ τ ].
The inflation-minimizing government described in Definition 3 is assumed to proceed
as follows: Given a value of π, constraint (37) determines the nominal interest rate, i.
If this value of i satisfies the nonnegativity constraint (36), then the government has two
instruments, γ and ρ, to satisfy the equilibrium intertemporal budget constraint (35). In
general, there can be multiple pairs (γ, ρ) consistent with the satisfaction of this constraint.
Among all such pairs, the government picks the one associated with the highest level oflifetime utility of the representative household.

4.2

Optimal Policy Under a Single Official Exchange Rate

Table 3 displays the predictions of the model under a single official exchange rate. The
main result is that the optimal policy (column 2) calls for virtually no exchange controls.
The optimal exchange rate gap is only 3 percent (γ = 0.03) and import restrictions are low(ρ = 0.15). Consequently, total revenue from exchange controls is virtually nil (0.2 percent
of GDP). The benevolent government relies almost exclusively on inflation to finance thebudget. Under the optimal policy the annual inflation rate is 35.6 percent and seignorage
30

revenue is 2.7 percent of GDP. Quantitatively, the optimal policy looks much like the policy
without exchange controls (column 1 of Table 3).
The reason why the social planner does not rely on exchange controls to finance thebudget is not that this instrument is incapable of collecting significant amounts of resources,
but that it is a highly inefficient way of doing so. The third column of Table 3 shows
the policy that minimizes inflation (see Definition 3). The inflation-minimizing government
follows the Friedman rule (i = 0) and therefore collects no seignorage revenue. Instead, it
collects 3 percent of GDP from exchange controls. It does so by increasing the exchange rate
gap from 3 percent to 87 percent (γ increases from 0.03 to 0.87) and by reducing exchangerate-based import subsidies (ρ increases from 0.15 to 0.52). About 60 percent of the increasein fiscal revenue from exchange controls stems from an increase in s (the tax on the official
trade balance induced by a positive exchange-rate gap). The remaining 40 percent comesfrom a reduction in the debt burden, that is, from a decline in the value of net externalinterest payments in terms of consumption (ei∗B ∗ /(1 + i∗)), caused by an appreciation of
the external real exchange rate (a fall in e).
The significant widening of the exchange-rate gap, γ, and tightening of import restrictions, ρ, necessary to generate the required fiscal space in the minimum-inflation regime
cause substantial misallocation. The reason is that when γ and ρ increase, the dollar shortage is exacerbated, and firms must rely more heavily on smuggled materials, which are more
expensive than materials imported at the official exchange rate, since they are priced at themarket exchange rate plus the contraband cost. The economy as a whole is forced to operatewith an inefficiently low level of imported materials, which has a large negative effect on
aggregate activity and domestic absorption. Consequently, financing a sizable part of thebudget through exchange controls is highly welfare reducing. The bottom row of Table 3
shows that households require a 4.57 percent increase in consumption each period to be aswell off under the minimum-inflation policy as under the optimal policy.
Next, we turn to an exchange-rate arrangement with multiple official exchange rates inwhich imports and exports receive differential exchange-rate treatments. Under this more
flexible—and arguably no less realistic—arrangement, the Ramsey government finds it optimal to finance a substantial fraction of the fiscal deficit with exchange controls.

4.3

Optimal Policy Under Multiple Official Exchange Rates

Consider now the existence of separate official exchange rates for exports and imports. Let’s
denote these two exchange rates Etox and Etoq , respectively. This policy arrangement nests
the regime with a single official exchange rate as a special case when Etox = Etoq .

31

Table 4: Optimal Policy With Multiple Official Exchange Rates

Variable
export exchange-rate gap γ ximport exchange-rate gap γ qimport restrictions ρinterest rate (%/yr)
inflation (%/yr)
seignorage (% GDP)
revenue FX controls (% GDP)
welfare cost (% consumption)

Single official
exchange rate
0.03
0.03
0.15
41.1
35.6
2.7
0.2
0

Multiple official
exchange rates
0.12
0
−∞
10.9
6.6
1.0
2.0
-0.22

Notes. See notes to Table 3. The variables γ x and γ q denote the exchange-rate gaps on exports andimports. The entry ρ = −∞ means that importers have unrestricted access to foreign exchange atoq
the official rate Et .

Direct government revenues from exchange controls on exports and imports, st, which
under a single official exchange rate are given in equation (24), now take the form
st = e t




γtq o
γtx x op x −q ,1 + γtx t t 1 + γtq twhere γtx ≡ Et /Etox − 1 and γtq ≡ Et /Etoq − 1 denote the exchange-rate gaps on official
exports and imports. With multiple official exchange controls, firm profits, previously given
in equation (12), become
F (ht, qto +qts −qtx)+

et
et
o
x s
s
s
s
px [X(qtx )−xst ]−q qt +et (pt xt −qt )−wt ht −C(qt , κq )−C(xt , κx ).
x t
1 + γt1 + γtAll other aspects of the model are as in the economy with a single official exchange rate.
The government now has four policy instruments, namely, two exchange rate gaps (γtxand γtq ), import restrictions (ρt ), and the nominal interest rate (it ). When γtq < γtx , theimplicit subsidy on imports is smaller in absolute value than the implicit tax on exports.
The case γtq = 0 and ρt = −∞ corresponds to a liberalization of the exchange market
for imports, because private agents can import unrestrictedly at the market exchange rate
without having to pay smuggling costs.10
Table 4 displays the predictions of the model under the Ramsey optimal monetary andexchange-control policy. The benevolent government finds it optimal not to subsidize imports
10Note that now ρt is allowed to take negative values. The reason is that a negative value of ρt need nolonger imply negative values of st .

32

(γtq = 0) and to allow unrestricted access to foreign currency at the market exchange rate
(ρt = −∞). Thus, liberalizing the foreign exchange market for imports is Ramsey optimal.
The intuition behind this result is as follows. If the foreign exchange market for imports isliberalized, importers have no incentive to engage in smuggling, which is a wasteful activity.
Also, the elimination of the exchange-rate gap on imports reduces the government’s drain of
foreign currency, boosting fiscal revenue. In turn, the improvement in the fiscal space allows
the government to reduce the inflation tax. The optimal inflation rate is now 6.6 percent
per year, compared to 35.6 percent per year under a single official exchange rate.
The exchange control regime with multiple official exchange rates welfare dominates theone with a single official exchange rate. Table 4 shows that the welfare gain relative to the
optimal policy with a single official exchange rate is equivalent to a permanent increase of 0.22
percent in consumption. This is a large number as welfare measures go in macroeconomics.
Because the government does not subsidize imports, exchange controls now represent a
tax on exports instead of a tax on the trade balance. Thus, exchange controls become a more
powerful fiscal tool, as its tax base is larger: For example, in Argentina over the calibration
period, exports represented 17 percent of GDP, whereas the trade balance represented only
1.5 percent of GDP. Consequently a relatively modest exchange-rate gap on exports (γtx =0.12) suffices to collect a substantial amount of resources (2.0 percent of GDP). Now thevast majority of the resources collected with exchange controls come from direct government
revenues, st , and virtually nothing from a reduction in the external debt burden, eti∗ B ∗/(1+i∗), as the real exchange rate appreciation is minor.
The finding that with multiple official exchange rates it is optimal for the government
to impose a lower exchange-rate gap on imports than on exports provides insight for why
exchange control regimes, even ones that start with a single official exchange rate, tend totransition toward multiple official exchange rates. For example, Argentina, the country used
to calibrate the model, by the end of the calibration period, introduced a tax on foreignexchange import transactions called “impuesto paı́s.” This tax reduces the implicit subsidy
on official imports and is therefore equivalent to a reduction in the import exchange rate
gap γtq . Because this type of tax is closely related to the exchange of currencies, the IMF’s
Article VIII considers it a multiple currency practice (IMF 2019, Box 1).

5

Conclusion

A sizeable number of emerging countries resort to exchange controls. Traditionally this typeof intervention has been viewed as a tax on exports and a subsidy on imports. We show
than when analyzed in the context of a general equilibrium framework this view can be33

misleading. First, exchange controls can give rise to rationing or dollar shortages, making
them more akin to an import quota than to an import subsidy. When this happens exchange
controls can cause widespread misallocation of resources and generate additional incentives
for smuggling. Second, exchange controls generate fiscal resources not only because they
represent a tax on exports but also because they reduce the real value of external public
debt through an appreciation of the real exchange rate.
The paper considers the problem of a government that runs chronic fiscal deficits and has
lost the political capacity to finance them through additional regular taxation, expenditurecuts, or further borrowing. Its remaining choices are to finance the deficit either by printing
money or by imposing exchange controls. A key insight from this investigation is that theRamsey government prefers a scheme with multiple official exchange rates, where exports
face higher exchange controls than imports. The social planner favors lighter controls on
imports to mitigate the misallocation caused by dollar shortages. This finding helps explain
why exchange control regimes often include multiple currency practices. Under the optimal
policy, both exchange controls and inflation finance substantial portions of the fiscal deficit.
This result provides theoretical and normative support for the empirical observation that a
primary reason for imposing exchange controls is to mobilize fiscal resources.

34

Appendix: Additional Results on the Macroeconomic
Effects of Exchange Controls
This appendix extends the analysis of section 3.2 to additional macroeconomic variables,
including the trade balance, the terms of trade, the real exchange rate, consumption, labor,
seignorage, and fiscal revenue from exchange controls. It shows that the government faces a
tradeoff between financing the fiscal deficit with the inflation tax or with exchange controls.
To simplify the intuition, in this appendix the analysis focuses on values of γ larger than
5 percent, for which the economy experiences dollar shortages and which represent the caseof greatest empirical interest.
The top left panel of Figure A.1 shows that the official trade balance, px xo − q o, declines
as the gap between the market exchange rate and the official exchange rate, γ, widens. Thisis a consequence of the binding import restriction. When import restrictions are binding,the official trade balance is proportional to official exports, px xo − q o = ρpx xo . And because xo is decreasing in γ, so is the official trade balance. This effect has negative fiscal
consequences, because the official trade balance is the base of the exchange-control “tax”(see equation (24)). The figure shows that the decline in the official trade surplus is offset
by an increase in the smuggling trade balance (px xs − q s ). The reason this is so is that by
the market clearing condition (28), the country’s overall trade balance surplus must equalinterest payments on external debt, i∗B ∗/(1 + i∗). As these payments are independent of γ,a declining official trade balance must be perfectly offset by an increasing smuggling tradebalance.
The exchange-rate gap distorts the terms of trade and the real exchange rate. The top
right panel of Figure A.1 shows that as exchange rate controls become more stringent, theinternal terms of trade deteriorate, that is, imported goods become more expensive relative toexported goods in the domestic economy. Put differently, as exchange rate controls increase,exporters perceive that they become less competitive in international goods markets. Thisis because as γ increases, they receive less income for their external sales and because they
have to pay higher marginal smuggling costs for imported inputs. The deterioration of theinternal terms of trade explains why the economy becomes more closed with tighter exchange
controls.
The bottom left panel of Figure A.1 shows that as the exchange rate gap increases, theinternal real exchange rate, e + C 0(q s , κq ), depreciates, that is, as γ increases, producers
of nontradable goods find that imported materials become more expensive relative to thefinal good they produce. The increase in the domestic price of imports results from higher
marginal smuggling costs as the dependence of firms on smuggled imports increases with γ
35

Figure A.1: The Real Exchange Rate, the Terms of Trade, and the Trade Balance as Functions of the Exchange Rate Gap

0.06

1

0.055
0.8

official
smuggling

0.05
0.045

0.6

0.04

0.4
0.2

0.4

0.6

0.8

1

external
internal

0.2

0.28
0.26

external
internal

0.24

0.2

0.4

0.6

0.8

1

Note. See notes to Figure 2.

36

0.4

0.6

0.8

1

Figure A.2: Fiscal Variables, the Nominal Interest Rate, and the Inflation Rate as Functionsof the Exchange Rate Gap

3% of GDP% of GDP

0.4
0.3
0.2

2.8

2.6

0.1
0.2

0.4

0.6

0.8

1

45

0.4

0.6

0.8

1

0.2

0.4

0.6

0.8

1

2.8

% of GDP

40

%/yr

0.2

35
30

2.6
2.4
2.2

25
0.2

0.4

0.6

0.8

1

Note. See notes to Figure 2.

(recall the discussion around Figure 2). By contrast, the external real exchange rate appreciates (e falls) with γ, that is, nontradable goods become more expensive relative to tradables
measured at world prices. This is because as γ increases domestic producers face higher
prices for imported inputs, as they have to rely increasingly on smuggling, which is expensive. As mentioned earlier, movements in the external real exchange rate are not relevant
for producers (because smuggling costs introduce a wedge between the world price and thedomestic price of imported inputs), but do matter for the government. The appreciation of
the external real exchange rate caused by higher values of γ has positive and negative fiscal
consequences. On the positive side, it reduces the value of interest payments on the external
debt in terms of consumption goods (ei∗B ∗ /(1 + i∗) falls). On the negative side, all else
equal, the appreciation of the external real exchange rate reduces the value of fiscal revenues
from exchange controls (eγ/(1 + γ)(px xo − q o ) falls).
The fiscal consequences of changing the exchange-rate gap are displayed in Figure A.2.
The fiscal space, s − τ − ei∗B ∗/(1 + i∗ ), improves with the exchange rate gap γ through twochannels, a tax channel and a debt-burden reduction channel. The tax channel is displayedin the top left panel of the figure. This panel shows that revenue from exchange controls,s = γ/(1+γ)e(px xo −q o), is increasing in the exchange-rate gap. This source of fiscal revenue
37

can be interpreted as the product of a tax rate, γ/(1 + γ), and a tax base, the official tradebalance expressed in units of the consumption good, e(px xo − q o). As γ increases, the tax
rate increases but the tax base falls (recall that both e and px xo − q o fall with γ). However,
the tax base declines proportionally less than the tax rate rises, resulting in increased fiscal
revenue from exchange controls. The debt-burden reduction channel is displayed in the top
right panel of Figure A.2. As γ increases, the value of external interest payments in termsof units of consumption, ei∗B ∗/(1 + i∗ ), falls (recall that the external real exchange rate eappreciates with γ). Jointly the tax channel and the debt-burden reduction channel raise
the fiscal space by 1 percentage point of GDP when γ increases from near 0 to 1, with ρ
fixed at 0.088.
Consider now the effects of increasing exchange rate controls on the nominal interest rate,i, inflation, π, and seignorage revenue, i/(1 + i)m, which are shown in the bottom panelsof Figure A.2. We have already shown that the fiscal space increases with γ. This meansthat a widening of the exchange rate gap allows the government to rely less on seignorage
revenue. As a result, as γ increases, inflation falls and the government lowers the nominalinterest rate. This connection between inflation and exchange controls is the key trade off
explored in this paper. Section 4 in the body of the paper studies how a Ramsey planner
resolves this trade off.
Figure A.3 shows that employment increases with the exchange-rate gap. The intuition
behind this result is as follows. The fall in the nominal interest rate resulting from anincrease in γ induces households to remonetize (recall that by equation (4) money velocity
is decreasing in the nominal interest rate). In turn, by optimality condition (5), the fall inmoney velocity reduces the distortion in the labor-consumption margin, 1 + s(v) + vs0(v),which causes an expansion in the supply of labor. In turn, the increase in the supply of labor
results in a fall in the real wage (top right panel of Figure A.3).
Figure A.3 also shows that consumption is a nonmonotonic function of the exchange
rate gap. An increase in γ has positive and negative effects on c. It depresses private
consumption because it exacerbates the misallocation of resources. This occurs for two
reasons. First, as the exchange rate gap increases, the economy suffers from a shortage ofimported intermediate inputs for the production of consumption goods (q n falls). Second, as
the exchange rate gap widens, smuggling increases, which is resource consuming (C(xs, κx )and C(q s, κq ) both go up). The positive effects of an increase in γ on consumption stem froma reduction in the distortions caused by inflation. Specifically, an increase in γ is associatedwith a fall in the interest rate, which reduces transactions costs (s(v) goes down) and, as
explained above, alleviates distortions in the labor-consumption margin, incentivizing the
supply of labor for the production of consumption goods. The resource misallocation effect38

Figure A.3: Hours, Wages, Consumption, and Welfare as Functions of the Exchange Rate
Gap

0.678

1.015

0.676
1.01

0.674
0.672

1.005

0.67
1

0.668
0.2

0.4

0.6

0.8

1

0.898

0.2

0.4

0.6

0.8

1

0.2

0.4

0.6

0.8

1

-67.5

0.896

-68

0.894

-68.5
-69

0.892
-69.5
0.2

0.4

0.6

0.8

1

Note. See notes to Figure 2.

and the disinflation effect of an increase in γ run in opposite directions, resulting in a humpshaped relationship between γ and consumption (bottom left panel of Figure A.3). However,for most values of the exchange-rate gap considered in Figure A.3, the misallocation effectdominates and consumption falls as the exchange-rate gap increases.
Welfare is decreasing in the exchange-rate gap (bottom right panel of Figure A.3). Thiseffect stems from two sources. First, labor is monotonically increasing in γ, so that, holding
consumption constant, an increase in γ reduces welfare. Second, for values of γ for which
consumption is decreasing, welfare unambiguously goes down with γ. And for values ofγ for which consumption is increasing in γ, the labor effect dominates. In summary, thenegative welfare effect of exchange-rate controls occur because by discouraging the use of
traded intermediate inputs, they cause a misallocation of resources away from imports andtoward labor effort.

39

References
Adams, Charles, and Jeremy Greenwood, “Dual exchange rate systems and capital controls:
An investigation,” Journal of International Economics 18, February 1985, 43–63.
Ámbito Financiero, “Cronologı́a del Cepo Cambiario: Se Cumple un Año de la Restricción
Impuesta por Macri,” September 2, 2020.
Argy, Victor, and Michael Porter, “The Forward Exchange Market and the Effects of Domestic and External Disturbances Under Alternative Exchange Rate Systems,” IMF Staff
Papers XIX, November 1972, 502–28.
Benati, Luca, Robert E. Lucas Jr., Juan Pablo Nicolini, and Warren Weber, “International
Evidence on Long-Run Money Demand,” Journal of Monetary Economics 117, 2021,
43–63.
Bhagwati, Jagdish, Anatomy and Consequences of Exchange Control Regimes, Ballinger
Publishing Company: Cambridge, MA, 1978.
Cavallo, Alberto, and Manuel Bertolotto, “Filling the Gap in Argentina’s Inflation Data,”
manuscript, MIT Sloan, May 2016.
Chari, V.V., Lawrence J. Christiano, and Patrick J. Kehoe, “Optimal fiscal and monetary
policy: some recent results,” Journal of Money Credit and Banking 23, 1991, 519–539.
Correia, Isabel, Juan Pablo Nicolini and Pedro Teles, “Optimal Fiscal and Monetary Policy:
Equivalence Results,” Journal of Political Economy 116, February 2008, 141–170.
Dornbusch, Rudiger, “Multiple Exchange Rates for Commercial Transactions,” in Sebastian
Edwards and Liaquat Ahamed (Eds.), Economic Adjustment and Exchange Rates in
Developing Countries, Chicago: University of Chicago Press, 1986.
Espino, Emilio, Alfonso Gauna, and P. Andrés Neumeyer, “Models of Balance of Payments
Crises with Capital Controls,” manuscript, Universidad Torcuato di Tella, 2023.
Flood, Robert P., and Nancy Peregrim Marion, “The Transmission of Disturbances under
Alternative Exchange-Rate Regimes with Optimal Indexing,” The Quarterly Journal of
Economics 97, February 1982, 43–66.
Gopinath, Gita, Oleg Itskhoki, and Roberto Rigobon, “Currency Choice and Exchange Rate
Pass-Through,” NBER working paper 13432, September 2007.
Ilzetzki, Ethan, Carmen Reinhart, and Kenneth Rogoff, “Exchange Arrangements Entering
the Twenty-First Century: Which Anchor will Hold?,” Quarterly Journal of Economics
134, May 2019, 599–646.
International Monetary Fund, “Review of the Fund’s Policy on Multiple Currency Practices:
Initial Considerations—Methodology to Assess Multiple Currency Practices (Background
Paper II),” IMF Staff Report, 2019.

40

International Monetary Fund, “Review of the Fund’s Policy on Multiple Currency Practices,” IMF Staff Report, July 2, 2022.
Itskhoki, Oleg, and Dmitry Mukhin, “Sanctions and the Exchange Rate,” working paper,
February 18, 2023.
Kamin, Steven B, “Multiple Exchange Rates Systems: The Case of Argentina,” in Richard
C. Bart and Chorng-Huey Wong (Eds.), Approaches to Exchange Rate Policy, Washington DC: International Monetary Fund, 1994.
Kehoe, Timothy J., and Juan Pablo Nicolini, A Monetary and Fiscal History of Latin America, 1960-2017, Minneapolis, MN: University of Minnesota Press, 2021.
Kehoe, Timothy J., Juan Pablo Nicolini, and Thomas J. Sargent, “A Framework for Studying the Monetary and Fiscal History of Latin America,” in Timothy J. Kehoe and Juan
Pablo Nicolini (Eds.), A Monetary and Fiscal History of Latin America, 1960-2017, Minneapolis, MN: University of Minnesota Press, 2021.
Kiguel, Miguel A., J. Saul Lizondo, and Steven A. O’Connell, Parallel Exchange Rates in
Developing Countries, Palgrave Macmillan: London, 1997.
Lucas, Robert E. Jr., and Nancy L. Stokey, “Optimal fiscal and monetary policy in an
economy without capital,” Journal of Monetary Economics 12, 1983, 55–93.
Mendoza, Enrique G., “Real Business Cycles in a Small Open Economy,” American Economic Review 81, September 1991, 797–818.
Mosquera, Santiago, and Federico Sturzenegger, “Cepo para principiantes,”

Desarrollo

Económico 61, December 2021, 101–124.
Ottonello, Pablo, Diego J. Perez, and William Witheridge, “The Exchange Rate as an
Industrial Policy,” NBER Working Paper 32522, May 2024.
Reinhart, Carmen M., and Kenneth S. Rogoff, “The Modern History of Exchange Rate
Arrangements: A Reinterpretation,” Quarterly Journal of Economics 119, February
2004, 1–48.
Schmitt-Grohé, Stephanie, and Martı́n Uribe, “Optimal fiscal and monetary policy understicky prices,” Journal of Economic Theory 114, February 2004a, 198–230.
Schmitt-Grohé, Stephanie, and Martı́n Uribe, “Optimal fiscal and monetary policy under
Imperfect Competition,” Journal of Macroeconomics 26, June 2004b, 193–209.
Schmitt-Grohé, Stephanie, and Martı́n Uribe, “Downward Nominal Wage Rigidity, Currency
Pegs, and Involuntary Unemployment,” Journal of Political Economy 124, October
2016, 1466–1514.
Sherwood, Joyce, “Revenue Features of Multiple Exchange Rate Systems: Some Case Studies,” IMF Economic Review 5, February 1956, 74–107.
Uribe, Martı́n, “Exchange-Rate-Based Inflation Stabilization: The Initial Real Effects of41

Credible Plans,” Journal of Monetary Economics 39, June 1997, 197–221.

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