currency pegs and unemployment

8/9/2019 Currency Pegs and Unemployment

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Currency Pegs and Unemployment

Stephanie Schmitt-Grohe Martn Uribe

This draft: August 3, 2010Preliminary and incomplete

1 Introduction

Countries can find themselves confined to a currency peg in a number of ways. For instance,

a country could have adopted a currency peg as a way to stop high or hyperinflation in

a fast and nontraumatic way. A classical example is the Argentine Convertibility Law of

April 1991, which, for a decade mandated a one-to-one exchange rate between the Argentine

peso and the U.S. dollar. Another route by which countries arrive at a currency peg is the

joining of a monetary union. Recent examples include Eastern European and Mediterranean

emerging countries, such as Greece, that joined the Eurozone.

The Achilles heel of currency pegs is that they hinder the efficient adjustment of the

economy to negative external shocks, such as drops in the terms of trade or hikes in thecountry interest-rate premium. The reason is that such shocks produce a contraction in

aggregate demand that requires a decrease in the relative price of nontradables, that is, a

real depreciation of the domestic currency, in order to bring about an expenditure switch

away from tradables and toward nontradables. In turn, the required real depreciation may

come about via a nominal devaluation of the domestic currency or via a fall in nominal prices

or both. The currency peg rules out a devaluation. Thus, the only way the necessary real

depreciation can occur is through a decline in the nominal price of nontradables. However,

if nominal prices, especially factor prices, are downwardly rigid, the real depreciation will

take place only slowly, causing recession and unemployment along the way.

This paper investigates the question of how costly are currency pegs in terms of unem-

ployment and welfare for an emerging economy facing external shocks. To this end, the

paper embeds downward nominal wage rigidity into a dynamic, stochastic, disequilibrium

Columbia University, CEPR, and NBER. E-mail: [email protected] University and NBER. E-mail: [email protected].


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(DSDE) model of a small open economy with traded and nontraded goods. The key feature

that distinguishes our theoretical framework from existing models of nominal wage rigidity

is that in our formulation wage rigidity gives rise to occasionally binding constraints that

prevent the real wage from falling to its efficient level. In turn, these constraints, when bind-

ing, produce involuntary unemployment. A second distinguishing feature of our model ofdownward wage rigidity is that it does not rely on the assumption of imperfect competition

in product or factor markets. This feature of the model has implications for the wage setting

process, which, as explained below, affects form of the optimal exchange-rate policy.

We show that in our DSDE model, the optimal monetary policy takes the form of a

time-varying rate of devaluation that allows the real wage to equal the efficient real wage at

all times. The resulting optimal exchange-rate policy is highly asymmetric in nature. The

central bank devalues the nominal currency only in periods in which the full-employment real

wage rate experiences a sizable decline. These are typically periods in which the economy

suffers negative external shocks. In all other periods, the monetary authority keeps the

nominal exchange rate constant. It follows that under the optimal policy, the devaluation

rate is positive on average. As a consequence, the optimal rate of inflation is also positive on

average. In this way, our DSDE model captures Oliveras (1960, 1964) concept of structural

inflation.

The first main quantitative result of this paper is that in a calibrated version of our

model, the average optimal rate of inflation is high, about 5 percent per year. This result

is important in light of the difficulties that the existing literature on the optimal rate of

inflation has faced in rationalizing actual inflation targets, which in virtually all inflationtargeting countries are at least two percent. In this literature, the optimal rate of inflation

is typically negative or insignificantly above zero (see Schmitt-Grohe and Uribe, 2010, for

a survey). The reason why the present DSDE model has the ability to generate sizable

optimal inflation rates is threefold. First, in our model labor markets are competitive. This

implies that no economic agent internalizes the downward rigidity of wages. By contrast, in

an environment in which wage setters do internalize the wage rigidity, nominal (and real)

wages tend to rise less during booms. Therefore, the central bank has an incentive to revalue

during booms and less need to devalue during recession, both of which tend to reduce the

average level of inflation. Second, our model of wage rigidity imposes asymmetric costs of

changing nominal wages. Firms face resistance only to nominal wage cuts, but not to nominal

wage increases. This asymmetry creates an incentive for the central bank to inflate away

the purchasing power of past real wages when they exceed the current full-employment real

wage. On the other hand, the fact that nominal wages are flexible upward implies that the

central bank has no incentives to deflate when the current full-employment real wage exceeds

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goods.

2.1 Households

The economy is populated by a large number of infinitely-lived households with preferences

described by the utility function

E0

t=0

tU(ct), (1)

where ct denotes consumption, U is a utility index assumed to be increasing and strictly

concave, (0, 1) is a subjective discount factor, and Et is the expectations operator

conditional on information available in period t. Consumption is assumed to be a composite

good made of tradable and nontradable goods via the aggregation process

ct = A(cTt , c

Nt ), (2)

where cTt denotes consumption of tradables, cNt denotes consumption of nontradables, and

A denotes an aggregator function assumed to be homogeneous of degree one, increasing,

concave, and to satisfy the Inada conditions. These assumptions imply that consumption of

tradables and nontradables are normal goods.

Households are assumed to be endowed with an exogenous and stochastic amount of

tradable goods, yTt , and a constant number of hours, h, which they supply inelastically to

the labor market. Because of the presence of nominal wage rigidities in the labor market,

households will in general only be able to work ht h hours each period. Households take

ht as exogenously determined. Households also receive from the government a lump-sum

transfer t and profits from the ownership of firms, denoted t. Both t and t are expressed

in terms of tradables. Following Mendoza and Yue (2010), we assume that households

do not directly participate in financial markets. Instead, the government does so on their

behalf by choosing transfers in a benevolent fashion. We make this assumption for technical

reasons, as it greatly facilitates the characterization and computation of equilibrium in an

economy with occasionally binding constraints and possibly incomplete asset markets. The

households budget constraint in period t is then given by

cTt + ptcNt = y

Tt + wtht + t + t, (3)

where pt denotes the relative price of nontradables in terms of tradables in period t and

wt denotes the real wage rate in terms of tradables in period t. The household takes the

right-hand side of the budget constraint as exogenously given.

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In each period t 0, the optimization problem of the household consists in choosing

cTt and cNt to maximize (2) subject to the budget constraint (3). The optimality conditions

associated with this maximization problem are the budget constraint (3) and

A2(cT

t

, cNt

)

A1(cTt , cNt ) = p

t,

where Ai denotes the partial derivative of A with respect to its i-th argument. Intuitively,

the above expression states that an increase in the relative price of nontradables induces

households to engage in expenditure switching by consuming relatively more tradables and

less nontradables. The maintained assumptions on the form of the aggregator function A

guarantee that the left-hand side of this expression is an increasing function of the ratio

cTt /cNt .

2.2 Firms

The nontraded good is produced using labor as the sole input by means of an increasing and

concave production function

yNt = F(ht),

where yNt denotes output of nontradables. The firm operates in competitive product and

labor markets. Profits, t, are given by

t = ptF(ht) wtht.

The firm chooses ht to maximize profits. The optimality condition associated with this

problem is

ptF(ht) = wt.

This first-order condition implicitly defines the firms demand for labor. It states that firms

are always on their labor demand curve. Put differently, in this model firms never display

unfilled vacancies nor are forced to keep undesired positions. As we will see shortly, this will

not be the case for workers, who will in general be off their labor supply schedule and will

experience involuntary unemployment.

2.3 Employment and Wages with Downward Nominal Rigidity

Let Wt denote the nominal wage rate and Et the nominal exchange rate, defined as the

domestic-currency price of one unit of foreign currency. Assume that the law-of-one-price

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holds for traded goods and that the foreign-currency price of traded goods is constant and

normalized to unity. Then, the real wage in terms of tradables is given by wt Wt/Et.

Nominal wages are assumed to be downwardly rigid in the spirit of Olivera (1960, 1964).

Specifically, in any given period nominal wages can at most fall by a factor [0, 1].

Formally, we impose thatWt Wt1.

This setup nests the cases of absolute downward rigidity, when 1, and full wage flexi-

bility, when 0. The presence of nominal wage rigidity implies the following restriction

on the dynamics of real wages:

wt wt1

t,

where t Et/Et1 denotes the gross nominal depreciation rate of the domestic currency.

The presence of downwardly rigid nominal wages implies that the labor market will in

general not clear at the inelastically supplied level of hours h. Instead, involuntary unem-

ployment, given by h ht, will be a regular feature of this economy. Actual employment

must satisfy

ht h

at all times. Finally, at any point in time, real wages and employment must satisfy the

slackness condition

(h ht)

wt

wt1t

= 0.

2.4 Price and Quantity Determination in the Private Sector

Given the level of government transfers, t, and the devaluation rate, t, which are both

determined by government policy and taken as exogenous by households and firms, and

given the past real wage, wt1, which is a predetermined variable, relative prices, pt and

wt, and quantities, cTt , c

Nt , and ht, are determined by the following system of equations and

inequalities:

cNt = F(ht), (4)

cTt = y

Tt + t, (5)

A2(cTt , c

Nt )

A1(cTt , cNt )

= pt, (6)

ptF(ht) = wt, (7)

(h ht)

wt

wt1t

= 0, (8)

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ht h, (9)

and

wt wt1

t. (10)

Consider first the real wage that would obtain in a full-employment equilibrium in whichht equals h. Setting ht = h and using equation (4) to eliminate c

Nt , equation (5) to eliminate

cTt , and equation (6) to eliminate pt, the labor demand equation (7) can be written as

wf,t =A2(y

Tt + t, F(h))

A1(yTt + t, F(h))F(h) f(y

Tt + t);

f > 0, (11)

where wf,t denotes the full-employment real wage. The assumed properties of the aggrega-

tor function A guarantee that the full-employment real wage is increasing in after-transfer

tradable income yTt + t. The intuition behind this result is that an increase in tradable

income makes households feel richer. Because nontradables are normal goods, the demand

for this type of good goes up. The supply of nontradables, however, cannot increase because

the labor market is already in full employment. Therefore, the relative price of nontradables

must rise. This increase in the relative price of nontradables raises the value of the marginal

product of labor, which translates into an increase in the real wage.

Using the above expression for the full-employment wage, equation (11), and condi-

tion (10), we have that the real wage rate satisfies

wt =

yTt + t,

wt1t

max

wt1t ,

f(yTt + t)

; 1, 2 0. (12)

Having derived the real wage rate that will prevail in each period, one can use expres-

sions (4)-(7) to obtain the value of all other variables determined in the private sector. In

particular, employment is implicitly give by

A2(yTt + t, F(ht))

A1(yTt + t, F(ht))F(ht) =

yTt + t,

wt1t

.

The normality of tradable and nontradable consumption guarantees that the left-hand side

of this expression is monotonically decreasing in ht. This fact in combination with the

assumptions that A satisfies the Inada conditions and that F is concave implies that, given

yTt + t and wt1/t, there exists a unique solution of the above expression for employment,

ht, which satisfies ht h. We therefore can express employment as a function ofyTt + t and

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wt1/t as follows:

ht = H

yTt + t,

wt1t

; H1 0; H2 0.

The results that H is nondecreasing in yTt + t and nonincreasing in wt1/t follows from the

properties of the functions A and . The intuition for why employment is nondecreasingin tradable income is that an increase in this source of income produces a positive wealth

effect that raises the demand for both tradable and nontradable goods. If the economy is

operating below full employment, the increase in the demand for nontradables translates

directly into an increase in employment in that sector. If the economy is already operating

at full employment, the increase in the demand for nontradables causes a rise in the price

of this type of good but leaves employment unchanged. Consider now an increase in the

lower bound for real wages, wt1/t. If this lower bound is binding an increase in wt1/t

will depress employment, because firms are always operating on the labor demand schedule

(i.e., employment is demand determined). On the other hand, if the economy is at full

employment, then an increase in wt1/t is in general not binding and has no effect on

employment.

Finally, one can express the relative price of nontradables, consumption of nontradables,

and total consumption as functions of tradable income and the real value of the lagged wage

rate as follows:

pt =A2

yTt + t, F

H

yTt + t,wt1t

A1

(yT

t + t, F

H

yT

t + t,wt1

t P(yTt + t,

wt1t

); P1 > 0, P2 0,

cNt = F

H

yTt + t,

wt1t

CN

yTt + t,

wt1t

; CN1 0; C

N2 0,

ct = A

yTt + t, C

N

yTt + t,

wt1t

C

yTt + t,

wt1t

; C1 0, C2 0,

where Pi, CNi , and Ci denote, respectively, the partial derivatives of the functions P, C

N,

and C with respect to their i-th arguments, for i = 1, 2. The signs of the partial derivatives

of these three functions follow directly from the previous analysis, with the exception of

P1, the partial derivative of the relative price of nontradables, pt, with respect to traded

income, yTt + t. The reason why the sign of this partial derivative is not obvious is that

the relative price of nontradables depends on the ratio of the consumptions of tradables and

nontradables. In turn, both tradable and nontradable consumption increase with tradable

income. It is possible to show, however, that an increase in tradable income will always induce

a proportionally larger increase in tradable consumption than in nontradable consumption.

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Figure 1: The Effect of Transfers and Devaluations on the Private Sector

h

Transfer, t

Hours, ht

wt1

t

Transfer, t

Real Wages, wt

Transfer, t

Price of Nontradables, pt

Transfer, t

Aggregate Consumption, ct

h

Devaluation Rate, t

Hours, ht

wt1

t

Devaluation Rate, t

Real Wages, wt

Devaluation Rate, t

Price of Nontradables, pt

Devaluation Rate, t

Aggregate Consumption, ct

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To see this, consider first a situation in which the economy is at full employment. In this case,

consumption of nontradables cannot increase with tradable income, because nontradable

production is at its upper bound F(h). Tradable consumption, however, increases one for

one with tradable income. Hence, given the assumed properties of the aggregator function

A, the ratio A2/A1, which equals pt, must rise. Consider now a situation in which theeconomy is operating below full employment. Suppose that in response to an increase in

tradable income cN increases by the same or a larger proportion than cTt . By equation (6)

and the assumptions made about the aggregator A, this is the only scenario under which

the relative price of nontradables, pt, will not rise. This scenario, however, is impossible.

To see this, note that the rise in cNt must be accompanied by a rise in ht (by equation (4)),

and, hence by a decline in the marginal product of labor (by the assumed concavity of the

production function F). Now, the fact that pt does not increase and that F(ht) falls, implies,

by the labor demand given in (7), that the real wage must fall. But because the economy

is operating below full employment, the real wage is at its lower bound wt1/t and thus

cannot fall further. It follows that pt must rise.

Figure 1 provides a graphical summary of the dependence of hours, the real wage rate,

the relative price of nontradables and total consumption on the real transfer t and the

devaluation rate t. The left column of figure 1 displays qualitatively the effect of changes

in transfers on the private sector. If the economy is operating below full employment, an

increase in transfers brings about a reduction in involuntary unemployment, a real appreci-

ation (i.e., an increase in the relative price of nontradables), and an expansion in aggregate

consumption. Note that in this case, employment increases even though real wages are un-changed and firms are on their demand schedule. The reason is that the relative price of

nontradables increases, thereby boosting the value of the marginal product of labor.

Consider now the macroeconomic effect of a devaluation, starting from a situation in

which the economy exhibits involuntary unemployment. The effects are illustrated in the

right column of figure 1. The primary effect of a devaluation is to lower the real wage when

wage rigidities are binding. In this case, the devaluation boosts employment by reducing

labor costs. The resulting increase in the supply of nontradables causes their relative price

to fall, allowing consumers to switch expenditures toward this type of good. The ability of

devaluations to stimulate private spending ceases once the economy reaches full employment.

We note that figure 1 considers partial equilibrium effects in which either transfers or

the devaluation rate are held constant. In general equilibrium, these two variables are

endogenously determined by the governments transfer and exchange rate policies. We turn

now to a characterization of the governments policy problem.

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2.5 The Government

The government is assumed to choose the process for transfers, t, in a benevolent fashion,

in the sense of maximizing the welfare of private households. The governments objective

function is to maximize the lifetime utility of the representative household taking into account

the resource allocations that result in the private sector through the optimizing behavior of

households and firms. Formally, the objective function of the government is given by

E0

t=0

tU

yTt + t,

wt1t

, (13)

where U is an indirect utility function given by

UyTt + t, wt1t

UCyTt + t, wt1t

; U1 > 0; U2 0.The optimal transfer process will depend, in general, on the assumed structure of financial

markets and on the monetary policy implemented by the central bank. The central focus of

this paper is the interaction between financial structure and the effectiveness of monetary

policy in an economy with downward nominal wage rigidity. We turn next to a description

of monetary policy.

3 Full-Employment Exchange-Rate Policy And Cur-

rency Pegs

We consider two polar exchange-rate arrangements. The first one is a currency peg. This

policy regime is meant to capture, for example, the monetary policy in place in Argentina

prior to the default episode of 2001 and the monetary restrictions faced by the small emerging

economies that are members of the Eurozone, such as Greece and Portugal. Under a currency

peg the government commits to keeping the nominal exchange rate constant over time,

Et = Et1 for t 0. As a result, the gross rate of devaluation equals unity at all times:

t = 1,

for t 0.

Under a currency peg, relative prices and quantities in the private sector are determined

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as functions of t and wt1 only as follows:

wt =

yTt + t, wt1

, (14)

ht

= HyTt

+ t, w

t1 , (15)

pt = P

yTt + t, wt1

, (16)

cNt = CN

yTt + t, wt1

, (17)

cTt = yTt + t,

and

ct = C

yTt + t, wt1

. (18)

The second exchange-rate arrangement we consider is one in which the central bank

always sets the devaluation rate to ensure full employment in the labor market. We refer

to this monetary arrangement as the full-employment exchange-rate policy. Formally, this

policy amounts to setting the devaluation rate to ensure that the real wage equals the full-

employment wage rate, wf,t, at all times. We assume that, if wf,t is greater than wt1,

then the monetary authority keeps the nominal exchange rate constant, that is, t = 1.

There is no need for a devaluation in this case, because the nominal wage rate will adjust

upward on its own accordrecall that nominal wages are fully flexible upward. If, on the

other hand, wf,t is lower than wt1, then the monetary authority chooses t to ensure

that wf,t = wt1/t. In this case, if the central bank chose not to devalue, the economywould experience unemployment, because downward wage rigidities would prevent the real

wage from falling to the flexible-wage level wf,t. It follows that under the full-employment

devaluation policy, the devaluation rate is given by

t = max

wt1wf,t

, 1

.

This exchange-rate policy ensures that in every period t > 0, the real wage rate equals the

full-employment real wage:

wt = f(yTt , t). (19)

Thus, using equation (11), we can write

t = max

f(yTt1 + t1)

f(yTt + t), 1

; t > 0. (20)

Because f is a strictly increasing function of tradable income, this expression states that

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the central bank will devalue the domestic currency only when tradable income falls. Be-

cause in equilibrium traded consumption equals tradable income, we have that the monetary

authority devalues only when tradable expenditure falls.

The full-employment exchange-rate policy guarantees that the labor market is always at

full employment:ht = h, (21)

for all t 0. This means that output of nontradables is constant, at yNt = F(h), and therefore

so is nontraded consumption,

cNt = F(h). (22)

We then have, using equation (6), that the relative price of nontradables under the full-

employment exchange-rate policy is given by

pt = f(yTt + t)

F(h). (23)

Finally, aggregate consumption is determined by

ct = A(yTt + t, F(h)). (24)

We have demonstrated that the full-employment exchange-rate policy completely eliminates

any effect that downward nominal wage rigidities may have on the real allocation. Put

differently, under the monetary regime assumed here, the economy becomes identical to one

with full wage flexibility. Indeed, in the context of our model, the full-employment exchange-

rate policy is always optimal. The reason is that, when the nontraded sector operates at full

employment, the equilibrium real allocation depends only on the level of transfers, which, in

turn, as will become clear shortly, is independent of the devaluation rate process.

4 Devaluation Incentives Under Complete Asset Mar-

kets

As a useful benchmark environment, we consider an economy with access to a complete

array of state-contingent claims. The main purpose of studying this type of asset structure

is to show that in emerging economies in which external shocks play an important role, the

countrys ability to insure against such shocks greatly simplifies the monetary-policy problem.

This benchmark will then be contrasted with environments featuring different forms of asset-

market incompleteness in which monetary policy will play a central stabilizing role.

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Under complete asset markets, the budget constraint of the government is given by

t + dt = Etq

t,t+1dt+1, (25)

where dt+1 is a state-contingent payment of the government to its international creditors

chosen in period t. The random variable dt+1 can take on positive or negative values. A

positive value of dt+1 in a particular state of period t + 1 can be interpreted as the external

debt due in that state and date. The variable qt,t+j denotes the period-t price of an asset

that pays one unit of tradable good in one particular state of period t + j divided by the

probability of occurrence of that particular state conditional upon information available in

period t. It follows that Etq

t,t+1dt+1 is the period-t price of the state-contingent payment

dt+1. The government faces a borrowing limit of the form

limjEtq

t,t+jdt+j 0, (26)

which prevents Ponzi schemes.

The government chooses processes {t, dt+1, wt} to maximize the indirect utility func-

tion (13) subject to (12), (25), and (26), given d0, w1, the process q

t,t+1, the endowment

process yTt , and a monetary policy regime. The first-order condition with respect to dt+1 is

tq

t,t+1 = t+1,

where t denotes the Lagrange multiplier on the governments budget constraint (25). For-eign households are assumed to have access to the same array of contingent claims available

to domestic agents. Thus, the following Euler equation holds abroad:

t q

t,t+1 =

t+1,

where t denotes the marginal utility of tradable consumption of foreign residents. Note

that we assume that domestic and foreign residents have the same subjective discount fac-

tor. Because the above two expressions hold on a state-by-state and date-by-date basis,

they imply that the domestic and foreign marginal utilities of consumption of tradables areproportional to each other at all dates and states:

t =

t ,

where > 0 is a constant reflecting a wealth differential between the domestic and the

foreign economies. We will assume that the country faces no systemic uncertainty from

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abroad. Therefore, we set t = , where is a positive constant. It then follows that t

is constant as well:

t = .

We wish to show that when financial markets are complete, full-employment at all times

is a solution to the governments problem independently of whether the government follows

an exchange-rate peg or a full-employment exchange-rate policy. To this end, we solve the

governments maximization problem without imposing restriction (12) and then show that

the solution to the less-constrained optimization problem indeed satisfies this constraint.1

The first-order condition with respect to the transfer t is given by

U(ct)

A1(c

Tt , c

Nt ) + A2(c

Tt , c

Nt )C

N1

yTt + t,

wt1t

= . (27)

Now consider a solution in which cNt = F(h) for all t. In this case, first-order condition (27)

implies that consumption of tradables, cTt = yTt + t, is constant across states and time,

at a level that we denote by cT. Replacing t by cT yTt in the sequential budget con-

straint of the government, equation (25), iterating forward, and imposing the no-Ponzi-game

constraint (26), one obtains

cT = (1 )

d0 + E0

t=0

tyTt

.

Let the wage rate be constant over time and given by:

wt =A2(c

T, F(h))

A1(cT, F(h))F(h). (28)

The right-hand side of this expression is the full-employment wage rate associated with

yTt + t = cT. What remains to be shown is that the suggested path of wages given in

equation (28) satisfies the omitted constraint (12) for both monetary policies considered.

This amounts to verifying that wt wt1/t for t 0 when wt is given by (28). Notice

that for any t > 0, wt = wt1. Note also that t = 1 for t > 0 under both a currency peg and

the full-employment exchange-rate policy. The fact that t = 1 under the full-employment

exchange-rate policy follows from equation (20) and the facts that < 1 and that, because

yTt + t = cT is constant, the full-employment real wage rate is also constant constant for

t 0. Therefore, because 1 for any t > 0, equation (12) holds for both monetary regimes.

1Alternatively, it is possible to impose (12) as a constraint and show that under the proposed full-employment solution, the Lagrange multiplier associated with (12) is nil.

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It remains to show that under our proposed real wage rate, equation (12) holds at t = 0.

Suppose monetary policy takes the form of an exchange rate peg. Then equation (12) holds

in period 0 as long as w1 w0. We will assume that the initial condition, w1, is such

that this condition is satisfied.2 Alternatively, if the central bank follows a full-employment

exchange rate policy, then equation (12) will be satisfied if and only if w1/0 w0. Thegovernment can always pick 0 so that this condition is met.

We have shown that, when asset markets are complete, the full-employment allocation

results under both monetary policies. The intuition for this result is that the fact that

the benevolent government has access to complete asset markets allows households to com-

pletely smooth consumption across dates and states. In this case stochastic variations in

tradable output only affect the transfer payments, but not consumption allocations. With

consumption constant over time, nominal rigidities no longer play any role in equilibrium

determination. We summarize this result in the following proposition:

Proposition 1 When financial markets are complete, the optimal transfer policy guarantees

full employment at all dates and times regardless of whether monetary policy is characterized

by a currency peg or by the full-employment exchange-rate-policy.

The stochastic environment considered in this section, featuring a single shock to tradable

output, was deliberately constructed to yield the strong monetary-policy-irrelevance result

of proposition 1. Our main interest is not however, the message of the proposition in its

strongest sense, but rather to build a benchmark scenario that is analytically tractable and

transparent to convey the main idea of the present study, namely that when key nominalprices are downwardly rigid, the real consequences of monetary policy are greatly influenced

by the underlying financial structure. The usefulness of this strategy will become apparent in

the next section when the macroeconomic consequences of a currency peg in an environment

with complete asset markets are contrasted with its consequences in an environment of

financial autarky.

5 Devaluation Incentives Under Financial Autarky

Under financial autarky, the government is unable to borrow or lend internationally. As a

result, transfers equal zero at all times

t = 0,

2One can show that if this initial condition is not satisfied, then a currency peg gives rise initially toinvoluntary unemployment. However, after a finite number of periods, the economy reaches full employmentforever. In this case, therefore, a currency peg yields full employment up to a finite initial transition.

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and consumption of tradables equals tradable output

cTt = yTt .

This represents a sharp contrast with the case of complete asset markets, in which consump-

tion of tradables is perfectly constant across dates and states.

More importantly for the purpose of our study is that under financial autarky, unlike in

the case of complete asset markets, the dynamics of the nontraded sector depend crucially

upon the assumed exchange-rate regime. Under the full employment exchange-rate policy,

nontraded consumption is constant over time and equal to F(h). This perfect smoothness

in nontradable consumption is the result of optimal monetary policy, which deflates the real

value of past wages whenever the efficient allocation requires a reduction in the equilibrium

real wage by a factor greater than 1 , a situation that happens when the tradable sector

is contracting. Formally, setting t = t1 = 0 in equation (20), we obtain the followingexpression for the optimal devaluation rate under financial autarky

t = max

f(yTt1)

f(yTt ), 1

; t > 0. (29)

Because the function f is strictly increasing, this expression states that the central bank

optimally devalues the domestic currency only when tradable output falls, yTt < yTt1.

These devaluations are designed to undue nominal frictions in states in which they would

otherwise be binding. Because in this economy devaluations occur when the economy is

contracting, non-micro founded statistical analysis would conclude that devaluations are

contractionary. However, the role of devaluations in this model is precisely the opposite,

namely, to prevent the contraction in the tradable sector to spill over into the nontraded

sector. It follows that in this economy devaluations are indeed expansionary in the sense that

should they not take place, aggregate contractions would be even larger. Thus, under the

optimal exchange-rate regime, our model with downward nominal rigidities turns the view

that devaluations are contractionary on its head and instead predicts that contractions are

devaluatory.

Under the optimal monetary policy, the average devaluation rate is positive (Et > 1).This result follows directly form the fact that, by equation (29), the equilibrium gross deval-

uation rate is time varying and bounded below by unity. The inflation rate in the nontraded

sector is also positive on average. To see this, notice that the relative price of nontradables,

pt, is given by the ratio of the nominal price of nontradables and the nominal exchange

rate. Because in our model the relative price of nontradables is a stationary variable and

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the nominal exchange rate grows on average at a positive rate, it follows that the nominal

price of nontradables must also grow on average at a positive rate, which means that the

inflation rate in the nontraded sector must be positive on average. The aggregate rate of

inflation is then also positive on average, because it is a weighted average of the inflation

rates of the traded and nontraded sectors. Therefore, our model formalizes Oliveras (1960,1964) structural or nonmonetary theory of the optimality of positive inflation.3

When the exchange-rate policy takes the form of a currency peg, macroeconomic dynam-

ics are characterized by equations (14)-(18) evaluated at t = 0 for all t. As in the case

of the optimal exchange-rate-policy, consumption of tradables equals tradable output at all

times, cTt = yTt . But the dynamics of employment, wages, and the real exchange rate are

quite different across the two monetary regimes. Under a currency peg, the economy will

display involuntary unemployment whenever the full employment wage rate, f(yTt ), falls

below wt1. Because f is strictly increasing, it follows that involuntary unemployment is

more likely to emerge the larger is the contraction in the tradable sector.

To illustrate the predictions of our model we perform a numerical simulation. We assume

a CRRA form for the period utility function, a CES form for the aggregator function and

an isoelastic form for the production function of nontradables:

U(c) =c1 1

1 ,

A(cT, cN) = a(cT)11 + (1 a)(cN)1 1

1

,

and

F(h) = h.

We calibrate the model at a quarterly frequency using data from Argentina. Reinhart and

Vegh (1995) estimate the intertemporal elasticity of substitution to be 0.21, using Argentine

quarterly data. We therefore set equal to 5. We normalize the steady-state levels of

output of tradables and hours at unity. The parameter a then represents the share of traded

consumption in total consumption. We set this parameter at 0.26, which is the share of

traded output observed in Argentine data over the period 1980:Q1-2010:Q1. This approachto calibrating the share of tradable consumption is justified in the context of a model without

investment and with financial autarky. We set the elasticity of substitution between traded

and nontraded consumption, , to 0.44 following the estimates of Stockman and Tesar (1995).

Following Uribes (1997) evidence on the size of the labor share in the nontraded sector in

Argentina, we set equal to 0.75.

3See also Tobin (1972).

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Table 1: Calibration

Parameter Value Description 5 Inverse of intertemporal elasticity of consumptiona 0.26 Share of tradables

0.44 Elasticity of substitution between tradables and nontradables 0.75 Labor share in nontraded sectorh 1 Labor endowment

yT 1 Steady-state tradable output 0.90 Serial correlation of log tradable output

T 0.0355 Standard deviation of innovation to log of tradable output 0.953 Quarterly subjective discount factorr 0.02 Quarterly world interest rate 0.0002 Debt sensitivity of country premium 0.99,0.95,0.9 Degree of downward nominal wage rigidity

The driving force in our model is the stochastic process for tradable output. Our empirical

measure ofyTt is Argentine GDP in agriculture, forestry, fishing, mining, and manufacturing.

After removing a log-quadratic time trend, we estimate the following AR(1) process using

data over the period 1980:Q1 to 2010:Q1:

ln(yTt /yT) = ln(yTt1/y

T) + Tt, (30)

where t is white noise with mean zero and variance equal to one. Our OLS estimates of

and T are, respectively, 0.90 and 0.0355.A key parameter in our model is , which measures the ability of firms to cut nominal

wages without facing worker resistance. To our knowledge, no econometric estimate of this

parameter exists. One difficulty in estimating is that it belongs to an occasionally binding

constraint. Therefore, the econometrician cannot rely on an equation that holds in every

period and features among its parameters. Also, empirical evidence on the observed

frequency of nominal wage cuts, taken in isolation, is in general not informative about the

size of. The reason is that the frequency of observed wage cuts in general depends on the

underlying monetary regime. For example, in the calibrated economy studied here, when

equals 0.95, nominal-wage cuts occur 60 percent of the time under an exchange-rate peg,

and 50 percent of the time under the optimal policy. These figures could erroneously be

interpreted as meaning that in the currency-peg economy nominal wages are less rigid than

in the optimal-monetary-policy economy. These arguments suggest that must be estimated

in the context of a fully-specified general equilibrium model featuring a full description not

only of the incentives of households, workers, and firms, but also of government policy.

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Table 2: Inflation, Unemployment, and Welfare

Wage Mean Inflation Mean Unemployment Std. Dev. log(ct) WelfareStickiness Optimal Currency Optimal Currency Optimal Currency Cost

Policy Peg Policy Peg Policy Peg of PegA. Complete Asset Marketsall 0 0 0 0 0 0 0

B. Financial Autarky0.99 12.01 0.01 0.00 7.08 2.10 5.47 4.880.95 5.60 0.00 0.00 1.33 2.10 2.88 0.840.90 1.66 0.00 0.00 0.26 2.10 2.25 0.16

Note. The inflation rate is expressed in percent per year. The mean unemployment rate and the

standard deviation of the log of consumption is in percent. The welfare cost of a peg is calculated

as the percentage increase in the entire consumption path associated with a peg required to yield

the same level of welfare as under the optimal monetary policy.

Therefore, we perform our simulations for three alternative values of , 0.99, 0.95, and 0.9.

We consider a value of of 0.9 to represent a case of high wage flexibility. For in this case

every firm in the economy can cut nominal wages by 40 percent each year without incurring

any cost or resistance on the part of workers. On the other hand, we interpret the case of

= 0.99, as representing a situation of relatively high downward nominal rigidity. For in

this case firms face high resistance to any wage cuts larger than 4 percent per year. The

case of = 0.95 represents a situation of intermediate nominal wage rigidity, in which firms

can cut nominal wages by 20 percent in one year, without facing much resistance. Table 1summarizes the calibration of the model.

Table 2 displays model predictions for the average inflation rate, the average rate of

unemployment, consumption volatility, and the welfare cost of a currency peg. Panel A of the

table presents the results derived theoretically for the economy with complete asset markets.

In this economy, agents are able to fully smooth consumption. As a result, monetary policy is

irrelevant, and, in particular, the welfare cost of a currency peg is nil. By contrast, in the case

of financial autarky, shown in panel B of table 2, monetary policy can play an important role

in moderating the aggregate effects of external shocks when nominal wages are downwardly

rigid. Under the optimal policy regime, the average rate of inflation is 5.6 percent per year

at the intermediate level of downward wage rigidity ( = 0.95). As explained earlier, the

optimality of positive average inflation is explained by the central banks policy of inflating

away the purchasing power of nominal wages when equilibrium in the labor market requires

cuts in real labor costs.

By contrast, the average rate of inflation is virtually zero under a currency peg regardless

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of the degree of downward wage rigidity. To see why inflation is near zero under a currency

peg, we note that with a CES aggregator of tradables and nontradables, the consumer price

index is given by

Pt = aE1t + (1 a)

PNt1

1

1

,

where Pt denotes the nominal price of one unit of the composite consumption good in period

t, and PNt denotes the nominal price of one unit of nontradable consumption in period

t. It follows from this expression that the gross rate of consumer-price inflation, denoted

t Pt/Pt1, is given by

t =

a + (1 a)pt

1

a + (1 a)pt11

11

t.

Because the relative price of nontradables, pt, is a stationary variable, it follows that under a

currency peg (i.e., when the central bank sets t = 1 at all times), the rate of inflation must

be approximately nil on average.

The low and stable rate of inflation induced by the currency peg comes at the cost of

poorer real macroeconomic performance. In particular, the currency peg causes unemploy-

ment, which ranges from 7 percent in the high-wage-rigidity case to about 0.25 percent in the

low-wage-rigidity case, and an elevated volatility of consumption, which reaches 5 percent

with high wage rigidity and 2 percent with low wage rigidity. The last column of table 2

shows that the welfare cost of a currency peg can be large. It shows that in the high-wage-

rigidity case, households require an increase of 5 percent in their consumption stream to feelas happy as in the economy with optimal monetary policy. The welfare cost of a peg is also

sizable in the economy with intermediate wage rigidities, reaching 1 percent. When firms

are allowed to cut nominal wages by 40 percent per year or more (i.e., when is less than

or equal to 0.9), the economy behaves virtually as an economy with full wage flexibility. We

conclude that in the economy under study, the central bank faces a clear tradeoff between

inflation on the one hand, and unemployment and aggregate instability on the other hand.

Moreover, this tradeoff can involve large numbers for both inflation and unemployment for

relatively mild levels of downward nominal rigidities. For instance, we have shown that when

firms can costlessly cut nominal wages y up to twenty percent per year, the rate of inflation

ranges from 6 percent per year under the optimal exchange-rate policy to zero percent under

a peg, and structural unemployment ranges from zero under the optimal policy to 1.3 percent

under a currency peg.

In the present model, the employment-inflation tradeoff is trivially resolved in favor of

inflation. This is because, for simplicity, we have assumed that inflation is costless. However,

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in a more realistic setting in which in secular price increases are costly, such as in models that

introduce a demand for liquidity or models with upwardly rigid product prices, the structural

inflationary pressures highlighted in this paper would give rise to a nontrivial resolution of

the employment-inflation tradeoff.

[TO BE CONTINUED]

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Olivera, Julio H. G., On Structural Inflation and Latin-American Structuralism, Oxford

Economic Papers 16, November 1964, 321-332.

Reinhart, Carmen M., and Carlos A. Vegh, Nominal interest rates, consumption booms,

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Schmitt-Grohe, Stephanie, and Martn Uribe, The Optimal Rate of Inflation, Handbook

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Stockman, Alan C., and Linda L. Tesar, Tastes and Technology in a Two-Country Modelof the Business Cycle: Explaining International Comovements, American Economic

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currency pegs and unemployment

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