Exchange Rate Policy

Advanced Macroeconomics

-3. Exchange Rate Policy

David Strauss

CIDE

Nominal frictions

Important question in open economy macroeconomics: What is the role of monetary and exchange-rate policy in stabilizing business cycles?

In the family of “real” models, nominal frictions are absent (such as product or factor price rigidities or a demand for fiat money).

By construction, in this type of environment there is little room for the central bank to affect real allocations.

Now we study environments with nominal frictions in which policy actions of the monetary authority have real effects and welfare consequences.

Theoretical framework with downward nominal wage

rigidity

Two objectives:

I Convey in an intuitive manner how nominal rigidities amplify the business cycle in open economies.

I Develop a framework from which one can derive quantitative predictions useful for policy evaluation.

Model of a small open economy in which nominal wages are downwardly

rigid. (Schmitt-Groh´e and Uribe (2010))

Setup - Households

Economy populated by a large number of identical households with preferences described by the utility function

E0 ∞

X

t=0

βtU(ct),

wherect denotes consumption in periodt, the period utility function U is

assumed to be strictly increasing and strictly concave and the subjective

discount factorβ∈(0,1).

ct is a composite of tradable consumption,ctT, and nontradable

consumption,cN

t . The aggregation technology is of the form

ct =A(ctT,c N t ),

where A is an increasing, concave, and linearly homogeneous function. All of the external liabilities of the household are denominated in foreign currency. (see, for example, Eichengreen, Hausmann, and Panizza (2005) for empirical evidence that virtually all of the debt issued by emerging countries is denominated in foreign currency)

In particular, households are assumed to have access to a one-period, internationally traded, state non-contingent bond denominated in tradables.

Setup - Households

Budget constraint:

p_tTc_tT+p_tNc_tN+Etdt=pTt y T

t +wtht+ Ψt+ Etdt+1

1 +rt

.

wherepTt (ptN) denotes the nominal price of tradable (nontradable) goods,Et

the nominal exchange rate defined as the domestic-currency price of one unit

of foreign currency,ytT the endowment of traded goods,wt the nominal wage

rate,ht hours worked, and Ψt nominal profits from the ownership of firms.

The variablesrt andytT are assumed to be exogenous and stochastic.

(Movements iny_tT can be interpreted either as shocks to the physical

availability of tradable goods or as shocks to the country’s terms of trade)

Households supply inelastically ¯hhours to the labor market (each period).

Due to nominal wage rigidities it may be that they are not able to sell all the

hours they supply. They takeht ≤¯hexogenously given.

HH are assumed to be subject to a debt level which prevents them from

engaging in Ponzi schemes, (¯d denotes the natural debt limit)

Setup - Firms

Nontraded output, denotedyN

t , is produced by perfectly competitive firms

with production technology

y_tN=F(ht).

Firms choose labor to maximize profits, given by

Ψt≡pNt ytN−wtht.

Setup

We assume that the law of one price holds for tradables

p_tT =EtptT∗

We further assume that the foreign-currency price of tradables is constant

and normalized to unity,pT∗t = 1. Hence, the nominal price of tradables

equals the nominal exchange rate

p_tT =Et.

Households choose contingent plans{ct,ctT,ctN,dt+1}to maximize utility

subject to the constraints (budget constraint, consumption aggregator, debt

limit) and taking prices as given (in particularpT

Optimality Conditions

The optimality conditions for HH are (wherept≡

pN t

pT t )

A2(cT t ,ctN) A1(cT

t ,ctN)

=pt, (1)

U0(ct)A1(ctT,c N

t ) =λt, (2)

λt

1 +rt

=βEtλt+1+µt, (3)

µt ≥0, (4)

µt(dt+1−¯d) = 0, (5)

where λt

pT t

andµt denote the Lagrange multipliers associated with the budget

constraint and the debt constraint. Optimality condition for firms:

ptNF0(ht) =wt

Dividing both sides bypT

t and using the facts thatpTt =Et and that

ht=F−1(ytN) yields a supply schedule for nontradables goods

pt =

wt

Et

F0_(F−1_(yN t ))

Figure 8.1: The Demand For Nontradables

quantity,cN

price,p

A2(cT0, cN) A1(cT0, cN) A2(cT1, cN) A1(cT1, cN)

Figure 8.2: The Supply Of Nontradables

W0/E0

F′_(F−1(yN))

W1/E0

F′_(F−1_(yN₎₎

quantity,yN

price,p

Real Exchange Rate - Price of Nontradables

Real exchange rate is defined as the relative price of a foreign basket of consumption goods in terms of domestic baskets of consumption goods

RERt ≡ EtPt∗

Pt

,

wherePt (Pt∗) denotes the nominal price of consumption in the domestic

(foreign) country in units of domestic (foreign) currency.

WhenRERt ↑the domestic economy becomes relatively cheaper and we say

that the real exchange rate depreciates.

Conversely, whenRERt ↓, the real exchange rate appreciates and the

domestic economy becomes relatively more expensive than the foreign economy.

Downward Nominal Wage Rigidity

Central friction: Downward nominal wage rigidity. Specifically, we impose that

Wt ≥γWt−1, γ >0.

The degree of rigidity is governed byγ. The biggerγ, the more rigid are

wages.

Downwardly rigid nominal wages imply that the labor market will in general not clear!

Involuntary unemployment results ifht<¯h. At any point in time, wages and

employment must satisfy the slackness condition

(¯h−ht)(wt−γwt−1) = 0

Market Clearing Conditions

The market for nontraded goods must clear at all times,

c_tN =y_tN, ∀t.

Using the definition of firms’ profits, and this market clearing condition in the budget constraint implies the following market clearing condition for traded goods:

c_tT+dt =ytT+ dt+1

1 +rt

Equilibrium

Definitions:

I The real wage in terms of tradables:

ωt ≡

wt Et

.

I The gross rate of devaluation of the domestic currency:

t≡

Et Et−1

An equilibrium is a set of stochastic processes{cT

t ,ht, ωt,dt+1,pt, λt, µt}∞t=0

that satisfies the following set of equations - given an exchange rate policy

{t}∞t=0, initial conditionsω?1 andd0, and exogenous stochastic processes {rt,ytT}∞t=0:

Equilibrium

c_tT +dt =ytT+ dt+1

1 +rt

, (6)

dt+1≤d¯, (7)

µt ≥0, (8)

µt(dt+1−d¯) = 0, (9)

λt=U0(A(ctT,F(ht)))A1((ctT,F(ht)), (10)

λt

1 +rt

=β_Etλt+1+µt, (11)

pt=

A2(ctT,F(ht)) A1(ctT,F(ht))

, (12)

pt =

ωt F0_(h

t)

, (13)

ωt≥γ

ωt−1

t

, (14)

ht≤¯h, (15)

(¯h−ht)(ωt−γ

ωt−1

t

Exchange-rate regime - Currency Pegs

It remains to specify the exchange-rate regime. We will study now currency pegs (an empirically realistic exchange-rate policy) that is frequently observed in the emerging-country world.

Achilles’ heel of currency pegs: They hinder the efficient adjustment of the

economy to negative external shocks, such as drops in the terms of trade (y_tT

in our model), or hikes in the country interest-ratert.

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.

Real depreciation may come about via a nominal devaluation of the domestic currency or via a fall in nominal prices or both.

I The currency peg rules out a devaluation.

I Only way the necessary real depreciation can occur is through a decline in the nominal price of nontradables.

I However, with rigid nominal wages, producers of nontradables are reluctant to lower prices, for doing so might render their enterprises no longer profitable. As a result, the necessary real depreciation takes place too slowly, causing recession and unemployment along the way.

Exchange-rate regime - Currency Pegs

A currency peg is an exchange rate policy in which the nominal exchange rate is fixed.

t= 1 ∀t

Under a currency peg, the economy is subject to two nominal rigidities.

The nominal exchange rate is kept fixed by the monetary authority.

The second is the downward rigidity of the nominal wage.

The combination of these two nominal rigidities results in a real rigidity.

Specifically, under a currency peg, the real wage expressed in terms of

tradables,ωt, is downwardly rigid. Formally, one equilibrum equation becomes

ωt ≥γωt−1

As a result of this real rigidity, in general the labor market is in disequilibrium and features involuntary unemployment.

The magnitude of the labor market disequilibrium is a function of the amount by which the past real wage exceeds the current full-employment real wage.

Figure 8.3: Currency Pegs, Downward Wage Rigidity, and Unemployment

h

p

A2(cT0, F(h)) A1(cT0, F(h)) A2(cT1, F(h)) A1(cT1, F(h))

W0/E0 F′(h) =

W1/E1 F′(h)

W1/E0 F′_(h)

¯ h A B C D p0 pbust pboom hbust

Exchange-rate regime - Currency Pegs

Recall that in equilibrium: cN

t =ytN =F(ht). Thus we can write output in

terms of employment,ht.

Suppose the economy starts off in point A, the labor market is operating at full employment.

Now: positive external shock (e.g. decline in the country interest rate)⇒

traded absorption increases fromcT

0 toc1T>c0T ⇒the demand function

shifts up and to the right.

Nominal wages have to adjust in order to satisfy the excess demand for labor

⇒the nominal wage raises toW1>W0. The supply of non-tradables shifts

up and to the left. New equilibrium point: C.

Now: External shock fades away, absorption of tradables goes back to its original levelcT

0.

This is when the downward nominal wage rigidity matters. The wage cannot

return immediately toW0. (In the graph,γ= 1). And the exchange rate

Exchange-rate regime - Currency Pegs

There, the economy suffers involuntary unemployment.

Negative externality:

In periods of economic expansion, elevated demand for nontradables drives nominal (and real) wages up. This places the economy in a vulnerable situation, because in the contractionary phase of the cycle, downward nominal wage rigidity and the currency peg hinder the downward adjustment of real wages, causing unemployment. Individual agents understand this mechanism, but are too small to internalize the fact that their own expenditure choices collectively exacerbate disruptions in the labor market.

Volatility And Average Unemployment

The present model implies an endogenous connection between the amplitude of the cycle and the average level of involuntary unemployment. The larger the degree of aggregate volatility, the larger the average level of involuntary unemployment.

This connection between a second moment (the volatility of the underlying shocks) and a first moment (average unemployment) opens the door to large welfare gains from optimal stabilization policy.

Optimal Exchange Rate Policy

The reason why the economy experiences unemployment is that real wages are too high to clear the labor market. This downward rigidity in real wages is the consequence of downwardly rigid nominal wages and a fixed exchange rate regime. The unemployment problem could hence be addressed by any policy that results in lower real wages.

Option: Devaluate the currency! Set the exchange rate such that you always have full employment...