devereux yet man

7/29/2019 Devereux Yet Man

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Monetary Policy and Exchange

Rate Pass-through: Theory and

EvidenceMichael B. Devereux and James

Yetman



Main Features:

The paper develop a model of exchange rate pass-through based on the frequency of price changesby importing firms;

The price change frequency is influenced by themonetary policy rule.

“looser” monetary policy rule lead to high meaninflation and high volatility of the exchange rate.

Prediction: there should be positive relationshipbetween pass through and mean inflation andbetween pass through and exchange rate volatility.



The Importing Firm:

• If the firm can freely

adjust the price, then

*

1)(

t t t tPSi P



A “menu cost” F

• As in Calvo (1983)

there is a probability

that firms change pricesat any period. The

optimal price for the

newly price setting

firm is:

1

)(])1

)[ln(1()( 1

~*

~

i p E p si p t t t t t t

(1)



Price index for imported goods

1

~

)1( t t t p p p(2)



Determination of the exchange rate

• Equations (1) and (2)determine the degree of pass-through fromexchange rates to prices.

• The monetary rule:

• The home consumer Eulerconditions:

1,11

)(

t

t t

P

Pei t

11

11

1

*

1

1

1

1

t t

t t t

t

t t t

t t t t

t

C P

C P E

i

SC P

SC P E

i

(3)

(4)

(5)



Inflation and real exchange rate

determination• The combination of the interest rule , (5),

the Euler equations, (3) and (4), and foreign

firm pricing equations, (1) and (2),determine inflation and real exchange rate

determination.



Inflation equation for imported

goods prices• Combining (1) and (2)

yields the imported

price inflation:

(6) t t t t t Eq

)(



Log Linearization

Approximation of the Eulerconditions yields:

Interest Parity —

Interest rule---

Combining the two

relationships yields

A relationship in realexchange rate andinflation--- (7)

11

*

1

*

t t t t t t t t

t t t

t t t t t

Eqq E r

i

s s Eii



Equations (6) and (7) give a simple

dynamic system in domestic

inflation and the real exchange rateWith autoregressive

stochastic processes

these equations aresolved:

t t t t

t t t t

b b r bq

a a r a

32

*

1

32

*

1

)1(

)1(

)1(



Intuition

If the monetary authorityhas a target fornominal interest ratewhich is smaller thanthe foreign interestrate,

, then the steady stateinflation is positive,and relatively high realexchange rate.

0



The higher is the coefficienton inflation in themonetary rule, the smaller

are both mean inflationand steady statedepreciation in the realexchange rate. Hence fora given parameter

tighter monetary policy (high ) implies alower mean inflation.



Exchange Rate Pass-Through

From equation (6) DY

write the equations

for the domestic pricelevel, and nominal

exchange rate:

111312

*

113322

*

11

*

132

*

1

)()()(1

1

t t t t t t t t t

t t t t t

p s b b r b a b a b r a b p s

p a a r a p

t



Real foreign interest rate shocks

• Focusing on the effect of realforeign interest shocks, orequivalently, domesticmonetary shocks, DY

demonstrate that the exchangerate responds by more than thedomestic price levels, sincesuch shocks cause bothimmediate real depreciation aswell as domestic inflation.

• For a given value of

Monetary policy has no effect onpass through.



Endogenous Price Rigidity

• With menu costs, the

higher is inflation, the

more costly it is for a firm

to set its price in terms of domestic currency, and

have the profits eroded by

exchange rate

depreciation. DY postulatethe following choice

problem for



]}))()(()([1

1min{min

2~~

0

1 i pi p E F L j t t

j

j

t t



Depends on the monetary rule. The

main finding is that the exchange

rate pass through also depends on

the monetary rule!



Critique

• Output is treated as an exogenous variable.

Thus, the output gap does not play a role in

the pass through from the exchange rate todomestic prices.

An extension will produce a new Keynesianaggregate supply relationship, as inLoungani, Razin and Yuen:



Open-Economy New-Keynesian

Phillips Curve

)log()log()1

1()

1(

))(1

)1(())(

1()

1()(

0*)1(

1

1

t t t

N

t

F

t

N

t

H

t t t t

N

t

e E en

n

Y Y n

Y Y n

E

C C r t



diidiihiw Bi f Bi M

B B M i

idiici pdiici p

dii pdii pP

diicdiicC

diihvP M C u E

n

t

n

t t t t t t t t t

t t t t

t

t

n

t t t

n

t t

n

t t

n

t t

n

t

n

t t

n

t t

t

t t t t

t

00

*

1

*

1,1111

*1 **

0

1

1

1

1*

0

1

11 1*

0

1

00

0

)()()()1()1(

1)()()()(

)()(

)()(

]));((); / ,([



0 000

00

0

0

*1

*1,111

1*

1**

0

));(();;(

)()()(

)()(

)()1()1(

1

)()()()(

t

n

t t t t

t t

t

n

t

n

t t t t

nt t

n

t t t t t t t

t t t t t t

t

nt t t

n

t t

diihvP

M C u E U

diidiihiw yP

diihiw

dii Bi f Bi

M B B M i

i

diici pdiici p



t

t

t t t c

t t h

t t t c

t t t c

t

t

t t t c

t t t m

t

t t t t

P

iw

mcu

ihv

r mcu

mcu

i

i

mcu

mcu

f ii

)(

);;(

));((

*)1();;(

);;(

1);;(

);;(

)1(1

111

1,*



))(()(

)()(

jh f A j y

P

j pC jc

t t t

t

t t t



Firm’s Optimization:

))(

(1

); / ,(

);(

1)

)((

)()(

)))(

(('

1)

)((

1)

)(()()(

))(

()()()(

1

1

t

t

t t t t t c

t t h

t t

t

t

t t

t

t t

t

t t

t t t

t

t t t t

A

i y

AP M C u

hv

A A

i y

P

iwismc

A

i y f f

A

i y

A A

i yiwiS MC

A

i y f iwihiwVC

Nominal

Real



t

t

t t t t

t

t

n

P

i yi pF

t

n

P

i yi p H

t

F

t

H

t

W

t

t

t W

t

d

t

t c

h

t

t t t t t

t t

p

p

AC ysP

p

diY

diY

Y Y Y

P

i pY y

A y f Af C u

A y f v AC ys

A j y f f AP

jw js

t

t t t

t

t t

2

1

1

1

1

)()(

0

)()(

1

1~

1

1

11

),;,(

))(

(

)); / ((');(

)); / ((),;,(

)); / )((('

)()(

**

Flexible prices

Set price one period in advance



ONE-PERIOD NOMINAL RIDIGITY

0)];;([);(

0)],;,((1

10)(

)(

1

1

)]()([1

1

][1

1

)(1

1

~1

1

22

1

1

2

1

1

1211

2

1

1

22

1

1

11

t t t t t t ct

t t t t

t

t t

W t

t

t

t

t

t

t

t

t t W t

t t t

W

t

t

t

t t t t

t

t

t t

t

y ys y yu E

AC ysP pPY

i E

i p

i

i

E

A

pPY f wi pPY

i MaxE

hw y pi

MaxE

ii MaxE



),;,(1

1

),;,()1(

),;,()1(

1

)1(])1([

)1 /(1)1(*1

)1 /(1)1(*1

1

1

)1(*1

2

1

1

][

][

t t N t

N t

t t N t

N t

t t

t

t

N t

N t

t t N t

N t

t t

t

t

t

t

t t

t

AY Y s

n

AY Y s pnnp

p

Y C

AC Y s pnnp

p

pn p pnP



x

x x

x

x

x

C C p p A Ao

r

t t t

t t t t t

)log(

. , , , ,

1*)1(

**

Steady state:



The Phillips Curve

c

cc

p

h

hh

w

pw

N

t t

N

t t

N

t t

u yu

f f f

A

y f f

f v

A

yv

C C Y yss

(.)(.))('

)(.))((''

,'

)(

)()(

1

1

1



„where

y A

y

y A

y

A A

y f v

y A

y

A

y

f v

A

y f f

A

y

C C u

C u

h

hh

cc

c

)(

)('

));((

)());((

))(('

1)(,

);(

);(

1

1

1

Elasticity of wage demands,

wrt to output, holding

marginal utility of income

constant

Elasticity of marginal product of

labor wrt output



Log-linearization of real mc:

n

t t t t

t t ss

t it

t t t ss

t it

t t t ss

t i

ssii

t t t t c

t

t t

t

t h

t t t

y yi yis

A A A

F

s y

y y y

y

F

si y

i yi yi y

i y

F

sss

i yF yu

A

i y

A

i yv

y ys

)()()(

)(1

))(1

)(

)())()((

)(

1)log()log(

));(();(

))(

();)(

(

);;(

11

_

_

_

_

Partial-equilibrium relationship?



)log()log()

1

1()

1(

))(1())(

1

)1(())(

1()

1()(

),log()log()(),log(

)log()1()]log()1()log([)log(

)]()()[log()log(

)()()log()log(

1

1

1

*

11

1

*

21

1

212

1

11

t t t

N

t

F

t

N

t

F

t

N

t

H

t t t t

t

t t t t t t t t t

t

t t

t t t t t

N

t t

N

t t t t t

N

t t

N

t t t t

e E e

n

n

C C Y Y n

Y Y n

E

P

PeP E P E

P

P

pn p pnP

C C Y yP E p

C C Y yP p

N N



)log()log()11()1(

))(1())(

1

)1(())(

1()

1()(

),log()log()(),log(

)][log()log()11(1)(

11)(

11)log()log(

)][log()log()1

1(

1)]log()[log(

1)log()log(

)]log()1()log()[log()1(

1)log(

)]log())[log(1()]log()log([

)]log())[log(1()]log()log([)log()log(

)log()1()]log()1()log([)log(

)log()log(

)](1

1)(

1)[log()log(

)(1

1)(1

)log()log(

)1(

)]log()[log(

)]()()[log()log(

)()()log()log(

1

1

1

11

1

11

1

*

111

*

12

*

1

*

21

*

1

*

1111

*

21

112

1

12

11

1

212

1

11

t t t

N

t

F

t

N

t

F

t

N

t

H

t t t t

t t t t t t

t

t t

t t t

N

t t

N

t

W

t t t t

t

t t t

t t t t t t t t

t t t t t

t t t t t t t

t t t t t t t t t t t

t t t t t

t t t

N

t t

N

t

W

t t t t

N

t t

N

t

W

t t t

F

t

H

t

W

t

t jt

W

t jt

N

t t

N

t t t t t

t t t t t t

e E enn

C C Y Y n

Y Y n

E

P E P E P

P

e E ennC C Y Y P E P

P

Pe

e E en

nP pP E P

pn pnPn

p

p E pn p pn

p E pn p E pnP E P

pn p pnP

p E p

C C Y Y P E p

C C Y Y P p

Y nY nY

P pY y

C C Y yP E p

C C Y yP p



Closing the capital account:

)log()log()1

1()

1(

))(1

)1(())(

1()

1()(

,

1

11

1

t t t

N

t

F

t

N

t

H

t t t t

N

t

N

t

H

t t

e E en

n

Y Y n

Y Y n

E

Y C Y C

Closing the trade account:

))(1

()1()(

1

1

1

N

t

H

t t t t Y Y E

n



Sacrifice Ratios in Closed vs.

Open Economies: An Empirical

TestPrakash Loungani, Assaf Razin, and

Chi-Wa Yuen



BackgroundLucas (1973) proposed a model in which the effect arises

because agents in the economy are unable to distinguish

perfectly between aggregate and idiosyncratic shocks; he

tested this model at the aggregate level by showing that the

Phillips curve is steeper in countries with more variable

aggregate demand. Ball, Mankiw and Romer (1988) showed

that sticky price Keynesian models predict that the Phillipscurve should be steeper in countries with higher average

rates of inflation and that this prediction too receives

empirical support



The data used in the regressions reported in this paper are taken from

Ball (1993, 1994) and Quinn (1997).

Sacrifice ratios and their determinants: Our regressions focus on

explaining the determinants of sacrifice ratios as measured by Ball. Hestarts out by identifying disinflations, episodes in which the trend

inflation rate fell substantially. Ball identifies 65 disinflation episodes

in 19

DATA

OECD countries over the period 1960 to 1987. For each of these

episodes he calculates the associated sacrifice ratio. The denominatorof the sacrifice ratio is the change in trend inflation over an episode.

The numerator is the sum of output losses, the deviations between

output and its trend (“full employment”) level.



Sacrifice ratios and their determinants: Our

regressions focus on explaining thedeterminants of sacrifice ratios as measured

by Ball. He starts out by identifying

disinflations, episodes in which the trend

inflation rate fell substantially. Ball identifies

65 disinflation episodes in 19 OECD countries

over the period 1960 to 1987. For each of these

episodes he calculates the associated sacrifice

ratio. The denominator of the sacrifice ratio is

the change in trend inflation over an episode.

The numerator is the sum of output losses, the

deviations between output and its trend (“fullemployment”) level.



For each disinflation episode identified by Ball, we use as an

independent variable the current account and capital account

restrictions that were in place the year before the start of theepisode. This at least makes the restrictions pre-determined with

respect to the sacrifice ratios, though of course not necessarily

exogenous.



Quinn (1997) takes the basic IMF

qualitative descriptions on the presence of

restrictions and translates them into a

quantitative measure of restrictions using

certain coding rules. This translation

provides a measure of the intensity of

restrictions on current account

transactions on a (0,8) scale andrestrictions on capital account

transactions on a (0,4) scale; in both cases,

a higher number indicates fewer

restrictions. We use the Quinn measures,

labeled CURRENT and CAPITAL,respectively, as our measures of

restrictions.

Capital Flow Restrictions

Sacrifice ratios and Openness Restrictions



Independent variable (1) (2) (3) (4)Constant -0.001

(0.012)

-0.059

(0.025)

-0.033

(0.022)

-0.058

(0/026)

Initial inflation 0.002(0.002)

0.003(0.002)

0.003(0.002)

0.003(0.002)

Length of Disinflation 0.004

(0.001)

0.004

(0.001)

0.004

(0.001)

0.004

(0.001)

Change of inflation

during episode

-0.006

(0.003)

-0.007

(0.003)

-0.006

(0.003)

-0.007

(0.003)

CURRENT 0.008

(0.003)

CAPITAL 0.010

(0.006)

OPEN 0.006

(0.002)

Adjusted R-Square 0.16 0.23 0.19 0.23

Number of

observations

65 65 65 65

Numbers In parantheses are standard errors

C l i



ConclusionIn our earlier work we showed that restrictions of

capital account transactions were significant

determinants of the slope of the Phillips curve, asmeasured in the studies of Lucas (1973), Ball-Mankiw-

Romer (1998), and others.

The findings of this note lend support to this line of

work, in particular to the open economy new

Keynesian Phillips curve developed in Razin and Yuen(2001). We find that sacrifice ratios measured from

disinflation episodes depend on the degree on

restrictions on the current account and capital

account. Of course, to be more convincing this finding

will have to survive a battery of robustness checks,

such as sub-sample stability, inclusion of many other

possible determinants (such as central bank

independence) in the regressions, and using

instruments to allow for the possible endogeneity of

the measures of openness.

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