the eﬀects of foreign shocks when u.s. interest … · consumption; investment ... trade...

The Effects of Foreign Shocks when U.S. Interest Rates are at

Zero

Martin Bodenstein, Christopher Erceg, Luca Guerrieri

International Finance Division

Board of Governors of the Federal Reserve System

October 2009

1

International Spillovers

Spillover effects of foreign shocks on the U.S. economy:

• DSGE model estimation as in de Adolfson, Laseen, Linde,

and Villani (2008), dynamic factor models as in Otrok,Crucini, and Kose (2008) indicate that even pronounced

slowdowns abroad have only modest contractionary impact

on large and relatively closed economies.

• Policy models such as FRB/Global and SIGMA in use at

the Federal Reserve reflect this view.

• Standard models generate considerable output correlationonly if shocks are correlated across countries (Backus,

Kehoe, and Kydland (1992), Baxter and Crucini (1995),

Justiniano and Preston (2008))

2

Our Paper

The literature on the effects of cross-country output spillovers

of idiosyncratic shocks has generally assumed that monetary

policy has complete latitude to offset foreign shocks.

In our analysis, the effects of foreign shocks on domestic

output are greatly amplified by a prolonged liquidity trap, even

for relatively closed economies such as the United States.

We analyze the spillover effects of country-specific foreign

shocks in a two country DSGE model that imposes the zero

bound constraint on policy rates.

Our benchmark simulations assume that only the home country

is constrained by the zero lower bound, though we also conduct

sensitivity analysis which allows for a global liquidity trap.

3

Literature on the Zero Bound

There is a growing literature on policy issues related the zero

bound constraint.

Phelps (1972), Summers (1991), and Fischer (1996) noted the

relevance of the zero bound to the determination of the

optimal inflation rate.

For these and additional aspects of monetary policy see

Eggertsson and Woodford (2003a,b), Jung, Teranishi, and

Watanabe (2005), Adam and Billi (2006, 2007), and Billi

(2009) who work with optimization-based frameworks.

Eggertsson (2006) and Christiano, Eichenbaum, and Rebelo

(2009) analyze the effectiveness of government spending at the

zero bound.

4

Related Open Economy Literature

McCallum (2000 and 2001), Svensson (2001) evaluate

alternative policies in small open economy models.

Coenen and Wieland (2003) build a three country model to

analyze alternative exit strategies from the ZLB suggested by

McCallum and Svensson for the case of Japan. However the

model is a mixture of optimization-based conditions and

non-optimization-based assumptions.

Our focus is on spillovers, and our model is a simple

optimization-based open economy macro model.

5

Model Overview

Standard DSGE model in the NK tradition with two countries:

• Each country produces a single final good by aggregating acontinuum of domestically-produced intermediate goods.

• Nominal and Real Rigidities:

- staggered wage and price contracts; habit persistence inconsumption; investment adjustment costs

• Exports are priced in the currency of the buyer (localcurrency pricing).

• Domestic financial markets are complete, but internationalmarkets incomplete.

6

Government Sector

• Government spending is determined exogenously.

• Government spending does not affect household utility or

production function but requires real resources to produce.

• Finances its expenditures with lump-sum taxes, budget is

balanced every period.

7

Monetary Policy

Monetary policy follows a Taylor-type rule and is constrained by

the zero bound on nominal interest rates.

Define the notional rate as:

xt = r + γx(xt−1 − r) + γππt + γy(yt − ynatt ). (1)

The effective rate is then given by:

it = max(0, xt). (2)

The steady state inflation rate is set equal to zero. ynatt is the

natural output level (output absent nominal rigidities).

8

Calibration

Home country is one third as large as foreign.

κw and κp consistent with 4 quarter contracts ; κx consistent

with 2 quarter contracts.

Trade elasticity of substitution is 1.1.

Import share is assumed to be 12 percent.

Baseline case for interest rate rule: γi = 0.7, γπ = 1.5,

γy = 0.125.

9

Model Solution

We replace the original equilibrium conditions by a log-linear

approximation except for the constraint on nominal interest

rates.

The only nonlinear equation in the model is given by

it = max(0, xt). (3)

We only consider perfect-foresight experiments, i.e., the shocks

surprise agents in the first period, but thereafter agents expect

that no more shocks will hit the system.

We employ two solution techniques: a Newton-Raphson-Type

algorithm and a piecewise linear approach.

10

Initial Baseline Path: Construction

The home country experiences a large and persistent preference

shock that leads to a sustained contraction of consumption in

the home country.

The expected duration of the liquidity trap is 10 quarters.

We then consider the effects of additional shocks that originate

in either the home or the foreign country.

These shocks may, or may not affect the expected duration of

the zero-lower-bound regime.

11

A Severe Domestic Recession

0 10 20 30 40−12

−10

−8

−6

−4

−2

0

2

% d

ev. f

rom

s.s

.

Home Absorption

Intial Conditions with ZLB enforcedIntial Conditions without ZLB enforced

0 10 20 30 40−4

−3

−2

−1

0

1

2Home Policy Rate

Per

cent

0 10 20 30 40−6

−5

−4

−3

−2

−1

0

1

2

3Home Inflation

Quarters

Per

cent

0 10 20 30 40−2

−1

0

1

2

3

4

5

6

7Home Real Interest Rate

Quarters

Per

cent

12

Initial Baseline Path: Description

Consumption preference shock that persistently lowers the

marginal utility of consumption in the home country.

Shock begins in period 1 and is unexpected. From period 2 on

agents operate under perfect foresight.

Policy rates in the home country drop by 2 percent and remain

at this level for 10 quarters.

Home inflation falls persistently, and real rates rise, depressing

home absorption even more. The real exchange rate

depreciation reduces effects but is not strong enough.

13

Foreign Consumption Shock when Home Country is at Zero

Lower Bound

In addition to the severe consumption shock in the home

country, the foreign country experiences a modestly sized

consumption shock.

The shock is sized such that foreign GDP declines by 1

percentage point.

14

A Foreign Shock Against the Backdrop of a Severe Domestic RecessionScenario

0 10 20 30 40−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

% d

ev. f

rom

bas

elin

e

Foreign GDP

ZLB bindsZLB does not bind

0 10 20 30 40−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2Foreign Policy Rate

% p

oint

dev

. fro

m b

asel

ine

0 10 20 30 40−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5Foreign Consumption

Quarters

% d

ev. f

rom

bas

elin

e

0 10 20 30 400

0.5

1

1.5

2

2.5

3

3.5

4

4.5Foreign Exports

Quarters

% d

ev. f

rom

bas

elin

e

15


0 5 10 15 20−0.8

−0.6

−0.4

−0.2

0

0.2

% d

ev. f

rom

bas

elin

e

Home GDP


0 5 10 15 20−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

0Home Policy Rate

% p

oint

dev

. fro

m b

asel

ine

0 5 10 15 200

0.2

0.4

0.6

0.8

1Home Absorption

Quarters

% d

ev. f

rom

bas

elin

e

0 5 10 15 20−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0Home Inflation

Quarters

% p

oint

dev

. fro

m b

asel

ine

16


0 5 10 15 20−4.5

−4

−3.5

−3

−2.5

−2

−1.5

−1

% d

ev. f

rom

bas

elin

e

Home Exports


0 5 10 15 20−0.05

0

0.05

0.1

0.15Home Real Interest Rate

% p

oint

dev

. fro

m b

asel

ine

0 5 10 15 20−4

−3.5

−3

−2.5

−2

−1.5

−1Real Exchange Rate

Quarters

% d

ev. f

rom

bas

elin

e

0 5 10 15 20−0.6

−0.5

−0.4

−0.3

−0.2

−0.1Home Trade Balance (GDP share)

Quarters

% p

oint

dev

. fro

m b

asel

ine

17

Foreign Consumption Shock ... (continued)

If interest rates can adjust without constraint (dashed line)

• the cut in foreign interest rates cushions the effects of the

shock on the foreign country,

• foreign shock depresses home net exports through activity

channel and real exchange rate appreciation of the home

currency,

• home output declines by 0.3 and inflation falls persistently,

• effect is mitigated by a rise in domestic absorption.

18


If interest rates are constrained by the zero bound constraint

(solid line)

• the cut in foreign interest rates cushions the effects of the

shock on the foreign country,

• shock is again transmitted to the home country through a

decline in foreign imports and an appreciation of the real

exchange rate,

• however, home interest rates remain unchanged and real

interest rates rise sharply as home prices deflate,

• home absorption and hence home GDP fall by more.

19


Decline in activity in the home country is magnified relative to

the case when initial conditions are such that home country is

far away from zero bound.

20

Some Features of the Model (continued)

Assume a shock ε1 that implies the zero lower bound binds

T (ε1) = T ∗ periods.

Two immediate consequences are:

• Limited relevance of initial shock ε1: for given T ∗, the

marginal effect of an additional shock µ1 does not depend

on the initial shock ε1.

• Symmetry of shocks: the marginal effects of a positive and

its corresponding negative shock are symmetric if the

duration at the zero bound remains at T ∗.

21

Some Features of the Model (continued)

If an additional shock changes T ∗, its effects are nonlinear.

Numerical simulations show that the effects of a marginal

shock are more pronounced the longer the economy is stuck at

the zero bound

22

Effects of Foreign Consumption Shock against the Backdrop of DomesticRecession

0 1 2 3 4 5 6 7 8 9 10 11 12 130

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Number of quarters at ZLB implied by initial domestic recession

Mar

gina

l spi

llove

r ef

fect

s **

Taylor ruleMore aggressive on inflationMore aggressive on output gap

23

Alternative Rules for Monetary Policy

−5 0 5 10 15 200

5

10

15

Average percent change in foreign GDP

Per

iods

Periods at the zero lower bound

Baseline monetary policyMore aggressive on inflationMore aggressive on output gap

−5 0 5 10 15 20

0.3

0.4

0.5

0.6

0.7

0.8


Domestic spillover of foreign shock

Spi

llove

r

0.3

0.4

0.5

0.6

0.7

0.8

Results when ZLB does not bind


Spi

llove

r

24

Alternative Trade Elasticities

−5 0 5 10 15 200

5

10

15

20


Per

iods

Periods at the zero lower bound

Baseline trade elasticityHigh trade elasticityLow trade elasticity

−5 0 5 10 15 20

0.4

0.6

0.8

1

1.2

1.4



Spi

llove

r

0.4

0.6

0.8

1

1.2

1.4

Results when ZLB does not bind


Spi

llove

r

25

What Else Do We Do?

• Alternative shocks: government spending, technology,

investment demand, other consumption preference shocks

• Alternative calibration: lagged indexation in the Phillips

curve, flatter Phillips curve, alternative monetary policy

rules

• A global liquidity trap

26

Conclusion

When monetary policy is unconstrained, it can cushion the

impact of foreign disturbances. By contrast, in a liquidity trap,

monetary policy cannot crowd in domestic demand as

effectively, and the spillover effects of foreign shocks can be

magnified greatly.

The amplification of idiosyncratic foreign shocks depends both

on the duration of the liquidity trap and the size of the foreign

shock, as well as on key structural features such as the trade

price elasticity.

Our analysis suggests that the benefits of policy coordination

across countries are enhanced in a liquidity trap.

27

Coordination has become frequent since 2008, when many

economies became constrained by the zero lower bound.

In future research, it will be useful to quantify the benefits of

such coordination.

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