A CONTAGIOUS MALADY? OPEN ECONOMYDIMENSIONS OF SECULAR STAGNATION

Gauti B. Eggertsson, Neil R. MehrotraSanjay Singh, and Lawrence Summers

Brown University and FRB Minneapolis

The views expressed here are the views of the authors and do not necessarily represent theviews of the Federal Reserve Bank of Minneapolis or the Federal Reserve System

Bank of CanadaNovember 3, 2016

1 / 19

SECULAR STAGNATION HYPOTHESIS

Secular stagnation hypothesis:

I Alvin Hansen (1938) and Lawrence Summers (2013)I Highly persistent decline in the natural rate of interestI Chronically binding zero lower bound

Secular stagnation in a closed economy:I ZLB of arbitrary durationI Distinct policy responsesI Eggertsson and Mehrotra (2015)

2 / 19

RESEARCH QUESTION AND KEY FINDINGS

Research questions:I Does secular stagnation survive in a open economy framework?I What are the channels by which secular stagnation spreads?I What are the interactions in policy across countries?

Key findings:I Capital integration spreads recessionsI Substantial policy externalities

I Fiscal policy (+ externalities)I Neomercantilism/competitiveness (- externalities)

3 / 19

HOUSEHOLDS

Objective function:

maxCyt ,C

mt+1,C

ot+2

U = Et{

log(

Cyt)+ β log

(Cmt+1

)+ β2 log

(Cot+2

)}

Budget constraints:

Cyt = Byt

Cmt+1 = Yt+1 − (1 + rt)Byt + A

dt+1 + A

intt+1

Cot+2 = (1 + rt+1)Adt+1 + (1 + r

∗t+1)A

intt+1

(1 + rt)Byt ≤ Dt0 ≤ Aintt+1 ≤ K

4 / 19

CASE OF r > r∗Credit-constrained youngest generation:

Cyt = Byt =

Dt1 + rt

Cy∗t = By∗t =

D∗t1 + r∗t

Saving by the middle generation:

1Cmt

= βEt1 + rtCot+1

1Cm∗t

= βEt1 + r∗tCo∗t+1

Spending by the old:

Cot = (1 + rt−1)Adt−1

Co∗t = (1 + r∗t−1)A

d∗t−1 + (1 + rt−1)K

∗

5 / 19

NATURAL RATE UNDER IMPERFECTINTEGRATION

Case of r > r∗:

NtByt = Nt−1A

dt + N

∗t−1A

int∗t

N∗t By∗t = Nt−1A

d∗t

Expression for the domestic and foreign real interest rate:

1 + rt =1 + β

β

(1 + gt)DtYt −Dt−1 + 1−ωt−1ωt−1

1+ββ K

∗

1 + r∗t =1 + β

β

(1 + g∗t )D∗t +

1+rt1+β K

∗

Y∗t −D∗t−1 − K∗

6 / 19

AGGREGATE SUPPLY RELATION

0.80  

0.85  

0.90  

0.95  

1.00  

1.05  

1.10  

1.15  

1.20  

0.80   0.85   0.90   0.95   1.00   1.05   1.10  

Output  

Gross  Infla5o

n  Ra

te  

Aggregate  Supply  

7 / 19

MONETARY POLICY

Inflation targeting:

Πt = Π̄ if i > 0

Π∗t = Π̄∗ if i∗ > 0

I Monetary policy attempts to track the natural rate of interest

I Cannot attain the natural rate once it falls below inverse ofinflation target

I Inflation target equivalent to simple Taylor rule as Taylorcoefficient becomes large

8 / 19

ASYMMETRIC STAGNATION UNDER IMPERFECTINTEGRATION

Home Output0.6 0.8 1 1.2

Gro

ss In

flatio

n at

Hom

e

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Home ASAD integrationAD partial integration

Foreign Output0.6 0.8 1 1.2

Gro

ss In

flatio

n at

For

eign

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Foreign ASAD integrationAD partial integration

9 / 19

NEOMERCANTILISM

Natural rate of interest:

1 + r =1 + β

β

D

Yf −D +1+β

β (K− Bg + IR)

1 + r∗ =1 + β

β

D∗ + 1+r1+β K

Y∗f −D∗ − K−1+β

β Bg∗

Implications:I Policies that target positive NFA positions or CA surplusesI Reserve acquisition lowers natural rate in debtor countryI May raise natural rate in creditor country depending on

financing (debt v. taxation)

10 / 19

NEOMERCANTILISM

Home Output0.6 0.8 1 1.2

Gro

ss In

flatio

n at

Hom

e

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Home ASAD integrationAD autarky

Foreign Output0.6 0.8 1 1.2

Gro

ss In

flatio

n at

For

eign

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Foreign ASAD integrationAD autarky

11 / 19

SYMMETRIC STAGNATION UNDER PERFECTINTEGRATION

Global Output0.5 0.6 0.7 0.8 0.9 1 1.1

Gro

ss In

flatio

n

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

ASAD w shockAD w/o shock

A

B

Linearized Equations

12 / 19

RAISING THE INFLATION TARGET

Global Output0.5 0.6 0.7 0.8 0.9 1 1.1

Gro

ss In

flatio

n

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

ASADAD higher & target

13 / 19

EFFECTS OF FISCAL POLICY

Balanced budget government purchases:

1 + r =(1 + g) 1+ββ (ωD + (1−ω)D

∗)

ω (Y−D) + (1−ω) (Y∗ −D∗)−ωG− (1−ω)G∗

Interest rate with domestic and foreign public debt:

1 + r =(1 + g) 1+ββ (ωD + (1−ω)D

∗)

ω (Y−D) + (1−ω) (Y∗ −D∗)− 1+ββ (ωBg + (1−ω)Bg∗)

Implications of fiscal expansion:I Role for coordinated fiscal expansion since benefits are shared

across countriesI Absent coordination, fiscal expansion would be undersuppliedI Coordination problem worsens with number of countries

14 / 19

MULTIPLE EQUILIBRIA UNDER PERFECTINTEGRATION

Global Output0.5 0.6 0.7 0.8 0.9 1 1.1

Gro

ss In

flatio

n

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2(A) Multiple Equilibria

Symm Stag ASForeign Stag ASHome Stag ASGlobal AD

Global Output0.5 0.6 0.7 0.8 0.9 1 1.1

Gro

ss In

flatio

n

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2(B) Unique Equilibrium

Symm Stag ASForeign Stag ASHome Stag ASGlobal AD

FS

SS

HS

SS

15 / 19

CURRENCY WARSNominal exchange rate:

St =P∗tPt

∆St =Π∗tΠt

Exchange rate policy when rw,Nat < 0:I A pegged exchange rate St = S̄ eliminates any asymmetric

stagnation equilibrium

I Benefits the nation in stagnation at the expense of the nation notin stagnation

I Sufficiently aggressive depreciation eliminates the symmetricstagnation as equilibrium

16 / 19

EFFECTS OF STRUCTURAL REFORM

Home Output0.6 0.8 1

Gro

ss In

flatio

n at

Hom

e

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

AS

Foreign Output0.6 0.8 1

Gro

ss In

flatio

n at

For

eign

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

ASAS structural reform

A A

B

A"

B

17 / 19

CONCLUSIONS FOR POLICY

1. Importance of a policy responseI ZLB can persist for arbitrarily long periods

2. Importance of fiscal policy coordinationI Fiscal expansions will tend to be undersupplied

I Fiscal austerity will tend to be oversupplied

3. Risks of beggar-thy-neighbor policiesI Exchange rate policies may alleviate stagnation in one country

while worsening in the other

I Structural reform and targeting trade surplus similar effects

4. Fiscal policy focused on diminishing oversupply of saving

18 / 19

Additional Slides

19 / 19

SECULAR STAGNATION EPISODES

4.55  

4.65  

4.75  

4.85  

4.95  

5.05  

5.15  

1990   1993   1996   1999   2002   2005   2008   2011  

United  States  

GDP  per  capita  

Real  GDP  per  Capita  

Projected  Output  

PotenCal  Output  

Model  Output  per  Capita  

0.0%  

1.0%  

2.0%  

3.0%  

4.0%  

5.0%  

6.0%  

7.0%  

2000   2002   2004   2006   2008   2010   2012   2014  

Interest  Rate  

0.0%  

0.5%  

1.0%  

1.5%  

2.0%  

2.5%  

2000   2002   2004   2006   2008   2010   2012   2014  

Infla/on  Rate  

5.30  

5.50  

5.70  

5.90  

6.10  

6.30  

1970   1975   1980   1985   1990   1995   2000   2005   2010  

Japan  

GDP  per  capita,  1970-‐2013  

Pre-‐Stagna

US REAL WAGE, 2003-2013EMPLOYER COST INDEX DIVIDED BY PCE PRICE INDEX

1.05

1.06

1.07

1.08

1.09

1.10

1.11

Apr

-03

Sep-

03

Feb-

04

Jul-0

4 D

ec-0

4 M

ay-0

5 O

ct-0

5 M

ar-0

6 A

ug-0

6 Ja

n-07

Ju

n-07

N

ov-0

7 A

pr-0

8 Se

p-08

Fe

b-09

Ju

l-09

Dec

-09

May

-10

Oct

-10

Mar

-11

Aug

-11

Jan-

12

Jun-

12

Nov

-12

Apr

-13

Sep-

13

Source: BLS and BEA

Back21 / 19

MONEYMoney demand condition:

Cmt v′ (Mt) =

it1 + it

Government budget constraint:

Bgt + Mt + Tmt +

11 + gt−1

Tot = Gt +1

1 + gt−1

(1 + it−1

ΠtBgt−1 +

1Πt

Mt−1

)

Implications:I Assume that money demand is satiated at the zero lower bound

I Fiscal policy keeps real government liabilities constant

I Open market operations and QE leave constant the consolidated level ofgovernment liabilities

Back

22 / 19

CALVO PRICINGEquilibrium conditions:

Yt =L̄∆t

∆t =∫ (pt (l)

Pt

)−θdl

1 = χΠθ−1t + (1− χ)(

p∗tPt

)1−θ∆t = χΠθt ∆t−1 + (1− χ)

(p∗tPt

)−θ

Aggregate supply relation:

Y = L̄1− χΠθ

1− χ

(1− χ

1− χΠθ−1

) θθ−1

Back

23 / 19

TEMPORARY INCREASE IN PUBLIC DEBT

Under constant population and set Gt = Tyt = B

gt−1 = 0:

Tmt = −Bgt

Tot+1 = (1 + rt)Bgt

Implications for natural rate:I Loan demand and loan supply effects cancel outI Temporary increases in public debt ineffective in raising real rateI Temporary monetary expansion equivalent to temporary expansion in

public debt at the zero lower boundI Effect of an increase in public debt depends on beliefs about future fiscal

policy

Back

24 / 19

INCORPORATING CAPITALObjective function:

maxCyt,,C

mt+1,C

ot+2

U = Et{

log(

Cyt)+ β log

(Cmt+1

)+ β2 log

(Cot+2

)}

Budget constraints:

Cyt = Byt

Cmt+1 + pkt+1Kt+1 + (1 + rt)B

yt = wt+1Lt+1 + r

kt+1Kt+1 + B

mt+1

Cot+2 + (1 + rt+1)Bmt+1 = p

kt+2 (1− δ)Kt+1

Rental rate and real interest rate:

rkt = pkt − pkt+1

1− δ1 + rt

≥ 0

r ≥ −δ

Back

25 / 19

LANDLand with dividends:

plandt = Dt +plandt+11 + rt

I Land that pays a real dividend rules out a secular stagnation

Land without dividends:I If r > 0, price of land equals its fundamental value

I If r < 0, price of land is indeterminate and land offers a negative return r

Absence of risk premia:I No risk premia on land

I Negative short-term natural rate but positive net return on capital

Back

26 / 19

DYNAMIC EFFICIENCY

Planner’s optimality conditions:

CoCm

= β (1 + g)

(1− α)K−α = 1− 1− δ1 + g

D (1 + g) + Cm +1

1 + gCo = K1−αL̄α − K

(1− 1− δ

1 + g

)Implications:

I Competitive equilibrium does not necessarily coincide with constrainedoptimal allocation

I If r > g, steady state of our model with capital is dynamically efficient

I Negative natural rate only implies dynamic inefficiency if populationgrowth rate is negative

27 / 19

DYNAMIC EFFICIENCYIs dynamic efficiency empirically plausible?

I Classic study in Abel, Mankiw, Summers and Zeckhauser (1989) says no

I Revisited in Geerolf (2013) and cannot reject condition for dynamicinefficiency in developed economies today

Absence of risk premia:

I No risk premia on capital in our model

I Negative short-term natural rate but positive net return on capital

I Abel et al. (2013) emphasize that low real interest rates not inconsistentwith dynamic efficiency

Back

28 / 19

LINEARIZED DYNAMICS UNDER SYMMETRICSTAGNATION

Equilibrium conditions:

Etπt+1 = ω̄syyt + (1− ω̄) y∗t + shocksyt = γwyt−1 + γwφπty∗t = γ

∗wy∗t−1 + γ

∗wφπt

Local determinacy condition:

1 + γwγ∗w(1 + syφ

)< φsy (ω̄γw − (1− ω̄) γ∗w) + γw + γ∗w

Back

29 / 19