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A CONTAGIOUS MALADY? OPEN ECONOMY
DIMENSIONS OF SECULAR STAGNATION
Gauti B. Eggertsson, Neil R. MehrotraSanjay Singh, and Lawrence Summers
Brown University
European CommissionNovember 23, 2015
1 / 27
LOW GLOBAL INTEREST RATES
NOMINAL SHORT-TERM AND LONG-TERM RATES, 1990-2015
-‐2.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
Mar-‐90
Jul-‐9
1
Nov-‐92
Mar-‐94
Jul-‐9
5
Nov-‐96
Mar-‐98
Jul-‐9
9
Nov-‐00
Mar-‐02
Jul-‐0
3
Nov-‐04
Mar-‐06
Jul-‐0
7
Nov-‐08
Mar-‐10
Jul-‐1
1
Nov-‐12
Mar-‐14
Japan Germany
US UK
Eurozone
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
Mar-‐90
Jul-‐9
1
Nov-‐92
Mar-‐94
Jul-‐9
5
Nov-‐96
Mar-‐98
Jul-‐9
9
Nov-‐00
Mar-‐02
Jul-‐0
3
Nov-‐04
Mar-‐06
Jul-‐0
7
Nov-‐08
Mar-‐10
Jul-‐1
1
Nov-‐12
Mar-‐14
Japan Germany
US UK
Eurozone
2 / 27
SHORTCOMINGS OF SOME EXISTING MODELSGlobal interest rates:
rss =1β− 1 > 0
I Real interest rate must be positive in steady stateI ZLB driven by temporary shocks to discount rate
Output shortfalls and low inflation:I Persistent global ZLB episodesI Fall in inflation and poor real GDP growth
Breaking Ricardian equivalence:I Role of public debtI Role of income redistribution
US, Eurozone and Japan
3 / 27
QUESTION AND APPROACH
QuestionI 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?
ElementsI Two-country OLG model:
I World natural rate of interest can be negative
I Steady state with world interest rate stuck at the zero lower bound
I Permanent slump in output:I Downward nominal wage rigidity with partial adjustment
I Output gaps in steady state across countries
4 / 27
HOUSEHOLDS
Objective function:
maxCy,Cm,Co
U ={
log (Cy) + β log (Cm) + β2 log (Co)}
Budget constraints:
Cy = By
Cm = Y − (1 + r)By + Ad + Aint
Co = (1 + r)Ad + (1 + r∗)Aint
(1 + r)By ≤ D
0 ≤ Aint
5 / 27
NATURAL RATE UNDER PERFECT INTEGRATION
Asset market clearing condition:
NtByt + N∗
t By∗t = Nt−1Am
t + N∗t−1Am∗
t
Expression for global real interest rate:
1 + rWt =
1 + β
β(1 + gt)
ωt−1Dt + (1 − ωt−1)D∗t
ωt−1 (Yt − Dt−1) + (1 − ωt−1)(Y∗
t − D∗t−1)
Determinants of the real interest rate:I Tighter average (population-weighted) global collateral
constraints reduce world real interest ratesI Higher global population growth rates raises world natural rate
6 / 27
GLOBAL SAVINGS GLUT
SYMMETRIC POPULATION: ω = 1/2
Government budget constraint and fiscal rule:
Bg∗t + To∗
t + (1 + rt) IRt−1 + Tm∗t = G∗
t +(1 + r∗t−1
)Bg∗
t−1 + IRt
To∗t+1 = β (1 + r∗t )Tm∗
t
Asset market clearing (r = r∗):
Byt + By∗
t + Bgt + Bg∗
t − IRt = Adt + Ad∗
t
Interest rate (r = r∗):
1 + rt =Dt + D∗
t
Amt − Bg
t + Am∗t − Bg∗
t + IRt
7 / 27
INFLATION TARGET AND NEGATIVE NATURAL
RATES
ZLB places a bound on steady state inflation:
Π̄ ≥ 11 + r
Π̄∗ ≥ 11 + r∗
I If the natural rate of interest is negative, steady state inflationmust be positive
I No equilibrium with stable inflationI But what happens with nominal rigidities and zero inflation
target?
8 / 27
AGGREGATE SUPPLY
Output and labor demand:
Yt = Lαt
Wt
Pt= αLα−1
t
Labor supply:I Middle-generation households supply a constant level of labor L̄I Implies a constant market clearing real wage W̄ = αL̄α−1
I Implies a constant full-employment level of output: Yfe = L̄α
9 / 27
DOWNWARD NOMINAL WAGE RIGIDITY
Partial wage adjustment:
Wt = max{
W̃t, PtαL̄α−1}
where W̃t = γWt−1Π̄ + (1 − γ)PtαL̄α−1
Wage rigidity and unemployment:
I W̃t is a wage normI If real wages exceed market clearing level, employment is
rationedI Unemployment: Ut = L̄ − Lt
10 / 27
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
11 / 27
MONETARY POLICYInflation targeting:
Πt = Π̄ if i > 0
Π∗t = Π̄∗ if i∗ > 0
Above the ZLB:I If rt > Π̄−1, nominal rate equals the natural rate
I Otherwise, zero lower bound must be binding: i = 0
Derivation of aggregate demand curve:
1 + rt+1 =1 + itΠt+1
1 + rWt =
1 + β
β(1 + gt)
ωt−1Dt + (1 − ωt−1)D∗t
ωt−1 (Yt − Dt−1) + (1 − ωt−1)(Y∗
t − D∗t−1)
12 / 27
WORLD OUTPUT AND INFLATION
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
13 / 27
PROPERTIES OF A SYMMETRIC STAGNATION
PROPOSITION 1Let 1 + rW,nat < Π̄−1 and γ, γ∗ > 0. Then, there exists a locallydeterminate symmetric stagnation equilibrium with Y < Yfe, Y∗ < Y∗
fe, andΠ < Π̄.
Characterization:I Steady state with nominal interest rate at ZLBI Inflation below target in steady state - possibly outright deflationI Business cycle fluctuations around this depressed steady state
14 / 27
QUANTITATIVE EXAMPLE: EUROZONE AND USCALIBRATION
Panel A: Common parameters Symbol ValueLabor share α 0.7Discount rate β 0.96Inflation target Π̄ 1.75%Population growth g 1%
Panel B: Country-specific parameters Symbol US EurozonePotential output Yfe, Y∗
fe 1 0.96Wage adjustment γ, γ∗ 0.926 0.941Collateral constraint D, D∗ 0.157 0.136
15 / 27
QUANTITATIVE EXAMPLE: EUROZONE AND USKEY AGGREGATES
Panel C: Baseline calibration Symbol US EurozoneOutput gap Y, Y∗ 10% 15%Nominal rate i, i∗ 0% 0%Inflation rate Π, Π∗ 1% 1%Net foreign asset position Bm − 1+g
1+r D −12% 12.6%
Panel D: Counterfactual under autarky Symbol US EurozoneOutput gap Y, Y∗ 0% 21.3%Nominal rate i, i∗ 0.25% 0%Welfare (rel. to integration) U, U∗ +7.5% −4.2%
16 / 27
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
17 / 27
GOVERNMENT PURCHASES
Balanced budget government purchases:
1+ r = (1 + g)1 + β
β
ωD + (1 − ω)D∗
ω (Y − D) + (1 − ω) (Y∗ − D∗)− ωG − (1 − ω)G∗
Implications of fiscal expansion:I Increase in global average government purchases increases
world rate
I Role for coordinated fiscal expansion since benefits are sharedacross countries
I Absent coordination, fiscal expansion would be undersupplied
I Coordination problem worsens with number of countries
18 / 27
PERMANENT INCREASE IN THE PUBLIC DEBT
Interest rate with domestic and foreign public debt:
1 + r =(1 + g) 1+β
β (ωD + (1 − ω)D∗)
ω (Y − D) + (1 − ω) (Y∗ − D∗)− 1+ββ (ωBg + (1 − ω)Bg∗)
Implications of fiscal expansion:I Under perfect integration, what matters is global average of
public debt
I Decline in public debt in Eurozone lowers world natural rate ofinterest
I Similar to government purchases, public debt expansion wouldbe undersupplied
19 / 27
QUANTITATIVE EXAMPLE: EUROZONE AND USFISCAL MULTIPLIERS
Symmetric increase in G = 0.5% Symbol US EurozoneOutput gap Y, Y∗ 7.1% 10.7%Nominal rate i, i∗ 0% 0%Inflation rate Π, Π∗ 1.2% 1.2%Net foreign asset position Bm − 1+g
1+r D −17.3% 18.0%
Asymmetric increase in G = 1% Symbol US EurozoneOutput gap Y, Y∗ 7.1% 10.7%Net foreign asset position Bm − 1+g
1+r D -20.2% 21.1%Welfare (rel. to symmetric) U, U∗ −0.2% +0.2%
20 / 27
NEOMERCANTILISM AND FOREIGN ASSET
TARGETS
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
21 / 27
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
22 / 27
MULTIPLE EQUILIBRIA UNDER PERFECT
INTEGRATION
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
23 / 27
CURRENCY WARS
Nominal 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
24 / 27
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
25 / 27
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<on Trend
Poten<al Output -‐ Model
Output -‐ Model
0.0%
1.0%
2.0%
3.0%
4.0%
5.0%
6.0%
7.0%
8.0%
1986 1990 1994 1998 2002 2006 2010 -‐1.5%
-‐1.0%
-‐0.5%
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
1986 1990 1994 1998 2002 2006 2010
4.55
4.60
4.65
4.70
4.75
4.80
4.85
4.90
4.95
5.00
1995 1997 1999 2001 2003 2005 2007 2009 2011 2013
Eurozone
Data
Pre-‐Stagna;on Trend
Poten;al Output
Output
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
4.0%
4.5%
5.0%
2002 2004 2006 2008 2010 2012 2014 -‐0.5%
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
2002 2004 2006 2008 2010 2012 2014
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27 / 27