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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
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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
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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
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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
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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
∗
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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∗
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Additional Slides
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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