gauti b. eggertsson, neil r. mehrotra sanjay singh, and lawrence summers · 2017. 1. 9. · gauti...
TRANSCRIPT
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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
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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)
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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)
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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
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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
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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
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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
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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)
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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