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A M ODEL OF S ECULAR S TAGNATION
Gauti B. Eggertsson and Neil R. Mehrotra
Brown University
Princeton
February, 2015
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S ECULAR S TAGNATION H YPOTHESIS
I wonder if a set of older ideas . . . under the phrase secular
stagnation are not profoundly important in understanding Japan’s
experience, and may not be without relevance to America’s
experience — Lawrence Summers
Original hypothesis:
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Alvin Hansen (1938): Suggests a permanent demand depression.
Reduction in population growth and investment opportunities.
Concerns about insufficient demand ended with WWII and
subsequent baby boom.
Secular stagnation resurrected:
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Lawrence Summers (2013)
Highly persistent decline in the natural rate of interest
Chronically binding zero lower bound
Goal here:
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Formlize these ideas in a simple model
Propose a OLG model in the spirit of Samuelson (1958)
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W HY ARE WE SO CONFIDENT INTEREST RATES
WILL RISE SOON ?
Interest rates in the US during the Great Depression:
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Started falling in 1929 (reach zero in 1933) ......
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...... only to increase in 1947
Started dropping in Japan in 1994:
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Remains at zero today
Why are we so confident interest rates are increasing in the next few
years?
Need a framework where the answer is not baked into the cake –
need a model that can account for arbitrary persistence of the
recession
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P REVIEW OF R ESULTS
Permanently negative natural rate of interest can be triggered by:
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Permanent deleveraging shock
Slowdown in population growth
Increase in income inequality
Fall in relative price of investment
Stagnation steady state
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Permanently binding zero lower bound
Low inflation or deflation
Permanent shortfall in output from potential – no obvious
adjustment mechanism (price flexibility paradox).
Monetary and fiscal policy responses
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Raising the inflation target
Increases in public debt
Increases in government purchases
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O UTLINE FOR P RESENTATION
1. Model
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Endowment economy
- deleveraging shocks, income inequality, population slowdown
- price level determination
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Endogenous production
2. Monetary and fiscal policy
3. Capital
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Fall in the relative price of investment
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E CONOMIC E NVIRONMENT
E NDOWMENT ECONOMY
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Time: t = 0, 1, 2, ...
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Goods: consumption good (c)
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Agents: 3-generations: ie {y, m, o}
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Assets: riskless bonds (Bi )
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Technology: exogenous borrowing constraint D
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H OUSEHOLDS
Objective function:
y
max
o
Ct, ,Cm
t+1 ,Ct+2
n
o
y
2
o
U = Et log Ct + β log Cm
+
β
log
C
t+1
t+2
Budget constraints:
y
y
Ct = Bt
y
m
m
Cm
t+1 = Yt+1 − (1 + rt )Bt + Bt+1
Cot+2 = Yto+2 − (1 + rt+1 )Bm
t+1
(1 + rt )Bit ≤ Dt
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C ONSUMPTION AND S AVING
Credit-constrained youngest generation:
y
y
Ct = Bt =
Dt
1 + rt
Saving by the middle generation:
1
1 + rt
= βEt o
Cm
Ct+1
t
Spending by the old:
Cot = Yto − (1 + rt−1 )Bm
t−1
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D ETERMINATION OF THE R EAL I NTEREST R ATE
Asset market equilibrium:
y
Nt Bt = −Nt−1 Bm
t
y
( 1 + gt ) Bt = − Bm
t
Demand and supply of loans:
1 + gt
Dt
1 + rt
β
1 Yto+1
Lst =
(Ytm − Dt−1 ) −
1+β
1 + β 1 + rt
Ldt =
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D ETERMINATION OF THE R EAL I NTEREST R ATE
Expression for the real interest rate (perfect foresight):
1 + rt =
Yto+1
1 + β (1 + gt )Dt
1
+
m
m
β Yt − Dt−1
β Yt − Dt−1
Determinants of the real interest rate:
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Tighter collateral constraint reduces the real interest rate
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Lower rate of population growth reduces the real interest rate
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Higher middle age income reduces real interest rate
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Higher old income increases real interest rate
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E FFECT OF A D ELEVERAGING S HOCK
Impact effect:
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Collateral constraint tightens from Dh to Dl
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Reduction in the loan demand and fall in real rate
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Akin to Eggertsson and Krugman (2012)
Delayed effect:
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Next period, a shift out in loan supply
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Further reduction in real interest rate
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Novel effect from Eggertsson and Krugman (2012)
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Potentially powerful propagation mechanism
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E FFECT OF A D ELEVERAGING S HOCK
1.20 Loan Supply Gross Real Interest Rate 1.15 1.10 1.05 A D 1.00 B 0.95 C Loan Demand 0.90 0.85 0.80 0.200 0.220 0.240 0.260 0.280 0.300 Loans 12 / 35
I NCOME I NEQUALITY
Does inequality affect the real interest rate?
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Our result due to generational inequality that triggers borrowing
and lending
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What about inequality within a given cohort?
- Irrelevant if output of each individual same over time
- Easy to come up with examples where it matter
Generalization of endowment process:
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High-type households with high income in middle period
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Low-type households with low income in middle period
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Both types receive same income in last period
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I NCOME I NEQUALITY AND R EAL I NTEREST
R ATE
Credit constrained middle income:
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Fraction ηs of middle income households are credit constrained
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True for low enough income in middle generation and high
enough income in retirement
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Fraction 1 − ηs lend to both young and constrained
middle-generation households
Expression for the real interest rate:
1 + rt =
1+β
(1 + gt + ηs ) Dt
β (1 − η ) Ym,h − D
s
t
t−1
+
Yto+1
1
β (1 − ηs ) Ym,h − D
t
t−1
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P RICE L EVEL D ETERMINATION
Euler equation for nominal bonds:
1
Pt
1
= βEt o (1 + it )
Cm
C
P
t+1
t
t+1
it ≥ 0
Bound on steady state inflation:
¯ ≥
Π
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1
1+r
If steady state real rate is negative, steady state inflation must be
positive
No equilibrium with stable inflation
But what happens when prices are NOT flexible and the central
bank does not tolerate inflation?
Then the central bank’s refusal to tolerate high enough inflation
will show up as a permanent recession.
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E NDOGENOUS P RODUCTION - A GGREGATE
S UPPLY - F ULL E MPLOYMENT
Output and labor demand:
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Labor only factor of production (capital coming up)
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Firms are perfectly competitive
Yt = Ltα
Wt
= αLtα−1
Pt
Labor supply:
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Middle-generation households supply a constant level of labor L¯
¯ = αL¯ α−1
Implies a constant market clearing real wage W
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Implies a constant full-employment level of output: Yfe = L¯ α
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D OWNWARD N OMINAL WAGE R IGIDITY
Partial wage adjustment:
o
n
˜ t , Pt αL¯ α−1
Wt = max W
˜ t = γWt−1 + (1 − γ)Pt αL¯ α−1
where W
Wage rigidity and unemployment:
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˜ t is a wage norm
W
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If real wages exceed market clearing level, employment is
rationed
Unemployment: Ut = L¯ − Lt
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Similar assumption in Kocherlakota (2013) and Schmitt-Grohe
and Uribe (2013)
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S TEADY S TATE A GGREGATE S UPPLY R ELATION
For positive steady state inflation:
Y = Yfe = L¯ α
For steady state deflation:
Y
=
Yfe
γ
1− Π
1−γ
!
α
1− α
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Upward sloping relationship between inflation and output
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Vertical line at full-employment
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A GGREGATE S UPPLY R ELATION
1.20 Aggregate Supply 1.15 Gross Infla5on Rate 1.10 1.05 1.00 0.95 0.90 0.85 0.80 0.80 0.85 0.90 0.95 1.00 1.05 1.10 Output 19 / 35
D ERIVATION OF A GGREGATE D EMAND
Monetary policy rule:
∗
1 + it = max 1, (1 + i )
Πt
Π∗
φπ !
Above binding ZLB:
1 + i∗
Π t+1
Πt
Π∗
φπ
=
1 + β (1 + gt )Dt
β Yt − Dt−1
Binding ZLB:
1
1 + β ( 1 + g t ) Dt
=
Π t+1
β Yt − Dt−1
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F ULL E MPLOYMENT S TEADY S TATE
1.20 Aggregate Supply 1.15 Gross Infla5on Rate 1.10 1.05 FE Steady State 1.00 Aggregate Demand 0.95 0.90 0.85 0.80 0.80 0.85 0.90 0.95 1.00 1.05 1.10 Output Parameter Values
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E FFECT OF A C OLLATERAL S HOCK
1.20 Aggregate Supply 1.15 Gross Infla5on Rate 1.10 1.05 1.00 0.95 Defla5on Steady State AD2 0.90 AD1 0.85 0.80 0.80 0.85 0.90 0.95 1.00 1.05 1.10 Output 22 / 35
P ROPERTIES OF THE S TAGNATION S TEADY
S TATE
Long slump:
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Binding zero lower bound so long as natural rate is negative
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Deflation raises real wages above market-clearing level
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Output persistently below full-employment level
Existence and stability:
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Secular stagnation steady state exists so long as γ > 0
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If Π∗ = 1, secular stagnation steady state is unique and
determinate
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Contrast to deflation steady state emphasized in Benhabib,
Schmitt-Grohe and Uribe (2001)
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Can do comparative statistics!
Linearized Conditions
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PARADOX OF F LEXIBILITY
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No obvious adjustment mechanisms to full employment
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As wages get more flexible output drops more
1.20 AD2 1.15 Gross Infla5on Rate 1.10 1.05 1.00 Defla5on Steady State 0.95 AS2 0.90 0.85 AS1 Higher Wage Flexibility Steady State 0.80 0.80 0.85 0.90 0.95 1.00 1.05 1.10 Output 24 / 35
PARADOX OF T OIL
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Say’s Law inverted: Destroying Aggregate supply creates
Aggregate Demand
Hysteresis/Reduction in labor force participation stabilizing
(reduces deflationary pressures)
1.20 AS1 AD2 AS2 1.15 1.10 Gross Infla5on Rate I
1.05 1.00 0.95 Defla5on Steady State 0.90 High Produc5vity Steady State 0.85 0.80 0.80 0.85 0.90 0.95 1.00 1.05 1.10 Output 25 / 35
M ONETARY P OLICY R ESPONSES
Forward guidance:
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Extended commitment to keep nominal rates low?
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Ineffective if households/firms expect rates to remain low
indefinitely
Raising the inflation target:
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For sufficiently high inflation target, full employment steady
state exists.
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Timidity trap (Krugman (2014))
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Multiple determinate steady states (secular stagnation and
reflation)
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Monetary policy not as powerful as in earlier models because no
way to exclude secular stagnation.
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R AISING THE I NFLATION TARGET
1.20 AD1 AD2 AD3 Aggregate Supply 1.15 Full Employment Steady State Gross Infla5on Rate 1.10 1.05 1.00 0.95 0.90 Defla5on Steady State 0.85 0.80 0.80 0.85 0.90 0.95 1.00 1.05 1.10 Output 27 / 35
F ISCAL P OLICY
Fiscal policy and the real interest rate:
1 + gt
g
Dt + Bt
1 + rt
β
1 Yto+1 − Tto+1
Lst =
(Ytm − Dt−1 − Ttm ) −
1+β
1+β
1 + rt
Ldt =
Government budget constraint:
g
y
Bt + Tt (1 + gt ) + Ttm +
1
1 + rt g
Tto = Gt +
B
1 + gt−1
1 + gt−1 t−1
Fiscal instruments:
g
y
Gt , Bt , Tt , Ttm , Tto
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T EMPORARY I NCREASE IN P UBLIC D EBT
y
g
Under constant population and set Gt = Tt = Bt−1 = 0:
g
Ttm = −Bt
g
Tto+1 = (1 + rt ) Bt
Implications for natural rate:
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Loan demand and loan supply effects cancel out
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Temporary increases in public debt ineffective in raising real rate
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Temporary monetary expansion equivalent to temporary
expansion in public debt at the zero lower bound
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Effect of an increase in public debt depends on beliefs about
future fiscal policy
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P ERMANENT I NCREASE IN P UBLIC D EBT ( OR
INVERSELY, AUSTERITY MEASURES )
Consider steady state following fiscal rule:
T o = β (1 + r) T m
1+g
Ld =
D + Bg
1+r
β
1
Yo
Ls =
( Ym − D ) −
1+β
1+β1+r
Implications for natural rate:
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Changes in taxation have no effects on loan supply
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Permanent rise in public debt always raises the real rate
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Equivalent to helicopter drop at the zero lower bound
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Public debt circumvents the tightening credit friction (Woodford
(1990))
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E XPANSIONARY F ISCAL P OLICY
1.20 AD2 AD3 Aggregate Supply 1.15 Gross Infla5on Rate 1.10 Full Employment Steady State 1.05 1.00 0.95 Defla5on Steady State 0.90 0.85 0.80 0.80 0.85 0.90 0.95 1.00 1.05 1.10 Output 31 / 35
G OVERNMENT P URCHASES M ULTIPLIER
Slope of the AD and AS curves:
1+β
(1 + g) D
β
1−α1−γ
κ=
α
γ
ψ=
Purchases multiplier at the zero lower bound:
Financing
Multiplier
Value
1+ β 1
β 1−κψ
>2
Tax on young generation
0
0
Tax on middle generation
1
1−κψ
− 1+β g 1−1κψ
>1
Increase in public debt
Tax on old generation
<0
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C APITAL AND S ECULAR S TAGNATION
Rental rate and real interest rate:
rkt = pkt − pkt+1
1−δ
≥0
1 + rt
rss ≥ −δ
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Negative real rate now constrained by fact that rental rate must
be positive
Relative price of capital goods:
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Decline in relative price of capital goods
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Need less savings to build the same capital stock
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–> downward pressure on the real interest rate.
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Global decline in price of capital goods (Karabarbounis and
Neiman, 2014)
Land
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C ONCLUSIONS
Policy implications:
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Higher inflation target needed
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Limits to forward guidance
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Role for fiscal policy
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Possible important implications for financial stability
Key takeaway:
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NOT that we will stay in a slump forever
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Slump of arbitrary duration
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OLG framework to model interest rates
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G OING FORWARD
In progress:
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A quantitative variation of the model: stochastic transitions
across age groups.
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Quantitatively decompose the effect of different channels on the
real interest rate during the crisis.
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Did the bubble mask a secular stagnation?
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