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Why Have Interest Rates FallenFar Below the Return on Capital
Magali MarxBanque de France
Benoıt MojonBanque de France
Francois R. VeldeFederal Reserve Bank of Chicago
Macroeconomic and Financial Imbalances and Spillovers, June 9
Why Have Interest Rates Fallen Far Below the Return on Capital 1
The decrease of real interest rates
1970 1975 1980 1985 1990 1995 2000 2005 2010 2015
Rea
l ra
tes
(%)
-2
0
2
4
6
8
10
12
Hamilton et al 10yr MA, US
King Low (indexed bonds)
US 10yr ex-ante real rate
Hamilton et al 10yr MA, France
Laubach-Williams r*
Why Have Interest Rates Fallen Far Below the Return on Capital 2
Which does not reflect the evolution of capital return
1970 1975 1980 1985 1990 1995 2000 2005 2010 2015
Rea
l re
turn
on c
apit
al (
%)
-2
0
2
4
6
8
10
12
14
16
18
US
EA large 4 countries
EA
Japan
Why Have Interest Rates Fallen Far Below the Return on Capital 3
The usual suspects
Low rates have been loosely tied to “secular stagnation”
A number of potential explanations have been cited:
I productivity slowdownI changing demographics (population slowdown, increased longevity)I change in the price of investment goodsI tightening of borrowing constraintI shortage of safe assetsI rising inequality
Why Have Interest Rates Fallen Far Below the Return on Capital 4
Our goal
quantitative assessment of the various factors cited
embed them in a single, tractable model
explain both the evolution of capital return and risk-free rateI this means having risk, and attitudes toward risk, in the model
Why Have Interest Rates Fallen Far Below the Return on Capital 5
Related literature
low rates: King and Low (2014); Hamilton et al. (2016); Holston et al. (2016)
safe assets: Coeurdacier et al. (2015); Caballero et al. (2008); Caballero and Farhi(2014)
deleveraging: Eggertsson and Krugman (2012); Korinek and Simsek (2016); Farhiand Werning (2013)
secular stagnation: Bean et al. (2015); Rachel and Smith (2015)
demographics: Carvalho et al. (2016); Gagnon et al. (2016)
risk: Kozlowski et al. (2015); Hall (2016)
return on capital: Caballero et al. (2017)
Why Have Interest Rates Fallen Far Below the Return on Capital 6
The Model
add risk to Eggertsson and Mehrotra (2014) and Coeurdacier et al. (2015).
time is discrete, infinite
3-period OLG structure (y , m, o)I population Nt , growth rate gL
recursive preferences with Epstein-Zin-Weil utility function
capital and labor (supplied inelastically), age-specific productivities (ey , 1, 0)
output Y = Kα(AL)1−α
I productivity A: trend growth gA + shock with variance σ (only source of risk)I growth in price of investment gI
Why Have Interest Rates Fallen Far Below the Return on Capital 7
Preferences
Epstein and Zin (1989)–Weil (1990) recursive preferences:
Vt = U(ct ,EtVt+1) =(c1−ρt + β ( (EtVt+1
1−γ)1
1−γ )1−ρ) 1
1−ρ
Why Have Interest Rates Fallen Far Below the Return on Capital 8
Preferences
Epstein and Zin (1989)–Weil (1990) recursive preferences:
Vt = U(ct ,EtVt+1) =(c1−ρt + β ( (EtVt+1
1−γ)1
1−γ )1−ρ) 1
1−ρ
CES functional form applied to
time:(c1−ρt + β (·t+1)1−ρ) 1
1−ρ
I ρ: inverse of intertemporal elasticity of substitution
risk: (EtVt+11−γ)
11−γ
I γ: risk aversion
when ρ = γI standard time-additive preferencesI tension between
F high γ required to match asset pricingF low ρ required to match consumption growth with interest rates
Why Have Interest Rates Fallen Far Below the Return on Capital 8
Budget constraints
young borrow from middle-aged up to a fraction θ of their t + 1 labor incomeI we focus on equilibria where this bindsI no other frictions (e.g., price stickiness)
middle-aged lend to young, buy capital from old, invest
old collect returns, sell depreciated capital
cyt = byt+1 + wte
yt
byt+1 ≤ θtEt(wt+1/Rt+1)
cmt+1 − bmt+2 + pk
t+1kmt+2 = wt+1 − Rt+1b
yt+1
cot+2 = (pkt+2(1− δ) + r kt+2)km
t+2 − Rt+2bmt+2
market-clearing:
gL,tbyt+1 + bm
t+1 = 0
gL,t+1byt+2 + bm
t+2 = 0
Why Have Interest Rates Fallen Far Below the Return on Capital 9
Production
Yt = (Nt−2kmt )α [At(e
yt Nt + Nt−1)]1−α
Nt−2kmt : capital (chosen by current old in the previous period)
eyt Nt + Nt−1: labor (of young and middle-aged)
Competitive factor markets:
wt = (1− α)A1−αt kαt
r kt = αA1−αt kα−1
t
both written in terms of the capital/labor ratio kt defined as
kt ≡Nt−2k
mt
eyt Nt + Nt−1=
kmt
gL,t−1(1 + eyt gL,t).
Why Have Interest Rates Fallen Far Below the Return on Capital 10
Solution strategy
only the middle-aged have an intertemporal problemI how much to saveI in what form: bonds or capital
write the middle-aged’s Euler equation and substitute equilibrium quantitiesI quantity of bonds determined by young’s constraintI Euler equation also relates risk-free rate R and return to capital Rk
we derive a law of motion expressed in terms of R or equivalently k
Why Have Interest Rates Fallen Far Below the Return on Capital 11
Solution strategy (2)
Middle-aged FOCs:
(cmt )−ρ = β[Et(c
ot+1)1−γ
] γ−ρ1−γ
Et
[(cot+1)−γRk
t+1
](cmt )−ρ = β
[Et(c
ot+1)1−γ
] γ−ρ1−γ
Et
[(cot+1)−γ
]Rt+1.
Define Rmt+1 = αtR
kt + (1− αt)Rt+1 and express budget constraints as
Wt = Yt − cmt
cot+1 = Rmt+1Wt .
Portfolio choice: set αt so that
Et(Rmt+1
−γ)Rt+1 = Et
(Rmt+1
−γRkt+1
)Saving decision:
Yt =(
1 + (βφtR1−ρt+1 )−
1ρ
)Wt
Then use market clearing to express Yt , Wt , Rmt+1 in term of the aggregate capital stock
Why Have Interest Rates Fallen Far Below the Return on Capital 12
Law of motion
(1 + (βφt)
−1/ρR1−1/ρt+1
)−1
︸ ︷︷ ︸saving rate
(1− θt−1
at)(1− α)(
Rkt+1
gI− 1 + δ)kt︸ ︷︷ ︸
income
= gL,t
α(1 + eygL,t+1)︸ ︷︷ ︸capital
+
(1
ξt
)(1− α)θt(1− gI
1− δRt+1
)︸ ︷︷ ︸bonds
kt+1
︸ ︷︷ ︸investments
Why Have Interest Rates Fallen Far Below the Return on Capital 13
Law of motion
(1 + (βφt)
−1/ρR1−1/ρt+1
)−1
︸ ︷︷ ︸saving rate
(1− θt−1
at)(1− α)(
Rkt+1
gI− 1 + δ)kt︸ ︷︷ ︸
income
= gL,t
α(1 + eygL,t+1)︸ ︷︷ ︸capital
+
(1
ξt
)(1− α)θt(1− gI
1− δRt+1
)︸ ︷︷ ︸bonds
kt+1
︸ ︷︷ ︸investments
overlapping generationsI saving only done out of labor income
borrowing constraintI disappears if θ = 0, ey = 0
riskI φt : precautionary saving, acts like discount factor distortion (≶ 1)I 1/ξt : portfolio choice
Why Have Interest Rates Fallen Far Below the Return on Capital 13
Risk terms
The factors φt and ξt are
ξt =Et(ut+1
−γ at+1)
Et(ut+1−γ)
φt =[Etut+1
1−γ](γ−ρ)/(1−γ)
Etut+1−γvt
ρ
with
ut+1 ≡ α(1 + eygL,t+1)at+1 + (1− α)θt
at+1 ≡A1−α
t+1
EtA1−αt+1
.
only functions of (moments of) the exogenous process At+1
when δ 6= 1, φt involves Rt+1 as well
Why Have Interest Rates Fallen Far Below the Return on Capital 14
Risky steady state
to account for risk in a tractable way, we appeal to the concept of “risky steady state”:
exogenous trends as in the data
productivity shock is assumed i.i.d.
in the law of motion, at set at its mean, at+1 is stochastic
agents take into account the uncertainty
Why Have Interest Rates Fallen Far Below the Return on Capital 15
Risk and borrowing constraint
When δ = 1, ρ < 1, θ = 0, ey = 0 (no young):
φt ' 1 +1
2γ(1− ρ)σ2
1
ξt' 1
Why Have Interest Rates Fallen Far Below the Return on Capital 16
Risk and borrowing constraint
When δ = 1, ρ < 1:
φt ' 1 +1
2γ(1− ρ)
α2(1 + eygL,t+1)2
(α(1 + eygL,t+1) + (1− α)θt)2σ2
1
ξt' 1+γ
α(1 + eygL,t+1)
α(1 + eygL,t+1) + (1− α)θtσ2
Why Have Interest Rates Fallen Far Below the Return on Capital 16
Risk and borrowing constraint
When δ = 1, ρ < 1:
φt ' 1 +1
2γ(1− ρ)
α2(1 + eygL,t+1)2
(α(1 + eygL,t+1) + (1− α)θt)2σ2
1
ξt' 1+γ
α(1 + eygL,t+1)
α(1 + eygL,t+1) + (1− α)θtσ2
law of motion: 1 + (βφtθ,σ−+
)−1/ρR1−1/ρt+1
−1
(1− θt−1
at)(1− α)
Rkt+1
gIkt
= gL,t
α(1 + eygL,t+1) +
(1
ξt
)θ,σ−+
(1− α)θt
kt+1
Why Have Interest Rates Fallen Far Below the Return on Capital 16
Long run determinantsof the bond interest rate r and the return on capital rK
δ = 1, ρ = 1:
Observable factorsI productivity growth gAI evolution of working age population gLI trend in investment price gI
Unobservable factorsI borrowing constraint θI variance of the shock on the trend of productivity σ.
Why Have Interest Rates Fallen Far Below the Return on Capital 17
Long run determinantsof the bond interest rate r and the return on capital rK
δ = 1, ρ = 1:
Observable factorsI productivity growth gAI evolution of working age population gLI trend in investment price gI
Unobservable factorsI borrowing constraint θI variance of the shock on the trend of productivity σ.
r = r + (gL − 1) + (gA − 1)− 1
2(gI − 1) + cθ + γu(θ|σ
+
, σ2
−)
rK = r + γv(θ|σ−, σ2
+)
The wedge between r and rK is only affected by θ and σ
Why Have Interest Rates Fallen Far Below the Return on Capital 17
Empirical strategy
our targets are the risk-free rate and the return on capitalwe segregate the usual suspects into
I the observables: productivity, demographics, price of investmentI the “less observables”: borrowing constraint, productivity risk
Three steps:1 input the observables, set θ and σ constant to match the levels of the targets2 input the observables, compute θ to match the risk-free rate, keep σ constant3 input the observables, compute σ to match the risk-free rate, keep θ constant4 input the observables, compute θ and σ to match both targets
repeat for US and Euro area (and the world)then stare at the pictures. . .caveats
I we interpret the generations loosely (10-year averages)I risk-free rates before the 1980s are less meaningful (financial repression etc), so we focus on
1990s to present
Why Have Interest Rates Fallen Far Below the Return on Capital 18
Model calibration and data sources
ParametersT length of period (years) 10β discount factor 0.98T
α capital share 0.28γ risk aversion 100ρ inverse of IES 0.8δ capital depreciation rate 0.1 ∗ Tey relative productivity of young 0.3FactorsgL,t growth rate of population 20-64 US, EA (France), China, Japan: OECDgI ,t investment price growth DiCecio (2009)gA,t productivity growth US: Fernald (2012), Euro: NAWM modelRt real interest rate US: Hamilton et al. (2016), FranceRkt return on capital US, EA: our calculations a la
Gomme et al. (2015)at productivity shock ln(a) is a i.i.d. N(−σ2/2, σ2)Free parametersθ borrowing constraint on youngσ2 variance of at
Why Have Interest Rates Fallen Far Below the Return on Capital 19
The inputs
1970 1980 1990 2000 20100
1
2
3
4
Productivity growth (gA − 1)
1970 1980 1990 2000 20100
1
2
3
Working age pop. growth (gL − 1)
1970 1980 1990 2000 2010
-2
0
2
4
Risk free rate (r)
1970 1980 1990 2000 2010
6
8
10
12
Capital return (rK)
US
EA
World
Why Have Interest Rates Fallen Far Below the Return on Capital 20
Impact of observable factors, in the USObservable factors explain about 1.4% from 1992 to 2014
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Borrowing ratio θ
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Productivity Risk (std) σ
1970 1980 1990 2000 2010
-5
0
5
10
15
Observed and simulated rates
1970 1980 1990 2000 2010
2
4
6
8
10
12
Observed and simulated risk premium
Why Have Interest Rates Fallen Far Below the Return on Capital 21
Impact of observable factors, in the EAObservable factors explain about 1.8% from 1992 to 2014
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Borrowing ratio θ
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Productivity Risk (std) σ
1970 1980 1990 2000 2010
-5
0
5
10
15
Observed and simulated rates
1970 1980 1990 2000 2010
2
4
6
8
10
12
Observed and simulated risk premium
Why Have Interest Rates Fallen Far Below the Return on Capital 22
Impact of the borrowing constraint, in the US.A tighter constraint can account for the fall in the risk-free rate and 0.8% increase of the risk premium
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Borrowing ratio θ
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Productivity Risk (std) σ
1970 1980 1990 2000 2010
-5
0
5
10
15
Observed and simulated rates
1970 1980 1990 2000 2010
2
4
6
8
10
12
Observed and simulated risk premium
Why Have Interest Rates Fallen Far Below the Return on Capital 23
Impact of the borrowing constraint, in the EA.A tighter constraint can account for the fall in the risk-free rate and 0.7% increase of the risk premium
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Borrowing ratio θ
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Productivity Risk (std) σ
1970 1980 1990 2000 2010
-5
0
5
10
15
Observed and simulated rates
1970 1980 1990 2000 2010
2
4
6
8
10
12
Observed and simulated risk premium
Why Have Interest Rates Fallen Far Below the Return on Capital 24
Impact of risk, in the US.A higher risk perception can account for the fall in the risk-free rate and the increase in the risk premium
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Borrowing ratio θ
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Productivity Risk (std) σ
1970 1980 1990 2000 2010
-5
0
5
10
15
Observed and simulated rates
1970 1980 1990 2000 2010
2
4
6
8
10
12
Observed and simulated risk premium
Why Have Interest Rates Fallen Far Below the Return on Capital 25
Impact of risk, in the EA.A higher risk perception can account for the fall in the risk-free rate and the increase in the risk premium
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Borrowing ratio θ
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Productivity Risk (std) σ
1970 1980 1990 2000 2010
-5
0
5
10
15
Observed and simulated rates
1970 1980 1990 2000 2010
2
4
6
8
10
12
Observed and simulated risk premium
Why Have Interest Rates Fallen Far Below the Return on Capital 26
Impact of risk and the borrowing constraint, in the US.With higher risk perception data are consistent with non decreasing debts
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Borrowing ratio θ
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Productivity Risk (std) σ
1970 1980 1990 2000 2010
-5
0
5
10
15
Observed rates
1970 1980 1990 2000 2010
2
4
6
8
10
12
Observed risk premium
Why Have Interest Rates Fallen Far Below the Return on Capital 27
Impact of risk and the borrowing constraint, in the EA.With higher risk perception data are consistent with non decreasing debts
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Borrowing ratio θ
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Productivity Risk (std) σ
1970 1980 1990 2000 2010
-5
0
5
10
Observed rates
1970 1980 1990 2000 2010
2
4
6
8
10
12
Observed risk premium
Why Have Interest Rates Fallen Far Below the Return on Capital 28
Borrowing constraint and risk, in the US.
1970 1980 1990 2000 2010
0
0.1
0.2
Borrowing ratio θ
1970 1980 1990 2000 2010
0
0.1
0.2
Productivity Risk (std) σ1970 1980 1990 2000 2010
0
5
10
Observed and simulated rates
1970 1980 1990 2000 2010
2
6
10
Observed and simulated risk premium
1970 1980 1990 2000 2010
0.1
0.2
0.3
Debt/income
Why Have Interest Rates Fallen Far Below the Return on Capital 29
Borrowing constraint and risk, in the EA.
1970 1980 1990 2000 2010
0
0.1
0.2
Borrowing ratio θ
1970 1980 1990 2000 2010
0
0.1
0.2
Productivity Risk (std) σ1970 1980 1990 2000 2010
0
5
10
Observed and simulated rates
1970 1980 1990 2000 2010
2
6
10
Observed and simulated risk premium
1970 1980 1990 2000 2010
0
0.2
0.4
Debt/income
Why Have Interest Rates Fallen Far Below the Return on Capital 30
Global perspectiveImpact of observable factors
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Borrowing ratio θ
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Productivity Risk (std) σ
1970 1980 1990 2000 2010
-5
0
5
10
15
Observed and simulated rates
1970 1980 1990 2000 2010
2
4
6
8
10
12
Observed and simulated risk premium
Why Have Interest Rates Fallen Far Below the Return on Capital 31
Global perspectiveImpact of the borrowing constraint
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Borrowing ratio θ
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Productivity Risk (std) σ
1970 1980 1990 2000 2010
-5
0
5
10
15
Observed and simulated rates
1970 1980 1990 2000 2010
2
4
6
8
10
12
Observed and simulated risk premium
Why Have Interest Rates Fallen Far Below the Return on Capital 32
Global perspectiveImpact of risk
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Borrowing ratio θ
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Productivity Risk (std) σ
1970 1980 1990 2000 2010
-5
0
5
10
15
Observed and simulated rates
1970 1980 1990 2000 2010
2
4
6
8
10
12
Observed and simulated risk premium
Why Have Interest Rates Fallen Far Below the Return on Capital 33
Global perspectiveImpact of risk and the borrowing constraint
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Borrowing ratio θ
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Productivity Risk (std) σ
1970 1980 1990 2000 2010
-5
0
5
10
15
Observed rates
1970 1980 1990 2000 2010
2
4
6
8
10
12
Observed risk premium
Why Have Interest Rates Fallen Far Below the Return on Capital 34
Conclusion
usual suspects aren’t enoughI deleveraging story
increased (perception of) risk can account for the patternsI but it’s a residual
more work to be done onI longevityI inequality (through a bequest motive)I exogenous supply of safe assets
Why Have Interest Rates Fallen Far Below the Return on Capital 35
Additional slides
Why Have Interest Rates Fallen Far Below the Return on Capital 36
Sensitivity to γ (US)
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2
Borrowing ratio
1970 1980 1990 2000 2010
0
0.05
0.1
0.15
0.2Productivity Risk (std)
γ = 100
γ = 50
1970 1980 1990 2000 2010
-5
0
5
10
15Observed and simulated rates
1970 1980 1990 2000 2010
2
4
6
8
10
12Observed and simulated risk premium
Why Have Interest Rates Fallen Far Below the Return on Capital 37
Sensitivity to γ (EA)
1980 1990 2000 2010 2020
0
0.05
0.1
0.15Borrowing ratio
1980 1990 2000 2010 2020
0
0.05
0.1
0.15
0.2Productivity Risk (std)
γ = 100
γ = 50
1980 1990 2000 2010 2020
0
5
10Observed and simulated rates
1980 1990 2000 2010 2020
0
5
10Observed and simulated risk premium
Why Have Interest Rates Fallen Far Below the Return on Capital 38
The inputs for the US
1970 1980 1990 2000 20100
1
2
3Productivity growth
1970 1980 1990 2000 20100
0.5
1
1.5
2Working Age Population
1970 1980 1990 2000 2010-5
-4
-3
-2
-1
0Relative investment price
1970 1980 1990 2000 20100
100
200
300Debt/GDP (%)
safe assets
private
total
Why Have Interest Rates Fallen Far Below the Return on Capital 39
The inputs for the EA
1980 2000 20200
1
2
3Productivity growth
1980 2000 20200
0.5
1
1.5
2Working Age Population
1980 2000 2020-5
-4
-3
-2
-1
0Relative investment price
1980 2000 202050
100
150
200
250Debt/GDP (%)
safe assets
private
total
Why Have Interest Rates Fallen Far Below the Return on Capital 40
Measures of risk
Why Have Interest Rates Fallen Far Below the Return on Capital 41
References I
Bean, S. C., C. Broda, T. Ito, and R. Kroszner (2015): “Low for Long? Causes andConsequences of Persistently Low Interest Rates,” Geneva Reports on the WorldEconomy 17, International Center for Monetary and Banking Studies.
Caballero, R. J. and E. Farhi (2014): “The Safety Trap,” Working Paper 19927, NBER.
Caballero, R. J., E. Farhi, and P.-O. Gourinchas (2008): “An Equilibrium Model of“Global Imbalances” and Low Interest Rates,” American Economic Review, 98, 358–93.
——— (2017): “Rents, Technical Change, and Risk Premia: Accounting for SecularTrends in Interest Rates, Returns on Capital, Earning Yields, and Factor Shares,”NBER Working Papers 23127, National Bureau of Economic Research, Inc.
Carvalho, C., A. Ferrero, and F. Nechio (2016): “Demographics and Real Interest Rates:Inspecting the Mechanism,” European Economic Review, 88, 208 – 226, sI: ThePost-Crisis Slump.
Coeurdacier, N., S. Guibaud, and K. Jin (2015): “Credit Constraints and Growth in aGlobal Economy,” American Economic Review, 105, 2838–81.
DiCecio, R. (2009): “Sticky wages and sectoral labor comovement,” Journal of EconomicDynamics and Control, 33, 538–553.
Eggertsson, G. B. and P. Krugman (2012): “Debt, Deleveraging, and the Liquidity Trap:A Fisher-Minsky-Koo Approach,”The Quarterly Journal of Economics, 127, 1469–1513.
Why Have Interest Rates Fallen Far Below the Return on Capital 42
References II
Eggertsson, G. B. and N. R. Mehrotra (2014): “A Model of Secular Stagnation,” WorkingPaper 20574, NBER.
Epstein, L. G. and S. E. Zin (1989): “Substitution, Risk Aversion, and the TemporalBehavior of Consumption and Asset Returns: A Theoretical Framework,”Econometrica, 57, 937–969.
Farhi, E. and I. Werning (2013): “A Theory of Macroprudential Policies in the Presenceof Nominal Rigidities,” Tech. rep., MIT.
Fernald, J. G. (2012): “A quarterly, utilization-adjusted series on total factorproductivity,” Working Paper Series 2012-19, Federal Reserve Bank of San Francisco.
Gagnon, E., B. K. Johannsen, and D. Lopez-Salido (2016): “Understanding the NewNormal: The Role of Demographics,” Finance and Economics Discussion Series2016-080, Board of Governors of the Federal Reserve System.
Gomme, P., B. Ravikumar, and P. Rupert (2015): “Secular Stagnation and Returns onCapital,” Federal Reserve Bank of St Louis Economic Synopsis, 19.
Hall, R. E. (2016): “Understanding the Decline in the Safe Real Interest Rate,” Workingpaper 22196, NBER.
Hamilton, J. D., E. S. Harris, J. Hatzius, and K. D. West (2016): “The Equilibrium RealFunds Rate: Past, Present and Future,” IMF Economic Review, 64, 660–707.
Why Have Interest Rates Fallen Far Below the Return on Capital 43
References III
Holston, K., T. Laubach, and J. C. Williams (2016): “Measuring the Natural Rate ofInterest: International Trends and Determinants,” Working paper 2016-11, FederalReserve Bank of San Francisco.
King, M. and D. Low (2014): “Measuring the “World” Real Interest Rate,” working paper19887, NBER.
Korinek, A. and A. Simsek (2016): “Liquidity Trap and Excessive Leverage,” AmericanEconomic Review, 106, 699–738.
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