global real rates: a secular approach · the questions we address: i why have global real interest...

Global Real Rates: A Secular Approach

Pierre-Olivier Gourinchas1 Helene Rey2

1UC Berkeley & NBER & CEPR

2London Business School & NBER & CEPR

FRBSF Fed, April 2017

Prepared for the conference “Do Changes in the Landscape Require aNew Policy Framework?”.

1 / 31

The Questions We Address:

I Why have global real interest rates declined so much?

I Propose a simple empirical approach using the world budgetconstraint and historical data.

1. Gives us insights regarding the forces behind low frequencymovements in real rates.

2. Allows us to forecast future global real rates.

2 / 31

Global Interest Rates (10-year nominal yields)

-2

0

2

4

6

8

10

12

14

16

18

1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016

percent

U.S. Germany U.K. Japan

Financial Crisis Eurozone Crisis

Sources: U.S.: 10-year bond constant maturity rate; Germany: 10-year benchmark bond; U.K.:

10-year government bond yield; Japan: 10-year government bond yield. Global Financial Database3 / 31

U.S. Real Rates

-6

-4

-2

0

2

4

6

8

10

12

1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016

percent

90-day 3-year 5-year 10-year

Ex-ante real yields on U.S. Treasury Securities constructed using median expected price changesfrom the University of Michigan’s Survey of Consumers. Source: FRED.

4 / 31

‘Historical’ U.S. Real Rates, 1871-2011

0

10,000

20,000

30,000

40,000

0

50,000

100,000

150,000

200,000

250,000

1875 1900 1925 1950 1975 2000

real consumption per capita real wealth per capita

.14

.16

.18

.20

.22

.24

.26

.28

1875 1900 1925 1950 1975 2000

consumption/wealth ratio

-.15

-.10

-.05

.00

.05

.10

.15

.20

1875 1900 1925 1950 1975 2000

short term real interest rate (percent)

The figure reports the annualized ex-post real 3-month interest rate for the U.S. since 1871.

Source: Jorda et al (2016).

5 / 31

Facts and Possible Stories

I Decline in natural rate: Holston et al (2017), Laubach and Williams(2016)

I Secular Stagnation:

1. Demography: Hansen (1939), Carvalho et al (2016)2. Productivity growth: Summers (2013), Gordon (2012)3. Demand for safe assets: Caballero et al (2016), del Negro et al

(2017)

I Savings Glut: Bernanke (2005), Caballero et al (2008)

I Deleveraging after the crisis (Eggertson Krugman (2012); Guerrieriand Lorenzoni (2011); Lo and Rogoff (2015))

I Technological progress is capital-augmenting (decline in price ofinvestment goods), Sajedi & Thwaites (2016)

6 / 31

Theoretical framework

I Law of accumulation of wealth for the world (closed economy):

Wt+1 = Rt+1(Wt − Ct)

I Wt : Total Private wealth: financial wealth (incl. gov. debt) as wellas housing, non incorporated businesses, land, + human wealth;Rt+1 gross return on total private wealth; Ct world privateconsumption. No Ricardian equivalence.

I Accounting identity.

7 / 31

Theoretical Framework

I Most models deliver a stationary C/W . Details unimportant.

I Log-linearize around the steady-state consumption-wealth ratio andderive the world’s intertemporal budget constraint (Campbell (1986)or Lettau and Ludvigson (2001)):

lnCt/Wt w Et

∑∞s=1 ρ

sw

(rwt+s −∆ lnCt+s

)

I Today’s aggregate consumption to wealth ratio is low if:I Expected future rates of return on wealth are lowI Expected future aggregate consumption growth is high

8 / 31

Theoretical Framework: Two Adjustments

I Private wealth vs. human wealth. W = W + H. H unobserved.

lnCt/Wt w Et

∑∞s=1 ρ

sw

(rwt+s −∆ lnCt+s

)+ εt

with εt ∝ Et

∑∞s=1 ρ

sw

(rht+s − rwt+s

)− (lnWt − lnHt). Interpretation.

I safe and risky returns. write rw = r f + rpw .I proxy rpw with rpw = νrp where rp is equity excess returnI estimate ν from the data to maximize fit.

I Present value relation:

lnCt/Wt w Et

∑s ρ

sw r

ft+s +νEt

∑s ρ

sw rpt+s −Et

∑s ρ

sw∆ ln Ct+s +εt

≡ cw ft +cw rp

t +cwct +εt

9 / 31

Identification ILook at co-movements of lnC/W and components.

I Productivity GrowthEuler equation: Etr

wt+1 = ρ+ σEtgt+1

lnCt/Wt w σEt

∑s ρ

swgt+s +νEt

∑s ρ

sw rpt+s −Et

∑s ρ

swgt+s +εt

≡ cw ft +cw rp

t +cw ct +εt

cw f and cw c negatively correlated.Impact on C/W depends on σ − 1. IES close to 1: no impact onC/W .

I DemographicsWrite ∆ lnCt = ∆ ln ct + nt .C/W depends on direct effect (cw c) and indirect effect (cw f ).Literature suggests n < 0 increases savings: corr(cw f , cw c) < 0.

10 / 31

Identification II

I Deleveraging: Shock to ρ.

I Outside the ELB: Etrft+1 = ρt+1.

lnCt/Wt w Et

∑s ρ

swρt+s +νEt

∑s ρ

sw rpt+s −0

≡ cw ft +cw rp

t +cw ct

I At the ELB: Etrft+1 = 0 and Et∆ lnCt+1 = −ρt+1

lnCt/Wt w 0 +νEt

∑s ρ

sw rpt+s +Et

∑s ρ

swρt+s

≡ cw ft +cw rp

t +cw ct

Either way, low ρt+s lowers C/WPositive comovement with cw f and cw c .

11 / 31

Identification III

I Demand for Safe AssetsSeparate IES from CRRA and shock CRRA. Epstein-Zin preferences:

Ut =

{(1− β)C 1−σ

t + β(EtU

1−γtt+1

) 1−σ1−γt

} 11−σ

Risk-free rate and risk premium: (θt = (1− γt)/(1− σ))

r ft+1 = ρ− 1− θt2

σ2r ,t

Etrwt+1 − r ft+1 = (1− θt)σ2

r ,t .

lnCt/Wt w − 12Et

∑s ρ

sw (1− θt+s)σ2

r ,t+s +Et

∑s ρ

sw (1− θt+s)σ2

r ,t+s +0

≡ cw ft +cw rp

t +cw ct

cw f negatively correlated with cw rp and C/W

12 / 31

Data

I World is an aggregate of the United States, the United Kingdom,Germany and France.

I Historical data on private wealth, population and privateconsumption for the period 1870-2011 for the United States, and1920-2011 for the United Kingdom, Germany and France fromPiketty et al. (2014) and Jorda et al. (2016).

I Risk-free return: ex-post real return on three-months Treasuriesminus CPI inflation.

I Real return on risky assets: total equity return for each countryminus CPI inflation.

13 / 31

‘Global’ Consumption & Wealth per capita, 1920-2011

0

5,000

10,000

15,000

20,000

25,000

30,000

0

40,000

80,000

120,000

160,000

200,000

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


.14

.16

.18

.20

.22

.24

.26

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


-.12

-.08

-.04

.00

.04

.08

.12

.16

.20

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


The figure reports real annual private consumption expenditures and real private wealth (land,

housing, financial assets) for the U.S., U.K., Germany and France in 2010 US dollars. Source:

Jorda et al (2016), Piketty & Zucman (2014).

14 / 31

‘Global’ Consumption/Wealth Ratio, 1920-20110

5,000

10,000

15,000

20,000

25,000

30,000

0

40,000

80,000

120,000

160,000

200,000

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


.14

.16

.18

.20

.22

.24

.26

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


-.12

-.08

-.04

.00

.04

.08

.12

.16

.20

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


The figure reports the ratio of aggregate annual private consumption expenditures to private

wealth (land, housing, financial assets) for the U.S., U.K., Germany and France. Source: Jorda et

al (2016), Piketty & Zucman (2014). Mean: C/W = 0.2

15 / 31

U.S. Consumption/Wealth Ratio, 1871-20110

10,000

20,000

30,000

40,000

0

50,000

100,000

150,000

200,000

250,000

1875 1900 1925 1950 1975 2000


.14

.16

.18

.20

.22

.24

.26

.28

1875 1900 1925 1950 1975 2000


-.15

-.10

-.05

.00

.05

.10

.15

.20

1875 1900 1925 1950 1975 2000


The figure reports the ratio of aggregate annual private consumption expenditures to private

wealth (land, housing, financial assets) for the U.S. Source: Jorda et al (2016), Piketty & Zucman

(2014).

16 / 31

Empirical Framework

I Assume ρw = 0.96 (Equivalently, asset income/output ≈ 0.2)

I Construct cw i using a reduced form VAR(p)

I Estimate ν to maximize fit, Find ν = 0.37. (interpretation)

17 / 31

Decomposing the Global Consumption/Wealth Ratio

-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

ln(c/w) Risk free comp.Risk premium comp. Consumption comp.Predicted

-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

LCWM

-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

ln(c/w) Risk free comp.

-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

ln(c/w) Risk free comp.Risk premium comp.

-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

ln(c/w) Risk free comp.Risk premium comp. Consumption comp.

-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

ln(c/w) Predicted

The figure decomposes the fluctuations in ln(C/W ) around its mean into a risk-free component

(cw f ), an excess return component (cw rp) and a consumption growth component (cwc).

18 / 31


-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

LCWM

-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

ln(c/w) Predicted

The figure decomposes ln(C/W ) into a risk-free component (cw f ), an excess return component

(cw rp) and a consumption growth component (cwc).

19 / 31


-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

LCWM

-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

ln(c/w) Predicted



20 / 31


-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

LCWM

-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

ln(c/w) Predicted



21 / 31


-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

LCWM

-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010


-.4

-.3

-.2

-.1

.0

.1

.2

.3

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

ln(c/w) Predicted



22 / 31

Unconditional Variance Dec.

# percent U.S. G41 βr f 1.364 1.4062 βrp 0.005 0.0253 βc -0.329 -0.336

of which:3 βcp 0.056 -0.1684 βn -0.386 -0.168

5 Total 1.041 1.094(lines 1+2+3)

23 / 31

Correlation Matrix

lnC/W cw f cw rp cw c cwn

lnC/W 1.000 0.901 0.121 -0.659 -0.872cw f 1.000 -0.054 -0.658 -0.923cw rp 1.000 0.0538 -0.061cw c 1.000 0.734cwn 1.000

24 / 31

Results & Interpretation

I Very good fit of the decomposition

I Most of the movements in C/W reflect expected movements in thefuture risk-free rate

I Productivity and demographic shocks: small contribution overall.

I Deleveraging shocks: largest component? Increase in savingpropensity. Risk free component decreases.

I Demand for Safe Assets: negative correlation between risk premiumand risk free component. Some contribution.

25 / 31

Interpretation

I Most of the action is in the joint dynamics of the consumptionwealth ratio and the return component, particularly the risk free rate.

I Plausible interpretation:I ‘Irrational exuberance’ in asset prices (in the 1920s and in the

1990-2000s) leads to fast growing financial wealth and fast decliningconsumption-wealth ratios.

I Large financial crises (in 1929 and in 2008) lead to deleveraging(increased savings and low consumption) for an extended time (lowconsumption wealth ratios) and to low real rates.

I Therefore low consumption wealth ratios tend to be associated withlow real rate components.

I This is consistent with debt overhang effects (Reinhart and Rogoff(2014)) and a global financial boom/bust cycle (Miranda-Agrippino& Rey (2015)).

I Demand for safe assets seem to play some role (Caballero et al(2016))

26 / 31

Interpretation

I Deleveraging post crisis leads to increased demand for ‘safe’ assetsand low risk free rate. Should also be associated with some negativecomovements between risk free rate and risk premium. A bit of that.

I Technological slowdown or demographic factors: Return compomentand consumption growth component should exhibit negativecomovements.

I But most of the action is in the joint dynamics of the consumptionwealth ratio and the risk free rate. How predictive is this relation?

27 / 31

Predicting Global Real Risk-free Rates

I Predictive power of the consumption-wealth ratio:

yt+k = α + βcwt + εt+k

I yt+k denotes the variable we are trying to forecast at horizon k andcwt is the consumption-wealth ratio at the beginning of period t.

I Candidates are: real risk free rates, equity premium, consumptiongrowth per capita, population growth, term premium.

I Strong predictive power for long run real rates. (Adj.R2 is 0.43 on a10 year horizon).

28 / 31

Predicting Global Real Risk-free Rates

-.12

-.08

-.04

.00

.04

.08

.12

.16

.20

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

1-year ahead

-.10

-.05

.00

.05

.10

.15

.20

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

2-years ahead

-.08

-.04

.00

.04

.08

.12

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

5-years ahead

-.12

-.08

-.04

.00

.04

.08

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

fittedactual

10-years ahead

The figure forecasts the 10-year average future short risk-free rate using ln(C/W ). Graph includes2 standard deviation bands.

2011-2021 forecast: −1.3%

29 / 31

Predicting The Global Term Premium

-.04

-.03

-.02

-.01

.00

.01

.02

.03

.04

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

1-year ahead

-.03

-.02

-.01

.00

.01

.02

.03

.04

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

2-years ahead

-.02

-.01

.00

.01

.02

.03

.04

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

5-years ahead

-.010

-.005

.000

.005

.010

.015

.020

.025

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

fittedactual

10-years ahead

The figure forecasts the 10-year average future term premium using ln(C/W ). Graph includes 2standard deviation bands.

2011-2021 forecast: 1.22%

30 / 31

Conclusions

I We use a very general almost a-theoretical framework to understanddeterminants of long run real rates.

I Empirical evidence favors global financial boom/bust cycle.

I Euphoria pre-crisis leads to rapid increase in wealth (1920s, 1990s).This is followed by deleveraging post crisis (1929, 2008) andincreased demand for ‘safe’ assets.

I Hence low consumption-wealth ratios are associated with lowerfuture real rates.

I Little evidence for technological slowdown or demography factors (?)

I Predictive power: How long will the real rates stay low? Into nextdecade! Unless major macroeconomic policy changes.

31 / 31

global real rates: a secular approach · the questions we address: i why have global real interest...

Documents