why are real interest rates so low?why are real interest rates so low? m. marx, b. mojon, f. velde...

Why are real interest rates so low?

M. Marx, B. Mojon, F. Velde

Warsaw

17 December, 2015

M. Marx, B. Mojon, F. Velde Why are real interest rates so low?

Motivation (1/2)

Why are interest rates so low ?

What can we do about it ?


Motivation (2/2)

The debate on the level of real interest rates is essentially qualitative.

Poor prospect on economic growth (Gordon, Summers)

1 demographics ⇒ lower investment and lower productivity2 demographics ⇒ higher savings and higher demand for safe assets, inc.

by EM (IMF view)

Debt deleveraging (which is somehow equivalent) (Koo, Eggertsson,Krugman)

Drop in the supply of safe assets (Caballero and Farhi)

We provide one attempt of a quantitative assessment of these variousforces


Related Literature

Eggertsson and Mehrotra (2014)

Bianchi and Mendoza (2015)

Buera and Nicolini (2014)

Hamilton et al. (2015)


Outline

1 Interest rates are indeed low

2 Show where it can come from in the simplest possible model

3 Where in the data do we see anything like what the model is askingfor


Evidence on real interest rates

0,00

1,00

2,00

3,00

4,00

5,00

6,00

7,00

8,00

EU SWAP 1Y

US SWAP 1Y

JAPAN SWAP 1Y



0,00

1,00

2,00

3,00

4,00

5,00

6,00

7,00

8,00

EU SWAP 5Y

US SWAP 5Y

JAPAN SWAP 5Y



-4,00

-3,00

-2,00

-1,00

0,00

1,00

2,00

3,00

4,00

2004 2005 2006 2007 2008 2009 2010 2010 2011 2012 2013 2014 2015

EU_1Y

US_1Y

JP_1Y

EU_5Y

US_5Y

JP_5Y



-3

-2

-1

0

1

2

3

4

5

6

7

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

real_EA_1Y

real_US_1Y

real_JP_1Y



-3,00

-2,00

-1,00

0,00

1,00

2,00

3,00

4,00

2004 2005 2006 2007 2008 2009 2010 2010 2011 2012 2013 2014 2015

real_EA_5Y

real_US_5Y

real_JP_5Y



1985 1990 1995 2000 2005 2010 2015−3

−2

−1

0

1

2

3

4

5

6

7

real 1−year interest rates

%

FRJPUS


Evidence on real interest rates :take away

Real interest rates have moved from 2% to somewhere between 0 and-2%

We care about -2% because it is their physical minimum withanchored inflation expectations at 2%

Real interest rates move together (Hamilton et al, 2015)


Model

adapted from Farhi and Werning (2013)

a 2-country minimalist New Keynesian model

3 periods t ∈ {0, 1, 2}, initial, intermediate, final (5 years)

2 countries with relative population shares φ1 and φ2.

Country 1 : linear technology to transform labor into outputI At embeds productivity and size of the working population

Country 2 : only endowment Et

Country 1 : savers/Germany, Country 2 : borrowers/Spain


Preferences

Agents in country 1 work and consume in every period :

V 1s =

2∑t=0

βt[u(C 1

t )− v(N1t )]

while agents in country 2 consume but do not work :

V 2s =

2∑t=0

βtu(C 2t )


Frictions

1 maximum rigidity : prices set once and for all

2 borrowing constraint on agent 2 in middle period (“deleveragingshock”)


Basic mechanics

the borrowing constraint reduces the demand for loans in the middleperiod

if large enough, it drives down the nominal interest rate to 0

then, monetary policy can’t stabilize fully

macroprudential policy : a borrowing constraint on agent 2 in the firstperiod can help

I under what parameter configuration will the ZLB bind in the middleperiod ?


Ramsey approach to macro-prudential policy

choose allocation {c it ,Nt} to maximize total welfare subject toequilibrium constraints

I the constraints boil down to feasibility at each t, the ZLB, anddeleveraging

I the ZLB u′(c1t ) ≥ βu′(c1t+1) embodies all the price rigidities (constantprices)

the social planner can do lump-sum transfersI countries’ BC are not constraintsI this makes decentralized interpretation awkward at times


Autarky

allocations are static : c2t = Et and c1t solves

u′(c1t ) =v ′(c1t /At)

At


Flexible price (no ZLB)

Again, allocation is static and solves

u′(c1t ) =v ′(c1t /At)

At

λ1u′(c1t ) = λ2u′(c2t )

φ1c1t + φ2c2t = φ1AtNt + φ2Et

or c1t solvesF (c1t ,Et ,At) = 0

F defines an increasing function C (Et ,At)


Calibration

λ2 = λ1

relative shares φ1 = 1, and φ2 = 0.5

u(c) = c1−σ

1−σ , and v(n) = n1+η

1+η

σ = 2, and η = 0.5

discount factor (1/1.02)N


Hitting the ZLB (representative agent)

the ZLB condition for country 1 :(A2

A1

) 1+ησ+η

< β1σ or ∆A < − σ + η

σ(1 + η)

(1

β− 1

)= −2

3

(1

β− 1

)the ZLB condition for country 2 : ∆E < − 1

σ

(1β − 1

)= −1

2

(1β − 1

)


Necessary conditions for ZLB to bind

Three ways to get the ZLB to bind :

1 There is a β-shock βS on the discount rate of country 1, such that atleast,

βs ∗ β >(c(E2,A2)

c(E1,A1)

)σ2 either E or A is decreasing (E2 < E1 or A2 < A1) and

c(E2,A2) < β1/σc(E1,A1)

3 For a borrowing constraint on country 2 to bind,

A(1+η)/(σ+η)2 < min{(φ2/φ1)1/σE2, β

1/σc(E1,A1)}


Hitting the ZLB : with the discount factor

0.8 0.9 1 1.1 1.20.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

A2

β

0.8 0.9 1 1.1 1.20.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

E2

β

r=-2r=0r=2

Value of the discount factor ensuring the ZLB, E1 = 1 and A1 = 1


Hitting the ZLB : with the discount factor

0.8 0.9 1 1.1 1.20.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

A2

β

0.8 0.9 1 1.1 1.20.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

E2

β

r=-2r=0r=2

t = 10 years


Hitting the ZLB : with productivity and endowments

0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.250.75

0.8

0.85

0.9

0.95

1

1.05

1.1

E2

A2

r=-2r=0r=2

Impact on productivity and endowment, E1 = 1 and A1 = 1



0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

E2

A2

r=-2r=0r=2

t = 10 years



0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.80.4

0.5

0.6

0.7

0.8

0.9

1

1.1

E2

A2

σ = 0.5σ = 2σ = 4

changing σ doesn’t make a difference


Hitting the ZLB : with borrowing constraint

0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.250.8

0.85

0.9

0.95

1

1.05

E2

A2

r=-2r=0r=2

t=5 years


Hitting the ZLB : with borrowing constraint

0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.250.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

E2

A2

r=-2r=0r=2

t=10 years


What features of the data look like what the modelrequires ?

Nothing !


Future US GDP/Income

FOMC : Growth of potential GDP =2.75%per capita = 2%

Gordon :Growth of GDP per capita (yoy growth)1891-2007 2%2007-2032 0.9%

Mainly due to lower labor market participation1972-1996 +0.4%2004-2014 -0.5%2007-2014 -0.8%

Income distribution : yet not worse than since 1984Public debt : Ambiguous


Future GDP/Income (OECD)


Debt deleveragingBy how much has debt decreased /is required to decreaseActually, Global Debt has kept on growing throughout the last decade !Buttiglione et al. (2014) : ”Contrary to a widely held belief, the world hasnot started to delever”


Debt deleveraging (within the EA)

By how much has debt decreased /is required to decrease


Debt deleveraging (a current account perspective)

Spanish current account adjusted from 10% of GDP in 2008 to 0 in 2013


Collapse in the supply of safe assets


why are real interest rates so low?why are real interest rates so low? m. marx, b. mojon, f. velde...

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