A Model of Secular Stagnation: Theory and Quantitative ... of \A Model of Secular Stagnation: Theory...

$: A Model of Secular Stagnation: Theory and Quantitative ... of \A Model of Secular Stagnation: Theory and Quantitative Evaluation" by Gauti Eggertsson, Neil Mehrotra and Jacob Robbins$
Discussion of “A Model of Secular Stagnation:Theory and Quantitative Evaluation”

by Gauti Eggertsson, Neil Mehrotra and Jacob Robbins

Andrea FerreroUniversity of Oxford

Federal Reserve Bank of San Francisco Conference on

“Do Changes in the Economic LandscapeRequire a New Policy Framework?”

San Francisco, 21 April 2017

Introduction Summary Level & Decomposition Policy Conclusions

Introduction

Central tenet of Secular Stagnation hypothesis (Summers, 2014):

Low (possibly negative) equilibrium real interest rate

Data: Negative measured real interest rates

I Here to stay

Need a model to construct equilibrium real interest rate

I And think about “real interest rate gap”

EMR provide a model of Secular Stagnation

A new framework for policy analysis

Andrea Ferrero (Oxford) Discussion of Eggertsson, Mehrotra and Robbins 21 April 2017 2 / 13


Introduction




1990 1995 2000 2005 2010

perc

enta

ge p

oint

s

-4

-2

0

2

4

6

8

10Real Short-Term Yields

Median Mean

Source: Carvalho, Ferrero, Nechio (2016)

I Here to stay







Introduction




I Here to stay

Source: Summers (2015)







Introduction




I Here to stay







Outline of Discussion

1 Brief summary and key findings

2 Decline of natural rate

3 Policy implications



Summary

First part: Three-period OLG model with borrowing constraint

maxC yt ,C

mt+1,C

ot+2

Et(lnCyt + β lnCm

t+1 + β2 lnCot+2)

subject to

C yt = By

t = Dt/(1 + rt)

Cmt+1 = Ym

t+1 − (1 + rt)Byt + Bm

t+1

Cot+2 = Y o

t+2 − (1 + rt+1)Bmt+1

Get expression for equilibrium real interest rate

rt =(1 + β)(1 + gt)(1 + xt)Dt + (1 + xt+1)Y

ot+1

β(Ymt − Dt−1)

− 1

where xt ≡ At/At−1 − 1

Three factors that can push down real interest rate

1 gt : Demographics (Carvalho, Ferrero and Nechio, 2016)

2 xt : Productivity (Gordon, 2015)

3 Dt : Deleveraging (Eggertsson and Krugman, 2012)



Summary


maxC yt ,C

mt+1,C

ot+2

Et(lnCyt + β lnCm

t+1 + β2 lnCot+2)

subject to

C yt = By

t = Dt/(1 + rt)

Cmt+1 = Ym

t+1 − (1 + rt)Byt + Bm

t+1

Cot+2 = Y o

t+2 − (1 + rt+1)Bmt+1

Population growth: Nt = (1 + gt)Nt−1 ⇒ (1 + gt)Byt = −Bm

t


rt =(1 + β)(1 + gt)(1 + xt)Dt + (1 + xt+1)Y

ot+1

β(Ymt − Dt−1)

− 1








Summary


maxC yt ,C

mt+1,C

ot+2

Et(lnCyt + β lnCm

t+1 + β2 lnCot+2)

subject to

C yt = By

t = Dt/(1 + rt)

Cmt+1 = Ym

t+1 − (1 + rt)Byt + Bm

t+1

Cot+2 = Y o

t+2 − (1 + rt+1)Bmt+1

Population growth: Nt = (1 + gt)Nt−1 ⇒ (1 + gt)Byt = −Bm

t

Productivity growth: Yt = At Y ⇒ Dt = At+1D


rt =(1 + β)(1 + gt)(1 + xt)Dt + (1 + xt+1)Y

ot+1

β(Ymt − Dt−1)

− 1








Summary



rt =(1 + β)(1 + gt)(1 + xt)Dt + (1 + xt+1)Y

ot+1

β(Ymt − Dt−1)

− 1








Summary


Temporary deleveraging shock ⇒ Permanently low real rate

Nice narrative:

I Real rate already on decline due to trends in demographics and productivity

I Becomes permanently negative because of crisis (deleveraging)



Summary


Nice narrative:

I Real rate already on decline due to trends in demographics and productivity

I Becomes permanently negative because of crisis (deleveraging)



Summary

Second part: Quantitative life-cycle model with

I Age-specific income profile

I Mortality risk

I Bequest motive

I Capital and CES production

I Exogenous process for relative price of capital

I Distortionary labor taxes

Calibrated to US data in 2015: Two options

I No output gap (Stock and Watson, 2012)

I Large output gap (Hall, 2016)

Legitimate to consider 2015 observed real rate as natural real rate but

I No output gap 6=⇒ Observed real interest rate = Natural rate

I Need additional assumption economy is in steady state

Results robust to alternative measures of output gap ∈ (−15%, 0)?

I Interesting that no deflation arises with large output gap

Paradox of wage flexibility (Galı and Monacelli, 2016)

I Need more flexibility to generate more deflation and larger output gap



Summary

Second part: Quantitative life-cycle model

Legitimate to consider 2015 observed real rate as natural real rate but

I No output gap 6=⇒ Observed real interest rate = Natural rate

I Need additional assumption economy is in steady state

Results robust to alternative measures of output gap ∈ (−15%, 0)?

I Interesting that no deflation arises with large output gap

Paradox of wage flexibility (Galı and Monacelli, 2016)

I Need more flexibility to generate more deflation and larger output gap



Level

Very low level of r∗ throughout sample (1970-2016)

I Compare with estimates from Holston, Laubach and Williams (2016)

I Large real interest rate gap since early 1980s?

Source: Justiniano and Primiceri (2010)



Level

Very low level of r∗ throughout sample (1970-2016)

I Large real interest rate gap since early 1980s?

Source: Justiniano and Primiceri (2010)



What Explains a Falling r ∗?

Major role of demographics and productivity growth

Government debt only factor that avoided much lower level

Some factors “disappear” from discussion

I How would have r∗ looked like without crisis?

I Role of increased inequality?

I Would be interesting to see counterfactuals with major driving forces



What Explains a Falling r ∗?

Some factors “disappear” from discussion

I How would have r∗ looked like without crisis?

I Role of increased inequality?

I Would be interesting to see counterfactuals with major driving forces



Demographics and the Natural Real Rate

Carvalho, Ferrero and Nechio (2016) find similar role for demographics

I Larger relative contribution of increase in life expectancy

1990 1993 1996 1999 2002 2005 2008 2011 2014

perc

enta

ge p

oint

s

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

4

4.2Real Interest Rate

Baseline Population Growth Life Expectancy

Main difference: In EMR, fixed lifetime horizon but decrease in mortality risk

I Cannot live more than 81 years

Life expectancy currently at about 80 in most OECD countries

I Increased over time and projected to keep increasing

I Makes natural rate likely to keep falling

Also, empirical consumption profile much less hump-shaped than in EFR



Demographics and the Natural Real Rate

Carvalho, Ferrero and Nechio (2016) find similar role for demographics

I Larger relative contribution of increase in life expectancy

Main difference: In EMR, fixed lifetime horizon but decrease in mortality risk

I Cannot live more than 81 years

Life expectancy currently at about 80 in most OECD countries

I Increased over time and projected to keep increasing

I Makes natural rate likely to keep falling

Also, empirical consumption profile much less hump-shaped than in EFR



Policy Implications

Why is negative r∗ a problem?

I Zero lower bound

: Level of r∗ puts lower bound on π∗

I Bubbles and financial stability

: Better raise r∗ than increase π∗

Also, in this model, limited effects of forward guidance

I What about quantitative easing?

Implication: Expansionary fiscal policy

I Debt/GDP from 118% to 215% raises r∗ from -1.47% to +1%

I But risk premia likely to rise

Similar conclusions in Carvalho, Ferrero and Nechio (2016)

I Additional option: Raise retirement age

I But need increase well beyond currently contemplated reforms (OECD, 2010)



Policy Implications


I Zero lower bound: Level of r∗ puts lower bound on π∗

I Bubbles and financial stability

: Better raise r∗ than increase π∗











Policy Implications



I Bubbles and financial stability: Better raise r∗ than increase π∗











Policy Implications









Other policies options are challenging

I Hard to increase fertility rates and productivity growth

I Probably don’t want to increase mortality...






Policy Implications














Conclusions

Very nice paper, definitely useful to think about current policy challenges

Decline in natural real interest rate product of

I Financial crisis

I Interacting with long-term trends

May still require some fine tuning on quantitative part

If Secular Stagnation is relevant scenario

I Limited options for monetary policy?

I Shift to more activist fiscal policy?


A Model of Secular Stagnation: Theory and Quantitative ... of \A Model of Secular Stagnation: Theory...

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