Jacopo Bonchi La Sapienza Universita di Roma Open seminar at Eesti Pank, 13 March 2018

1. Intro
Model
Conclusions
Secular Stagnation and Rational Bubbles
How Bubbles Postpone Low Interest Rates
Jacopo Bonchi
La Sapienza Universit´a di Roma
Eesti Pank, 13 March 2018
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

2. Intro
Model
Conclusions
Secular Stagnation
Definition
Negative real interest rates are needed to equate saving and
investment with full employment
Specific Features
1 limited effectiveness of the standard monetary policy tools
2 trade-off between full employment, low inflation and financial
stability
Empirical Evidence
The declining trend of the US real interest rates Figure 1
Benchmark Model
Eggertsson et al. (2017)
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

3. Intro
Model
Conclusions
Debate About SecStag
Three theories:
1 Demand-Side View (Summers 2015)
2 Supply-Side View (Gordon 2015)
3 Saving Glut (Bernanke 2015)
Even if a consensus has not emerged regarding the causes of low
interest rates:
many works point to demographic factors (e.g., Carvalho et
al. 2016; Eggertsson et al., 2017)
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

4. Intro
Model
Conclusions
Motivation
The drivers of SecStag were already at work before the recent
financial crisis Figure 2
HOWEVER the FED never hit the ZLB and the US did not
experience low interest rates
WHY?
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

5. Intro
Model
Conclusions
Motivation
The drivers of SecStag were already at work before the recent
financial crisis Figure 2
HOWEVER the FED never hit the ZLB and the US did not
experience low interest rates
WHY?
Asset price bubbles counteracted the downward pressure on
interest rates
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

6. Intro
Model
Conclusions
My Paper
I augment the model of Eggertsson et al. (2017) with rational
bubbles. In this way:
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

7. Intro
Model
Conclusions
My Paper
I augment the model of Eggertsson et al. (2017) with rational
bubbles. In this way:
I account for the stylized facts of the US economy before the
Great Recession (Looking Backward)
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

8. Intro
Model
Conclusions
My Paper
I augment the model of Eggertsson et al. (2017) with rational
bubbles. In this way:
I account for the stylized facts of the US economy before the
Great Recession (Looking Backward)
I study the mechanisms through which bubbles affect interest
rates and their implications for the allocation of resources
(Looking Forward)
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

9. Intro
Model
Conclusions
Related Literature
Debate on Secular Stagnation
Summers (2014, 2015), Bernanke (2015), Gordon (2015)
Rational Bubbles
Tirole (1985), Kraay and Ventura (2007), Martin and Ventura
(2011, 2012), Gal´ı (2014), Asriyan et al. (2016)
Modelling Secular Stagnation
Michau (2015), Teulings (2016), Eggertsson et al. (2017)
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

10. Intro
Model
Conclusions
Setup
OLG structure with population growth (gt > 0)
Exogenous debt limit Dt
No capital
Perfectly competitive goods market
Downward nominal wage
Bubbly assets (they exist iff 1 + r < 1 + g)
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

11. Intro
Model
Conclusions
About Bubbles
Bubble creation and destruction
Middle-aged households receive a fraction δ ∈ (0, 1) of a new
bubbly asset and a portion δ of old bubbly assets loses value
Bubble growth
The quantity of bubbles grows at the same rate as population
Bubbles as store of value
Households can invest in bubbly assets or riskless bonds
Bubbles as collateral
Young households can pledge the bubbly assets they will
receive the next period
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

12. Intro
Model
Conclusions
Household
max
C
m
t+1,C
o
t+2,ZB
t+1|t+1−k
Et lnCy
t + βlnCm
t+1 + β2
lnCo
t+2)
subject to:
Cy
t = By
t
Cm
t+1 = Yt+1+δQB
t+1|t+1−(1 + rt) By
t −Bm
t+1−
∞
k=0
QB
t+1|t+1−kZB
t+1|t+1−k
Co
t+2 = (1 + rt+1) Bm
t+1+(1 − δ) (1 + gt)
∞
k=0
QB
t+2|t+1−kZB
t+1|t+1−k
By
t =
Dt + δEtQB
t+1|t+1
(1 + rt)
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

13. Intro
Model
Conclusions
FOCs
Euler equation:
1
Cm
t
= β (1 + rt) Et
1
Co
t+1
Price of the bubbly asset:
QB
t|t−k = (1 − δ) (1 + gt) βEt
Cm
t
Co
t+1
QB
t+1|t−k
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

14. Intro
Model
Conclusions
Firm
Production function:
Yt = Lα
t
Labor demand:
Wt
Pt
= αLα−1
t
Nominal Wage:
Wt = max ˜Wt, Ptα¯Lα−1
where:
˜Wt = γWt−1 + (1 − γ) Ptα¯Lα−1
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

15. Intro
Model
Conclusions
Monetary Policy
Taylor rule:
1 + it = max 1, 1 + ¯i
Πt
Π
φπ
where:
(1 + ¯i) = (1 + rf
)Π
HINT: it’s less likely to hit the ZLB with a high natural interest
rate. This is crucial in a bubbly environment
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

16. Intro
Model
Conclusions
Bubbles Market
Aggregate index for old bubbles:
Bt =
˜Bt
Nt−1
= δ
∞
k=1
(1 − δ)k
QB
t|t−k
Aggregate bubble index (all bubbles):
QB
t =
˜QB
t
Nt−1
= δ
∞
k=0
(1 − δ)k
QB
t|t−k
or:
QB
t = Ut + Bt = (1 + gt) βEt
Cm
t
Co
t+1
Bt+1
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

17. Intro
Model
Conclusions
Loan Market
Market clearing condition:
NtBy
t = Nt−1Bm
t
Loan demand:
Ld
t =
(1 + gt)
(1 + rt)
(Dt + EtUt+1)
Loan supply:
Ls
t =
β
1 + β
(Yt − Dt−1 − Ut − Bt) −
1
1 + β
(Bt + Ut)
Equilibrium real interest rate:
(1 + rt) = (1 + gt)
(1 + β) (Dt + EtUt+1)
β (Yt − Dt−1 − Ut − Bt) − (Bt + Ut)
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

18. Intro
Model
Conclusions
How Bubbles Affect Interest Rates
2 Channels:
1 Saving Channel (effect a la Tirole)
Bubbly assets divert savings away from riskless bonds
Bubbles induce to save less by providing an income in the old
age
2 Borrowing Channel (effect a la Martin and Ventura)
Bubbly collateral increases the total amount of debt
Higher debt implies less savings
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

19. Intro
Model
Conclusions
How Bubbles Affect Interest Rates
2 Channels:
1 Saving Channel (effect a la Tirole)
Bubbly assets divert savings away from riskless bonds
Bubbles induce to save less by providing an income in the old
age
2 Borrowing Channel (effect a la Martin and Ventura)
Bubbly collateral increases the total amount of debt
Higher debt implies less savings
SO: the real interest rate is higher in a bubbly economy than in a
bubbleless one Figure 3
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

20. Intro
Model
Conclusions
Saving Channel vs Borrowing Channel
Saving channel > Borrowing channel Figure 4
The strength of the channels varies according to the size of the
aggregate bubble:
Borrowing channel: for small aggregate bubbles its effect is
greater
Saving channel: for large aggregate bubbles its effect is
greater
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

21. Intro
Model
Conclusions
Aggregate Supply
Vertical AS (Π ≥ 1):
Yt = ¯Lα
= Y f
Upward sloping AS (Π < 1):
γ
Π
= 1 − (1 − γ)
Y
Y f
1−α
α
AS kink:
Π = 1
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

22. Intro
Model
Conclusions
Aggregate Demand
Downward sloping AD (i > 0):
Y = D +
1 + β
β
(U + B) +
1 + β
β
(1 + g)
Γ
Πφπ−1
(D + U)
Upward sloping AD (i = 0):
Y = D +
1 + β
β
(U + B) +
1 + β
β
(1 + g) Π (D + U)
where Γ = Π
φπ−1
1 + rf )−1
AD kink:
Πkink =
1
(1 + rf )
1
φπ
Π
φπ−1
φπ
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

23. Intro
Model
Conclusions
Bubbleless and Bubbly SS
Effects of bubbles:
Lower AD kink
it’s less likely to hit the
ZLB for the CB
Redistributive Bubbles
The full employment E is
unchanged, but resources
are redistributed
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

24. Intro
Model
Conclusions
Redistributive Bubbles: Bubbleless FE SS
(1 + r) =
(1 + g) (1 + β) D
β (Y f − D)
By
=
D
(1 + r)
Bm
=
β
1 + β
Y f
− D
Cy
= By
=
1
(1 + g)
β
1 + β
Y f
− D
Cm
=
1
1 + β
Y f
− D
Co
= (1 + g) D
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

25. Intro
Model
Conclusions
Redistributive Bubbles: Bubbly FE SS
(1 + r) =
(1 + g) (1 + β) (D + U)
β (Y f − D − U − B) − (U + B)
By
=
D + U
(1 + r)
Bm
=
β
1 + β
Y f
− D − (U + B)
Cy
= By
=
1
(1 + g)
β
1 + β
Y f
− D − (U + B)
Cm
=
1
1 + β
Y f
− D
Co
= (1 + g) (D + U + B)
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

26. Intro
Model
Conclusions
Welfare Analysis
Bubbles redistribute resources from young to old households
Net effect on welfare:
UB
− UNB
= ln 1 −
(1 + β) (U + B)
β (Y f − D)
+ β2
ln 1 +
U + B
D
It depends on the parameters β and D, as well as the size of the
aggregate bubble. β D
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

27. Intro
Model
Conclusions
Welfare Analysis
Bubbles redistribute resources from young to old households
Net effect on welfare:
UB
− UNB
= ln 1 −
(1 + β) (U + B)
β (Y f − D)
+ β2
ln 1 +
U + B
D
It depends on the parameters β and D, as well as the size of the
aggregate bubble. β D
Result: the representative agent is worse off
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

28. Intro
Model
Conclusions
Calibration
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

29. Intro
Model
Conclusions
How Bubbles Prevent SecStag
The mechanism: Figure 5
Bubbles push the natural interest rate up
As a consequence, demographic change does not lead to a
negative natural interest rate
The central bank can escape the ZLB and the economy does
not reach the SecStag equilibrium
Furthermore:
the size of the bubble necessary to keep the natural interest
rate positive is 5% of GDP
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

30. Intro
Model
Conclusions
Summing Up
I have explained how speculative movements in asset prices
postponed SecStag:
bubbles redistribute resources across generations by serving as
store of value (saving channel) and collateral (borrowing
channel)
this redistribution is welfare reducing
and raise the natural interest rate avoiding SecStag
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

31. US Natural and Real Interest Rates 1982-2015
Source: Laubach and Williams (2003), Federal Reserve Bank of Cleveland.
Back
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

32. US Life Expectancy and Population Growth
Source: World Bank.
Back
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

33. Loan Market Equilibrium
Back
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

34. Saving Channel vs Borrowing Channel
Back
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

35. Welfare Analysis: Different Values of β
Back
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

36. Welfare Analysis: Different Values of D
Back
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

37. How Bubbles Prevent SecStag
Back
Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles