Monetary Policy and Asset Price Bubbles

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The E¤ects of Monetary Policy on Asset Price Bubbles:

Some Evidence

Jordi Galí Luca Gambetti

September 2013

Jordi Galí, Luca Gambetti () Monetary Policy and Bubbles September 2013 1 / 17

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Monetary Policy and Asset Price Bubbles

Should monetary policy respond to asset price bubbles?

Pre-crisis consensus:

- focus on in‡ation and output gap

- ignore asset price developments, unless threat to objectives - the case against a monetary response to bubbles:

(i) di¢ cult detection

(ii) interest rate: "too blunt" an instrument Challenges to the pre-crisis consensus:

- macro stability ; …nancial stability

- bubble-driven asset price booms ) " risk of …nancial crisis

) calls for a "leaning against the wind" policy: raise interest rates in response to developing asset price bubbles

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Monetary Policy and Asset Price Bubbles

Key maintained assumption:

"interest rate) # ^bubble ...but no theoretical or empirical support

Galí (2013): What does economic theory have to say regarding...

...the e¤ects of monetary policy on (rational) asset price bubbles?

...the desirability of leaning against the wind policies?

Present paper: What is the evidence on the e¤ects of monetary policy on asset price bubbles?

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Interest Rates and Rational Bubbles: Theoretical Issues

Key assumption in the case for leaning against the wind policies:

"interest rate) # ^bubble Based on "fundamentals" intuition:

"interest rate) # asset price It ignores two key features of a bubble:

(i) no payo¤s to be discounted

(ii) return on the bubble = growth in bubble size Equilibrium requirement:

"interest rate ) " expected bubble growth

) risk of ampli…ed ‡uctuations in the size of the bubble resulting from

"leaning against the wind" policies (Galí (2013))

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Interest Rates and Bubbles: Theoretical Issues

Asset yielding a stream of dividendsf^D^tg Exogenous time-varying (gross) real ratef^R^tg Risk neutral investors

Fundamental price:

Q_t^F Et

( _∞

k

∑

=1 k 1 j∏=0

(1/Rt+j)

! D_t+k

)

or, in log-linear version:

q_t^F =const+

∑

∞ k=0

Λ^k[(1 Λ)Etf^d^t⁺^k⁺¹g ^E^tf^r^t⁺^kg]

where Λ Γ/R <1

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Interest Rates and Bubbles: Theoretical Issues

Observed stock price

Qt =Q_t^F +Q_t^B

Dynamic response of stock price to an interest rate shock:

∂q_t₊_k

∂ε^m_t = (1 γ_t ₁)^∂q

F t+k

∂ε^m_t +γ_t ₁

∂q_t^B₊_k

∂ε^m_t whereγ_t Q_t^B/Qt

Theory (and evidence) suggest:

∂q^F_t₊_k

∂ε^m_t <0 Conventional view:

∂q^B_t₊_k

∂ε^m_t 0 ) ^∂q^t⁺^k

∂ε^m_t <0

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The Rational Bubble Theory Perspective

Asset pricing equation

QtRt =Etf^D^t⁺¹+Qt+1g Fundamental component:

Q_t^FR_t =E_tf^D^t⁺¹+Q_t^F₊₁g Bubble component:

Q_t^BRt =Etf^Qt^B+1g or, equivalently

∆q_t^B =r_t ₁+ξ_t

whereξ_t q_t^B Et 1f^qt^Bg^and^E^t ¹f^ξtg=0. Without loss of generality ξ_t =ψ_t(r_t E_t ₁f^r^tg) +ξ_t

whereE_t ₁f^ξtg= 0 and. Ef^ξtr_{t k}g=0, for k =0, 1, 2, ..

) both the sign and the size of ψ_t are indeterminate

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The Rational Bubble Theory Perspective

Predicted dynamic response of the bubble to an interest rate shock

∂q^B_t₊_k

∂ε^m_t = (

ψ_t_∂ε^∂rm^t

t for k=0

ψ_t_∂ε^∂rm^t

t +_∑^k_j₌₀¹ ^∂r_∂ε^t⁺m^j

t for k =1,2, ...

Predicted dynamic response of the stock price:

∂q_t₊_k

∂ε^m_t 7⁰

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The Rational Bubble Theory Perspective: An Example

Assumptions:

∂r_t₊_k

∂ε^m_t =ρ^k_r ; ∂d_t₊_k

∂ε^m_t =0 for k =0,1,2, ...

Dynamic response of the asset price

∂q_t₊_k

∂ε^m_t = (1 γ_t ₁) ^ρ

k r

1 Λρ_r +γ_t ₁ ψ_t +¹ ^ρ

k r

1 ρ_r

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The Rational Bubble Theory Perspective: An Example

Assumptions:

∂r_t₊_k

∂ε^m_t =ρ^k_r ; ∂d_t₊_k

∂ε^m_t =0 for k =0,1,2, ...

Dynamic response of the asset price

∂q_t+k

∂ε^m_t = (1 γ_t ₁) ^ρ

k r

1 Λρ_r +γ_t ₁ ψ_t +¹ ^ρ

k r

1 ρ_r Implications for the response of asset prices to an interest rate shock:

γ_t ' ⁰ ) ^∂q^t⁺^k

∂ε^m_t <0

γ_t 0, ψ_t &⁰ ) ^∂q^t⁺^k

∂ε^m_t >0 for largek Simulated responses under alternative calibrations

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Figure 1 : Asset Price Response to an Exogenous Interest Rate Increase:

Alternative Calibrations

0 5 10 15 20

-6 -4 -2 0 2 4 6

periods after shock

asset price response

gamma = 0

gamma = 0.5, psi =0 gamma = 0.5, psi = -8 gamma = 0.5, psi = 6

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Evidence based on Vector Autoregressions

VAR with constant coe¢ cients

x_t =A₀+A₁x_t ₁+A₂x_t ₂+...+A_px_{t p}+u_t

where

x_t [_∆y_t,∆d_t,∆p_t,i_t,∆q_t]⁰ E_tf^u^t^ut k⁰ g=_Σ

u_t =Sεt

with Ef^ε^t^ε⁰tg=I and Ef^ε^t^εt k⁰ g=0 fork =1,2,3, ...

Identi…cationof monetary policy shocks:

- i_t instrument of monetary policy

- (_∆y_t,∆d_t,∆p_t) predetermined with respect toi_t - S block lower-triangular (CEE (2005))

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Evidence based on Vector Autoregressions

VAR with time-varying coe¢ cients

x_t =A_0,t +A_1,tx_t ₁+A_2,tx_t ₂+...+A_p,tx_{t p}+u_t

where

E_tf^u^t^ut k⁰ g=_Σt

u_t =S_tεt

with Ef^ε^t^ε⁰tg=I and Ef^ε^t^εt k⁰ g=0 fork =1,2,3, ...

Identi…cationof monetary policy shocks:

- i_t instrument of monetary policy

- (_∆y_t,∆d_t,∆p_t) predetermined with respect toi_t - St block lower-triangular, for all t

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Assumptions

Letting θt =vec([A_0,t,A_1,t...,A_p,t]),

θt =θt 1+ωt

where ωt N(0,Ω)is white noise.

Letting Σt F_tD_tF_t⁰ whereF_t is lower triangular with ones on the diagonal and Dt diagonal. De…ne φ_t =vec(F_t ¹)andσt =vec(Dt).

φ_t =φ_t ₁+ζ_t logσt =logσt 1+ξ_t

where ζ_t N(0,Ψ) andξ_t N(0,Ξ)are (uncorrelated) white noise.

Estimation: Bayesian approach (Primiceri (2005))

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Evidence

Impulse responses: VAR with constant coe¢ cients

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Figure 2.a : Estimated Responses to Monetary Policy Shock

Nominal interest rate

Dividends Stock prices

Real interest rate

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Figure 2.b : Estimated Responses to Monetary Policy Shock

Observed (red, dotted) vs. Fundamental (blue, solid) Stock Price

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Evidence

Impulse responses: VAR with constant coe¢ cients Impulse responses: VAR with time-varying coe¢ cients

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Figure 3.a : Estimated Responses to Monetary Policy Shock: TVC-VAR

Nominal Interest Rate

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Figure 3.b : Estimated Responses to Monetary Policy Shock: TVC-VAR

Real Interest Rate

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Figure 3.c : Estimated Responses to Monetary Policy Shock: TVC-VAR

Dividends

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Figure 3.d : Estimated Responses to Monetary Policy Shock: TVC-VAR

Stock Prices

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Evidence

Impulse responses: VAR with constant coe¢ cients Impulse responses: VAR with time-varying coe¢ cients

∂(q_t+k q^F_t₊_k)

∂ε^m_t = γ_t ₁

∂q_t^B₊_k

∂ε^m_t

∂q_t^F₊_k

∂ε^m_t

!

In the simple example above:

∂(q_t₊_k q^F_t₊_k)

∂ε^m_t = γ_t ₁ ρ^k_r

1 Λρ_r +ψ_t +¹ ^ρ

k r

1 ρ_r ' ^γt 1

1

1 ρ_r +ψ_t which is positive, as long as γ_t ₁ >0 and ψ_t &^0.

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Figure 3.e : Estimated Responses to Monetary Policy Shock: TVC-VAR

Fundamental Stock Price

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Figure 3.f : Estimated Responses to Monetary Policy Shock: TVC-VAR

Observed minus Fundamental Stock Price

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Figure 4.a : Response of q – q

^F

at different horizons

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Figure 4.b : Probability of a positive response of q – q

^F

at different horizons

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Figure 5.a : Estimated Responses to Monetary Policy Shock: TVC-VAR Observed vs. Fundamental Stock Price: 1965Q1-1967Q4

Fundamental: blue, solid Observed: red, dotted

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Figure 5.b : Estimated Responses to Monetary Policy Shock: TVC-VAR Observed vs. Fundamental Stock Price: 1976Q1-1978Q4

Fundamental: blue, solid Observed: red, dotted

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Figure 5.c : Estimated Responses to Monetary Policy Shock: TVC-VAR Observed vs. Fundamental Stock Price: 1984Q4-1987Q3

Fundamental: blue, solid Observed: red, dotted

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Figure 5.d : Estimated Responses to Monetary Policy Shock: TVC-VAR Observed vs. Fundamental Stock Price: 1997Q1-1999Q4

Fundamental: blue, solid Observed: red, dotted

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Concluding Remarks

Maintained assumption in the case for "leaning against the wind" policies:

higher interest rates reduce the size of asset price bubbles Theoretical foundations: at best, fragile.

Empirical evidence:

- no clear support for the conventional view

- consistent with the possibility ofdestabilizing "leaning against the wind"

policies emphasized in Galí (2013)

Need to understand better how monetary policy a¤ects asset prices before such policies are adopted

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Monetary Policy and the 1928-29 Stock Market Bubble

3 3.5 4 4.5 5 5.5

150 170 190 210 230 250 270 290 310 330

Stock Price Index Discount Rate

(34)

Monetary Policy and the Dotcom Bubble

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Monetary Policy and Asset Price Bubbles

The E¤ects of Monetary Policy on Asset Price Bubbles:

Some Evidence

Monetary Policy and Asset Price Bubbles

Monetary Policy and Asset Price Bubbles

Interest Rates and Rational Bubbles: Theoretical Issues

Interest Rates and Bubbles: Theoretical Issues

∑

∑

Interest Rates and Bubbles: Theoretical Issues

The Rational Bubble Theory Perspective

The Rational Bubble Theory Perspective

The Rational Bubble Theory Perspective: An Example

The Rational Bubble Theory Perspective: An Example

Figure 1 : Asset Price Response to an Exogenous Interest Rate Increase:

Alternative Calibrations

Evidence based on Vector Autoregressions

Evidence based on Vector Autoregressions

Evidence

Figure 2.a : Estimated Responses to Monetary Policy Shock

Nominal interest rate

Dividends Stock prices

Real interest rate

Figure 2.b : Estimated Responses to Monetary Policy Shock

Observed (red, dotted) vs. Fundamental (blue, solid) Stock Price

Evidence

Figure 3.a : Estimated Responses to Monetary Policy Shock: TVC-VAR

Nominal Interest Rate

Figure 3.b : Estimated Responses to Monetary Policy Shock: TVC-VAR

Real Interest Rate

Figure 3.c : Estimated Responses to Monetary Policy Shock: TVC-VAR

Dividends

Figure 3.d : Estimated Responses to Monetary Policy Shock: TVC-VAR

Stock Prices

Evidence

Figure 3.e : Estimated Responses to Monetary Policy Shock: TVC-VAR

Fundamental Stock Price

Figure 3.f : Estimated Responses to Monetary Policy Shock: TVC-VAR

Observed minus Fundamental Stock Price

Figure 4.a : Response of q – q

at different horizons

Figure 4.b : Probability of a positive response of q – q

at different horizons

Figure 5.a : Estimated Responses to Monetary Policy Shock: TVC-VAR Observed vs. Fundamental Stock Price: 1965Q1-1967Q4

Fundamental: blue, solid Observed: red, dotted

Figure 5.b : Estimated Responses to Monetary Policy Shock: TVC-VAR Observed vs. Fundamental Stock Price: 1976Q1-1978Q4

Fundamental: blue, solid Observed: red, dotted

Figure 5.c : Estimated Responses to Monetary Policy Shock: TVC-VAR Observed vs. Fundamental Stock Price: 1984Q4-1987Q3

Fundamental: blue, solid Observed: red, dotted

Figure 5.d : Estimated Responses to Monetary Policy Shock: TVC-VAR Observed vs. Fundamental Stock Price: 1997Q1-1999Q4

Fundamental: blue, solid Observed: red, dotted

Concluding Remarks

Monetary Policy and the 1928-29 Stock Market Bubble

Monetary Policy and the Dotcom Bubble

Monetary Policy and the Housing Bubble