The Effects 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
Monetary Policy and Asset Price Bubbles Should monetary policy respond to asset price bubbles? Pre-crisis consensus: - focus on inflation and output gap - ignore asset price developments, unless threat to objectives - the case against a monetary response to bubbles: (i) diffi cult detection (ii) interest rate: "too blunt" an instrument Challenges to the pre-crisis consensus: - macro stability financial stability - bubble-driven asset price booms risk of financial crisis calls for a "leaning against the wind" policy: raise interest rates in response to developing asset price bubbles Jordi Galí, Luca Gambetti () Monetary Policy and Bubbles September 2013 2 / 17
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 effects of monetary policy on (rational) asset price bubbles?...the desirability of leaning against the wind policies? Present paper: What is the evidence on the effects of monetary policy on asset price bubbles? Jordi Galí, Luca Gambetti () Monetary Policy and Bubbles September 2013 3 / 17
Interest Rates and Rational Bubbles: Theoretical Issues Key assumption in the case for leaning against the wind policies: Based on "fundamentals" intuition: interest rate bubble interest rate asset price It ignores two key features of a bubble: (i) no payoffs to be discounted (ii) return on the bubble = growth in bubble size Equilibrium requirement: interest rate expected bubble growth risk of amplified fluctuations in the size of the bubble resulting from "leaning against the wind" policies (Galí (2013)) Jordi Galí, Luca Gambetti () Monetary Policy and Bubbles September 2013 4 / 17
Interest Rates and Bubbles: Theoretical Issues Asset yielding a stream of dividends {D t } Exogenous time-varying (gross) real rate {R t } Risk neutral investors Fundamental price: Q F t or, in log-linear version: q F t = const + where Λ Γ/R < 1 E t { k=0 k=1 ( k 1 j=0 (1/R t+j ) ) D t+k } Λ k [(1 Λ)E t {d t+k+1 } E t {r t+k }] Jordi Galí, Luca Gambetti () Monetary Policy and Bubbles September 2013 5 / 17
Interest Rates and Bubbles: Theoretical Issues Observed stock price Q t = Qt F + Qt B Dynamic response of stock price to an interest rate shock: q t+k = (1 γ t 1 ) qf t+k + γ t 1 q B t+k where γ t Q B t /Q t Theory (and evidence) suggest: q F t+k < 0 Conventional view: q B t+k 0 q t+k < 0 Jordi Galí, Luca Gambetti () Monetary Policy and Bubbles September 2013 6 / 17
The Rational Bubble Theory Perspective Asset pricing equation Q t R t = E t {D t+1 + Q t+1 } Fundamental component: Qt F R t = E t {D t+1 + Qt+1} F Bubble component: Qt B R t = E t {Qt+1} B or, equivalently qt B = r t 1 + ξ t where ξ t qt B E t 1 {qt B } and E t 1 {ξ t } = 0. Without loss of generality ξ t = ψ t (r t E t 1 {r t }) + ξt where E t 1 {ξt } = 0 and. E {ξ t r t k } = 0, for k = 0, ±1, ±2,.. both the sign and the size of ψ t are indeterminate Jordi Galí, Luca Gambetti () Monetary Policy and Bubbles September 2013 7 / 17
The Rational Bubble Theory Perspective Predicted dynamic response of the bubble to an interest rate shock q B t+k = { r ψt t r ψ t t + k 1 j=0 r t+j for k = 0 for k = 1, 2,... Predicted dynamic response of the stock price: q t+k 0 Jordi Galí, Luca Gambetti () Monetary Policy and Bubbles September 2013 8 / 17
The Rational Bubble Theory Perspective: An Example Assumptions: for k = 0, 1, 2,... r t+k = ρ k r ; Dynamic response of the asset price q t+k ρ k r d t+k = (1 γ t 1 ) + γ 1 Λρ t 1 r = 0 ( ψ t + 1 ) ρk r 1 ρ r Jordi Galí, Luca Gambetti () Monetary Policy and Bubbles September 2013 9 / 17
The Rational Bubble Theory Perspective: An Example Assumptions: for k = 0, 1, 2,... r t+k = ρ k r ; Dynamic response of the asset price q t+k ρ k r d t+k = (1 γ t 1 ) + γ 1 Λρ t 1 r = 0 ( ψ t + 1 ) ρk r 1 ρ r Implications for the response of asset prices to an interest rate shock: γ t 0 q t+k γ t 0, ψ t 0 q t+k < 0 Simulated responses under alternative calibrations > 0 for large k Jordi Galí, Luca Gambetti () Monetary Policy and Bubbles September 2013 10 / 17
6 Figure 1 : Asset Price Response to an Exogenous Interest Rate Increase: Alternative Calibrations 4 2 asset price response 0-2 -4-6 0 5 10 15 20 periods after shock gamma = 0 gamma = 0.5, psi =0 gamma = 0.5, psi = -8 gamma = 0.5, psi = 6
Evidence based on Vector Autoregressions VAR with constant coeffi cients x t = A 0 + A 1 x t 1 + A 2 x t 2 +... + A p x t p + u t where x t [ y t, d t, p t, i t, q t ] E t {u t u t k } = Σ u t = Sε t with E {ε t ε t} = I and E {ε t ε t k } = 0 for k = 1, 2, 3,... Identification of monetary policy shocks: - i t instrument of monetary policy - ( y t, d t, p t ) predetermined with respect to i t - S block lower-triangular (CEE (2005)) Jordi Galí, Luca Gambetti () Monetary Policy and Bubbles September 2013 11 / 17
Evidence based on Vector Autoregressions VAR with time-varying coeffi cients x t = A 0,t + A 1,t x t 1 + A 2,t x t 2 +... + A p,t x t p + u t where E t {u t u t k } = Σ t u t = S t ε t with E {ε t ε t} = I and E {ε t ε t k } = 0 for k = 1, 2, 3,... Identification of monetary policy shocks: - i t instrument of monetary policy - ( y t, d t, p t ) predetermined with respect to i t - S t block lower-triangular, for all t Jordi Galí, Luca Gambetti () Monetary Policy and Bubbles September 2013 12 / 17
Assumptions Letting θ t = vec([a 0,t, A 1,t..., A p,t ]), where ω t N(0, Ω) is white noise. θ t = θ t 1 + ω t Letting Σ t F t D t F t where F t is lower triangular with ones on the diagonal and D t diagonal. Define φ t = vec(ft 1 ) and σ t = vec(d t ). φ t = φ t 1 + ζ t log σ t = log σ t 1 + ξ t where ζ t N(0, Ψ) and ξ t N(0, Ξ) are (uncorrelated) white noise. Estimation: Bayesian approach (Primiceri (2005)) Jordi Galí, Luca Gambetti () Monetary Policy and Bubbles September 2013 13 / 17
Evidence Impulse responses: VAR with constant coeffi cients Jordi Galí, Luca Gambetti () Monetary Policy and Bubbles September 2013 14 / 17
Dividends Stock prices Figure 2.a : Estimated Responses to Monetary Policy Shock Nominal interest rate Real interest rate
Figure 2.b : Estimated Responses to Monetary Policy Shock Observed (red, dotted) vs. Fundamental (blue, solid) Stock Price
Evidence Impulse responses: VAR with constant coeffi cients Impulse responses: VAR with time-varying coeffi cients Jordi Galí, Luca Gambetti () Monetary Policy and Bubbles September 2013 15 / 17
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 Impulse responses: VAR with constant coeffi cients Impulse responses: VAR with time-varying coeffi cients (q t+k q F t+k ) In the simple example above: (q t+k q F t+k ) = γ t 1 ( q B t+k qf t+k ( ρ k = γ r t 1 + ψ 1 Λρ t + 1 ) ρk r r 1 ρ ( ) r 1 γ t 1 + ψ 1 ρ t r which is positive, as long as γ t 1 > 0 and ψ t 0. ) Jordi Galí, Luca Gambetti () Monetary Policy and Bubbles September 2013 16 / 17
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 F at different horizons
Figure 4.b : Probability of a positive response of q q F 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 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 of destabilizing "leaning against the wind" policies emphasized in Galí (2013) Need to understand better how monetary policy affects asset prices before such policies are adopted Jordi Galí, Luca Gambetti () Monetary Policy and Bubbles September 2013 17 / 17
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