Monetary Policy Design
Monetary Theory University of Bern
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Aim
• Start from our baseline toy model • Captures the propagation of monetary policy shocks • More Importantly Understand how active monetary policy affects this propagation
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How to represent monetary policy?
• So far: Very crude and parsimonious representation Mt = µt Mt−1 log(µt ) = ρµ log(µt−1 ) + (1 − ρµ ) log(µ) + εµ,t • Very passive monetary policy • Purely discretionary policy • Does not represent the mandate of the central bank
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How to represent monetary policy?
• Make it endogenous: Mt = g(πt , yt ) • Candidate: Mt = M + αy
Yt − Y⋆ − απ (πt − π ⋆ )(+εM,t ) Y⋆
• Difficult to control Mt ! • Or? µt = µ + αy
Yt − Y⋆ − απ (πt − π ⋆ )(+εM,t ) Y⋆
• Does not fit usual practice.
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How to represent monetary policy?
• Interest rates: open market operations • The central bank sells and buys assets on the market to reach a particular level of the interest rate • Or decide on the discount rate • At the end of the day: Control of the interest rate • Idea: Represent monetary policy by an interest rate rule
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How to represent monetary policy? Taylor [1993] • Very simple rule it = πt + 0.5e yt + 0.5(πt − 2) + 2 • What matters is • Position of inflation wrt targeted inflation (2%) • Position of output wrt trend (e yt )
• Assume inflation=2% and e y = 0 =⇒ it = 4% • The economy plunges in a recession: πt = 1% and e yt = −1%, then the CB should decrease the interest rate to it = 1 + 0.5 × (−1) + 0.5(1 − 2) + 2 = 2% 6/36
How to represent monetary policy? Taylor [1993]
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How to represent monetary policy? Taylor [1993]
• Works remarkably well on this period (not so nice outside of this sub–sample) • This is just a representation of monetary policy • Not a micro–founded behavior (optimal monetary policy) • Accounts for conditional correlations • Observational Equivalence • Largely extended and studied in literature
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How to represent monetary policy? Clarida, Galí and Gertler [2000] • Extend Taylor [1993] • Estimate the rule by GMM • Instruments: 4 lags of inflation, output gap, fed funds rate, short–run spread, commodity price inflation it = ρi it−1 + (1 − ρi )i⋆t + εi,t i⋆t = i⋆ + β(Et πt+k − π ⋆ ) + γEte yt+q k, q ⩾ 0. • The rule now features • Expectations: the central bank reacts to expected deviations of inflation from target, and expected output gap; • Interest rate smoothing.
• Break the sample into 2 parts 9/36
How to represent monetary policy? Clarida, Galí and Gertler [2000]
Baseline Results
Pre-Volcker Post-Volcker
π⋆
β
γ
ρ
p
4.24
0.83
0.27
0.68
0.83
(1.09)
(0.07)
(0.08)
(0.05)
3.58
2.15
0.93
0.79
(0.50)
(0.40)
(0.42)
(0.04)
0.32
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How to represent monetary policy? Robustness to Indicators β
γ
ρ
p
Detrended Output Pre-Volcker 4.17
0.75
0.29
0.67
0.80
(0.68)
(0.07)
(0.08)
(0.05)
4.52
1.97
0.55
0.76
(0.58)
(0.32)
(0.30)
(0.05)
π⋆
Post-Volcker
Unemployment Rate Pre-Volcker 3.80 Post-Volcker CPI Pre-Volcker Post-Volcker
0.84
0.60
0.63
(0.87)
(0.05)
(0.11)
(0.04)
4.42
2.01
0.56
0.73
(0.44)
(0.28)
(0.41)
(0.05)
4.56
0.68
0.28
0.65
(0.53)
(0.06)
(0.08)
(0.05)
3.47
2.14
1.49
0.88
(0.79)
(0.52)
(0.87)
(0.03)
0.29
0.64 0.31
0.43 0.14 11/36
How to represent monetary policy? Clarida, Galí and Gertler [2000] Taylor Principle For the equilibrium to be determinate, the coefficient on inflation should be greater than 1. • Proof: Consider the stripped down version of the model πt = κxt + βEt πt+1 1 xt = Et xt+1 − (Rt − Et πt+1 ) σ Rt = αEt πt+1 • CGG: The equilibrium was indeterminate in the pre–Volcker period! • Why? Simple intuition: Monetary policy is not aggressive enough. • Means that the CB generates additional volatility! 12/36
How to represent monetary policy? Clarida, Galí and Gertler [2000]
• Post–Volcker: Determinate equilibrium • Aggressive vis–à–vis inflation • Increase in inflation leads to a more than 1 for 1 increase in interest rate • Drop in the real interest rate =⇒ stabilize demand and inflation
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Benchmark Model
bt − Et π AD : b yt = Etb yt+1 − (R bt+1 ) + ξy,t bt ) + βEt π AS : π bt = κ(b yt − a bt+1 + ξπ,t ( ) b t = ρR R bt−1 + (1 − ρR ) απ π MP : R bt + αyb yt + ξR,t
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Response to an AD Shock
4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.5
Output
0
5
10
15
20
1.2 1.0 0.8 0.6 0.4 0.2 0.0
Inflation
0
5
10
15
20
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
Nom. Int. Rate
0
5
10
15
20
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Response to an Inflation Shock
Output
1 2 3 4 5 6
0
5
10
15
20
3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
Inflation
0
5
10
15
20
1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2
Nom. Int. Rate
0
5
10
15
20
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Response to a Monetary Policy Shock
3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.5
Output
0
5
10
Inflation
15
20
0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.1
Nom. Int. Rate 0.0 0.2 0.4 0.6
0
5
10
15
20
0.8
0
5
10
15
20
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Monetary Policy Design
• We want to understand the role of the parameters of the rule: • απ : Reaction to Inflation • αy : Reaction to Output Gap • ρR : Interest Smoothing
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Reaction to Inflation: απ , AD Shock
6 5 4 3 2 1 0
Output
0
5
10
15
20
απ =1,
1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
Inflation
0
5
απ =1.5,
10
15
20
απ =2.5,
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
Nom. Int. Rate
0
5
10
15
20
απ =10
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Reaction to Inflation: απ , Inflation Shock
2 0 2 4 6 8 10
Output
0
5
10
15
20
απ =1,
6 5 4 3 2 1 0
Inflation
Nom. Int. Rate
2.0 1.5 1.0 0.5
0
5
απ =1.5,
10
15
20
απ =2.5,
0.0
0
5
10
15
20
απ =10
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Reaction to Inflation: απ , Monetary Policy Shock
3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
Output
0
5
10
15
20
απ =1,
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
Inflation
0
5
απ =1.5,
10
15
20
απ =2.5,
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Nom. Int. Rate
0
5
10
15
20
απ =10
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Reaction to Inflation: απ
• The larger απ the smoother inflation • Clearly the mandate of the Central Bank • True for all shocks • Buys output stability in face AD shocks BUT not true for all shocks (π) • Illustrate the real need for a structural model
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Reaction to Output Gap: αy , AD Shock
Output
5 4 3 2 1 0
0
5
10
15
20
αy =0,
1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
Inflation
0
5
10
αy =0.125,
15
20
αy =0.5,
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
Nom. Int. Rate
0
5
10
15
20
αy =1.0
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Reaction to Output Gap: αy , Inflation Shock
2 1 0 1 2 3 4 5 6 7
Output
0
5
10
15
20
αy =0,
7 6 5 4 3 2 1 0
Inflation
0
5
10
αy =0.125,
15
20
αy =0.5,
4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
Nom. Int. Rate
0
5
10
15
20
αy =1.0
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Reaction to Output Gap: αy , Monetary Policy Shock
3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
Output
0
5
10
15
20
αy =0,
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
Inflation
0
5
αy =0.125,
10
15
20
αy =0.5,
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Nom. Int. Rate
0
5
10
15
20
αy =1.0
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Reaction to Output Gap: αy
• The larger αy the smoother output • True for all shocks • Buys inflation stability in face AD and MP shocks BUT not true for all shocks (π)
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Interest Smoothing: ρR , AD Shock
6 5 4 3 2 1 0 1
Output
0
5
10
15
20
ρR =0,
1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.2
Inflation
Nom. Int. Rate
2.0 1.5 1.0 0.5
0
5
ρR =0.5,
10
15
20
ρR =0.8,
0.0
0
5
10
15
20
ρR =0.95
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Interest Smoothing: ρR , Inflation Shock
0 1 2 3 4 5 6 7 8
Output
0
5
10
15
20
ρR =0,
3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
Inflation
0
5
ρR =0.5,
10
15
20
ρR =0.8,
3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
Nom. Int. Rate
0
5
10
15
20
ρR =0.95
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Interest Smoothing: ρR , Monetary Policy Shock
9 8 7 6 5 4 3 2 1 0
Output
0
5
10
15
20
ρR =0,
3.0 2.5 2.0 1.5 1.0 0.5 0.0
Inflation
0
5
ρR =0.5,
10
15
20
ρR =0.8,
0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Nom. Int. Rate
0
5
10
15
20
ρR =0.95
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Interest Smoothing: ρR
• The larger ρR the smoother the nominal interest rate • Not good for all shocks • Stabilize interest rate but de–stabilize output and inflation.
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The role of expectations
• Basic Taylor rule:
( ) bt−1 + (1 − ρR ) απ π b t = ρR R bt + αyb yt + ξR,t R
• Role of Expectations: ( ) b t = ρR R bt−1 + (1 − ρR ) απ Et π R bt+1 + αy Etb yt+1 + ξR,t • How much does it matter?
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Role of Expectations, AD Shock
6 5 4 3 2 1 0
Output
0
5
10
15
20
1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
Inflation
0
5
Baseline,
10
15
20
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
Nom. Int. Rate
0
5
10
15
20
Expected Values
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Role of Expectations, Inflation Shock
Output
1 2 3 4 5 6
0
5
10
15
20
4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
Inflation
0
5
Baseline,
10
15
20
1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2
Nom. Int. Rate
0
5
10
15
20
Expected Values
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Role of Expectations, Monetary Policy Shock
3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.5
Output
0
5
10
15
20
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.1
Inflation
Nom. Int. Rate 0.0 0.2 0.4 0.6
0
5
Baseline,
10
15
20
0.8
0
5
10
15
20
Expected Values
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Optimal Policy Design
• Let us go back to the basic Phillips Curve π bt = κb st + βEt π bt+1 • Inflation moves because of the distortions • Distortions are costly in terms of welfare because of 1. Very existence of markup (in steady state) 2. Fluctuations in markup (in the cycle)
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Optimal Policy Design
• Assume that we totally stabilize inflation π bt = π bτ = 0 then the Phillips curve reduces to b st = 0 • How to do that? Set απ = ∞ • Replicate the flexible price allocation • This is the optimal policy
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