CREST February 2009

Question • Did US monetary policy change over time? – Monetary policy=Rule Example of a rule: Change in the monetary policy=change in

• Is the yield curve helpful in addressing this issue?

2

Motivation: Macro Perspective • The debate over monetary policy changes in the US – Monetary policy changed: Clarida, Gali and Gertler (2000) – Monetary policy did not change: Sims and Zha (2005)

• Use term structure data to identify the changes in monetary policy?

– Yields are forward-looking – Yields must reflect expectations about the future monetary policy

3

Rates Contain Information about Future Regimes • Simple rule

with two regimes:

and

• Expectations involve information about regimes

4

Motivation: Finance Perspective • Existing no-arbitrage regime-switching term structure models are reduced-form

– Bansal and Zhou (2002) – Dai, Singleton and Yang (2006) – Ang, Bekaert and Wei (2008)

• What are the economic forces driving regime switches? – Monetary policy changes? – Changes in the volatility of exogenous shocks?

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Approach • We specify and estimate a no-arbitrage regime-switching term structure model with observable macro variables.

• Key innovations of this paper – The model explicitly separates Regime-switching Fed’s behavior (monetary policy regimes) Private sector dynamics

– Solve a rational expectations model with regime switches – New and accurate approximate bond pricing method

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Term Structure Is Informative About Regimes 1

Estimated Probability of the Policy Regime without Term Structure

0.8 0.6 0.4 0.2 0 1970

1

1975

1980

1985

1990

1995

2000

2005

Estimated Probability of the Policy Regime with Term Structure

0.8 0.6 0.4 0.2 0 1970

1975

1980

1985

1990

1995

2000

2005

7

Outline 1. 2. 3. 4. 5. 6.

Model Empirical Methodology Model Properties Importance of Term Structure Model Implications Conclusion

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Outline 1. 2. 3. 4. 5. 6.

Model Empirical Methodology Model Properties Importance of Term Structure Model Implications Conclusion

9

State Dynamics • State vector • State equations

systematic policy

policy shock

• Regime variables - Systematic monetary policy - Volatility of monetary policy shock (discretion) - Volatilities of exogenous shocks 10

Regime Variables Specification • Regime variables independent

,

• Each regime variable

and

are mutually

takes two states: 1 and 2

8 states in total

• Each regime variable follows a Markov chain with constant transition probabilities

11

Rational Expectations Solution • Assumptions: – Agents know in which regime they are in – Exogenous regime switches (constant transition probabilities)

• Rational expectations solution

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Need for Identification Assumptions • State vector • Generic form of dynamics (no regimes) • Rational expectations solution: • Relations among the parameters:

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Prices of Risk • Pricing kernel • Risk premium • “Preferences” (Duffee 2002) • Bond prices

14

Outline 1. 2. 3. 4. 5. 6.

Model Empirical Methodology Model Properties Importance of Term Structure Model Implications Conclusion

15

Empirical Approach • 1970:Q1-2004:Q4, quarterly frequency • Macro variables – Inflation: Implicit Price Deflator – Output gap: Linearly detrended log of real GDP

• 4 Fama-Bliss zero yields with maturities 3 months, 2 years, 5 years and 10 years

• Estimation – Maximum likelihood – Output, inflation and 3 month yield observed exactly 16

Outline 1. 2. 3. 4. 5. 6.

Model Empirical Methodology Model Properties Importance of Term Structure Model Implications Conclusion

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Parameter Estimates

18

Parameter Estimates

19

Parameter Estimates

20

Parameter Estimates

21

Parameter Estimates

22

Regimes e

1

Probability of High Volatility Regime st=1

0.5

0 1970

1975

1980

1985

1990

1995

Probability of Active Policy Regime

1

2000

2005

2000

2005

2000

2005

m st=1

0.5

0 1970

1975

1980

1985

1990

1995

Probability of Discretionary Regime

1

d st=1

0.5

0 1970

1975

1980

1985

1990

1995

23

Goodness of Fit • Pricing errors

• Unconditional Moment Tests – Mean, variance, skewness, kurtosis and autocorrelations – All moments are matched except for the kurtosis of the curvature 24

Outline 1. 2. 3. 4. 5. 6.

Model Empirical Methodology Model Properties Importance of Term Structure Model Implications Conclusion

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Is Short Rate Informative About Regimes?

• Short Rate (SR) Model

is estimated without term structure data (using short interest rate only)

• The full model is referred to as the Term Structure (TS) Model.

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Parameter Estimates. Model SR.

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Estimated Regimes. Model SR. e

1

Probability of High Volatility Regime st=1. Model TS.

0.8 0.6 0.4 0.2 0 1970

1975

1980

1985

1990

1995

2000

2005

e

1

Probability of High Volatility Regime st=1. Model SR.

0.8 0.6 0.4 0.2 0 1970

1975

1980

1985

1990

1995

2000

2005

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Policy Regimes Are Better Identified with TSM Probability of Active Regime sm=1. Model TSM. 1 0.8 0.6 0.4 0.2 0 1970

1975

1980

1985

1990

1995

2000

2005

2000

2005

Probability of Active Regime sm=1. Model SRM. 1 0.8 0.6 0.4 0.2 0 1970

1975

1980

1985

1990

1995

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Term Structure Matters • Simulate 1000 paths from TS • Estimate both TS and SR • Compute

for both

datasets

• Distribution of

:

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Outline 1. 2. 3. 4. 5. 6.

Model Empirical Methodology Model Properties Importance of Term Structure Model Implications Conclusion

31

Causes of “Great Moderation”

• Lower volatility of exogenous shocks helped reduce volatility

• What is the role of monetary policy? 32

Exogenous shocks/Counterfactual analysis

• Indeed, low volatility of shocks contributed to the decline •

of volatilities of output and inflation Monetary policy has minimal impact on the volatilities

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Trade-Off Between Output and Inflation Output Shock 1

Ou tpu t A ctive MP Pas s ive MP

0.8

Inflatio n Shock

0

Ou tpu t

-0.02 -0.04

0.6

-0.06

0.4 -0.08

0.2

-0.1

0 -0.2

-0.12

-0.4

-0.14 5

10

15

20

Outpu t Shock

0.6

25

30

35

40

Inflatio n

5

0.6

0.5

10

15

20

25

Inflatio n Shock

30

35

40

Inflatio n

0.5

0.4

0.4

0.3

0.3

0.2 0.2

0.1

0.1

0

0

-0.1 -0.2

5

10

15

20

25

30

35

40

-0.1

5

10

15

20

25

30

35

40

34

Counterfactual Time Series

Counterfactual Time Series

• Active/Discretionary regimes appears to be preferred for •

inflation/output trade-off However…

Rates Volatility Is Greater in Active Regime

The Great Moderation Summary

• Inflation is the lowest in the data, not in a specific regime • Output is higher in active regimes, but so is long rate; •

output and yields are more volatile It appears that the overall balance achieved in sample was pretty good

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Outline 1. 2. 3. 4. 5. 6.

Model Empirical Methodology Model Properties Importance of Term Structure Model Implications Conclusion

39

Conclusion • Long term rates help identify monetary policy regimes • At least two systematic monetary policy regimes occurred: active and passive

• Monetary policy was important for “great moderation”

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