Advanced dynamic models

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Advanced dynamic models

• Martin Ellison
• University of Warwick and CEPR
• Bank of England, December 2005

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More complex models

• Frisch-Slutsky paradigm

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Impulses

• Can add extra shocks to the model

Shocks may be correlated
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Propagation

• Add lags to match dynamics of data (Del
  Negro-Schorfeide, Smets-Wouters)

Taylor rule
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Solution of complex models
Blanchard-Kahn technique relies on invertibility
of A0 in state-space form.
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QZ decomposition

• For models where A0 is not invertible

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Recursive equations
stable unstable
Recursive structure means unstable equation can
be solved first
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Solution strategy
Solve unstable transformed equation
Substitute into stable transformed equation
Translate back into original problem
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Simulation possibilities

• Stylised facts
• Impulse response functions
• Forecast error variance decomposition

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Optimised Taylor rule

• What are best values for parameters in Taylor
  rule ?

Introduce an (ad hoc) objective function for
policy
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Brute force approach

• Try all possible combinations of Taylor rule
  parameters

Check whether Blanchard-Kahn conditions are
satisfied for each combination
For each combination satisfying B-K condition,
simulate and calculate variances
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Brute force method

• Calculate simulated loss for each combination

Best (optimal) coefficients are those satisfying
B-K conditions and leading to smallest simulated
loss
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Grid search
For each point check B-K conditions
2
1
Find lowest loss amongst points satisfying B-K
condition
0
1
2
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Next steps

• Ex 14 Analysis of model with 3 shocks
• Ex 15 Analysis of model with lags
• Ex 16 Optimisation of Taylor rule coefficients