Advanced dynamic models

1. Advanced dynamic models Martin Ellison University of Warwick and CEPR Bank of England, December 2005

2. Impulses Propagation Fluctuations More complex models Frisch-Slutsky paradigm

3. Impulses Can add extra shocks to the model Shocks may be correlated

4. Propagation Add lags to match dynamics of data (Del Negro-Schorfeide, Smets-Wouters) Taylor rule

5. Solution of complex models Blanchard-Kahn technique relies on invertibility of A0 in state-space form.

6. QZ decomposition: s.t. upper triangular QZ decomposition For models where A0 is not invertible

7. Recursive equations stable unstable Recursive structure means unstable equation can be solved first

8. Solution strategy Solve unstable transformed equation Substitute into stable transformed equation Translate back into original problem

9. Simulation possibilities Stylised facts Impulse response functions Forecast error variance decomposition

10. Optimised Taylor rule What are best values for parameters in Taylor rule ? Introduce an (ad hoc) objective function for policy

11. 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

12. Brute force method Calculate simulated loss for each combination Best (optimal) coefficients are those satisfying B-K conditions and leading to smallest simulated loss

13. Grid search For each point check B-K conditions 2 1 Find lowest loss amongst points satisfying B-K condition 0 1 2

14. Next steps Ex 14: Analysis of model with 3 shocks Ex 15: Analysis of model with lags Ex 16: Optimisation of Taylor rule coefficients