1. Robust Monetary Policy Student: Adam Altar – Samuel Coordinator: Professor Ion Stancu

2. Robust control Allows policymakers to formulate policies that guard against model misspecification. Provides a set of tools to assist decisionmakers confronting uncertainty. Allows private agents to express concern, or pessimism, when forming expectations.

3. Relevant literature Hansen and Sargent (1999, 2001, 2002, 2006) Svensson (1997) Dennis, Leitemo and Soderstrom (2004, 2005, 2006) Giordani and Soderlind (2004)

4. Robust control problems can be solved using:  State – space methods  Structural methods Two distinct equilibria of interest:  “Worst – case” equilibrium  “Approximating” equilibrium

5. “Worst – case” equilibrium is the equilibrium that pertains when the policymaker and private agents design policy and form expectations based on the worst-case misspecification and the worst- case misspecification is realized

6. “Approximating” equilibrium is the equilibrium that pertains when the policymaker and private agents design policy and form expectations based on the worst-case misspecification, but the reference model transpires to be specified correctly

7. State – space form (1) (2) where z t - vector of endogenous variables

8. State – space form u t – vector of control variables ε t – vector of white – noise innovations v t+1 – vector of specification errors θ – shadow price, inversely related to the budget for misspecification

9. Structural form (3) (4)

10. An empirical New Keynesian model Variables:  π – inflation rate  y – output gap  i – interest rate  ε π – supply shock  ε y – demand shock

11. Equations (5) (6) Objective function: (7)

12. Solution method The problem is, both in the nonrobust and in the robust case, a discrete – time stochastic LQ problem. The optimal control is given by (8) where F is the optimal feedback matrix.

13. Solution method In the nonrobust case: In the robust case:

14. Results Inflation responses to unit supply shock Nonrobust Robust

15. Results Output gap responses to unit supply shock Nonrobust Robust

16. Results Interest rate responses to unit supply shock Nonrobust Robust

17. Results Inflation responses to unit demand shock Nonrobust Robust

18. Results Output gap responses to unit demand shock Nonrobust Robust

19. Results Interest rate responses to unit demand shock Nonrobust Robust

20. Conclusions In the robust case, the optimal policy of the central bank is more activist than in the nonrobust case