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This study examines the implications of robust control in monetary policy formulation. Policymakers can utilize robust control to create policies that mitigate the risks of model misspecification and navigate uncertainties. By providing tools to express private agents' concerns during expectation formation, it allows central banks to design more effective strategies. The paper discusses key literature, methodologies, and the distinct equilibria of interest—”worst-case” and “approximating” equilibria—while analyzing inflation and output gap responses to various shocks. The findings indicate that robust policies encourage more activist approaches from central banks.
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Robust Monetary Policy Student: Adam Altar – Samuel Coordinator: Professor Ion Stancu
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.
Relevant literature • Hansen and Sargent (1999, 2001, 2002, 2006) • Svensson (1997) • Dennis, Leitemo and Soderstrom (2004, 2005, 2006) • Giordani and Soderlind (2004)
Robust control problems • can be solved using: • State – space methods • Structural methods • Two distinct equilibria of interest: • “Worst – case” equilibrium • “Approximating” equilibrium
“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
“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
State – space form (1) (2) where zt - vector of endogenous variables
State – space form • ut– vector of control variables • εt– vector of white – noise innovations • vt+1– vector of specification errors • θ – shadow price, inversely related to the budget for misspecification
Structural form (3) (4)
An empirical New Keynesian model • Variables: • π– inflation rate • y – output gap • i – interest rate • επ– supply shock • εy – demand shock
Equations (5) (6) Objective function: (7)
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.
Solution method • In the nonrobust case: • In the robust case:
ResultsInflation responses to unit supply shockNonrobust Robust
ResultsOutput gap responses to unit supply shockNonrobust Robust
ResultsInterest rate responses to unit supply shockNonrobust Robust
ResultsInflation responses to unit demand shockNonrobust Robust
ResultsOutput gap responses to unit demand shockNonrobust Robust
ResultsInterest rate responses to unit demand shockNonrobust Robust
Conclusions • In the robust case, the optimal policy of the central bank is more activist than in the nonrobust case
