Robustly Optimal Instrument Rules and Robust Control: An Equivalence Result

Giannoni and Woodford (2003a, 2003b) and Hansen and Sargent (2003, 2004) have recently developed different notions of robust policy, and both approaches have been applied in the context of optimal monetary policy. In this note, I demonstrate that both approaches lead to exactly the same implicit instrument rule for the policy maker in a standard, forward-looking, new Keynesian model. Despite the equivalence of the policy rules, the two approaches predict different macroeconomic behavior because of difference assumptions about the formation of expectations.