Essays on robust optimal policy under ambiguity
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This dissertation examines robust optimal macroeconomic policy under ambiguity in a general discrete-time linear-quadratic framework. This dissertation is composed of three independent but closely-related essays. The first essay studies robust Ramsey policy problems when the Ramsey planner faces three types of ambiguity. This framework includes both exogenous and endogenous state variables. In addition, the equilibrium system from the private sector contains both backward-looking and forward-looking dynamics. This chapter provides recursive characterizations and algorithms to solve for robust policy and then apply it to a basic New Keynesian model of optimal monetary policy with persistent cost-push shocks. The main findings are: (i) all three types of ambiguity make optimal monetary policy more history-dependent but with different reasons for each type; and (ii) they deliver qualitatively different initial responses of inflation and the output gap following a cost-push shock. The second essay extends Woodford's (2010) approach to the robustly optimal monetary policy. This paper provides algorithms to solve for a time-invariant linear robustly optimal policy in a timeless perspective and for a time-invariant linear Markov perfect equilibrium under discretion. The main findings include: i) the robustly optimal commitment inflation is less responsive to a cost-push shock when the shock is more persistent; ii) the robustly optimal discretionary policy is more responsive to lagged inflation when inflation is more persistent. The third essay documents the impact of belief ambiguity by changing the relative degree of concern for ambiguity associated with two different shocks: cost-push shocks and the natural rate of interest shocks. The main results are: i) belief ambiguity relating to cost-push shocks matters to a central bank much more than belief ambiguity associated with the natural rate of interest shocks; ii) in some cases, after a positive cost-push shock robust optimal monetary policy allows initial inflation higher than under rational expectations; iii) robust optimal monetary policy is not symmetrical in terms of its response to different signs of a shock.