Robust Control Made Simple : Lecture

Some of the recent literature on robust control in economics (for instance, Giannoni [3], Hansen and Sargent [4] and [5], Onatski [6], Onatski and Stock [7], Sargent’s [10] comment on Ball, [1] and Stock’s [12] comment on Rudebusch and Svensson [9]) is somewhat technical and difficult to see through. This note attempts to use a simple example of optimal monetary policy to convey the gist of robust control. Let m ∈ M denote a particular model of the transmission mechanism of monetary policy, whereM denotes a feasible set of models. Let f ∈ F denote a particular monetary policy, where F is the feasible set of policies. Let V be an (expected) loss function, so V (f,m) denotes the (expected) loss of policy f in model m. A Bayesian approach to optimal policy under model uncertainty, as in Brainard [2], assigns a prior probability measure, Φ, on the feasible set of models M . The expected loss for given policy is then EMV (f,m) ≡ Z m∈M V (f ;m)dΦ(m). The optimal policy f∗ minimizes the expected loss, f∗ = argmin f∈F EMV (f ;m). The optimal policy will be a function of M , Φ and V , f∗(M,Φ, V ). A robust-control approach to optimal policy under model uncertainty, as in Hansen and Sargent [4] and Onatski and Stock [7], does not assign any prior probability measure on the feasible set of models. Instead, it focuses on the maximum loss for any given policy f ,2