Risk-sensitive Optimal Control with Forward-looking Variables

Book excerpt: We discuss how to solve infinite-horizon optimal control problems with recursive preferences à la Hansen and Sargent (1995) when both backward and forward-looking variables enter into the law of motion regulating the system dynamics. With our analysis we establish: 1) under which conditions the risk-adjustment in the objective function of the standard linear-quadratic formulation introduced by Hansen and Sargent affects the optimal policy; 2) how the optimal rule in a stationary solution is identified solving two distinct fixed-point problems, the former pertaining to the optimization exercise, the latter to the expected values of the forward-looking variables. Applying our methodology to Smets and Wouters' (Smets and Wouters, 2003) new-Keynesian model of monetary policy, we show how a central bank endowed with recursive preferences `a la Hansen and Sargent (1995) selects a more aggressive policy than one furnished with quadratic costs.