(551c) Optimal Rules for Central Bank Interest Rate Subject to Zero Lower Bound

The celebrated Taylor rule (Taylor, 1993) is a feedback policy used to regulate the output gap and inflation of an economy by adjusting the central bank interest rate.  The main issue addressed in this work is the effect of zero lower bound on the optimal interest rate determined by a central bank.  We address this issue in a multi-parametric model predictive control (mpMPC) framework, which allows the derivation of explicit feedback rules even when inequality constraints are present.  Application of this framework to a simple model of the US economy produced a number of Taylor-like rules (Singh and Nikolaou 2012), depending on the form and parameter values in the objective function employed by MPC.  The results suggest that one from a small number of simple Taylor-like rules can be applied at each time, depending on the state of the economy.  However, it was also shown that simply setting to zero negative interest rates produced by unconstrained Taylor rules is optimal in situations of negative output gap, as happened recently.  Furthermore, it was observed, as has been noted elsewhere, that rules with inertia appear to better capture past decisions by the Federal Reserve Bank.  Such rules have been systematically derived here by considering penalties on the rate of interest rate change in the MPC objective function.  The proposed approach is illustrated through simulations on US economy data.  A number of issues for future study are proposed.

  Reference:

Taylor, J.B., 1993. Discretion versus policy rules in practice, Carnegie-Rochester Conference Series on Public Policy 39, North-Holland, pp. 195-214.

Singh, A. P. and M. Nikolaou (2012). "Optimal Rules for Central Bank Interest Rate Subject to Zero Lower Bound." Journal of Economic Dynamics and Control.(submitted)