We develop a simple and intuitive approach for analytically deriving unconditionally optimal (UO) policies, a topic of enduring interest in optimal monetary policy analysis. The approach can be employed in both general linear-quadratic problems and in the underlying non-linear environments. A detailed example is provided using a canonical New Keynesian framework.
In this paper we take up a theme from Taylor (1979), who proposes adopting a monetary policy, under rational expectations, which is optimal “on average”. That is, given a model of the economy, including knowledge of the time series properties of the underlying shocks, and assuming rational expectations, Taylor proposes that optimal monetary policy optimize the unconditional expectation of the policymaker's objective function. That approach to policy evaluation has been adopted many times since; for example, Rotemberg and Woodford (1998), Woodford (1999), Clarida et al. (1999), Erceg et al. (2000), Kollmann (2002) and Schmitt-Grohe and Uribe (2007), to name but a few. More recently, Blake (2001) and Jensen and McCallum, 2002 and Jensen and McCallum, 2006 also suggest a procedure for determining optimal, time-invariant monetary policy based on optimization of the unconditional value of the criterion function. However, these analyses employ numerical approaches to recover the unconditionally optimal (UO) monetary policy. An exception to that is Whiteman (1986). In a simple linear, rational expectations model with endogenous variables which are partly a function of their own expected future values, he derives a closed-form solution for optimal policy. However, Whiteman's proof of optimality is algebraically intensive.
This paper develops a straightforward, intuitive and easy-to-implement approach for deriving policies that are UO in a general setting which is developed in Section 2. The key technical challenge involves constructing an optimal policy program taking expectations over all feasible initial conditions. Section 2.1 constructs these optimal continuation policies, to use Jensen and McCallum's terminology, in a way that is applicable to both linear-quadratic (LQ) and non-linear models. Section 2.2 demonstrates the approach in the simplest LQ New Keynesian monetary policy model (whilst a general LQ problem is set out in Appendix A). Section 3 then applies the approach to the underlying non-linear New Keynesian model. We show that linear approximation is possible around the “unconditionally optimal” deterministic steady state, analogous to the approach adopted by Khan et al. (2003) in the context of (conditionally) optimal monetary policy under commitment. The optimality conditions of the non-linear model are linearized and it is demonstrated how one can obtain a LQ framework and the same optimal policy as in the simple LQ set-up of Section 2.2.
Section 4 discusses briefly the two defining characteristics of UO policies. The first key property is the treatment of initial conditions. The second is the sense in which consumers’ discount rates do not matter for UO policies, an observation going back to Taylor's (1979) contribution. Section 5 offers some brief concluding remarks.
The simple procedure we have presented for uncovering UO policies appears to be useful in a wide variety of environments of practical interest to researchers. An interesting and important question is whether actual monetary (and other) policies are, or should be, optimal from the unconditional perspective.
