The Past is Present: Optimal Monetary Policy at the Effective Lower Bound September, 2020
(with Fernando Duarte)

We use a New Keynesian model with an effective lower bound (ELB) and a general stochastic process for the natural rate to study optimal monetary policy. The central bank has perfect commitment and an interest rate smoothing term in its loss function. Despite the ELB binding occasionally and endogenously, we can derive a closed-form solution for the optimal interest rate: it is the maximum of zero and a weighted average of all past realizations of the output gap. This implies that the optimal interest rate (i) takes a simple form, (ii) is path dependent at all times, (iii) should be pre-emptively lowered when close to the ELB — or kept at zero if at the ELB — if and only if the weighted average of past output gaps is negative, and (iv) behaves very differently from the Taylor rule. We illustrate these insights by solving for key variables in the New Keynesian model using a neural network.