Optimal Negative Interest Rate under Uncertainty

I employ a simple overlapping-generations model of money and nominal bonds with Epstein-Zin preferences and study the optimal negative interest rate. A subzero lower bound can arise in the model due to the illiquidity of money as a savings instrument. This model of negative interest rates differentiates from conventional ones based on exogenous money holding costs in that the subzero lower bound as well as the optimal negative rate turn out to crucially depend upon agents' preferences for the timing of uncertainty resolution. Both the lower bound and the optimal interest rate for aggregate consumption can fall into a negative territory only if agents prefer late resolution of uncertainty. In the latter case, the lower bound and the optimal rate both decrease even further when aggregate output uncertainty rises. However, the optimal interest rate turns out to be non-negative and to have a positive relationship with the degree of aggregate uncertainty if agents prefer early resolution of uncertainty.