Optimal Monetary Policy at the Zero Interest Rate Bound: The Case of Endogenous Capital Formation

This paper characterizes optimal monetary policy in an economy with the zero interest rate bound and endogenous capital formation. First, we show that, given an adverse shock to productivity growth, the natural rate of interest is less likely to fall below zero in an economy with endogenous capital than the one with fixed capital. However, our numerical exercises show that, unless investment adjustment costs are very close to zero, we still have a negative natural rate of interest for large shocks to productivity growth. Second, the optimal commitment solution is characterized by a negative interest rate gap (i.e., real interest rate is lower than its natural rate counterpart) before and after the shock periods during which the natural rate of interest falls below zero. The negative interest rate gap after the shock periods represents the history dependence property, while the negative interest rate gap before the shock periods emerges because the central bank seeks to increase capital stock before the shock periods, so as to avoid a decline in capital stock after the shock periods, which would otherwise occur due to a substantial decline in investment during the shock periods. The latter property may be seen as central bank’s preemptive action against future binding shocks, whic