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, which is entirely absent in fixed capital models. We also show that the targeting rule to implement the commitment solution is characterized by history-dependent inflation-forecast targeting. Third, a central bank governor without sophisticated commitment technology tends to resort to preemptive action more than the one with it. The governor without commitment technology controls natural rates of consumption, output, and so on in the future periods, by changing capital stock today through monetary policy.
Recent literature on optimal monetary policy with the zero interest rate bound has assumed that capital stock is exogenously given. This assumption of fixed capital stock has some important implications. First, the natural rate of interest is exogenously determined simply due to the lack of endogenous state variables: namely, it is affected by exogenous factors such as changes in technology and preference, but not by changes in endogenous variables. For example, Jung et al. (2005) and Eggertsson and Woodford (2003a, b) among others, start their analysis by assuming that the natural rate of interest is an exogenous process, which is a deterministic or a two-state Markov process. More recent researches such as Adam and Billi (2004a, b) and Nakov (2005) extend analysis to a fully stochastic environment, but continue to assume that the natural rate process is exogenously given. These existing researches typically consider a situation in which the natural rate of interest, whether it is a deterministic or a stochastic process, declines to a negative level entirely due to exogenous shocks, and conduct an exercise of characterizing optimal monetary policy responses to the shock, as well as monetary policy rules to implement the optimal outcome.