||Numerical Analysis of Three Time Delays in Monetary Policy: The Case of a Sticky-Price Model
都築 栄司 ,
黒川 太品川 俊介
In this study, we develop a New Keynesian model that includes the policy rule with which the nominal interest rate's responses are induced according to fluctuations in three economic variables, namely output, the inflation rate, and asset prices. In this model, we also assume that there is a time lag in the interest rate's response to each variable. The model economy is represented as a “differential equation system with three delays.” For the determinacy analysis, we use the numerical method developed by Gu and Naghnaeian [K. Gu and M. Naghnaeian, Stability crossing set for systems with three delays, IEEE Transactions on Automatic Control 56 (2011), pp. 11-26] to find the parameter regions that achieve local determinacy in order to examine the effects of the three policy lags on local equilibrium determinacy. This is the first such application of this method to New Keynesian economics. We demonstrate that implementations of monetary policy should be “purposefully” delayed to achieve local equilibrium determinacy. Hence, the central bank should determine its target variables by considering not only the responsiveness of the nominal interest rate to output, the inflation rate, and asset prices but also the lag lengths associated with policy implementations.