Zero Lower Bounds and a Stackelberg Problem: A Stochastic Analysis of Unconventional Monetary Policy

Abstract

There exist difficulties to escape from stagnation and/or deflation if the economy hits zero lower bounds on short-term nominal interest rates because the central bank cannot stimulate the economy using rate cuts. How to escape from them? Answering the question, we extend a closed-looped solution of a Stackelberg problem (also known as a Ramsey problem) by introducing zero lower bounds. In this paper, we formulate a constrained Stackelberg problem and derive a solution of it. In our extension, we found that the discounted Lyapunov equation is required to obtain the shadow price of the economy which hits the zero lower bounds. Additionally, we stress that our method is consistent with rational expectations hypothesis. In this paper, we apply our method to new Keynesian models with zero lower bounds. In the numerical analysis, we evaluate the quantitative effects of zero interest rate policies with committing mild or zero inflation. Our simulation indicates that committing mild inflation causes positive effects on the economy and managing inflation expectations is necessary to escape from the bounds.