Zero Lower Bounds in New Keynesian Models and a Constrained Ramsey Problem

There exist difficulties in escaping 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 further using rate cuts. How can it escape from them? Answering the question, we extend a closed-looped solution of a Ramsey problem (also known as a Stackelberg problem) by introducing zero lower bounds. Herein, we formulate a constrained Ramsey problem and derive a solution for it. In our extension, we found that the discounted Lyapunov equation is necessary to obtain the shadow price of the economy that hits the zero lower bounds. Herein we apply our method to new Keynesian models with zero lower bounds. Our simulation shows that committing to mild inflation engenders positive effects on the economy and that managing inflation expectations is necessary to escape from the bounds