Optimal monetary policy under negative interest rate

In responding to the extremely weak global economy after the financial crisis in 2008, many industrial nations have been considering or have already implemented negative nominal interest rate policy. This situation raises two important questions for monetary theories: (i) Given the widely held doctrine of the zero lower bound on nominal interest rate, how is a negative interest rate (NIR) policy possible? (ii) Will NIR be effective in stimulating aggregate demand? (iii) Are there any new theoretical issues emerging under NIR policies? This article builds a model to show that (i) money injections can remain effective even when the nominal bank lending rate has reached zero or become negative; (ii) it is a good policy to keep the nominal interest rate as low as possible by purchasing government bonds with money; and (iii) the conventional wisdom on the notion of the liquidity trap and the Fisherian decomposition between the nominal and real interest rate can be invalid