The Japanese economy has suffered from the cumulative interest-bearing debt since the bubble economy collapsed. The non-performing loan is pointed out as one of the main reasons for the prolonged recession in Japan. The Bank of Japan adopted what we called the zero-interest rate policy and now adopts the quantitative easing policy. The Reserve Bank of New Zealand adopted the inflation target in 1990. Some economists insist that the Bank of Japan should adopt the inflation target. Ninomiya (2001.a) examined the effect of the interest rate target when the economy is in financial instability. Taylor and Dalziel (2002) presented a basic model of inflation target. However, they did not consider the interest-bearing debt. We can point out the cumulative interest-bearing debt as an aspect of financial instability. If the lenders' risk enhances by the increase in debt burden and so on, the interest rate would rise in spite of a recession. The rise in interest rate increases the interest payment burden. As a result, there is a possibility that firms can not help issuing a new debt for the purpose of the payment and so on. In other words, the cumulative interest-bearing debt occurs in the economy. Some economists took the interest-bearing debt into account and discussed the financial instability (Jarsulic (1990), Keen(1995)). However, the interest-bearing debt did not have an important role and the effect of monetary policy was not examined in their models. In this paper, we construct a macro dynamic model which considers the interest-bearing debt. The dynamic equation of debt burden considering the interest-bearing debt has an important role in our model. We discuss the financial instability by the cumulative interest-bearing debt and examine the effect of the interest rate target for the financial instability in the dynamic model. We also show a financial cycle by applying Hopf bifurcation theorem. The main result of this paper is that the interest rate target has an effect when the cumulative interest-bearing debt makes the economy unstable. The result means that the zero-interest rate policy is very useful if the cumulative interest-bearing debt produces the prolonged recession in Japan.
