Stabilization policy in a Keynes–Goodwin model with debt accumulation

In this paper, we investigate the macroeconomic impact of government's stabilization policy by using an analytical framework of Keynes–Goodwin model of growth cycle with debt accumulation. Formally, our model is formulated as a five-dimensional system of non-linear differential equations. We consider both of private debt and public debt, and we explicitly formulate the budget constraint of the ‘consolidated government’ including the central bank. We mainly study the case of ‘liquidity trap’ under money and debt financing of the government deficit.We study the local stability/instability of the system and the conditions for the existence of cyclical fluctuations analytically by means of the linear approximation method. We show that the sufficiently active monetary/fiscal policy can stabilize the intrinsically unstable economy if the inflation targeting by the central bank is sufficiently credible. We also present some numerical examples, which support our analysis.