A Keynesian Approach to Fiscal Policy for Full Employment and Continuous Time Debt Dynamics

It is widely argued that public debt is a burden on the future generations. We analyze another aspect of public debt as an economic stimulus program, that is, the measure to realize full employment from an under-employment state. Using a continuous time version of a dynamic analysis of debt-to-GDP ratio we show that a fiscal policy to realize full employment from a state of under-employment can reduce the debt-to-GDP ratio. More precisely we show that the larger the extra growth rate (increasing rate) of real GDP by a fiscal policy is, the smaller the debt-to-GDP ratio at the time when full employment is realized is. Also we show that even if the marginal propensity to consume is very small (including zero), an aggressive fiscal policy can realize full employment without increasing the debt-to-GDP ratio. Further, we consider a condition to realize full employment from a state of under-employment within one year without increasing debt-to-GDP ratio.