Some recent contributions to Economic Dynamics have shown an increasing interest on the impact that fiscal policy lags may have on the income adjustment processes. Lags dealing with fiscal policy come from delays either in the government expenditure or in the tax revenues. These two lags yield jointly their macroeconomic effects. They are such that to make traditional fiscal policy rules ineffectual to control, and stabilize the GDP dynamics. Here we study a dynamic IS–LM model where the public expenditure and the tax revenues have a delayed functional form. We show that the equilibrium of the system may lose or gain its local stability depending either on the length of the lags or on their particular combinations. When instability arises, very complicated dynamics may characterize the national income time path.

The interest in the impact of fiscal policy lags on economic stability increased in the last decade. Several studies have been made on delays either in the government expenditure or in the tax system, where lags exist between the accrual and the payment of taxes. Nevertheless there is in the literature no model where time delays in government expenditures and in tax revenues are considered together as it happens in the real world. In this paper we remedied this defect and proposed a macro-dynamic model where two delays appear: the first pertains to the public expenditure, the second, to the tax revenue. The resulting system of delayed differential equations is studied qualitatively and numerically. The analysis suggests that only particular combinations of the two delays make the system stable. Prevalently the system is unstable and chaotic motions may arise. This implies that the economy may need appropriate structural changes in the public sector to improve fiscal policy outcomes in such a way they may really be consistent with their stabilization purposes.