Fiscal policy delays and the classical growth cycle

This paper deals with the impact of fiscal policy delays on the national income adjustment process. Here we reconsidered the pioneering work by Wolfstetter, who introduced the public sector in the well-known Goodwin’s classical growth cycle model, where the conflict between capital and labor on the distribution of income is formalized. Unlike Wolfstetter, we take into account two finite time delays characterizing the public economic activity. The former delay concerns the structure of the tax system and the government tax revenues; the latter pertains the political process governing the public purchase decisions and the actual expenditures. The result is a system of delayed differential equations (DDEs). Choosing delay terms as bifurcation parameters, we proved the existence of Hopf bifurcations. Therefore, we studied the stability and the direction of the bifurcating periodic solutions by using the first Lyapunov coefficient. Some numerical simulations carried out to support theoretical results show that, in the basic model, which coincides with the one by Wolfstetter. The effectiveness of policies (pro-cyclical and counter-cyclical) are strictly dependent on the length of the lags and on their particular combinations. As the basic model lacks an investment function, because investments passively equals the saving, we add that function taking into account the profit expectations. Furthermore, we assumed that the size of the public expenditure decreases quickly with the rise of the employment rate. These new hypotheses are such that to yield an extended model, where, unlike the basic model, we proved that, without lags, a pro-cyclical policy does not assure the stabilization of the economy if the government adopts weak reduction of the public expenditure. In this case, regular cycles around the equilibrium arise. When the lags are positive, the government might stabilize the system only by a low discretional expenditure, if the policy is counter-cyclical, and by low reduction of its expenditure, if the policy is pro-cyclical. This on condition that some particular pairs of the two delays subsist.