One Sector Models, Indeterminacy, and Productive Public Spending

This paper studies the influence of different modelling assumptions on the stability of the steady state in one--sector models of economic growth with externalities in the production function. We start with a standard Benhabib&Farmer 1994 one--sector model and study the combined effect on the stability of variable capital utilization, progressive taxation, and productive public spending subject to congestion. As was shown earlier by Wen 1998, variable capacity utilization leads to indeterminacy or absolute instability for low degrees of social increasing returns to scale. Introduction of productive public spending further lowers the degree of IRS necessary to break saddle--path stability of the steady state. The degree of progressivity of the tax schedule influences only the indeterminate and absolute unstable regions in the space spanned by externality parameters. More progressive tax schedule increases the area of indeterminacy at the expense of the absolute instablity region. We perform calibration of the model to the tax regimes observed in the USA