Long-Run Tax Incidence: A Comparative Dynamic Approach

Abstract

The long-run incidence of tax changes has typically been analysed from a comparison of steady states. The recent contributions of Feldstein (1974) and Grieson (1975) consider the comparative steady-state effects of substituting a tax on capital income for a tax on income in standard single-sector neo-classical growth models with a constantly growing supply.' This is a natural extension of the comparative stationary-state tax incidence studies of Harberger (1962), Mieszkowski (1967) and many subsequent authors,2 and it has the merit that it is algebraically quite simple to analyse. The results obtained in the long-run models are in striking contrast to those obtained in the models with fixed capital stocks. In a static model with fixed factor supplies, a general-factor tax is entirely borne by the factor whose income is taxed.3 Under reasonable assumptions about elasticities of substitution in production and demand, a partial factor tax (e.g. corporate income tax) will also be largely borne by the owners of the partially-taxed factor. In the long run, however, radically different results can occur owing to the ability of the taxed factor to shift the tax by an induced change in factor proportions in the economy. Thus, Feldstein finds that for a wide range of plausible parameter values, a substantial fraction of the burden of a general profits tax is borne by labour (page 505). Similarly, Grieson finds that substitution of a wage for a profits tax may well make wage earners better off since the increased capital-labour ratio may cause the gross-of-tax wage rate to rise by more than tax payments on wages. It would be premature to derive policy prescriptions from these results based on a comparison of steady states. The difficulty is that economies may never reach the steady state either before or after the tax changes under consideration and, therefore, at best comparative steady-state analysis may indicate only long-run tendencies.4 Since the process of tax shifting through a change in capital accumulation takes time, comparative steadystate analysis may be quite inappropriate for considering the effects of tax changes over more limited time horizons. In this paper, we shall analyse the effect of tax changes on the growth path of an economy between two arbitrary points of time in a single-sector neoclassical model similar to those used by Feldstein and Grieson. The method of analysis, which we may call comparative dynamics, allows us to study the process of tax shifting over time. While the analysis is not restricted to the steady state, we can use it to study the movement of the economy from one steady state to another in response to a tax change. The results that we obtain indicate that, indeed, comparative steady-state analysis is likely to be misleading in analysing tax incidence over finite periods of time.