A Dynamic Analysis of Taxation

In a paper published in this Review, Jacob Stockfisch uses a two-sector model of a competitive economy which devotes a constant fraction of income to capital accumulation to show, inter alia, that "A general tax on consumer items makes it possible for a given level of money investment to buy more real physical assets. Economic growth will be encouraged and the economy will have a larger physical stock of capital with the passage of time" (p. 298). One of the purposes of this paper is to present an alternative model which gives the result that a general tax on consumption is dynamically neutral, leaving the path of capital accumulation unaffected. Stockfisch's result hinges on the peculiar savings behavior he assumed. It can be shown that models of capital accumulation in which savings is assumed to be equal to a certain fraction of income (such a fraction may be either constant or a function of the interest rate and/or the distribution of income) give the result that consumption tax favors capital accumulation and growth.1 This result, however, does not hold in the intertemporal optimizing model employed in this paper. Nonetheless, a consumption tax is sometimes proposed to foster capital accumulation and growth along the lines suggested by Stockfisch. As stated by R. J. Chelliah, "When we look upon commodity taxation as a weapon for promoting economic growth, its justification lies in the fact that it has a tendency to restrain consumption" (p. 86). Or in the words of John Due, "The tax structure must reduce private consumption. Thus, the tax structure must be designed to strike the portion of income spent on consumption" (p. 33). On the other hand, arguments have been produced showing that a consumption tax would not have any effect on the path of capital accumulation. This is essentially Nicholas Kaldor's contention about the neutrality of the expenditure tax. Accordingly, the replacement of an income tax by an expenditure tax will increase savings. Richard Goode writes, "It is usually taken for granted that this policy will promote savings, but the basis of the belief is not obvious and is worthy of attention" (p. 232). The preceding exposition points out the necessity of a systematic analysis of the effects of taxation in the long run, which is precisely the topic of this paper. In the context of an intertemporal optimizing model, I analyze the welfare implications of tax-induced changes in the path of capital accumulation and show the dynamic neutrality of a consumption tax. The model is also used to compare the welfare costs of income taxation and investment taxation. The results show that the welfare cost per dollar of tax revenue of income taxation is smaller than the welfare cost per dollar of tax revenue of investment taxation. It is also shown that an investment tax at a constant-over-time rate is equiva* Visiting professor of economics at the Universidad Cat6lica de Chile. This paper is based on part of my Ph.D. dissertation. I wish to acknowledge my gratitude to the members of my thesis committee, Stanley Fischer, William Brock, and Stephen Magee for guiding me throughout this study. I would also like to thank Arnold Harberger and George Borts for their comments and suggestions. A referee's comments were also very helpful. 1 This has been shown in the first chapter of my dissertation.