Taxes, Income Determination, and the Balanced Budget Theorem

Abstract

THE proposition that a tax-financed change in expediture will lead to an equal change in income has been subjected to critical examination in two recent articles.' Both emphasize that the proposition, which has been christened the budget applies only when certain conditions are fulfilled, and they dismiss it as a special case of little interest because of the restrictive character of these conditions. There is undoubtedly a danger that conclusions drawn from simplified models will be applied beyond the context in which they are valid and will be invested with the aura of universal truths. By defining and calling attention to the limitations on the validity of the balanced budget theorem, the articles cited serve as a useful corrective against this danger in this case. There is, however, some danger that in two respects they may be the source of confusion rather than clarification. In the first place, they concentrate attention on the limitations of the balanced budget theorem in such a way that the reader may easily lose sight of its essential core of truth. Second, they may create a somewhat inaccurate impression as to the exact location of those limits. The first danger is discussed in the succeeding paragraphs; the second in the later portions of the present paper. It may well be that the balanced budget theorem has little direct application to the world of reality because the necessary preconditions to its validity are rarely fulfilled in that world. Nevertheless, it does not follow that the theorem is completely uninteresting and that it provides no insight whatever into the real world. In order to recognize its role in the evolution of income theory, it is only necessary to recall that, until the balanced budget theorem was advanced, it was generally believed that, under exactly the same general conditions that are assumed in the development of the theorem, a change in expenditures balanced by a change in taxes had no effect on income whatever. That is, it was believed that the multiplier for a balanced budget was zero. Whatever its limitations, the balanced budget theorem represents an important refinement of this earlier view. That view followed from the assumption (or impression) that taxes could be treated simply as deductions from expenditure. In the balanced budget analysis, it was recognized that, while expenditures (on currently produced domestic goods and services) generate income directly, taxes do not directly reduce expenditure and income. Instead, they reduce the flow of funds available either for spending or nonspending. If this flow is subject to further leakages (after the taxes have been paid), such as through saving, the distinction becomes significant. The balanced budget theorem can best be regarded as a corollary of this treatment of taxes. In a still more refined analysis, it is true, the effect upon spending of different kinds of taxes would be distinguished (and the substitution effect as well as the income effects of taxes might be considered, as Baumol and Peston have suggested). Nevertheless, it remains true that the first step was to introduce taxes explicitly as a distinct entity in the analysis and to formulate some hypothesis, however simple, as to their effect on the flow of income. Turvey has pointed out that, in his model, the balanced budget multiplier is unity when household saving is the only leakage.2 Does this mean, as he seems to imply, that the balanced budget multiplier will not be unity if there are any other leakages, or, to put it more precisely, if there are any dependent variables other than household saving and consumption? Here we must distinguish between taxes themselves and other variables. The case in which taxes are a dependent variable, assumed to be a function of income, is considered ' Ralph Turvey, Some Notes on Multiplier Theory, American Economic Review, xLm (June I953), 282-86; and W. J. Baumol and M. H. Peston, More on the Multiplier Effects of a Balanced Budget, American Economic Review, XLV (March I955), I40. 2 Turvey, loc. cit., 285-86.