Front Page Titles (by Subject) 5.2.: The Timing of Rate Announcement - The Collected Works of James M. Buchanan, Vol. 9 (The Power to Tax: Analytical Foundations of a Fiscal Constitution)
Return to Title Page for The Collected Works of James M. Buchanan, Vol. 9 (The Power to Tax: Analytical Foundations of a Fiscal Constitution)
The Online Library of Liberty
A project of Liberty Fund, Inc.
Search this Title:
5.2.: The Timing of Rate Announcement - James M. Buchanan, The Collected Works of James M. Buchanan, Vol. 9 (The Power to Tax: Analytical Foundations of a Fiscal Constitution) 
The Collected Works of James M. Buchanan, Vol. 9 The Power to Tax: Analytical Foundations of a Fiscal Constitution, Foreword by Geoffrey Brennan (Indianapolis: Liberty Fund, 2000).
About Liberty Fund:
Liberty Fund, Inc. is a private, educational foundation established to encourage the study of the ideal of a society of free and responsible individuals.
Foreword and coauthor note © 2000 Liberty Fund, Inc. © 1980 Cambridge University Press.
Fair use statement:
This material is put online to further the educational goals of Liberty Fund, Inc. Unless otherwise stated in the Copyright Information section above, this material may be used freely for educational and academic purposes. It may not be used in any way for profit.
The Timing of Rate Announcement
In the single-period or instantaneous models discussed in Chapters 3 and 4, it was not meaningful to introduce announcement effects. Implicitly, we presumed that tax rates were announced at the start of the period and that taxpayers made behavioral adjustments in full knowledge of prevailing tax arrangements. Once we introduce a multiperiod setting, however, announcement effects become important and must be explicitly discussed before we examine particular taxes.
Initially, let us consider a simple two-period model in which a Leviathan or revenue-maximizing government is operative in both periods, and in which the government is assigned the authority to impose a capital levy. The two-period model here is a simple extension of one version of the model outlined in Chapter 3. The behavior of only one taxpayer-citizen is examined, and Leviathan is constrained by the restriction that all tax rates are to be proportional. Characteristics of the model are specified in the following way: the individual lives for two periods only; in period 1, he expends effort to derive income from labor, income that he can either consume in that period or save; in period 2, he consumes any income “saved” from the previous period’s income, plus any interest these savings have earned, but does not derive any labor income. (To counter possible objections to the “realism” of some of the corner solutions to be discussed, we can assume also that the individual can subsist without receiving either labor or interest income. We may, if we want, assume that subsistence levels are guaranteed by governmental provision of relief payments, payments computed in the a share of total revenues collected.)
The in-period behavioral adjustments in this simple intertemporal model can be depicted diagramatically in Figure 5.1. Period 1 labor income is measured along the ordinate. 0A represents the maximum level of consumption, including leisure, that is feasible or possible in period 1. If none of this income is taken in leisure, and all of it should be saved, the maximum feasible consumption of 0B could be attained in period 2; 0B is larger than 0A to the extent that the interest rate on saving is positive. The rate of interest is given by A″B/0A″, where A″ is the abscissa terminal of the 45° line drawn from A. In the absence of tax, the citizen would allocate consumption intertemporally to attain the equilibrium position shown by the point L. He would consume 0J in period 1, save AJ and consume 0K in period 2.
Into this extremely simplified model, we now introduce a capital levy. The effects clearly depend on the extent to which the taxpayer, at the time of his consumption-saving choice, anticipates such a tax. Initially consider the case of extreme ignorance, and suppose that the taxpayer makes his saving decision without taking any account of the possibility of tax at all. He will then behave as he would in the complete absence of tax. That is, he will save AJ in period 1 for an expected consumption of 0K in period 2. Hence, AJ would represent his capital stock at the end of period 1. In this case, and remaining within the limits of the two-period setting defined, a Leviathan government will maximize its revenue collection by appropriating all the capital. In the absence of explicit restrictions to the contrary, it will always pay Leviathan to impose a completely confiscatory capital levy. Regardless of the size of the capital stock, Leviathan does best by appropriating it all. More than this, where the taxpayer does not anticipate any capital levy, Leviathan may do even better by somehow inducing the taxpayer to increase saving in period 1 above that which would be chosen in absence of tax. In Figure 5.1, Leviathan might achieve this goal by preannouncing a tax rate on capital just sufficient to induce the taxpayer to move to the minimum of the price-consumption curve AN′L, shown by M in Figure 5.1. After the taxpayer makes the predicted behavioral adjustment, Leviathan would then levy a confiscatory tax that would acquire all of the capital as revenue. If the price-consumption curve should have its minimum beyond L to the right, beyond the no-tax equilibrium position, Leviathan might actually subsidize accumulation.
Especially in a model where Leviathan is perpetual, however, it is unreasonable to endow the taxpayer with such naive expectations. It is surely more reasonable to move to the opposite extreme and assume that the taxpayer will recognize Leviathan’s interests in confiscating whatever capital might be accumulated. In this expectational setting, the citizen will consume all his income in period 1; he will save nothing, and a Leviathan that is limited to a capital levy will obtain no revenue at all. In this case, point A represents the highest level of utility the taxpayer can achieve.3
Under these conditions, in fact, Leviathan and the taxpayer are locked into a genuine dilemma-type situation.4Both could be made better off than at A—the “independent adjustment equilibrium”—but only if a relevant binding agreement can be entered into. For this reason, it is rational for Leviathan to bind itself, even if no explicit constitutional restrictions are imposed by the citizenry. In choosing among all possible rules, Leviathan will select the revenue-maximizing rule—that rule which enables it to “preannounce” the revenue-maximizing tax rate on capital. In this way, Leviathan selects a rate so as to generate taxpayer equilibrium at N′ in Figure 5.1, where a line parallel to AB is tangent to the price-consumption curve AN′L. This rate on capital is BY/0B and leaves the taxpayer consuming 0J′ in period 1 and saving AJ′ for consumption in period 2. From this saving, the tax taken is N′N″ (equal to X′B) leaving the taxpayer with a net consumption in period 2 of 0K′. However, it is quite clear that mere preannouncement of the rate BY/0B is not enough—the taxpayer must believe that this tax rate will in fact apply, and he will only have such faith if the preannouncement is genuinely binding. If it is not binding, the taxpayer may recognize it as such, and retreat to position A prior to the imposition of the tax in expectation of Leviathan’s rational strategy of imposing a confiscatory capital levy.
In a sense, the same analysis could be applied to the income tax, and Figure 5.1 could be reinterpreted to apply to the taxpayer’s choice between leisure and income-producing effort. As the analysis in Chapter 3 (particularly that illustrated in Figure 3.1) demonstrated, there will be a definitive revenue-maximizing rate of tax, given preannouncement, that enables the taxpayer to respond optimally to the tax. The preannouncement of the tax rate was, in Chapter 3, more or less assumed to be inherent in the fiscal structure. The multiperiod setting under consideration here allows us to raise the meaningful and highly relevant question as to whether the government should be granted power to set tax rates to apply to the income already earned, that is in the period just completed, as distinct from the power to set tax rates on income to be earned in the period subsequent to announcement. Would a perpetual or continuous Leviathan prefer to have the former authority? What we have succeeded in showing with our analysis of the capital levy is that, in the perpetual Leviathan case, the ability to set tax rates ex post might be desired neither by the citizen-taxpayer nor by government. And this result applies equally to all taxes, including the income tax, provided only that taxpayers in their in-period behavioral adjustments are expected to anticipate Leviathan’s rational taxing strategy.
It should be emphasized, however, that certain aspects of the discussion on this point are restricted by the simple two-period nature of the model. For one thing, the simple “dominant strategy” character of the dilemma situation in which Leviathan and the taxpayer are placed becomes moderated as we extend the model to include many periods. Even in the absence of any binding agreement and in the presence of some positive saving by the taxpayer, a Leviathan government may refrain from imposing a confiscatory tax over some sequence of periods. It might do better over some initial sequence of periods by encouraging the taxpayer to save something, to accumulate capital, thereby enlarging the revenue base. If the “game” is finite, of course, Leviathan would impose the confiscatory levy during the final period, but with a continuing Leviathan an infinite sequence may be a more appropriate characteristic of the model than a finite one. Modeled in an infinite sequence, whether Leviathan would forbear to impose the confiscatory rate over some periods will depend on such things as its own rate of discount and its predictions of the individual taxpayer’s attitude toward risk. If Leviathan’s discount rate is very high, it may still be rational to appropriate all capital as soon as it appears. In the same way, if the taxpayer is highly risk averse, he will tend to prefer the certainty of a dollar’s current consumption to some probability of more future consumption or confiscation. In this case, Leviathan would find it difficult to encourage the taxpayer to save by merely refraining from the capital levy over some sequence of periods. However, it seems unlikely that a zero saving-confiscatory tax solution would prevail indefinitely: scope for implicit collusion over successive “plays” of the game seems likely to secure at least some of the mutual gains. Nevertheless, a more explicit constitutional restriction relating to preannouncement with enforceability will be preferred by both parties, except in those situations where the taxpayer can be consistently fooled.
An important aspect of the discussion to this point has been the assumption of perpetual or continuing Leviathan. In the one-period models of Chapters 3 and 4, the assumption of a revenue-maximizing Leviathan required no direct consideration of the prospects for perpetuation of fiscal powers. As we move to a multiperiod setting, however, a new issue more or less naturally emerges. How will the constitutional calculus of the potential taxpayer-beneficiary be affected if he predicts that a true revenue-maximizing Leviathan will show up only in the occasional time period? In other periods, a government more closely modeled as a “benevolent despot” may be predicted. Alternatively, nonfiscal constitutional constraints (including electoral rules) may be expected to be operational part of the time. The possibility of Leviathan in any period will, nonetheless, imply that the potential taxpayer’s constitutional decision must incorporate such possibility.
In this setting, which we can call that of the “probabilistic Leviathan,” two departures from the previous analysis emerge. The first is that it can no longer be in Leviathan’s interest to have preannouncement of tax rates. The dilemma situation between the taxpayer and Leviathan discussed earlier depends on the mutual expectation that the latter will continue in existence over some sequence of periods. The second is that, even if preannouncement of taxes is somehow required, the nature of capital is such that significant current or in-period adjustment is not feasible. A distinction arises here between capital taxation and income taxation that is not relevant in the perpetual Leviathan case.
The first of these differences is easily explained. The results of introducing a probabilistic Leviathan are twofold. First, the taxpayer cannot predict with certainty what the tax rate in any period will be. He cannot anticipate that revenue-maximizing tax rates will be imposed, whether these be estimated in simple one-period terms, as in Chapters 3 and 4, or in complex present values, as introduced in this chapter. Any sequence that allows for non-Leviathan government, even probabilistically, becomes less definitive. Second, the occasional Leviathan does not bear the full future period cost of current-period reductions in the tax base.
Consider, for example, an income tax in an environment where Leviathan is operative with probability 1 in 10 and where postbehavioral announcement of tax rates is permitted. When and if it comes into effective power, even for one period, Leviathan can collect all income earned in a single period by announcing a rate of 100 percent after the income has been earned (i.e., after the relevant leisure-effort choices have been made). In the multiperiod perpetual or continuing Leviathan setting, this fiscal behavior would not, of course, be rational because the individual would respond by supplying no tax base in all future periods. Assume that the taxpayer expects the non-Leviathan government to impose a tax rate of 10 percent, but he expects a Leviathan government to impose wholly confiscatory rates of 100 percent, announced after income-leisure choices are made. In the probabilistic setting indicated, the risk-neutral taxpayer will respond to the threat of Leviathan in accordance with his expected tax rate—which is [0.9(10) + 0.1(100)], or 19 percent. If p, the probability of a Leviathan-like fiscal authority, is one-tenth, then the taxpayer, in maximizing his expected utility, in each period will supply the amount of taxable base that he would supply if he faced a certain tax rate of 19 percent in each period. In this case, Leviathan would clearly prefer the possibility of ex post announcement. Correspondingly, the citizen-taxpayer would prefer a constitutional requirement that income-tax rates be preannounced before he makes behavioral adjustments. In the latter case, the taxpayer would always know at the start of each period whether Leviathan is operative or not, and with appropriate planning, he could presumably arrange to transfer leisure intertemporally so that he would earn relatively little income in those periods when Leviathan comes into being.
The advantages of preannouncement to the taxpayer are less dramatic, however, in the case of the capital levy than they are with the income tax. If he is given enough advance notice, the individual can presumably dissave drastically; he can “eat up his capital” and eventually deplete his entire stock of value. But the essence of the distinction between capital (a stock) and income (a flow) implies that whereas a strictly current tax (i.e., one not announced ex post) on income permits behavioral adjustments in leisure-effort choices to occur, a current tax on capital does not permit comparably efficacious adjustment because the capital that becomes the base of the tax is already in existence. Capital does not primarily emerge out of any decisions made currently. The size of the tax base is determined by past decisions on the accumulation of savings and what has been done is not readily undone. Hence, any tax on capital is, by the nature of capital itself, ex post, unless, of course, the tax is to be imposed only on new capital formation subsequent to the announcement. A distinction between capital and income taxation thereby emerges in the probabilistic Leviathan setting, a distinction that is much less striking when a Leviathan government exists continuously. Capital taxation has the effect of permitting the occasional revenue-maximizing government to extend its appetites so as to “enjoy” the fruits of many periods. Income taxation does not have this effect, or at least it does so only to the extent that a tax on interest income is an indirect form of a tax on capital.
Two implications for the individual’s constitutional calculus emerge from a recognition of the points made in this section:
[3. ] We set aside at this stage any limits on taxpayer behavior caused by the recognition that some proportion of revenue is spent on public goods which would otherwise not be provided. This is entirely reasonable if we bear in mind that the taxpayer in question is one among many, each of whom will rationally “free-ride” by avoiding taxes.
[4. ] The game may be depicted as follows:
where the taxpayer’s payoff is the first-mentioned in the pair and Leviathan’s payoff is the second-mentioned. Since the confiscatory levy is dominant for Leviathan, the taxpayer consumes everything.