The later you pay, the higher the k.

• Author: Seidman, Laurence S.
• Position: Capital per labor

1. Introduction

   The age path (life-cycle timing) of a tax is an important yet often overlooked property of the tax because it affects the capital accumulation of the economy. By contrast, attention usually focuses on the incentive effect of a tax. For example, suppose a wage tax is replaced by a consumption tax. Neither tax reduces the net return to saving below the gross return, so a focus on the incentive effect might suggest that the capital accumulation of the economy would be unaffected by the replacement. But this reasoning neglects the fact that a consumption tax has a different age path from a wage tax; the individual pays less tax while working and more during retirement. It turns out that this postponement of tax over the life cycle tends to raise the capital per labor (k) in the economy.

   Consider the proposal to terminate the taxation of capital income. This can be done in two different ways: convert the income tax to a wage (labor income) tax (exempt interest, dividends, and capital gains from the income tax) or convert the income tax to a consumption tax (tax consumption spending, not income). Does it matter which way? The impression is often given in the public finance literature that either way would have the same effect. But this ignores the fact that a consumption tax has a different age path from a wage tax.

   Similarly, it has been shown that conversion of an income tax to a consumption tax raises the steady-state k of the economy regardless of the interest elasticity of saving and that the magnitude of the increase in k is unaffected by the magnitude of the saving elasticity (Seidman and Lewis 1999); but if the saving elasticity is irrelevant, what raises the steady-state k? This paper investigates the conjecture that "the later you pay, the higher the k" and demonstrates the importance of the age path of any tax for the capital accumulation of the economy.

   Wage, income, consumption, and capital income taxes differ in their age paths as well as their incentive effects. Under a wage tax, a person pays tax while working, but not in retirement. Under an income tax, a person usually pays less annual tax during retirement than while working. But under a consumption tax, a person would pay as much annual tax whether retired or working, assuming the person saves enough to maintain consumption on retirement. Under a capital income (interest) tax, annual tax would rise and fall over the life cycle as the individual accumulates and decumulates wealth. This paper analyzes how the differing age path of each tax affects the capital accumulation of the economy.

   The impact of the age path of a tax on the capital accumulation of the economy has been noted by other researchers (e.g., Diamond 1970; Atkinson and Stiglitz 1980; Bradford 1980; Summers 1981; Auerbach and Kotlikoff 1987; Ihori 1987, 1996; Gravelle 1994). Summers (1981, p. 538) shows that in a life-cycle growth model, a consumption tax generally achieves a higher steady-state capital per effective labor than a wage tax which raises the same revenue because "consumption taxation extracts revenue later in the individual's lifetime than does wage taxation and so causes more savings in the younger years." Ihori (1987, p. 386) writes that "the lump-sum approach shows clearly that even with the incentive effects ignored, the differing timing of tax payments would cause consumption, wage, and income taxes to achieve different intergeneration incidence during the transition process when tax rates are set to achieve identical tax revenue per worker." Auerbach and Kotlikoff (1987, p. 57) note the significance of the ag e path of a tax and find that "the consumption tax base generates significantly more long-run capital formation than either the wage tax or the income tax." Gravelle (1994, p. 42) recognizes this point, stating that "a switch to a consumption tax should increase the savings rate, while a switch to a wage tax has ambiguous effects."

   Nevertheless, there continues to be a neglect of the importance of the age path of taxes in the public finance literature. For example, many public finance journal articles and textbooks continue to assert that a consumption tax is "equivalent" to a wage tax even though the two taxes have different age paths and consequently generate different steady-state k's for the economy.

   Why this neglect? One reason is that some economists argue that the impact of the age path of a tax on capital accumulation can be offset by the appropriate government debt policy (Bradford 1980). This point is correct in theory. For example, although conversion from a wage tax to a consumption tax generally raises steady-state k when there is no change in debt policy, k can be kept the same with the appropriate change in debt policy (Seidman 1990).

   In practice, however, when tax conversion occurs, it is doubtful that there will be any change in debt policy. For this reason, Summers (1981) analyzes tax conversion on the assumption that the budget remains balanced each year despite tax conversion--that is, there is no offsetting debt policy in response to conversion. When challenged by Bradford (1980), Summers makes this reply (p. 539): "David Bradford emphasizes the importance of this 'balanced budget' requirement. He argues that without such a requirement the government by running surpluses or deficits can control the level of the capital stock given any tax structure. The 'real world' feasibility of this sort of policy seems unclear."

   We would go further than Summers and argue that there is no empirical evidence that proposals for tax conversion are accompanied by changes in debt policy that nullify the impact of tax conversion on capital accumulation. On the contrary, governments almost invariably discuss, debate, and set their debt policy--for example, a balanced budget rule--independently of tax policy. For example, in the debate in the U.S. Congress over fundamental tax reform in the 1990s, involving the pros and cons of a flat tax, a progressive consumption tax (Seidman 1997), and a national sales tax, there was never any discussion of altering government debt policy by legislators or even by economists testifying on the merits of each tax proposal. It is therefore important for economists to analyze the impact on capital accumulation of pure tax conversion--that is, tax conversion unaccompanied by offsetting debt policy.

   A second reason for neglecting the impact of the age path of a tax on capital accumulation is the assumption that it is quantitatively unimportant. Indeed, if incentive effects were large in magnitude but timing effects were small, ignoring timing effects would be justified. But is this the case? A major purpose of this paper is to estimate the quantitative impact of the timing effect. We therefore utilize a model with numerical parameter values based on econometric studies. It turns out that the timing effect is in fact quantitatively important.

   This paper builds specifically on the papers of Summers (1981) and Ihori (1987). Like Summers, we use a multiage life-cycle growth model, but unlike Summers, we compare conventional transactions-based taxes (wage, income, and consumption taxes) with lump-sum "age taxes" to isolate the impact of the timing effect. Like Ihori, we use lump-sum taxes, but unlike Ihori, we use a multiage model that is empirically calibrated, enabling us to estimate whether the timing effect is quantitatively important. We estimate that perhaps half the capital-stock gap between a consumption tax and an income tax is due to the timing effect.

   In this paper, we investigate systematically the conjecture that the later you pay, the higher the k, first in a two-age (two-period) life-cycle model and then in a multiage (multiperiod) life-cycle model. The two-age model is simply the special case of the multiage model in which there are just two "ages"--work age and retirement age. We use the term "age" rather than "period" to emphasize the fact that it is time from birth, not calendar time, that is the focus of the model. The multiage model is empirically calibrated on the basis of recent econometric studies.

   A central element of our analysis is to replace a transactions-based tax (income, wage, consumption, and capital income) with a corresponding lump-sum age tax that has the identical age path of tax payments over the life cycle. By doing so, we can isolate the impact that the pure timing effect has on capital accumulation and investigate its magnitude. It turns out, for an empirically plausible range of parameter values, that the quantitative impact can be considerable. Moreover, the timing effect often causes the impact of a tax on capital accumulation to be very different from what would be predicted from the incentive effect.

   It is important to be precise about our assumptions concerning government spending. Like Summers (1981), we make the following assumptions. First, we assume that government spending consists entirely of government consumption purchases so that government spending has no direct impact on capital accumulation, thereby enabling us to clearly isolate the impact of taxes on capital accumulation. Second, we assume that the government annually balances its budget so that there is no government debt. As shown by Diamond (1965), this assumption matters for capital accumulation in a life-cycle growth model. Third, we assume that budget balance is adhered to regardless of the tax chosen to finance government spending. We share Summer's (1981) view that it is important to investigate what happens if debt is not varied when taxes change because such variation has virtually never been mentioned by legislators proposing fundamental tax reform. Fourth, in our multiage model, government spending per effective labor (which alw ays equals tax revenue per effective labor in each period) is the same regardless of the tax chosen to finance the government spending.

   We begin with the...