Generational Accounts, Aggregate Savings, and Intergenerational Distribution

Willem H. Buiter

doi:10.5089/9781451849820.001.A001

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Generational Accounts, Aggregate Savings, and Intergenerational Distribution

Author: Mr. Willem H. Buiter¹

¹ 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

Publication Date:: 01 Jul 1996

eISBN:: 9781451849820

Language:: English

Keywords:: WP; present value; interest rate; after-tax rate of return; public goods; equilibrium price; production function; labor income

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Are generational accounts informative about the effect of the budget on the intergenerational distribution of resources and on aggregate saving? First, the usefulness of generational accounts lives or dies with the strict life-cycle model of household consumption. Second, even if the life-cycle model holds, generational accounts ignore the intergenerational redistribution associated with the government’s provision of public goods and services and with intergenerational externalities. Third, generational accounting ignores the effect of the budget on tax and transfer bases and on before-tax incomes and prices. That is, it does not handle incidence or general equilibrium repercussions.

Abstract

I. Introduction

In a number of influential papers, Larry Kotlikoff, Alan Auerbach and Jagadeesh Gokhale have extolled the virtues of generational accounts, both as the correct way of measuring how the government budget affects intergenerational distribution and as an essential input into the analysis of the effect of the budget on saving (Auerbach, Gokhale, and Kotlikoff, 1991, 1992, 1994; see also Auerbach and Kotlikoff, 1987; Kotlikoff, 1989, 1992). In addition to the empirical implementations of this methodology by various subsets of the three aforementioned authors, a not inconsiderable research effort has been undertaken in recent years by a number of national governments and by multilateral organizations such as the IMF and the World Bank, to implement the methodology empirically.

The definition of generational accounts is straightforward. Their empirical implementation makes quite heavy demands on data gathering capacity and involves some quite subtle conceptual problems, many of which are treated extensively in e.g., Auerbach, Gokhale, and Kotlikoff (1991). Generational accounts

“… are accounts-one for each generation-that tally up, in present value, the amount of receipts less payments the government can expect to collect from each generation over its remaining life span.” (Auerbach, Gokhale, and Kotlikoff, 1991, p. 2).

Strong claims are made by its proponents concerning the merits of the approach:

“Generational accounting measures directly the amount current and future generations can, under existing public policies, be expected to pay over time in net taxes (taxes paid less transfer payments received) to the government. This type of analysis is essential if we really want to know the burden we are imposing on future generations. It is also critical for understanding how economic policy directly affects national saving and collaterally influences investment, interest rates and growth” (Kotlikoff, 1992, p. 22).

This paper asks and answers two questions. The first is: what do generational accounts tell us about the way the government budget affects intergenerational distribution? The second is: what do generational accounts (augmented with generation-specific propensities to consume out of life-time resources) tell us about the effect of the budget on saving?

The answer to the first question can be summarized as follows:

First, the usefulness of generational accounts as a summary of the budget’s impact on the intergenerational distribution of private consumption (and indeed for private decisions in general) lives or dies with the validity of the life-cycle model. The life-cycle model is characterized by the following assumptions: (i) finite individual lifetimes; (ii) no operative Ricardian ³ intergenerational gift motive; and (iii) complete markets ⁴ permitting meaningful present discounted value calculations for streams of future taxes and transfer payments. For our purposes, this can be weakened to the condition that financial markets are sufficiently rich to ensure that the timing of government taxes and transfer payments over the life cycle of an individual does not matter, but only the present value of these taxes and transfers over the life cycle, when they are discounted at the government’s rate of interest. One of the points this paper makes is the obvious but important one, that generational accounts are uninformative as regards the budget’s impact on intergenerational distribution and saving behavior when consumers’ decision horizons are longer than those characteristic of the life-cycle model (when there is an operative Ricardian bequest motive) or when decision horizons are shorter than those postulated by the life-cycle model, because of the appropriate kind of capital market imperfections. Even when the strict life-cycle model holds, great caution should be exercised in interpreting the generational accounts. What prima facie they appear to tell us may be misleading and at worst quite incorrect.

Second, the generational accounts, as currently constructed, have nothing to say about the intergenerational distribution of public consumption.

Third, generational accounting does not allow for the general equilibrium repercussions of alternative budgetary policies. That is, all tax incidence issues are ignored (the changes in tax bases and transfer, benefit or subsidy bases due to the budget). In addition, generational accounting ignores all changes in before-tax incomes and relative prices caused by alternative budget programs. These general equilibrium responses of pretax, pretransfer and presubsidy factor incomes and rates of return may reinforce, counteract or even reverse the impact effects of budgetary policy changes (conditional on the original equilibrium configuration of prices and quantities).

The answer to the second question is that the usefulness of generational accounts as a tool for evaluating the impact of budgetary policy on saving is only as high as the degree of validity of the life-cycle model.

Nothing in this paper should be construed as a justification of the use of the conventional government budget deficit (or of its structural, full-employment or inflation-corrected siblings) as an indicator of the effect of fiscal policy on aggregate demand or private saving or as an indicator of how much current policy is adding to the amount of the resources that will have to be extracted from current and future generations in order for the government to satisfy its intertemporal budget constraint. Indeed I have long argued against the common abuse of this indicator (see e.g., Buiter, 1983).

The empirical implementation of measures of government net worth, and of other indices of the current and future resource extraction implications of budgetary policy is a task that is both daunting and important. An important example of such empirical intertemporal accounting is Bohn (1992). The purpose of this paper is different. Its focus is on the “crucial normative and positive questions” (Drazen, 1992) left unanswered by generational accounting.

The outline of the rest of the paper is as follows. In Section II, I present a small familiar macroeconomic model to guide the consideration of the issues associated with the construction and use of generational accounts. In Section III, I show how the presence of a Ricardian intergenerational gift motive may rob the generational accounts of their informativeness as regards the effect of the budget both on intergenerational distribution and on saving. In Section IV, the implications of capital market imperfections are discussed. In Section V, I discuss the intergenerational distribution aspects of public consumption. In Section VI issues to do with incidence and the general equilibrium repercussions of the budget on the after-tax intergenerational distribution of private resources are considered. Section VII concludes.

II. A Simple Two-Period Overlapping Generations Model

To motivate the discussion that follows, I illustrate how the generational accounts are constructed in a very simple two-period overlapping generations model of a competitive closed economy. The tax structure does not try to mimic real-world complexities and consists of generation-specific lump-sum taxes and a single distortionary tax. In Section II, this distortionary tax is a proportional tax on all factor income.

1. The household accounts

Each household lives for two periods. All households within a generation are identical. Consider a representative household born in period t. She works during the first period of her life for a before-tax real wage w_t and is retired during the second period. Labor supply is exogenous and scaled to unity. She accumulates assets during period t for retirement in period t + 1 in the form of noninterest bearing government money, M _{t, t+1}, one-period index-linked government interest-bearing debt, D_{t, t+1} with a real rate of interest r_{t, t+1}, and real reproducible capital K_{t, t+1}. The one-period nominal rate of interest in period t is denoted i_{t-1, t} while P_t. is the general price level in period t. The before-tax marginal product of capital in period t (which equals the capital rental rate) is denoted p_t. The generation t household consumes private goods, $\begin{matrix} C_{t}^{1} \end{matrix}$ while young and $\begin{matrix} C_{t}^{2} \end{matrix}$ while old. She may also derive utility from two public consumption goods provided free of charge by the government. The quantities of the two public consumption goods provided in period t by the government are $\begin{matrix} G_{t}^{0} a n d G_{t}^{y} \end{matrix}$ , respectively. For simplicity, we model a pure public consumption good, that is a good that is completely nonrival and completely nonexcludable. Households can leave nonnegative bequests to the next generation; l_{t, t+1} denotes the real bequest left by a member of generation t to generation t + 1. Since population growth is inessential for the issues addressed by this paper, I assume that each young household has only one descendant. Reproduction is exogenous and occurs through parthenogenesis. By choice of units, the size of the population is set equal to 1. Generation t makes her bequest during the second period of her life; it becomes available to generation t + 1 during her youth. When young, generation t pays a lump-sum tax (which can be negative) whose real value is τ¹_t. When old, a lump-sum tax with real value τ²_t is paid. Labor income and capital income in period t are taxed at the constant proportional rate θ_t.

The budget constraints while young and while old for a representative member of generation t are given in equations 1 and 2.

P_{t} [w_{t} (1 - θ_{t}) - τ_{t}^{1} + ℓ_{t - 1, t} - c_{t}^{1}] = P_{t} K_{t, t + 1} + P_{t} D_{t, t + 1} + M_{t, t + 1} (1)

\begin{matrix} P_{t + 1} (c_{t}^{2} + ℓ_{t, t + 1} + τ_{t}^{2}) \\ = P_{t + 1} K_{t, t + 1} [1 + ρ_{t + 1} (1 - θ_{t + 1})] + P_{t + 1} D_{t, t + 1} (1 + r_{t, t + 1}) + M_{t, t + 1} \end{matrix} (2)

From equations 1 and 2, it follows that the nominal value at period t prices of net taxes paid by a representative member of generation t while young is $P_{t} (θ_{t} w_{t} + τ_{t}^{1})$ . In addition to these involuntary transfers to the government, a member of generation t transfers while young M_{t, t+1} + P_tD_{t, t+1} to the government through the voluntary acquisition of government liabilities, both interest-bearing and noninterest bearing. The nominal value (at period t + 1 prices) of the net taxes paid by the representative member of generation t while old is:

P_{t + 1} (θ_{t + 1} ρ_{t + 1} K_{t, t + 1} + τ_{t}^{2}) .

In addition, the old member of generation t receives from the government, in period t + 1 the gross return (interest plus principal) on the government debt it acquired the previous period, that is, $M_{t, t + 1} + (1 + r_{t, t + 1}) P_{t + 1} D_{t, t + 1} .$

By combining and rearranging equations 1 and 2, we obtain the following present value relationship for a representative member of generation t:

P_{t} c_{t}^{1} + \frac{P_{t + 1} c_{t}^{2}}{1 + i_{t, t + 1}} = P_{t} w_{t} + P_{t} ℓ_{t - 1, t} - \frac{P_{t + 1} ℓ_{t, t + 1}}{1 + i_{t, t + 1}} - T_{t, t} + Φ_{t, t + 1} + Ψ_{t, t + 1} (3)

where

T_{t, t} \equiv P_{t} τ_{t}^{1} + \frac{P_{t + 1} τ_{t}^{2}}{1 + i_{t, t + 1}} + P_{t} θ_{t} w_{t} + \frac{θ_{t + 1}}{1 + i_{t, t + 1}} ρ_{t + 1} P_{t + 1} K_{t, t + 1} + \frac{i_{t, t + 1}}{1 + i_{t, t + 1}} M_{t, t + 1} (4)

\begin{array}{l} Φ_{t, t + 1} \equiv [1 + r_{t, t + 1} - \frac{P_{t}}{P_{t + 1}} (1 + i_{t, t + 1})] \frac{P_{t + 1} D_{t, t + 1}}{1 + i_{t, t + 1}} \\ + [1 + ρ_{t + 1} (1 - θ_{t + 1}) - \frac{P_{t}}{P_{t + 1}} (1 + i_{t, t + 1})] \frac{P_{t + 1} K_{t, t + 1}}{1 + i_{t, t + 1}} \end{array} (5)

and

Ψ_{t, t + 1} \equiv θ_{t + 1} ρ_{t + 1} \frac{P_{t + 1} K_{t, t + 1}}{1 + i_{t, t + 1}} . (6)

The interpretation of the terms on the R.H.S. of equations 3 and 4 is straightforward. The L.H.S. of equation 3 is the present value (discounting to the end of period t (or the beginning or period t + 1) at before-tax nominal interest rates) of lifetime private consumption of a representative member of generation t. The R.H.S. of equation 3 is the present value of all resources available to a member of generation t for financing her lifetime consumption of private goods. The first term on the R.H.S. is the wage income of a member of generation t. The negative of the next two terms, $\frac{P_{t + 1} ℓ_{t, t + 1}}{1 + i_{t, t + 1}} - P_{t} ℓ_{t - 1, t}$ , could be called the private generational account of a representative member of generation t that is the present value of bequests made when old minus the value of bequests received when young. The fourth term on the R.H.S. of equation 3, T_{t, t}, is the present value of the taxes net of transfers paid by a representative member of generation t to the government during its lifetime.

Considering T_{t, t} in more detail, the first two terms on the R.H.S. of equation 4, $P_{t} τ_{t}^{1} + \frac{P_{t + 1} τ_{t}^{2}}{1 + i_{t, t + 1}}$ , is the value of net lump-sum taxes paid by generation t when young plus the present discounted value of net lump-sum taxes paid by generation t when old. Note that here, (and throughout the generational accounts computation of the next subsection), discounting is at pre-tax rates of interest (see Auerbach, Gokhale, and Kotlikoff, 1991, p. 5).

The third term on the R.H.S. of equation 4, P_tθ_tW_t, is the value of labor income taxes paid when young.

The fourth term on the R.H.S. of equation 4, $\frac{θ_{t + 1}}{1 + i_{t, t + 1}} ρ_{t + 1} P_{t + 1} K_{t, t + 1}$ , represents the present value of the capital income tax paid by generation t as asset owners when old.

The fifth term on the right-hand side of equation 4, $\frac{i_{t, t + 1}}{1 + i_{t, t + 1}} M_{t, t + 1}$ , can be interpreted, again following Auerbach (1991) as the present value of the seigniorage paid by generation t to the government over its lifetime. Starting off its life with zero money holdings, the generation t household accumulates M_{t, t+1} worth of money balances during the first period of its life. In the second and last period of its life, it again rims its money balances down to zero. The present value of the net acquisitions of money balances by generation t over its lifetime is therefore $M_{t, t + 1} - \frac{M_{t, t + 1}}{1 + i_{t, t + 1}} = \frac{i_{t, t + 1}}{1 + i_{t, t + 1}} M_{t, t + 1} .$

Note that:

\sum_{k = t}^{\infty} Δ_{k - 1, t} (M_{k, k + 1} - M_{k - 1, k}) \equiv - M_{t - 1, t} + \sum_{k = t}^{\infty} Δ_{k, t} i_{k + 1} M_{k, k + 1} (7)

where Δ_{k, t-1} is the pre-tax nominal discount factor

\begin{matrix} Δ_{m, n} \equiv \prod_{j = n + 1}^{m} \frac{1}{1 + i_{j - 1, j}} f o r m \geq n + 1 \\ \equiv 1 f o r m = n . \end{matrix}

The initial stock of base money plus the present value of the government’s current and future issues of base money equal the present value of the imputed interest cost foregone by the government because of its ability to issue noninterest-bearing monetary liabilities (see Buiter, 1983).

The term Φ_{t, t+1} on the R.H.S. of equation 3 reflects differences in after-tax rates of return on nonmonetary assets. If all (pecuniary) after-tax rates of return are equalized, that is, if

1 + r_{r, t + 1} - \frac{P_{t}}{P_{t + 1}} (1 + i_{t, t + 1}) = 1 + ρ_{t + 1} (1 - θ_{t + 1}) - \frac{P_{t}}{P_{t + 1}} (1 + i_{t, t + 1}) = 0,

then the term Φ_{t, t+1} equals zero. Ideally, in a stochastic model, risk-adjusted expected rates of return would be equalized, but not ex-post or realized rates of return. Since the results of this section go through even if Φ_{t, t+1} = 0, I shall assume that this condition holds from now on; pecuniary after-tax rates of return (both ex-ante and ex-post) are therefore assumed to be equalized.

The esthetic spoiler term on the R.H.S. of equation 3 is Ψ_{t, t+1}, defined in equation 6. When after-tax rates of return are equalized,

Ψ_{t, t + 1} = [1 + ρ_{t + 1} - \frac{P_{t}}{P_{t + 1}} (1 + i_{t, t + 1})] \frac{P_{t + 1} K_{t, t + 1}}{1 + i_{t, t + 1}} . (8)

It therefore will not disappear unless the before-tax rates of return are also equalized, which will not be the case if, as in our example, different assets are taxed at different rates.

2. Generational accounts

The generational account (perhaps better characterized as the public generational account) for any generation, say the one born in period fc, is the present value of net remaining lifetime payments to the government by the generation born in period k, discounted back to the beginning of period t (or the end of period t -1). In our model, k ranges from t—1 to ∞ and there are but two generations co-existing in any period t. With a constant size population (scaled to unity) the generational account for a representative member of generation k, denoted T_{k, t-1}, is also the generational account of her whole generation.

T_{t, t-1}, the generational account of a representative member of generation t, discounted back to the beginning of period t is given by:

T_{t, t - 1} \equiv (\frac{1}{1 + i_{t - 1, t}}) T_{t, t} (9)

where T_{t, t} is defined in equation 4.

The generational accounts for the generations other than t are now derived easily. For generation t—1, (the old in period t), we have:

T_{t - 1, t - 1} \equiv (\frac{1}{1 + i_{t - 1, t}}) {\begin{matrix} P_{t} τ_{t - 1}^{2} + θ_{t} ρ_{t} P_{t} K_{t - 1, t} \\ - [M_{t - 1, t} + (1 + r_{t - 1, t}) P_{t} D_{t - 1, t}] \end{matrix}} . (10)

For all generations, k ≥ t, we have:

T_{k, t - 1} \equiv Δ_{k, t - 1} T_{k, k} (11)

where T_{k, k} is defined from equation 4.

3. The government account

The government’s single-period budget identity for period t is given in equation 12:

\begin{matrix} M_{t + 1} - M_{t} + P_{t} (D_{t + 1} - D_{t}) K \equiv \\ P_{t} (G_{t}^{0} + G_{t}^{y}) + P_{t} τ_{t - 1, t} D_{t} - τ_{t}^{1} - τ_{t - 1}^{2} - θ_{t} P_{t} (w_{t} + ρ_{t} K_{t}) . (12) \end{matrix}

M_t is the aggregate stock of government money at the beginning of period t, D_t is the stock of short index-linked government interest-bearing debt at the beginning of period t and K_t is the aggregate stock of private capital at the beginning of period t.

We note that:

\begin{array}{l} M_{t} = M_{t - 1, t} \\ K_{t} = K_{t - 1, t} \\ D_{t} = D_{t - 1, t} . \end{array}

Rearranging the government budget identity 12, we obtain (assuming equalization of after-tax rates of return):

P_{t - 1} D_{t} \equiv \frac{1}{1 + i_{t - 1, t}} {\begin{matrix} P_{t} D_{t + 1} + τ_{t}^{1} + τ_{t - 1}^{2} + P_{t} θ_{t} (w_{t} + ρ_{t} K_{t}) \\ - P_{t} (G_{t}^{0} + G_{t}^{y}) + M_{t + 1} - M_{t} \end{matrix}} . (13)

Solving 13 recursively forward, we obtain the familiar government present value budget constraint or government solvency constraint given in equation 14, provided the terminal condition given in equation 15 is satisfied.

P_{t - 1} D_{t} \equiv \sum_{k - t}^{\infty} Δ_{k, t - 1} {\begin{cases} τ_{k}^{1} + τ_{k - 1}^{2} + P_{k} θ_{k} (w_{k} + ρ_{k} κ_{k}) \\ - P_{k} (G_{k}^{0} + G_{k}^{y}) + M_{k + 1} - M_{k} \end{cases}} (14)

\lim_{k \to \infty} Δ_{k, t - 1} P_{k} D_{k + 1} = 0 (15)

The government solvency constraint given in equation 15 is the no-Ponzi-finance condition stating that, in the long run, the debt cannot grow faster than the rate of interest, i.e. that, if there is a positive stock of debt outstanding, the government ultimately will have to run primary surpluses or resort to seigniorage (see Buiter and Kletzer, 1994).

Equation 14 can be rewritten using the generational accounts of all generations currently alive and yet to be born as in equation 16.

P_{t - 1} D_{t} + \sum_{k = t}^{\infty} Δ_{k, t - 1} P_{k} (G_{k}^{0} + G_{k}^{y}) = \sum_{k = t - 1}^{\infty} T_{k, t - 1} (16)

Equation 16 states that the value of the government’s net outstanding financial liabilities plus the present value of its future consumption program must be covered by the sum of the generational accounts of all existing and future generations.

4. Private consumption behavior

The decision problem of a competitive, and “policy taking” representative household born in period t is as follows. Taking as given market prices, $P_{t}, P_{t + 1}, w_{t}, ρ_{t + 1}, r_{t, t + 1}, i_{t, t + 1}$ and government policy instrument values, $τ_{t}^{1}, τ_{t}^{2}, θ_{t}, θ_{t + 1}, G_{t}^{y}$ and $G_{t + 1}^{0}$ and taking as given the bequest received from the previous generation, l_{t-1, t} choose ${c_{t}^{1}, c_{t}^{2}, M_{t, t + 1}, D_{t, t + 1}, K_{t, t + 1}, ℓ_{t, t + 1}}$ to maximize the utility functional given in equation 17,

\begin{array}{l} W_{t} = \frac{1}{1 - η} {(c_{t}^{1})}^{1 - η} + \frac{α_{1}}{1 - η} {(c_{t}^{2})}^{1 - η} + \frac{α_{2}}{1 - η} {(\frac{M_{t + 1}}{P_{t + 1}})}^{1 - η} \\ + α_{3} \ln (1 + G_{t}^{y}) + α_{4} \ln (1 + G_{t + 1}^{0}) + δ W_{t + 1}^{*} (17) \\ η \geq 0; α_{1} > 0; α_{j} \geq 0, j = 2, 3, 4; 0 \leq δ < 1 \end{array}

subject to the private budget constraints 1 and 2 and the weak inequalities

c_{t}^{1} \geq 0, c_{t}^{2} \geq 0, M_{t, t + 1} \geq 0, K_{t, t + 1} \geq 0, a n d ℓ_{t, t + 1} \geq 0 . (18)

$W_{t + 1}^{*}$ is the maximized value of the utility of the generation born in period t + 1.

Inada conditions on the utility function ensure that the nonnegativity constraints on $c_{t}^{i}, c_{t}^{2} a n d M_{t, t + 1}$ are satisfied. The Inada condition on the production function (see Section 5) will ensure $K_{t, t + 1} \geq 0$ in equilibrium. That leaves just one nontrivial nonnegativity constraint, $ℓ_{t, t + 1} \geq 0$ , bequests to the next generation cannot be negative.

The way the bequest motive is introduced is consistent with debt neutrality: generation t cares not about the act of giving or about the consumption levels achieved by the next generation, but by the level of utility achieved by the next generation. All generations have the same utility functions. For simplicity, only one-sided (parent-to-child) intergenerational caring is considered. More is required, however, to generate the potential for equilibria with debt neutrality. Specifically, I have ruled out strategic bequests by assuming something akin to “intergenerational open-loop Nash behavior” (see Buiter, 1990). Each member of generation t takes as given when she chooses $c_{t}^{i}, c_{t}^{2}, M_{t, t + 1}, D_{t, t + 1}, K_{t, t + 1}, a n d ℓ_{t, t + 1}$ the bequest she gets from generation t—1, that is l_{t-1, t}.

The interesting first-order conditions are the following:

\frac{1}{α_{1}} {(\frac{c_{t}^{1}}{c_{t}^{2}})}^{- η} = 1 + r_{t, t + 1} (19)

{(\frac{\frac{M_{t + 1}}{P_{t + 1}}}{c_{t}^{2}})}^{- η} = \frac{α_{1}}{α_{2}} i_{t, t + 1} (20)

α_{1} {(c_{t}^{2})}^{- η} \geq (1 + r_{t, t + 1}) δ α_{1} {(c_{t + 1}^{2})}^{- η} . (21)

If there is an interior solution for bequests, l_{t, t+1} > 0, then equation 21 holds with equality. If equation 21 holds with strict inequality, then l_{t, t+1} = 0, (the bequest constraint is binding).

Equation 19 equates the marginal rate of intertemporal substitution in consumption over the life of generation t to the real rate of interest. Equation 20 equates the marginal utility of the services yielded by money when old to its opportunity cost, the marginal utility of consumption when old. Equation 21 says that if one is leaving a positive bequest to the next generation, the marginal utility of one’s own consumption when old should just be equal to the marginal utility of bequests. If the marginal utility of own consumption exceeds the marginal utility of bequests at l_{t, t+1} = 0, the nonnegativity constraint on bequests is binding.

5. Production and factor market equilibrium

A homogeneous durable commodity, that can be used as a private consumption good, a private capital good or a public consumption good is produced by competitive profit-maximizing firms using a production function with constant returns to scale in capital and labor. The production function is twice continuously differentiable, with positive but diminishing marginal products and satisfies the Inada conditions. Let Y_t denote real output in period t. Then

\begin{matrix} Y_{t} = F (K_{t}, 1) = f (K_{t}) \\ f' > 0; f'' < 0; f (0) = 0; \lim_{K \to 0} f' (K) = \infty; \lim_{K \to \infty} f' (K) = 0. \end{matrix} (22)

The marginal product of labor equals the before (income)-tax real wage and the before-tax capital rental rate equals the marginal product of capital.

w_{t} = f (K_{t}) - K_{t} f^{'} (K_{t}) (23)

ρ_{t} = f^{'} (K_{t}) (24)

III. Debt Neutrality, Generational Accounts, Intergenerational Redistribution and Saving Behavior

Consider an initial or reference equilibrium, whose prices and quantities are denoted by a single star. Let $ℓ_{t, t + 1}^{*} > 0$ , that is, generation t is planning to leave a strictly positive bequest to generation t + 1. Now consider a balanced-budget, lump-sum redistribution from generation t to generation t + 1, that is, $Δ r_{t}^{2} = - Δ r_{t + 1}^{1} > 0$ . As long as the value of bequests planned in the original equilibrium by generation t is not less that the increase in the tax on generation $t (ℓ_{t, t + 1}^{*} \geq Δ τ_{t}^{2})$ ) generation t will reduce its bequest to generation t + 1 by the exact amount of the increase in the tax it pays, that is, in the new equilibrium, whose prices and quantities are denoted by double stars, $ℓ_{t, t + 1}^{*} - ℓ_{t, t + 1}^{* *} = Δ τ_{t}^{2} = - Δ τ_{t + 1}^{1} .$ No other real or nominal equilibrium price or quantity will change.

Under the policy experiment just considered, the (public) generational account of generation t, T_{t, t-1} increases by $(\frac{1}{1 + i_{t - 1, t}}) (\frac{P_{t + 1} Δ τ_{t}^{2}}{1 + i_{t, t + 1}})$ and the (public) generational account of generation t + 1, T_{t+1, t-1} falls by the same amount. The (public) generational accounts of all other future generations are unchanged. However, the private generational account of generation t falls by the same amount, $(\frac{1}{1 + i_{t - 1, t}}) (\frac{P_{t + 1} Δ τ_{t}^{2}}{1 + i_{t, t + 1}})$ , as its public generational account increases through a reduction in l_{t, t+1} and the private generational account of generation t + 1, increases by the same amount as its public generational account decreases through that same reduction in l_{t, t+1}. Total lifetime resources available to each generation are invariant under lump-sum redistributions that do alter the public generational accounts. This suggests the following two (obvious) propositions.

Proposition 1: When the conditions for debt neutrality or Ricardian equivalence are satisfied, the generational accounts are uninformative about the effect of the budget on the intergenerational distribution of resources.

Corollary 2: When the conditions for debt neutrality or Ricardian equivalence are satisfied, the generational accounts are uninformative about the effect of the budget on saving.

Strict Ricardian equivalence is a priori and empirically implausible. For some relevant empirical evidence see (Cox and Rank, 1992; Altonji, Hayashi and Kotlikoff, 1992, 1996; Hayashi, 1995). Note that most tests of Ricardian equivalence test (and reject) the null of full Ricardian equivalence. Even if Ricardian equivalence only characterizes a subset of each generation, or if intergenerational transfers through the government budget are only partly offset by changes in private intergenerational transfers, applications of the generational accounts that do not allow for such “partial Ricardian offsets” will lead to exaggerated estimates of the effect of the budget on intergenerational distribution and on national saving. Models of strategic bargaining among generations suggest the possibility that additional transfers toward older cohorts strengthen their bargaining position vis-é-vis the young, creating the paradoxical possibility that private intergenerational transfers may reinforce rather than offset public ones. In this case, the life-cycle model would understate the effect of public intergenerational redistribution on private saving and on the intergenerational distribution of wealth.

IV. Is a Tax Cut Tomorrow as Good as a Government Bond Today?

Consider a world without distortionary taxes and transfers and hold constant the government’s consumption program. For simplicity, money is also omitted in what follows (α₂ = 0). The life-cycle model holds and there is no uncertainty. Under these conditions, an individual’s generational account or lifetime net payment (LNP) to the government

…is a sufficient statistic for the government’s treatment of individuals; any intertemporal equilibrium will be unaffected by changes in the timing of lifetime net payments to the government that leave individual LNPs unchanged (Kotlikoff, 1989).

Uncertainty does not change the validity of this statement as long as markets are complete and the proper state-contingent prices are used to price uncertain future government taxes and transfers.

There are two distinct approaches to the micro foundations of credit rationing and liquidity constraints. The first stresses asymmetric or private information and the associated potential for adverse selection or moral hazard. The second approach emphasizes the importance of the fact that few contracts involve the simultaneous and final exchange of objects of equal value. This creates a key role for third-party enforcement of contracts whenever the net benefits from abiding by the contract vary over the life of the contract and become negative for one party to the contract before they do so for the other party or parties. The two approaches are complementary rather than mutually exclusive.

Since most of the literature has emphasized the asymmetric information motivation for credit rationing, I will elaborate here on the contract enforcement argument.

Within national economies, the owners of human capital are in a position rather similar to that of a sovereign borrower (see e.g., Eaton and Gersovitz, 1981). Ever since the abolition of slavery, of indentured labor and of the debtor’s prison, it has not been possible to attach (to offer a creditor a legally enforceable lien on) future labor income (see e.g., Gavin Wright (1995) for a historical perspective on the inalienability of labor income).

From the point of view of the informativeness of the generational accounts, what matters is that this inalienability of labor income makes future labor income very poor collateral for borrowing. In the most extreme case, considered below, it is impossible to borrow against the security of anticipated future labor income at all.

The example below works because of the key assumption that it is future labor income net of taxes and transfer payments that is inalienable and therefore unsuitable as collateral for consumption loans. In other words, future receipts of government transfer payments are not collateralizable because it is impossible to write a legally binding contract earmarking future welfare checks for the servicing and repayments of consumption loans. While extreme, this assumption is clearly much more realistic than the opposite polar case considered in Hayashi (1987), Yotsuzuka (1987), and Kotlikoff (1989) where it is assumed that a credit-constrained borrower can increase her consumption by the same amount through additional borrowing when she is unexpectedly designated the beneficiary of a future government tax cut or transfer payment worth $100 one period from now, as she would if she unexpectedly discovered today, government bonds under the mattress worth $100/(1 + i) where i is the appropriate risk-free discount rate.

I now consider a very simple example, described in a few words in Hayashi (1987), p. 117, of how aggregate consumption is affected by the government reducing taxes on each of the young of generation t by an amount ξ in period t and raising taxes by an amount ξ(1 + r_{t, t+1}) per capita on the same generation when old in period t + 1.

Each household of generation t maximizes $\ln c_{t}^{1} + α_{1} \ln c_{t}^{2}$ subject to the following constraints:

c_{t}^{1} \leq w_{t} - τ_{t}^{1} (25)

c_{t}^{2} \leq e w_{t + 1} - τ_{t}^{2} + (1 + r_{t, t + 1}) (w_{t} - τ_{t}^{1} - c_{t}^{1}) . (26)

In this example, households work in both periods of their life. The exogenous labor endowments are 1 when young and e when old. The inalienability of after-tax labor income means that the young may face a borrowing constraint: non-human wealth cannot become negative (equation 25). The riskless lending rate for households and the riskless lending and borrowing rate for the government is r.

If the borrowing constraint is nonbinding, the consumption decisions of generation t are as given in equations 27 and 28.

c_{t}^{1} = (\frac{1}{1 + α_{1}}) (w_{t} - τ_{t}^{1} + \frac{e w_{t + 1} - τ_{t}^{2}}{1 + r_{t, t + 1}}) (27)

c_{t}^{2} = (\frac{α_{1} (1 + r_{t, t + 1})}{1 + α_{1}}) (w_{t} - τ_{t}^{1} + \frac{e w_{t + 1} - τ_{t}^{2}}{1 + r_{t, t + 1}}) (28)

If the borrowing constraint is binding, the consumption decisions of the household are as given in equations 29 and 30.

c_{t}^{1} = w_{t} - τ_{t}^{1} . (29)

c_{t}^{2} = e w_{t + 1} - τ_{t}^{2} (30)

It now becomes essential to introduce some within-generation heterogeneity. We therefore assume that there is a constant number N^H of households each period who have a high value, e^H of the old age labor endowment and that a constant number N^L has a low old age labor endowment e^L. We furthermore assume that e^L < 1 < e^H and that e^L is sufficiently far below and e^H sufficiently far above 1 (the labor endowment when young), that the households endowed with e^L are never faced with a borrowing constraint while those endowed with e^H always are.

This means that aggregate consumption at time t, denoted C_t, is given by:

\begin{array}{l} C_{t} = N^{L} (\frac{1}{1 + α_{1}}) (w_{t} - τ_{t}^{1} + \frac{e^{L} w_{t + 1} - τ_{t}^{2}}{1 + τ_{t, t + 1}}) + N^{H} (w_{t} - τ_{t}^{1}) \\ + N^{L} (\frac{α_{1} (1 + r_{t - 1, t})}{1 + α_{1}}) (w_{t - 1} - τ_{t - 1}^{1} + \frac{e^{L} w_{t} - τ_{t - 1}^{2}}{1 + r_{t - 1, t}}) + N^{H} (e^{H} w_{t} - τ_{t - 1}^{2}) . (31) \end{array}

At given interest rates and wage rates, the effect of the debt-financed tax cut of ξ per capita for young members of generation t, combined with the credible’announcement of a future (period t + 1) increase in taxes of ξ(1 + r_{t, t+1}) per capita on members of that same generation t will raise aggregate consumption by N^Hξ, the per capita tax cut times the number of borrowing-constrained members of generation t.

There will obviously be general equilibrium repercussions for equilibrium prices and quantities, but these are not our concern here. The main point is that the generational accounts are not a sufficient statistic for the government’s treatment of individuals. The intertemporal equilibrium will be affected by changes in the timing of lifetime net payments to the government that leave individual generational accounts unchanged. The reason is that the generational accounts discount the future tax increase at the government’s lending and borrowing rate r_{t, t+1}. The riskless interest factor, 1 + r_{t, t+1}, however, is below the marginal rate of intertemporal substitution for the borrowing-constrained households.

The empirical evidence suggests overwhelmingly that liquidity constraints are relevant to the consumption behavior of at least some households. There is no agreement on the quantitative significance of this departure from the life-cycle hypothesis (see e.g., Zeldes, 1989; Shea, 1995; Deaton, 1991; Hajivassiliou and Ioannides, 1995; Cox and Jappelli, 1990, 1993; Cox, 1990).

I summarize this as the following proposition:

Proposition 3: Liquidity constraints or borrowing constraints may cause the timing of the net taxes paid to the government over the lifecycle of a household to matter, in addition to their present value calculated using the government’s discount rate.

V. Government Consumption and Intergenerational Distribution

The proponents of generational accounting do not ignore the “resource exhaustion” aspect of government consumption, but do not attach (intergenerational) distributional significance to the size and composition of the government consumption program.

The potential importance of the issue is recognized in Auerbach, Gokhale and Kotlikoff (1991). Atkinson and Stiglitz (1980) surveying quite a sizable literature on the subject (see especially Musgrave, Case, and Leonard, 1974) suggest that two classes of public (consumption) spending be recognized.

The first consists of goods where particular beneficiaries can (in theory) be identified—“allocable expenditures” -or of broadly publicly provided private goods (e.g., highways and education). The second group consists of “public goods” that cannot be directly allocated to particular individuals (e.g., defense). For allocable goods, the procedure adopted by Musgrave et al. is similar for that for taxes. For example, unemployment insurance benefits are allocated according to receipts from that source…., education expenditure is allocated to the families of students, …. The second group of public goods are simply allocated on three assumptions: (1) in proportion to total income; (2) in proportion to taxes; and (3) equally to all persons.

Not all generations alive during a period benefit equally from government consumption during that period and the distribution across generations of benefits from public consumption will depend on its composition. In this paper, this issue is dramatized by assuming that one form of public consumption, $\begin{matrix} G_{t}^{y} \end{matrix}$ benefits only the young in period t, while the second public consumption good, $\begin{matrix} G_{t}^{0} \end{matrix}$ , benefits only the old in period t. It is therefore possible in our model, while keeping total government consumption constant over time to completely deprive a particular generation (or indeed every other generation) from the benefits of public consumption. For generation t, for instance, this would involve setting $\begin{matrix} G_{t}^{y} = G_{t + 1}^{0} = 0 a n d G_{t}^{0} = G_{t + 1}^{y} = \bar{G} > 0 \end{matrix}$

In practice, both the magnitude and the composition of public consumption vary over time, with potentially important distributional consequences. Conceptually, there is no special problem valuinǵ public consumption. By analogy with the compensating variation of standard consumer theory, we can define the value to a member of generation t of the government’s consumption program during her lifetime ${G_{t}^{y}, G_{t}^{o}, G_{t + 1}^{y}, G_{t + 1}^{o}}$ as the value of the smallest lump-sum transfer payment that would have to be made to this household in order to just compensate it for the loss of the government consumption program (holding constant everything else that is assumed parametric to the individual consumer). Alternatively, we could define, by analogy with the equivalent variation of standard consumer theory, the value to a member of generation t of the government’s consumption program to be the largest lump-sum tax the household would be willing to pay in order not to forego the government’s consumption program. These compensating or equivalent lump-sums would then be summed over all members of a generation, discounted properly and subtracted from the conventional generational accounts of each generation, thus providing us with the true generational accounts.

In practice, of course, the quantification of the welfare consequences of public consumption is likely to be an extremely complicated job. If we throw in the towel, however, we are ignoring the welfare implication of real resources amounting, in most industrial countries, to between 20 percent and 30 percent of GDP.

We can summarize this Section with the following proposition:

Proposition 4: The generational accounts do not recognize the intergenerational distributional implications of the government consumption program. This limits their usefulness as a guide to budgetary policy that is intergenerationally neutral or fair.

VI. Incidence and Other Unpleasant General Equilibrium Repercussions

Having made the point about Ricardian equivalence, we assume in’what follows that the life-cycle model applies (δ = 0 or no intergenerational gift motive). Money is also omitted in what follows {α₂ = 0). The tax structure is simplified even further by assuming that labor income is not taxed. The only taxes (transfers) considered are a lump-sum tax on the young, a lump-sum tax on the old, and either a proportional tax, at a rate τ^K_t, on just the rental income from capital (in example 1) or a proportional tax on all asset income, at a rate τ_t^A (in example 3). The government budget is balanced, there is no public debt and no public consumption spending.

Consider the case of a tax on capital income, first analyzed in an OLG model by Diamond (1970), see also Atkinson and Stiglitz (1980). Since the after-tax rate of return on capital equals the real interest rate we have:

τ_{t, t + 1} = (1 - τ_{t + 1}^{κ}) ρ_{t + 1} . (32)

The model can be summarized in the following two equations:

\begin{array}{l} (\frac{α_{1}^{\frac{1}{η}} {(1 + f^{'} (K_{t + 1}) (1 - τ_{t + 1}^{κ}))}^{\frac{1 - η}{η}}}{1 + α_{1}^{\frac{1}{η}} {(1 + f^{'} (K_{t + 1}) (1 - τ_{t + 1}^{κ}))}^{\frac{1 - η}{η}}}) (f (K_{t}) - K_{t} f^{'} (K_{t}) - τ_{t}^{1}) \\ + (\frac{1}{1 + α_{1}^{\frac{1}{η}} {(1 + f^{'} (K_{t + 1}) (1 - τ_{t + 1}^{κ}))}^{\frac{1 - η}{η}}}) (\frac{τ_{t}^{2}}{1 + f^{'} (K_{t + 1}) (1 - τ_{t + 1}^{κ})}) = K_{t + 1} (33) \end{array}

τ_{t}^{1} + τ_{t - 1}^{2} + τ_{t}^{κ} f^{'} (K_{t}) K_{t} = 0 . (34)

The generational account of generation t—1 is given in equation 35, that of generation t in equation 36. All future generations are like generation t, with the appropriate discounting to the beginning of period t.

T_{t - 1, t - 1} = (\frac{τ_{t - 1}^{2} + τ_{t}^{κ} f^{'} (K_{t}) K_{t}}{1 + f^{'} (K_{t}) (1 - τ_{t}^{κ})}) (35)

T_{t, t - 1} = (\frac{1}{1 + f^{'} (K_{t}) (1 - τ_{t}^{κ})}) (τ_{t}^{1} + \frac{τ_{t}^{2} + τ_{t + 1}^{κ} f^{'} (K_{t + 1}) K_{t + 1}}{1 + f^{'} (K_{t + 1}) (1 - τ_{t + 1}^{κ})}) (36)

In examples 1 and 2, we also assume that η = 1 (logarithmic preferences over private goods).

Example 1: Nothing registers in the generational accounts, but potentially significant changes occur in the pre- and post-tax distribution of life-time resources among generations.

In this example, it is assumed that $\begin{matrix} τ_{t}^{1} = 0 \end{matrix}$ . We also assume that the increase in τ^K is evaluated at τ^K = 0. From the government budget identity, this implies that the capital income tax is refunded to the old (who are paying the tax) through lump-sum taxes, that is $τ_{t}^{2} = - τ_{t + 1}^{κ} f^{'} (K_{t + 1}) K_{t + 1} .$ .

The impact effect of an increase in $\begin{matrix} τ_{t + 1}^{k} o n K_{t + 1} \end{matrix}$ is given by:

\frac{d K_{t + 1}}{d τ_{t + 1}^{κ}} = - \frac{f^{'} (K_{t + 1}) K_{t + 1}}{(1 + α_{1}) (1 + f^{'} (K_{t + 1}))} . (37)

As expected, an increase in the capital income tax rate refunded to the taxpayers as a lump-sum benefit, reduces the saving of the young in period t + 1 (and of all future generations) for standard life-cycle reasons. This reduces the equilibrium capital-labor ratio in the short run. Given a diminishing marginal product of capital, this will raise the before-tax capital rental rate. The effect on the after-tax capital rental rate is obtained from equations 32 and 37.

\frac{d τ_{t, t + 1}}{d τ_{t + 1}^{κ}} = - f^{'} (K_{t + 1}) (1 + \frac{f^{"} (K_{t + 1}) K_{t + 1}}{(1 + α_{1}) (1 + f^{'} (K_{t + 1}))}) (38)

It is clear from 38 that the after-tax capital-rental rate will increase with the tax rate on capital rental income if:

\frac{- f^{"} (K_{t + 1}) K_{t + 1}}{(1 + α_{1}) (1 + f^{'} (K_{t + 1}))} > 1 . (39)

This will occur for a low enough elasticity of substitution between labor and capital. The local stability condition for the model is:

\frac{- α_{1} K_{t} f^{"} (K_{t})}{1 + α_{1}} < 1 . (40)

Thus, even if the model is dynamically efficient (f′(K) > 0 which will be the case in our model because of the Inada conditions and the assumption that the natural rate of growth is zero), both 39 and 40 can be satisfied. If the model is dynamically inefficient (which would be possible if our model were extended to allow for a positive rate of growth of efficiency labor), there is a larger set of parameter values for which both 39 and 40 are satisfied.

Considering the effect of an increase in τ^K on the steady-state capital-labor ratio $\bar{K}$ and the steady-state after-tax rental rate, $\begin{matrix} \bar{ρ} \end{matrix}$ we find that:

\frac{d \bar{K}}{d τ^{κ}} = (\frac{- 1}{1 + α_{1}}) (\frac{1}{1 + f^{'} (\bar{K})}) [\frac{f^{'} (\bar{K}) \bar{K}}{(\frac{α_{1}}{1 + α_{1}}) \bar{K} f^{"} (\bar{K})}] (41)

and

\frac{d \bar{τ}}{d τ^{κ}} = \frac{- f^{'} (\bar{K}) [f^{"} (\bar{K}) \bar{K} (α_{1} [1 + f^{'} (\bar{K})]) + (1 + α_{1}) [1 + f^{'} (\bar{K})]]}{(1 + α_{1}) [1 + f^{1} (\bar{K})] (\frac{α_{1}}{1 + α_{1}}) \bar{K} f^{"} (\bar{K})} . (42)

Assuming local stability, the denominators of 41 and 42 are positive. Thus, in the long-run, an increase in the capital income tax rate refunded as lump-sum transfers to the old paying the tax reduces the capital-labor ratio. Again, a low enough value of the elasticity of substitution between labor and capital could result in the after-tax rate of return to capital rising.

The generational accounts for this economy will show zero for all generations, before and after the increase in the capital income tax. If the economy is dynamically efficient, the increase in the capital income tax rate from an initial value of zero will cause efficiency losses as well as welfare losses for at least one generation. Assume the increase in the tax rate is unanticipated and starts in period t + 1. The old in period t + 1 are not affected at all. Next period and forever after, the capital-labor ratio will be less that it would otherwise have been. Real wages are lower for each generation, starting with the one born in period t + 1. If the after-tax rate of return is lower than it would have been without the tax rate increase, all generations starting with those born in period t + 1 are worse off: their new intertemporal budget constraint lies strictly inside the old one. If the after-tax rate of return is higher, it is possible that some, but not all, generations starting with t + 1 are better off. The key point is that fiscal policy here works entirely outside the generational accounts. Yet fiscal policy certainly influences the life-time private consumption opportunities of the various generations by changing the post-tax labor income and the intertemporal terms of trade faced by successive generations.

Example 2. Changes in equilibrium factor returns reinforce the intergenerational redistribution recorded in the generational accounts.

The second example is a lump-sum redistribution from the old to the young (a reverse unfunded social security retirement scheme). We now assume $\begin{matrix} τ_{t}^{k} = 0, \end{matrix}$ and $\begin{matrix} τ_{t}^{1} = - τ_{t - 1}^{2} . \end{matrix}$ The introduction of the scheme in period t + 1 is unexpected and permanent. We evaluate the increase in τ² from an initial value τ² = 0.

The generational accounts of equations t and t + 1 from period t + 1 (discounted to the end of period t) on are given below in equations 43 and 44.

T_{t, t} = \frac{τ_{t}^{2}}{1 + f^{'} (K_{t + 1})} (43)

T_{t + 1, t} = \frac{1}{1 + f^{'} (K_{t + 1})} (- τ_{t}^{2} + \frac{τ_{t + 1}^{2}}{1 + f^{'} (K_{t + 2})}) (44)

The short-run effect of an increase in $\begin{matrix} τ_{t}^{2} \end{matrix}$ on the capital-labor ratio is given in equation 45, the long run effect in equation 46.

\frac{d K_{t + 1}}{d τ_{t}^{2}} = (\frac{1}{1 + α_{1}}) (\frac{1}{1 + f^{'} (K_{t + 1})}) > 0 (45)

\frac{d \bar{K}}{d τ^{2}} = (\frac{1}{1 + α_{1}}) (\frac{1}{1 + f^{'} (\bar{K})} + α_{1}) [\frac{1}{(\frac{α_{1}}{1 + α_{1}}) \bar{K} + f^{"} (\bar{K})}] (46)

In period t, the young receive a larger transfer and anticipate a higher tax when old. This raises their saving and thus next period’s capital stock. In the long-run, this effect is reinforced because each generation, in addition to saving part of the increase in period 1 transfer income, now also reduces its consumption while young in anticipation of the higher taxes when old. The saving rate of the young therefore rises unambiguously in the short-run and in the long-run; the capital stock in period t + 1 and the long-run capital-labor ratio increase.

It is clear that the old in period t + 1 are unambiguously worse off. At given factor prices, the increase in τ² will raise the permanent income of all generations beginning with t + 1 if the economy is dynamically efficient. The young in period t + 1 will enjoy a higher wage because of the larger capital stock inherited by the economy. The interest rate they face will be lower than in the counterfactual scenario without the redistribution to the young. If their tastes are skewed sufficiently towards early consumption (if α₁ is small enough), generation t + 1 is unambiguously better off. All subsequent generations in addition have a higher wage than they would have had without the tax-transfer scheme. With sufficiently low α₁, they will all be better off.

From equations 43 and 44, it is clear that the generational accounts only register the effects on the intergenerational distribution of life-time resources of the direct redistribution at given factor prices. The general equilibrium repercussions of the policy change can be decomposed as follows. First, there is the effect of the endogenous response of the interest rate (which declines) on the present value of lifetime taxes net of transfers. This effect is absent when we consider an infinitesimal change in τ² from an initial value of 0. Second, there is the positive effect of the lump-sum intergenerational redistribution on the equilibrium wage rate. Neither effect is captured by the generational accounts. In this example, the intergenerational distributional consequences of the general equilibrium repercussions on real wages and interest rates reinforce the distributional effects of the initiating lump-sum tax-transfer change itself.

Example 3. The intergenerational redistribution recorded in the generational accounts is counteracted by changes in equilibrium factor incomes.

For this example, we change the distortionary tax on capital income to a proportional tax rate $τ_{t}^{A}$ on all asset income. All revenues from the asset income tax are paid as a lump-sum transfer payment to the young. We also assume $τ_{t}^{2} = 0$ and $τ_{t}^{2} = 1 τ_{t}^{A} f' (K_{t}) K_{t}$ for all t. The model can be reduced to equation 47. The intertemporal elasticity of substitution can be different from 1.

({\frac{α_{1}^{\frac{1}{η}} (1 + f' (k_{t + 1}) (1 - τ_{t + 1}^{A}))^{\frac{1 - η}{η}}}{1 + α_{1}^{\frac{1}{η}} (1 + f' (K_{t + 1}) (1 - τ_{t + 1}^{A}))^{\frac{1 - η}{η}}}) (f (k_{t}) - k_{t f'} (k_{t}) + τ_{t}^{A} f' (K_{t}) K_{t}) = K_{t + 1} (47)}^{}

Consider an unanticipated, permanent increase in the asset tax rate, starting in period t. The effect on K_t+1 comes through two channels. The first is the intergenerational redistribution effect, given in 48. Since the asset tax imposed in period t was unanticipated, it is effectively a lump-sum tax on the old in period t; since the tax is redistributed to the young in period t, their saving will increase.

\frac{\partial K_{t + 1}}{\partial τ_{t}^{A}} = Ω Ξ f^{'} (K_{t}) K_{t} > 0 (48)

where Ω is positive if the model is locally stable and Ξ is always positive.

The second channel is the intertemporal substitution channel. It will reduce saving by the young in period t if and only if η > 1. It is given in equation 49.

\frac{\partial K_{t + 1}}{\partial τ_{t + 1}^{A}} = Ω Θ f^{'} (K_{t + 1}) [w_{t} + τ_{t}^{A} f^{'} (K_{t}) K_{t}] < 0 i . f . f . Θ < 0 (49)

where Θ is negative if and only if η < 1.

The short-run effect of an increase in both $\begin{matrix} τ_{t}^{A} a n d τ_{t + 1}^{A} \end{matrix}$ on K_t+1 is the sum of the effects given in 48 and 49, given in 50. It will be negative provided η is sufficiently below 1.

\frac{\partial K_{t + 1}}{\partial τ_{t}^{A}} + \frac{\partial K_{t + 1}}{\partial τ_{t + 1}^{A}} = Ω (Ξ f^{'} (K) K + Θ f^{'} (K) [w + τ^{A} f^{'} (K) K]) (50)

The long-run effect of the asset income tax rate increase, with the proceeds transferred lump-sum to the young are given in equation 51.

\frac{d \bar{K}}{d τ^{A}} = \hat{Ω} (Ξ f^{'} (\bar{K}) \bar{K} + Θ f^{'} (\bar{K}) [w + τ^{A} f^{'} (\bar{K}) \bar{K}]) (51)

where $\hat{Ω}$ is positive if the model is locally stable.

As shown in equation 50, a necessary condition for the impact effect on the capital-labor ratio (and therefore on the period t + 1 wage) to be negative is that the intertemporal substitution effect be negative, which will be the case if, and only if, the intertemporal elasticity of substitution $\frac{1}{η}$ has a value larger than 1. In addition, the negative intertemporal substitution effect has to dominate the positive intergenerational redistribution effect. The long-run effect on the capital-labor ratio and on the real wage can also be negative under very similar conditions (see equation 51). We now consider the distributional consequences when these conditions are satisfied.

The old in period t are obviously worse off. The young in period t face a predetermined real wage and receive the lump-sum transfer payment. If the after-tax rate of return to saving they face declines as a result of the increase in τ^A_t and τ^A_t+1, they too may be worse off, despite the receipt of the transfer payment, if they are sufficiently patient (have a high enough value of α₁). All later generations still receive the lump-sum payment while young, but now have a lower real wage than they would have had without the increase in the asset income tax rate. It is possible that their disposable income while young actually falls (for a high enough intertemporal elasticity of substitution). If disposable income while young falls for generations later than t, then a lower after-tax rate of interest is sufficient for them to be worse off. Even if the after-tax rate of return increases, they will be worse of if they are sufficiently impatient (small values for α₁).

The generational accounts for the old and the young in period t are given below. All generations born after period t have generational accounts like the one for generation t.

T_{t - 1, t - 1} = \frac{τ_{t}^{A} f^{'} (K_{t}) K_{t}}{1 + f^{'} (K_{t})} (52)

T_{t, t - 1} = (\frac{1}{1 + f^{'} (K_{t})}) [- τ_{t}^{A} f^{'} (K_{t}) K_{t} + (\frac{1}{1 + f^{'} (K_{t + 1})}) τ_{t + 1}^{A} f^{'} (K_{t + 1}) K_{t + 1}] (53)

It is clear that, for generations t and later, changes in the generational accounts at constant factor prices may be offset by endogenous changes in factor returns.

One response to the “general equilibrium” critique in this paper of the use made of generational accounts is that changes in factor prices and incomes and other (“tax avoidance”) behavioral responses to redistributive fiscal policy changes are likely to occur gradually over a number of decades. This slow response, coupled with the fact that future taxes and transfers are discounted when computing generational accounts, implies that most of the fiscally induced wealth redistribution would be accounted for by the unadjusted present value of the direct effect of the policy change. Factor price changes and tax avoidance are, therefore, likely to account for only a minor fraction of the total wealth distribution.

I consider this to be an unconvincing argument on a number of counts. First, recent simulation studies by Fehr and Kotlikoff (1995) using the Auerbach and Kotlikoff 55-generation overlapping generations model (Auerbach and Kotlikoff, 1987) support the position that the tax-transfer side of the budget can have significant general equilibrium effects through medium-term and long-run changes in the capital-labor ratio⁵. These effects are especially dramatic in a small open economy with perfect international financial capital mobility and equalization of the after-tax marginal product of capital and the rate of interest. An increase in the (source-based) capital income tax rate will leave the after-tax rate of return to capital unaffected. The before-tax marginal product of capital rises (through a reduction in the capital-labor ratio) to offset the increase in the capital income tax rate. The incidence of the capital income tax in this case falls entirely on labor (the young). The generational accounts miss this completely.

Second, current and anticipated future budgetary policy changes can instantaneously change the valuation of existing real and financial capital assets, even if any significant response of the quantities of these assets is delayed (as it would be e.g. in the case of physical capital assets subject to strictly convex costs of adjustment). Note that while, in the absence of adjustment costs, installed capital trades at its current reproduction cost, capital gains or losses on financial claims (such as fixed interest securities with a positive maturity) can occur even when there are no adjustment costs and when the securities in question are traded in frictionless, efficient financial markets⁶. Such capital gains or losses are not, in general, reflected in the generational accounts.

I want to end, though, on a positive note concerning generational accounts. I firmly believe, that the data that go into the construction of generational accounts are worth collecting and that they are an essential input into any informed discussion of the intergenerational distributional consequences of alternative budgetary policies. However, without the aid of a numerical model of the economy, it is impossible to extract and interpret the message in the generational accounts.

Proposition 5: Generational accounts do not measure the general equilibrium repercussions on tax and transfer bases of changes in budgetary policy nor do they allow for the general equilibrium effects of such policy changes on before-tax factor incomes and on key static and intertemporal relative prices. The generational accounts can only be interpreted with the help of a fully articulated model of the economy.

VII. Conclusion

Our simple general equilibrium model ignored intergenerational externalities as a potentially important dimension of intergenerational transmission and redistribution. Intergenerational externalities are the external effects of the consumption, investment, R&D, production, resource extraction and human capital accumulation activities of current generations on the wealth and well-being of future generations. These externalities are not priced properly in the available markets. Neither are they recorded in the government budget. Environmental pollution, ozone depletion, deforestation, desertification, greenhouse effects, and reductions in biodiversity are examples of negative.

intergenerational externalities. Increases in the stock of knowledge generated either as the result of purposeful activity or as the unintended by-product of other activities are examples of positive intergenerational externalities. Budgetary policy, both the expenditure and the revenue sides of the government budget, influence the transmission of these intergenerational externalities. In principle, the conventional generational accounts could be turned into full-fledged “green” and “knowledge-aware” generational accounts by pricing the intergenerational externalities along the lines suggested for public consumption in Section 5.

There are three main conclusions: (1) The informativeness of generational accounts for the effect of the budget on private behavior and welfare, and thus their usefulness in budgetary policy evaluation or design lives or dies with the life-cycle model of consumption; (2) even if the life-cycle of consumption is valid, there is no straightforward interpretation of the generational accounts unless there are no significant general equilibrium effects of budgetary policy on the tax and transfer bases and on before-tax and before-transfer incomes, that is, unless incidence questions can be ignored;.and (3) before any conclusion can be reached about the effect of the budget on intergenerational distribution and welfare, it is necessary to allow for the intergenerational distribution of the benefits from public consumption and for the impact of the budget on the transmission of intergenerational externalities.

Despite these three cautionary reminders of potential pitfalls in the use and interpretation of generational accounts, I consider the construction of generational accounts to be a valuable enterprise that will benefit all researchers interested in saving behavior or in the effect of the budget on the intergenerational distribution of private resources. However, without (1) explicit consideration of the intergenerational distributional implications of the government consumption program; (2) convincing evidence that the life-cycle model adequately characterizes private consumption behavior; and (3) a fully articulated model of the general equilibrium repercussions of budgetary policy (including possible intergenerational external effects), the generational accounts do not speak clearly. Indeed they barely whisper, and what they whisper could be misleading.

References

Altonji, J., F. Hayashi, and L.J. Kotlikoff, “Are Extended Families Altruistically Linked? Direct Tests Using Micro Data” American Economic Review Vol. 82 (December 1992) pp. 1177–98.
- Search Google Scholar
- Export Citation
Atkinson, Anthony B., and Joseph E. Stiglitz, Lectures on Public Economics (New York: McGraw-Hill Book Company 1980).
- Search Google Scholar
- Export Citation
Auerbach, Alan J., Jagadeesh Gokhale, and Laurence J. Kotlikoff, “Generational Accounts, A Meaningful Alternative to Deficit Accounting” NBER Working Paper No. 3589, January, published in David Bradford ed. (1991) Tax Policy and the Economy Vol. 5, (Cambridge: National Bureau of Economic Research and the MIT Press 1991).
- Search Google Scholar
- Export Citation
Auerbach, Alan J., “Generational Accounting: A New Approach to Understanding the Effects of Fiscal Policy on Saving” Scandinavian Journal of Economics Vol. 94, No. 2 (1992) pp. 303–19.
- Search Google Scholar
- Export Citation
Auerbach, Alan J., “Generational Accounting: A Meaningful Way to Evaluate Fiscal Policy” Journal of Economic Perspectives Vol. 8, (1994) pp. 73–94.
- Search Google Scholar
- Export Citation
Auerbach, Alan J., and Laurence J. Kotlikoff, Dynamic Fiscal Policy (New York: Cambridge University Press, 1987).
- Search Google Scholar
- Export Citation
Bohn, Henning, “Budget Deficits and Government Accounting” Carnegie Rochester Conference Series on Public Policy No. 37 (December 1992,) pp. 1–84.
- Search Google Scholar
- Export Citation
Buiter, Willem H., “Measurement of the Public Sector Deficit and Its Implications for Policy Evaluation and Design” Staff Papers IMF Vol. 30 (Washington)(June 1983) pp. 306–49.
- Search Google Scholar
- Export Citation
Buiter, Willem H., “A Guide to Public Sector Debt and Deficits” Economic Policy Vol. 1 (November 1983) pp. 13–79.
- Search Google Scholar
- Export Citation
Buiter, Willem H., “Debt Neutrality, Redistribution and Consumer Heterogeneity: A Survey and Some Extensions” in Willem H. Buiter Principles of Budgetary and Financial Policy (Cambridge, Massachusetts: MIT Press 1990) pp. 183–222.
- Search Google Scholar
- Export Citation
Buiter, Willem H., “Generational Accounts, Aggregate Saving and Intergenerational Distribution” NBER Working Paper No. 5087 (April 1995).
- Search Google Scholar
- Export Citation
Buiter, Willem H., and Kenneth M. Kletzer, “Ponzi Finance, Government Solvency and the Redundancy or Usefulness of Public Debt” Revised Version, Mimeo (New Haven: Yale University April 1994).
- Search Google Scholar
- Export Citation
Cox, Donald C., “Intergenerational Transfers and Liquidity Constraints” Quarterly Journal of Economics Vol. 105 (February 1990) pp. 187–217.
- Search Google Scholar
- Export Citation
Cox, Donald C., and Tullio Jappelli, “Credit Rationing and Private Transfers: Evidence from Survey Data” Review of Economic Studies Vol. 72 (August 1990) pp. 445–54.
- Search Google Scholar
- Export Citation
Cox, Donald C., “The Effect of Borrowing Constraints on Consumer Liabilities” Journal of Money, Credit and Banking Vol. 25 (May 1993) pp. 197–213.
- Search Google Scholar
- Export Citation
Cox, Donald C., and Mark R. Rank, “Inter-vivos Transfers and Intergenerational Exchange” Review of Economics and Statistics Vol. 74 (May 1992) pp. 305–14.
- Search Google Scholar
- Export Citation
Deaton, Angus, “Saving and Liquidity Constraints” Econometrica Vol. 59 (September 1991) pp. 1221–48.
- Search Google Scholar
- Export Citation
Diamond, Peter, “Incidence of an Interest Income Tax” Journal of Economic Theory Vol. 2 (1970) 211–24.
- Search Google Scholar
- Export Citation
Drazen, Allan, “Problems of Government Accounting: A Comment” Carnegie Rochester Conference Series on Public Policy No. 37 (December 1992) pp. 85–92.
- Search Google Scholar
- Export Citation
Eaton, Jonathan, and Mark Gersovitz, “Debt With Potential Repudiation: Theoretical and Empirical Analysis” Review of Economic Studies Vol. 48 No. 152 (1981a) pp. 289–309.
- Search Google Scholar
- Export Citation
Fehr, Hans, and Laurence J. Kotlikoff, “Generational Accounting in General Equilibrium,” NBER Working Paper No. 5090 (April 1995).
- Search Google Scholar
- Export Citation
Hajivassiliou, Vassilis, and Yannis M. loannides, “Unemployment and Liquidity Constraints” Cowles Foundation Discussion Paper No. 1090 (January 1995).
- Search Google Scholar
- Export Citation
Hayashi, Fumio, “Tests for Liquidity Constraints: A Critical Survey and Some New Observations,” Chapter 13 in Truman F. Bewley ed., Advances in Econometrics Fifth World Congress Vol. II, (Cambridge: Cambridge University Press 1987), pp. 91–120.
- Search Google Scholar
- Export Citation
Hayashi, Fumio, “Is the Japanese Extended Family Altruistically Linked? A Test Based on Engel Curves” Journal of Political Economy Vol. 103 (June 1995) pp. 661–74.
- Search Google Scholar
- Export Citation
Hayashi, Fumio, J. Altonji and L.J. Kotlikoff, “Risk Sharing Between and Within Families” Econometrica, forthcoming (1996).
- Search Google Scholar
- Export Citation
Kotlikoff, Laurence J., “From Deficit Delusion to The Fiscal Balance Rule: Looking for an Economically Meaningful Way to Assess Fiscal Policy” NBER Working Paper No. 2841 (February 1989).
- Search Google Scholar
- Export Citation
Kotlikoff, Laurence J., Generational Accounting: Knowing Who Pays, and When, for What We Spend (New York: The Free Press 1992).
- Search Google Scholar
- Export Citation
Musgrave, Richard A., K.E. Case, and H. Leonard, “The Distribution of Fiscal Burdens and Benefits” Public Finance Quarterly Vol. 2 (1974) pp. 259–311.
- Search Google Scholar
- Export Citation
Shea, John, “Myopia, Liquidity Constraints and Aggregate Consumption: A Simple Test” Journal of Money Credit and Banking Vol. 27 (August 1995) pp. 798–805.
- Search Google Scholar
- Export Citation
Wright, Gavin, “The Origins and Economic Significance of Free Labor in America” mimeo, Faculty of Economics and Politics, University of Cambridge (1995).
- Search Google Scholar
- Export Citation
Yotsuzuka, Toshiki, “Ricardian Equivalence in the Presence of Capital Market Imperfections” Journal of Monetary Economics, Vol. 20 (1987) pp. 411–36.
- Search Google Scholar
- Export Citation
Zeldes, Stephen P., “Consumption and Liquidity Constraints: An Empirical Investigation” Journal of Political Economy, Vol. 97 (April 1989) pp. 305–46.
- Search Google Scholar
- Export Citation

Willem H. Buiter is a professor of international macroeconomics at the University of Cambridge. The author would like to thank Vito Tanzi and Sheetal K. Chand for enabling him to spend five productive and pleasant weeks as a visiting scholar in the Fiscal Analysis Division of the Fiscal Affairs Department at the International Monetary Fund in the summer of 1994, when the first version of this paper was written. The author received helpful comments on earlier versions of this paper during seminars at the International Monetary Fund, at the University of Cambridge and at the London School of Economics (LSE), especially from Beth Allen, David Newbery, Hashem Pesaran, Alan Marin, Jay Sri Dutta, Ralph Turvey, and Tony Venables.

This paper is a comprehensive revision of Buiter (1995). This paper will be forthcoming in the Economica.

By Ricardian gift motive, I mean the following: (1) the utility of other generations positively affects my utility; (2) there is no strategic behavior among the generations.

There may be incomplete market participation, because both the unborn and the dead will clearly have trouble participating in transactions today.

Fehr and Kotlikoff only consider examples of fiscal policy changes in which the general equilibrium repercussions reinforce the direct effects reflected in the generational accounts, like example 2 of this paper.

Fehr and Kotlikoff (1995) appear to be confused on this issue, see especially pp. 20-21.

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Generational Accounts, Aggregate Savings, and Intergenerational Distribution

Author: Mr. Willem H. Buiter

Volume/Issue:: Volume 1996: Issue 076

Publisher:: International Monetary Fund

ISBN:: 9781451849820

ISSN:: 1018-5941

Pages:: 32

DOI:: https://doi.org/10.5089/9781451849820.001

Keywords
I. Introduction
II. A Simple Two-Period Overlapping Generations Model
III. Debt Neutrality, Generational Accounts, Intergenerational Redistribution and Saving Behavior
IV. Is a Tax Cut Tomorrow as Good as a Government Bond Today?
V. Government Consumption and Intergenerational Distribution
VI. Incidence and Other Unpleasant General Equilibrium Repercussions
VII. Conclusion
References

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Abstract

I. Introduction

II. A Simple Two-Period Overlapping Generations Model

1. The household accounts

2. Generational accounts

3. The government account

4. Private consumption behavior

5. Production and factor market equilibrium

III. Debt Neutrality, Generational Accounts, Intergenerational Redistribution and Saving Behavior

IV. Is a Tax Cut Tomorrow as Good as a Government Bond Today?

V. Government Consumption and Intergenerational Distribution

VI. Incidence and Other Unpleasant General Equilibrium Repercussions

VII. Conclusion

References

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