# Altruism, deficit policies, and the wealth of future generations.

I. INTRODUCTION

There is now a substantial body of evidence suggesting that altruistic financial bequests are zero for the vast majority of households.(1) Other studies seem to indicate that the financial bequests which are made, are not likely to be altruistically motivated.(2) While this evidence against the importance of altruistic financial bequests seems reasonably convincing, it is by no means clear that the importance of altruism per se has been dismissed.(3) For example, the results reported in Altonji, Hayashi, and Kotlikoff [1992, Tables 14-17] indicate that extended- family resources, while not perfectly linked to own resources, are important for explaining own consumption. The authors do not reject the notion that substantial altruistically motivated transfers occur in the U.S. Rather, they suggest the altruistically motivated transfers which are made take the form of less than fully efficient human capital transfers to children.

If most altruistic transfers do take place via educational expenditures, how does this affect the Ricardian equivalence theorem? Robert Barro [1974; 1989] argues the presence of any altruistic transfer is sufficient to guarantee that intergenerational transfers caused by government policy are neutral. Other forms of intergenerational transfers, such as inter vivos gifts to children, support of children's education, and so on, can work in a similar manner. Therefore, the Ricardian results will hold even if many persons leave little in the way of formal bequests [1989, 41].(4)

An alternative view, however, is expressed by Allan Drazen [1978]. He argues if parents possess an insufficient mix of wealth and altruism, intergenerational transfers could be exhausted before the efficient level of human capital investment is achieved. If explicit or implicit loans between parents and children are not possible, then the government may be able to improve welfare by generating intergenerational transfers from children to parents.(5) A cut in the parents' tax burden, and an equal present value increase in the tax on the next generation, is equivalent to a government-enforced loan at the going market interest rate. Since educational expenditures are inefficiently low, the return on human capital investment exceeds the loan rate. Therefore, parents could put an amount less than the tax cut into their children's education, and still leave the children with enough additional income to pay for the future tax increase. Thus, a deficit policy serves to expand the consumption possibility set of the family. Viewed in this way, Drazen [1978, 514, footnote 7] imagines an argument for a Pareto optimal level of public debt issue.(6)

A third possibility was identified by Nerlove, Razin and Sadka [1988], who conduct the most explicit analysis of government transfers in an economy with altruistic but financial bequest- constrained households. They also find a transfer or implicit "loan" to parents, from their children, will make the parents unambiguously better-off. However, they were the first to point out that a deficit policy may lower the welfare of the children (although they fail to explain why). Thus, even in the presence of altruistic transfers from parents to children, the effect of deficits on the consumption of future generations is far from clear.

In this paper we wish to clarify the effect of intergenerational transfers on bequest-constrained families. The next section intuitively explains why a government loan or deficit policy generates an ambiguous effect on the children's consumption, even though altruistic parents are fully capable of making both generations better off after the loan. We also identify the key structural determinants of the change in the children's wealth due to the loan. In section III, we extend the simple model of section II to a more quantitatively realistic multi-period, life-cycle simulation model of a bequest-constrained household. The simulation model is then used in section IV to examine how a government intergenerational transfer affects the consumption of each generation under various settings of the key structural determinants identified in section II. The results suggest that deficits can hurt future generations, even if they are members of altruistic families linked by private transfers for human capital. Section V goes a step further and demonstrates that the majority of current voters favor such policies, despite their negative impact on the family's children. Thus, the popular view of generation fighting is not necessarily precluded by the presence of altruistically motivated private transfers.

II. THE THEORY

Consider the following simple model of intergenerational wealth transmission, previously analyzed by Becker and Tomes [1979], Davies [1986], Nerlove, Razin and Sadka [1988] and Rangazas [1991b]. This model is sufficiently rich to articulate the factors leading to the ambiguous effects of deficit policies on the consumption of future generations. Let each period represent a generation. During the period, a family has one child. The parents are altruistic in the sense that the child's lifetime wealth, [W.sub.t+1], gives them satisfaction.(7) Parents choose own lifetime consumption, [c.sub.t], human capital expenditures on the child, [x.sub.t], and a financial bequest, [B.sub.t], to maximize lifetime utility. The constraints include parental wealth, [W.sub.t], the child's human capital production function, h, as well as child's lifetime budget constraint.

Formally, the current generation maximizes

(1) [V.sup.t] = U([c.sub.t], [W.sub.t+1])

subject to

(2.1) [c.sub.t] + [x.sub.t] + [p.sub.t][B.sub.t] = [W.sub.t]

(2.2) [c.sub.t+1] + [x.sub.t+1] + [p.sub.t+1][B.sub.t+1] = [w.sub.t+1]h([x.sub.t]) + [B.sub.t]

(2.3) [B.sub.t] [is greater than or equal to] 0

where [p.sub.t] = [(1 + [r.sub.t+1]).sup.-1] is the price of making a transfer of net wealth to the child, [w.sub.t+1] is the wage rate per unit of human capital, and h is a strictly concave and increasing human capital production function. The necessary conditions for a maximum are

(3.1) [U.sub.1] = [Mu]

(3.2) [U.sub.2][w.sub.t+1]h[prime] = [Mu]

(3.3) [U.sub.2] [is less than or equal to] [Mu][p.sub.t]

where [Mu] is a Lagrange multiplier. A family is said to be bequest constrained if [U.sub.2] [is less than] [Mu][p.sub.t]; the benefit of a financial bequest is less than the cost. This implies [w.sub.t+1]h[prime] [is greater than] 1 + [r.sub.t+1], so that all bequests are made in human form, with [B.sub.t] set equal to zero. Inefficiently low levels of human capital expenditures are being made due to an insufficient mix of parental wealth and concern for the next generation. In this case, household behavior is characterized by solving (3.1) and (3.2) simultaneously for [c.sub.t] and [x.sub.t]. Ricardian equivalence will not hold if financial bequests are zero, despite the presence of positive human capital transfers. For a bequest-constrained household, an intergenerational redistribution of wealth toward the current generation will increase [x.sub.t]; since the shadow price of future wealth in (3.2), [U.sub.2]/[U.sub.1], rises everything else constant.

A sketch of the model is given in Figure 1.(8) The next generation's wealth is plotted on the vertical axis, and the current generation's consumption is plotted on the horizontal axis. The curve labelled FD depicts the tradeoff between [W.sub.t+1] and [c.sub.t], assuming all intergenerational transfers take the form of human capital expenditures. At point D, no discretionary transfers are made by parents, and the children's wealth reflects only exogenous human capital inputs or exogenous wealth transfers. Altruistic parents will begin planning their transfers as human capital investments which cause the next generation's wealth to increase up along the FD curve. The curve is strictly concave due to the assumption of decreasing returns to scale in human capital production. If the parents' altruism is sufficiently strong, their total planned transfers will push them to point A, where 1 + r = [w.sub.t+1]h[prime]. If any additional transfers are planned beyond A, they will take the form of investment in physical, rather than human, capital. Thus, the effective budget constraint for the family is ED. A bequest-constrained family is one where the optimal choice of the parents places them at a point to the right of A, such as B.

Now imagine a lump-sum reduction in the tax burden of the current generation by one unit, paid for by an increase in the tax burden of the next generation by 1 + r units. Everything else constant, the policy will shift each point on ED one unit to the right and 1 + r units down. This shifts the family's possibilities frontier to ED[prime]. As pointed out by Drazen, the bequest-constrained family's wealth has clearly risen due to the "loan." The existence of points on the new budget line to the northeast of B is due to the wealth effect ([w.sub.t+1]h[prime] [is greater than] 1 + r). Such points demonstrate the feasibility of a Pareto improvement associated with the policy.

Note, however, that following the loan parents may choose a point such as C, where [W.sub.t+1] is below its original level. The intuition behind a possible fall in the absolute value of [W.sub.t+1] is perhaps not immediately clear. After all, if parents were not initially content with the intergenerational distribution of wealth, they could have simply reduced the level of investment to begin with. Why then would they reduce [W.sub.t+1] in response to a policy which allows possible increases in both [c.sub.t] and [W.sub.t+1]? Recall that children must repay the loan plus interest. Consequently, larger flows of human capital investment are required of parents to achieve any level of [W.sub.t+1] after the loan is repaid. With diminishing returns to scale in human capital production, this implies a lower wh[prime] and thus a higher price to parents for any given unit of [W.sub.t+1]. This negative substitution effect on investment is what leads to the ambiguous effect on the children's welfare in Nerlove et al. If it is sufficiently strong, the parents may choose a point like C, where the increase in human capital investment is not sufficient to restore the after-tax wealth of the next generation.

Further insight can be gained by considering some extreme cases. In doing so, the role of two key structural parameters will be highlighted. Figure 2 assumes constant returns to scale in human capital production. In this case there is no substitution effect, since the rate of return on human capital investment is independent of the scale of investment. The unopposed wealth effect implies both generations will be better off as a result of government redistribution, provided [W.sub.t+1] and [c.sub.t] are normal goods. Figure 3 assumes the intertemporal elasticity of substitution is infinite. In other words, own consumption and the next generation's wealth are perfect substitutes in the parents' utility function. Following an intergenerational redistribution, the return on human capital investment falls at each level of [W.sub.t+1]. The resulting lower relative price of own consumption implies parents will unambiguously increase their consumption at the expense of their children's wealth. Thus, the two extreme cases indicate the higher are the returns to scale, relative to the intertemporal elasticity of substitution, the more likely it is that the next generation's wealth will rise due to the policy.

In summary, even if all households are bequest-constrained and factor prices are held constant, the question of whether or not a simple government debt policy benefits both parents and their children remains an empirical matter.(9) In the next two sections, this issue is examined quantitatively. We synthesize the limited empirical evidence and various assumptions within a more realistic multi-period life-cycle simulation model with altruistic transfers. While such simulation studies are not a substitute for empirical work, they do allow the implications of alternative assumptions and estimates to be examined. At a minimum, the simulations will enable us to assess the case for public debt issue in an artificial economy inhabited by bequest-constrained households, as well as focus attention on the most critical structural parameters.

III. A SIMULATION MODEL OF BEQUEST-CONSTRAINED HOUSEHOLDS

Recently, we extended the standard life-cycle simulation models used in the study of tax policies by Summers [1981] and Auerbach and Kotlikoff [1987] to include human capital and altruistic bequests. A representative-agent version of the model was used to examine the role of human capital and bequests in determining aggregate savings rates by Lord and Rangazas [1991] and in determining the effects of various tax reforms by Lord [1989] and Lord and Rangazas [1992]. In these papers, the representative household was not bequest constrained, so that efficient levels of human transfers, as well as physical bequests, were always made. The present paper represents a first step in extending the model to allow for both bequest-constrained and unconstrained households. The current version of the model focuses on the behavior of bequest-constrained families. This is precisely the setting required to empirically examine the ambiguous welfare effects of a loan, between parents and their children, enforced by the government. The model can also be used to assess the impact effects of various macroeconomic policies which cause intergenerational transfers.

Many features of the constrained model are the same as the unconstrained, so we shall primarily focus on the differences. A complete formal description of the unconstrained model, and its calibration, can be found in the appendix and in our previous papers. Individuals are economically dependent on their parents for twenty periods, through age nineteen. At age twenty, they begin their independent economic life. At age twenty-five, the unisex individual "produces" 1.3 children, which corresponds to an annual population growth rate of 1 percent. Retirement occurs at age sixty-three and individuals die after seventy-five years of life.

Each individual begins economic life with an initial quantity of non-depreciating human capital, which is determined by the parents' investments.(10) This initial human capital stock is assumed to augment adult human capital additively. Throughout their lives, individuals choose levels of family consumption, goods and human time inputs for their children's development, as well as goods and time inputs for their own development. An insufficient mix of altruism and wealth prevents constrained families from making physical bequests, i.e. the nonnegativity constraint on the choice of financial bequests is binding. Adult human capital decisions remain separated from consumption decisions since there are no life-cycle credit market constraints. However, because of the inability to incur debt obligations for the next generation, investments in children must be simultaneously determined with family consumption, and, thus, investment is affected by marginal changes in wealth.

The utility function is an extension of the additively separable, constant elasticity of substitution specification found in Summers [1981], Lord [1989] and the appendix of this paper. Altruism is introduced through an additive term involving the wealth of the next generation,

[(1 - 1/[Sigma]).sup.-1]m[(1.3)W*].sup.(1-1/[Sigma])](1 + [Delta]).sup.-54],

where m is an altruistic taste parameter, W* is the lifetime wealth of a member of the next generation, [Sigma] is the intertemporal elasticity of substitution in consumption and [Delta] is the pure rate of time preference.

The children's and adult's human capital production function follows the Cobb-Douglas specification found in Ben-Porath [1967]. In both functions the inputs are goods and the parents' effective, or human capital adjusted, time. The parameters of the utility and production functions are set in accordance with empirical results from both econometric and descriptive studies. To reflect the range of findings in these studies, we consider values for [Sigma] within a range from 0.20 to 0.50, and returns to scale in human capital production ([Gamma]), from 0.45 to 0.75.(11) To satisfy certain stylized facts regarding expenditures profiles for the children's human capital investment, either the returns to scale for children must decline throughout the period of dependency or the efficiency scalar must decline while keeping the returns to scale roughly constant.(12) We report results using both simulation strategies. For the simulations with declining returns to scale, the reported returns to scale are the returns in the childs' first year.

The constrained household differs from an unconstrained household by the initial level of wealth and the altruistic parameter. These were chosen to keep the expenditure shares on the children's human capital near those chosen for the unconstrained family (3 to 7 percent of human wealth), and to keep the ratio of the young adult's initial, actual to efficient human capital stock between .3 and .5. Turchi [1975] contains evidence that expenditure shares do not differ much according to wealth. Davies and St. Hilaire [1987] present the fraction of aggregate lifetime earnings and inheritances belonging to each quintile of the Canadian population. The top quintile receives 74 percent of inheritances, and the top two quintiles receive 90 percent. The ratio of lifetime earnings of constrained to unconstrained households is 0.38, whether regarding the top or the top two quintiles as unconstrained.(13) If, during adulthood, children from bequest-constrained families do not dramatically fall behind, or catch up to, those from unconstrained families, this ratio will be a reasonable measure of the initial, actual-to-efficient human capital stock ratio for bequest- constrained households.

In our analysis, we assume all households are bequest constrained. This is the simplest and clearest contrast to the assumption that all households have operative financial bequest motives. Auerbach and Kotlikoff [1987, 64, 168] and Kotlikoff [1988, 48] point out that realistically calibrated life-cycle simulation models fail to generate high enough national savings rates, especially when expenditures on children are included. Our life-cycle framework with bequest-constrained households, augmented with a Cobb-Douglas production to close the model, faces the same difficulty. The high interest rates generated in general equilibriums with low savings rates could potentially affect the conclusions of our study. It should be stressed, however, that our main qualitative conclusions about deficit policies hold in a partial equilibrium setting with exogenously imposed, but more realistic, interest rates. The advantage of following the general equilibrium approach is internal consistency. It enables us to show that the equilibrium interest rates, generated by the empirically supported parameter settings used to calibrate the household model, are consistent with both the financial bequest constraint and with some surprising conclusions about deficit policy.

The general equilibrium, steady-state baselines for six different parameterization are given in Table I.(14) For each parameter setting we present the expenditure share, the actual-to-efficient human capital ratio, the equilibrium interest rate and aggregate savings rate. Recall from section II, that high [Sigma] and low [Gamma] imply parents have a relatively strong willingness to substitute consumption across generations and that the returns to human capital investment in their children fall off quickly. Under these conditions, the substitution effect identified in section II is relatively strong, suggesting that an increase in the children's welfare is less likely following a government intergenerational transfer. Case 1, with [Gamma] = 0.45 and [Sigma] = 0.50, should produce relatively large reductions or small increases in children's wealth, other things constant. In contrast, case 3 has a high [Gamma] = 0.75 and low [Sigma] = 0.20, which should increase the prospects for increases in the children's wealth. Case 2 is an intermediate parameter setting with [Gamma] = 0.60 and [Sigma] = 0.35. Within each of these three cases, the substitution effect will be stronger for case (a), TABULAR DATA OMITTED where the returns to scale fall over the child's lifetime, than for case (b), where the returns to scale are kept roughly constant over time.

The wealth effect from a government intergenerational transfer is larger the greater is the difference between the initial return to human capital and the loan terms implied by the policy. The terms of the loan are determined by the equilibrium interest rate in each case and the particular fashion in which the intergenerational transfer to parents is distributed and financed. For a given financing method, the higher the interest rate the less favorable are the loan terms. The return to human capital varies less across the different cases than does the interest rate, so the higher the interest rate, the weaker will be the wealth effect. In case 1, with relatively low interest rates, the family will then experience relatively large wealth effects (with a relatively large fraction of the wealth increment going to parents as opposed to children due to the stronger substitution effect in that case).

IV. INTERGENERATIONAL TRANSFERS AND CONSUMPTION OF FUTURE GENERATIONS

In this section we analyze the impact of various government policies which redistribute wealth across generations. We begin with a simple loan enforced by the government. Here, the government provides a loan to parents at the beginning of their adult life which is paid back by taxing the children of the family. It does not matter whether the loan is or is not tied to educational expenditures, provided the loan is less than the total amount the parent was initially spending on the children's human capital.

The analysis of the simple loan is then used to examine the effects of macroeconomic policies. Many macroeconomic policies are qualitatively similar to a simple loan in the sense that resources are transferred across generations. In general, however, the redistribution caused by macroeconomic policies differs quantitatively from simple loans. In particular, the terms of the implicit loans embedded in macroeconomic policies will differ from those of a simple loan. As a TABULAR DATA OMITTED consequence, macroeconomic policies cause distributional effects across generations that may differ even qualitatively from simple loan policies.

Simple Loan Policy within the Family

Consider a $1 loan, intermediated by the government, to the parents of a single bequest-constrained household at the beginning of their adult life. The loan is paid for by a $1[(1 + r).sup.25] tax increase on the children of the same family, twenty-five years later. The second column of Table II presents the terms of the loan for the different equilibrium interest rates associated with the different parameter settings. The last column of Table II gives the change in the children's wealth, net of their increased tax burden, per dollar loaned to the parents. In all cases, while the parents use some of the transfer to increase human capital investments in their children, it is not sufficient to maintain the children's after-tax wealth. In case (1a), children lose almost forty cents on every dollar transferred to parents. Assuming returns to scale remain constant over a child's lifetime, case (1b), lowers the loss to a quarter on every dollar transferred to parents. As one moves to cases 2 and 3, the losses become smaller, as the substitution effect weakens relative to the wealth effect.

Macroeconomic Policies

While the simple loan policy is interesting in it own right, we will now use it as an analytical tool to examine how standard macroeconomic deficit policies affect the behavior of bequest- constrained households. The simple loan policy is equivalent to a temporary tax cut of $1 on all working households only if the economy is inhabited by working households of identical age who retire before the tax increase. For example, the two policies would be equivalent in a standard two-period overlapping generations model, where all households work in the first period only. In a more realistic multi-period model, a tax cut simultaneously affects many different working households, at various stages of their life cycle and, in particular, at various stages of their children's development. Also, the method of financing a tax cut will affect families differently than the financing of a simple loan. In a many-period model, those households benefiting from a bond-financed tax cut will generally have to help pay it back. If the debt is paid back gradually over time, younger households spend a longer period paying for the tax cut than will older households. These types of considerations imply the terms of the implicit loan induced by the deficit policy will vary according to the age of the household at the time of the tax cut, and, thus, will not be the same as the terms of the simple loan studied in the last section. Finally, a full-fleged tax cut, as opposed to a loan made to households of a particular age, is more likely to affect factor prices.

In summary, a macroeconomic deficit policy is more complicated than a simple loan policy granted to households of a given age because it transfers wealth to parents of different ages, transfers wealth across unconnected households, and is more likely to cause a change in factor prices. However, one can readily understand the effects of macroeconomic policies on bequest-constrained households by contrasting the nature of the intergenerational transfers caused by such policies to that of a simple loan.

Recall that the household in our model begins its economic life at age twenty, has children at age twenty-five, works until sixty- three, and dies after seventy-five years of life. During any single time period, there are then fifty-six different cohorts, forty- three of which are working, in the full overlapping generations macroeconomic model. Now, suppose there is a temporary and unexpected lump-sum tax cut of $1 for all working households. There are, of course, many ways the tax cut could be financed. We shall consider two financing schemes which seem realistic and which create an impact similar to an intergenerational loan. Under the first policy an increase in lump-sum taxes occurs in the period following the initial tax cut lasting for all periods thereafter, to pay the interest on the debt. In each period the tax increase is divided equally across all working households. Thus, the policy corresponds to a permanent $1 increase in the public debt per household alive at the time of the tax cut. We will follow the analysis of this policy, which will be referred to as the constant debt policy, with a discussion of a second policy where debt per capita is permanently increased by $1.

Those households with heads age forty-five or older will not transfer any of the tax cut to their children and thus receive a clear net transfer from future generations. No transfer is returned to their children because the period of economic dependence is over and all families are bequest constrained.(15) For these older households, the macroeconomic policy works nothing like a loan since they are completely disconnected from the future generations paying for the tax cut.

Households with heads between the ages of twenty and forty-four, either have, or are going to have, dependent children. The parents of these households will transfer a portion of their tax cut to their children via human capital investments. The children, who indirectly benefit from the tax through additional parental investment, will also have to pay higher taxes during every year of their working lives. This group, bequest-constrained households connected to their children only through human capital investment, is the main focus of our study. While the policy works like a loan for these families, the terms of the loan will generally differ from that of the simple loan.

Households with heads between the ages of twenty and forty-four at the time TABULAR DATA OMITTED of the tax cut will each be affected by the policy differently. Table III summarizes the impact effect (before behavioral responses) of the constant debt policy on the wealth of parents and children, according to the age of the parent at the time of the tax cut.(16) The ratio in the last column gives the tax cost to children per dollar of wealth (net of tax) transferred to parents. This should be compared to the terms of the simple loan policy presented in Table II. The macroeconomic policy offers more favorable terms (a larger wealth effect) than the simple loan for only very young households, and less favorable terms for most other households. In addition, the lower wealth effect is but one reason the simple loan policy overestimates the ultimate change in the wealth of children from most families when taxes are cut. Other reasons include the substitution and factor price effects of the policy, which are discussed later in this section.

To explain the differential wealth effects, first note that older parents receive the per capita tax cut later in life (lowering its present value), but have fewer years of tax payments. Younger parents receive the cut earlier, but pay taxes longer. We assume annual population growth of 1 percent. This growth successively lowers the annual per capita tax required to service the debt. With this growth rate and the equilibrium interest rates generated in our six cases, our calculations show the net of tax transfer falls with the age of the parent; the disadvantage of receiving the tax cut later in life outweighs the fewer years over which older households must pay taxes. In addition, the differential impact effect on the children of each household also favors younger households. Children of younger parents will become adults later in life. As a result their tax share TABULAR DATA OMITTED will be smaller, since the population of workers will be larger during their tax paying years. In combination, the impact effects on parents and children explain why the wealth effect in Table III is stronger for younger households.

The computations necessary to provide a complete quantitative assessment of the general equilibrium effect of the constant debt policy on each of the fifty-six families of the model are beyond the scope of this paper. However, the partial equilibrium effect (holding the initial equilibrium interest rate and wage rate constant) on the family with parents age twenty, is readily obtained using the method which generated Table II, but employing the loan terms of Table III rather than that of the simple loan policy. Fortunately, the youngest cohort is important in that their loan terms provide an upper bound on the wealth effect of all cohorts alive at the time of the tax cut. The impact of the policy on the children of this family will provide an upper bound to the changes in wealth of all other families.

Table IV presents the effect of a tax cut on the net wealth of children (including behavioral responses) from the family with parents age twenty, for the constant debt and constant debt per capita financing schemes. Under the constant debt assumption, net wealth of the children falls in all cases, just as for the simple loan experiment. The last column assumes a constant debt-per-capita ratio over time. This policy allows debt to increase at the rate of population growth each period, rather than keeping debt constant at the initial level following the tax cut. Thus, the amount of tax revenue necessary to finance the interest payments by the first two generations of each family is reduced.(17) The reduced tax payments for parents and their children increases the wealth effect, and therefore increases the likelihood that consumption will rise for both generations. However, the policy still lowers the net wealth of children from most households. In case 1, the net wealth of children from all families is necessarily lower. In the other cases, the family benefiting most from the policy, with parents age twenty at the time of the tax cut, only experiences an increase in the wealth of its children of at most eleven cents per dollar of tax cut. As discussed below, it is likely that the children of older parents experience losses.

In addition to smaller wealth effects, the substitution effect is stronger for older households, making it more likely that their children's wealth will fall.(18) There are two reasons for this. First, since there are diminishing returns within a period, the average cost of augmenting children's wealth by some fixed amount increases if the investments must be spread over fewer years. Second, if returns to scale fall as children become older (one of the assumptions we use to smooth investments through dependency, see footnote 13), this will further increase costs. All things considered, it is quite possible that the children of most families suffer from such debt policies.

It is also important to note that the general equilibrium factor price effects of any deficit policy may also work against future generations. At the time of the tax cut, consumption will increase for every working household which experiences a net increase in family wealth due to the policy. It is possible that family wealth may fall for some of the older households, but as we indicate in section V, this is at most a small fraction of the population. As a consequence, savings will not increase one-for-one with the increased government demand for funds (provided the tax cut is lump sum as assumed here). The excess demand for funds will raise interest rates and lower wage rates. The change in factor prices will then lower the return to human capital investment and reduce the quantity of transfers made by parents even further than we have already indicated. As pointed out by Poterba and Summers [1987], the aggregate marginal propensity to consume out of a temporary tax cut (financed as in our paper) is very small, even in life-cycle models where generations are completely disconnected. The marginal propensities to consume are yet smaller in our model because of the altruistic connection between parents and dependent children. Thus, including the factor price effects will not alter our qualitative conclusions, and would not change our quantitative estimates significantly.

V. VOTING FOR THE DEFICIT

In the previous section we established that, under realistic parameter settings, a tax cut financed by borrowing will lower the wealth of future generations even if they are linked to current generations by altruistically motivated educational transfers. In this section we ask if the current population of voting households would actually favor such a policy.

Cukierman and Meltzer [1989, 731] suggest that bequest-constrained households who make human capital investment in their children would always have a strict preference for government debt. This is true in the context of the simple overlapping generations model where agents live for two periods, since the terms of the implicit loan induced by a deficit-financed tax cut are the same as for a simple loan. With the return on human capital greater than the interest rate for a bequest-constrained household, a simple loan would expand the families' consumption possibilities and, thus, would clearly be favored by voters. However, remember that when agents live for many periods, the terms of the implicit loan induced by a deficit policy differ according to the age of the household. The question is whether or not the loan terms are favorable enough to cause the majority of households to vote in favor of the temporary tax cut.(19)

To answer the voting question we need to consider the effect of the policy on the welfare of each of the fifty-six voters in the model. Retired voters, between the ages of sixty-three and seventy-five, would clearly favor the policy. They receive no tax cut and pay no additional taxes. Their children, ages thirty-eight to fifty, receive the tax cut which causes their net wealth to rise. Since utility is derived from own consumption and the net wealth of children, households between sixty-three and seventy-five experience a rise in welfare and therefore favor the tax cut.

For working voters between the ages of twenty and sixty-two (in periods of life twenty-one to sixty-three), consider the following maximum value functions:

[J.sub.[t.sub.0]]([T.sub.[t.sub.0]], [T.sub.*[t.sub.0]]) [is equivalent to] max U

subject to (A-1)-(A-3) and (A-5)-(A-7), for [t.sub.0] = 21 to 63, where U (equation (A-4)) and the constraints are defined in the appendix for the case of [t.sub.0] = 21, and where [T.sub.[t.sub.0]] and [T.sub.*[t.sub.0]] are the lump-sum net transfer to parents and lump-sum tax to each child as result of the deficit policy. Totally differentiating [J.sub.[t.sub.0]]([T.sub.[t.sub.0]], [T.sub.*[t.sub.0]]) with respect to the policy and using the envelope theorem gives us

d[J.sub.[t.sub.0]]([T.sub.[t.sub.0]],[T.sub.*[t.sub.0]]) = [([C.sub.[t.sub.0]]).sup.-1/[Sigma]]d[T.sub.[t.sub.0]]

-m[[(1.3)[W.sub.*]].sup.(1-1/[Sigma])][(1+[Delta]).sup.-(54 - [t.sub.0])](1.3)d[T.sub.*[t.sub.0]].

In the appendix, we show the expression above can be rewritten as

[Mathematical Expression Omitted],

where [[Gamma].sub.[t.sub.0]] [is greater than] 0, wH[prime] is the many-period analogue to wh[prime] from section II (see the appendix for an explicit formula), and where the terms for the implicit loans are

[Mathematical Expression Omitted],

[t.sub.0] = 21 to 63, the many-period analogues to 1 + r from section II. It is [Mathematical Expression Omitted], which is reported in Table III as the terms of the implicit loan induced by the deficit policy. Households for which wH[prime] exceeds [Mathematical Expression Omitted], will vote in favor of a marginal decrease in lump-sum taxes financed by government borrowing. A vote in favor of the policy is more likely, the younger is the household, since [Mathematical Expression Omitted] increases with age and wH[prime] is a constant, independent of age.

Households aged sixty-three to seventy-five comprise 18.9 percent of the voting population. This implies that the decisive voter is age thirty-four (just over 31.1 percent of the voting population falls between ages twenty and thirty-four, while just under 31.1 percent of the voting population falls between ages twenty and thirty-three). For the deficit policy to be favored by the majority of households, it is sufficient that the age thirty-four household favors the policy.

Table V presents the oldest working household favoring the policy in each of our six parameter settings under the constant debt financing scheme. Under the first three cases listed, the policy is unanimously favored by all households. As the interest increases under the remaining cases, the cost of financing the debt increases. Consequently, the wealth effect turns negative for older households and support for the policy diminishes.

Notes: The (a)-case assumes falling returns to scale in the child's human capital production over time, while the (b)-case assumes approximately constant returns over time.

In case (3b), with the highest interest rate, the majority of the population votes against the policy. At first glance, it is somewhat surprising to note that this is also the case where the children's wealth falls the least for the age twenty parents. However, both voter support and the relatively small decrease in the children's wealth are endogenous consequences of the same underlying factors. In case (3b), both the wealth and substitution effects of the policy are weak. Family wealth increases weakly for the age twenty parent and the cost of passing the increment in wealth forward to the children is relatively low. As a result, children's wealth does not fall by much. Thus, the same factors causing the wealth effect to be weak (low [Sigma] and high [Gamma] producing the high interest rate) cause voter support to be weak and the cost of increasing the children's wealth to be low.

VI. CONCLUSION

It is becoming increasingly clear that the mere presence of private intergenerational transfers does not immediately imply the neutrality of government debt policy. First, as shown by Abel [1985], Bernheim, Shleifer, and Summers [1985], and Kotlikoff and Spivak [1981], bequests not motivated by altruism do not imply neutrality. Second, Feldstein [1988] showed that if income is uncertain, a temporary lump-sum tax cut (paid for by a lump-sum tax increase on the next generation) will increase consumption even for households who eventually leave altruistically motivated bequests. Third, Altig and Davis [1989] and Laitner [forthcoming] explain that altruistically motivated inter vivos transfers do not imply neutrality if such transfers are insufficient to relax binding liquidity constraints.

We examine the situation where households are bequest constrained, but where generations remain linked by altruistically motivated human capital investment. Understanding the behavior of such households is important, since they constitute the vast majority of the population. It is well known that deficit policies can shift the consumption possibility frontier outward for bequest- constrained families and, thus, have real effects. The wealth effect of a deficit policy causes consumption to rise for all generations. If, however, there are diminishing returns to human capital investment, the policy also contains a substitution effect. Greater investment is now required to maintain a given level of after-tax wealth for the next generation. As a result, the return on investment falls at every level of parental consumption. This discourages investment and creates the possibility that consumption for the next generation could fall.

We develop a simulation model of bequest-constrained households in order to begin a quantitative examination of deficit polices. For plausible parameter settings, our results indicate that a simple deficit policy will reduce the next generation's wealth for most families. While these results are suggestive rather than conclusive, they do provide an example showing why government intervention into imperfect capital markets may not benefit both generations. The government intervention fails in this sense, despite the fact that, in our example, the government is clearly superior to the private sector in enforcing loans across generations. However, this enforcement ability only applies to the repayment of the loan.(20) There is no straightforward enforcement mechanism which ensures that a sufficient portion of the loan is invested in the family's children, guaranteeing that the loan repayment does not reduce the children's net wealth. We show that the absence of such a mechanism is important. As a consequence, our results weaken the case for deficit financing and pay-as-you-go social security in the presence of bequest-constrained households.

APPENDIX

The Simulation Model

The simulation model assumes individuals are economically dependent on their parents for twenty years. At age twenty, in the twenty- first year of life, they begin independent economic life. At age twenty-five, the unisex individual "produces" approximately 1.3 children, corresponding to a population growth rate of 1 percent. Retirement occurs at age sixty-three and individuals die after seventy-five years of life.

Each individual begins economic life with an initial quantity of non-depreciating human capital, based on their parents' investment, which augments their adult human capital stock in an additive fashion. Throughout their economic life, individuals choose levels of family consumption, and goods and time inputs for both their own adult and their childrens' human capital development.

The modeling of adult human capital decisions is based on Yoram Ben-Porath [1967]. During adult years the production function for gross additions to the stock of human capital follows a Cobb- Douglas specification with decreasing returns to scale, constant output elasticities, and a constant rate of depreciation. Denote the contribution to lifetime wealth of adult human capital accumulation, net of the cost of inputs, by [V.sup.A]. [V.sup.A] is determined solely by wealth maximizing considerations and is independent of the initial stock of human capital bequeathed by parents. Complete discussions of the adult human capital decision are provided in both Ben-Porath and Lord [1989].

The technology constraining a child's human capital production is distinct from adults, although of the same basic Cobb-Douglas form. Parents face the following production function for augmenting their childrens' human capital:

(A-1) [Q.sub.t] = [v.sub.t][([s.sub.t][H.sub.t]).sup.[[Gamma].sub.t]][([D.sub.t]) .sup.[[Lambda].sub.t]],

where

(A-2) [v.sub.t] = [v.sub.26]/[(1+[Tau]).sup.t-26]

(A-3) [[Gamma].sub.t] = [[Gamma].sub.26]/[(1+[Alpha]).sup.t-26]

and

(A-4) [[Lambda].sub.t] = [[Gamma].sub.26]/[(1+[Beta]).sup.t-26]

for parental years twenty-six through forty-five. Here [s.sub.t], [D.sub.t] and [H.sub.t] are parental time and goods inputs, and parental human capital stock at t, while, [v.sub.26], [[Gamma].sub.26] and [[Beta].sub.26] are production function parameters. This specification allows the efficiency scalar and the output elasticities of parental time and goods inputs to vary with the age of the child. These parameters are chosen to mimic characteristics of the input profiles reported by Hotz and Miller [1988]. After the first year, they estimate that the parental time input declines geometrically at a rate of 12 percent. They also could not reject the hypothesis that goods inputs had a constant profile.

We employ the familiar constant-elasticity-of-substitution utility function, augmented with altruistic preferences toward the next generation, as discussed in section II of the text:

[Mathematical Expression Omitted]

where [Sigma] is the intertemporal elasticity of substitution, [Delta] is the pure rate of time preference, [C.sub.t] is family consumption in year t, and m is a relative preference parameter. [W.sub.*], the aggregate wealth of children, is

[Mathematical Expression Omitted]

Here [P.sub.21] is the present value to children of a nondepreciating unit of human capital in the twenty-first year of life, which contributes the wage per unit of human capital (w) to current earnings each year from twenty-one to sixty-three. [H.sub.20] is the number of units inherited per child.

Parental investments in children in each year t are:

(A-7) [I.sub.t] = w[s.sub.t][H.sub.t] + P[D.sub.t]

where P is the price per unit of goods input. Efficiency requires that parents minimize the [I.sub.t] of any [Q.sub.t] by appropriate choice of the goods and time inputs. Consequently, minimum [I.sub.t] depends upon [Q.sub.t] and the lifetime wealth budget constraint may be expressed as:

[Mathematical Expression Omitted]

Outlays on consumption and child development must equal parents' wealth W, the sum of the values of human capital produced as adults [V.sup.A] and the value of the human capital they inherit.

Since both childrens' wealth and parental investment costs depend upon the annual flows of human capital, the [Q.sub.t]s, we may maximize (A-4) subject to (A-7) and the production function equations (A-1) to (A-3) (and utilizing (A5)), by choice of annual consumption [C.sub.t] and human capital flows [Q.sub.t].

The F.O.C. for [C.sub.t] are:

[Mathematical Expression Omitted]

and those for [Q.sub.t] are:

(A-10) m[[(1.3)[W.sub.*]].sup.-1/[Sigma]][P.sub.21]/[(1+[Delta]).sup.5 4]

= [Rho]M[C.sub.t]/[(1+r).sup.t-21]

for t = 26,...,45

where [Rho] is a Lagrange multiplier for parental wealth. The F.O.C. for [Q.sub.t] require that the discounted marginal costs in each period M[C.sub.t] be equated.

It is straightforward to find the [Q.sub.t]s. Equating the M[C.sub.t]s, each [Q.sub.t] may be expressed in terms of [Q.sub.26] and [Rho]. Using (A-5) and combining the F.O.C. for [C.sub.t] and [Q.sub.t], [Rho] may be eliminated and [C.sub.t] and [I.sub.t] expressed in terms of [Q.sub.26], and then all other choice variables, as a function of parents' wealth. The full simulation simultaneously models parents and their children (when adults). In the initial steady state, parental wealth and wealth per child are made equal.

Impact Effect of Macroeconomic Policy

We wish to compute the impact effect of the deficit policy on the wealth of each parent between the ages of twenty and forty-four, and on the wealth of their children. Each parent receives the tax cut of $1. In the following year, taxes are increased by r on all those working. Since the work force grows by the factor (1 + g) each period, next year's tax burden per working household is r/(1 + g). Similar computations are made each year thereafter, until the household retires. From the perspective of the date when taxes are cut, the present value impact of the policy on parents is,

1 - r/[(1 + g)(1 + r)] + r/[[(1 + g)(1 + r)].sup.2]+ ...

+ r/[[(1 + g)(1 + r)].sup.x]}

= 1 - r/[(1 + g)(1 + r)]}

( 1 - 1/[[(1 + g)(1 + r)].sup.x]}/ 1 - 1/[(1 + g)(1 + r)]})

[is equivalent to] 1 - [D.sub.x],

where x = the number of years over which the household pays the tax. The quantity 1 - [D.sub.x] is then discounted back to the household's first period of economic life to get the impact on household wealth,

[[1/(1 + r)].sup.42-x](1 - [D.sub.x]).

The children from each family must pay taxes for their entire lives. The children of the youngest parents must pay,

[(1 + r)/[(1 + g).sup.25]][D.sub.43]}[(1 + g).sup.25] = (1 + r)[D.sub.43].

If the population growth rate was zero, the child would pay the same tax as his twenty-year-old parent, plus an additional amount r in the first period of economic life. With population growth the tax burden is reduced for the child relative to the parent by the factor 1/[(1 + g).sup.25]. However, there are [(1 + g).sup.25] children, so we get (1 + r)[D.sub.43] as the decrease in the wealth of the children from the household with a twenty-year-old parent.

The children of the next oldest parent, age twenty-one, have a smaller cohort of workers to share the tax with, so they pay

[(1 + r)/[(1 + g).sup.24]][D.sub.42]}[(1 + g).sup.25] = (1 + r)(1 + g)[D.sub.43].

The same reasoning applies for the children of all remaining households. For example, the children of the oldest parents pay,

(1 + r)[(1 + g).sup.25][D.sub.43].

Derivation of equation (4)

From differentiating [J.sub.[t.sub.0]]([T.sub.[t.sub.0]], [T.sub.*[t.sub.0]]) with respect to the policy, we have

[([C.sub.[t.sub.0]]).sup.-1/[Sigma]]d[T.sub.[t.sub.0]]

-m[[(1.3)[W.sub.*]].sup.(1-1/[Sigma])][(1+[Delta]).sup.-(75 - [t.sub.0])(1.3)d[T.sub.*[t.sub.0]].

From the first-order conditions ((A-9) and (A-10)), we have

[([C.sub.[t.sub.0]]).sup.-1/[Sigma]] = [[(1 + [Delta])/(1 + r)].sup.([t.sub.0]-21)]

[([C.sub.21]).sup.-1/[Sigma]]} = [[(1 + [Delta])/(1 + r)].sup.([t.sub.0]-21)]

m[[(1.3)[W.sub.*]].sup.-1/[Sigma]][(1+[Delta]).sup.-(75-21)]

[[P.sub.21]/M[C.sub.26][(1 + r).sup.5]]},

where

[[P.sub.21]/M[C.sub.26][(1 + r).sup.5]] [is equivalent to] wH[prime].

Substituting for [([C.sub.[t.sub.0]]).sup.-1/[Sigma]] above and pulling out common terms gives

[Mathematical Expression Omitted].

1. Blinder [1976] and Davies and St. Hillaire [1987] report that most households receive little or no inheritance. Menchik and David [1983] find only the upper quintile in their sample exhibit bequest shares which are responsive to variations in wealth, suggesting that they were planned. Moreover, their sample initially omits about one-third of the population, who, because of small estates, were not required to file probate records. This implies the upper quintile of their study actually represents the upper 14 percent of the population. Mariger [1987] claims his estimates of a life-cycle model indicate only those with financial net worth in excess of $250,000 in 1963, the top 6 percent of the sample, have a bequest motive. Hurd [1987; 1989], contrary to previous cross-sectional studies, presents panel data evidence showing the elderly do dissave. He concludes that intentional bequests are only concentrated among the very wealthy. Kotlikoff [1988] disputes the empirical importance of Hurd's findings, arguing instead that the amount of wealth decumulation is insignificant. More importantly, however, Hurd shows that elderly households with children do not dissave any less rapidly than those without children.

2. Menchik [1980; 1985] finds bequests tend to be evenly spilt among children. This is in contradiction with altruism if there are significant differences in earnings capacities across children. Cox [1987; 1990] finds that recipient income and the size of inter vivos transfers are positively correlated, instead of negatively correlated as predicted by altruistic models. Finally, Altonji et al. [1992] were able to reject the notion that total family resources, and not the distribution of resources across generations, is the primary determinant of a generation's consumption.

3. In fact, many of the studies cited above also contain results consistent with the idea that altruism between family members is an important source of intergenerational transfers. Hurd's [1987] data shows there are substantial transfers from parents to children early in life. When first entering retirement, couples with children have about one-third less wealth than those without children. Also, some inter vivos transfers are reported for approximately 20 percent of the families in his sample.

The sign and statistical significance of the result reported by Cox [1987; 1990] are sensitive to the sample chosen. His finding of a positive relationship between transfers and recipient income was based on a sample which excludes recipients who were students. When students are included, as in Chiswick and Cox [1987], the effect of recipient income on the transfer amount becomes negative or statistically insignificant, depending on which estimation technique is employed. Furthermore, Cox [1990] reveals that recipients of inter vivos transfers have lower permanent income than non-recipients. This is not only consistent with altruism, it also helps to explain the equal division result of Menchik. Most of the "equalizing" transfers may well take place inter vivos rather than at death.

4. The presence of inter vivos transfers does not necessarily imply Ricardian Equivalence if there are liquidity constraints and the transfers are not sufficient to overcome them. See Altig and Davis [1989] and Laitner [forthcoming].

5. The existence of such loans is, apparently, the point on which Barro and Drazen depart. As explained by Rangazas [1991b], implicit loans are logically equivalent to an operative "gift", from children to parents, during the parents' later years. An operative gift motive guarantees the Ricardian theorem holds, provided there are no liquidity constraints (see footnote 4).

6. Gary Becker [1988] recently used Drazen's argument to explain the tandem upward trends in expenditures per adult over sixty-five and per child under age twenty-two. Becker sees households as rationally voting for a combination of policies which effectively create a welfare-improving implicit loan between the generations. He states, "... the popular view of generation fighting--that public expenditures on the elderly grew rapidly because the old became politically powerful as they become more numerous--cannot explain why expenditures on children grew just as rapidly" [1988, 9]. Cukierman and Meltzer [1989], also building from Drazen's insight, were able to construct a model of the political process where households vote for public debt issue in order to relieve their inability to enforce liabilities on their children.

7. This analysis assumes either that altruism runs in just one direction, from parent to child, or that both bequest and gift motives are not operative. It will also be noted that this specification of preferences differs from that where the next generation's utility enters the current generation's utility function. The two specifications will produce different predictions only if (1) there is a labor-leisure choice or (2) the analysis includes a change in the interest rate. Parents will fail to recognize the full implications of a change in work effort or the interest rate if they focus solely on the "sources of funds" side of the next generation's budget constraint. Since our analysis involves the partial equilibrium effects of lump-sum transfers, with a fixed level of leisure consumption, the two specifications can be viewed as very close substitutes.

8. Davies and St. Hilaire [1987] use a similar diagrammatic approach to analyze different issues.

9. As a referee points out, a more elaborate sequence of taxes and transfers could conceivably generate a theoretically unambiguous Pareto improvement.

10. For the typical household, basic reading, writing and arithmetic skills, as well as health habits, are likely to be maintained by the daily experiences of production and consumption. For this reason, the initial stock of human capital is not subject to depreciation.

11. The empirical support for these parameter ranges is discussed in Lord and Rangazas [1991]. It should also be noted

There is now a substantial body of evidence suggesting that altruistic financial bequests are zero for the vast majority of households.(1) Other studies seem to indicate that the financial bequests which are made, are not likely to be altruistically motivated.(2) While this evidence against the importance of altruistic financial bequests seems reasonably convincing, it is by no means clear that the importance of altruism per se has been dismissed.(3) For example, the results reported in Altonji, Hayashi, and Kotlikoff [1992, Tables 14-17] indicate that extended- family resources, while not perfectly linked to own resources, are important for explaining own consumption. The authors do not reject the notion that substantial altruistically motivated transfers occur in the U.S. Rather, they suggest the altruistically motivated transfers which are made take the form of less than fully efficient human capital transfers to children.

If most altruistic transfers do take place via educational expenditures, how does this affect the Ricardian equivalence theorem? Robert Barro [1974; 1989] argues the presence of any altruistic transfer is sufficient to guarantee that intergenerational transfers caused by government policy are neutral. Other forms of intergenerational transfers, such as inter vivos gifts to children, support of children's education, and so on, can work in a similar manner. Therefore, the Ricardian results will hold even if many persons leave little in the way of formal bequests [1989, 41].(4)

An alternative view, however, is expressed by Allan Drazen [1978]. He argues if parents possess an insufficient mix of wealth and altruism, intergenerational transfers could be exhausted before the efficient level of human capital investment is achieved. If explicit or implicit loans between parents and children are not possible, then the government may be able to improve welfare by generating intergenerational transfers from children to parents.(5) A cut in the parents' tax burden, and an equal present value increase in the tax on the next generation, is equivalent to a government-enforced loan at the going market interest rate. Since educational expenditures are inefficiently low, the return on human capital investment exceeds the loan rate. Therefore, parents could put an amount less than the tax cut into their children's education, and still leave the children with enough additional income to pay for the future tax increase. Thus, a deficit policy serves to expand the consumption possibility set of the family. Viewed in this way, Drazen [1978, 514, footnote 7] imagines an argument for a Pareto optimal level of public debt issue.(6)

A third possibility was identified by Nerlove, Razin and Sadka [1988], who conduct the most explicit analysis of government transfers in an economy with altruistic but financial bequest- constrained households. They also find a transfer or implicit "loan" to parents, from their children, will make the parents unambiguously better-off. However, they were the first to point out that a deficit policy may lower the welfare of the children (although they fail to explain why). Thus, even in the presence of altruistic transfers from parents to children, the effect of deficits on the consumption of future generations is far from clear.

In this paper we wish to clarify the effect of intergenerational transfers on bequest-constrained families. The next section intuitively explains why a government loan or deficit policy generates an ambiguous effect on the children's consumption, even though altruistic parents are fully capable of making both generations better off after the loan. We also identify the key structural determinants of the change in the children's wealth due to the loan. In section III, we extend the simple model of section II to a more quantitatively realistic multi-period, life-cycle simulation model of a bequest-constrained household. The simulation model is then used in section IV to examine how a government intergenerational transfer affects the consumption of each generation under various settings of the key structural determinants identified in section II. The results suggest that deficits can hurt future generations, even if they are members of altruistic families linked by private transfers for human capital. Section V goes a step further and demonstrates that the majority of current voters favor such policies, despite their negative impact on the family's children. Thus, the popular view of generation fighting is not necessarily precluded by the presence of altruistically motivated private transfers.

II. THE THEORY

Consider the following simple model of intergenerational wealth transmission, previously analyzed by Becker and Tomes [1979], Davies [1986], Nerlove, Razin and Sadka [1988] and Rangazas [1991b]. This model is sufficiently rich to articulate the factors leading to the ambiguous effects of deficit policies on the consumption of future generations. Let each period represent a generation. During the period, a family has one child. The parents are altruistic in the sense that the child's lifetime wealth, [W.sub.t+1], gives them satisfaction.(7) Parents choose own lifetime consumption, [c.sub.t], human capital expenditures on the child, [x.sub.t], and a financial bequest, [B.sub.t], to maximize lifetime utility. The constraints include parental wealth, [W.sub.t], the child's human capital production function, h, as well as child's lifetime budget constraint.

Formally, the current generation maximizes

(1) [V.sup.t] = U([c.sub.t], [W.sub.t+1])

subject to

(2.1) [c.sub.t] + [x.sub.t] + [p.sub.t][B.sub.t] = [W.sub.t]

(2.2) [c.sub.t+1] + [x.sub.t+1] + [p.sub.t+1][B.sub.t+1] = [w.sub.t+1]h([x.sub.t]) + [B.sub.t]

(2.3) [B.sub.t] [is greater than or equal to] 0

where [p.sub.t] = [(1 + [r.sub.t+1]).sup.-1] is the price of making a transfer of net wealth to the child, [w.sub.t+1] is the wage rate per unit of human capital, and h is a strictly concave and increasing human capital production function. The necessary conditions for a maximum are

(3.1) [U.sub.1] = [Mu]

(3.2) [U.sub.2][w.sub.t+1]h[prime] = [Mu]

(3.3) [U.sub.2] [is less than or equal to] [Mu][p.sub.t]

where [Mu] is a Lagrange multiplier. A family is said to be bequest constrained if [U.sub.2] [is less than] [Mu][p.sub.t]; the benefit of a financial bequest is less than the cost. This implies [w.sub.t+1]h[prime] [is greater than] 1 + [r.sub.t+1], so that all bequests are made in human form, with [B.sub.t] set equal to zero. Inefficiently low levels of human capital expenditures are being made due to an insufficient mix of parental wealth and concern for the next generation. In this case, household behavior is characterized by solving (3.1) and (3.2) simultaneously for [c.sub.t] and [x.sub.t]. Ricardian equivalence will not hold if financial bequests are zero, despite the presence of positive human capital transfers. For a bequest-constrained household, an intergenerational redistribution of wealth toward the current generation will increase [x.sub.t]; since the shadow price of future wealth in (3.2), [U.sub.2]/[U.sub.1], rises everything else constant.

A sketch of the model is given in Figure 1.(8) The next generation's wealth is plotted on the vertical axis, and the current generation's consumption is plotted on the horizontal axis. The curve labelled FD depicts the tradeoff between [W.sub.t+1] and [c.sub.t], assuming all intergenerational transfers take the form of human capital expenditures. At point D, no discretionary transfers are made by parents, and the children's wealth reflects only exogenous human capital inputs or exogenous wealth transfers. Altruistic parents will begin planning their transfers as human capital investments which cause the next generation's wealth to increase up along the FD curve. The curve is strictly concave due to the assumption of decreasing returns to scale in human capital production. If the parents' altruism is sufficiently strong, their total planned transfers will push them to point A, where 1 + r = [w.sub.t+1]h[prime]. If any additional transfers are planned beyond A, they will take the form of investment in physical, rather than human, capital. Thus, the effective budget constraint for the family is ED. A bequest-constrained family is one where the optimal choice of the parents places them at a point to the right of A, such as B.

Now imagine a lump-sum reduction in the tax burden of the current generation by one unit, paid for by an increase in the tax burden of the next generation by 1 + r units. Everything else constant, the policy will shift each point on ED one unit to the right and 1 + r units down. This shifts the family's possibilities frontier to ED[prime]. As pointed out by Drazen, the bequest-constrained family's wealth has clearly risen due to the "loan." The existence of points on the new budget line to the northeast of B is due to the wealth effect ([w.sub.t+1]h[prime] [is greater than] 1 + r). Such points demonstrate the feasibility of a Pareto improvement associated with the policy.

Note, however, that following the loan parents may choose a point such as C, where [W.sub.t+1] is below its original level. The intuition behind a possible fall in the absolute value of [W.sub.t+1] is perhaps not immediately clear. After all, if parents were not initially content with the intergenerational distribution of wealth, they could have simply reduced the level of investment to begin with. Why then would they reduce [W.sub.t+1] in response to a policy which allows possible increases in both [c.sub.t] and [W.sub.t+1]? Recall that children must repay the loan plus interest. Consequently, larger flows of human capital investment are required of parents to achieve any level of [W.sub.t+1] after the loan is repaid. With diminishing returns to scale in human capital production, this implies a lower wh[prime] and thus a higher price to parents for any given unit of [W.sub.t+1]. This negative substitution effect on investment is what leads to the ambiguous effect on the children's welfare in Nerlove et al. If it is sufficiently strong, the parents may choose a point like C, where the increase in human capital investment is not sufficient to restore the after-tax wealth of the next generation.

Further insight can be gained by considering some extreme cases. In doing so, the role of two key structural parameters will be highlighted. Figure 2 assumes constant returns to scale in human capital production. In this case there is no substitution effect, since the rate of return on human capital investment is independent of the scale of investment. The unopposed wealth effect implies both generations will be better off as a result of government redistribution, provided [W.sub.t+1] and [c.sub.t] are normal goods. Figure 3 assumes the intertemporal elasticity of substitution is infinite. In other words, own consumption and the next generation's wealth are perfect substitutes in the parents' utility function. Following an intergenerational redistribution, the return on human capital investment falls at each level of [W.sub.t+1]. The resulting lower relative price of own consumption implies parents will unambiguously increase their consumption at the expense of their children's wealth. Thus, the two extreme cases indicate the higher are the returns to scale, relative to the intertemporal elasticity of substitution, the more likely it is that the next generation's wealth will rise due to the policy.

In summary, even if all households are bequest-constrained and factor prices are held constant, the question of whether or not a simple government debt policy benefits both parents and their children remains an empirical matter.(9) In the next two sections, this issue is examined quantitatively. We synthesize the limited empirical evidence and various assumptions within a more realistic multi-period life-cycle simulation model with altruistic transfers. While such simulation studies are not a substitute for empirical work, they do allow the implications of alternative assumptions and estimates to be examined. At a minimum, the simulations will enable us to assess the case for public debt issue in an artificial economy inhabited by bequest-constrained households, as well as focus attention on the most critical structural parameters.

III. A SIMULATION MODEL OF BEQUEST-CONSTRAINED HOUSEHOLDS

Recently, we extended the standard life-cycle simulation models used in the study of tax policies by Summers [1981] and Auerbach and Kotlikoff [1987] to include human capital and altruistic bequests. A representative-agent version of the model was used to examine the role of human capital and bequests in determining aggregate savings rates by Lord and Rangazas [1991] and in determining the effects of various tax reforms by Lord [1989] and Lord and Rangazas [1992]. In these papers, the representative household was not bequest constrained, so that efficient levels of human transfers, as well as physical bequests, were always made. The present paper represents a first step in extending the model to allow for both bequest-constrained and unconstrained households. The current version of the model focuses on the behavior of bequest-constrained families. This is precisely the setting required to empirically examine the ambiguous welfare effects of a loan, between parents and their children, enforced by the government. The model can also be used to assess the impact effects of various macroeconomic policies which cause intergenerational transfers.

Many features of the constrained model are the same as the unconstrained, so we shall primarily focus on the differences. A complete formal description of the unconstrained model, and its calibration, can be found in the appendix and in our previous papers. Individuals are economically dependent on their parents for twenty periods, through age nineteen. At age twenty, they begin their independent economic life. At age twenty-five, the unisex individual "produces" 1.3 children, which corresponds to an annual population growth rate of 1 percent. Retirement occurs at age sixty-three and individuals die after seventy-five years of life.

Each individual begins economic life with an initial quantity of non-depreciating human capital, which is determined by the parents' investments.(10) This initial human capital stock is assumed to augment adult human capital additively. Throughout their lives, individuals choose levels of family consumption, goods and human time inputs for their children's development, as well as goods and time inputs for their own development. An insufficient mix of altruism and wealth prevents constrained families from making physical bequests, i.e. the nonnegativity constraint on the choice of financial bequests is binding. Adult human capital decisions remain separated from consumption decisions since there are no life-cycle credit market constraints. However, because of the inability to incur debt obligations for the next generation, investments in children must be simultaneously determined with family consumption, and, thus, investment is affected by marginal changes in wealth.

The utility function is an extension of the additively separable, constant elasticity of substitution specification found in Summers [1981], Lord [1989] and the appendix of this paper. Altruism is introduced through an additive term involving the wealth of the next generation,

[(1 - 1/[Sigma]).sup.-1]m[(1.3)W*].sup.(1-1/[Sigma])](1 + [Delta]).sup.-54],

where m is an altruistic taste parameter, W* is the lifetime wealth of a member of the next generation, [Sigma] is the intertemporal elasticity of substitution in consumption and [Delta] is the pure rate of time preference.

The children's and adult's human capital production function follows the Cobb-Douglas specification found in Ben-Porath [1967]. In both functions the inputs are goods and the parents' effective, or human capital adjusted, time. The parameters of the utility and production functions are set in accordance with empirical results from both econometric and descriptive studies. To reflect the range of findings in these studies, we consider values for [Sigma] within a range from 0.20 to 0.50, and returns to scale in human capital production ([Gamma]), from 0.45 to 0.75.(11) To satisfy certain stylized facts regarding expenditures profiles for the children's human capital investment, either the returns to scale for children must decline throughout the period of dependency or the efficiency scalar must decline while keeping the returns to scale roughly constant.(12) We report results using both simulation strategies. For the simulations with declining returns to scale, the reported returns to scale are the returns in the childs' first year.

The constrained household differs from an unconstrained household by the initial level of wealth and the altruistic parameter. These were chosen to keep the expenditure shares on the children's human capital near those chosen for the unconstrained family (3 to 7 percent of human wealth), and to keep the ratio of the young adult's initial, actual to efficient human capital stock between .3 and .5. Turchi [1975] contains evidence that expenditure shares do not differ much according to wealth. Davies and St. Hilaire [1987] present the fraction of aggregate lifetime earnings and inheritances belonging to each quintile of the Canadian population. The top quintile receives 74 percent of inheritances, and the top two quintiles receive 90 percent. The ratio of lifetime earnings of constrained to unconstrained households is 0.38, whether regarding the top or the top two quintiles as unconstrained.(13) If, during adulthood, children from bequest-constrained families do not dramatically fall behind, or catch up to, those from unconstrained families, this ratio will be a reasonable measure of the initial, actual-to-efficient human capital stock ratio for bequest- constrained households.

In our analysis, we assume all households are bequest constrained. This is the simplest and clearest contrast to the assumption that all households have operative financial bequest motives. Auerbach and Kotlikoff [1987, 64, 168] and Kotlikoff [1988, 48] point out that realistically calibrated life-cycle simulation models fail to generate high enough national savings rates, especially when expenditures on children are included. Our life-cycle framework with bequest-constrained households, augmented with a Cobb-Douglas production to close the model, faces the same difficulty. The high interest rates generated in general equilibriums with low savings rates could potentially affect the conclusions of our study. It should be stressed, however, that our main qualitative conclusions about deficit policies hold in a partial equilibrium setting with exogenously imposed, but more realistic, interest rates. The advantage of following the general equilibrium approach is internal consistency. It enables us to show that the equilibrium interest rates, generated by the empirically supported parameter settings used to calibrate the household model, are consistent with both the financial bequest constraint and with some surprising conclusions about deficit policy.

The general equilibrium, steady-state baselines for six different parameterization are given in Table I.(14) For each parameter setting we present the expenditure share, the actual-to-efficient human capital ratio, the equilibrium interest rate and aggregate savings rate. Recall from section II, that high [Sigma] and low [Gamma] imply parents have a relatively strong willingness to substitute consumption across generations and that the returns to human capital investment in their children fall off quickly. Under these conditions, the substitution effect identified in section II is relatively strong, suggesting that an increase in the children's welfare is less likely following a government intergenerational transfer. Case 1, with [Gamma] = 0.45 and [Sigma] = 0.50, should produce relatively large reductions or small increases in children's wealth, other things constant. In contrast, case 3 has a high [Gamma] = 0.75 and low [Sigma] = 0.20, which should increase the prospects for increases in the children's wealth. Case 2 is an intermediate parameter setting with [Gamma] = 0.60 and [Sigma] = 0.35. Within each of these three cases, the substitution effect will be stronger for case (a), TABULAR DATA OMITTED where the returns to scale fall over the child's lifetime, than for case (b), where the returns to scale are kept roughly constant over time.

The wealth effect from a government intergenerational transfer is larger the greater is the difference between the initial return to human capital and the loan terms implied by the policy. The terms of the loan are determined by the equilibrium interest rate in each case and the particular fashion in which the intergenerational transfer to parents is distributed and financed. For a given financing method, the higher the interest rate the less favorable are the loan terms. The return to human capital varies less across the different cases than does the interest rate, so the higher the interest rate, the weaker will be the wealth effect. In case 1, with relatively low interest rates, the family will then experience relatively large wealth effects (with a relatively large fraction of the wealth increment going to parents as opposed to children due to the stronger substitution effect in that case).

IV. INTERGENERATIONAL TRANSFERS AND CONSUMPTION OF FUTURE GENERATIONS

In this section we analyze the impact of various government policies which redistribute wealth across generations. We begin with a simple loan enforced by the government. Here, the government provides a loan to parents at the beginning of their adult life which is paid back by taxing the children of the family. It does not matter whether the loan is or is not tied to educational expenditures, provided the loan is less than the total amount the parent was initially spending on the children's human capital.

The analysis of the simple loan is then used to examine the effects of macroeconomic policies. Many macroeconomic policies are qualitatively similar to a simple loan in the sense that resources are transferred across generations. In general, however, the redistribution caused by macroeconomic policies differs quantitatively from simple loans. In particular, the terms of the implicit loans embedded in macroeconomic policies will differ from those of a simple loan. As a TABULAR DATA OMITTED consequence, macroeconomic policies cause distributional effects across generations that may differ even qualitatively from simple loan policies.

Simple Loan Policy within the Family

Consider a $1 loan, intermediated by the government, to the parents of a single bequest-constrained household at the beginning of their adult life. The loan is paid for by a $1[(1 + r).sup.25] tax increase on the children of the same family, twenty-five years later. The second column of Table II presents the terms of the loan for the different equilibrium interest rates associated with the different parameter settings. The last column of Table II gives the change in the children's wealth, net of their increased tax burden, per dollar loaned to the parents. In all cases, while the parents use some of the transfer to increase human capital investments in their children, it is not sufficient to maintain the children's after-tax wealth. In case (1a), children lose almost forty cents on every dollar transferred to parents. Assuming returns to scale remain constant over a child's lifetime, case (1b), lowers the loss to a quarter on every dollar transferred to parents. As one moves to cases 2 and 3, the losses become smaller, as the substitution effect weakens relative to the wealth effect.

Macroeconomic Policies

While the simple loan policy is interesting in it own right, we will now use it as an analytical tool to examine how standard macroeconomic deficit policies affect the behavior of bequest- constrained households. The simple loan policy is equivalent to a temporary tax cut of $1 on all working households only if the economy is inhabited by working households of identical age who retire before the tax increase. For example, the two policies would be equivalent in a standard two-period overlapping generations model, where all households work in the first period only. In a more realistic multi-period model, a tax cut simultaneously affects many different working households, at various stages of their life cycle and, in particular, at various stages of their children's development. Also, the method of financing a tax cut will affect families differently than the financing of a simple loan. In a many-period model, those households benefiting from a bond-financed tax cut will generally have to help pay it back. If the debt is paid back gradually over time, younger households spend a longer period paying for the tax cut than will older households. These types of considerations imply the terms of the implicit loan induced by the deficit policy will vary according to the age of the household at the time of the tax cut, and, thus, will not be the same as the terms of the simple loan studied in the last section. Finally, a full-fleged tax cut, as opposed to a loan made to households of a particular age, is more likely to affect factor prices.

In summary, a macroeconomic deficit policy is more complicated than a simple loan policy granted to households of a given age because it transfers wealth to parents of different ages, transfers wealth across unconnected households, and is more likely to cause a change in factor prices. However, one can readily understand the effects of macroeconomic policies on bequest-constrained households by contrasting the nature of the intergenerational transfers caused by such policies to that of a simple loan.

Recall that the household in our model begins its economic life at age twenty, has children at age twenty-five, works until sixty- three, and dies after seventy-five years of life. During any single time period, there are then fifty-six different cohorts, forty- three of which are working, in the full overlapping generations macroeconomic model. Now, suppose there is a temporary and unexpected lump-sum tax cut of $1 for all working households. There are, of course, many ways the tax cut could be financed. We shall consider two financing schemes which seem realistic and which create an impact similar to an intergenerational loan. Under the first policy an increase in lump-sum taxes occurs in the period following the initial tax cut lasting for all periods thereafter, to pay the interest on the debt. In each period the tax increase is divided equally across all working households. Thus, the policy corresponds to a permanent $1 increase in the public debt per household alive at the time of the tax cut. We will follow the analysis of this policy, which will be referred to as the constant debt policy, with a discussion of a second policy where debt per capita is permanently increased by $1.

Those households with heads age forty-five or older will not transfer any of the tax cut to their children and thus receive a clear net transfer from future generations. No transfer is returned to their children because the period of economic dependence is over and all families are bequest constrained.(15) For these older households, the macroeconomic policy works nothing like a loan since they are completely disconnected from the future generations paying for the tax cut.

Households with heads between the ages of twenty and forty-four, either have, or are going to have, dependent children. The parents of these households will transfer a portion of their tax cut to their children via human capital investments. The children, who indirectly benefit from the tax through additional parental investment, will also have to pay higher taxes during every year of their working lives. This group, bequest-constrained households connected to their children only through human capital investment, is the main focus of our study. While the policy works like a loan for these families, the terms of the loan will generally differ from that of the simple loan.

Households with heads between the ages of twenty and forty-four at the time TABULAR DATA OMITTED of the tax cut will each be affected by the policy differently. Table III summarizes the impact effect (before behavioral responses) of the constant debt policy on the wealth of parents and children, according to the age of the parent at the time of the tax cut.(16) The ratio in the last column gives the tax cost to children per dollar of wealth (net of tax) transferred to parents. This should be compared to the terms of the simple loan policy presented in Table II. The macroeconomic policy offers more favorable terms (a larger wealth effect) than the simple loan for only very young households, and less favorable terms for most other households. In addition, the lower wealth effect is but one reason the simple loan policy overestimates the ultimate change in the wealth of children from most families when taxes are cut. Other reasons include the substitution and factor price effects of the policy, which are discussed later in this section.

To explain the differential wealth effects, first note that older parents receive the per capita tax cut later in life (lowering its present value), but have fewer years of tax payments. Younger parents receive the cut earlier, but pay taxes longer. We assume annual population growth of 1 percent. This growth successively lowers the annual per capita tax required to service the debt. With this growth rate and the equilibrium interest rates generated in our six cases, our calculations show the net of tax transfer falls with the age of the parent; the disadvantage of receiving the tax cut later in life outweighs the fewer years over which older households must pay taxes. In addition, the differential impact effect on the children of each household also favors younger households. Children of younger parents will become adults later in life. As a result their tax share TABULAR DATA OMITTED will be smaller, since the population of workers will be larger during their tax paying years. In combination, the impact effects on parents and children explain why the wealth effect in Table III is stronger for younger households.

The computations necessary to provide a complete quantitative assessment of the general equilibrium effect of the constant debt policy on each of the fifty-six families of the model are beyond the scope of this paper. However, the partial equilibrium effect (holding the initial equilibrium interest rate and wage rate constant) on the family with parents age twenty, is readily obtained using the method which generated Table II, but employing the loan terms of Table III rather than that of the simple loan policy. Fortunately, the youngest cohort is important in that their loan terms provide an upper bound on the wealth effect of all cohorts alive at the time of the tax cut. The impact of the policy on the children of this family will provide an upper bound to the changes in wealth of all other families.

Table IV presents the effect of a tax cut on the net wealth of children (including behavioral responses) from the family with parents age twenty, for the constant debt and constant debt per capita financing schemes. Under the constant debt assumption, net wealth of the children falls in all cases, just as for the simple loan experiment. The last column assumes a constant debt-per-capita ratio over time. This policy allows debt to increase at the rate of population growth each period, rather than keeping debt constant at the initial level following the tax cut. Thus, the amount of tax revenue necessary to finance the interest payments by the first two generations of each family is reduced.(17) The reduced tax payments for parents and their children increases the wealth effect, and therefore increases the likelihood that consumption will rise for both generations. However, the policy still lowers the net wealth of children from most households. In case 1, the net wealth of children from all families is necessarily lower. In the other cases, the family benefiting most from the policy, with parents age twenty at the time of the tax cut, only experiences an increase in the wealth of its children of at most eleven cents per dollar of tax cut. As discussed below, it is likely that the children of older parents experience losses.

In addition to smaller wealth effects, the substitution effect is stronger for older households, making it more likely that their children's wealth will fall.(18) There are two reasons for this. First, since there are diminishing returns within a period, the average cost of augmenting children's wealth by some fixed amount increases if the investments must be spread over fewer years. Second, if returns to scale fall as children become older (one of the assumptions we use to smooth investments through dependency, see footnote 13), this will further increase costs. All things considered, it is quite possible that the children of most families suffer from such debt policies.

It is also important to note that the general equilibrium factor price effects of any deficit policy may also work against future generations. At the time of the tax cut, consumption will increase for every working household which experiences a net increase in family wealth due to the policy. It is possible that family wealth may fall for some of the older households, but as we indicate in section V, this is at most a small fraction of the population. As a consequence, savings will not increase one-for-one with the increased government demand for funds (provided the tax cut is lump sum as assumed here). The excess demand for funds will raise interest rates and lower wage rates. The change in factor prices will then lower the return to human capital investment and reduce the quantity of transfers made by parents even further than we have already indicated. As pointed out by Poterba and Summers [1987], the aggregate marginal propensity to consume out of a temporary tax cut (financed as in our paper) is very small, even in life-cycle models where generations are completely disconnected. The marginal propensities to consume are yet smaller in our model because of the altruistic connection between parents and dependent children. Thus, including the factor price effects will not alter our qualitative conclusions, and would not change our quantitative estimates significantly.

V. VOTING FOR THE DEFICIT

In the previous section we established that, under realistic parameter settings, a tax cut financed by borrowing will lower the wealth of future generations even if they are linked to current generations by altruistically motivated educational transfers. In this section we ask if the current population of voting households would actually favor such a policy.

Cukierman and Meltzer [1989, 731] suggest that bequest-constrained households who make human capital investment in their children would always have a strict preference for government debt. This is true in the context of the simple overlapping generations model where agents live for two periods, since the terms of the implicit loan induced by a deficit-financed tax cut are the same as for a simple loan. With the return on human capital greater than the interest rate for a bequest-constrained household, a simple loan would expand the families' consumption possibilities and, thus, would clearly be favored by voters. However, remember that when agents live for many periods, the terms of the implicit loan induced by a deficit policy differ according to the age of the household. The question is whether or not the loan terms are favorable enough to cause the majority of households to vote in favor of the temporary tax cut.(19)

To answer the voting question we need to consider the effect of the policy on the welfare of each of the fifty-six voters in the model. Retired voters, between the ages of sixty-three and seventy-five, would clearly favor the policy. They receive no tax cut and pay no additional taxes. Their children, ages thirty-eight to fifty, receive the tax cut which causes their net wealth to rise. Since utility is derived from own consumption and the net wealth of children, households between sixty-three and seventy-five experience a rise in welfare and therefore favor the tax cut.

For working voters between the ages of twenty and sixty-two (in periods of life twenty-one to sixty-three), consider the following maximum value functions:

[J.sub.[t.sub.0]]([T.sub.[t.sub.0]], [T.sub.*[t.sub.0]]) [is equivalent to] max U

subject to (A-1)-(A-3) and (A-5)-(A-7), for [t.sub.0] = 21 to 63, where U (equation (A-4)) and the constraints are defined in the appendix for the case of [t.sub.0] = 21, and where [T.sub.[t.sub.0]] and [T.sub.*[t.sub.0]] are the lump-sum net transfer to parents and lump-sum tax to each child as result of the deficit policy. Totally differentiating [J.sub.[t.sub.0]]([T.sub.[t.sub.0]], [T.sub.*[t.sub.0]]) with respect to the policy and using the envelope theorem gives us

d[J.sub.[t.sub.0]]([T.sub.[t.sub.0]],[T.sub.*[t.sub.0]]) = [([C.sub.[t.sub.0]]).sup.-1/[Sigma]]d[T.sub.[t.sub.0]]

-m[[(1.3)[W.sub.*]].sup.(1-1/[Sigma])][(1+[Delta]).sup.-(54 - [t.sub.0])](1.3)d[T.sub.*[t.sub.0]].

In the appendix, we show the expression above can be rewritten as

[Mathematical Expression Omitted],

where [[Gamma].sub.[t.sub.0]] [is greater than] 0, wH[prime] is the many-period analogue to wh[prime] from section II (see the appendix for an explicit formula), and where the terms for the implicit loans are

[Mathematical Expression Omitted],

[t.sub.0] = 21 to 63, the many-period analogues to 1 + r from section II. It is [Mathematical Expression Omitted], which is reported in Table III as the terms of the implicit loan induced by the deficit policy. Households for which wH[prime] exceeds [Mathematical Expression Omitted], will vote in favor of a marginal decrease in lump-sum taxes financed by government borrowing. A vote in favor of the policy is more likely, the younger is the household, since [Mathematical Expression Omitted] increases with age and wH[prime] is a constant, independent of age.

Households aged sixty-three to seventy-five comprise 18.9 percent of the voting population. This implies that the decisive voter is age thirty-four (just over 31.1 percent of the voting population falls between ages twenty and thirty-four, while just under 31.1 percent of the voting population falls between ages twenty and thirty-three). For the deficit policy to be favored by the majority of households, it is sufficient that the age thirty-four household favors the policy.

Table V presents the oldest working household favoring the policy in each of our six parameter settings under the constant debt financing scheme. Under the first three cases listed, the policy is unanimously favored by all households. As the interest increases under the remaining cases, the cost of financing the debt increases. Consequently, the wealth effect turns negative for older households and support for the policy diminishes.

TABLE V Oldest Working-Voter Favoring Deficit Policy Cases Age (1a) [Sigma] = 0.5, [Gamma] = 0.45, 62 (1b) [Sigma] = 0.5, [Gamma] = 0.45, 62 (2a) [Sigma] = 0.35, [Gamma] = 0.60, 62 (2b) [Sigma] = 0.35, [Gamma] = 0.60, 54 (3a) [Sigma] = 0.20, [Gamma] = 0.75, 37 (3b) [Sigma] = 0.20, [Gamma] = 0.75, 27

Notes: The (a)-case assumes falling returns to scale in the child's human capital production over time, while the (b)-case assumes approximately constant returns over time.

In case (3b), with the highest interest rate, the majority of the population votes against the policy. At first glance, it is somewhat surprising to note that this is also the case where the children's wealth falls the least for the age twenty parents. However, both voter support and the relatively small decrease in the children's wealth are endogenous consequences of the same underlying factors. In case (3b), both the wealth and substitution effects of the policy are weak. Family wealth increases weakly for the age twenty parent and the cost of passing the increment in wealth forward to the children is relatively low. As a result, children's wealth does not fall by much. Thus, the same factors causing the wealth effect to be weak (low [Sigma] and high [Gamma] producing the high interest rate) cause voter support to be weak and the cost of increasing the children's wealth to be low.

VI. CONCLUSION

It is becoming increasingly clear that the mere presence of private intergenerational transfers does not immediately imply the neutrality of government debt policy. First, as shown by Abel [1985], Bernheim, Shleifer, and Summers [1985], and Kotlikoff and Spivak [1981], bequests not motivated by altruism do not imply neutrality. Second, Feldstein [1988] showed that if income is uncertain, a temporary lump-sum tax cut (paid for by a lump-sum tax increase on the next generation) will increase consumption even for households who eventually leave altruistically motivated bequests. Third, Altig and Davis [1989] and Laitner [forthcoming] explain that altruistically motivated inter vivos transfers do not imply neutrality if such transfers are insufficient to relax binding liquidity constraints.

We examine the situation where households are bequest constrained, but where generations remain linked by altruistically motivated human capital investment. Understanding the behavior of such households is important, since they constitute the vast majority of the population. It is well known that deficit policies can shift the consumption possibility frontier outward for bequest- constrained families and, thus, have real effects. The wealth effect of a deficit policy causes consumption to rise for all generations. If, however, there are diminishing returns to human capital investment, the policy also contains a substitution effect. Greater investment is now required to maintain a given level of after-tax wealth for the next generation. As a result, the return on investment falls at every level of parental consumption. This discourages investment and creates the possibility that consumption for the next generation could fall.

We develop a simulation model of bequest-constrained households in order to begin a quantitative examination of deficit polices. For plausible parameter settings, our results indicate that a simple deficit policy will reduce the next generation's wealth for most families. While these results are suggestive rather than conclusive, they do provide an example showing why government intervention into imperfect capital markets may not benefit both generations. The government intervention fails in this sense, despite the fact that, in our example, the government is clearly superior to the private sector in enforcing loans across generations. However, this enforcement ability only applies to the repayment of the loan.(20) There is no straightforward enforcement mechanism which ensures that a sufficient portion of the loan is invested in the family's children, guaranteeing that the loan repayment does not reduce the children's net wealth. We show that the absence of such a mechanism is important. As a consequence, our results weaken the case for deficit financing and pay-as-you-go social security in the presence of bequest-constrained households.

APPENDIX

The Simulation Model

The simulation model assumes individuals are economically dependent on their parents for twenty years. At age twenty, in the twenty- first year of life, they begin independent economic life. At age twenty-five, the unisex individual "produces" approximately 1.3 children, corresponding to a population growth rate of 1 percent. Retirement occurs at age sixty-three and individuals die after seventy-five years of life.

Each individual begins economic life with an initial quantity of non-depreciating human capital, based on their parents' investment, which augments their adult human capital stock in an additive fashion. Throughout their economic life, individuals choose levels of family consumption, and goods and time inputs for both their own adult and their childrens' human capital development.

The modeling of adult human capital decisions is based on Yoram Ben-Porath [1967]. During adult years the production function for gross additions to the stock of human capital follows a Cobb- Douglas specification with decreasing returns to scale, constant output elasticities, and a constant rate of depreciation. Denote the contribution to lifetime wealth of adult human capital accumulation, net of the cost of inputs, by [V.sup.A]. [V.sup.A] is determined solely by wealth maximizing considerations and is independent of the initial stock of human capital bequeathed by parents. Complete discussions of the adult human capital decision are provided in both Ben-Porath and Lord [1989].

The technology constraining a child's human capital production is distinct from adults, although of the same basic Cobb-Douglas form. Parents face the following production function for augmenting their childrens' human capital:

(A-1) [Q.sub.t] = [v.sub.t][([s.sub.t][H.sub.t]).sup.[[Gamma].sub.t]][([D.sub.t]) .sup.[[Lambda].sub.t]],

where

(A-2) [v.sub.t] = [v.sub.26]/[(1+[Tau]).sup.t-26]

(A-3) [[Gamma].sub.t] = [[Gamma].sub.26]/[(1+[Alpha]).sup.t-26]

and

(A-4) [[Lambda].sub.t] = [[Gamma].sub.26]/[(1+[Beta]).sup.t-26]

for parental years twenty-six through forty-five. Here [s.sub.t], [D.sub.t] and [H.sub.t] are parental time and goods inputs, and parental human capital stock at t, while, [v.sub.26], [[Gamma].sub.26] and [[Beta].sub.26] are production function parameters. This specification allows the efficiency scalar and the output elasticities of parental time and goods inputs to vary with the age of the child. These parameters are chosen to mimic characteristics of the input profiles reported by Hotz and Miller [1988]. After the first year, they estimate that the parental time input declines geometrically at a rate of 12 percent. They also could not reject the hypothesis that goods inputs had a constant profile.

We employ the familiar constant-elasticity-of-substitution utility function, augmented with altruistic preferences toward the next generation, as discussed in section II of the text:

[Mathematical Expression Omitted]

where [Sigma] is the intertemporal elasticity of substitution, [Delta] is the pure rate of time preference, [C.sub.t] is family consumption in year t, and m is a relative preference parameter. [W.sub.*], the aggregate wealth of children, is

[Mathematical Expression Omitted]

Here [P.sub.21] is the present value to children of a nondepreciating unit of human capital in the twenty-first year of life, which contributes the wage per unit of human capital (w) to current earnings each year from twenty-one to sixty-three. [H.sub.20] is the number of units inherited per child.

Parental investments in children in each year t are:

(A-7) [I.sub.t] = w[s.sub.t][H.sub.t] + P[D.sub.t]

where P is the price per unit of goods input. Efficiency requires that parents minimize the [I.sub.t] of any [Q.sub.t] by appropriate choice of the goods and time inputs. Consequently, minimum [I.sub.t] depends upon [Q.sub.t] and the lifetime wealth budget constraint may be expressed as:

[Mathematical Expression Omitted]

Outlays on consumption and child development must equal parents' wealth W, the sum of the values of human capital produced as adults [V.sup.A] and the value of the human capital they inherit.

Since both childrens' wealth and parental investment costs depend upon the annual flows of human capital, the [Q.sub.t]s, we may maximize (A-4) subject to (A-7) and the production function equations (A-1) to (A-3) (and utilizing (A5)), by choice of annual consumption [C.sub.t] and human capital flows [Q.sub.t].

The F.O.C. for [C.sub.t] are:

[Mathematical Expression Omitted]

and those for [Q.sub.t] are:

(A-10) m[[(1.3)[W.sub.*]].sup.-1/[Sigma]][P.sub.21]/[(1+[Delta]).sup.5 4]

= [Rho]M[C.sub.t]/[(1+r).sup.t-21]

for t = 26,...,45

where [Rho] is a Lagrange multiplier for parental wealth. The F.O.C. for [Q.sub.t] require that the discounted marginal costs in each period M[C.sub.t] be equated.

It is straightforward to find the [Q.sub.t]s. Equating the M[C.sub.t]s, each [Q.sub.t] may be expressed in terms of [Q.sub.26] and [Rho]. Using (A-5) and combining the F.O.C. for [C.sub.t] and [Q.sub.t], [Rho] may be eliminated and [C.sub.t] and [I.sub.t] expressed in terms of [Q.sub.26], and then all other choice variables, as a function of parents' wealth. The full simulation simultaneously models parents and their children (when adults). In the initial steady state, parental wealth and wealth per child are made equal.

Impact Effect of Macroeconomic Policy

We wish to compute the impact effect of the deficit policy on the wealth of each parent between the ages of twenty and forty-four, and on the wealth of their children. Each parent receives the tax cut of $1. In the following year, taxes are increased by r on all those working. Since the work force grows by the factor (1 + g) each period, next year's tax burden per working household is r/(1 + g). Similar computations are made each year thereafter, until the household retires. From the perspective of the date when taxes are cut, the present value impact of the policy on parents is,

1 - r/[(1 + g)(1 + r)] + r/[[(1 + g)(1 + r)].sup.2]+ ...

+ r/[[(1 + g)(1 + r)].sup.x]}

= 1 - r/[(1 + g)(1 + r)]}

( 1 - 1/[[(1 + g)(1 + r)].sup.x]}/ 1 - 1/[(1 + g)(1 + r)]})

[is equivalent to] 1 - [D.sub.x],

where x = the number of years over which the household pays the tax. The quantity 1 - [D.sub.x] is then discounted back to the household's first period of economic life to get the impact on household wealth,

[[1/(1 + r)].sup.42-x](1 - [D.sub.x]).

The children from each family must pay taxes for their entire lives. The children of the youngest parents must pay,

[(1 + r)/[(1 + g).sup.25]][D.sub.43]}[(1 + g).sup.25] = (1 + r)[D.sub.43].

If the population growth rate was zero, the child would pay the same tax as his twenty-year-old parent, plus an additional amount r in the first period of economic life. With population growth the tax burden is reduced for the child relative to the parent by the factor 1/[(1 + g).sup.25]. However, there are [(1 + g).sup.25] children, so we get (1 + r)[D.sub.43] as the decrease in the wealth of the children from the household with a twenty-year-old parent.

The children of the next oldest parent, age twenty-one, have a smaller cohort of workers to share the tax with, so they pay

[(1 + r)/[(1 + g).sup.24]][D.sub.42]}[(1 + g).sup.25] = (1 + r)(1 + g)[D.sub.43].

The same reasoning applies for the children of all remaining households. For example, the children of the oldest parents pay,

(1 + r)[(1 + g).sup.25][D.sub.43].

Derivation of equation (4)

From differentiating [J.sub.[t.sub.0]]([T.sub.[t.sub.0]], [T.sub.*[t.sub.0]]) with respect to the policy, we have

[([C.sub.[t.sub.0]]).sup.-1/[Sigma]]d[T.sub.[t.sub.0]]

-m[[(1.3)[W.sub.*]].sup.(1-1/[Sigma])][(1+[Delta]).sup.-(75 - [t.sub.0])(1.3)d[T.sub.*[t.sub.0]].

From the first-order conditions ((A-9) and (A-10)), we have

[([C.sub.[t.sub.0]]).sup.-1/[Sigma]] = [[(1 + [Delta])/(1 + r)].sup.([t.sub.0]-21)]

[([C.sub.21]).sup.-1/[Sigma]]} = [[(1 + [Delta])/(1 + r)].sup.([t.sub.0]-21)]

m[[(1.3)[W.sub.*]].sup.-1/[Sigma]][(1+[Delta]).sup.-(75-21)]

[[P.sub.21]/M[C.sub.26][(1 + r).sup.5]]},

where

[[P.sub.21]/M[C.sub.26][(1 + r).sup.5]] [is equivalent to] wH[prime].

Substituting for [([C.sub.[t.sub.0]]).sup.-1/[Sigma]] above and pulling out common terms gives

[Mathematical Expression Omitted].

1. Blinder [1976] and Davies and St. Hillaire [1987] report that most households receive little or no inheritance. Menchik and David [1983] find only the upper quintile in their sample exhibit bequest shares which are responsive to variations in wealth, suggesting that they were planned. Moreover, their sample initially omits about one-third of the population, who, because of small estates, were not required to file probate records. This implies the upper quintile of their study actually represents the upper 14 percent of the population. Mariger [1987] claims his estimates of a life-cycle model indicate only those with financial net worth in excess of $250,000 in 1963, the top 6 percent of the sample, have a bequest motive. Hurd [1987; 1989], contrary to previous cross-sectional studies, presents panel data evidence showing the elderly do dissave. He concludes that intentional bequests are only concentrated among the very wealthy. Kotlikoff [1988] disputes the empirical importance of Hurd's findings, arguing instead that the amount of wealth decumulation is insignificant. More importantly, however, Hurd shows that elderly households with children do not dissave any less rapidly than those without children.

2. Menchik [1980; 1985] finds bequests tend to be evenly spilt among children. This is in contradiction with altruism if there are significant differences in earnings capacities across children. Cox [1987; 1990] finds that recipient income and the size of inter vivos transfers are positively correlated, instead of negatively correlated as predicted by altruistic models. Finally, Altonji et al. [1992] were able to reject the notion that total family resources, and not the distribution of resources across generations, is the primary determinant of a generation's consumption.

3. In fact, many of the studies cited above also contain results consistent with the idea that altruism between family members is an important source of intergenerational transfers. Hurd's [1987] data shows there are substantial transfers from parents to children early in life. When first entering retirement, couples with children have about one-third less wealth than those without children. Also, some inter vivos transfers are reported for approximately 20 percent of the families in his sample.

The sign and statistical significance of the result reported by Cox [1987; 1990] are sensitive to the sample chosen. His finding of a positive relationship between transfers and recipient income was based on a sample which excludes recipients who were students. When students are included, as in Chiswick and Cox [1987], the effect of recipient income on the transfer amount becomes negative or statistically insignificant, depending on which estimation technique is employed. Furthermore, Cox [1990] reveals that recipients of inter vivos transfers have lower permanent income than non-recipients. This is not only consistent with altruism, it also helps to explain the equal division result of Menchik. Most of the "equalizing" transfers may well take place inter vivos rather than at death.

4. The presence of inter vivos transfers does not necessarily imply Ricardian Equivalence if there are liquidity constraints and the transfers are not sufficient to overcome them. See Altig and Davis [1989] and Laitner [forthcoming].

5. The existence of such loans is, apparently, the point on which Barro and Drazen depart. As explained by Rangazas [1991b], implicit loans are logically equivalent to an operative "gift", from children to parents, during the parents' later years. An operative gift motive guarantees the Ricardian theorem holds, provided there are no liquidity constraints (see footnote 4).

6. Gary Becker [1988] recently used Drazen's argument to explain the tandem upward trends in expenditures per adult over sixty-five and per child under age twenty-two. Becker sees households as rationally voting for a combination of policies which effectively create a welfare-improving implicit loan between the generations. He states, "... the popular view of generation fighting--that public expenditures on the elderly grew rapidly because the old became politically powerful as they become more numerous--cannot explain why expenditures on children grew just as rapidly" [1988, 9]. Cukierman and Meltzer [1989], also building from Drazen's insight, were able to construct a model of the political process where households vote for public debt issue in order to relieve their inability to enforce liabilities on their children.

7. This analysis assumes either that altruism runs in just one direction, from parent to child, or that both bequest and gift motives are not operative. It will also be noted that this specification of preferences differs from that where the next generation's utility enters the current generation's utility function. The two specifications will produce different predictions only if (1) there is a labor-leisure choice or (2) the analysis includes a change in the interest rate. Parents will fail to recognize the full implications of a change in work effort or the interest rate if they focus solely on the "sources of funds" side of the next generation's budget constraint. Since our analysis involves the partial equilibrium effects of lump-sum transfers, with a fixed level of leisure consumption, the two specifications can be viewed as very close substitutes.

8. Davies and St. Hilaire [1987] use a similar diagrammatic approach to analyze different issues.

9. As a referee points out, a more elaborate sequence of taxes and transfers could conceivably generate a theoretically unambiguous Pareto improvement.

10. For the typical household, basic reading, writing and arithmetic skills, as well as health habits, are likely to be maintained by the daily experiences of production and consumption. For this reason, the initial stock of human capital is not subject to depreciation.

11. The empirical support for these parameter ranges is discussed in Lord and Rangazas [1991]. It should also be noted

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Author: | Lord, William; Rangazas, Peter |
---|---|

Publication: | Economic Inquiry |

Date: | Oct 1, 1993 |

Words: | 9459 |

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