Marginal welfare costs of taxation with human and physical capital.

Allgood, Sam ; Snow, Arthur

I. INTRODUCTION

Marginal welfare cost of taxation is the amount by which the social cost of an additional tax dollar differs from 1 because of distortionary taxation. Browning and Johnson (1984), Stuart (1984), Browning (1987), Ballard (1988), and Allgood and Snow (1998) use static models of the U.S. economy, in which labor supplies adjust but the stocks of human and physical capital are fixed, to calculate estimates of this welfare cost relevant to cost-benefit analysis. The studies by Lucas (1990) and Perroni (1995) incorporate human and physical capital into calculations of excess burden for the purpose of comparing alternative tax systems but do not address the welfare costs of marginal tax and spending reforms. Ballard et al. (1985) and Judd (1987) provide estimates of welfare cost using models that allow the stock of physical capital to change in response to marginal reforms, but the stock of human capital is exogenous in these studies. However, Judd (2001) argues that there is ample evidence indicating that human capital investment decisions have a significant effect on the cost of altering the tax system, which suggests that these decisions could also have an important influence on marginal welfare cost.

In this article we present estimates of welfare costs for marginal reforms to government tax and spending policies when labor supply, saving, and education decisions are all endogenous. We focus our analysis on marginal reforms because as Skinner and Slemrod (1985) observe, most policy reforms enacted do not involve replacing one tax or spending system with another, but instead typically entail marginal adjustments in tax laws and government appropriations. Using a perfect foresight, overlapping generations model with a three-period life cycle, we derive analytical expressions for the changes in labor supply, saving, and education and use them to calculate marginal welfare cost. As shown by Auerbach et al. (1983) in overlapping generations models, steady-state welfare comparisons of alternative tax policies are biased unless households are compensated for intergenerational redistribution along the transition path. To arrive at our steady-state estimates of welfare costs, we adapt the compensation method introduced by Gravelle (1991) for analyzing fundamental tax reforms to the context of incremental tax and spending reforms.

In a static, one-consumer model, Triest (1990) has shown that marginal welfare cost (MWC) is positive solely because of tax "leakage," the decline in tax revenue caused by reductions in the tax base. We extend this insight to an intertemporal context that incorporates tax leakage arising from changes in both human and physical capital investment. We evaluate three sets of reforms: first, a revenue-neutral reduction in the tax on capital income funded by a higher tax on labor income; second, spending on a public good financed by either a higher tax on labor or interest income; third, a per capita lump-sum transfer, or demogrant, also funded by either a higher tax on labor or interest income. We find that marginal welfare costs are uniformly lower in the dynamic model, where investment decisions are endogenous, than in the static model, where investment decisions are fixed, and that the majority of the difference between the dynamic and static estimates is attributable to human capital decisions. The principal reason is that a reallocation of time between labor hours and human capital investment has opposing and potentially offsetting effects on (effective) labor supply. As a result, labor supply responds less elastically in the dynamic model, and changes in labor supply are the main source of tax leakage, because wage taxation is the main source of tax revenue. We also find that shifting marginal financing from capital to labor results in a lower welfare cost, the reason being that such a change encourages saving, which increases wage rates and stimulates labor supply, leading to a reduction in marginal welfare costs.

Our calculations are based on parameter values that are broadly representative of the U.S. economy. Judd (2001) suggests that little is known about welfare cost of taxation because estimates for key parameters can be found over a wide range of values. Accordingly, we calculate estimates of MWC using two sets of parameter values, one with higher tax rates and labor supply elasticities than the other set. Our numerical results are largely consistent with the theoretical literature on optimal taxation and the applied literature that reports estimates of welfare gains and losses when one tax system replaces another. For example, our finding that a marginal shift from interest to wage taxation reduces welfare cost is consistent with the conclusion reached by Judd (1985), who argues that the optimal tax on physical capital is 0, and with the results obtained by Ballard et al. (1985) and Judd (1987) using models with exogenous human capital. Our results are also consistent with the conclusion reached by Auerbach et al. (1983) and Gravelle (1991) in the context of fundamental reforms, that ignoring redistributional effects that arise in dynamic models of tax reform can substantially bias upward estimates of welfare cost.

As a further sensitivity analysis, we calculate estimates of MWC holding human capital investment fixed using both sets of parameter values along with a third set in which the higher tax rates are paired with higher wage and income elasticities of labor supply. In each case, the values obtained for MWC are higher when households are not allowed to adjust human capital investments than when they are free to adjust both saving and education decisions. Not surprisingly, higher wage elasticities result in higher estimates of MWC.

In the next section we set out a dynamic model of welfare cost estimation that implements a compensation mechanism to isolate efficiency from redistributional effects. In section III, we present estimates of welfare costs for the U.S. economy and explore the importance of the human capital decision. Conclusions are presented in the final section.

II. MEASUREMENT OF WELFARE COST

We study welfare cost in a perfect foresight, overlapping generations model with three-period life cycles. Young households may invest in human capital, whereas young and middle-aged households supply labor and invest in physical capital. Old households are retired. We abstract from government debt and private bequests to focus on life-cycle motivations for investment in human and physical capital. After defining welfare cost in this context, we provide calculations of steady-state welfare costs for alternative policy reforms.

Welfare Cost of Taxation and Public Spending

To define welfare cost, we adopt the cost-benefit criterion and add together the benefits and costs accruing to each household, using the equivalent variation money-metric measures of utility change. In a comparison of steady states, this measure of the change in social welfare is proportional to the discounted lifetime net benefits of all living and future generations. After isolating social costs from social benefits, welfare cost is identified by subtracting from social costs the increase in tax revenue. When the change in social welfare is evaluated in this manner and there are no utility interdependencies, lump-sum redistributions of income have no social value, except insofar as they influence welfare cost. In the absence of distortionary taxation, welfare cost equals 0 and, along a golden rule path, the model yields the Samuelson rule for efficiency in the supply of a public good. When the economy is not on a golden rule path, changes in investment behavior have welfare effects that can be allocated either to social benefits or to social costs. Our model also incorporates an externality involving human capital investment, whereby the stock of human capital directly affects the productivity of investment in education. We allocate the welfare effects of changes in this externality to social costs, along with any golden rule effects.

Households consume a numeraire good [x.sub.t] and leisure time [l.sub.t] in each period t of the life cycle. A household may also devote time to education [e.sub.t] in period 1 of the life cycle (so [e.sub.t] = 0 for t = 2, 3). Once a household has decided how much education to obtain and how to allocate income over the life cycle, the household maximizes period t utility [u.sub.t]([x.su.t], [l.sub.t], z) by choosing [x.sub.t] and [l.sub.t] given the quantity z of a public good supplied exclusively by government, and given the budget constraint

(1) [x.sub.t] + [w.sub.t][[delta].sub.t][l.sub.t] = [I.sub.t],

where[w.sub.t]= (1 - [m.sub.t])W is the after-tax wage rate,[m.sub.t] is the marginal tax rate, W is the marginal product of effective labor hours, and [[delta].sub.t] is the household's labor productivity factor. Let [V.sup.t]([w.sub.t][[delta].sub.t], Z, [I.sub.t]) denote the resulting indirect utility function for the household in period t. The income [I.sub.t] allocated by the household to period t is determined by lifetime decisions concerning investment in human and physical capital. Specifically,

(2) [I.sub.t] [equivalent to] [w.sub.t][[delta].sub.t] (T - [e.sub.t]) + [A.sub.t] + ([K.sub.t]/p) - [K.sub.t+1],

where T is the time endowment, [A.sub.t] is a governmental lump-sum transfer, [K.sub.t] is the amount of capital owned by the household in period t, and p is the discount factor, so that 1/p [equivalent to] [1 + (1 - [tau])r] is the gross after-tax return to capital, given the tax rate [tau] and the interest rate r. [K.sub.t+1] is the amount the household saves in period t. W and r equal the marginal products of labor and capital, respectively, and the before-tax factor prices are therefore endogenous, varying with changes in aggregate factor supplies. (1) Finally, government collects

(3) [R.sub.t] [equivalent to] [m.sub.t]W[[delta].sub.t][h.sub.t] + [tau]r[K.sub.t]

in tax revenue, where

(4) [h.sub.t] [equivalent to] T - [e.sub.t] - [l.sub.t]

is the household's supply of labor hours. (2)

Education undertaken in the first period increases productivity in the second period according to the relation

(5) [[delta].sub.2] = [[delta].sub.1] + [[bar.[delta]].sub.2] f([[delta].sub.1][e.sub.1])

for an increasing concave function f, with f(0) = 0. Here we incorporate an education externality, inasmuch as the average productivity of households currently in middle age, denoted by [[bar.[delta]].sub.2], is assumed to have a direct affect on the addition to human capital realized by young households. Since households are retired during the third period of the life cycle, [[delta].sub.3] equals 0.

A household's education and saving decisions maximize discounted lifetime utility,

(6) [V.sup.1]([w.sub.1][[delta].sub.1], z [I.sub.1] + [sigma][V.sup.2]([w.sub.2][[delta].sub.2], z, [I.sub.2]) + [[sigma].sup.2][V.sup.3](0, z, [I.sub.3])

subject to the lifetime budget constraint

(7) [I.sub.1] + p[I.sub.2] + [p.sup.2][I.sub.3] + [w.sub.1][[delta].sub.1] [e.sub.1] - p[w.sub.2][[bar.[delta]].sub.2] f ([[delta].sub.1][e.sub.1])T = [I.sup.y],

where [sigma] is the subjective discount factor, and

(8) [I.sup.y] = [w.sub.y][[delta].sub.1]T + [A.sub.1] + p([w.sub.2][[delta].sub.1]T + [A.sub.2]) + [p.sup.2][A.sub.3]

is a young household's lifetime income consisting of the current and discounted future value of the time endowment plus the current and discounted lump-sum transfers [A.sub.t]. (3)

We assume that an incremental policy reform leads to a small change in the steady state so that we can identify net benefits with marginal changes in utility, in keeping with previous studies of welfare cost. For a household in period t of the life cycle, the net benefit [NB.sub.t] [equivalent to] d[V.sup.t]/[V.sup.t.sub.I] can be evaluated by using Roy's identity to obtain

(9) [NB.sub.t] = [MRS.sub.t]dz -[l.sub.t]d([w.sub.t][[delta].sub.t]) + d[I.sub.t] =[[MRS.sub.t]dz + d[A.sub.t]] - d[A.sub.t] + [l.sub.t]d([w.sub.t][[delta].sub.t]) - d[I.sub.t]],

where [V.sup.t.sub.I] denotes the household's marginal utility of income, and [MRS.sub.t] [equivalent to] [V.sup.t.sub.z]/[V.sup.t.sub.I] is the marginal benefit of an increase in consumption of the public good. (4) The second line follows by adding and subtracting d[A.sub.t] to isolate marginal benefit within the first set of brackets and marginal cost within the second set.

By combining the differential changes d[I.sub.t] And d[R.sub.t] implied by equations (2) and (3), the expression for marginal cost can be rewritten in terms of the change in tax revenue and then aggregated to obtain marginal social cost per household (MSC). The resulting expression can be decomposed into four distinct elements, (5)

(10) MSC [equivalent to] - G - E + dR + WC.

The first element consists of golden rule effects that arise in the overlapping generations context,

(11) G [equivalent to] [1/p -(1 + n)] x {d[K.sub.3] + (1 + n)[d[K.sub.2] + [w.sub.1][[delta].sub.1]d[e.sub.1]}'

where n is the exogenous population growth rate. These effects vanish when the economy is on a golden rule path and 1/p= 1 + n. If the economy is not on a golden rule path and (1 + n) < 1/p because the growth rate n is less than the after tax rate of return (1 - [tau])r, then equation (11) shows that any reform that encourages capital investment has a positive golden rule effect that lowers the reform's marginal social cost. The second element of MSC,

(12) E [equivalent to] (1 + n) [w.sub.1]f([[delta].sub.1][e.sub.1])/pf' ([[delta].sub.1][e.sub.1])](d[[bar.[delta]].sub.2])/ [[bar.[delta]].sub.2],

is the marginal externality cost borne when the average stock of human capital held by middle-aged households declines (f' denotes the first derivative). Thus, reforms that encourage human capital investment have positive human capital externality effects that lower marginal social cost.

The remaining elements of MSC are associated with changes in taxation. The first of these is the change in aggregate tax revenue per household, dR, and the second is the welfare cost which, for a household in period t of the life cycle, amounts to

(13) [WC.sub.t] [equivalent to] -[m.sub.t]Wd([[delta].sub.t] [h.sub.t]) - [tau]rd[K.sub.t],

where the changes in labor supply and investments in human and physical capital are calculated for the steady state. Aggregating equation (13) across households, we obtain WC. As in Triest's analysis, we find that welfare cost is the loss in tax revenue that must be made up when the tax bases decline in response to the policy reform. The education externality influences welfare cost through its effect on the steady-state stock of human capital, since equation (5) implies

(14) d[[delta].sub.2] = [[bar.[delta]].sub.2]f'([[delta].sub.1]d[e.sub.1]) [[delta].sub.1]d[e.sub.1] + f([[delta].sub.1][e.sub.1]) d[[bar.[delta]].sub.2].

Thus a reduction in the human capital stock of middle aged households (d[[bar.[delta]].sub.2] < 0) contributes to welfare cost through a reduction in their descendants' effective labor supplies ([h.sub.2]d[[delta].sub.2]).

The change in social welfare is determined by adding net benefits across households to obtain (6)

(15) NB/dR = [beta]([SIGMA][MRS.sub.t]/c) + (1 - [beta]) + [(G + E)/dR] - (1 + MWC)

after dividing by dR. The parameter [beta] represents the proportion of the increase in tax revenue spent on the public good, the remainder being allocated to equal per capita transfer payments, c is the marginal cost of the public good, [SIGMA][MRS.sub.t] denotes the sum of each household's willingness to pay for the public good, (1 + MWC) is the marginal cost of public funds, and

(16) MWC [equivalent to] WC/dR

denotes marginal welfare cost. In the absence of distortionary taxation, welfare cost equals 0 and the marginal cost of a tax dollar is equal to 1. However, in the presence of distortionary taxation, welfare cost is equal to the tax leakage, which is positive when tax bases decline in response to the policy reform, and the marginal cost of a tax dollar then exceeds 1 by the marginal welfare cost, MWC.

Equations (11), (12), and (13) suggest that welfare costs arising from changes in effective labor supply will be the major contributor to marginal social cost. The golden rule effects in equation (11) are multiplied by [1/p - (1 + n)] < 1, and this dampens the relative contribution of these changes to MSC. The marginal externality cost in equation (12) depends on the percentage change in the average stock of human capital, d[[bar.[delta]].sub.2]/[[bar.[delta]].sub.2]. Although the absolute change in [[bar.[delta]].sub.2] may be large, the percentage change may not be, in which case the contribution of E to MSC is small. For welfare cost, given in equation (13), we note that [tau]r is typically quite small so that changes in the capital stock will tend to have a small impact on welfare cost. However, the change in hours worked is multiplied by [m.sub.t]W[[delta].sub.t] and the change in labor productivity is multiplied by [m.sub.t]W[h.sub.t]. These effects will tend to be large relative to the others. Because welfare cost is tax leakage, it is not surprising that the primary source of welfare cost derives from the primary source of tax revenue. However, this does not mean that changes in the capital stock are unimportant. As we show, changes in saving decisions have a substantial effect on the response of labor supply to a given reform.

To evaluate the change in steady-state tax revenue and the associated welfare cost of a specified policy reform, changes in labor supply and investments in physical and human capital must be determined for each generation. Accordingly, we introduce our method of compensating households to control for transitional effects that would otherwise compromise estimates of both the change in tax revenue and welfare cost.

Compensated Income Changes for Incremental Policy Reforms

To isolate efficiency consequences from redistribution associated with transitional effects, we compensate each household for changes in taxation and factor prices before evaluating optimal adjustments in labor supply and investment decisions. Because capital decisions made earlier in the life cycle cannot be changed, those households retired when the policy change is implemented do not contribute to welfare cost, but over the transition path, households living in earlier periods of the life cycle make capital decisions that do ultimately contribute to welfare cost. For this reason our compensation for a given household has two parts. The first is household-specific and returns to a household the "gross" change in its current tax payment, that is, the change that would occur if capital and time allocations were perfectly inelastic, plus any reduction in the current value of its capital and labor caused by changes in before-tax factor prices. The second part of the compensation payment is the same for each household and subtracts the per-household tax leakage plus the per household change in tax revenue. Because the change in tax revenue includes the tax leakage, the second part of the compensation paid to households is simply the per household change in tax revenue that would occur if savings and time allocations were supplied inelastically. Thus, each household's compensation depends only on changes that are exogenous to it. In the aggregate, these compensation payments net out to 0.

By way of illustration, consider a reform that shifts the tax burden from wages toward lump-sum taxation, which has a positive social value of--WC. Under our approach to compensation, all generations share in the welfare gain, with the young gaining the most and the old gaining the least. Young and middle-aged households also enjoy the reduced cost of their leisure time, whereas the young bear the cost of reduced compensation for the tax on their return to human capital investment. (7)

As emphasized by Gravelle (1991), a compensation scheme must not only control for transitional redistribution but also specify the distribution of efficiency gains or losses among cohorts. Alternative schemes would have different distributional consequences, whether compensation is effected along a transition path, as in the procedure followed by Auerbach et al. (1983) to analyze the efficiency of fundamental tax reforms, or only for the steady state, as in the procedure developed by Gravelle for fundamental tax reforms and adapted here to analyze incremental tax and spending reforms. As a result, there is no unique measure of welfare cost. Our method is recommended by being computationally straightforward and, as illustrated by the preceding example, by allocating gains (and losses) in a pattern consistent with the life cycle.

Calculation of Compensated Changes in Steady State

Young and middle-aged households adjust their labor supply and investment decisions by reallocating income over their remaining lifetimes in response to a specified policy reform along with the compensated income changes just discussed. We assess the changes in steady-state values by determining the optimal responses of young households to a specified policy reform that is accompanied by the compensated change in lifetime income. The first-order necessary conditions for the optimal allocation of income over the life cycle and allocation of time to education given by the maximization of equation (6) yield comparative statics equations for [I.sub.1], [I.sub.2], [I.sub.3], and el that can be evaluated using the compensated change in lifetime income along with specified changes in tax rates and in public spending on transfers and on the supply of the public good.

Population Heterogeneity

Thus far, age is the only source of heterogeneity in the population. In our calculations, we introduce heterogeneity within each generation in three dimensions. We allow the endowment of human capital ([[delta].sub.1]) and the number of persons per household to vary within each generation, and we admit a graduated tax structure for wage income so that wage tax rates may differ among households who are in the same period of the life cycle. Ten lifetime profiles are constructed using the 1991 Panel Study of Income Dynamics to incorporate these sources of heterogeneity in a fashion that mirrors the U.S. economy. (8) Because we consider only incremental policy reforms, we assume that no household changes its lifetime tax bracket profile. Hence, we can analyze the effects of incremental changes in the progressivity of the rate structure by adjusting both the tax brackets and the marginal rates applying within each bracket.

III. ESTIMATES OF WELFARE COST

As in the static, one-consumer model reviewed by Snow and Warren (1996), neither the sign nor the magnitude of MWC can be determined without specifying several behavioral and technological elasticities. These values are taken from previous research intended to be representative of the U.S. economy. Consistent with Lucas (1990) and Judd (1987), the tax on capital income is set at 40% ([tau] = 0.4). As in Engen et al. (1997) and Altig et al. (2001), the population growth rate is set to 3% (n = 0.03), and the before-tax rate of return to capital at 8% (r = 0.08). We note that our estimates are not sensitive to small variations in the values chosen for these parameters.

There is still substantial debate over the correct choice of tax parameters and labor supply elasticities for the U.S. economy. In studies of marginal changes to the Earned Income Tax Credit, Browning (1995) assumes that effective marginal tax rates on wage income are high, some exceeding 60%, while Triest (1994) uses marginal tax rates less than 40%. To illustrate the effects of parameter choice, we adopt the tax rates and elasticities first employed by Browning and Johnson (1984) and subsequently by Allgood and Snow (1998) and Allgood (2003). These parameter values are labeled Parameter set A in Table 1. For comparative purposes, we also adopt the lower values employed by Triest (1994). These parameters are labeled Parameter set B in Table 1.

The magnitude of the intertemporal elasticity of substitution, which governs the willingness to transfer income across time, plays a prominent role in previous studies, and is important here as well. Even though our analysis is confined to incremental reforms and our approach does not require knowledge of a transition path, dynamic estimates of marginal welfare cost can be quite sensitive to the value of the intertemporal elasticity of substitution, especially in the case of capital taxation. We report estimates based on a value of one-half for this elasticity, which is representative of the literature. (9) As in previous studies, the estimated values fall as this elasticity falls, and we note the values obtained when the elasticity is one quarter and one eighth.

Differential Incidence: Revenue-Neutral Reform

Table 2 presents estimates of the positive and normative effects of a differential incidence reform that shifts taxation from capital toward labor income (dm = 0.0001, d[tau] < 0) while collecting the same amount of revenue in total. The intuitive predictions of a decline in human capital investment accompanied by an increase in savings are confirmed for both parameter sets. The conclusion that welfare is enhanced by shifting the tax burden away from physical capital toward labor income is consistent with the results reported by Chamley (1981), Judd (1985), and Coleman (2000). Their studies of an infinitely lived representative consumer reveal that in the absence of capital market imperfections, the optimal tax rate on capital income is 0. Although our result applies only for a marginal reform, the implication is that taxing capital income is inconsistent with efficiency.

The magnitudes of the positive and normative effects of this reform are quite sensitive to the choice of tax and labor supply parameters. The estimated welfare gain using parameter set A is about 4.5 times larger than the gain estimated with set B, and the increase in labor supply is 10 times larger, whereas the increase in the capital stock is only about 30% larger.

A closer inspection of Table 2 and formula (13) for welfare cost reveals that the welfare gain is largely derived from the fact that the reform encourages labor supply. The tax gained from increased saving ([tau]rdK) is very small because the product of the tax and interest rates is small (0.2 x 0.08 = 0.016). For this reason, changes in saving have a relatively small direct effect on welfare cost estimates. However, because the reform encourages investment in physical capital, the after-tax wage rate increases, which in turn leads to an increase in labor supply to take advantage of the higher wage rate and the enhanced incentive to save out of wage income.

Balanced Budget Analysis: Exhaustive Spending Reform

Table 3 reports our estimates of MWC for fiscal reforms in which the increase in tax revenue finances greater spending on a public good under the assumption of ordinary independence. (10) MWC is lower for increased taxation of labor rather than capital income. Our estimates of MWC for increased labor and capital income taxation are 7.00 cents and 12.84 cents per dollar of tax revenue, respectively, using parameter set A, and are reduced by about half using the smaller parameter values in set B. (11) These estimates contrast sharply with those derived by Ballard et al., who obtained estimates of 23.4 cents for labor taxes and 21.7 cents for capital taxes from a computable general equilibrium model. Their model, however, ignores human capital investment decisions and treats capital accumulation in an ad hoc fashion by including savings as an argument in utility. A more sophisticated accounting for intertemporal margins of choice, including human capital investment, and lower labor-supply elasticities are responsible for the much lower estimates of welfare costs that we obtain. (12)

Balanced Budget Analysis: Incremental Demogrant Reform

The estimates of MWC for a demogrant reform, in which increased tax revenue is redistributed as an equal per capita lump-sum transfer, are reported in Table 4. They are uniformly higher than those for exhaustive spending because the spending effect of the demogrant transfer reduces labor supply, and we assumed that an increase in public good supply has no spending effects. It is also the case that raising the additional revenue through a higher tax on interest rather than wage income results in a higher estimate for MWC.

Judd (1987), analyzing an incremental demogrant in a perfect foresight model with an infinitely lived consumer, obtains an estimate of 4 cents for MWC in the case of increased wage taxation, and 36 cents in the case of increased capital taxation, compared with our estimates of 14.70 cents and 20.97 cents, respectively. (13) When we use the smaller parameter values in set B, the estimates are 5.50 for increased labor taxation and 6.53 for an increase in the tax on interest income. Thus, like Judd, we find that welfare cost is higher for capital rather than labor taxes, but our results suggest that life cycle and human capital decisions, which are absent from Judd's model, along with the absence from our model of a bequest motive for capital accumulation, which is present in Judd's model, have a substantial mitigating effect on the estimated welfare costs of demogrant reforms financed by capital taxation. We return to this issue in the next section.

Our predictions concerning human capital are consistent with the conclusion reached by Lin (1998) who, in analyzing an overlapping generations model, found that when an increase in wage taxation reduces the interest rate, time spent on human capital investment increases. Yet this stands in contrast to arguments often given in support of lower tax rates. Becker et al. (2003) argue in a Wall Street Journal editorial that reducing tax rates on labor income will encourage investment in human capital by increasing its rate of return. Yet as Judd (2001) points out, reducing tax rates on labor income also increases the cost of human capital investment, so that the net effect is theoretically ambiguous. Lucas (1990) reports, for example, that the costs and benefits of schooling are equally affected for the reforms he considers, and endogenous growth in human capital has little effect on his results. For both sets of parameters used here, we find that in most cases human capital investment increases in response to an increase in wage taxation.

The results in Table 4 illustrate the role of the marginal tax rate. With parameter set B, an incremental demogrant funded by a higher tax on wage income reduces investment in human capital, but with parameter set A the opposite occurs. We also calculated MWC for this reform using the labor supply elasticities and average tax rates of set A, with the marginal tax rates from set B. Switching to the lower marginal tax rates of set B causes the change in human capital investment to switch from positive (0.8640) to negative (-0.2120). When we use the labor supply elasticities and average tax rates from parameter set B with the marginal tax rates from set A, the change in human capital investment again changes sign, this time from negative (-0.3253) to positive (0.6955). Thus we find that increased wage taxation encourages human capital investment when marginal cost and benefit are initially low, but has the opposite effect when they are initially high.

The Importance of Compensation

Gravelle (1991) reports that with labor supply endogenous, the switch from an income to a wage tax lowers welfare by 1.10% using an uncompensated procedure but raises welfare by 0.15% using a compensated procedure. Our estimates reveal a similar pattern. The marginal welfare costs of the exhaustive spending reform and the demogrant are both lower when the compensation method is used. With parameter set A, MWC for the exhaustive spending reform is 21.36 cents for an increase in wage taxes without the compensation scheme. In general, estimates of MWC obtained without using the compensation scheme are about twice those obtained when compensation is implemented. For the revenue-neutral reform, estimates of welfare cost fit the same pattern but are not so strongly affected by the compensation method. Welfare cost without compensation is -0.1113 compared with -0.1088 with compensation.

The Role of Human Capital Investment

Our discussion thus far suggests only a limited role for human capital decisions in determining the welfare cost of marginal reforms. To reveal the importance of human capital investment, we recalculate MWC for balanced budget reforms financed by increased wage taxation while artificially holding the level of human and physical capital investment constant. The results are reported in Table 5 in the column labeled Static Model. Next, we estimate the dynamic model allowing physical capital investments (and labor supply) to change but holding investment in human capital constant. These results are reported in the second column of entries in Table 5 labeled Exogenous Education.

For exhaustive spending and parameter set A, the static value of 16 cents per dollar for MWC is in the range of estimates obtained by Browning (1987) (23.0 cents) and Ballard (10.3 cents). We observe that the static estimate of MWC overstates the dynamic estimate by 9 cents, or more than 100%, for our base case. However, when Triest's smaller parameter values are used, MWC for the static model is only 5.50 cents and falls to 4.25 cents for the dynamic model. The direction of the bias is the same, but its relative magnitude is much smaller. The same pattern emerges for the demogrant reform. Table 5 also reports estimates of MWC using parameter set A after doubling the uncompensated wage elasticities for the second through fifth quintiles and increasing all of the income elasticities by 50%, resulting in compensated elasticities ranging from 0.38 to 0.66. (14) The resulting parameters (set A') yield the highest values of MWC, but these show the same pattern, falling from 0.2946 in the static model to 0.158 in the dynamic model.

Our finding that MWC is uniformly smaller in the dynamic model is explained by three factors. The first recognizes that a household's future consumption levels are fixed in the static model, where investments cannot be adjusted, but are endogenous in the dynamic model, where investments can be freely altered. Hence, the dynamic response of labor supply to an increase in the wage rate is equal to the static response plus the response to increases in future consumption levels multiplied by the response of these consumption levels to an increase in the tax rate, as in equation (30) of Neary and Roberts (1980). As long as leisure and future consumption levels are normal, these products are positive. (15) As a consequence, the decline in labor is smaller when saving decisions are endogenous than in the static model, where saving decisions are fixed. The second factor has already been noted, namely that in the dynamic model, welfare cost is predominantly the tax leakage associated with reductions in labor supply, which is the only cause of welfare cost in the static model. Because labor supply falls by less when savings are endogenous, welfare cost is correspondingly smaller as reflected in the estimates in the second column of Table 5.

The third factor concerns human capital investment. The estimates reported in Table 5 reveal that the majority of the decline in moving from the static to the dynamic model is attributable to human capital decisions. This finding is consistent with the conclusion reached by Judd (2001), that making human capital endogenous increases the welfare gain of replacing income taxation with a tax on consumption. In our balanced budget analysis, the increased investment in human capital (see Table 3) would allow labor hours to decline while maintaining effective labor supply. In our experiments, households choose to reduce labor hours further, so that effective labor supply declines. However, the resulting tax leakage is smaller than it would be if households could not substitute between labor hours and human capital investment.

Golden Rule and Human Capital Externality Effects

In the overlapping generations framework, a marginal reform that moves the economy toward its golden rule path improves welfare, as discussed by Nerlove et al. (1993), an effect that is not present in static models or in dynamic models with infinitely lived consumers. Our specifications for the population growth rate (n = 0.03), interest rate (r = 0.08), and capital tax rate ([tau] = 0.4), place the economy off its golden rule path in such a way that reforms leading to greater investment in human and physical capital have a positive golden rule effect and reduce marginal social costs. Our model also incorporates a human capital externality whereby an increase in the aggregate stock of human capital raises the marginal productivity of education activities and reduces marginal social costs. In theory, these two welfare effects may be large. For the reforms and parameters considered here, however, the two effects are very small relative to the welfare cost. (16)

IV. CONCLUSIONS

Building on the insights of Auerbach et al. (1983) and Gravelle (1991) concerning the need to control for redistribution in estimating the efficiency effects of fundamental tax reforms in a dynamic context, we develop and implement an overlapping generations model for estimating welfare costs of marginal policy reforms for both differential incidence and balanced budget analyses. All of our estimates of marginal welfare costs are lower when households are compensated for transitional redistribution, confirming the potential for upward bias in estimates of steady-state welfare gains when this redistribution is ignored.

We find that estimates of marginal welfare costs are uniformly lower in the dynamic model where households can adjust their human and physical capital investments than in the static model where these investments are fixed. Part of the explanation for this finding is that welfare cost is predominantly the tax leakage caused by reduced labor supply. With an increase in wage taxation, there is a smaller decline in labor supply when saving is endogenous, because the static response is dampened by the response to changes in saving and future consumption. Additionally, with human capital investment endogenous, a reallocation of time between education and labor hours has opposing effects on effective labor supply, and as a consequence the negative effect of a tax increase on labor supply is mitigated by the opportunity to adjust human capital. Indeed, we find that the majority of the upward bias in static estimates of MWC is attributable to their failure to account for the endogeneity of human rather than physical capital investment.

Estimates of MWC are higher when the spending reform is financed by an increase in the tax on interest income rather than wage income. This result is a reflection of our finding that a marginal shift of the tax burden from capital to labor is welfare enhancing. This reform increases the after-tax return to saving, thereby encouraging physical capital investment, which in turn increases the after-tax wage rate. As a result, labor supply increases to take advantage of the higher wage rate and the enhanced incentive to save out of wage income. Therefore, shifting the financing of an incremental spending reform from wage to interest income results in a higher welfare cost.

Finally, for each of the reforms we examine, higher marginal tax rates and greater labor supply elasticities result in both higher values for MWC and a greater degree of upward bias in the static estimate. It follows that our estimates of MWC are biased downward insofar as tax-deductible expenditures and employer-provided fringe benefits are not incorporated. As emphasized by Feldstein (1999), the elasticity of taxable income may be increased substantially when these tax-favored goods are taken into account. For example, in a representative consumer model with tax-favored goods but no human or physical capital investment, Parry (2002) obtains estimates of MWC that range between 0.2 and 0.4 for an exhaustive spending reform and between 0.3 and 0.5 for an incremental demogrant. These are approximately twice the values we obtain for the static model using parameter set A, whose values are similar to those adopted by Parry. Thus incorporating tax-favored goods could double our dynamic estimates of MWC. Nonetheless, our results indicate that opportunities to adjust investment decisions, especially those involving human capital, play an important role in reducing the marginal welfare cost of tax and spending reforms.

APPENDIX

In this appendix we (i) present details of the income compensation scheme, (ii) outline the derivation of equation (10) for marginal social cost, (iii) describe the method used to calculate changes in labor supplies and investments, and (iv) discuss our choices for parameter values not indicated in the text. A more detailed appendix is available from the authors.

(i) The incomes of households that are retired, [I.sup.0] [equivalent to] ([K.sub.3]/p) + [A.sub.3]; middle-aged, [I.sup.m] = [w.sub.2][[delta].sub.2]T + ([K.sub.2]/p) + [A.sub.2] + p[A.sub.3]; and young, given in equation (8), change as a result of policy reforms, and these changes are adjusted to control for transitional effects by compensating additions that net out to 0 in the aggregate. The income compensation is [C.sup.0] [equivalent to] [K.sub.3][d[tau]r) - dr] - d[R.sup.*] for retired households, where d[R.sup.*] = dR + WC is the amount by which per household tax revenue would change if tax bases were perfectly inelastic; for middle aged households, the compensation is [C.sup.m] [equivalent to] [[delta].sub.2][h.sub.2][d(W[m.sub.2]) - dW] + [K.sub.2][d([tau]r) - dr] - d[R.sup.*] + p[C.sup.0]; and for young households is [C.sup.y] [equivalent to] [[delta].sub.1][h.sub.1][d(W[m.sub.1]) - dW] - d[R.sup.*] + p[C.sup.m]. Thus, after compensation, the income of a household in period t [member of] {y, m, o} of the life cycle changes by d[I.sup.t] + [C.sup.t].

(ii) Equation (10) for marginal social cost is obtained by totally differentiating equation (2) for income [I.sub.t], solving for the cost term d[A.sub.t] + [l.sub.t]d([w.sub.t][[delta].sub.t]) - d[I.sub.t], substituting for [h.sub.t]d([m.sub.t]W[[delta].sub.t]) + d([tau]r[K.sub.t]) from the total differential of equation (3) for tax revenue [R.sub.t], and then aggregating across households. The terms involving dW and dr net out to 0, d[R.sub.t] aggregates to dR, and the tax leakage terms given in equation (13) yield welfare cost, WC. The remaining changes in physical capital are allocated to the golden rule effect G given in equation (11), along with two terms involving the change in education, d[e.sub.1]. The first of these terms enters through the differential d[I.sub.1], and the second enters through d[I.sub.2] from the change in human capital d[[delta].sub.2] given in equation (14). The term involving d[[bar.[delta]].sub.2] in equation (14) yields the education externality E given in equation (12). Finally, we use the first-order condition for human capital investment,

(A1) p[w.sub.2][h.sub.2][[bar.[delta]].sub.2]f' ([[delta].sub.1][e.sub.1]) = [w.sub.1],

to eliminate [w.sub.2][h.sub.2][[bar.[delta]].sub.2]f' from the golden rule effect and to eliminate [w.sub.2][h.sub.2] from the education externality.

(iii) To calculate changes in labor supplies and investments, we solve the differential equation system derived from the lifetime budget constraint (7) and the first-order conditions (A1) for human capital investment and

(A2) [sigma][V.sup.2.sub.I]/[V.sup.1.sub.I] = p and [sigma][V.sup.3.sub.I]/[V.sup.2.sub.I] = p

for optimal spending over the life cycle. The resulting set of partial derivatives of [e.sub.1] and [I.sub.t] with respect to [I.sup.y], p, [w.sub.1], [w.sub.2], and z can be evaluated numerically once the initial equilibrium is specified along with four elasticities needed to determine the coefficient matrix for the comparative statics effects. First, from (A2) we have

(A3) [partial derivative]([sigma][V.sup.t.sub.I]/V.sup.t-1.sub.I])/ [partial derivative][I.sub.t-1] = -p[V.sup.t-1.sub.II]/[V.sup.t-1.sub.I] = -p[[rho].sub.t-1]/[I.sub.t-1],

which depends on the index of relative risk aversion [rho] (the inverse of the intertemporal elasticity of substitution). Second, we have

(A4) [partial derivative]([sigma][V.sup.2.sub.I]/V.sup.1.sub.I])/ [partial derivative]e = ([[rho].sub.2] + [[eta].sub.I][h.sub.2]/[l.sub.2]) [w.sub.1][[delta].sub.1][l.sub.2]/[I.sub.2][h.sub.2],

which depends on the income elasticity of labor supply, [[theta].sub.I], whose values are recorded in Table 1. Third, we assume that both the marginal utility of income and labor supply are independent of z, so that changes in the supply of z have no affect on either human or physical capital investment. Finally, the partial derivative of (A1) with respect to [e.sub.1] depends on the elasticity of marginal labor productivity with respect to education. (Notice that the subjective discount factor plays no role in the calculations, since it is eliminated from the terms such as (A3) and (A4) in the comparative statics coefficient matrix.)

The behavioral changes d[I.sub.t] and d[e.sub.1] can be expressed as linear equations of the changes in factor prices and public spending with coefficients that depend solely on the numerical values obtained for the comparative statics effects. Using the relation dr = -(H/K)dW, we can then express d[I.sub.t] as a linear function of dR and dW, whose coefficients have numerical values that depend on the policy reform d[tau], d[m.sub.t], and [beta]. Following Mayshar (1991), we introduce general equilibrium effects through the parameter [gamma] = -[HF.sub.HH]/ [F.sub.H], allowing us to write dW = -[gamma]W[(dH/H) - (dK/K)]. Using this equation along with the differential equations for tax revenue, saving, and labor supply, expressed in elasticity form and aggregated across households, we arrive at a system of four linear equations in dR, dW, dK, and dH that we solve to evaluate changes in labor supply and investment decisions for a specified policy reform, allowing us to calculate the associated welfare cost and MWC.

(iv) Following Ballard (1988), we assume [gamma] = 0.3215. Our base case tax rates and labor supply elasticities are taken from Browning and Johnson (1984) who specify five tax brackets. Our comparison set is taken from Triest (1994), whose deciles are combined to create quintiles, which also provide the explicit lump-sum transfers used in our calculations. We assume households may change income brackets over the life cycle, and construct 10 lifetime profiles using the 1991 cohort of the Panel Study of Income Dynamics to specify the proportion of households in each profile along with household size (which determines a household's demogrant). We also rely on the Panel Study to determine initial productivities by dividing incomes by hours worked for young households. We adopt the function f([[delta].sub.1][e.sub.1]) = [alpha]ln([[delta].sub.1] [e.sub.1] + 1) to determine [[delta].sub.2] and the elasticity of marginal labor productivity with respect to education. Following Driffil and Rosen (1983), we assume that a year of education increases productivity by 10%, and we rely on Davies and Whalley (1991) who estimate that young workers devote 32% of their time to education (or training) to arrive at the assumption that [[bar.[delta]].sub.2] is 3.2% higher than [[bar.[delta]].sub.1] = 9.833. We then choose a value for a that results in [[bar.[delta]].sub.2] = 10.14, allowing us to deduce values for and [e.sub.1] and [[delta].sub.2]. Using the Panel Study to obtain labor hours for households in middle age, we then determine second period wages. Finally, we draw on Fullerton and Rogers (1993) to generate saving rates and capital holdings.

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(1.) We assume that aggregate output is produced by a surrogate production function with constant returns to scale F(H, K), where H is aggregate effective labor supplied per household and K is the capital stock per household. The wage rate for effective units of labor is W [equivalent to] [F.sub.H] and the interest rate is r [equivalent to] [F.sub.K], where subscripts denote partial derivatives. Thus, dW = [F.sub.HH]dH + [F.sub.HH]dK, and dr = [F.sub.KH]dH + [F.sub.KK]dK. With constant returns to scale, the marginal products are homogenous of degree 0, implying that [F.sub.KH]H + [F.sub.KK]K = 0 and [F.sub.HH]H + [F.sub.HK]K = 0. As a result, dW = [F.sub.KH][-(K/H)dH + dK] and dr = [F.sub.KH][dH--H/K)dK], implying that dr = -(H/K)dW. Thus, W and r are endogenous, but they are not age-specific because we focus on steady states for the economy. Consequently, they are not subscripted by t.

(2.) Note that tax revenue as defined in (3) includes the implicit lump-sum transfer (tax) that arises under a progressive (regressive) rate structure, because wage tax revenue is calculated in equation (3) as though the marginal tax rate equals the average tax rate. We account for these implicit transfers effected through the wage tax by including them in public spending and adding them to any explicit lump-sum transfers to arrive at the amount denoted by [A.sub.t]. As emphasized by Allgood and Snow (1998), this procedure ensures that all intended redistribution, whether implemented through the wage tax structure or through explicit transfers, is treated the same when calculating welfare cost and the change in tax revenue.

(3.) The first three terms on the left-hand side of the budget constraint (7) represent the allocation of income over the life cycle. The next term represents spending on education, which we assume consists entirely of forgone wages. The final term represents the present value of the gross return to human capital investment.

(4.) [NB.sub.t] = d[V.sup.t]/[V.sup.t.sub.I] = [([V.sup.t.sub.w[delta]]d ([w.sup.t][[delta].sub.t] + [V.sup.t.sub.z]dz + [V.sup.t.sub.I]d[I.sub.t])]/ [V.sup.t.sub.I]. Substitute for the definition of [MRS.sub.t], and use Roy's identity, [V.sup.t.sub.w[delta]]/[V.sup.t.sub.I] = -[l.sup.t], to obtain the first line of equation (9). Note that d([w.sub.t][[delta].sub.t]) = [[delta].sub.t][dw.sub.t] + [w.sub.t]d[[delta].sub.t].

(5.) The derivation of MSC is discussed in the appendix.

(6.) Note that NB is the sum of the per household net benefits accruing to contemporaneous old, middle, and young households, NB = [NB.sup.o] + (1 + n)[NB.sup.m] + [(1 + n).sup.2] [NB.sup.y]. If we discount lifetime net benefits to the present and aggregate over all living and future generations, then we obtain

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

for a steady-state change. Thus, the social welfare change NB given in equation (15) is proportional to the discounted lifetime net benefits accruing to all living and future households.

(7.) Our compensation scheme is described further in the appendix. A more detailed description of our scheme and the example discussed in the text is available from the authors on request.

(8.) These profiles, along with the data and parameters used to construct the initial equilibrium of the model, are available from the authors on request.

(9.) Judd (1985, 1987) and Engen et al. (1997) adopt a value of one-half for the intertemporal elasticity of substitution for their central cases. Gravelle (1991) follows Auerbach et al. (1983) and assumes a value of one-quarter. Perroni (1995) sets the elasticity equal to 1, while Trostel (1993) suggests that a value between 1/4 and I is appropriate.

(10.) Under this assumption, discussed by Wildasin (1984), labor supply is perfectly inelastic with respect to spending on the public good. We also assume that the same is true of investments in physical and human capital.

(11.) The dynamic estimates reported in the tables assume a value of one-half for the intertemporal elasticity of substitution. For parameter set A, the estimated value for MWC in the case of wage taxation falls from 0.07 to 0. 05 and 0.001 as this elasticity falls to 1/4 and 1/8, and with capital taxation the estimated value correspondingly falls from 0.13 to 0.09 and 0.01.

(12.) Our results confirm the conclusion reached by Goulder and Roberton (2003), who show that general equilibrium effects can make a substantial contribution to excess burden as a tax on one commodity influences other tax bases. For example, an increase in the tax on capital income (d[tau] > 0) contributes very little to welfare cost through the capital tax base, since [tau]r is very small, but makes a substantial contribution through the labor tax base. (Note that although the decline in labor supply is greater when the labor tax increases, there is a much smaller offsetting increase in human capital investment when the capital tax increases.)

(13.) For parameter set A, the estimated value for MWC falls from 0.15 to 0.14 and 0.12 as the intertemporal elasticity of substitution falls from one-half to one-quarter and one-eighth, and with capital taxation the estimated value falls from 0.21 to 0.19 and 0.13.

(14.) In parameter set A the compensated elasticities range from 0.22 to 0.52. The average value of the compensated elasticity increases from 0.32 to 0.51, whereas the average value of the uncompensated elasticity increases from 0.23 to 0.39. These higher average elasticities are consistent with many of the estimates reviewed in Blundell and MaCurdy (1999).

(15.) For simplicity, consider a household in middle age with [[delta].sub.2] = 1, and assume the budget constraint is [I.sub.l] + pI = wT with x + wl = [I.sub.1] for consumption of x and leisure l = T - h in middle age, and consumption I in retirement. Let labor supply in the static model where I is fixed be denoted by [h.sup.o] (w, I), let labor supply in the dynamic model be denoted by h(w, p), and let I(w, p) denote optimal retirement income. Then h(w, p) = [h.sup.o](w, I[w, p]) implies [h.sub.w] = [h.sup.o.sub.w] + [h.sup.o.sub.I][I.sub.w] so that we have [h.sub.w] < [h.sup.o.sub.w] if [h.sup.o.sub.I][I.sub.w] > O. The last inequality holds because an increase in I implies a reduction in [I.sub.1] and an increase in static labor supply ([h.sup.o.sub.I] > 0), wheras an increase in w increases lifetime income so that I increase ([I.sub.w] > 0).

(16.) For example, for the demogrant funded by an increase in the marginal tax on labor income reported in Table 3, dG/dR = -0.0001 and dE/dR = 0.0001.

SAM ALLGOOD and ARTHUR SNOW *

* The authors gratefully acknowledge the helpful comments of two anonymous referees.

Allgood: Associate Professor, Department of Economics, University of Nebraska, Lincoln, NE 68588-0489. Phone 1-402-472-3367, Fax 1-402-472-9700, E-mail sallgood@unl.edu

Snow: Professor, Department of Economics, University of Georgia, Athens, GA, 30605. Phone 1-706-542-3752, Fax 1-706-543-3376.

TABLE 1
Tax Rates and Elasticities by
Income Bracket

 Average Marginal Elasticity of Labor Supply
Income Tax Tax
Bracket Rate Rate Uncompensated Income

Parameter set A
First 0.39 0.544 0.435 -0.016
Second 0.33 0.471 0.263 -0.027
Third 0.33 0.408 0.169 -0.024
Fourth 0.34 0.388 0.138 -0.036
Fifth 0.56 0.446 0.213 -0.047

Parameter set B
First 0.060 0.275 0.105 -0.008
Second 0.166 0.235 0.100 -0.005
Third 0.182 0.270 0.113 -0.005
Fourth 0.208 0.335 0.123 -0.005
Fifth 0.268 0.395 0.133 -0.008

TABLE 2
Welfare Cost of Revenue Neutral Reforms

Parameter WC dm d[tau] dW dr

Set A -0.1088 0.0001 -0.0314 0.0002 -0.0040
Set B -0.0194 0.0001 -0.0197 0.0001 -0.0025

 d[e.sub.1]/
Parameter dH/H (%) dK/K (%) [e.sub.1] (%) dR

Set A 0.0011 0.0569 -0.0043 0.00
Set B 0.0011 0.0448 -0.0119 0.00

TABLE 3
Marginal Welfare Cost of Exhaustive Spending Reforms

Parameter WC dm d[tau] dW dr

Set A 0.0700 0.01 0.00 0.0013 -0.0309
 0.1284 0.00 0.01 -0.0001 0.0012
Set B 0.0425 0.01 0.00 0.0015 -0.0262
 0.0528 0.00 0.01 -0.0001 0.0011

 d[e.sub.1]/
Parameter dH/H (%) dK/K (%) [e.sub.1] (%) dR

Set A -0.1492 0.2821 2.0311 186.37
 -0.0008 -0.0200 0.0079 0.59
Set B -0.1249 0.3466 0.7534 188.13
 -0.0007 -0.0210 0.0099 0.96

TABLE 4 Marginal Welfare Cost of Demogrant Reforms

 MWC dm d2 dW dr

Set A 0.1470 0.01 0.00 0.0005 -0.0115
 0.2097 0.00 0.01 -0.0001 0.0012
Set B 0.0550 0.01 0.00 0.0005 -0.0081
 0.0653 0.00 0.01 -0.0001 0.0012

 d[e.sub.1]/
 dH/H (%) dK/K (%) [e.sub.1] (%) dR

Set A -0.2892 -0.1286 0.8640 173.51
 -0.0013 -0.0185 0.0041 0.55
Set B -0.1609 -0.0152 -0.3253 187.62
 -0.0009 -0.0228 0.0044 0.95

TABLE 5
Marginal Welfare Cost and the Role of
Human Capital

 Static Exogenous Full
Parameter Reform Model Education Model

Set A Exhaustive 0.1600 0.1165 0.0700
 Spending
 Demogrant 0.2427 0.1987 0.1470

Set B Exhaustive 0.0550 0.0537 0.0425
 Spending
 Demogrant 0.0628 0.0665 0.0550

Set A' Exhaustive 0.2946 0.2494 0.1580
 Spending
 Demogrant 0.4020 0.3904 0.2858