Redistributing income and relative efficiency.

Allgood, Sam

I. INTRODUCTION

The welfare costs associated with a demo-grant reform and with spending on a publicly provided good have been extensively investigated, as in Browning and Johnson (1984), Stuart (1984), and Ballard (1988). The welfare cost of marginal spending on earnings or wage subsidies has received less attention, even though, as Scholz (1996) reports, the income subsidy rate of the Earned Income Tax Credit (EITC) has increased from 10% to 40% in the past 20 years. (1) Triest (1994) and Browning (1995) are two articles that analyze the welfare gains and losses associated with reforms to the EITC. Triest concludes that the EITC is a relatively efficient way to redistribute income, whereas Browning suggests considering alternative methods of assisting the working poor.

This article calculates the welfare gains and losses for marginal reforms to three different policies designed to redistribute income. Increased spending on an earnings subsidy program, as defined by the EITC, is compared with the effects of higher spending on means-tested cash transfers to low-income households, a negative income tax (NIT). An NIT is used to represent welfare policies because Hoffman and Siedman (1990) suggest that programs such as Aid to Families with Dependent Children (AFDC) have properties similar to an NIT. Reforms to the NIT and EITC are compared to the effects of increasing the subsidy rate of a wage subsidy, or a negative wage tax as defined by Browning (1973).

Understanding the normative effects of an earnings subsidy are important because the EITC has grown, and it is now larger than the food stamp program. Although the EITC is best known as an earnings subsidy, it actually has three phases. For a household with one child (in 1997), labor income up to $6,500 is subsidized at a rate of 34%. Households receive the subsidy in the form of a refundable tax credit, and the household receives a check from the government if their credit exceeds their tax liability. For income between $6,500 and $11,930 households receive the maximum tax credit, but for earnings above $11,930 the tax credit diminishes 15.98 cents for every dollar earned. According to Rosen (1999), over 70% of those receiving a tax credit are in the last two phases of the program. For these households, the credit takes the form of a cash transfer, and for most it is a means-tested transfer.

Unlike traditional assistance to the poor, the EITC only provides assistance to those employed. A priori, one might expect a subsidy on labor earnings to be more efficient than an NIT at redistributing income to the working poor. This view is consistent with the survey results of Fuchs et al. (1998), who find that economists do not generally support increased funding of programs such as AFDC. However, if the EITC is just an NIT for most households it services, it is not obvious that the EITC is more efficient at marginally redistributing income to the poor.

Steuerle (1990) envisioned that effort would be made to convert the tax credit system to an hourly wage subsidy. More recently, Browning (1995) suggested that a negative wage tax (NWT) be considered instead of the EITC. An NWT, like that proposed by Browning (1973; 1995), involves subsidizing the difference between a target wage rate and a household's actual wage rate, and it does not have a cash transfer or the high (positive) implicit marginal tax rates (MTRs) associated with most redistributive programs. Browning (1973) demonstrates that a wage subsidy is more efficient that an NIT, but less is known about the relative efficiency of an NWT and the EITC.

Traditional welfare programs, such as AFDC and food stamps, provide most of their benefits to those who receive no labor income, whereas wage and income subsidies only aid those employed. How does one compare redistributive programs that serve different populations? To address this question, two different sets of reforms are considered. First, the MTR on labor income for the nonpoor is increased by 0.10 percentage point and the additional tax revenue is spent on one of the three programs. These reforms compare the additional benefit generated by each program for its target audience when each reform imposes the same burden on the nonpoor. Triest (1994) argues that to meaningfully compare reforms that redistribute income, the reforms must have the same redistributional outcomes. For this context, the same redistributional outcome is taken to mean that different reforms alter the utility of low-income households by the same magnitude. Thus, the second set of reforms compare the additional cost to the nonpoor of generating a specific increase in the utility of the poor.

Much of the literature surrounding welfare reform, earnings subsidies, and wage subsidies deals with job creation. An NIT does not create jobs, and Bartik (2001) finds that the EITC has only modest effects on labor force participation. On the other hand, Bartik argues that targeted wage subsidy programs (such as the Targeted Jobs Tax Credit) can create jobs for marginal workers. As wage and earnings subsidies take larger shares of the government budget relative to traditional welfare assistance, it seems likely that subsidy programs will also play some role in future efforts to marginally redistribute income. However, a program that is effective at increasing labor supply may not be efficient at marginally redistributing income. Thus, the question addressed here is which of these three programs, given that they are already in place, is more efficient at marginally redistributing income?

The legislative emphasis on employment suggests the possibility of an imperfection in the market for unskilled labor (demand is too low) and/or the possibility that household or social welfare is somehow affected by the employment status of those receiving government assistance. The analysis of marginal reforms builds on the works of Triest (1990) and Allgood and Snow (1998), among others, and ignores these concerns. In addition, the analysis here is on marginal reforms that involve changes in tax rates of less than 1 percentage point, and the income tax brackets defining the tax on labor income and participation in government programs are assumed to remain fixed. As a result, it is assumed that changes in household behavior are marginal.

Numerical calculations show that the nonpoor lose 60% more than the poor gain for a marginal reform to the EITC, given that labor supply is moderately responsive to price. For a reform that collects the same amount of revenue from the nonpoor, the NWT only results in a 7% loss for the nonpoor relative to the gain of the poor. Interestingly, the loss to the nonpoor for the NIT is only 34%. The overall efficiency loss is much smaller if labor supply is less responsive to wages and income. In addition, the EITC and the NIT have similar efficiency properties, whereas the NWT is only slightly more efficient.

For the second set of reforms, where the household utility of the working poor is increased by the same amount, the NIT is found to be highly inefficient relative to the other two programs regardless of the response of labor supply to wages and income. In addition, the EITC is much less efficient than the NWT for the case of responsive labor supply, but the difference inefficiency costs is small for less responsive labor supply. Thus, the relative efficiency of the EITC and the NIT is reversed from the first set of reforms. Browning (1995) points out that the efficiency costs of reforming a tax and/or spending policy will depend on the type of reform considered. The results here support this view.

The article proceeds as follows. Section II develops the household's budget set given government tax and spending policy. Section III derives a model for evaluating the positive and normative effects of the fiscal reforms. Section IV discusses different statistics for evaluating the reforms, and section V discusses the data and the calculations. Finally, section VI contains concluding remarks.

II. THE BUDGET SET

The EITC and NIT

Assume that government generates revenue by a tax on labor income and that the revenues are used to finance an earnings subsidy that takes the form of the EITC. With the emphasis on redistributive reforms the amount spent on a publicly provided good is assumed constant, so it is omitted from the model. Figure 1 illustrates the three phases of the EITC: phase-in, plateau, and phase-out. During the phase-in range labor income is subsidized at a rate s, s [less than or equal to]0, and the subsidy lasts until earnings reach [Y.sub.a]. The plateau range lasts until an income of [Y.sub.b], and earnings are not subsidized or implicitly taxed, but the household receives a lump-sum transfer equal to --s [Y.sub.a]. During the phase-out range the tax credit is diminished at a rate [m.sup.c] until the break-even income level [Y.sub.c]. To phase-out households the EITC is an NIT. This structure implies that [Y.sub.c] = [Y.sub.b] -- s[Y.sub.a]/[m.sup.c], or

(1) [m.sup.c] = -[alpha]s,

where [alpha] = [Y.sub.a]/( [Y.sub.c] - [Y.sub.b]).

Assume that a household's budget constraint without government spending or taxes is the dashed line [Y.sub.T]T in Figure 2. For simplicity, assume a three-bracket tax on labor income, where [Y.sub.t] represents the personal exemption level, so that only payroll and Social Security taxes apply. Households face a tax of [m.sup.[t.sub.1]] on labor income earned up to [Y.sub.t], a tax rate of [m.sup.[t.sub.2]] on additional labor income up to [Y.sub.c], and a tax rate of [m.sup.[t.sub.3]] on all further labor income, where [m.sup.[t.sub.1]] [less than or equal to][m.sup.[t.sub.2]] [less than or equal] [m.sup.[t.sub.3]]. The result is budget line ABCT. If the EITC described in Figure 1 is imposed on the budget line ABCT, the budget line becomes ABDEFT, assuming that -s > [m.sup.[t.sub.1]] and assuming that the personal exemption level lies above the plateau range of the EITC ([Y.sub.b] < [Y.sub.t]). The EITC does not affect the marginal cost of leisure in the plateau range because earning more does not alter the size of the tax credit. This can be seen in Figure 2 by noting that segment EF has the same slope as segment CT.

Now assume that the government also spends tax revenue on an NIT. Households are guaranteed a minimum income level, but this transfer is reduced by [m.sup.e] for every dollar of labor income earned. The break-even income is [Y.sub.e]. To simplify the analysis, assume that the break-even income equals the exemption level of the income tax ([Y.sub.e] = [Y.sub.t]). (2)

The income tax, the EITC, and the NIT imply five household types.

* (Type 1) 0 < Income [less than or equal to] [Y.sub.a]: Households are in the phase-in range of the EITC and they participate in the NIT. Their gross MTR is [m.sup.e] + s + [m.sup.[t.sub.1]].

* (Type 2) [Y.sub.a] < Income [less than or equal to] [Y.sub.b]: Households are in the plateau of the EITC, and they receive a cash transfer from the NIT. Because they do not have an implicit tax on their tax credit, they face an MTR of [m.sup.e] + [m.sup.[t.sub.1]].

* (Type 3) [Y.sub.b] < Income [less than or equal to] [Y.sub.t]: Households are in the phase-out range of the EITC but below the exemption level [Y.sub.t]. They receive a tax credit and a cash transfer from the NIT, Their gross MTR is [m.sup.e] + [m.sup.e] + [m.sup.[t.sub.1]].

* (Type 4) [Y.sub.t] < Income [less than or equal to] [Y.sub.c]: Households are above the exemption level, and they no longer receive a cash transfer via the NIT, but they are still eligible for a tax credit. Their gross MTR is [m.sup.c] + [m.sup.[t.sub.2]].

* (Type 5) Income > [Y.sub.c]: Households are not eligible for the EITC or the NIT, their gross MTR is [m.sup.[t.sub.3]]

In general, if i indexes the five household types, a household's gross MTR is

(2) [m.sup.g.sub.i] = [m.sup.e.sub.i] + [m.sup.c.sub.i] + [m.sup.t.sub.i],

where [m.sup.e.sub.i] is i's implicit MTR for the NIT, [m.sup.c.sub.i] is a household's implicit MTR from the EITC, and [m.sup.t.sub.j] is the MTR from the explicit tax on labor income. (3) Note that type 1 households are in the phase-in range of the EITC, but they still face a positive gross marginal tax rate unless [m.sup.e] + [m.sup.[t.sub.1]] < - s.

A common redistributive reform considered in the literature is to increase the gross MTR ([m.sup.g.sub.i]) for all households by the same amount and use the additional revenue to fund larger lump-sum transfers to all households, as in Browning and Johnson (1984), Ballard (1988), and Allgood and Snow (1998). The purpose of raising the tax rate is to generate additional tax revenue, but requiring to be the same for all households imposes restrictions on the spending part of the reform as well. For example, suppose that the purpose of raising the gross MTR 1 percentage point is to redistribute more income to poor households through the EITC. For a household in the phase-in range of the EITC, this implies that d[m.sup.g] = ds + d[m.sup.t] = 0.01 given that d[m.sup.e] = 0. Yet the only statutory tax rates faced by such households are Social Security and payroll taxes, which are unlikely to be altered for this purpose. This means that d[m.sup.t] = 0 and ds = 0.01, which lowers the (absolute value of the) subsidy ra te instead of raising it.

To consider reforms that intend to redistribute, it is important to specify which labor income taxes rates are being increased to generate additional tax revenues. A separate, but interdependent, part of the reform is how the implicit tax rates of the spending programs are altered. The calculations of welfare cost assume that the government raises more tax revenue by increasing the explicit MTR on labor income, but only for households not participating in the NIT or EITC (type 5). That is, d[m.sup.[t.sub.3]] > 0, but d[m.sup.[t.sub.1]] = d[m.sup.[t.sub.2]] = 0. MTRs for low-income households will change, but only because of changes in implicit tax rates that arise from changes in the spending component of the reform.

The NWT

A NWT provides an alternative method of redistributing income because it does not involve a cash transfer or high (positive) implicit MTRs. The two policy parameters of the NWT are a subsidy rate and a break-even wage rate. If the subsidy rate is s' and the break-even wage is [W.sub.b], a household with a wage rate of W receives a per-hour subsidy of s'([W.sub.b] - W). The size of the subsidy is inversely related to the household's wage rate. If, for example, s' = 0.4, [W.sub.b] = 10, and W= 4, the per-hour subsidy is 2.40. The subsidy increases the wage rate from $4 to $6.40, which is equivalent to facing an MTR of -60%. If the household's wage is $5 the implicit tax rate is only -40%. For a given market wage rate, an NWT can be expressed as a negative MTR on labor income. In this sense, the NWT is similar to the phase-in range of the EITC.

Unlike the EITC and the NIT, the NWT cannot be expressed as a series of piece-wise linear budget constraints because a household's marginal wage rate does not change as their earnings change. Furthermore, the NWT does not involve any form of lump-sum payments. Also notice in Figure 2 that a household chooses its MTR by its initial choice of leisure and income. With the NWT, however, the subsidy rate is exogenous if the household's wage rate is exogenous. (4) Segment FT of the budget constraint in Figure 2 shows the phase-in range of the EITC given the labor income tax. For this market wage rate, an NWT could be constructed that yields the same slope to the budget constraint as the EITC. The difference, however, is that there is no phasing out. The household's effective wage rate does not change unless they enter the next labor income tax bracket. Thus, the budget constraint for the household facing a NWT in the first bracket of the labor income tax is GFT.

III. A MODEL OF FISCAL REFORM

The Fiscal Environment for the EITC and NIT

First consider the fiscal environment that exists when there is an explicit tax on labor earnings, an earnings subsidy, and an NIT. The model developed is based on evaluating the change in household labor supply when households are defined by the five types given in the last section. Households supply effective labor [[delta].sub.i][h.sub.i] where [[delta].sub.i] is labor effectiveness, [h.sub.i] is hours of labor supplied, and [[delta].sub.i] < [[delta].sub.i+1] for all i. Output for the economy is produced by a constant returns to scale production function f(K, H), where K is the aggregate, per household stock of (fixed)capital and H = [summation over (i=5/i=1)] [n.sub.i][[delta].sub.i][h.sub.i] is aggregate, per household effective labor supply, given that [n.sub.i], is the proportion of each household type. Households are assumed to earn the marginal product of their labor. The marginal product of an hour of type i's labor supply is [partial]f(K,H)/[partial]hi = [n.sub.i] [[delta].sub.i] W, where [partial ]f/[partial]H = H/is the marginal product of aggregate effective labor supplied. Thus, the wage rate of a type I household is [[delta].sub.i] W, and differences in wage rates across households reflect differences in labor effectiveness. A household's after tax wage rate given the fiscal environment is

(3) [w.sub.i] = (1 - [m.sup.g.sub.i])[[delta].sub.i]W,

where [m.sup.g.sub.i] is the gross MTR.

A household may receive up to four different lump-sum transfers. Two of these transfers arise as explicit cash transfers from the government. First, households of the first three types receive the same guaranteed income of E from the NIT. That is, [E.sub.i] = E for i = 1, 2, 3, and [E.sub.i] is zero for i = 4, 5. Second, plateau and phase-out households (types 2, 3, and 4) receive lump-sum tax credits from the EITC [C.sub.i] = -s[Y.sub.a], where [C.sub.i] is zero for phase-in and nonpoor households (types 1 and 5), and [Y.sub.a] defines the end of the phase-in range of the EITC.

Equation (3) shows that households are treated as if they face a single tax rate on all labor income. If MTRs increase with income, then some households overpay their taxes. This is dealt with by providing households an implicit transfer to compensate for the overpayment. Implicit transfers arise for phase-out households because MTRs increase with income for EITC participants. The implicit transfer is [N.sup.c.sub.i] = [m.sup.c] [Y.sub.b] for phase-out households (i = 3, 4), and [N.sup.c.sub.i] is zero for phase-in, plateau, and nonpoor households (types 1, 2, and 5), where [Y.sub.b] defines the end of the plateau range. Last, the labor income tax also has a graduated rate structure so that another implicit transfer ([N.sup.t.sub.i]) is needed to compensate households that overpay. Households in the first income bracket do not overpay income taxes because only one tax rate is applied to their income, and they do not receive this implicit transfer ([N.sup.t.sub.1] = [N.sup.t.sub.2] = [N.sup.t.sub.3] = 0). The implicit transfer for type 4 households is [N.sup.t.sub.4] = ([m.sup.[t.sub.2]] - [m.sup.[t.sub.1]]) [Y.sub.t], and for type 5 households it is [N.sup.t.sub.5] = ([m.sup.[t.sub.3]] - [m.sup.[t.sub.2]]) [Y.sub.c] + [N.sup.t.sub.4]. Allgood and Snow (1998) define a single implicit transfer in terms of the gross MTR. The specificity of the model used here makes it possible to identify the source of the implicit transfer, which makes it possible to explicitly define the tax and spending reform.

A household's virtual income is

(4) [I.sub.i] = [w.sub.i]T + [N.sup.t.sub.i] + [N.sup.c.sub.i] + [E.sub.i] + [C.sub.i] + r[K.sub.i],

where T is the time endowment, r is the gross rental rate of capital, and [K.sub.i] is capital holdings. A household faces the time constraint T = [l.sub.i] + [h.sub.i], where [l.sub.i] is the choice of leisure.

Explicit tax revenue is raised by a tax on labor income,

(5) [R'.sub.i] = [m.sup.t.sub.i][[delta].sub.i]W[h.sub.i] - [N.sup.t.sub.i].

Per-household explicit tax revenue is R' = [summation over (i=5/i=1)] [n.sub.i][R'.sub.i]. It is assumed that revenues equal expenditures,

(6) R' = [summation over (i=5/i=1)] [n.sub.i]([E.sub.i] - [m.sup.e.sub.i][[delta].sub.i]W[h.sub.i]) - [n.sub.1]s[[delta].sub.1]W[h.sub.1]

+ [summation over (i=4/i=2)][n.sub.i][[C.sub.i] - ([m.sup.c.sub.i][[delta].sub.i]W[h.sub.i] - [N.sup.c.sub.i])].

Tax revenue is typically defined in terms of gross MTRs. Equating Equations (5) and (6) and rearranging terms generates the more common definition of government tax revenue,

(7) R = [summation over (i=5/i=1)][n.sub.i]([m.sup.g.sub.i][[delta].sub.i]W[h.sub.i] - [N.sup.t.sub.i] - [N.sup.c.sub.i]),

Which equals

(8) R = [summation over (i=5/i=1)][n.sub.i]([E.sub.i] + [C.sub.i]).

Although the lump-sum tax credit ([C.sub.i]) is technically part of the tax system, it is treated here as expenditures because this component of the EITC involves cash transfers to households similar to the NIT. (5) In general, defining Equations (7) and (8) as revenues and expenditures is misleading. For example, the revenue equation includes explicit government expenditures to phase-in households from the subsidy of the EITC (s[[delta].sub.1]W[h.sub.1]).

In contrast to Triest (1994), the fiscal reforms considered here are evaluated given fixed income brackets because this allows the reform to be defined almost solely in terms of changes in MTRs. (6) An advantage to this approach is that it is easier to understand how the household's budget set is altered by the reform. Allgood and Snow (1998) demonstrate that several studies of marginal welfare costs contain changes in implicit transfers that arise from unspecified changes in the progressivity of the tax structure. Assuming that tax brackets are fixed eliminates these ambiguities and allows for the fiscal reform to be more clearly defined. For example, it now follows from equation (1) that changes in the benefit reduction rate of the EITC are proportional to changes in the subsidy rate, d[m.sup.c] = - [alpha]ds.

Marginal tax revenue dR is found by taking the total differential of Equation (7)

(9) dR = [summation over (i-5/i=1)] [n.sub.i] [[[delta].sub.i] W[h.sub.i](d[m.sup.e.sub.i] + d[m.sup.t.sub.i]) - d[N.sup.t.sub.i]

+ [m.sup.g.sub.i] [[delta].sub.i]d(W[h.sub.i])] + [[n.sub.1][[delta].sub.1]W[h.sub.1]

- [alpha] [summation over (i=4/i=3)] [n.sub.i]([[delta].sub.i]W[h.sub.i] - [Y.sub.b])]ds,

given that d[m.sup.g.sub.i] = d[m.sup.c.sub.i] + d[m.sup.e.sub.i] + d[m.sup.t.sub.i], d[N.sup.c.sub.i] = [Y.sub.b]d[m.sup.c] for I = 3,4 (and 0 if I = 1,2, 5), and d[m.sup.c] = -[alpha]ds. Because income brackets are assumed fixed, changes in the implicit tax rates of the spending reforms (ds and d[m.sup.e]) can be expressed as functions of the change in aggregate tax revenue. First, take the total differential of aggregate expenditures (8) and solve for ds to obtain

(10) ds = -[(1 - [summation over (i=5/i=1)] [n.sub.i][[beta].sub.i])/s] dR = [phi]dR,

where d[E.sub.i] = [[beta].sub.i][dR, d[C.sub.i],= -[Y.sub.a]ds for i = 2, 3, 4 (and 0 for i = 1, 5), S = [Y.sub.a] [summation over (i=4/i-2)] [n.sub.i], and [[beta].sub.i] is the proportion of additional tax revenue spent on cash transfers to household i as part of the NIT. If all additional revenue is spent on transfers ([phi]) = 0) then ds = 0, and if all the revenue is spent on the EITC, then ds = dRIS. Equation (10) and S show that for a given amount of marginal tax revenue, ds is negatively related to the number of plateau and phase-out households, but it is independent of the number of households in the phase-in range.

Second, the implicit MTR for the NIT is [m.sup.e.sub.i]= [E.sub.i]/[Y.sub.e], so

(11) d[m.sup.e.sub.i] = ([[beta].sub.i] = ([Y.sub.e])dR,

where [[beta].sub.4] = [[beta].sub.5] = 0. Substituting into Equation (9) for d[m.sup.e.sub.i] and ds yields

(12) dR = (1/0) [[summation over (i=5/i=1)] [n.sub.i]([[delta].sub.i]W[h.sub.i]d[m.sup.t.sub.i] - d[N.sub.i])

+ [summation over (i=5/i=1)] [n.sub.i][m.sup.g.sub.i][[delta].sub.i]W(d[h.sub.i] - [gamma]W[h.sub.i][dH/H])],

where

[theta] = 1 - [[summation over (3/i=1)] [n.sub.i][[beta].sub.i][[delta].sub.i]W[h.sub.i]/[Y.sub.e]]

+ [phi][n.sub.1][[delta].sub.1]W[h.sub.1] - [alpha] [summation over (i=4/i=3)] [n.sub.i]([[delta].sub.i]W[h.sub.i] - [Y.sub.b])],

dH = [summation over (i=5/i=1)] [n.sub.i][[delta].sub.i]d[h.sub.i] and [gamma] = -(dW/dH)(HIW) is the elasticity of the wage rate with respect to labor supply. Equation (12) gives an expression for the change in tax revenue as a function of two policy reform variables, d[m.sup.t.sub.i] and [[beta].sub.i], values for the economy's initial position and measures of aggregate changes in labor supply.

A formula for the household change in labor supply is used to evaluate the changes in aggregate labor supply and tax revenue. The change in a household's labor supply, [h.sub.i]([w.sub.i], [I.sub.i]), is expressed as a weighted sum of the uncompensated labor supply elasticity and the income elasticity,

(13) (d[h.sub.i]/[h.sub.i]) = [eta](d[w.sub.i]/[w.sub.i]) - [member of]([K.sub.i]dr + d[E.sub.i] + d[C.sub.i] + d[N.sup.t.sub.i] + d[N.sup.c.sub.i]),

where [member of] = ([[eta].sup.c] - [eta])/[w.sub.i][h.sub.i], and [eta] and [[eta].sup.c] are the uncompensated and compensated wage elasticities, respectively. (7) Equation (13) shows how explicit changes in government transfers from the NIT (dE) and EITC (dC), along with changes in implicit transfers from the income tax (d[N.sup.t]) and EITC (d[N.sup.c]), affect labor supply through the income effect.

From Equation (3), the change in a household's wage rate is

d[w.sub.i] = -[[delta].sub.i]W(d[m.sup.t.sub.i] + d[m.sup.e.sub.i] + d[m.sup.c.sub.i]) + (1 - [m.sup.g.sub.i])[[delta].sub.i]dW.

Substituting in for Equations (10) and (11), and given that d[m.sup.c] = -[alpha]ds, the change in a household's wage rate is

(14) d[w.sub.i] = -[[delta].sub.i]Wd[m.sup.t.sub.i] - [[delta].sub.i]W [[LAMBDA].sub.i]dR + (1 - [m.sup.g.sub.i])[[delta].sub.i]dW,

where [[LAMBDA].sub.1] = [[beta].sub.1]/[Y.sub.e] - [phi]; [[LAMBDA].sub.j] = [[beta].sub.j]/[Y.sub.e] + [alpha][phi], j = 3, 4; [[LAMBDA].sub.2] = [[beta].sub.2]/[Y.sub.e]; and [[LAMBDA].sub.5] = 0. The first term of [LAMBDA] ([[beta].sub.i]/[Y.sub.e]) reflects that a larger guaranteed income for the NIT results in a higher tax rate and a lower wage rate. The second term reflects how additional spending on the EITC affects the wage rate. Phase-in households (i = 1) receive a higher wage through the higher subsidy, and the wage of plateau households (i = 2) is unchanged. The wage of phase-out households (i = 3, 4) is lowered, however, because of an increase in the reduction rate of the EITC.

Equations (13) and (14) help identify how marginal reforms to the EITC and NIT alter labor supply. Ignoring general equilibrium changes in factor prices (dW = dr = 0), a reform to the EITC reduces the labor supply of plateau households via the single income effect generated by dC. Phase-out households face a lower wage rate (d[m.sup.c] > 0) and two income effects (d[N.sup.c] + dC) that reduce labor supply. Thus, phase-out households will have a larger decline in labor supply than will plateau households. The EITC reform does not generate income effects for phase-in households (ignoring dr), but labor supply is encouraged with a higher wage rate (ds < 0). However, Equation (10) suggests that ds is small if there are a large number of plateau and phase-out households, which is true of the current EITC. Last, a marginal reform to the NIT affects household labor supply similarly to the phase-out range of the EITC. Labor supply is discouraged by increasing income (dE) and decreasing the wage rate (d[m.sup.e] > 0) .

By substituting into Equation (13) for the changes in MTRs, factor prices, transfers, and government revenue, it is possible to express the individual change in labor supply as a function of the aggregate changes in labor supply. It is then possible, once the economies initial position and the reform is fully specified, to evaluate the positive effects of a marginal reform. The details are in the Appendix.

The NWT

Marginal changes to a NWT can be evaluated after making a few simplifications to the model. The five household types considered to this point are classified by labor earnings, but an NWT is defined in terms of a household's wage rate. It is possible that some households have low earnings because they have a high wages and work few hours, and some households with the same earnings may have a low wage and work many hours. To maintain our analysis of the five household types, it is assumed that all households of the same type have the same effective wage rate and that [[delta].sub.j] < [[delta].sub.j+1] for j = 1...4.

The discussion in section II shows that given a market wage rate the NWT can be defined as a system of negative MTRs ([s.sup.w.sub.i]). For a reform to the NWT, the change in a household's gross MTR is d[m.sup.g.sub.i] = d[m.sup.t.sub.i] + d[s.sup.w.sub.i], and the change in the after-tax wage rate is d[w.sub.i] = [[delta].sub.i] Wd[m.sup.g.sub.i]+ (1 - [m.sup.g.sub.i])[[delta].sub.i]dW. The change in a household's labor supply becomes

(15) d[h.sub.i]/[h.sub.i] = -[eta](d[m.sup.t.sub.i] + d[s.sup.w.sub.i])/(1 - [m.sup.g.sub.i]) - [member of]([K.sub.i]dr + d[N.sup.t.sub.i]).

From Equation (9) and the fact that dR = 0 for this reform, it follows that

(16) [summation over (i=5/i=1)] [n.sub.i] [[[delta].sub.i]W[h.sub.i]d[m.sup.t.sub.i] - d[N.sup.t.sub.i] + [m.sup.g.sub.i] [[delta].sub.i]d(W[h.sub.i])]

= - [summation over (i=5/i=1)] [n.sub.i][[delta].sub.i][h.sub.i]d[s.sup.w.sub.i].

A reform can be evaluated once values of d[m.sup.t.sub.i] and d[s.sup.w.sub.i] are chosen that satisfy Equation (16).

Comparing Equations (13) and (14) with Equations (15) and (16) illustrates how the NWT is similar to the phase-in range of the EITC. If the household is in the first bracket of the income tax (d[N.sup.t] = 0), then the only income effect is the change in the interest rate dr, and the NWT encourages labor supply by increasing the wage rate. One difference is that d[s.sup.w] is a function of the number of households receiving the NWT, whereas the size of the change in the subsidy of the EITC is determined by the number of households in the plateau and phase-out ranges.

IV. EVALUATING THE NORMATIVE EFFECTS OF A REFORM

The change in a household's utility following a policy reform is measured by changes in the household's expenditure function [e.sub.i]([w.sub.i], [V.sub.i]), where the indirect utility function is [V.sub.i]([w.sub.i], [I.sub.i]). This is the approach taken by Allgood and Snow (1998), who define a household's net benefit from a reform as N[B.sub.i] = ([delta][e.sub.i]/([delta][V.sub.i])[d[V.sub.i].

Triest (1990) shows that [NB.sub.i] is a money metric equivalent variation method for calculating changes in utility. Substituting in for d[V.sup.i]/ = [V.sup.i.sub.w] d[w.sub.i] + [V.sup.i.sub.I]d[I.sub.i], where [V.sup.i.sub.k] is the partial derivative of a type i's indirect utility function with respect to k, substituting in for d[I.sub.i], and using Roy's identity yields

(17) [NB.sub.i] = d[E.sub.i] + d[C.sub.i] + [[h.sub.i]d[w.sub.i] + d[N.sup.c.sub.i] + [K.sub.i]dr],

where d[E.sub.i] is the change in the guaranteed income of the NIT, d[C.sub.i] is the change in the maximum tax credit of the EITC, and d[N.sup.t.sub.i] and d[N.sup.c.sub.i] are changes in the implicit transfers arising from the labor income tax and the EITC, respectively.

The equation above can be rewritten by substituting in for d[w.sub.i], dW, dr, and dR to obtain

(18) [NB.sub.i] = (d[E.sub.i] + d[C.sub.i]) - (d[R.sub.i] + [WC.sub.i]),

where

(19) [WC.sub.i] = -[m.sup.g.sub.i][[delta].sub.i]Wd[h.sub.i]

-[gamma]WH([K.sub.i]/K - [[delta].sub.i][h.sub.i]/H)(dH/H).

The classification of benefits and costs follows the definitions of aggregate tax revenue and aggregate spending from Equations (7) and (8), respectively. The first three terms of Equation (18) reflect the monetary affect of the reform on the households. The welfare cost measures the decrease (increase) in household utility because the household is induced to consumer more (less) leisure. Equation (19) shows that a household's welfare cost is the tax leakage arising from the change in their labor supply and the effects of general equilibrium changes arising from changes in factor prices. This measure of the change in a household's utility creates a metric that treats a dollar of income gained (lost) as a dollar increase (decrease) in utility.

A simple utilitarian approach is taken to aggregating welfare changes, such that NB = [summation over (i)][n.sub.i][NB.sub.i] = - [summation over (i)] [n.sub.i][WC.sub.i]. This approach to aggregating preferences ignores who pays for and who receives the redistribution. In addition, individual and aggregate preferences ignore the possibility that the market supplies too few jobs to low-skilled households or that households have some preference for equality or altruism. Thus, this approach makes the analysis directly comparable with the work of Browning and Johnson (1984), Ballard (1988), Browning (1994), Triest (1995), and Allgood and Snow (1998).

A popular statistic in the literature for expressing the trade-off between efficiency and redistribution is the cost-benefit ratio (C/B). If [NB.sup.L] is the aggregate change in utility for all households made worse off by a reform and [NB.sup.G] is the aggregate change in utility for all households made better off by a reform, then C/B is [NB.sup.L]/[NB.sup.G]. Subtracting one from C/B gives, as a percentage, how much worse off the losers are relative to the winners. Browning and Johnson (1984) and Allgood and Snow (1998) report C/B, and Triest (1994) reports C/B-1. Browning (1995) reports the benefit-cost ratio.

V. WELFARE COST CALCULATIONS

Data and Parameters

To evaluate reforms, the parameters of the model must be specified and data collected on the average household of each type. First, the five household types are defined using 1997 values for the EITC for a household with one child: [Y.sub.a] = $6,500, [Y.sub.b] =$ll,930, [Y.sub.c] = [Y.sub.b-s] [Y.sub.a]/[m.sup.c], s= -0.34 and [m.sup.c]= 0.1598 (Committee on Ways and Means, l998). (8) It is further assumed that [Y.sub.t] = [Y.sub.e] = $15,300. Data on labor income are taken from the 1991 wave of the Panel Study of Income Dynamics (PSID), and households are categorized into one of the five types by the combined labor income of the head and spouse, when applicable. Table 1 shows the average income of the five household types (in 1997 constant dollars), where mean values are calculated using the family weights provided by the PSID. Table 1 also shows the average number of persons per household.

Households with zero labor earnings makeup most of the participants of government programs that have the characteristics of an NIT. Therefore, Table 1 includes a sixth household type: those that report no labor income. It is assumed for all calculations that these households supply zero hours of labor and that the change in their labor supply is zero. It is further assumed that no household changes their income bracket or type due to marginal fiscal reforms. The percent of each type of household for the PSID data is given under the column Percent of Households Total in Table 1.

Not all households with income less than $6,500 and greater than zero participate in the ELTC. Participation in the EITC by households with income above $10,000 is determined by using data on the number of tax filers and the number of households receiving tax credits with income in this range. The participation rate for phase-in and plateau households are set to ensure (1) that 15% of the sample participates, and (2) that 30% of those receiving the EITC are in the phase-in range, as reported in Rosen (1999). (9) For example, of the 6.9% of type 1 households, 4.4% are assumed to participate in the EITC. Data on participation in the food stamp program is used to determine participation in the NIT. (10) Participation rates for type 1, 2, and 3 households are assigned so that the population participation rate is about 9.5%, and using the assumption that participation rates drop dramatically with income. (11)

A wage subsidy would likely target the same households as the EITC, therefore, the NWT reforms are assumed to affect the same percentage of households as the EITC with one exception. Type 4 households do not receive a higher subsidy as part of the NWT with the understanding that the purpose of the high breakeven income level of the EITC is to keep the benefit reduction rate low in the phase-out range, not because of a desire to redistribute income to households with incomes over $20,000. (12)

Table 1 also shows two sets of elasticities and tax rates for each household type. The labor supply elasticities for parameter set 1 are taken from Browning (1995), and the MTRs are also adapted from Browning (1995, Table 2). Triest argues that labor supply is much less responsive to changes in wages and income than what is suggested by these elasticities. The parameter set 2 labor supply elasticities and MTRs are adapted from Triest (1994, Tables 3 and 4). All households with income in a given range are assumed to have the same average income, household size, elasticities, and MTRs.

Reforms with Similar Tax Burdens

Table 2 shows the aggregate positive and normative effects of increasing mt3 by 0.00 1 and using the additional tax revenue to finance either a higher subsidy rate for the EITC, larger cash transfers for the NIT, or larger subsidy rates for the NWT. For the NIT reform, larger lump-sum transfers are given to the first three household types, and the distribution is done on a per person basis. The NWT reform increases the subsidy rate the same for each of the first three household types. (13)

Aggregate Efficiency. Using parameter set 1, the reform to the EITC increases the (absolute value of the) subsidy by 0.019, and it increases the benefit reduction rate by 0.009. For the NIT, the implicit tax on transfers increases by an average of 0.01. The NWT reform increases the subsidy rate 2.4 percentage points. Expectedly, the decline in labor supply is smallest for the NWT and largest for the EITC. Given that each reform has the same effect on the labor supply of type 5 households, the difference in aggregate labor supply across programs reflects the responses of other households. d[R.sub.5] is the increase in annual tax burden of the nonpoor and multiplying by [n.sub.5] indicates the contribution of the nonpoor to the aggregate change in tax revenue dR. By this measure, each reform is redistributing a similar amount of income from the nonpoor to the poor. Parameter set 2 generates comparable positive effects. The primary difference is that more income is redistributed because there is a smaller decrea se in labor supply.

Turning to the normative effects with parameter set 1, the annual per household welfare cost (WC = [summation over (i=5/i=1)] [n.sub.i][WC.sub.i]) is about $2.30 higher for the EITC than the NIT. Welfare cost for the NWT is one-fourth that of the NIT and one-sixth that of the EITC. If welfare cost is divided by [n.sub.5]d[R.sub.5], the result is a measure of the welfare Cost per dollar of income redistributed from nonpoor to poor households. The EITC (parameter set 1) generates 48.9 cents in welfare cost for every dollar redistributed, which is higher than the 31.3 cents of the NIT. The NWT only generates a per dollar cost of 8.9 cents. Turning to the C/B, the nonpoor lose 60% more than the poor gain for the EITC reform. The nonpoor fair much better with the NIT, but the NWT imposes a burden on the nonpoor that is only 7% larger than the gain to the poor. (14)

When using parameter set 2, aggregate welfare cost is $1.63 for both the EITC and NIT reforms. For these two programs, the efficiency costs are much smaller with the smaller elasticities and MTRs. Aggregate welfare cost and C/B are larger for the NWT with parameter set 2 than with set 1. The wage subsidy is less efficient with smaller elasticities and MTRs because the advantage of this spending program is that it encourages labor supply for all recipients. The lower elasticities lead to much smaller increases in labor supply of poor households, and because the initial MTR is smaller the initial distortion to the choice of leisure is smaller.

Also of note is that C/B-1 is slightly smaller for the EITC than for the NIT with parameter set 2. Because the EITC leads to higher tax rates for type 3 and type 4 households, it generates a substantial tax leakage with the larger elasticities. Parameter set 2 generates a smaller tax leakage, which means that more income is redistributed, and there is a larger change in the earnings subsidy component of the reform. Thus, more income is redistributed at a lower cost. As the wage and income elasticities decline, the efficiency of the three reforms become almost identical.

For all calculations reported [gamma] is set to 0.3 125. (15) Positive values of this parameter mean that the market wage rate (W) increases as labor supply decreases (dW = -[gamma]dH/H). The values of dH/H in Table 2 suggest that the change in factor prices is largest for the EITC and smallest for the NWT. The model employed assumes that all households participate in the same labor market, which means that W and dW are the same for all households. If recipients of a wage or earnings subsidy participated in a separate labor market, their market wage might decrease in response to increased labor supply. Bartik (2001) argues that these wage effects would be very small. To see if increases in the market wage are affecting the relative efficiency of the reforms, the calculations in Table 2 are repeated (but not reported in a table) assuming that [gamma] = dW = 0. Because parameter set 2 yields very small changes in labor supply, assuming dW = 0 only increases C/B-1 by 0.005 for each reform. For parameter set 1, C /B-1 increases to 0.75 for the EITC, 0.42 for the NIT, and 0.10 for the NWT. The ranking of the reforms is unchanged, but the gap between the reforms is larger.

Household-Specific Effects. Table 3 provides household-specific changes for the reforms for the two parameter sets, and the information suggests at least three major points. (16) First, the positive effects of the reforms are dependent on the choice of wage and income elasticities. Compared with parameter set 1, phase-in households receive a 30% larger subsidy for the EITC reform with set 2. Similarly, plateau and phase-out households receive a 30% larger EITC transfer (dC) with parameter set 2. The change in the NIT transfer (dE) is also larger with set 2, but most of this is lost due to the household's larger tax burden. Interestingly, the NWT subsidy to type 1 households, as measured by d[R.sub.1], is smaller with set 2 because the increase in labor supply is only one-third what it is with parameter set 1.

Second, the distribution of welfare cost across households is very different for the NWT when compared to the EITC and the NIT. For the EITC, type 1 households have a small negative welfare cost with both parameter sets, whereas welfare cost for types 2, 3, and 4 households is larger. No households respond to the NIT reform by increasing labor supply, but the decrease in labor supply for type 2 and 3 households is not as large as it is for the EITC. For the NWT, the first three household types increase labor supply, and the magnitudes are large relative to the other two reforms. Parameter set 2 preassumes a very low or zero welfare cost, but the NWT still causes a nontrivial decrease in welfare cost for the first three household types.

Third, the EITC is politically popular because of the labor supply effects that arise from subsidizing income, but this does not necessarily lead to a similar increase in household utility. Although, the EITC increases the subsidy rate of type 1 households, they receive a small net benefit from the subsidy. The NIT serves a smaller percent of type 1 households, but it provides at least twice the net benefit. The NIT greatly improves the welfare of the unemployed and the poorest working households, but the benefit to the remaining households is small. Conversely, the EITC has a larger effect on the welfare of type 2 and 3 households. Except for the NWT, net benefit is higher with parameter set 2 than with set 1. Not surprisingly, a program that generates much of its benefit by increasing labor supply is less effective if labor supply is unresponsive to wages and income.

Reforms with the Same Redistribution

Triest (1994) argues that it is difficult to rank reforms to different programs because looking at aggregate welfare costs ignores the redistributional effects of the reform. He suggests comparing the efficiency of reforms that yield the same redistribution of income. Reforms to the three expenditure policies are said to have the same redistribution if they yield the same net benefit for the average household of a given type participating in that program. This means that redistribution must focus only on households with positive labor earnings because tax credits and wage subsidies only go to the employed. The EITC is the least flexible of the three programs, so a reform to the EITC is first specified and the net gains of the first three household types are identified. Policy parameters for the NIT and NWT are chosen to generate the same change in net benefit. (17) The process is then duplicated for parameter set 2.

Is the NIT still more efficient than the EITC? Table 4 shows that the answer is no. The NIT generates a very high cost relative to the benefit generated for this reform. (18) This EITC reform is similar to the one presented in Tables 2 and 3, and C/B-1 reflects this. Comparing the results of Tables 2 and 4, the NIT is more efficient at redistributing to its target audience than the EITC is at servicing its audience, but the NIT does not efficiently redistribute to the working poor serviced by the EITC. Even with the smaller elasticities, the NIT has a substantially higher cost because a large increase in the guaranteed income is needed to generate the redistribution because of the higher tax burden accompanying the reform.

The NWT accomplishes the redistribution at a lower cost than the other two programs. For parameter set 1, ds = -0.024 for both the EITC and NWT, but d[m.sup.[t.sub.3]] is twice as large for the EITC. Although d[m.sup.[t.sub.3]] is lowest for the NIT, the redistribution is going to only 2% of households relative to 9% for the EITC and the NWT. As with the first reform, however, the NWT is only slightly more efficient than the EITC with parameter set 2.

Comparisons with Two Earlier Studies

Triest (1994) and Browning (1995) reach different conclusions about the efficiency of the EITC. The results from Table 2 suggest that much of this difference is due to how the two authors parameterize their models. Aside from using different elasticities and MTRs, the studies consider different reforms. Triest reforms the EITC by extending the phase-in range, under the assumptions that ds = d[m.sup.c] =0. Because MTRs are not altered, the reform has only income effects, and because income elasticities are zero (or almost zero) the change in labor supply is small. The major response to the reform comes in the form of increased labor force participation. Parameter set 1 in Triest's study most closely matches parameter set 2 of this study. Triest reports a C/B-1 of 0.16 versus the 0.12 reported here in Table 2. The results obtained by Triest rely on the fact that new households join the labor force in response to the reform. For his base case set of parameters he extends the phase-in range by $7,000. Changes in labor force participation may be a relevant consideration for nonmarginal reforms such as the one he considers, but they are unlikely to occur with the marginal reforms considered here.

Browning (1995) argues that labor force participation is unlikely to be seriously affected by marginal reforms to the EITC. He evaluates reforms by calculating the ratio of a household's net benefit to the 'marginal budgetary cost" of providing the benefit, where the marginal budgetary cost is d[E.sub.i] + d[C.sub.i] - d[R.sub.i]. Browning reports 0.46 cents as the average benefit-cost ratio for households in the phaseout range. For the reforms considered in Table 3, benefit--cost ratios for types 3 and 4 households are 0.768 and 0.679, respectively. For households in the phase-in range Browning reports a benefit--cost ratio of 1.03 and a value of 1.00 for plateau households. Benefit--cost ratio for type 1 (phase-in) households is 1.00, and for type 2 (plateau) it is 0.873. The differences reflect in part that Browning's definition of welfare cost considers only the distortionary component of the reform and not the full value of the tax leakage, which is the definition of welfare cost used here. In addition, Browning's model does not allow for general equilibrium changes in the wage rate.

VI. CONCLUSIONS

The efficiency costs associated with marginal reforms are dependent on the nature of the reform and the responsiveness of labor supply to wages and income. For moderately responsive labor supply, the NIT generates larger net benefits for its target population than does the EITC for its participants. The difference is substantial. For less responsive labor supply, however, the EITC may by slightly more efficient. The NIT has much higher efficiency costs than the EITC when the two programs redistribute to a similar population of the working poor. The NWT has lower efficiency costs than the other two programs regardless of the nature of the reform or choice of elasticities. As labor supply elasticities decrease, however, the difference in the efficiency costs of the EITC and the NWT become small. Certainly if one is most concerned with maximizing labor supply, increasing the size of welfare programs is the wrong approach. On the other hand, the EITC may not be an efficient means of redistributing income to the p oorest working households. An NWT or other type of wage subsidy may be best at increasing labor supply and targeting redistribution to the poorest working households.

The NWT is not a panacea. Bartik (2001) and Hoffman and Siedman (1990) detail many of the difficulties that are likely to accompany wage subsidy programs. (19) Yet Bartik (2001) argues that wage subsidies are preferable to the EITC as a means of creating jobs. The analysis here suggests that an NWT is also more efficient than the EITC at marginally redistributing income. Subsidies only assist the employed; therefore, it is not reasonable to think that either a subsidy on income or wages can completely replace the current welfare system. Further work must be done to determine if a wage subsidy can be combined with assistance for unemployed households without eliminating the positive work incentives of the subsidy.

APPENDIX

To finish the derivation of the change in labor supply, consider that [[LAMBDA].sub.i] from Equation (14) can be written as a single equation for all households by using the notation [[alpha].sub.1] - 1, [[alpha].sub.2] = [[alpha].sub.5] = 0, and [[alpha].sub.3] = [[alpha].sub.4] = [alpha]. Now, the expression is

[[LAMBDA].sub.i] = [[beta].sub.i]/[Y.sub.e] + [[alpha].sub.i][phi].

Similar notation is used to indicate changes in d[C.sub.i] and d[E.sub.i] so that d[h.sub.i] can be written as a single equation for all household types. The change in the explicit transfer from the EITC is d[C.sub.i] = -[Y.sup.a.sub.i] ds, where [Y.sup.a.sub.i] = [Y.sub.a] for i = 2, 3, 4; and [Y.sup.a.sub.i] = 0 for i = 1, 5; and [Y.sub.a] defines the end of the phase-in range of the EITC. Thechange in the implicit transfer arises for phase-out households from the EITC is d[N.sup.c.sub.i] - [Y.sup.b.sub.i] d[m.sup.c], where [Y.sup.b.sub.1] = [Y.sup.b.sub.2] = [Y.sup.b.sub.5] = 0, [Y.sup.b.sub.3] = [Y.sup.b.sub.4] = [Y.sub.b], and [Y.sub.b] defines the end of the plateau range. Given that [[beta].sub.4] = [[beta].sub.5] = 0, one equation for the change in labor can he written for alt household types.

Substituting Equation (14), d[E.sub.i], d[C.sub.i], and dr = -(H/K)dW into Equation (13) yields

d[h.sub.i]/[h.sub.i] = - [eta](d[m.sup.t.sub.i]/[1-[m.sup.g.sub.i]]) - [member of]d[N.sup.t.sub.i] - [gamma][[eta] + [member of] ([K.sub.i]/K) WH] (dH/H) - [[eta][[LAMBDA].sub.i]/(1-[m.sup.g.sub.i]) + [member of][[OMEGA].sub.i]]dR,

where

[[OMEGA].sub.i] = [[beta].sub.i] + ([[alpha].sub.i][Y.sub.b] + [Y.sup.a.sub.i] (1 - [summation over (i=5/i=1)] [n.sub.i][[beta].sub.i])/S,

and K = [summation over (i=5/i=1)] [n.sub.i][K.sub.i]. Note that one condition of the economies general equilibrium is that WH + rK = F(H,K), where F(H, K) is the constant returns to scale production function. If capital is fixed, then HdW + WdH + Kdr = [F.sub.H]dH, from which it follows that dr = - (H/K)dW = [gamma]WdH/K.

The change in individual labor supply is written as a linear function of the aggregate changes in effective labor supply and aggregate tax revenue,

d[h.sub.i]/[h.sub.i] = [D.sup.1.sub.i] + [gamma][D.sup.2.sub.i](dH/H) + [D.sup.3.sub.i]dR.

A final expression for the individual household change in labor supply is found by substituting in for dR from Equation (12),

d[h.sub.i]/[h.sub.i] = [D.sup.1.sub.i] + )[D.sup.3.sub.i]/[theta]) [summation over (5/i=4)] [n.sub.i] ([[delta].sub.i]W[h.sub.i]d[m.sup.t.sub.i] - d[N.sup.t.sub.i])

+ ([D.sup.3.sub.i]/[theta]) [summation over (i=5/l=1)] [n.sub.i][m.sup.g.sub.i][[delta].sub.i]Wd[h.sub.i].

+ [gamma][[D.sup.2.sub.i] - ([D.sup.3.sub.i]/[theta]) [summation over (i=5/i=1)] [n.sub.i][m.sup.g.sub.i][[delta].sub.i]W[h.sub.i]] (dH/H).

The equation can be rewritten as d[h.sub.i]/[h.sub.i] = [D.sup.1.sub.i] + [D.sup.2.sub.i] [summation over (i=5/i=1)] [n.sub.i][m.sup.g.sub.i][[delta].sub.i]Wd[h.sub.i] + [gamma] [D.sup.3.sub.i](dH/H). An expression for dH/H is found by multiplying the individual household change in labor supply by [n.sub.i][[delta].sub.i][h.sub.i], summing, and dividing by H. Next, multiply d[h.sub.i]/[h.sub.i] by [n.sub.i][m.sup.g.sub.i][[delta].sub.i] W[h.sub.i], and sum to obtain an equation for [summation over (i=5/i=1)] [n.sub.i][m.sup.g.sub.i][[delta].sub.i] Wd[h.sub.i]. Once these two equations are solved for the two unknowns, household changes in labor supply can be calculated.

The change in labor supply with the wage subsidy reform is found by expanding Equation (15) to obtain

d[h.sub.i]/[h.sub.i] = -[eta](d[m.sup.t.sub.i] + d[s.sup.w.sub.i])/(1 - [m.sup.g.sub.i]) - [member of]d[N.sup.t.sub.i]

- [gamma][eta] + [member of]([K.sub.i]/K) WH](dH/H).

This expression can be evaluated using the procedures outlined.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

TABLE 1

Data and Parameters by Household Type

 Percent of Households
 Average
Type Income Total EITC NIT NWT

 0 23.4 0.0 7.6 0.0
1 2,891 6.9 4.4 1.5 4.4
2 8,736 5.1 2.2 0.3 2.2
3 13,001 5.3 2.4 0.2 2.4
4 20,042 12.5 6.1 0.0 0.0
5 58,539 46.8 0.0 0.0 0.0

 Parameter Set 1

Type PPH [[eta].sup.c] [eta] [m.sup.g.sub.i]

 1.74
1 2.18 0.3 0.2 10.1
2 2.15 0.3 0.2 44.1
3 2.10 0.3 0.2 60.1
4 2.24 0.3 0.2 51.1
5 2.83 0.3 0.2 40.0

 Parameter Set 2

Type [[eta].sup.c] [eta] [m.sup.g.sub.i]


1 0.05 0.05 29
2 0.04 0.04 26
3 0.04 0.04 24
4 0.06 0.06 27
5 0.10 0.10 38

Notes: Data on income, percent of total population, and persons per
household is from the 1991 PSID. Parameter set 1 is from Browning
(1995). Parameter set 2 is from Triest (1994). Participation rates for
the EITC and NIT are estimated from figures in the Green Book (Committee
on Ways and Means, 1998). Each column gives the percent of households of
each type that are affected by the spending component of that reform.
PPH is the average number of persons per household.

TABLE 2

Aggregate Effects of Reforms--Same Tax Burden ([gamma] = 0.3125;
d[m.sup.[t.sub.3]] = 0.001; d[N.sup.t] = 12.05)

 Parameter Set 1
 EITC NIT NWT

ds -0.019 -- -0.024
d[m.sup.c] 0.009 -- --
d[m.sup.e] -- 0.010 --
dH/H x 100 -0.046 -0.033 -0.014
[n.sub.5]d[R.sub.5] 13.120 13.000 12.270
dR 12.959 13.971 0.000
d[N.sup.c] 6.664 -- --
WC 6.412 4.063 1.087
C/B-1 0.603 0.341 0.070

 Parameter Set 2
 EITC NIT NWT

ds -0.024 -- -0.024
d[m.sup.c] 0.011 -- --
d[m.sup.e] -- 0.011 --
dH/H x 100 -0.014 -0.014 -0.011
[n.sub.5]d[R.sub.5] 14.000 14.800 14.800
dR 17.084 15.724 0.000
d[N.sup.c] 8.786 -- --
WC 1.629 1.629 1.420
C/B-1 0.115 0.138 0.095

Notes; Values for d[N.sup.t], d[m.sup.e], dR, d[N.sup.c], and WC are
per-household values. d[N.sup.t], [n.sub.5]d[R.sub.5], dR, d[N.sup.c],
and WC are annual amount in dollars.

TABLE 3

Household-Specific Effects of Reforms

 Household
 No Income 1 2 3 4

Parameter set 1
EITC
 d[C.sub.i] -- 0.000 120.327 120.327 120.327
 d[h.sub.i] -- 0.138 -39.599 -55.273 -44.608
 d[R.sub.i] -- -53.454 -16.888 -22.722 49.323
 [WC.sub.i] -- -0.014 17.463 33.208 22.786
 [NB.sub.i] -- 53.468 119.751 109.840 48.219
NIT
 d[E.sub.i] 140.109 175.254 172.861 168.692 --
 d[h.sub.i] 0.000 -19.401 -30.576 -41.636 --
 d[R.sub.i] 0.000 31.183 85.621 119.159 --
 [WC.sub.i] 0.000 1.960 13.484 25.015 --
 [NB.sub.i] 140.109 142.112 73.756 24.518 --
NWT
 d[h.sub.i] -- 15.673 76.127 158.606 --
 d[R.sub.i] -- -68.676 -178.621 -220.422 --
 [WC.sub.i] -- -1.583 -33.572 -95.290 --
 [NB.sub.i] -- 70.259 212.193 315.712 --
Parameter set 2
 EITC
 d[C.sub.i] -- 0.000 158.626 158.626 158.626
 d[h.sub.i] -- 0.008 0.015 0.224 0.052
 d[R.sub.i] -- -70.505 0.104 12.430 93.297
 [WC.sub.i] -- -0.002 -0.004 -0.005 -0.014
 [NB.sub.i] -- 70.507 158.525 146.202 65.342
NIT
 d[E.sub.i] 157.687 197.240 194.548 189.855 --
 d[h.sub.i] 0.000 0.005 0.015 0.023 --
 d[R.sub.i] 0.000 37.304 111.183 161.473 --
 [WC.sub.i] 0.000 -0.002 -0.004 -0.006 --
 [NB.sub.i] 157.687 159.938 83.369 28.388 --
NWT
 d[h.sub.i] -- 4.801 11.137 16.140 --
 d[R.sub.i] -- -66.682 -202.836 -302.323 --
 [WC.sub.i] -- -1.392 -2.896 -3.874 --
 [NB.sub.i] -- 68.074 205.731 306.196 --

 Household
 5

Parameter set 1
EITC
 d[C.sub.i] 0.000
 d[h.sub.i] -20.601
 d[R.sub.i] 28.036
 [WC.sub.i] 8.240
 [NB.sub.i] -36.276
NIT
 d[E.sub.i] 0.000
 d[h.sub.i] -21.289
 d[R.sub.i] 28.195
 [WC.sub.i] 8.516
 [NB.sub.i] -36.711
NWT
 d[h.sub.i] -22.613
 d[R.sub.i] 26.221
 [WC.sub.i] 9.045
 [NB.sub.i] -35.267
Parameter set 2
 EITC
 d[C.sub.i] 0.000
 d[h.sub.i] -9.183
 d[R.sub.i] 30.273
 [WC.sub.i] 3.490
 [NB.sub.i] -33.763
NIT
 d[E.sub.i] 0.000
 d[h.sub.i] -9.183
 d[R.sub.i] 31.722
 [WC.sub.i] 3.490
 [NB.sub.i] -35.211
NWT
 d[h.sub.i] -9.233
 d[R.sub.i] 31.514
 [WC.sub.i] 3.508
 [NB.sub.i] -35.022

Notes: Values are for individual households. d[h.sub.i] is in
hours/year, and all other values are annual values in dollars.

TABLE 4

Aggregate Effects of Reforms--Same Redistribution ([gamma] = 0.3125)

 Parameter Set 1 Parameter Set
 2
 EITC NIT NWT EITC

d[m.sup.t3] 0.0013 0.0003 0.0007 0.0012
ds -0.024 -- -0.024 -0.028
d[m.sup.c] 0.011 -- -- 0.013
d[m.sup.e] -- 0.002 -- --
dHIH x 100 -0.060 -0.012 -0.011 -0.016
[n.sub.5]d[R.sub.5] 17.057 3.926 8.291 16.293
C/B-1 0.603 1.976 0.113 0.115

 Parameter Set 2
 NIT NWT

d[m.sup.t3] 0.0003 0.0008
ds -- -0.028
d[m.sup.c] -- --
d[m.sup.e] 0.002 --
dHIH x 100 -0.004 -0.009
[n.sub.5]d[R.sub.5] 4.035 11.504
C/B-1 1.268 0.090

Notes: The value of ds for the NWT is the value for type 1 households.
Using parameter set 1, ds for type 2 is -0.018, and for type 3 it is
-0.011. Using parameter set 2, the values are -0.013. The given value of
d[m.sup.e] is the weighted average of d[m.sup.e.sub.i], where the weight
is the proportion of each type of household.

(1.) This is not to imply that the expansion of the EITC has gone unnoticed, but most of the literature focuses on evaluating the labor market effects. See, for example, Hoffman and Siedman (1990), Keane (1995), Eissa and Liebman (1996), and Bartik (2001).

(2.) The assumptions that households with income above [Y.sub.e] do not receive cash assistance and that [Y.sub.E] = [Y.sub.t ]are not critical to the model. These assumptions are designed to (1) differentiate household's that are on welfare from those that are not, and (2) to reduce the number of different household types that must be considered.

(3.) This is a simplification, of course. Households may receive welfare but not participate in the EITC, or vice versa. The assumption of only five household types is relaxed when computing the effects of reforms (see section V).

(4.) A fuller model of a wage subsidy would allow for endogenous changes in the wage rate through human capital investment or promotion. Similarly, a NIT and the EITC distort the decision of how many children to have. The analysis here focuses on the more commonly considered decision of labor supply.

(5.) If [C.sub.i] is treated as tax revenue then dR = 0 for all reforms to the EITC.

(6.) Triest (1994) reforms the EITC by extending the phase-in range. Browning (1995) argues that reforming the EITC by changing the MTRs instead of the income brackets is preferable for two reasons. First, past changes in the program have revolved around changes in the implicit MTRs. Second, adjusting MTRs has superior redistributional effects.

(7.) The change in household labor supply is found by taking the total differential of the uncompensated demand for leisure d[h.sub.i] = -d[l.sub.i] = -([l.sup.i.sub.w]d[w.sub.i] + [l.sup.i.sub.I]d[I.sub.i]), where [l.sup.i.sub.j] is the partial derivative of [l.sub.i] with respect to j. Equation (13) follows after substituting in for the Slutsky equation for leisure, d[I.sub.i], and converting partial derivatives to elasticities.

(8.) This is a simplification of the EITC because the subsidy and benefit reduction rates, as well as the income ranges over which they apply, vary with the number of children in a household. A one-child household is chosen because the average number of children per household is about one for the data set used.

(9.) Of the 133 million tax returns filed in 1997, about 15% received a tax credit, so it is assumed that 15% of households in the sample receive a tax credit. These figures are consistent with those reported by Hoffman and Siedman (1990). They also use the PSID and find that about 11% of families received a tax credit in 1988.

(10.) In 1996 only 4.8% of the U.S. population participated in the AFDC program. According to Browning (1995), only 10% of participants work. Using participation rates for the food stamp program increases the number of working households affected by the NIT reform. Almost 80% of those receiving food stamps have no earnings and there is a 9.6% participation rate for the U.S. population. If we assume that the 9.6% participation rate applies to households, then 7.6% (0.8 x 0.096) of households have no market earnings and receive the full transfer from the NIT.

(11.) This is not to imply that only 1.5% of working households with income less than $6,500 receive government assistance. Reforms to the NIT are designed to represent a reform to a type of welfare, such as AFDC or food stamps, and not to all welfare programs. The percent of the working population taking part in any given welfare program is very small.

(12.) The relative efficiency of the reforms is not affected by this assumption.

(13.) All calculations are done with the assumption that a household's capital share equals its share of the effective labor supply.

(14.) The results for parameter set 1 are not driven by the fact that type 1 households have such a low gross MTR. if the effects of each reform are recalculated by assuming that [m.sup.g.sub.1] = 0.24, there is no change in the relative efficiency of reforms.

(15.) For a constant elasticity of substitution production function [gamma] = (1 - [theta])/[sigma], where [theta] is labor's share and [sigma] is the elasticity of substitution. Given that [theta] = 0.75 and using [sigma] = 0.8 in Ballard (1988), [gamma] = 0.3125.

(16.) The results are only for households directly affected by the reforms, and they do not include households only affected by general equilibrium changes in input prices because changes to these households are small. A dash (-) indicates the reform does not directly affect any households with income in that range.

(17.) The net benefit of type 1 households is $69, $156 for type 2 households, and $143 for type 3 households.

(18.) To ensure that the ranking for the NIT is not affected by differences in the affected population, the numbers in Table 4 were calculated assuming that the NIT services the same population as the EITC and NWT. The NIT remained the least efficient reform.

(19.) Alstott (1994) suggests that the integration of the tax and transfer systems that occurs with the EITC--and would undoubtedly occur with a wage subsidy--yields a number of neglected problems. Besides problems discussed here, she identifies the problems of accurately measuring the family unit and responsiveness to the transfer recipient's changing circumstances.

REFERENCES

Allgood, S., and A. Snow. "The Marginal Cost of Raising Tax Revenue and Redistributing Income." Journal of Political Economy, 106(6), 1998, 1246-73.

Alstott, A. L. "The Earned Income Tax Credit and Some Fundamental Institutional Dilemmas of Tax-Transfer Integration." National Tax Journal, 47(3), 1994, 608-19.

Ballard, C. L. "The Marginal Efficiency Cost of Redistribution." American Economic Review, 78(5), 1988, 101 9-33.

Bartik, T. J. Jobs for the Poor: Can Labor Demand Policies Help? New York: Russell Sage Foundation, 2001.

Browning, E. K. "Alternative Programs for Income Redistribution: The NIT and the NWT." American Economic Review, 63(1), 1973, 38-49.

-----. "Effects of the Earned Income Tax Credit on Income and Welfare." National Tax Journal, 48(1), 1995, 23-43.

Browning, E. K., and W. R. Johnson. "The Trade-Off between Equality and Efficiency." Journal of Political Economy, 92(2), 1984, 175-203.

Committee on Ways and Means. Overview of Entitlement Programs (Green Book). Washington, DC: Government Printing Office, 1998.

Eissa, N., and J. B. Liebman. "Labor Supply Response to the Earned Income Tax Credit." Quarterly Journal of Economics, 111(2), 1996, 605-37.

Fuchs, V. R., A. B. Krueger, and J. M. Poterba. "Economists' Views about Parameters, Values, and Policies: Survey Results in Labor and Public Economics." Journal of Economic Literature, 36(3), 1998, 1387-425.

Hoffman, S.D., and L. S. Siedman. The Earned Income Tax Credit: Antipoverty Effectiveness and Labor Market Effects. Kalamazoo, MI: W. E. Upjohn Institute, 1990.

Keane, M. P. "A New Idea for Welfare Reform." Quarterly Review Federal Reserve Bank of Minnesota, 19(2), 1995, 2-28.

Rosen, H. S. Public Finance. Boston: Irwin McGraw-Hill, 1999.

Scholz, J. K. "In-Work Benefits in the United States: The Earned Income Tax Credit." Economic Journal, 106(434), 1996, 156-69.

Steuerle, C. E. "Tax Credits for Low-Income Workers with Children." Journal of Economic Perspectives, 4(3), 1990, 201-12.

Stuart, C. "Welfare Costs per Dollar of Additional Tax Revenue in the United States." American Economic Review, 74(3), 1984, 352-61.

Triest, R. K. "The Relationship between the Marginal Cost of Public Funds and Marginal Excess Burden." American Economic Review, 80(3), 1990, 557-66.

-----. "The Efficiency Cost of Increased Progressivity," in Tax Progressivity and Income In equality, edited by Joel Slemrod. Cambridge: Cambridge University Press, 1994.

RELATED ARTICLE: ABBREVIATIONS

AFDC: Aid to Families with Dependent Children

C/B: Cost-Benefit Ratio

EITC: Earned Income Tax Credits

MTR: Marginal Tax Rate

NIT: Negative Income Tax

NWT: Negative Wage Tax

PSID: Panel Study of Income Dynamics

SAM ALLGOOD *

* I am grateful for the helpful comments of Arthur Snow and three 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 [email protected]