# Decentralized income redistribution reconsidered.

DECENTRALIZED INCOME REDISTRIBUTION RECONSIDERED

I. INTRODUCTION

Which is the appropriate level of government to undertake income redistribution? This issue is receiving renewed attention from economists examining how migration and labor supply responses affect the costs of transfer payments at the state or federal level. In a recent paper, Brown and Oates [1987! use a formal public choice model to show that the possibility of migration of transfer recipients between states leads to suboptimal transfer levels even when taxpayers care only about transfer recipients within their own states. With benefit spillovers across states, their argument for federal responsibility for redistribution is, presumably, even stronger. Gramlich [1985! also argues that migration is large enough to lead to suboptimal levels of transfers at the state level because states with low benefit levels will be able to "export" their poor, increasing the cost of redistribution to high-benefit states. Gramlich's conclusion is based on the empirical work in Gramlich and Laren which finds that the migration effect is "very strong" .... though only in the very long run" [1984, 510!. The implicit argument is that migration raises the cost of redistribution at the state level compared to the federal level. (1) However, neither Brown and Oates nor Gramlich consider labor supply responses (that is, hours and participation) in their analyses.

On the other hand, several recent papers have attempted to estimate the cost of redistribution at the national level, incorporating labor supply responses to taxes and transfers but not interjurisdictional migration. (2) Some empirical evidence is available which is consistent with either migration or labor supply effects. For example, Helms [1985!, uses time series-cross section data on state expenditure and tax policies, and finds that while spending on public services (schools, highways, etc.) increases personal income, increased state transfer payments financed by state taxes significantly reduce total state personal income. This reduction could be caused by either migration or labor supply responses to taxes and transfers. Indeed, Helms's estimates indicate a very large response to transfer spending one more dollar of transfers reduces state personal income in the long run by $14.83. Helms concludes,

"States which seek to devote substantial tax revenues to transfer payments will experience significantly reduced growth prospects, which limits the scope for redistribution at the state and local levels" [1985, 581!.

A concise summary of the standard argument concerning federalism and redistribution might be as follows:

1. Interstate migration of taxpayers and transfer recipients raises the taxpayer cost of income redistribution at the state level above the cost at the federal level.

2. State-wide redistribution confers spillover benefits to residents of other states.

3. Therefore, as compared with a national system, decentralized responsibility for income redistribution yields

a. less redistribution (because its cost is higher) and

b. less than the socially optimal amount of redistribution (because of externalities).

My 1988 paper shows that step 1 of the above argument is not necessarily true because the migration effect, which previous authors have stressed, can be offset by a tax-exporting effect by which residents of one state shift some of the fiscal cost of redistribution to residents of other states. Both the income effect and the substitution effect of increased redistribution will reduce the labor supply (and hence earnings) of transfer recipients the labor supply (and earnings) of taxpayers may also fall if substitution effects are strong enough. The tax-exporting effect arises if taxes and transfers, on net, reduce total earnings in a state, since the state's federal tax obligations depend on its earnings. Essentially, the federal tax system subsidizes state redistribution and offsets (at least partially) the migration externality. The tax-exporting effect is magnified by the deductibility of state taxes in the federal income tax but can exist even without deductibility. Thus, the validity of step 1 is an empirical question which depends on behavioral responses (labor supply and migration) as well as the existing pattern of taxes and transfers.

In this paper I attempt to shed some light on this empirical question by comparing simulations of small changes in redistribution at the state and federal levels for a variety of labor supply and migration responses. I focus here only on the cost of redistribution and not on the benefits that it costs the non-poor more than a dollar to raise the income of the poor by a dollar does not imply that redistribution should not be undertaken. The externality to the non-poor created by raising the incomes of the poor is ignored here as is any other externality arising from proximity to low-income households. Although this paper and previous work in the area focuses on the fiscal costs of redistribution, if proximity to low-income persons makes high-income taxpayers worse off, increased redistribution which attracts transfer recipients imposes more than a monetary cost on taxpayers. The cost estimates in this paper ignore this externality of proximity. The question addressed here is whether the cost to the upper four income quintiles of redistribution to the lowest quintile is greater at the state or federal level, when labor supply and migration responses of both taxpayers and transfer recipients are considered. State redistribution here refers to the combined redistributive effect of state and local governments.

The simulations show that, in some (but not all) plausible cases, the tax-exporting effect is large enough that voters face a smaller cost of redistributing at the state level than at the federal level. Deductibility of state taxes may strengthen this result. Section II of the paper introduces the model used to estimate marginal redistribution costs in the context of a single jurisdiction. Section III extends the model to a federal system and estimates the relative cost of state redistribution.

II. A SAMPLE MODEL WITH ONE JURISDICTION

Before introducing the complication of a federal system of taxes and expenditures, it is useful to present a basic model of income redistribution. Current net income of household i, including the effects of existing taxes and transfers, is denoted by [Y.sub.i!, i = 1,..., n. Since attention is focussed on incremental changes in redistribution financed by taxes on labor income alone, gross taxable income should be interpreted as labor earnings, [W.sub.i.L.sub.i!, where [W.sub.i! is the gross return to each unit of labor, [L.sub.i!, supplied to the market. Although the global budget constraint facing the household is highly non-linear, due to the complex system of taxes and transfers now in place, it can be approximated locally by the linear constraint [Y.sub.i! = [B.sub.i! + (1-[t.sub.i!) [W.sub.i.L.sub.i!. Hence [B.sub.i! is the "virtual income" of household i and [t.sub.i! is its marginal tax rate. Small changes in the tax-transfer system can be represented by changes in the parameters of this linear budget constraint, which is the local approximation to the global non-linear budget constraint.

The response of labor supply, [L.sub.i!, to small changes in [t.sub.i! and [b.sub.i! is parameterized as follows:

(1) [Mathematical Expression Omitted!

Equation (1) can be easily interpreted. The left-hand side is the change in gross labor income induced by tax and transfer changes which, in this partial equilibrium analysis, are assumed not to affect the gross wage rate, [W.sub.i!. The first term on the right is the response to changes in the marginal tax rate, [t.sub.i! as parameterized by [epsilon!, the uncompensated elasticity of supply of [L.sub.i! with respect to the net wage rate, [W.sub.i!(1-[t.sub.i!). Note that for a given value of [epsilon!, the effect of [dt.sub.i! the greater the larger is [t.sub.i! because a given change in the tax rate implies a greater percentage change in net factor returns. The second term on the right-hand side of (1) is the pure income effect of changes in [B.sub.i! the parameter C is the marginal propensity to consume leisure out of unearned income.

Suppose the government attempts to increase marginally the current amount of redistribution by rotating each household's budget constraint in goods-leisure space slightly in the counter-clockwise direction. High-income households will pay more net taxes while low-income households receive more net transfers. Such a rotation is identical to a uniform additional tax, dt, on the labor incomes of all households which is used to finance a uniform addition, dB, to every household's virtual income. (3) In other words, redistribution at the margin is undertaken by a demogrant financed by proportional taxes on labor income. Of course, the amount of the demogrant dB depends on additional tax revenue, by the marginal government budget constraint:

(2) [Mathematical Expression Omitted!

The left-hand side of (2) is total extra demogrants paid, or ndB. The right-hand side of (2) expresses the change in tax revenue as the sum of the additional tax rate, dt, applied to current taxable income, and the current marginal tax rate, [t.sub.i!, applied to the change in factor income induced by the new policy.

Substituting (2) into (1) and rearranging yields

(3) [Mathematical Expression Omitted!

where summations are henceforth understood to be taken over i = 1,...,n. Equation (3) gives the additional per capita transfer (dB) produced by an incremental tax (dt). When factor supplies are completely unresponsive to any economic variable (C = [epsilon! = 0), then dB/dt is just average taxable income (the revenue produced by a 100 percent tax).

The change in the net income of any one household induced by the marginal policy change is

(4) [Mathematical Expression Omitted!

where [Omega! = dB/dt, as given by (3). Equation (4) states that the income of household i rises by the amount of the additional demogrant ([Omega!dt) but falls by the amount of additional taxes on the original income ([W.sub.i.L.sub.i!dt) plus the change in after-tax income induced by the behavioral response to the policy change [-(1-[t.sub.i!)C[Omega! - [[epsilon!W.sub.i.L.sub.i!!dt.

To analyze the welfare costs of a change in policy, I assume that individual utility is the sum of two functions, one solely a function of private goods and leisure, and the other solely a function of other households' income and leisure. This latter function captures the external benefits of redistribution that may explain its existence it does not play a role in this analysis which focuses instead on the relative costs of redistributing at the state and federal level. Subsequent references to welfare exclude the public goods externality of redistribution.

The change in the welfare of any one household, [dZ.sub.i!, induced by the marginal policy changes is just the change in that household's net transfers less the additional welfare cost (excess burden) of the marginal redistribution. Since a conventional measure of this last term is the tax revenue lost by the compensated change in labor supply, (4) we have

(5) [Mathematical Expression Omitted!

In (5), the first three terms are the change in net transfers while the terms in square brackets are the excess burden of the tax increase. (5) Note that when labor supply is completely unresponsive (C = [epsilon! = dL = 0, the welfare change is just the change in net income. The change in welfare for any household subject to the marginal redistribution policy of a demogrant financed by a proportional tax can be found by substituting [dB.sub.i! = dB = [Omega!dt, [dt.sub.i! = dt, and equation (1) into (5):

(6) [Mathematical Expression Omitted!

Equation (6) says that household i is better off if and only if the new budget constraint lies above the point chosen on the previous budget constraint.

To estimate the effect of a marginal increase in redistribution on income and welfare, simulations were performed

using all the households in the March, 1976 Current Population Survey (CPS). This data set is somewhat dated, especially considering recent changes in the federal tax structure, but includes a wealth of detail on transfers and taxes. (6) In the simulations, the demogrant that can be financed by a marginal increase in taxation, dt, is first calculated using (3). Then, that value of [OMEGA! is used to compute the impact on income and welfare of each household, according to (4) and (6). The information needed for these calculations is labor income, [W.sub.i.L.sub.i!, and marginal tax rates, [T.sub.i!, for each household as well as values for the parameters, C and [epsilon!.

The economic assumptions underlying the results reported here (as summarized by eqs. (1), (3), (4) and (6)) are not the same as those used in my 1984 paper with Browning. To evaluate these expressions, reasonable values for [epsilon! and C must also be established. The uncompensated elasticity of labor supply, [epsilon!, is assumed to fall between -.2 and .4 with the midpoint of the range reflecting the fact that the negative elasticity sometimes estimated for men is more than offset by the substantial positive wage elasticities estimated for women. (7) The marginal propensity to consume leisure, C, is a less familiar concept but can be related to the income elasticity of labor supply by

(7) C = [- gamma! (1 [THETA!)

where [gamma! is the pure income elasticity of labor supply and [THETA! is the share of leisure in full income. If [THETA! is roughly .5 then C is roughly half the income elasticity of labor supply. A range of C between zero and .4 is chosen. (8) Recall that C is the fraction of an additional dollar of pure income spent on leisure. Parameter values roughly at the midpoints of these ranges seem most consistent with empirical evidence on labor supply.

For each set of parameter values, I compute the effect of a .01 change in t (and the associated value od dB) on each household's income and welfare. To distill the changes for many thousands of households into an easily comprehensible form, the total welfare (or income) change for all households is divided by the welfare (or income) change for those households in the bottom quintile of the income distribution. This ratio assumes the value of zero when redistribution is a zero-sum game (that is, socially costless) and can be interpreted as the social cost of increasing the bottom quintile's welfare (or income) by one dollar.

III. REDISTRIBUTION IN A FEDERAL SYSTEM

To compare the costs of redistribution for local and national governments in a federal system, three simplifying assumptions are made. First, state and local governments are not distinguished in the model all local taxes and redistributive expenditures are attributed to the state. Second, the voters in each state are assumed to take the behavior of other states as given. (9) As I discuss in my 1988 paper, relaxing this assumption to allow other states to respond to one state's policy change will certainly weaken the tax-exporting effect but will likely weaken the migration effect even more. Hence, adopting the no-response assumption biases against finding that tax exporting dominates migration. The third assumption is that the state income distribution mirrors the national income distribution this assumption focuses the analysis on issues of federalism rather than interstate income redistribution.

The most important difference between state and federal taxation is that factors of production are more mobile between states than between countries to reflect this, no international mobility is assumed here. State populations are assumed to be a function of differences in the budget constraints faced by residents in those states. Specifically, let [X.sub.i! be the vertical displacement of the budget constraint for residents at income level [Y.sub.i!, caused by a change in a state's tax or transfer policy. Then the percent change in the number of residents at income level [Y.sub.i!, is assumed to be [eta!(X/Y) percent. Hence, [eta! is the elasticity of the population with respect to net income, an elasticity which is assumed to characterize residents at all income levels. An increase in state taxes used to finance more redistribution will reduce the welfare of high-income citizens (X 0) and induce out-migration. The same policy enhances the incomes of low-income residents (X 0) and so induces in-migration. Since additional redistribution will have a larger percentage effect on the incomes of the poor than of the wealthy, the migration response of the ppor should exceed that of the rich, as it does with this formulation. (10) An assumption (not pursued here) of no taxpayer migration only strengthens the paper's conclusion by reducing the tax competition effect.

Most of the recent research on migration responses to redistribution focuses on the behavior of transfer recipients. Gramlich and Laren [1984! estimate the long-run elasticity of transfer recipient populations with respect to benefits levels, with results for various models and data sets ranging from .11 to 1.7. (11) Blank [1988! has also estimated the migratory response of transfer recipients to changes in benefit levels. For example, she estimates that, for New York, a 20-25 percent reduction in benefits implies an increase in the out-migration rate which would yield a 16 percent lower recipient population after twenty years. Since she does not consider in-migration, her estimates put an upper bound on the long-run population elasticity of About .75.

Redistribution costs can be computed for states analogously to the cost computations for a national government presented in section II. Both migration and labor supply responses will now affect the incremental benefit that can be financed by an increase in state taxes. Once the incremental benefit is found, changes in household income and welfare are given by equations (4) and (6).

To incorporate migration responses into the analysis of redistribution costs at the state level, we must adjust the number of persons at each income level by the migratory response to marginal tax and transfer changes. The change in net income for household i at the previous level of labor supply, [X.sub.i!, induced by changes in marginal tax rates, d [t.sub.i!, and virtual income, [dB.sub.i!, is (12)

[X.sub.i!=-([W.sub.i.L.sub.i!)[dt.sub.i!+[dB.sub.i!.

If i is now interpreted as an index of income levels corresponding to each of the original resident households, [N.sub.i! = 1 for all i. Then the change in the number of households with income [Y.sub.i! dN.sub.i!, is given by

[eta! = ([Y.sub.i*dN.sub.i!)/(-[W.sub.i.L.sub.i.dt.sub.i+dB.sub.i.!),

or

(8) [Dn.sub.i!=[eta!(-[W.sub.i.L.sub.i.dt.sub.i+dB.sub.i!)/[Y.sub.i!

Without deductibility of state taxes from federal taxes (which will be considered below), the overall marginal tax rate, [t.sub.i!, is just the sum of nominal federal and state rates, [t.sub.i!=[t.sub.fi.+t.sub.si!. Federal taxes and benefits do not respond to changes in one state's taxes or transfers, so

[dt.sub.i!=[dt.sub.si!and[dB.sub.i!=[dB.sub.si!.

Restricting states to imposing, on the margin, proportional taxes to finance demogrants, (yielding a net tax system which is linear with a non-zero intercept) we have

[dt.sub.si!=[dt.sub.s!i=1,...,n

[dB.sub.si!=[dB.sub.s!i=1,...,n.

Now consider the marginal budget constraint faced by the state. The change in expenditures is the sum of additional benefits paid to existing residents, of whom there are [n.sub.s!, plus (minus) the state's share of full benefits paid to new in-migrants (out-migrants), or

(9)[n.sub.s.dB.sub.s!+[SIGMA![B.sub.si.dN.sub.i!.

The change in tax revenue is the sum of the changes due to the new tax rate, to labor supply responses of existing residents, and to migratory responses:

(10) [Mathematical Expression Omitted!

Equating (9) and (10), and substituting (8) yields the marginal budget constraint for a state government:

(11) [Mathematical Expression Omitted!

where [b.sub.i!=[W.sub.i.L.sub.i./Y.sub.i!.

The only additional data needed to calculate [dB.sub.s!/[dt.sub.s! from (11), beyond that used to compute redistribution costs in the single-government case in the previous section, is information on [B.sub.si! and [t.sub.si!, that portion of total taxes and benefits attributable to state (and local) governments. For the purpose of these calculations I assume that state taxes and benefits are the same proportion, [delta!, of overall taxes and benefits, where [delta! is the share of state and local government spending in total government spending (equal to .43 in 1976). (13) Thus,

(12) [t.sub.si!=[delta![t.sub.si!=[delta![B.sub.i!.

[B.sub.i! is computed as the vertical intercept of each household's linearized budget constraint:

[B.sub.i!=[Y.sub.i!-(1-[t.sub.i!)[W.sub.i.L.sub.I!.

The income and welfare changes induced by a marginal change in state redistribution can be analyzed in a way similar to that already described above for the single-government case (just below equation (6)). First the incremental state benefit financed by a small change in state taxes is computed using equation (11). In addition to the parameters and data already required for the single-government case, equation (11) depends on [eta!, the population elasticity, [Y.sub.i!, total household income, and [B.sub.s! and [t.sub.s!, state benefits and tax rates, as computed by (12).

Results

Armed with these estimates of the incremental benefit available from a small rise in taxes,[OMEGA!, each household's income and welfare change is computed using (4) and (6). Summed over all households, the aggregate welfare changes are negative (recall that the external benefits of redistribution are ignored here) but income changes may be positive. The cost of redistribution is taken to be the ratio of aggregate income or welfare lost per dollar of extra income (or welfare) transferred to the bottom quintile of households. In the case of state government redistribution, the gains and losses of non-migrating persons only are counted. Recall that there is no migration or tax-exporting effect for the federal government since labor is assumed to be internationally immobile and there is no supranational government taxing U.S. residents.

Table I presents the ratio of marginal redistribution costs for a state to the cost for the federal government for a range of values of [eta!, the population elasticity, and labor supply parameters. A cost ratio less than one indicates a situation in which costs are lower at the state level than at the federal level an infinite cost ratio implies that federal redistribution is costless, a zero-sum game. As Table I indicates, lower population elasticities and higher labor supply responses lead to lower relative costs of state redistribution. When labor supply is unresponsive (as in the first row of the table), only the migration effect operates so federal redistribution is costless while state redistribution is costly. The last two rows of the table pertain to two vertical or backward-bending labor supply curves. Here the state cost exceeds the federal cost because redistribution increases money incomes and federal tax burdens. Table I indicates that for some plausible labor supply and migration parameters, state costs or redistribution are less than federal costs.

Deductibility and Matching Grants

The estimates in Table I do not assume that state and local taxes can be deducted from income taxable at the federal level. The effect of deductibility depends on (1) the marginal federal tax rates of net taxpayers and net transfer recipients (2) who itemizes deductions and (3) the exact form of the increased redistribution. If everyone's marginal federal rate were identical and if everyone itemized deductions and if redistribution to low-income households took the form of lower state taxes or taxable transfer payments, then deductibility would not affect the relative cost of state redistribution. In that case, the lower federal tax bills of high-income taxpayers would be matched by higher federal tax bills of the beneficiaries of redistribution.

Deductibility can reduce the relative cost of state redistribution if, for example, low-income households are less likely to itemize and redistribution is accomplished by reducing the state tax burden on these households, or if high income households face higher marginal federal tax rates. Since both of these conditions exist to some degree, it is safe to conclude that deductibility will reduce the estimated relative costs of state and local redistribution given in Table I. However,

precise estimates of the effect of deductibility are not possible with the data available.

Another feature of the current federal systems in the U.S. which affects the marginal cost of state redistribution is the availability of federal matching grants for redistributional expenditures. A large empirical literature, such as Moffitt [1984!, exists which shows that these matching formulae do increase state expenditures on redistribution. Hence, consideration of matching grants would reduce even further the relative state costs of redistribution found in Table I.

IV. CONCLUSION

This paper has examined the effect of additional income redistribution at the state and national level when both labor supply and location respond to economic incentives. Marginal redistribution is accomplished by a proportional tax on labor income which finances a per person demogrant, a policy which, in effect, flattens each individual's budget constraint. Although it is possible that other redistributive policies might be more efficient than this one, it is unlikely that the paper's conclusions concerning the relative costs of state and national redistributive policies would be radically different. Another point that bears repeating is that the costs of redistribution computed here are the costs borne only by the residents of the redistributing jurisdiction, not true social costs.

To summarize, this paper has attempted to compute the marginal costs of income redistribution by states in a federal system as a function of labor supply and migration responses. The major conslusions are that: (1) marginal costs for states are sensitive to labor supply elasticities as well as migration flows and (2) marginal state costs can be less than federal costs, especially with deductibility and matching grants. It is important to realize exactly what this result means. As stated in the introduction, the proposition that states face higher costs of income redistribution than the national government is just one part of the conventional argument about redistribution in a federal system. Showing that this proposition may not be true does not necessarily invalidate the positive or normative implications of the conventional argument. Cross-state benefit spillovers surely exist and these are important for assessing the overall welfare effects of state versus national redistribution policy. In any case, a national policy internalizes all the relevant externalities and might still be preferred to decentralized policy. Still other arguments might then come into play such as heterogeneous tastes among taxpayers for redistribution.

(*1) University of Virginia. Research supported from N.B.E.R.'s project on State and Local Public Finance is gratefully acknowledged. Helpful comments were received from Charles Brown, Don Fullerton, Robert Moffitt, Edgar Olsen, Harvey Rosen, Jon Skinner and anonymous referees.

(1) However, Gramlich [1985! acknowledges that benefits would remain low in low-benefit states even if costs were reduced, since federal matching grants now in place effectively reduce the cost of states.

(2) For example, Browning and Johnson [1984! and Ballard [1988!.

(3) A proportional tax-cum-demogrant policy is studied both because of computational ease and because it approximates an expansion of the current U.S. redistributional system see Browning and Johnson [1984, 180!. At first glance, it would appear that a more efficient policy would restrict the demogrant to the lowest income quintile. This, however, would require very high marginal taxes rates, or a notch, on low income households. Also, note that the restriction that dt and dB be equal for all households preserves the kink-points of the piecewise linear budget constraint.

(4) That is, the burden of the tax is the area to the left of the compensated labor supply curve between the gross wage and the net wage. The excess burden is the triangle left after subtracting the tax revenue rectangle. An additional tax, dt, increases excess burden by an area approximately equal to the compensated change in labor supply times the gap between the gross and net wage rate. See also Auerbach [1985, 73!.

(5) The compensated change in labor supply due to a tax change dt is the total effect less the income effect. The total effect is given by (1) as (-epsilonL/(1-t).dt). The income effect is the additional tax revenue at the original labor supply (W . L . dt) times the pure income effect on labor supply (C/W) from equation (1).

(6) The details of the imputation of total transfers and total taxes to each CPS household are described in Browning and Johnson [1984!. Labor income is given directly for each household marginal tax rates were computed by relating changes in after-tax, after-transfer income to changes in before-tax, before-transfer income by $1000 income brackets. Different marginal tax rates are computed for households with aged heads and for different household sizes. Thus, marginal tax rates include the effect of benefit reductions in transfer programs.

(7) Killingsworth's [1983! survey indicates roughly inelastic male elasticities but substantially positive female elasticities.

(8) Hausman's [1981! very large estimates of income effects imply a value of C of about 8.

(9) The assumption of Nash equilibrium is common in this context see Bergstrom, Blume and Varian [1986!.

(10) This specification of migration behavior does not prelude fixed costs of moving. Every resident compares the present value of utility in the current residence with the present value of utility in the next best alternatives minus the fixed cost of moving. With a continuous distribution of this fixed cost, some residents will be on the margin a small change in redistribution policies will push them to move.

(11) Gramlich and Laren argue that taxpayer migration is much less important since a change in redistribution has a much smaller impact on their incomes than on the incomes of the poor. While this is true, since the number of taxpayers is large relative to transfer recipients, the effect of taxpayers migration on [omega! may be significant.

(12) Comparing the expression for [X.sub.i! and that for [dZ.sub.i! (equation (6) above) reveals that [X.sub.i! = [dZ.sub.i!/(1 + [Ct.sub.i!). Since C is assumed to be the same for all households and [t.sub.i! does not vary too much, [X.sub.i! is approximately proportiopnal to [dZ.sub.i!. Thus one could interpret the migration behavior in (8) as responding to changes in welfare (dZ.sub.i).

(13) This simplification ignores intergovernmental grants and the fact that state tax and expenditure patterns are probably less progressive than the federal government's. These omissions overstate the tax competition effect and hence bias the results against the proposition being advanced.

REFERENCES

Auerbach, Alan. "The Theory of Excess Burden and Optimal Taxation," in Handbook of Public Economics, vol. 1, edited by A. Auerbach and M. Feldstein. Amsterdam: North-Holland, 1985, 61-127.

Ballard, Charles. "The Marginal Efficiency Cost of Redistribution." American Economic Review, December 1988, 1019-33.

Bergstrom, Theodore, Lawrence Blume, and Hal Varian. "On the Private Provision of Public Goods." Journal of Public Economics, February 1986, 25-50.

Blank, Rebecca. "The Effect of Welfare and Wage Levels on the Location Decisions of Female-Headed Households." Journal of Urban Economics, September 1988, 186-211.

Brown, Charles and Wallace Oates. "Assistance to the Poor in a Federal System." Journal of Public Economics, April 1987, 307-30.

Browning, Edgar and William Johnson. "The Trade-off between Equality and Efficiency." Journal of Political Economy, April 1984, 175-203.

Gramlich, Edward M. "Reforming U.S. Fiscal Arrangements," in American Domestic Priorities, edited by D. Rubinfield and J. Quigley. Berkeley: University of California press, 1985, 34-69.

Gramlich, Edward M. and Deborah S. Laren. "Migration and Income Redistribution Responsibilities." Journal of Human Resources, Fall 1984, 489-511.

Hausman, Jerry. "Labor Supply" in How Taxes Affect Economic Behavior, edited by H. Aaron and J. Pechman. Washington, D.C.: Brookings Institution, 1981, 27-72.

Helms, L. Jay. "The Effect of State and Local Taxes on Economic Growth: A Time-Series--Cross Section Approach." Review of Economics and Statistics, November 1985, 574-82.

Johnson, William. "Income Redistribution in a Federal Systems." American Economic Review, June 1988, 570-73.

Killingsworth, Mark. Labor Supply. Cambridge: Cambridge University Press, 1983.

Moffitt, Robert. "The Effects of Grants-in-aid on State and Local expenditures: The Case of AFDC." Journal of Public Economics, April 1984, 279-305.

I. INTRODUCTION

Which is the appropriate level of government to undertake income redistribution? This issue is receiving renewed attention from economists examining how migration and labor supply responses affect the costs of transfer payments at the state or federal level. In a recent paper, Brown and Oates [1987! use a formal public choice model to show that the possibility of migration of transfer recipients between states leads to suboptimal transfer levels even when taxpayers care only about transfer recipients within their own states. With benefit spillovers across states, their argument for federal responsibility for redistribution is, presumably, even stronger. Gramlich [1985! also argues that migration is large enough to lead to suboptimal levels of transfers at the state level because states with low benefit levels will be able to "export" their poor, increasing the cost of redistribution to high-benefit states. Gramlich's conclusion is based on the empirical work in Gramlich and Laren which finds that the migration effect is "very strong" .... though only in the very long run" [1984, 510!. The implicit argument is that migration raises the cost of redistribution at the state level compared to the federal level. (1) However, neither Brown and Oates nor Gramlich consider labor supply responses (that is, hours and participation) in their analyses.

On the other hand, several recent papers have attempted to estimate the cost of redistribution at the national level, incorporating labor supply responses to taxes and transfers but not interjurisdictional migration. (2) Some empirical evidence is available which is consistent with either migration or labor supply effects. For example, Helms [1985!, uses time series-cross section data on state expenditure and tax policies, and finds that while spending on public services (schools, highways, etc.) increases personal income, increased state transfer payments financed by state taxes significantly reduce total state personal income. This reduction could be caused by either migration or labor supply responses to taxes and transfers. Indeed, Helms's estimates indicate a very large response to transfer spending one more dollar of transfers reduces state personal income in the long run by $14.83. Helms concludes,

"States which seek to devote substantial tax revenues to transfer payments will experience significantly reduced growth prospects, which limits the scope for redistribution at the state and local levels" [1985, 581!.

A concise summary of the standard argument concerning federalism and redistribution might be as follows:

1. Interstate migration of taxpayers and transfer recipients raises the taxpayer cost of income redistribution at the state level above the cost at the federal level.

2. State-wide redistribution confers spillover benefits to residents of other states.

3. Therefore, as compared with a national system, decentralized responsibility for income redistribution yields

a. less redistribution (because its cost is higher) and

b. less than the socially optimal amount of redistribution (because of externalities).

My 1988 paper shows that step 1 of the above argument is not necessarily true because the migration effect, which previous authors have stressed, can be offset by a tax-exporting effect by which residents of one state shift some of the fiscal cost of redistribution to residents of other states. Both the income effect and the substitution effect of increased redistribution will reduce the labor supply (and hence earnings) of transfer recipients the labor supply (and earnings) of taxpayers may also fall if substitution effects are strong enough. The tax-exporting effect arises if taxes and transfers, on net, reduce total earnings in a state, since the state's federal tax obligations depend on its earnings. Essentially, the federal tax system subsidizes state redistribution and offsets (at least partially) the migration externality. The tax-exporting effect is magnified by the deductibility of state taxes in the federal income tax but can exist even without deductibility. Thus, the validity of step 1 is an empirical question which depends on behavioral responses (labor supply and migration) as well as the existing pattern of taxes and transfers.

In this paper I attempt to shed some light on this empirical question by comparing simulations of small changes in redistribution at the state and federal levels for a variety of labor supply and migration responses. I focus here only on the cost of redistribution and not on the benefits that it costs the non-poor more than a dollar to raise the income of the poor by a dollar does not imply that redistribution should not be undertaken. The externality to the non-poor created by raising the incomes of the poor is ignored here as is any other externality arising from proximity to low-income households. Although this paper and previous work in the area focuses on the fiscal costs of redistribution, if proximity to low-income persons makes high-income taxpayers worse off, increased redistribution which attracts transfer recipients imposes more than a monetary cost on taxpayers. The cost estimates in this paper ignore this externality of proximity. The question addressed here is whether the cost to the upper four income quintiles of redistribution to the lowest quintile is greater at the state or federal level, when labor supply and migration responses of both taxpayers and transfer recipients are considered. State redistribution here refers to the combined redistributive effect of state and local governments.

The simulations show that, in some (but not all) plausible cases, the tax-exporting effect is large enough that voters face a smaller cost of redistributing at the state level than at the federal level. Deductibility of state taxes may strengthen this result. Section II of the paper introduces the model used to estimate marginal redistribution costs in the context of a single jurisdiction. Section III extends the model to a federal system and estimates the relative cost of state redistribution.

II. A SAMPLE MODEL WITH ONE JURISDICTION

Before introducing the complication of a federal system of taxes and expenditures, it is useful to present a basic model of income redistribution. Current net income of household i, including the effects of existing taxes and transfers, is denoted by [Y.sub.i!, i = 1,..., n. Since attention is focussed on incremental changes in redistribution financed by taxes on labor income alone, gross taxable income should be interpreted as labor earnings, [W.sub.i.L.sub.i!, where [W.sub.i! is the gross return to each unit of labor, [L.sub.i!, supplied to the market. Although the global budget constraint facing the household is highly non-linear, due to the complex system of taxes and transfers now in place, it can be approximated locally by the linear constraint [Y.sub.i! = [B.sub.i! + (1-[t.sub.i!) [W.sub.i.L.sub.i!. Hence [B.sub.i! is the "virtual income" of household i and [t.sub.i! is its marginal tax rate. Small changes in the tax-transfer system can be represented by changes in the parameters of this linear budget constraint, which is the local approximation to the global non-linear budget constraint.

The response of labor supply, [L.sub.i!, to small changes in [t.sub.i! and [b.sub.i! is parameterized as follows:

(1) [Mathematical Expression Omitted!

Equation (1) can be easily interpreted. The left-hand side is the change in gross labor income induced by tax and transfer changes which, in this partial equilibrium analysis, are assumed not to affect the gross wage rate, [W.sub.i!. The first term on the right is the response to changes in the marginal tax rate, [t.sub.i! as parameterized by [epsilon!, the uncompensated elasticity of supply of [L.sub.i! with respect to the net wage rate, [W.sub.i!(1-[t.sub.i!). Note that for a given value of [epsilon!, the effect of [dt.sub.i! the greater the larger is [t.sub.i! because a given change in the tax rate implies a greater percentage change in net factor returns. The second term on the right-hand side of (1) is the pure income effect of changes in [B.sub.i! the parameter C is the marginal propensity to consume leisure out of unearned income.

Suppose the government attempts to increase marginally the current amount of redistribution by rotating each household's budget constraint in goods-leisure space slightly in the counter-clockwise direction. High-income households will pay more net taxes while low-income households receive more net transfers. Such a rotation is identical to a uniform additional tax, dt, on the labor incomes of all households which is used to finance a uniform addition, dB, to every household's virtual income. (3) In other words, redistribution at the margin is undertaken by a demogrant financed by proportional taxes on labor income. Of course, the amount of the demogrant dB depends on additional tax revenue, by the marginal government budget constraint:

(2) [Mathematical Expression Omitted!

The left-hand side of (2) is total extra demogrants paid, or ndB. The right-hand side of (2) expresses the change in tax revenue as the sum of the additional tax rate, dt, applied to current taxable income, and the current marginal tax rate, [t.sub.i!, applied to the change in factor income induced by the new policy.

Substituting (2) into (1) and rearranging yields

(3) [Mathematical Expression Omitted!

where summations are henceforth understood to be taken over i = 1,...,n. Equation (3) gives the additional per capita transfer (dB) produced by an incremental tax (dt). When factor supplies are completely unresponsive to any economic variable (C = [epsilon! = 0), then dB/dt is just average taxable income (the revenue produced by a 100 percent tax).

The change in the net income of any one household induced by the marginal policy change is

(4) [Mathematical Expression Omitted!

where [Omega! = dB/dt, as given by (3). Equation (4) states that the income of household i rises by the amount of the additional demogrant ([Omega!dt) but falls by the amount of additional taxes on the original income ([W.sub.i.L.sub.i!dt) plus the change in after-tax income induced by the behavioral response to the policy change [-(1-[t.sub.i!)C[Omega! - [[epsilon!W.sub.i.L.sub.i!!dt.

To analyze the welfare costs of a change in policy, I assume that individual utility is the sum of two functions, one solely a function of private goods and leisure, and the other solely a function of other households' income and leisure. This latter function captures the external benefits of redistribution that may explain its existence it does not play a role in this analysis which focuses instead on the relative costs of redistributing at the state and federal level. Subsequent references to welfare exclude the public goods externality of redistribution.

The change in the welfare of any one household, [dZ.sub.i!, induced by the marginal policy changes is just the change in that household's net transfers less the additional welfare cost (excess burden) of the marginal redistribution. Since a conventional measure of this last term is the tax revenue lost by the compensated change in labor supply, (4) we have

(5) [Mathematical Expression Omitted!

In (5), the first three terms are the change in net transfers while the terms in square brackets are the excess burden of the tax increase. (5) Note that when labor supply is completely unresponsive (C = [epsilon! = dL = 0, the welfare change is just the change in net income. The change in welfare for any household subject to the marginal redistribution policy of a demogrant financed by a proportional tax can be found by substituting [dB.sub.i! = dB = [Omega!dt, [dt.sub.i! = dt, and equation (1) into (5):

(6) [Mathematical Expression Omitted!

Equation (6) says that household i is better off if and only if the new budget constraint lies above the point chosen on the previous budget constraint.

To estimate the effect of a marginal increase in redistribution on income and welfare, simulations were performed

using all the households in the March, 1976 Current Population Survey (CPS). This data set is somewhat dated, especially considering recent changes in the federal tax structure, but includes a wealth of detail on transfers and taxes. (6) In the simulations, the demogrant that can be financed by a marginal increase in taxation, dt, is first calculated using (3). Then, that value of [OMEGA! is used to compute the impact on income and welfare of each household, according to (4) and (6). The information needed for these calculations is labor income, [W.sub.i.L.sub.i!, and marginal tax rates, [T.sub.i!, for each household as well as values for the parameters, C and [epsilon!.

The economic assumptions underlying the results reported here (as summarized by eqs. (1), (3), (4) and (6)) are not the same as those used in my 1984 paper with Browning. To evaluate these expressions, reasonable values for [epsilon! and C must also be established. The uncompensated elasticity of labor supply, [epsilon!, is assumed to fall between -.2 and .4 with the midpoint of the range reflecting the fact that the negative elasticity sometimes estimated for men is more than offset by the substantial positive wage elasticities estimated for women. (7) The marginal propensity to consume leisure, C, is a less familiar concept but can be related to the income elasticity of labor supply by

(7) C = [- gamma! (1 [THETA!)

where [gamma! is the pure income elasticity of labor supply and [THETA! is the share of leisure in full income. If [THETA! is roughly .5 then C is roughly half the income elasticity of labor supply. A range of C between zero and .4 is chosen. (8) Recall that C is the fraction of an additional dollar of pure income spent on leisure. Parameter values roughly at the midpoints of these ranges seem most consistent with empirical evidence on labor supply.

For each set of parameter values, I compute the effect of a .01 change in t (and the associated value od dB) on each household's income and welfare. To distill the changes for many thousands of households into an easily comprehensible form, the total welfare (or income) change for all households is divided by the welfare (or income) change for those households in the bottom quintile of the income distribution. This ratio assumes the value of zero when redistribution is a zero-sum game (that is, socially costless) and can be interpreted as the social cost of increasing the bottom quintile's welfare (or income) by one dollar.

III. REDISTRIBUTION IN A FEDERAL SYSTEM

To compare the costs of redistribution for local and national governments in a federal system, three simplifying assumptions are made. First, state and local governments are not distinguished in the model all local taxes and redistributive expenditures are attributed to the state. Second, the voters in each state are assumed to take the behavior of other states as given. (9) As I discuss in my 1988 paper, relaxing this assumption to allow other states to respond to one state's policy change will certainly weaken the tax-exporting effect but will likely weaken the migration effect even more. Hence, adopting the no-response assumption biases against finding that tax exporting dominates migration. The third assumption is that the state income distribution mirrors the national income distribution this assumption focuses the analysis on issues of federalism rather than interstate income redistribution.

The most important difference between state and federal taxation is that factors of production are more mobile between states than between countries to reflect this, no international mobility is assumed here. State populations are assumed to be a function of differences in the budget constraints faced by residents in those states. Specifically, let [X.sub.i! be the vertical displacement of the budget constraint for residents at income level [Y.sub.i!, caused by a change in a state's tax or transfer policy. Then the percent change in the number of residents at income level [Y.sub.i!, is assumed to be [eta!(X/Y) percent. Hence, [eta! is the elasticity of the population with respect to net income, an elasticity which is assumed to characterize residents at all income levels. An increase in state taxes used to finance more redistribution will reduce the welfare of high-income citizens (X 0) and induce out-migration. The same policy enhances the incomes of low-income residents (X 0) and so induces in-migration. Since additional redistribution will have a larger percentage effect on the incomes of the poor than of the wealthy, the migration response of the ppor should exceed that of the rich, as it does with this formulation. (10) An assumption (not pursued here) of no taxpayer migration only strengthens the paper's conclusion by reducing the tax competition effect.

Most of the recent research on migration responses to redistribution focuses on the behavior of transfer recipients. Gramlich and Laren [1984! estimate the long-run elasticity of transfer recipient populations with respect to benefits levels, with results for various models and data sets ranging from .11 to 1.7. (11) Blank [1988! has also estimated the migratory response of transfer recipients to changes in benefit levels. For example, she estimates that, for New York, a 20-25 percent reduction in benefits implies an increase in the out-migration rate which would yield a 16 percent lower recipient population after twenty years. Since she does not consider in-migration, her estimates put an upper bound on the long-run population elasticity of About .75.

Redistribution costs can be computed for states analogously to the cost computations for a national government presented in section II. Both migration and labor supply responses will now affect the incremental benefit that can be financed by an increase in state taxes. Once the incremental benefit is found, changes in household income and welfare are given by equations (4) and (6).

To incorporate migration responses into the analysis of redistribution costs at the state level, we must adjust the number of persons at each income level by the migratory response to marginal tax and transfer changes. The change in net income for household i at the previous level of labor supply, [X.sub.i!, induced by changes in marginal tax rates, d [t.sub.i!, and virtual income, [dB.sub.i!, is (12)

[X.sub.i!=-([W.sub.i.L.sub.i!)[dt.sub.i!+[dB.sub.i!.

If i is now interpreted as an index of income levels corresponding to each of the original resident households, [N.sub.i! = 1 for all i. Then the change in the number of households with income [Y.sub.i! dN.sub.i!, is given by

[eta! = ([Y.sub.i*dN.sub.i!)/(-[W.sub.i.L.sub.i.dt.sub.i+dB.sub.i.!),

or

(8) [Dn.sub.i!=[eta!(-[W.sub.i.L.sub.i.dt.sub.i+dB.sub.i!)/[Y.sub.i!

Without deductibility of state taxes from federal taxes (which will be considered below), the overall marginal tax rate, [t.sub.i!, is just the sum of nominal federal and state rates, [t.sub.i!=[t.sub.fi.+t.sub.si!. Federal taxes and benefits do not respond to changes in one state's taxes or transfers, so

[dt.sub.i!=[dt.sub.si!and[dB.sub.i!=[dB.sub.si!.

Restricting states to imposing, on the margin, proportional taxes to finance demogrants, (yielding a net tax system which is linear with a non-zero intercept) we have

[dt.sub.si!=[dt.sub.s!i=1,...,n

[dB.sub.si!=[dB.sub.s!i=1,...,n.

Now consider the marginal budget constraint faced by the state. The change in expenditures is the sum of additional benefits paid to existing residents, of whom there are [n.sub.s!, plus (minus) the state's share of full benefits paid to new in-migrants (out-migrants), or

(9)[n.sub.s.dB.sub.s!+[SIGMA![B.sub.si.dN.sub.i!.

The change in tax revenue is the sum of the changes due to the new tax rate, to labor supply responses of existing residents, and to migratory responses:

(10) [Mathematical Expression Omitted!

Equating (9) and (10), and substituting (8) yields the marginal budget constraint for a state government:

(11) [Mathematical Expression Omitted!

where [b.sub.i!=[W.sub.i.L.sub.i./Y.sub.i!.

The only additional data needed to calculate [dB.sub.s!/[dt.sub.s! from (11), beyond that used to compute redistribution costs in the single-government case in the previous section, is information on [B.sub.si! and [t.sub.si!, that portion of total taxes and benefits attributable to state (and local) governments. For the purpose of these calculations I assume that state taxes and benefits are the same proportion, [delta!, of overall taxes and benefits, where [delta! is the share of state and local government spending in total government spending (equal to .43 in 1976). (13) Thus,

(12) [t.sub.si!=[delta![t.sub.si!=[delta![B.sub.i!.

[B.sub.i! is computed as the vertical intercept of each household's linearized budget constraint:

[B.sub.i!=[Y.sub.i!-(1-[t.sub.i!)[W.sub.i.L.sub.I!.

The income and welfare changes induced by a marginal change in state redistribution can be analyzed in a way similar to that already described above for the single-government case (just below equation (6)). First the incremental state benefit financed by a small change in state taxes is computed using equation (11). In addition to the parameters and data already required for the single-government case, equation (11) depends on [eta!, the population elasticity, [Y.sub.i!, total household income, and [B.sub.s! and [t.sub.s!, state benefits and tax rates, as computed by (12).

Results

Armed with these estimates of the incremental benefit available from a small rise in taxes,[OMEGA!, each household's income and welfare change is computed using (4) and (6). Summed over all households, the aggregate welfare changes are negative (recall that the external benefits of redistribution are ignored here) but income changes may be positive. The cost of redistribution is taken to be the ratio of aggregate income or welfare lost per dollar of extra income (or welfare) transferred to the bottom quintile of households. In the case of state government redistribution, the gains and losses of non-migrating persons only are counted. Recall that there is no migration or tax-exporting effect for the federal government since labor is assumed to be internationally immobile and there is no supranational government taxing U.S. residents.

Table I presents the ratio of marginal redistribution costs for a state to the cost for the federal government for a range of values of [eta!, the population elasticity, and labor supply parameters. A cost ratio less than one indicates a situation in which costs are lower at the state level than at the federal level an infinite cost ratio implies that federal redistribution is costless, a zero-sum game. As Table I indicates, lower population elasticities and higher labor supply responses lead to lower relative costs of state redistribution. When labor supply is unresponsive (as in the first row of the table), only the migration effect operates so federal redistribution is costless while state redistribution is costly. The last two rows of the table pertain to two vertical or backward-bending labor supply curves. Here the state cost exceeds the federal cost because redistribution increases money incomes and federal tax burdens. Table I indicates that for some plausible labor supply and migration parameters, state costs or redistribution are less than federal costs.

Deductibility and Matching Grants

The estimates in Table I do not assume that state and local taxes can be deducted from income taxable at the federal level. The effect of deductibility depends on (1) the marginal federal tax rates of net taxpayers and net transfer recipients (2) who itemizes deductions and (3) the exact form of the increased redistribution. If everyone's marginal federal rate were identical and if everyone itemized deductions and if redistribution to low-income households took the form of lower state taxes or taxable transfer payments, then deductibility would not affect the relative cost of state redistribution. In that case, the lower federal tax bills of high-income taxpayers would be matched by higher federal tax bills of the beneficiaries of redistribution.

Deductibility can reduce the relative cost of state redistribution if, for example, low-income households are less likely to itemize and redistribution is accomplished by reducing the state tax burden on these households, or if high income households face higher marginal federal tax rates. Since both of these conditions exist to some degree, it is safe to conclude that deductibility will reduce the estimated relative costs of state and local redistribution given in Table I. However,

precise estimates of the effect of deductibility are not possible with the data available.

Another feature of the current federal systems in the U.S. which affects the marginal cost of state redistribution is the availability of federal matching grants for redistributional expenditures. A large empirical literature, such as Moffitt [1984!, exists which shows that these matching formulae do increase state expenditures on redistribution. Hence, consideration of matching grants would reduce even further the relative state costs of redistribution found in Table I.

IV. CONCLUSION

This paper has examined the effect of additional income redistribution at the state and national level when both labor supply and location respond to economic incentives. Marginal redistribution is accomplished by a proportional tax on labor income which finances a per person demogrant, a policy which, in effect, flattens each individual's budget constraint. Although it is possible that other redistributive policies might be more efficient than this one, it is unlikely that the paper's conclusions concerning the relative costs of state and national redistributive policies would be radically different. Another point that bears repeating is that the costs of redistribution computed here are the costs borne only by the residents of the redistributing jurisdiction, not true social costs.

To summarize, this paper has attempted to compute the marginal costs of income redistribution by states in a federal system as a function of labor supply and migration responses. The major conslusions are that: (1) marginal costs for states are sensitive to labor supply elasticities as well as migration flows and (2) marginal state costs can be less than federal costs, especially with deductibility and matching grants. It is important to realize exactly what this result means. As stated in the introduction, the proposition that states face higher costs of income redistribution than the national government is just one part of the conventional argument about redistribution in a federal system. Showing that this proposition may not be true does not necessarily invalidate the positive or normative implications of the conventional argument. Cross-state benefit spillovers surely exist and these are important for assessing the overall welfare effects of state versus national redistribution policy. In any case, a national policy internalizes all the relevant externalities and might still be preferred to decentralized policy. Still other arguments might then come into play such as heterogeneous tastes among taxpayers for redistribution.

(*1) University of Virginia. Research supported from N.B.E.R.'s project on State and Local Public Finance is gratefully acknowledged. Helpful comments were received from Charles Brown, Don Fullerton, Robert Moffitt, Edgar Olsen, Harvey Rosen, Jon Skinner and anonymous referees.

(1) However, Gramlich [1985! acknowledges that benefits would remain low in low-benefit states even if costs were reduced, since federal matching grants now in place effectively reduce the cost of states.

(2) For example, Browning and Johnson [1984! and Ballard [1988!.

(3) A proportional tax-cum-demogrant policy is studied both because of computational ease and because it approximates an expansion of the current U.S. redistributional system see Browning and Johnson [1984, 180!. At first glance, it would appear that a more efficient policy would restrict the demogrant to the lowest income quintile. This, however, would require very high marginal taxes rates, or a notch, on low income households. Also, note that the restriction that dt and dB be equal for all households preserves the kink-points of the piecewise linear budget constraint.

(4) That is, the burden of the tax is the area to the left of the compensated labor supply curve between the gross wage and the net wage. The excess burden is the triangle left after subtracting the tax revenue rectangle. An additional tax, dt, increases excess burden by an area approximately equal to the compensated change in labor supply times the gap between the gross and net wage rate. See also Auerbach [1985, 73!.

(5) The compensated change in labor supply due to a tax change dt is the total effect less the income effect. The total effect is given by (1) as (-epsilonL/(1-t).dt). The income effect is the additional tax revenue at the original labor supply (W . L . dt) times the pure income effect on labor supply (C/W) from equation (1).

(6) The details of the imputation of total transfers and total taxes to each CPS household are described in Browning and Johnson [1984!. Labor income is given directly for each household marginal tax rates were computed by relating changes in after-tax, after-transfer income to changes in before-tax, before-transfer income by $1000 income brackets. Different marginal tax rates are computed for households with aged heads and for different household sizes. Thus, marginal tax rates include the effect of benefit reductions in transfer programs.

(7) Killingsworth's [1983! survey indicates roughly inelastic male elasticities but substantially positive female elasticities.

(8) Hausman's [1981! very large estimates of income effects imply a value of C of about 8.

(9) The assumption of Nash equilibrium is common in this context see Bergstrom, Blume and Varian [1986!.

(10) This specification of migration behavior does not prelude fixed costs of moving. Every resident compares the present value of utility in the current residence with the present value of utility in the next best alternatives minus the fixed cost of moving. With a continuous distribution of this fixed cost, some residents will be on the margin a small change in redistribution policies will push them to move.

(11) Gramlich and Laren argue that taxpayer migration is much less important since a change in redistribution has a much smaller impact on their incomes than on the incomes of the poor. While this is true, since the number of taxpayers is large relative to transfer recipients, the effect of taxpayers migration on [omega! may be significant.

(12) Comparing the expression for [X.sub.i! and that for [dZ.sub.i! (equation (6) above) reveals that [X.sub.i! = [dZ.sub.i!/(1 + [Ct.sub.i!). Since C is assumed to be the same for all households and [t.sub.i! does not vary too much, [X.sub.i! is approximately proportiopnal to [dZ.sub.i!. Thus one could interpret the migration behavior in (8) as responding to changes in welfare (dZ.sub.i).

(13) This simplification ignores intergovernmental grants and the fact that state tax and expenditure patterns are probably less progressive than the federal government's. These omissions overstate the tax competition effect and hence bias the results against the proposition being advanced.

REFERENCES

Auerbach, Alan. "The Theory of Excess Burden and Optimal Taxation," in Handbook of Public Economics, vol. 1, edited by A. Auerbach and M. Feldstein. Amsterdam: North-Holland, 1985, 61-127.

Ballard, Charles. "The Marginal Efficiency Cost of Redistribution." American Economic Review, December 1988, 1019-33.

Bergstrom, Theodore, Lawrence Blume, and Hal Varian. "On the Private Provision of Public Goods." Journal of Public Economics, February 1986, 25-50.

Blank, Rebecca. "The Effect of Welfare and Wage Levels on the Location Decisions of Female-Headed Households." Journal of Urban Economics, September 1988, 186-211.

Brown, Charles and Wallace Oates. "Assistance to the Poor in a Federal System." Journal of Public Economics, April 1987, 307-30.

Browning, Edgar and William Johnson. "The Trade-off between Equality and Efficiency." Journal of Political Economy, April 1984, 175-203.

Gramlich, Edward M. "Reforming U.S. Fiscal Arrangements," in American Domestic Priorities, edited by D. Rubinfield and J. Quigley. Berkeley: University of California press, 1985, 34-69.

Gramlich, Edward M. and Deborah S. Laren. "Migration and Income Redistribution Responsibilities." Journal of Human Resources, Fall 1984, 489-511.

Hausman, Jerry. "Labor Supply" in How Taxes Affect Economic Behavior, edited by H. Aaron and J. Pechman. Washington, D.C.: Brookings Institution, 1981, 27-72.

Helms, L. Jay. "The Effect of State and Local Taxes on Economic Growth: A Time-Series--Cross Section Approach." Review of Economics and Statistics, November 1985, 574-82.

Johnson, William. "Income Redistribution in a Federal Systems." American Economic Review, June 1988, 570-73.

Killingsworth, Mark. Labor Supply. Cambridge: Cambridge University Press, 1983.

Moffitt, Robert. "The Effects of Grants-in-aid on State and Local expenditures: The Case of AFDC." Journal of Public Economics, April 1984, 279-305.

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Title Annotation: | cost of state redistribution of income compared to that being handled by the national government |
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Author: | Johnson, William R. |

Publication: | Economic Inquiry |

Date: | Jan 1, 1991 |

Words: | 5411 |

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