CRS Report Examines Redistribution Effects of Federal Taxes, Selected Tax Provisions

Several policy makers and analysts have voiced concern over federal budget deficits and growing federal debt. Publicly held federal debt as a percentage of GDP stood at 53% at the end of FY2009; the Congressional Budget Office's (CBO's) baseline projection has it growing to 66% by 2011. CBO's projection of the President's budget has debt as a percentage of GDP growing to 90% by 2020. The 112^th Congress will likely face several tax issues. Congress passed the Statutory Pay-As-You-Go Act, which would enact PAYGO into law, and the President signed it into law on February 12, 2010 (P.L. 111-139). The recently extended Bush tax cuts expire at the end of 2012 and the alternative minimum tax relief expires at the end of 2011. Furthermore, the National Commission on Fiscal Responsibility and Reform has recommended changes to the tax code to help achieve fiscal sustainability. Each of these will likely affect federal revenues and redistribute income among families.

The redistributive effect of a policy can be decomposed into a progressivity effect (a vertical effect) and a reranking effect (a horizontal effect). The progressivity effect measures how individuals in the income distribution are pushed together or pulled apart (without changing relative positions in the distribution). The reranking effect captures the extent to which individuals are moved above or below others in the distribution as a result of a policy. This reranking is often perceived as unfair and reduces the public's confidence in the fairness of the tax system or policy proposal. These two effects can work together or in opposite directions to affect income inequality.

The results highlight the trade-offs policy makers could face in developing policies to raise revenue, reduce income inequality, and reform the tax system. Overall, the results show that U.S. taxes reduce income inequality. The redistributive effect, however, could be larger if the reranking effect were reduced or eliminated. In addition, the individual tax provisions have small but important effects on income inequality. Reranking is more severe for some tax provisions than for other provisions. The method used in this study can very easily be applied to any tax provision to determine how the provision would affect income inequality and where in the income distribution the impact would be most felt.

                            Contents

Arguments have been offered for and against reducing income inequality. The classic argument against rising income inequality is the rich get richer and the poor get poorer. This can increase poverty, reduce well-being, and reduce social cohesion. Consequently, many argue that reducing income inequality may reduce various social ills. In contrast, there are those arguing that rising inequality is nothing to worry about because average real income has been rising -- so while the rich are getting richer, the poor are not necessarily getting poorer. In addition, many argue that some income inequality is necessary to encourage innovation and entrepreneurship -- the possibility of large rewards and high income are incentives to bear the risks of innovation and entrepreneurship. Therefore, they assert the economic costs of reducing or eliminating income inequality may be high.

Some researchers are concerned about the consequences of rising income inequality. Research has demonstrated that large income and class disparities adversely affect health and economic well-being. Michael Marmot has studied health and social-status disparities, concluding that health follows a social gradient -- people higher in the social hierarchy tend to be in better health than people of lower status.³ Richard Wilkinson provides evidence that high income inequality -- large income disparities -- and less social cohesion have a negative impact on the health of a country's citizens.⁴ Robert Frank argues that even if all incomes are increasing and rising inequality is due solely to those at the top of the income distribution pulling away from the rest, the middle class can be hurt by the pressure to keep up with the upper class.⁵

The tax system is used to meet other social and economic objectives such as encouraging certain behaviors, discouraging other behaviors, and reducing inequality. More fundamentally, however, a tax system is expected to meet several goals. Perhaps the most important is to raise revenue to fund government activities. Another goal is to be efficient by minimizing the excess burden of taxes. A third goal is for the tax system to be equitable and fair. Often these goals and objectives conflict with one another. Policy makers attempt to meet these goals and objectives through the choice of the parameters of the tax system (e.g., tax rates), and through the use of "loopholes" -- those special deductions, exclusions, and exemptions known as tax expenditures.

The National Commission on Fiscal Responsibility and Reform has advocated broadening the tax base by eliminating many tax expenditures as a way to raise revenue for deficit reduction and tax rate reductions.⁶ This could also help reduce the growth in income inequality if the tax expenditures with the "upside-down" subsidy feature are the ones eliminated. At the same time, however, the President and many Members of Congress have proposed additional tax expenditures as a means to achieving economic and social goals. Each of these proposals would affect the equity of the tax system and income inequality.

This study focuses on the redistributive effect of government transfers and taxes, and, in particular, nine selected federal tax provisions. The nine tax provisions are (1) the exclusion of Social Security benefits, (2) the phase-outs of personal exemptions (PEP) and itemized deductions (Pease), (3) itemized deductions, (4) the earned income tax credit (EITC), (5) the child tax credit, (6) the alternative minimum tax (AMT), (7) the reduced post-2001 tax rates, (8) the exclusion of interest on state bonds, and (9) reduced tax rates on long-term capital gains and qualified dividends.

The redistributive effect can be decomposed into a progressivity effect (a vertical effect) and a reranking effect (a horizontal effect).

• The progressivity effect measures how individuals in the income distribution are pushed together or pulled apart (without changing relative positions in the distribution). This captures the extent to which the gap between the poorest and richest families is widened or narrowed.

• The reranking effect captures the extent to which families are moved above or below others in the income distribution as a result of a policy. This reranking is often perceived as unfair and reduces the public's confidence in the fairness of government programs and the tax system.

The Principle of Equity

Richard Musgrave argues that there are two parts to the principle of equity, which "are but different sides of the same coin."⁷ A basic sense of fairness suggests that those with equal ability to pay taxes should pay equal taxes; this is referred to as horizontal equity. Most analysts also argue for the principle of vertical equity -- how the taxation of people in different positions should differ. Considerable theoretical and empirical work has been devoted to explicitly linking redistribution, vertical equity, and horizontal equity.

Beginning with Martin Feldstein, researchers have worked to develop an operational measure of horizontal equity.⁸ Early work identified horizontal equity as changes in the pre-tax and post-tax orderings or rankings in the income distribution.⁹ Nanak Kakwani decomposed the change in the Gini coefficient between pre-and post-tax income (the redistributive effect) into a vertical effect and a horizontal or reranking effect.¹⁰ He notes that the reranking effect (a violation of horizontal equity) will reduce the redistributive effect of taxation.

More recently, some analysts have argued that reranking does not really measure the classical definition of horizontal inequity.¹¹ Their preferred method of directly calculating a measure of horizontal inequity involves defining groups of individuals or families having the same pre-tax income. For example, Kim and Lambert break a horizontal inequity component out of Kakwani's vertical equity measure. Consequently, the redistributive effect is decomposed into a vertical effect, horizontal inequity, and a reranking effect. The horizontal inequity effect is based on defining an income band width in which to partition the sample units into groups of equals; the estimate depends on the chosen band width. In two studies the estimated horizontal inequity term was very small -- typically less than 2% of the total redistributive effect.¹²

In this study, the redistributive effect (change in the Gini coefficient or the generalized Gini) is decomposed into a progressivity effect (a vertical effect) and a reranking effect (a horizontal effect).¹³ The focus of the study is not to come up with a clean decomposition of the redistributive effect resulting from government policies into vertical and horizontal effects or to argue that reranking captures a pure horizontal equity effect. Rather the focus is on how these policies (1) expand or compress the income distribution holding each family's place in the income distribution (ranking) constant, and (2) move families ahead or behind other families in the income distribution.

Redistributive Effect of Taxes and Government Transfers

The redistributive effect is measured using the Gini coefficient and generalized Gini, which permits an explicit examination on effects in different parts of the income distribution. The Gini coefficient varies from 0 to 1. A Gini coefficient of 0 indicates that income is evenly distributed among the population (that is, everyone has the same income) while a value of 1 indicates perfect income inequality (that is, one individual has all the income). The generalized Gini (of which the Gini coefficient is a special case) is employed to examine how different parts of the income distribution could be affected by policy changes (see the Appendix for details on the data and methods used for the analysis). The methods employed pick up several important dimensions of the redistributive effect of government programs and provisions often overlooked in analyses.

The Gini coefficient for equivalence-adjusted family income before government transfers are added and taxes are subtracted is 0.5116 (see the first row of Table 1Error! Reference source not found.).¹⁴ It must be emphasized that this is the Gini coefficient before transfers and taxes are included in income and not what it would be if the transfers and taxes did not exist. In the latter case, the disincentive (and incentive) effects of transfers and taxes would be eliminated and family income would likely be very different from the former measure of before tax and transfer income.

              Table 1. Redistributive Effect ofTaxes and Transfers

The next table (Table 2) reports the results for the cases that (1) place greater relative weight on inequality at the top of the income distribution (panel A), and (2) place greater relative weight on inequality at the bottom of the income distribution (panel B). The redistributive effect of transfers is greater at the bo.ttom of the income distribution than at the top since the percentage change in the generalized Gini is larger in panel B than in panel A (9.3% versus 7.9%). Conversely, the redistributive effect of taxes is greater at the top of the distribution than at the bottom. The reranking effect of both taxes and transfers (individually and combined), however, is more important at the lower parts of the income distribution than at the top.

  Table 2. Redistributive Effect in Different Parts of the Income Distribution

Many of the tax provisions examined in this report reduce federal tax revenues; the exceptions are the personal exemption phaseout (PEP), the limitation on itemized deductions (Pease), and the alternative minimum tax (AMT).¹⁶ The Economic Growth and Tax Relief Reconciliation Act of 2001 (EGTRRA) enacted the phase-in of the repeal of PEP and Pease and were scheduled to be eliminated in 2010 and reinstated beginning in 2011. The Tax Relief, Unemployment Insurance Reauthorization, and Job Creation Act of 2010 (P.L. 111-312). The reinstatement of PEP and Pease for tax years after 2012 could increase tax revenues by about $18 billion per year. The AMT was originally enacted to make sure all taxpayers paid some minimum amount in taxes and is primarily targeted to higher-income taxpayers. The Tax Policy Center estimates the AMT raised about $32 billion in 2008.¹⁷

The earned income tax credit (EITC) is a refundable credit targeted to lower-earning taxpayers.¹⁸ The Joint Committee on Taxation (JCT) estimates that the EITC results in almost $56 billion in lost tax revenue ($51 billion from the refundable portion).¹⁹ The child tax credit was adopted in 1997 to address concerns that larger families were less able to pay taxes.²⁰ Families with qualifying children under 17 are allowed up to a $1,000 credit against taxes for each child. The credit is refundable for most families. The child tax credit does phase out for higher-income taxpayers, but it is much more widely distributed throughout the income distribution than the EITC -- 21% of the benefits of the credit go to taxpayers with annual incomes above $100,000. The JCT estimates that the credit loses about $55 billion in tax revenue ($33 billion from the refundable portion).

Some interest income and Social Security benefits are excluded from taxable income. Up to 85% of Social Security benefits can be subject to taxation.²¹ For most lower-income recipients, however, Social Security benefits are not taxable (estimated revenue loss of $27 billion). Interest earned from certain state and local government obligations (e.g., municipal bonds) is excluded from taxable income with an estimated revenue loss of $19 billion.²²

Income from realized long-term capital gains and qualified dividends are taxed at lower rates than ordinary income.²³ For the 2010 tax year, long-term capital gains and qualified dividends were taxed at a 0% rate for taxpayers in the two lowest tax brackets and at 15% for other taxpayers. The reduced tax rates on long-term capital gains and qualified dividends is estimated to have resulted in a revenue loss of $78 billion in 2010.

Itemizing deductions allows taxpayers to reduce their taxable income. Taxpayers itemize deductions if the total is larger than the standard deduction ($5,700 for single taxpayers and $11,400 for married taxpayers in 2010). There are several itemized deductions but the major deductions are the mortgage interest deduction ($91 billion revenue loss), the deduction for state and local taxes ($31 billion revenue loss), the deduction for charitable contributions ($37 billion revenue loss), and the property tax deduction ($15 billion revenue loss).

Congress created the 10% tax bracket and began the phase-in of the reduced tax rates with the passage of EGTRRA. It was estimated at the time that these provisions would reduced tax revenue by $103.8 billion in 2008. The tax rate reductions were accelerated with the passage of the Jobs and Growth Tax Relief Reconciliation Act of 2003.

Five of the nine tax provisions reduce income inequality as measured by the Gini coefficient since the redistributive effect is positive. The results for these five provisions are reported in the first five rows of Table 3. The child tax credit has the largest redistributive effect of the five and reduces the Gini coefficient by 0.7%. The redistributive effect would have been about 2% larger in the absence of reranking. The EITC has a smaller redistributive effect and the reranking effect is smaller as well. Both of these tax credits are targeted to lower- and middle- (in the case of the child tax credit "middle" is rather broadly defined) income taxpayers, but the redistributive effect of the child tax credit appears to be more important in the upper part of the distribution. The negative impact of reranking, however, is more important at the bottom of the income distribution.

       Table 3. Redistributive Effects of Selected Tax Provisions

Unlike the two tax credits and the Social Security exclusion, the AMT and PEP/Pease are targeted toward higher-income taxpayers and reduce income inequality by increasing the tax bite on these taxpayers. The AMT reduces the Gini coefficient by 0.3%, and the redistributive effect would be slightly larger (1.5%) in the absence of reranking. PEP and Pease reduce the Gini coefficient by about 0.2%; there is essentially no reranking effect from PEP and Pease. As would be expected, both the redistributive and reranking effects of these tax provisions are more important in the upper part of the income distribution.

The final four tax provisions considered all increase income inequality (see the final four rows of Table 3). Additionally, both the gap changing and the reranking effects work in the same direction to increase inequality. Of the four provisions, the reduced rates on long-term capital gains and dividends has the largest effect of increasing inequality, increasing the Gini coefficient by 1.1%. About 96% of the increase in the Gini coefficient is due to the progressivity effect and the remaining 4% is due to reranking -- the regressive effect of this provision would be lower in the absence of reranking. The effects are more important in the upper part of the income distribution.

The exclusion of municipal bond interest has a very small effect on inequality (considerably less than a 0.1% change in the Gini coefficient) probably because only 3% of 2004 taxpayers reported receiving any tax exempt interest. The EGTRRA tax rate reductions increased inequality by about 0.6% with most (almost 99%) due to the progressivity effect, which widens the gap between the poorest and richest families. For the reduced (post-EGTRRA) tax rates, the redistributive effect is more important in the upper part of the distribution, but the reranking effect is more important at the bottom of the income distribution. This could be due to the introduction of the 10% tax bracket. Itemized deductions increases the Gini coefficient by almost 1% with 96% of the redistributive effect due to the gap widening effect and 4% to the reranking effect.

Concluding Remarks

Government transfers and taxes affect both the federal budget and the distribution of income. With large federal deficits projected over the next several years, the policy response may include increasing tax revenues by changing, adding, and eliminating various tax provisions. Furthermore, the policies will likely involve trade-offs between raising revenue, reducing inequality, and changing the public's perceptions of the fairness of the tax system.

This study examined the redistributive effect of various federal tax provisions using methods that pick up important dimensions of redistribution often missed in analyses. The redistributive effect was decomposed into two components that reflect important equity principles. Furthermore, the methods allow for a more detailed look at how different parts of the income distribution are affected by public policy changes. Overall, the results are as expected -- both U.S. taxes and transfers reduce income inequality. The redistributive effect, however, could be larger if the reranking effect were reduced or eliminated. The reranking effect tends to be relatively more important for transfers than for taxes.

The results could offer some guidance for tax reform given the twin goals of raising revenue and reducing income inequality. For example, the reintroduction of PEP and Pease after 2012 could raise a not insignificant amount of tax revenue and reduce inequality with a small to negligible reranking effect, which could limit any perceived unfairness of the provision. The method used in this report can be applied to any tax provision to determine how the provision would affect income inequality and where in the income distribution the impact would be most felt.

Appendix. Data and Methods

The 2005 wave of the University of Michigan's Panel Study of Income Dynamics (PSID) is employed to study the redistributive effects of taxes, transfers, and specific tax provisions. The 2005 wave of the PSID includes information on family income and its components in 2004. The PSID is a nationally representative longitudinal data set of the nonimmigrant U.S. population that has been ongoing since 1968. The replacement mechanism of the PSID for births is designed to yield a representative sample of the nonimmigrant population in each year. The PSID oversamples low-income households because it was created by combining the Survey of Economic Opportunity (SEO), a survey of low-income households, with a representative group of households from the Survey Research Center (SRC) national sampling frame.²⁴ Consequently, family weights are used throughout the analysis.

The unit of observation for the analysis is the family, but a family may contain more than one taxpayer. To estimate taxes, each family was split into taxpaying units. For 75% of the PSID families there is only one taxpayer. There are two taxpayers in another 17% of families. The remaining families have three or more taxpayers. The second taxpayer was either a cohabitor or a working child who cannot be claimed as a dependent.

Income from long-term and short-term capital gains was imputed based on information from the IRS's 2004 Statistics of Income (SOI) public use file. The imputations were based on the taxpayer's income (from wages, total interest, total dividends, and Social Security), filing status, and number of dependents. A two-step method was employed. In the first step, whether taxpayers have capital losses, capital gains, or no capital gains/losses was projected using the parameter estimates of a multinomial logit using the SOI data. In the second step, cell averages (with the cells based on the above variables) were calculated from the SOI data and matched to the PSID.

The PSID contains information on income from interest, but does not contain any information on the proportion that is taxable and the proportion that is tax exempt. Similarly, the information on dividends does not contain information on the proportion that are ordinary (taxed as ordinary income) and the proportion that are qualified (taxed at lower tax rates). The proportion of interest that is tax exempt and the proportion of dividends that are qualified were also imputed based on tobit estimates from the SOI data. The variables cited above are used in the imputation procedure.

Federal income taxes were estimated using a tax module created by CRS using the income and other information from the PSID. State tax information was estimated using the National Bureau of Economic Research's TAXSIM model.²⁵ Payroll taxes were computed from reported earnings using the legislated 2004 payroll tax parameters. Taxes are estimated for each tax unit within the family and then summed over all tax units within the family to arrive at a total family tax burden. Property taxes are included in the PSID data file.

Income

A precise definition of income is important in studying inequality. Most people think of income as the salary they receive from their employer or adjusted gross income as reported on their income tax return. A broader definition of income is the Haig-Simons concept of income. Henry Simons started from the proposition that "[p]ersonal income connotes, broadly, the exercise of control over the use of society's scarce resources."²⁶ Robert Haig defined "income in terms of power to satisfy economic wants rather than in terms of satisfactions themselves."²⁷ Both economists argue that income is the sum of consumption and additions to wealth.²⁸ Additions to wealth reflect rights that could have been exercised in consumption and may be so exercised in the future; the same reasoning would apply to an increase in debt which is a subtraction from wealth. The Haig-Simons definition would include home production, the rental value of housing and durable goods, and accrued capital gains.

For analytic purposes, however, income has to be measured and expressed in numerical terms in terms of national currency. Consequently, consumed goods and services produced through home production (such as child care services provided by family members and food grown by family members) are not included in income, since a monetary value is difficult to calculate. In this analysis, income is measured in dollars and includes earnings, asset income (interest and dividends), business and farm income, government cash transfers, pension payments, the face value of food stamps, and transfers from private individuals. Realized capital gains are also included since accrued capital gains are difficult to measure especially for assets that are not traded often. Following the tax code, only up to $3,000 in capital losses are included in the measure of income. Family income is adjusted for family size and composition using a two parameter equivalence scale proposed by the National Research Council:

 

 

Methods

The generalized Gini coefficient is employed to measure income inequality and the redistributive effect. The generalized Gini is:

 

 

The change in the Gini or redistributive effect can be decomposed into a progressivity (vertical) effect and a reranking (horizontal) effect:

 

 

Robert Lerman and Shlomo Yitzhaki note that the redistributive effect can be decomposed in a different way by adding and subtracting the concentration curve of initial income against the final (post-government) ranking.³⁰ Thus there is an index number problem. They argue that the post-government (final) ranking "is the appropriate ranking for calculating progressivity." Most analysts, however, use the pre-government (initial) income ranking for calculating progressivity. Using Lerman and Yitzhaki's example, suppose a rich family is made poor by a tax. The index number problem basically becomes asking who is paying the tax -- a rich family or a poor family? Most observers would probably argue that a rich family is paying the tax (which just happens to make them poor). Furthermore, most government transfers and tax benefits are targeted to particular people or groups based on their position before the transfer or tax. Consequently, the initial ranking is used for calculating progressivity.

Author Contact Information

² CBO's baseline projection starts with Congress's most recent budgetary decisions and then assumes that no policy changes will be made over the projection period. For entitlement programs CBO assumes that current laws will continue unchanged and by law assumes that discretionary spending will grow at the rate of inflation throughout the projection period. For revenues, CBO assumes that more individuals will be subject to the alternative minimum tax (AMT). CBO's baseline is not intended to be a prediction of future budgetary outcomes.

³ Michael Marmot, The Status Syndrome: How Social Standing Affects Our Health and Longevity (New York: Henry Holt and Co., 2004).

⁴ Richard G. Wilkinson, Unhealthy Societies: The Afflictions of Inequality (New York: Routledge, 1996).

⁵ Robert Frank, Falling Behind: How Rising Inequality Hurts the Middle-Class (Berkeley, CA: University of California Press, 2007).

⁶ The National Commission on Fiscal Responsibility and Reform, The Moment of Trust: Report of the National Commission on Fiscal Responsibility and Reform, December 2010.

⁷ Richard A. Musgrave, The Theory of Public Finance (New York: McGraw-Hill Book Co., 1959), p. 160.

⁸ Martin Feldstein, "On the Theory of Tax Reform," Journal of Public Economics, vol. 6, no. 1-2 (1976), pp. 77-104.

⁹ See A.B. Atkinson, "Horizontal Equity and the Distribution of the Tax Burden," in The Economics of Taxation, ed. Henry J. Aaron and Michael J. Boskin (Washington: Brookings Institution, 1980), pp. 3-18; Robert Plotnick, "A Measure of Horizontal Equity," Review of Economics and Statistics, vol. 63, no. 2 (May 1981), pp. 283-288; and Mervyn A. King, "An Index of Inequality: With Applications to Horizontal Equity and Social Mobility," Econometrica, vol. 51, no. 1 (January 1983), pp. 99-115.

¹⁰ Nanak Kakwani, "On the Measurement of Tax Progressivity and Redistributive Effect of Taxes with Applications to Horizontal and Vertical Equity," Advances in Econometrics, vol. 3 (1984), pp. 149-168.

¹¹ See, for example, J. Richard Aronson and Peter J. Lambert, "Decomposing the Gini Coefficient to Reveal the Vertical, Horizontal, and Reranking Effects of Income Taxation," National Tax Journal, vol. 47, no. 2 (June 1994), pp. 273-294; Peter J. Lambert, The Distribution and Redistribution of Income (Manchester, UK: Manchester University Press, 2001); Xavier Ramos and Peter J. Lambert, "Horizontal Equity and Differences in Income Tax Treatment: A Reconciliation," Research on Economic Inequality, vol. 10 (2003), pp. 45-63; Jean-Yves Duclos, Vincent Jalbert, and Abdelkrim Araar, "Classical Horizontal Inequity and Reranking: An Integrating Approach," Research on Economic Inequality, vol. 10 (2003), pp. 65-100; and Kinam Kim and Peter J. Lambert, "Redistributive Effect of U.S. Taxes and Public Transfers, 1994-2004," Public Finance Review, vol. 37, no. 1 (January 2009), pp. 3-26.

¹² See Aronson and Lambert, and Kim and Lambert.

¹³ This is the decomposition developed by Kakwani.

¹⁴ The redistributive effect is the difference in the Gini coefficients between initial income (the base case) and final income (after taxes and/or transfers have been included). See the Appendix for a description of the data used for the analysis and the methods used to calculate the various effects.

¹⁵ The progressivity and reranking effects sum to 100% of the redistributive effect.

¹⁶ See CRS Report R40508, Personal Exemption Phaseout (PEP) and Limitation on Itemized Deductions (Pease), by Gary Guenther; and CRS Report RL30149, The Alternative Minimum Tax for Individuals, by Steven Maguire for more information on PEP, Pease, and the AMT.

¹⁷ Tax Policy Center, Aggregate AMT Projections, 2008-2019, Table T09-0186, available at http://www.taxpolicycenter.org.

¹⁸ For more details of the EITC, see CRS Report RL31768, The Earned Income Tax Credit (EITC): An Overview, by Christine Scott.

¹⁹ U.S. Congress, Joint Committee on Taxation, Estimates of Federal Tax Expenditures for Fiscal Years 2010-2014, Joint Committee Print, JCS-3-10, December 15, 2010.

²⁰ See CRS Report RL34715, The Child Tax Credit, by Maxim Shvedov for more details.

²¹ See CRS Report RL32552, Social Security: Calculation and History of Taxing Benefits, by Christine Scott and Janemarie Mulvey for more details.

²² See CRS Report RL30638, Tax-Exempt Bonds: A Description of State and Local Government Debt, by Steven Maguire.

²³ See CRS Report R40411, The Economic Effects of Capital Gains Taxation, by Thomas L. Hungerford.

²⁴ Martha S. Hill, The Panel Study of Income Dynamics (Newbury Park, CA: Sage Publications, 1992).

²⁵ Daniel Feenberg and Elisabeth Coutts, "An Introduction to the TAXSIM Model," Journal of Policy Analysis and Management, vol. 12, no. 1 (1993), pp. 189-194.

²⁶ Henry C. Simons, Personal Income Taxation: The Definition of Income as a Problem of Fiscal Policy (Chicago: University of Chicago Press, 1938), p. 49.

²⁷ Robert Murray Haig, "The Concept of Income -- Economic and Legal Aspects," in The Federal Income Tax, ed. R.M. Haig (New York: Columbia University Press, 1921), p. 6.

²⁸ Simons states that "[p]ersonal income may be defined as the algebraic sum of (1) the market value of rights exercised in consumption and (2) the change in the value of the store of property rights between the beginning and end of the period in question" (p. 50).

²⁹ Constance F. Citro and Robert T. Michael, Measuring Poverty: A New Approach (Washington: National Academy Press, 1995).

³⁰ Robert I. Lerman and Shlomo Yitzhaki, "Changing Ranks and the Inequality Impact of Taxes and Transfers," National Tax Journal, vol. 48, no. 1 (March 1995), pp. 45-59.