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Decomposition of progressivity and inequality indices: Inferences from the US federal income tax system
J. Account. Public Policy 31 (2012) 258–276
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Decomposition of progressivity and inequality indices: Inferences from the US federal income tax system Govind S. Iyer a,⇑, Philip M.J. Reckers b a b
Department of Accounting, University of North Texas, Denton, TX 76201, United States School of Accountancy, Arizona State University, Tempe, AZ 85281, United States
a b s t r a c t Vertical equity is an important criterion in evaluating a tax system. Vertical equity has two elements: progressivity and income equality. In this paper, we analyze the vertical equity effects of the US income tax system during 1995–2006 and show that income inequality increased substantially during the period combined with a significant reduction in real progressivity. Using a Lorenz-curve-based graphical method, we decompose progressivity and income inequality indices and identify and quantify how much each source of income contributes to overall progressivity and income inequality. Results for the 1995–2006 period indicate that US income tax treatment of Salaries and Wages income were distributed and taxed progressively and contributed to a decrease in income inequality. However, the treatment of Net Capital Gains not only decreased progressivity, it negated the income inequality reduction achieved by salaries and wages. These results show that to evaluate the vertical equity of a tax system, both income inequality and progressivity indexes must be considered. Additionally, the decomposition method allows policy makers to estimate the progressivity and income inequality effects of marginal changes in income source and how each source is taxed. Ó 2011 Elsevier Inc. All rights reserved.
1. Introduction and motivation Amid fears of a double dip recession and ever increasing budget deficit, tax reform is emerging as one of the most important issues faced by the US Congress. Significant debate on changes to current ⇑ Corresponding author. E-mail addresses: [email protected] (G.S. Iyer), [email protected] (P.M.J. Reckers). 0278-4254/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.jaccpubpol.2011.08.008
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tax law are underway in the Congress and will also be a platform issue on which 2012 presidential candidates will seek to differentiate themselves. At the center of the tax reform debate is the issue of equity or who should bear the tax burden. Supporters of tax increases argue tax increases on the wealthy are appropriate and necessary to ‘‘undo years of stagnant wages, declining incomes and growing (income) inequality,’’ while opponents claim that ‘‘the income tax system has never been more progressive’’. In this study, we seek to enrich the unfolding tax debate by analyzing the inequality and progressivity effects of the US Federal Income Tax system using Internal Revenue Service data from 1995 to 2006. In doing so, we introduce a graphical method of decomposing two widely used income inequality and progressivity indices to precisely identify and quantify how much different sources of income contribute to inequality and progressivity. Two principal factors motivate our study. First, following the healthcare debate, income tax reform promises to be a key battleground in the new Congress and in the 2012 presidential election. Claims are already being made regarding the changing distribution of income and taxes across taxpayers over the past decade, and the need (or lack thereof) for tax reform and redistribution of wealth. While some claim that the income tax system has never been more progressive than at present, others bemoan the increasing inequality of the income distribution in the past decade. For instance, Congressman Kevin Brady, the Ranking Republican House member on the Joint Economic Committee recently claimed that individuals in the top bracket paid the highest share of income tax in decades (press release July 31, 2009).1 On the other hand, speaking for the Democrats, former New York Senator and now Secretary of State Hillary Clinton, cites ‘‘seven (Bush) years of stagnant wages, declining incomes and increasing inequality.’’2 To support their claims, policymakers provide half-truths by ‘‘cherry picking’’ facts that support their position. The same tax bill is praised by some as one that restores fairness, while others pillory it for being blatantly inequitable.3 Economists likewise split on whether higher taxes on the rich are desirable. For instance, regarding the current debate in Congress as to how the budget deficit should be addressed, Princeton Professor and New York Times columnist Paul Krugman calls for higher taxes on the rich4 while Columbia Dean Glenn Hubbard supports extending the Bush tax cuts.5 A recent poll shows a country divided along party lines on what type of tax cut is desirable: fifty-three (53) percent of Americans say that raising taxes on households earning $250,000 or more is a good idea while 38% say it is a bad idea. Allowing the Bush tax cuts to expire for high income taxpayers found support with 65% of Democrats, 57% of independents but with only 33% of Republicans. We believe that in order to advance an analysis free of partisan rhetoric, it is important to understand what has contributed to income inequality in the past and what elements of tax law have mitigated it. From a policy perspective, we showcase the effect of income source distribution on income inequality and tax progressivity in the US over a 12 year period from 1995 to 2006. Our thesis is that, for any meaningful discussion of tax policy changes, it is not sufficient to simply focus on the distribution of income. Current tax law does not treat all income equally. There are tax favored income streams and there are highly taxed income streams. Consequently, after-tax income distribution is dependent not only on how aggregate before-tax income is distributed but also on the sources of before-tax income (because different sources are taxed differently). Therefore, policy discussions regarding how income inequality can be mitigated cannot be addressed unless there is a clear understanding of how different income sources (some fully taxed and some tax favored) are distributed among different income classes. In contrast, policy and political discussions seem to be fixated on the tax rate schedule and tend to treat all income as homogeneous. The hesitation in political and policy circles is understandable because changes to taxability of different income
1 Congress of the United States, Joint Economic Committee, Congressman Kevin Brady, Ranking Republican House Member, News Release, July 31, 2009, Press Release #111-19. 2 The Inequality Myth, by Brad Schiller, The Wall Street Journal Online, March 10, 2008. 3 For instance, when debating the (Bush) tax reform bill in 2001, Sen. Baucus called it an equitable tax reform while Sen. Conrad characterized it as an unfair tax bill. Congressional Record – Senate 107th Congress, 1st Session, 147 Cong Rec S 5028 Restoring Earnings to Lift Individuals and Empower Families (Relief) Act of 2001, May 17, 2001; Sen. Baucus: ‘‘[t]he bill before us today will make the tax system more progressive than under current law.’’; Sen. Conrad: ‘‘There is something wrong with this bill, and what is wrong is it is not fair.’’ 4 The Tax Cut Racket, The New York Times, September 17, 2010, Section A, p. 27, Op-Ed Columnist; Now That’s Rich, The New York Times, August 23, 2010, Section A, p. 23, Op-Ed Columnist. 5 Fairness and the Capital Tax Fetish, The Wall Street Journal, August 9, 2010, Opinion Journal.
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sources involve not just equity considerations but also economic, efficiency, productivity and political considerations. Nonetheless, we want to make it clear that equity considerations cannot be fully addressed unless the causes of inequity are fully acknowledged. The cause of inequality and progressivity changes are not merely due to changes in the distribution of pre-tax income or the tax rate schedule, but also due to how each source of pre-tax income is distributed and taxed. In addition, it is inadequate to rely only on summary indices when addressing vertical equity issues.6 Several studies in both accounting and economic literature have used summary indices to document the progressivity and inequality effects of different tax systems (Seetharaman and Iyer, 1995; Young et al., 1999; Ryan, 1997). For example, Iyer et al. (1996) used the Kakwani and Suits indices to document the vertical equity effects of replacing the progressive income tax with a flat tax. Likewise, Dunbar (1996) used the Kakwani and the Suits index to estimate the effect of personal credits on federal income tax progressivity. While summary indices are useful in documenting the changes in income and/or tax distributions, they do not identify or quantify the sources that underlie such changes. From a methodological perspective, we introduce a graphical counterpart to Silber (1989)’s matrix method of decomposing the Gini index and also extend it to commonly used inequality and progressivity indexes (Kakwani, 1976). The advantages of the graphical method are (a) it is based on the well documented Lorenz and concentration curves; (b) it is easy to compute without the complications of the matrix methods and therefore easily understood by non-economists and (c) it is intuitive, graphical and the results can be easily highlighted and showcased. Based on our literature review, this is the first paper that has attempted to extend the Lorenz curve decomposition method to progressivity and inequality indexes (at least in the tax accounting area). From a policy standpoint, the decomposition of the indices allows lawmakers and the public to gauge the impact of tax law changes on vertical equity. To summarize, this paper has a twofold purpose: (i) document the income inequality and progressivity changes in the US tax system over a 12 year period between 1995 and 2006; and (ii) develop a method that can isolate the inequality and progressivity effects by source of income.7 Results indicate that income inequality increased over the 12 year period from 1995 to 2006. While nominal progressivity increased over the same time, real progressivity measured after controlling for changes in before-tax income distribution decreased over the period. The decrease in real progressivity can be attributed to increasing inequality in before-tax incomes and protection of some sources of income (capital gains among them) from progressive taxation. With respect to income sources, salaries and wages income contribute to greater equality and greater progressivity. The positive effect of salaries and wages is more than counterbalanced by the negative effect of capital gains. Unequal distribution of capital gains causes an increase in income inequality and reduction in total progressivity. Thus, despite the ‘‘rich’’ paying a greater share of total taxes than ever before, income inequality of ‘‘after-tax income’’ continued to rise. Our results are consistent with those observed by Picketty and Saez (2007). Picketty and Saez (2007) documented the progressivity of the US Federal Tax System (individual income tax, payroll tax, federal estate and gift tax, and federal corporate taxes). They found that between 1964 and 2004, the US Federal Tax system became less progressive. While our results are consistent with those of Piketty and Saez, our study is distinct because (i) we focus on individual income tax, (ii) we separate the progressivity and the inequality effects by source, and (iii) we show how the distribution of income that is subject to special tax rates impacts overall progressivity and income inequality. The remainder of the paper is organized as follows: the next section provides a brief overview of the indices used in this paper, an explanation of how they are computed and a discussion of the relationship between progressivity and income inequality based indices. In the third section, we delineate the Lorenz-Curve-based graphical method for decomposing the indices. In the fourth section, we present the data and results of our analyses of the 1995–2006 12 year period. We end the paper with a summary, conclusion, and limitations.
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Gini based indexes such as the Suits index (Suits, 1977) or the Kakwani indices (Kakwani, 1976). In contrast to the inter-period decomposition presented in Iyer et al. (2008) in which the Gini difference between 2 years is split into average tax rate effect, standardized tax rate effect and pre-tax income effect, the decomposition method discussed in this paper is an intra-period decomposition. Inequality and progressivity indices (of any single year) are split into relative contributions from various income sources. 7
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2. Inequality and progressivity indices Equity is an important criterion in evaluating a tax system. Citizens demand a tax system that they perceive to be ‘‘fair’’; voluntary compliance indeed depends on acceptance of the tax system as fair and equitable. Equity, however, has two dimensions: horizontal equity and vertical equity. A system is defined as horizontally equitable if taxpayers with equal incomes pay equal taxes. Vertical equity deals with the distribution of taxes across income groups. Vertical equity is currently a highly contested issue; it is accordingly the focus of this article. The vertical equity of a tax system relates to the distribution of taxes across taxpayers; and the vertical equity of a tax system is measured by the change in the after-tax net income distribution vis-à-vis the before tax income distribution. However, a second concept of vertical equity also exists. In a progressive tax system, higher income earners pay a greater share of their income in tax as compared to lower income earners. The distribution of tax burden across income strata constitutes a second measure of vertical equity. Most indices that measure progressivity relate tax shares to income shares while most indices of income inequality relate pre-tax income shares to post-tax income shares (Stroup, 2005). The Gini index forms the basis of almost all inequality and progressivity indices, including the Kakwani indices. Nygaard and Sandstrom (1981) and Seetharaman and Iyer (1995) provide a detailed discussion of various indexes of income inequality and tax progressivity. We chose to focus on the Kakwani indices of inequality and progressivity in this paper because they are among the most widely used in economic literature and are also relatively simple to understand. 2.1. Computation of the Gini Index A Lorenz (Income) Curve shows the relation between the cumulative proportion of taxpayers on the x-axis (arrayed by size of income from lowest to highest) and the cumulative proportion of their corresponding income on the y-axis. Tax curves are similar to Lorenz curves, except one plots the cumulative proportion of taxes paid (instead of income) on the y-axis. A Lorenz curve is a graphical representation of the income distribution and a tax curve is a graphical representation of the tax distribution. Most income inequality and progressivity indices are based on Lorenz income and tax curves and their related Gini coefficients (Gini). The Gini coefficient is the most widely used measure of income inequality and is measured as twice the area bounded by the income curve and the egalitarian line (line of perfect equality which is graphically represented by a 45° line).8 See Fig. 1. If income becomes more unequal, the line moves to the right and the area bounded by the curve and the egalitarian line increases, thereby increasing the Gini index value (representing greater inequality). Thus, higher values of the Gini index denote greater inequality. In this study we consider two widely used Gini based indices: the Kakwani index of income inequality – K(I), and the Kakwani index of progressivity – K(P). We demonstrate the computation of these indices using data from IRS Statistics of Income Bulletin for the year 2006.9 Extracted information is reproduced in Table 1. Table 1, column A shows the cumulative share of income recipients; column B shows the adjusted gross income (AGI or before-tax income) corresponding to the income intervals; columns C and D shows the shares of the salaries and wages and net capital gain, column E shows cumulative tax (after credit) shares and column F shows the cumulative proportions of after tax income. 2.2. Kakwani index of inequality K(I) The Kakwani index of income inequality, K(I), measures the change in income inequality as result of the tax system. That is, it compares the before-tax income distribution (curve) to the after-tax income distribution (columns B and F in Table 1). K(I) is defined as the difference between the Gini indexes of 8 Intuitively, it measures how far an income distribution is from the egalitarian line. The farther the income curve is from the egalitarian line, the greater is the income inequality. 9 Statistics of Income Bulletin, Fall 2008, Vol. 28, No. 2, Table 1 (p. 21) and Table 2 (p. 40).
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Gini Index of Inequality = 2 x (Area bounded by income curve and egalitarian line) Fig. 1. Computation of the Gini Index of Inequality. Gini Index of Inequality = 2 (Area bounded by income curve and egalitarian line).
the before-tax and after-tax income distributions; that is, K(I) = Ginibefore-tax income Giniafter-tax income. A change in either the before-tax income distribution and/or the tax system influences the value of K(I). If the two (before and after tax) income distributions are identical, then the two corresponding Lorenz curves perfectly overlap, their Gini indexes are the same and K(I) equals zero. A zero value indicates that the tax system did not affect income inequality. If the after-tax income is more equal than the before tax income distribution, its curve moves toward the egalitarian line and lies to the left (and above) the before-tax income curve (see Fig. 2). The before-tax income Gini index is greater than the after-tax income Gini index, resulting in a positive value for K(I) index. Larger positive K(I) Index values indicate greater vertical equity (i.e., less inequity). Thus, for year 2006 the K(I) index is K(I) is computed as 0.601–0.570 = 0.031 (see Table 1).
2.3. Kakwani index of progressivity K(P) The Kakwani index of progressivity, K(P), measures vertical equity by comparing the distribution of tax burden across income strata (that is the distribution of tax burden is compared to the distribution of income (Kakwani, 1976)). For a proportional (or flat) tax, the before-tax income curve and the tax curve will overlap since the cumulative proportion of tax paid will be equal to the cumulative proportion of income earned regardless of the income level. For a progressive tax, the tax curve moves away and to the right of the before-tax income curve (see Fig. 3). That is, the cumulative proportion by tax paid by lower income earners is less than the cumulative proportion of income earned by them. The Gini index for the tax curve is referred to as the concentration coefficient (Ctax). The Kakwani index of progressivity denoted as K(P) is measured as the difference between the tax concentration coefficient and the before-tax income Gini index. That is K(P) = Ctax Ginibefore-tax income. Like the K(I) index, a change in either the before-tax income distribution and/or the tax system influences the value of K(P).
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G.S. Iyer, P.M.J. Reckers / J. Account. Public Policy 31 (2012) 258–276 Table 1 Selected internal revenue service statistics of income data for 2006. Income range
Proportion of taxpayers A
Before-tax income B
Salaries and wages C
Net capital gain D
Cumulative proportions – Taxpayers arrayed by size of income from lowest to highest Under $10,000 0.1726 0.0147 0.0175 0.0031 Under $15,000 0.2589 0.0327 0.0371 0.0053 Under $20,000 0.3394 0.0562 0.0643 0.0079 Under $25,000 0.4125 0.0836 0.0979 0.0103 Under $30,000 0.4770 0.1132 0.1342 0.0131 Under $40,000 0.5812 0.1738 0.2091 0.0192 Under $50,000 0.6600 0.2328 0.2805 0.0263 Under $75,000 0.7989 0.3754 0.4491 0.0492 Under $100,000 0.8810 0.4937 0.5869 0.0766 Under $200,000 0.9700 0.6915 0.8080 0.1628 Under $500,000 0.9930 0.8017 0.9079 0.2895 Under $1,000,000 0.9974 0.8509 0.9425 0.3858 Under $1,500,000 0.9985 0.8733 0.9554 0.4420 Under $2,000,000 0.9990 0.8868 0.9623 0.4811 Under $5,000,000 0.9997 0.9232 0.9787 0.6002 Under $10,000,000 0.9999 0.9443 0.9868 0.6879 All Income 1.0000 1.0000 1.0000 1.0000 Share in total income 1.0000 0.6712 0.0959 Area under the curve 0.1994 0.2367 0.0312 Gini index 0.6013 0.5266 0.9376 K(P) index 0.0212 0.1923 0.0119 K(I) index 0.0306 0.0296 0.0351
Tax after credits E
After-tax income F
0.0007 0.0030 0.0077 0.0150 0.0252 0.0518 0.0836 0.1758 0.2638 0.4683 0.6412 0.7333 0.7764 0.8025 0.8725 0.9111 1.0000
0.0167 0.0369 0.0632 0.0935 0.1259 0.1914 0.2543 0.4042 0.5268 0.7236 0.8248 0.8678 0.8873 0.8990 0.9305 0.9491 1.0000
0.0934 0.8132
0.2147 0.5707
For a proportional tax, K(P) will be zero and for a progressive tax, K(P) will be positive.10 Larger values of K(P) indicate greater progressivity. For 2006, the K(P) index is computed as 0.813–0.601 = 0.212 (see Table 1 and Fig. 3). 3. Decomposition of the Kakwani Indices 3.1. Decomposing the Gini index using Silber method Silber (1989) demonstrates a mathematical method of decomposing the Gini coefficient by income source.11 According to Silber (1989), the Gini index may be written (using matrix notation) as
Gini ¼ e0 Gs where e is a column vector of n elements where each element is equal to 1n (and e0 is the corresponding row vector), s is a column vector of n elements being respectively equal to s1, s2, . . ., sn, G is an n by n matrix whose elements gij are equal to 1 when i > j, +1 when i < j, and 0 when i = j. For the Gini index of income inequality, the column vector e represents shares of income recipients, and the column vector s represents the corresponding income shares. Let us assume that total income is made up of k sources. The Gini index of the income from source i is expressed using the formula provided above, except for replacing share si (share of income recipient in total income) by yi (share of income recipient in income from source i)
Ginii ¼ e0 Gyi
10 For a regressive tax, the tax curve moves away and to the left of the income curve. The area bounded by the two curves is considered negative. Thus, larger negative values of the K(P) indicate greater regressivity. 11 Other researchers have demonstrated similar methods for decomposing the Gini coefficient. See for example Kakwani (1977), Fei et al. (1978), and Lerman and Yitzhaki (1985).
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Fig. 2. Computation of the Kakwani’s Index of Inequality – K(I). Kakwani’s Index K(I) = 2 (Area bounded by the Before-Tax and After-Tax Income curves). Area under Before-Tax Income curve = 0.1994. Area under the After-Tax income curve = 0.2146. Area bounded by the curves = 0.0152. K(I) = 2 (0.2146–0.1994) = 0.0304.
Fig. 3. Computation of the Kakwani’s Index of Progressivity – K(P). Kakwani’s Index K(P) = 2 (Area bounded by the Before-Tax Income curve and Tax curve). Area under the Lorenz curve of before-tax income = 0.1994. Area under the tax curve = 0.0934. Area bounded by the curves = 0.106. K(P) = 2 (0.1994–0.0934) = 0.2119.
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The Gini for each source may be computed by using the above formula. Finally, the Gini index of income inequality for the total income is simply the sum of all Gini indices of all the income sources scaled by their respective share in total income.
GiniTotal ¼
k X
Si I i
i¼1
where si is share of income source i in total income. The graphical counterpart to decomposing the Gini coefficient consists of constructing Lorenz curves for each income source and computing a Gini for each income source. The Gini multiplied by the relative importance of the income source in total income (proportion) is the contribution of that source to the overall Gini index. To illustrate, Table 1 column A shows the cumulative proportion of taxpayers, and column C shows the corresponding cumulative proportion of salaries and wages (S&W). Using the method described in Section 2.1, we can compute the Gini index for S&W as twice the area bounded by the egalitarian line and the S&W curve. This area is 0.263 and the Gini is 0.526.12 The Gini for Capital Gains (CG) calculated likewise is 0.938 (see Table 1). Multiplying by their respective shares in total income, we can say that S&W contributes 0.353 and CG contributes 0.09 to the overall Gini value of 0.601. That is, S&W constitutes 67% of total income and accounts for 58% of overall inequality and CG constitutes 9.5% of total income and accounts for 15% of overall inequality. 3.2. Decomposing the Kakwani index of inequality K(I) We continue with the same illustration to demonstrate how the K(I) index is decomposed. The Gini for before-tax income distribution is 0.601 while the Gini for S&W is 0.526. That is, the before-tax income distribution is less equal than the S&W distribution (its curve is closer to the egalitarian line, see Fig. 4 and Table 1). Recall that the overall K(I) index is computed as K(I) = Ginibefore-tax income Giniafter-tax income. The K(I) for total income is 0.601–0.570 = 0.031. To compute the effect of S&W on the K(I) index, we replace the before-tax income distribution by the S&W distribution and scale it based on S&W’s share in total income. That is, K(I) share of S&W is computed as K(I)S&W = (GiniS&W Giniafter-tax income) Share of S&W = (0.526–0.570) 0.671 = 0.0296. We find that S&W is more equally distributed than the after-tax income distribution. That is, compared to the after-tax income distribution, S&W results in an increase in equality of 0.0296. In percentage terms of the overall K(I) index of 0.031, it may be expressed as a 95% increase in equality. Following the same method detailed above, we compute the separable equity effect of CG. Table 1 also shows that the Gini index of Capital Gains is 0.938. As compared to the before-tax income, CG is more unequally distributed (concentrated at higher incomes and its curve is farther away from the egalitarian line, see Fig. 4). K(I) for CG is computed as K(I)CG = (GiniCG Giniafter-tax income) Share of CG = (0.938–0.570) 0.096 = 0.0353. That is, compared to the after-tax income distribution, CG results in a decrease in equality of 0.0353. In percentage terms of the overall K(I) index of 0.031, it may be expressed as a 114% decrease in equality. 3.2.1. Decomposing the Kakwani index of progressivity K(P) Decomposition of the K(P) index follows an identical procedure. Recall that K(P) index is computed as the difference between the Gini index of before-tax income and the concentration coefficient of tax. For 2006, K(P) = Ctax Ginibefore-tax income = 0.813–0.601 = 0.212. Because S&W is more equally distributed (G = 0.526), it has a vertical equity enhancing effect on K(P). To compute the separable effect of S&W on K(P) we replace the before-tax income distribution with S&W and scale it based on S&W’s share in total income. That is, K(P)S&W = (Ctax GiniS&W) Share of S&W = (0.813–0.526) 0.671 = 0.192. That is, of the overall K(P) progressivity index of 0.212, S&W accounts for 91%. 12 Salaries and Wages constitute 67.12% of total income. Following Silber (1989), the contribution of Salaries and Wages to the overall Gini index is 0.526 0.6712 = 0.353. Note that this is not the Gini of S&W, but the contribution of S&W to the overall Gini value of 0.601.
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Fig. 4. Vertical equity impact of salaries and wages and capital gains. Area A = Gain in vertical equity due to salaries and wages. Area B = Loss in vertical equity due to Capital Gain.
In contrast, CG is less equally distributed than before-tax income (Gini = 0.938). Consequently, it has a vertical equity decreasing effect on overall K(P). The separable value of CG is computed as K(P)CG = (Ctax GiniCG) Share of CG = (0.813–0.938) 0.0959 = 0.012. When compared to the CG distribution, the tax distribution is regressive. That is, of the overall K(P) value of 0.212, CG contributes to a 6% reduction in progressivity. 3.2.2. Nominal progressivity and real progressivity Because K(P) is computed as the difference between Gini index of before-tax income and concentration coefficient of tax, any change to the before-tax income distribution will cause the K(P) value to change even if there is no change in the tax system. Nominal progressivity, K(P)nominal, simply describes how progressive the tax system is for a given income distribution. When K(P)nominal is compared over time, one cannot unequivocally attribute the differences between the K(P) values to changes in the tax system; a change in the pre-tax income distribution may have caused the K(P) values to be different. Note that K(P)nominal value for the current year is based on the current income distribution and the current tax distribution. To isolate the effect of just the tax system, a K(P)real index is computed in which the income distribution is held constant and the tax distribution is allowed to vary so that only the effect of changing tax system is measured. K(P)real computes the K(P) value for each year by assuming that the income distribution is the same as the 1995 income distribution. Based on the A new tax distribution is then simulated for this income distribution based on the current year tax distribution data. For example, the real progressivity index for 2006 is based on the 1995 income distribution and 2006 tax data. Because K(P)real for every year is based on the 1995 income distribution (only the tax system changes) they can be compared over time as well. Besides the tax rate, two factors determine the tax share of a group: the proportion of taxpayers in the group (distribution of taxpayers) and the proportion of income received by the group (distribution of income to the taxpayers). We adjust for these two elements in computing the simulated tax distribution. The simulated tax share for each income group for the 1995 income distribution (based on the current year tax data) equals
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year 1995 income share current year income share year 1995 proportion of taxpayers in the group current year proportion of taxpayers in the group
Current year tax share
The first element is the tax share based on current year tax data, the second element scales it so that it reflects the 1995 income share (of that group of taxpayers) and the third element scales it to reflect the 1995 proportion of taxpayers in that group.13 The index K(P)real for 2006 measures what the progressivity would have been had the year 2006 tax rates been applied to the 1995 income distribution.14 3.3. Separating the equity effect of income subject to regular tax rates and special tax rates The decomposition method described above shows the impact of various sources of income on the K(I) and K(P) indices. It does so by holding the tax curve constant. However, in order to fully measure the impact of distribution of income subject to special tax rates, it is necessary to separate such income and the tax incidence on such income. During the period 1995–2006, long-term capital gains and qualified dividends were taxed at a lower rate while all other income was taxed at the taxpayers’ regular marginal rate. Consequently, we created two groups of income: (i) net long-term capital gains and qualified dividends (special income), and (ii) all other income except net-long term capital gains and qualified dividends (regular income). We also separated the tax on special income (special tax) and regular income (regular tax).15 The Kakwani indices K(I) and K(D) were computed based on these distributions. For instance, the K(P) index for special income (long-term capital gains and qualified dividends) considered only the distribution of special income and the tax on special income, while the K(P) index for regular income was based on distribution of regular income and regular tax. 4. Results and analysis 4.1. Overall results Using the above methods, we analyze the progressivity and income inequality measures for each year from 1995 to 2006. The overall K(P) and the K(I) indices for the 1995–2006 are presented in Table 2. The K(I) index shows a decreasing trend in vertical equity and likewise real progressivity has also decreased over time. Note that real progressivity has dramatically decreased after the Bush tax cuts in went into effect in 2003. The trend in K(I) and K(P) values over 1995–2006 period is shown in Fig. 5A and B. Decomposition of the indices into the various sources provides a more consistent explanation of the observed changes with respect to the two major sources contributing to income inequality and progressivity. Salaries and wages increase progressivity and decrease income inequality every year (except 1995). Conversely, capital gains decrease progressivity and increase income inequality every year. 4.2. Inequality effects In Table 3 we show the various income source components, K(I) and its percentage of the overall index value. The same items for the K(P) index are shown in Table 4. 13 Because the total income recipients, total income and total tax collected is not be the same in the 2 years, tax shares computed using the above method is scaled so that that the sum of the tax shares equals 1. 14 This is an estimate of the tax shares. If microdata is available, actual tax burdens can be computed by applying the new tax rules to individual tax returns. 15 This data was also collected from www.irs.gov/taxstats/indtaxstats. The table is Returns with Modified Taxable Income: Tax Generated – SOI Bulletin article – Individual Income Tax rates and Tax Shares, Table 2.
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Table 2 Overall K(I) and K(P) indices for the years 1995–2006. Year
Kakwani K(I) index
Kakwani K(P)nominal index
Kakwani K(P)real index
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
0.0320 0.0332 0.0331 0.0332 0.0343 0.0355 0.0343 0.0340 0.0300 0.0302 0.0307 0.0306
0.1997 0.1994 0.1957 0.1988 0.1983 0.1970 0.2070 0.2268 0.2222 0.2196 0.2162 0.2119
0.1997 0.1808 0.1571 0.1441 0.1285 0.1136 0.1370 0.1686 0.1575 0.1370 0.1207 0.1070
Comparing the K(I) values of income sources over the 12 year period, we find that S&W consistently produces equality gains vis-à-vis the after-tax income distribution (columns C and D of Table 3) while CG consistently produces equality losses (columns K and L of Table 3). The equality gains of the S&W distribution are more than offset by the equality losses of the CG distribution. S&W forms at least 50% of total income every year while the share of CG has more than doubled over the same period – from a low of 4.2% in 1995 to 9.6% in 2006. The increasing equality gains of S&W over the years and the increasing equality losses of CG over the years also indicate that (i) despite the doubling of CG’s share in total income, S&W not only continues to be the most important source of income to low-income taxpayers but its importance has been rising among them; (ii) the bulk of the increase in CG’s share in total income has been garnered by high-income taxpayers and (iii) the tax structure has not fully offset the equality losses caused by the unequal distribution of CG. This is likely the result of CG being taxed at a preferential lower rate. Because long-term capital gains are taxed at a maximum 15% rate, the tax paid on capital gains by higher income earners fall below the tax rate paid by many lower income earners whose incomes predominantly consist of salaries and wages and/or Schedule C income. This has the effect of pushing the after-tax income distribution away from the egalitarian line thereby increasing inequality. Note that increases in income inequality are correlated with performance of stock market returns. For example, large returns in the stock market during 1998, 1999 and the first half of 2000 (when the NASDAQ first reached 5000) coincide with large increases in inequality due to CG. In contrast, low or negative returns (during 2001 and 2002) coincide with relatively modest inequality increases due CG. As shown in Fig. 6, inequality reduction of S&W is offset by the inequality increase of CG every year. Dividend income results in inequality increase every year. The inequality increases are more pronounced after 2003 when qualified dividends began to be taxed a lower tax rate. Like CG, dividend income is unequally distributed to high-income taxpayers and the unequal distribution is not fully offset by the tax structure. The impact of dividend income is modest because of its low relative share in total income. Dividend income forms about 2% of total before-tax income each year. Despite its low share in total income, its impact on income inequality is rather large; about 10% before qualified dividend change in 2003 and about 15% (17.5% in 2006) after 2003. This also supports the findings of Chetty and Saez (2005) that the large tax rate cut on individual dividend income in 2003 was followed by an unusually large number of firms initiating dividends or increasing dividends to shareholders. The change was particularly pronounced in firms with strong principals whose tax incentives changed (i.e., high income taxpayers). The effects of Schedule C income are rather modest for most years and generally lead to inequality reduction. The modest inequality reduction due to Schedule C income may be attributed to a more equal distribution of Schedule C income vis-à-vis after-tax income and its taxability as ordinary income using the regular graduated tax rate schedule.
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(A)
(B)
Fig. 5. A K(I) index values from 1995 to 2006. B K(P)nominal and K(P)real index values from 1995 to 2006.
4.3. Progressivity effects About 85–90% of the overall progressivity is explained by S&W (see columns C and D of Table 4). S&W is the largest component of total income. It is also more equally distributed than total before-tax income. Also, the tax on S&W is based on the regular graduated tax rate schedule. Consequently, S&W has the greatest impact on progressivity. In contrast, CG reduces progressivity every year (about 3–6%;
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Year
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
Salaries and wages
Interest
A Value
Overall B %
C Value
D %
E Value
F %
G Value
Dividends H %
I Value
Sch C income J %
K Value
Capital gain L %
M Value
All other sources N %
0.0320 0.0332 0.0331 0.0332 0.0343 0.0355 0.0343 0.0340 0.0300 0.0302 0.0307 0.0305
100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00
0.0013 0.0039 0.0104 0.0140 0.0160 0.0167 0.0047 0.0006 0.0060 0.0161 0.0264 0.0296
4.02 11.87 31.32 42.04 46.56 47.08 13.7 1.76 20.09 53.41 85.92 97.00
0.0001 0.0001 0.0002 0.0004 0.0005 0.0011 0.0009 0.0004 0.0005 0.0009 0.0019 0.0028
0.48 0.27 0.71 1.10 1.39 3.16 2.86 1.04 1.65 3.13 6.16 9.18
0.0032 0.0035 0.0041 0.0037 0.0037 0.0039 0.0029 0.0025 0.0030 0.0041 0.0044 0.0053
10.02 10.45 12.31 11.27 10.73 11.13 8.58 7.23 10.05 13.69 14.26 17.45
0.0024 0.0014 0.0008 0.0005 0.0003 0.0001 0.0003 0.0001 0.0009 0.0013 0.0013 0.0019
7.42 4.15 2.39 1.54 0.97 0.33 0.04 0.02 3.25 4.46 4.27 6.35
0.0142 0.0199 0.0251 0.0293 0.0327 0.0349 0.0208 0.0164 0.0194 0.0272 0.0337 0.0352
44.36 59.76 75.72 88.14 95.32 98.54 60.45 48.19 64.83 90.07 109.59 115.12
0.0111 0.0124 0.0133 0.0133 0.0131 0.0123 0.0144 0.0154 0.0140 0.0154 0.0185 0.0188
34.65 37.23 40.19 39.98 38.15 34.58 41.85 45.34 46.81 50.99 60.18 61.60
Note: Equality gains are expressed in bold characters. Also note that index and percentage value of each component sums to the overall value and overall percentage respectively for each year (each row).
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Table 3 Decomposition of the K(I) index for 1995–2006.
Year
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
Salaries and wages
Interest
Sch C income
Capital gain
A Value
Overall B %
C Value
D %
E Value
F %
G Value
Dividends H %
I Value
J %
K Value
L %
M Value
All other sources N %
0.1997 0.1994 0.1957 0.1988 0.1983 0.1970 0.2070 0.2268 0.2222 0.2196 0.2162 0.2119
100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00
0.1731 0.1747 0.1747 0.1782 0.1783 0.1775 0.1807 0.1945 0.1919 0.1943 0.1955 0.1923
86.67 87.61 89.25 89.67 89.90 90.15 87.30 85.75 86.36 88.51 90.41 90.79
0.0084 0.0081 0.0330 0.0070 0.0063 0.0059 0.0065 0.0058 0.0044 0.0035 0.0033 0.0037
4.20 4.07 3.79 3.54 3.18 3.02 3.14 2.56 1.99 1.58 1.52 1.73
0.0019 0.0018 0.0014 0.0012 0.0015 0.0013 0.0016 0.0019 0.0015 0.0011 0.0010 0.0006
0.95 0.88 0.70 0.62 0.75 0.67 0.77 0.82 0.68 0.50 0.47 0.26
0.0071 0.0078 0.0079 0.0082 0.0080 0.0081 0.0086 0.0097 0.0104 0.0106 0.0104 0.0106
3.54 3.90 4.03 4.13 4.05 4.09 4.17 4.28 4.70 4.82 4.82 5.00
0.0049 0.0072 0.0087 0.0102 0.0116 0.0125 0.0076 0.0052 0.0068 0.0095 0.0115 0.0119
2.44 3.62 4.47 5.14 5.86 6.33 3.65 2.31 3.05 4.32 5.31 5.63
0.0141 0.0143 0.0131 0.0143 0.0158 0.0166 0.0171 0.0202 0.0207 0.0196 0.0175 0.0166
7.08 7.16 6.69 7.17 7.99 8.42 8.28 8.90 9.30 8.91 8.10 7.86
Note: Progressivity Losses are expressed in bold characters. Also note that index and percentage value of each component sums to the overall value and overall percentage respectively for each year (each row).
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Table 4 Decomposition of the K(P) index for the years 1995–2006.
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Fig. 6. Percentage of K(I) of source of income to overall K(I) for 1995–2006.
see columns K and L of Table 4). The reduction in progressivity may be attributed to a top heavy capital gain distribution and being taxed at preferential rates. The negative effect of net capital gains was the highest in the 3 years 1998 through 2000 and again in 2005 and 2006 indicated by the high negative numbers during those years. As mentioned earlier, these periods coincide with the high equity return, resulting in large gains to high-income earners that were preferentially taxed. Fig. 6 shows that while S&W contributes overall progressivity (above the x-axis, positive values), CG reduces progressivity (below the x-axis, negative values). The contribution of dividend income to progressivity is rather modest due to its low share in total income. Additionally, contribution of dividend income to progressivity reduces significantly after the 2003 tax change of taxability of dividend income (see Fig. 7). Tables 3 and 4 (columns C and D) show that the source that causes the greatest inequality reduction also contributes the most to progressivity and vice versa (columns K and L). For instance, the greatest inequality reduction was achieved by S&W in 2006 (97%). In the same year S&W contributed the most to progressivity (91%). Likewise, the smallest decrease to progressivity due to capital gains occurred in 2002 (2.3%). In the same year, capital gains led to the smallest inequality reduction (48%). The decomposition method allows us to examine each individual source separately and obtain intuitive explanations for the equity impacts of a tax system. The decomposition method pinpoints how much each source contributes to reduction (or increase) in inequality and progressivity. Consequently, policy makers can assess the marginal impact of changes in sources of income and how each source is taxed on overall progressivity and income inequality. 4.4. Separating the effects of long-term capital gains and qualified dividends Long-term capital gains and qualified dividends were subject to special rates during 1995–2006. To fully measure the impact of such income on K(I) and K(P), we computed separate K(I)s and K(P)s for such ‘‘special income’’ and the remaining ‘‘regular income.’’ Results are provided in Table 5. Note that the K(I) and K(P) values for regular income are almost the same as the overall K(I) and K(P) values (in many cases they are even higher). In contrast, the K(I) and K(P) values for special income are close to zero. These values indicate that while tax on regular income is progressive and
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Fig. 7. Percentage of K(P) of source of income to overall K(I) for 1995–2006.
Table 5 K(I) and K(P) indexes for regular tax rate items and special tax rate items for the years 1995–2006. Year
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
Overall index
Index for regular tax rate items (all income except long-term capital gains and qualified dividends)
Index for special tax rate items (long-term capital gains and qualified dividends)
K(I)
K(P)
K(I)
K(P)
K(I)
K(P)
0.0320 0.0332 0.0331 0.0332 0.0343 0.0355 0.0343 0.0340 0.0300 0.0302 0.0307 0.0305
0.1997 0.1994 0.1957 0.1988 0.1983 0.1970 0.2070 0.2268 0.2222 0.2196 0.2162 0.2119
0.0308 0.0316 0.0326 0.0336 0.0349 0.0365 0.0346 0.0297 0.0306 0.0315 0.0325 0.0325
0.1982 0.1979 0.2001 0.2071 0.2081 0.2087 0.2126 0.2254 0.2286 0.2322 0.2327 0.2296
0.0001 0.0001 0.0061 0.0061 0.0059 0.0055 0.0053 0.0052 0.0070 0.0052 0.0046 0.0044
0.0001 0.0001 0.0216 0.0254 0.0245 0.0228 0.0222 0.0218 0.0433 0.0314 0.0276 0.0263
reduces before-tax income inequality, the tax on special income is almost proportional and does not significantly impact before-tax income inequality. Indeed, the smaller overall K(P) values as compared to the K(P) values of the regular income indicate that distribution of special income and special tax contributes to a decrease in overall progressivity. Similarly, the tax on regular income mitigated before-tax income inequality, while the tax on special income had little or no effect on income inequality. Clearly, high income taxpayers with large long-term capital gains and qualified dividends are able to shield much of their total income from the graduated tax rate structure. The relative effects of regular income and special income for 2006 are illustrated in Fig. 8.
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Fig. 8. Distribution of regular tax income and special tax income for 2006.
5. Summary, conclusion and limitations 5.1. Summary In this paper, we analyzed the progressivity and income inequality effects of the US income tax system for the years 1995–2006 using two commonly employed Kakwani indices. Income inequality increased during this period accompanied by a decrease in real progressivity. While nominal progressivity exhibited an increasing trend during this period, the increase was due to changing income distribution: higher income taxpayers getting an increasing share of before tax income. Inequality increase and real progressivity decrease resulted because progressive tax rates applied to only certain sources of income, salaries and wages, interest, schedule C income; yet, those income sources diminished in importance as compared to capital gains. Using a graphical, Lorenz curve based method to decompose the Kakwani indices, we show that salaries and wages contributed to the greatest increase in progressivity and the biggest reduction in income inequality. However, the treatment of net capital gains contributes to a decrease in progressivity and more than negates the inequality reduction achieved by salaries and wages. 5.2. Discussion and conclusion Vertical equity is an important criterion in evaluating a tax system. The two main culprits increasing inequality and decreasing progressivity are the distribution of capital gains and dividend income along with the tax incident on them. Not only are capital gains concentrated at the high end of the income scale, they are also taxed preferentially. Not only does CG make the before-tax income unequal, it also renders the after-tax income even more unequal since high-income taxpayers with large capital gains are less impacted by the graduated rate structure. Consequently, we observe the dual effect of inequality increase as measured by the K(I) index but also a real progressivity loss as measured by the K(P)real index. That is, the distribution of pre-tax capital gains and the preferred rate on capital gains provides substance to the oft repeated statement that the ‘‘rich are becoming richer’’ vis-à-vis the middle income and lower income taxpayers.
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Changes to the existing tax structure seem imminent as Congress grapples with alternatives to deal with the growing budget deficit. Most of the discussion in popular press is centered on how high the tax rates ought to be for different income groups and how the tax burden ought to be distributed. What we show in this paper is that, it is important to focus on how different types of income are distributed and how each type of income is taxed. For instance, the equity effect of raising the tax rates on ordinary income is likely to be very different than raising the tax rates on capital gains. Vertical equity can be enhanced, for instance, by (i) subjecting capital gains to a graduated rate structure the same or similar to ordinary income; and/or (ii) making the rate structure on other income even more progressive by raising tax rates on high income earners. The first choice is likely to face very stiff political opposition from very high income taxpayers who derive a large percentage of their income from capital gains. The second choice is likely to face very stiff political opposition from a larger group of high but still less-high income taxpayers who derive a large percentage of their income from salary and wages. Both groups have significant political influence. The former, in part because of their wealth, and size of political contributions. The latter, in part because of their number of potential votes. Nevertheless, there are limits to how much a tax system can address the issue of pre-tax income inequality when (i) inequality of pre-tax incomes continue to rise and (ii) certain sources of income are protected from progressive taxation and (iii) and wealth is protected by favorably inheritance tax exemptions. We believe that the current discussion on tax reform must be expanded to explicitly consider how income from different sources is distributed and how income from each source is taxed. Our decomposition method allows policy makers to pinpoint what sources increase (or decrease) overall progressivity and how each source impacts income inequality. Although this study did not consider the impact of payroll taxes, it can only be expected to (i) reduce the progressivity of the system even further and (ii) increase the inequality of the after-tax income even more. The negative vertical equity effects of the payroll tax may be attributed to the following: Payroll taxes are imposed primarily on wage income. Consequently, the payroll tax will reduce the progressivity of the salaries and wages source (the most progressive source of income). Likewise, the payroll tax will also mitigate the income inequality reduction caused by salaries and wages (the source that contributes the most to reduction in income inequality). Additionally, income subject to the payroll tax is also capped (for instance the maximum earnings subject to OASDI tax was $94,200). Consequently, any income in excess of the ceiling is treated as special income not subject to the 6.2% payroll tax. Obvious beneficiaries are high income taxpayers. That is, although the payroll tax rate is a proportional rate, the OASDI tax ceiling renders it as a regressive tax resulting in an overall reduction in progressivity and increase in income inequality. 5.3. Limitations As with studies of this nature, there are several caveats: First, our study is based on aggregate data publicly available from the Internal Revenue Service Statistics of Income Bulletin. All the limitations of the data source apply to this study. Having micro data on individual tax returns would enhance analysis, if they were available, but are not. An important caveat with respect to the decomposition method is that the Gini indices expressed for the different source of income are bounded by the Gini of the total pre-tax income distribution. That is, they are not unbounded but are scaled based on their share in total income, and consequently, the Gini of different sources will add up to the overall Gini of the pretax income distribution. Also, this study considers only the reported income tax after credits and ignores all other taxes including social security taxes, sales taxes and excise taxes. Furthermore, we also do not consider nontaxable sources of income in our analysis. Finally, it is important to note that we consider only the equity dimension of tax law. However, we do not intend to imply that other dimensions (administrative, efficiency, behavior, social) are less important. What may seem unjustified from an equity standpoint may be justified based on efficiency or sound social policy. However, policy makers must consider income source distribution and income source taxability if they want to address the equity dimension of a tax system.
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References Chetty, R., Saez, E., 2005. Dividend taxes and corporate behavior: evidence from the 2003 dividend tax cut. The Quarterly Journal of Economics 120 (3), 791–833. Dunbar, A., 1996. The impact of personal credits on the progressivity of the individual income tax. Journal of the American Taxation Association 18 (1), 1–18. Fei, J.C.H., Ranis, G., Kuo, S.W.Y., 1978. Growth and the family distribution of income by factor components. The Quarterly Journal of Economics 92 (1), 17–53. Iyer, G.S., Schmidt, A., Seetharaman, A., 2008. The effects of standardized tax rates, average tax rates and the distribution of income on tax progressivity. Journal of Accounting and Public Policy 27 (1), 88–96. Iyer, G.S., Seetharaman, A., Englebrecht, T., 1996. An analysis of the distributional effects of replacing the progressive income tax with a flat tax. Journal of Accounting and Public Policy 15 (2), 83–110. Kakwani, N.C., 1976. Measurement of tax progressivity: an international comparison. Economic Journal 87 (March), 71–80. Kakwani, N.C., 1977. Applications of Lorenz curves in economic analysis. Econometrica 45, 719–727. Lerman, R.I., Yitzhaki, S., 1985. Income inequality effects by income source. A new approach and applications to the United States. The Review of Economics and Statistics 67, 151–156. Nygaard, F., Sandstrom, A., 1981. Measuring Income Inequality. Almqvist and Wiksell, Stockholm. Picketty, T., Saez, E., 2007. How progressive is the US federal tax system? A historical and international perspective. Journal of Economic Perspectives 21 (1), 3–24. Ryan, David, 1997. Vertical equity and interstate effects of the state and local tax deduction after the Tax Reform Act of 1986: evidence from tax returns. Advances in Taxation 9, 153–174. Seetharaman, A., Iyer, G., 1995. A comparison of alternative measures of tax progressivity: the case of the child and dependent care credit. The Journal of the American Taxation Association 17 (1), 42–70. Stroup, M.D., 2005. An index for measuring tax progressivity. Economic Letters 86 (2), 205–213. Silber, Jacques, 1989. Factor components, population subgroups and the computation of the Gini index of inequality. The Review of Economics and Statistics 71, 107–115. Suits, D., 1977. Measurement of tax progressivity. American Economic Review 67 (4), 747–752. Young, J.C., Nutter, S.E., Wilkie, P.J., 1999. A re-examination of the effects of personal deductions, tax credits and the tax rate schedule on progressivity and income inequality. The Journal of the American Taxation Association 21 (1), 32–44.
Contents lists available at SciVerse ScienceDirect
J. Account. Public Policy journal homepage: www.elsevier.com/locate/jaccpubpol
Decomposition of progressivity and inequality indices: Inferences from the US federal income tax system Govind S. Iyer a,⇑, Philip M.J. Reckers b a b
Department of Accounting, University of North Texas, Denton, TX 76201, United States School of Accountancy, Arizona State University, Tempe, AZ 85281, United States
a b s t r a c t Vertical equity is an important criterion in evaluating a tax system. Vertical equity has two elements: progressivity and income equality. In this paper, we analyze the vertical equity effects of the US income tax system during 1995–2006 and show that income inequality increased substantially during the period combined with a significant reduction in real progressivity. Using a Lorenz-curve-based graphical method, we decompose progressivity and income inequality indices and identify and quantify how much each source of income contributes to overall progressivity and income inequality. Results for the 1995–2006 period indicate that US income tax treatment of Salaries and Wages income were distributed and taxed progressively and contributed to a decrease in income inequality. However, the treatment of Net Capital Gains not only decreased progressivity, it negated the income inequality reduction achieved by salaries and wages. These results show that to evaluate the vertical equity of a tax system, both income inequality and progressivity indexes must be considered. Additionally, the decomposition method allows policy makers to estimate the progressivity and income inequality effects of marginal changes in income source and how each source is taxed. Ó 2011 Elsevier Inc. All rights reserved.
1. Introduction and motivation Amid fears of a double dip recession and ever increasing budget deficit, tax reform is emerging as one of the most important issues faced by the US Congress. Significant debate on changes to current ⇑ Corresponding author. E-mail addresses: [email protected] (G.S. Iyer), [email protected] (P.M.J. Reckers). 0278-4254/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.jaccpubpol.2011.08.008
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tax law are underway in the Congress and will also be a platform issue on which 2012 presidential candidates will seek to differentiate themselves. At the center of the tax reform debate is the issue of equity or who should bear the tax burden. Supporters of tax increases argue tax increases on the wealthy are appropriate and necessary to ‘‘undo years of stagnant wages, declining incomes and growing (income) inequality,’’ while opponents claim that ‘‘the income tax system has never been more progressive’’. In this study, we seek to enrich the unfolding tax debate by analyzing the inequality and progressivity effects of the US Federal Income Tax system using Internal Revenue Service data from 1995 to 2006. In doing so, we introduce a graphical method of decomposing two widely used income inequality and progressivity indices to precisely identify and quantify how much different sources of income contribute to inequality and progressivity. Two principal factors motivate our study. First, following the healthcare debate, income tax reform promises to be a key battleground in the new Congress and in the 2012 presidential election. Claims are already being made regarding the changing distribution of income and taxes across taxpayers over the past decade, and the need (or lack thereof) for tax reform and redistribution of wealth. While some claim that the income tax system has never been more progressive than at present, others bemoan the increasing inequality of the income distribution in the past decade. For instance, Congressman Kevin Brady, the Ranking Republican House member on the Joint Economic Committee recently claimed that individuals in the top bracket paid the highest share of income tax in decades (press release July 31, 2009).1 On the other hand, speaking for the Democrats, former New York Senator and now Secretary of State Hillary Clinton, cites ‘‘seven (Bush) years of stagnant wages, declining incomes and increasing inequality.’’2 To support their claims, policymakers provide half-truths by ‘‘cherry picking’’ facts that support their position. The same tax bill is praised by some as one that restores fairness, while others pillory it for being blatantly inequitable.3 Economists likewise split on whether higher taxes on the rich are desirable. For instance, regarding the current debate in Congress as to how the budget deficit should be addressed, Princeton Professor and New York Times columnist Paul Krugman calls for higher taxes on the rich4 while Columbia Dean Glenn Hubbard supports extending the Bush tax cuts.5 A recent poll shows a country divided along party lines on what type of tax cut is desirable: fifty-three (53) percent of Americans say that raising taxes on households earning $250,000 or more is a good idea while 38% say it is a bad idea. Allowing the Bush tax cuts to expire for high income taxpayers found support with 65% of Democrats, 57% of independents but with only 33% of Republicans. We believe that in order to advance an analysis free of partisan rhetoric, it is important to understand what has contributed to income inequality in the past and what elements of tax law have mitigated it. From a policy perspective, we showcase the effect of income source distribution on income inequality and tax progressivity in the US over a 12 year period from 1995 to 2006. Our thesis is that, for any meaningful discussion of tax policy changes, it is not sufficient to simply focus on the distribution of income. Current tax law does not treat all income equally. There are tax favored income streams and there are highly taxed income streams. Consequently, after-tax income distribution is dependent not only on how aggregate before-tax income is distributed but also on the sources of before-tax income (because different sources are taxed differently). Therefore, policy discussions regarding how income inequality can be mitigated cannot be addressed unless there is a clear understanding of how different income sources (some fully taxed and some tax favored) are distributed among different income classes. In contrast, policy and political discussions seem to be fixated on the tax rate schedule and tend to treat all income as homogeneous. The hesitation in political and policy circles is understandable because changes to taxability of different income
1 Congress of the United States, Joint Economic Committee, Congressman Kevin Brady, Ranking Republican House Member, News Release, July 31, 2009, Press Release #111-19. 2 The Inequality Myth, by Brad Schiller, The Wall Street Journal Online, March 10, 2008. 3 For instance, when debating the (Bush) tax reform bill in 2001, Sen. Baucus called it an equitable tax reform while Sen. Conrad characterized it as an unfair tax bill. Congressional Record – Senate 107th Congress, 1st Session, 147 Cong Rec S 5028 Restoring Earnings to Lift Individuals and Empower Families (Relief) Act of 2001, May 17, 2001; Sen. Baucus: ‘‘[t]he bill before us today will make the tax system more progressive than under current law.’’; Sen. Conrad: ‘‘There is something wrong with this bill, and what is wrong is it is not fair.’’ 4 The Tax Cut Racket, The New York Times, September 17, 2010, Section A, p. 27, Op-Ed Columnist; Now That’s Rich, The New York Times, August 23, 2010, Section A, p. 23, Op-Ed Columnist. 5 Fairness and the Capital Tax Fetish, The Wall Street Journal, August 9, 2010, Opinion Journal.
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sources involve not just equity considerations but also economic, efficiency, productivity and political considerations. Nonetheless, we want to make it clear that equity considerations cannot be fully addressed unless the causes of inequity are fully acknowledged. The cause of inequality and progressivity changes are not merely due to changes in the distribution of pre-tax income or the tax rate schedule, but also due to how each source of pre-tax income is distributed and taxed. In addition, it is inadequate to rely only on summary indices when addressing vertical equity issues.6 Several studies in both accounting and economic literature have used summary indices to document the progressivity and inequality effects of different tax systems (Seetharaman and Iyer, 1995; Young et al., 1999; Ryan, 1997). For example, Iyer et al. (1996) used the Kakwani and Suits indices to document the vertical equity effects of replacing the progressive income tax with a flat tax. Likewise, Dunbar (1996) used the Kakwani and the Suits index to estimate the effect of personal credits on federal income tax progressivity. While summary indices are useful in documenting the changes in income and/or tax distributions, they do not identify or quantify the sources that underlie such changes. From a methodological perspective, we introduce a graphical counterpart to Silber (1989)’s matrix method of decomposing the Gini index and also extend it to commonly used inequality and progressivity indexes (Kakwani, 1976). The advantages of the graphical method are (a) it is based on the well documented Lorenz and concentration curves; (b) it is easy to compute without the complications of the matrix methods and therefore easily understood by non-economists and (c) it is intuitive, graphical and the results can be easily highlighted and showcased. Based on our literature review, this is the first paper that has attempted to extend the Lorenz curve decomposition method to progressivity and inequality indexes (at least in the tax accounting area). From a policy standpoint, the decomposition of the indices allows lawmakers and the public to gauge the impact of tax law changes on vertical equity. To summarize, this paper has a twofold purpose: (i) document the income inequality and progressivity changes in the US tax system over a 12 year period between 1995 and 2006; and (ii) develop a method that can isolate the inequality and progressivity effects by source of income.7 Results indicate that income inequality increased over the 12 year period from 1995 to 2006. While nominal progressivity increased over the same time, real progressivity measured after controlling for changes in before-tax income distribution decreased over the period. The decrease in real progressivity can be attributed to increasing inequality in before-tax incomes and protection of some sources of income (capital gains among them) from progressive taxation. With respect to income sources, salaries and wages income contribute to greater equality and greater progressivity. The positive effect of salaries and wages is more than counterbalanced by the negative effect of capital gains. Unequal distribution of capital gains causes an increase in income inequality and reduction in total progressivity. Thus, despite the ‘‘rich’’ paying a greater share of total taxes than ever before, income inequality of ‘‘after-tax income’’ continued to rise. Our results are consistent with those observed by Picketty and Saez (2007). Picketty and Saez (2007) documented the progressivity of the US Federal Tax System (individual income tax, payroll tax, federal estate and gift tax, and federal corporate taxes). They found that between 1964 and 2004, the US Federal Tax system became less progressive. While our results are consistent with those of Piketty and Saez, our study is distinct because (i) we focus on individual income tax, (ii) we separate the progressivity and the inequality effects by source, and (iii) we show how the distribution of income that is subject to special tax rates impacts overall progressivity and income inequality. The remainder of the paper is organized as follows: the next section provides a brief overview of the indices used in this paper, an explanation of how they are computed and a discussion of the relationship between progressivity and income inequality based indices. In the third section, we delineate the Lorenz-Curve-based graphical method for decomposing the indices. In the fourth section, we present the data and results of our analyses of the 1995–2006 12 year period. We end the paper with a summary, conclusion, and limitations.
6
Gini based indexes such as the Suits index (Suits, 1977) or the Kakwani indices (Kakwani, 1976). In contrast to the inter-period decomposition presented in Iyer et al. (2008) in which the Gini difference between 2 years is split into average tax rate effect, standardized tax rate effect and pre-tax income effect, the decomposition method discussed in this paper is an intra-period decomposition. Inequality and progressivity indices (of any single year) are split into relative contributions from various income sources. 7
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2. Inequality and progressivity indices Equity is an important criterion in evaluating a tax system. Citizens demand a tax system that they perceive to be ‘‘fair’’; voluntary compliance indeed depends on acceptance of the tax system as fair and equitable. Equity, however, has two dimensions: horizontal equity and vertical equity. A system is defined as horizontally equitable if taxpayers with equal incomes pay equal taxes. Vertical equity deals with the distribution of taxes across income groups. Vertical equity is currently a highly contested issue; it is accordingly the focus of this article. The vertical equity of a tax system relates to the distribution of taxes across taxpayers; and the vertical equity of a tax system is measured by the change in the after-tax net income distribution vis-à-vis the before tax income distribution. However, a second concept of vertical equity also exists. In a progressive tax system, higher income earners pay a greater share of their income in tax as compared to lower income earners. The distribution of tax burden across income strata constitutes a second measure of vertical equity. Most indices that measure progressivity relate tax shares to income shares while most indices of income inequality relate pre-tax income shares to post-tax income shares (Stroup, 2005). The Gini index forms the basis of almost all inequality and progressivity indices, including the Kakwani indices. Nygaard and Sandstrom (1981) and Seetharaman and Iyer (1995) provide a detailed discussion of various indexes of income inequality and tax progressivity. We chose to focus on the Kakwani indices of inequality and progressivity in this paper because they are among the most widely used in economic literature and are also relatively simple to understand. 2.1. Computation of the Gini Index A Lorenz (Income) Curve shows the relation between the cumulative proportion of taxpayers on the x-axis (arrayed by size of income from lowest to highest) and the cumulative proportion of their corresponding income on the y-axis. Tax curves are similar to Lorenz curves, except one plots the cumulative proportion of taxes paid (instead of income) on the y-axis. A Lorenz curve is a graphical representation of the income distribution and a tax curve is a graphical representation of the tax distribution. Most income inequality and progressivity indices are based on Lorenz income and tax curves and their related Gini coefficients (Gini). The Gini coefficient is the most widely used measure of income inequality and is measured as twice the area bounded by the income curve and the egalitarian line (line of perfect equality which is graphically represented by a 45° line).8 See Fig. 1. If income becomes more unequal, the line moves to the right and the area bounded by the curve and the egalitarian line increases, thereby increasing the Gini index value (representing greater inequality). Thus, higher values of the Gini index denote greater inequality. In this study we consider two widely used Gini based indices: the Kakwani index of income inequality – K(I), and the Kakwani index of progressivity – K(P). We demonstrate the computation of these indices using data from IRS Statistics of Income Bulletin for the year 2006.9 Extracted information is reproduced in Table 1. Table 1, column A shows the cumulative share of income recipients; column B shows the adjusted gross income (AGI or before-tax income) corresponding to the income intervals; columns C and D shows the shares of the salaries and wages and net capital gain, column E shows cumulative tax (after credit) shares and column F shows the cumulative proportions of after tax income. 2.2. Kakwani index of inequality K(I) The Kakwani index of income inequality, K(I), measures the change in income inequality as result of the tax system. That is, it compares the before-tax income distribution (curve) to the after-tax income distribution (columns B and F in Table 1). K(I) is defined as the difference between the Gini indexes of 8 Intuitively, it measures how far an income distribution is from the egalitarian line. The farther the income curve is from the egalitarian line, the greater is the income inequality. 9 Statistics of Income Bulletin, Fall 2008, Vol. 28, No. 2, Table 1 (p. 21) and Table 2 (p. 40).
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Gini Index of Inequality = 2 x (Area bounded by income curve and egalitarian line) Fig. 1. Computation of the Gini Index of Inequality. Gini Index of Inequality = 2 (Area bounded by income curve and egalitarian line).
the before-tax and after-tax income distributions; that is, K(I) = Ginibefore-tax income Giniafter-tax income. A change in either the before-tax income distribution and/or the tax system influences the value of K(I). If the two (before and after tax) income distributions are identical, then the two corresponding Lorenz curves perfectly overlap, their Gini indexes are the same and K(I) equals zero. A zero value indicates that the tax system did not affect income inequality. If the after-tax income is more equal than the before tax income distribution, its curve moves toward the egalitarian line and lies to the left (and above) the before-tax income curve (see Fig. 2). The before-tax income Gini index is greater than the after-tax income Gini index, resulting in a positive value for K(I) index. Larger positive K(I) Index values indicate greater vertical equity (i.e., less inequity). Thus, for year 2006 the K(I) index is K(I) is computed as 0.601–0.570 = 0.031 (see Table 1).
2.3. Kakwani index of progressivity K(P) The Kakwani index of progressivity, K(P), measures vertical equity by comparing the distribution of tax burden across income strata (that is the distribution of tax burden is compared to the distribution of income (Kakwani, 1976)). For a proportional (or flat) tax, the before-tax income curve and the tax curve will overlap since the cumulative proportion of tax paid will be equal to the cumulative proportion of income earned regardless of the income level. For a progressive tax, the tax curve moves away and to the right of the before-tax income curve (see Fig. 3). That is, the cumulative proportion by tax paid by lower income earners is less than the cumulative proportion of income earned by them. The Gini index for the tax curve is referred to as the concentration coefficient (Ctax). The Kakwani index of progressivity denoted as K(P) is measured as the difference between the tax concentration coefficient and the before-tax income Gini index. That is K(P) = Ctax Ginibefore-tax income. Like the K(I) index, a change in either the before-tax income distribution and/or the tax system influences the value of K(P).
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Proportion of taxpayers A
Before-tax income B
Salaries and wages C
Net capital gain D
Cumulative proportions – Taxpayers arrayed by size of income from lowest to highest Under $10,000 0.1726 0.0147 0.0175 0.0031 Under $15,000 0.2589 0.0327 0.0371 0.0053 Under $20,000 0.3394 0.0562 0.0643 0.0079 Under $25,000 0.4125 0.0836 0.0979 0.0103 Under $30,000 0.4770 0.1132 0.1342 0.0131 Under $40,000 0.5812 0.1738 0.2091 0.0192 Under $50,000 0.6600 0.2328 0.2805 0.0263 Under $75,000 0.7989 0.3754 0.4491 0.0492 Under $100,000 0.8810 0.4937 0.5869 0.0766 Under $200,000 0.9700 0.6915 0.8080 0.1628 Under $500,000 0.9930 0.8017 0.9079 0.2895 Under $1,000,000 0.9974 0.8509 0.9425 0.3858 Under $1,500,000 0.9985 0.8733 0.9554 0.4420 Under $2,000,000 0.9990 0.8868 0.9623 0.4811 Under $5,000,000 0.9997 0.9232 0.9787 0.6002 Under $10,000,000 0.9999 0.9443 0.9868 0.6879 All Income 1.0000 1.0000 1.0000 1.0000 Share in total income 1.0000 0.6712 0.0959 Area under the curve 0.1994 0.2367 0.0312 Gini index 0.6013 0.5266 0.9376 K(P) index 0.0212 0.1923 0.0119 K(I) index 0.0306 0.0296 0.0351
Tax after credits E
After-tax income F
0.0007 0.0030 0.0077 0.0150 0.0252 0.0518 0.0836 0.1758 0.2638 0.4683 0.6412 0.7333 0.7764 0.8025 0.8725 0.9111 1.0000
0.0167 0.0369 0.0632 0.0935 0.1259 0.1914 0.2543 0.4042 0.5268 0.7236 0.8248 0.8678 0.8873 0.8990 0.9305 0.9491 1.0000
0.0934 0.8132
0.2147 0.5707
For a proportional tax, K(P) will be zero and for a progressive tax, K(P) will be positive.10 Larger values of K(P) indicate greater progressivity. For 2006, the K(P) index is computed as 0.813–0.601 = 0.212 (see Table 1 and Fig. 3). 3. Decomposition of the Kakwani Indices 3.1. Decomposing the Gini index using Silber method Silber (1989) demonstrates a mathematical method of decomposing the Gini coefficient by income source.11 According to Silber (1989), the Gini index may be written (using matrix notation) as
Gini ¼ e0 Gs where e is a column vector of n elements where each element is equal to 1n (and e0 is the corresponding row vector), s is a column vector of n elements being respectively equal to s1, s2, . . ., sn, G is an n by n matrix whose elements gij are equal to 1 when i > j, +1 when i < j, and 0 when i = j. For the Gini index of income inequality, the column vector e represents shares of income recipients, and the column vector s represents the corresponding income shares. Let us assume that total income is made up of k sources. The Gini index of the income from source i is expressed using the formula provided above, except for replacing share si (share of income recipient in total income) by yi (share of income recipient in income from source i)
Ginii ¼ e0 Gyi
10 For a regressive tax, the tax curve moves away and to the left of the income curve. The area bounded by the two curves is considered negative. Thus, larger negative values of the K(P) indicate greater regressivity. 11 Other researchers have demonstrated similar methods for decomposing the Gini coefficient. See for example Kakwani (1977), Fei et al. (1978), and Lerman and Yitzhaki (1985).
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Fig. 2. Computation of the Kakwani’s Index of Inequality – K(I). Kakwani’s Index K(I) = 2 (Area bounded by the Before-Tax and After-Tax Income curves). Area under Before-Tax Income curve = 0.1994. Area under the After-Tax income curve = 0.2146. Area bounded by the curves = 0.0152. K(I) = 2 (0.2146–0.1994) = 0.0304.
Fig. 3. Computation of the Kakwani’s Index of Progressivity – K(P). Kakwani’s Index K(P) = 2 (Area bounded by the Before-Tax Income curve and Tax curve). Area under the Lorenz curve of before-tax income = 0.1994. Area under the tax curve = 0.0934. Area bounded by the curves = 0.106. K(P) = 2 (0.1994–0.0934) = 0.2119.
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The Gini for each source may be computed by using the above formula. Finally, the Gini index of income inequality for the total income is simply the sum of all Gini indices of all the income sources scaled by their respective share in total income.
GiniTotal ¼
k X
Si I i
i¼1
where si is share of income source i in total income. The graphical counterpart to decomposing the Gini coefficient consists of constructing Lorenz curves for each income source and computing a Gini for each income source. The Gini multiplied by the relative importance of the income source in total income (proportion) is the contribution of that source to the overall Gini index. To illustrate, Table 1 column A shows the cumulative proportion of taxpayers, and column C shows the corresponding cumulative proportion of salaries and wages (S&W). Using the method described in Section 2.1, we can compute the Gini index for S&W as twice the area bounded by the egalitarian line and the S&W curve. This area is 0.263 and the Gini is 0.526.12 The Gini for Capital Gains (CG) calculated likewise is 0.938 (see Table 1). Multiplying by their respective shares in total income, we can say that S&W contributes 0.353 and CG contributes 0.09 to the overall Gini value of 0.601. That is, S&W constitutes 67% of total income and accounts for 58% of overall inequality and CG constitutes 9.5% of total income and accounts for 15% of overall inequality. 3.2. Decomposing the Kakwani index of inequality K(I) We continue with the same illustration to demonstrate how the K(I) index is decomposed. The Gini for before-tax income distribution is 0.601 while the Gini for S&W is 0.526. That is, the before-tax income distribution is less equal than the S&W distribution (its curve is closer to the egalitarian line, see Fig. 4 and Table 1). Recall that the overall K(I) index is computed as K(I) = Ginibefore-tax income Giniafter-tax income. The K(I) for total income is 0.601–0.570 = 0.031. To compute the effect of S&W on the K(I) index, we replace the before-tax income distribution by the S&W distribution and scale it based on S&W’s share in total income. That is, K(I) share of S&W is computed as K(I)S&W = (GiniS&W Giniafter-tax income) Share of S&W = (0.526–0.570) 0.671 = 0.0296. We find that S&W is more equally distributed than the after-tax income distribution. That is, compared to the after-tax income distribution, S&W results in an increase in equality of 0.0296. In percentage terms of the overall K(I) index of 0.031, it may be expressed as a 95% increase in equality. Following the same method detailed above, we compute the separable equity effect of CG. Table 1 also shows that the Gini index of Capital Gains is 0.938. As compared to the before-tax income, CG is more unequally distributed (concentrated at higher incomes and its curve is farther away from the egalitarian line, see Fig. 4). K(I) for CG is computed as K(I)CG = (GiniCG Giniafter-tax income) Share of CG = (0.938–0.570) 0.096 = 0.0353. That is, compared to the after-tax income distribution, CG results in a decrease in equality of 0.0353. In percentage terms of the overall K(I) index of 0.031, it may be expressed as a 114% decrease in equality. 3.2.1. Decomposing the Kakwani index of progressivity K(P) Decomposition of the K(P) index follows an identical procedure. Recall that K(P) index is computed as the difference between the Gini index of before-tax income and the concentration coefficient of tax. For 2006, K(P) = Ctax Ginibefore-tax income = 0.813–0.601 = 0.212. Because S&W is more equally distributed (G = 0.526), it has a vertical equity enhancing effect on K(P). To compute the separable effect of S&W on K(P) we replace the before-tax income distribution with S&W and scale it based on S&W’s share in total income. That is, K(P)S&W = (Ctax GiniS&W) Share of S&W = (0.813–0.526) 0.671 = 0.192. That is, of the overall K(P) progressivity index of 0.212, S&W accounts for 91%. 12 Salaries and Wages constitute 67.12% of total income. Following Silber (1989), the contribution of Salaries and Wages to the overall Gini index is 0.526 0.6712 = 0.353. Note that this is not the Gini of S&W, but the contribution of S&W to the overall Gini value of 0.601.
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Fig. 4. Vertical equity impact of salaries and wages and capital gains. Area A = Gain in vertical equity due to salaries and wages. Area B = Loss in vertical equity due to Capital Gain.
In contrast, CG is less equally distributed than before-tax income (Gini = 0.938). Consequently, it has a vertical equity decreasing effect on overall K(P). The separable value of CG is computed as K(P)CG = (Ctax GiniCG) Share of CG = (0.813–0.938) 0.0959 = 0.012. When compared to the CG distribution, the tax distribution is regressive. That is, of the overall K(P) value of 0.212, CG contributes to a 6% reduction in progressivity. 3.2.2. Nominal progressivity and real progressivity Because K(P) is computed as the difference between Gini index of before-tax income and concentration coefficient of tax, any change to the before-tax income distribution will cause the K(P) value to change even if there is no change in the tax system. Nominal progressivity, K(P)nominal, simply describes how progressive the tax system is for a given income distribution. When K(P)nominal is compared over time, one cannot unequivocally attribute the differences between the K(P) values to changes in the tax system; a change in the pre-tax income distribution may have caused the K(P) values to be different. Note that K(P)nominal value for the current year is based on the current income distribution and the current tax distribution. To isolate the effect of just the tax system, a K(P)real index is computed in which the income distribution is held constant and the tax distribution is allowed to vary so that only the effect of changing tax system is measured. K(P)real computes the K(P) value for each year by assuming that the income distribution is the same as the 1995 income distribution. Based on the A new tax distribution is then simulated for this income distribution based on the current year tax distribution data. For example, the real progressivity index for 2006 is based on the 1995 income distribution and 2006 tax data. Because K(P)real for every year is based on the 1995 income distribution (only the tax system changes) they can be compared over time as well. Besides the tax rate, two factors determine the tax share of a group: the proportion of taxpayers in the group (distribution of taxpayers) and the proportion of income received by the group (distribution of income to the taxpayers). We adjust for these two elements in computing the simulated tax distribution. The simulated tax share for each income group for the 1995 income distribution (based on the current year tax data) equals
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year 1995 income share current year income share year 1995 proportion of taxpayers in the group current year proportion of taxpayers in the group
Current year tax share
The first element is the tax share based on current year tax data, the second element scales it so that it reflects the 1995 income share (of that group of taxpayers) and the third element scales it to reflect the 1995 proportion of taxpayers in that group.13 The index K(P)real for 2006 measures what the progressivity would have been had the year 2006 tax rates been applied to the 1995 income distribution.14 3.3. Separating the equity effect of income subject to regular tax rates and special tax rates The decomposition method described above shows the impact of various sources of income on the K(I) and K(P) indices. It does so by holding the tax curve constant. However, in order to fully measure the impact of distribution of income subject to special tax rates, it is necessary to separate such income and the tax incidence on such income. During the period 1995–2006, long-term capital gains and qualified dividends were taxed at a lower rate while all other income was taxed at the taxpayers’ regular marginal rate. Consequently, we created two groups of income: (i) net long-term capital gains and qualified dividends (special income), and (ii) all other income except net-long term capital gains and qualified dividends (regular income). We also separated the tax on special income (special tax) and regular income (regular tax).15 The Kakwani indices K(I) and K(D) were computed based on these distributions. For instance, the K(P) index for special income (long-term capital gains and qualified dividends) considered only the distribution of special income and the tax on special income, while the K(P) index for regular income was based on distribution of regular income and regular tax. 4. Results and analysis 4.1. Overall results Using the above methods, we analyze the progressivity and income inequality measures for each year from 1995 to 2006. The overall K(P) and the K(I) indices for the 1995–2006 are presented in Table 2. The K(I) index shows a decreasing trend in vertical equity and likewise real progressivity has also decreased over time. Note that real progressivity has dramatically decreased after the Bush tax cuts in went into effect in 2003. The trend in K(I) and K(P) values over 1995–2006 period is shown in Fig. 5A and B. Decomposition of the indices into the various sources provides a more consistent explanation of the observed changes with respect to the two major sources contributing to income inequality and progressivity. Salaries and wages increase progressivity and decrease income inequality every year (except 1995). Conversely, capital gains decrease progressivity and increase income inequality every year. 4.2. Inequality effects In Table 3 we show the various income source components, K(I) and its percentage of the overall index value. The same items for the K(P) index are shown in Table 4. 13 Because the total income recipients, total income and total tax collected is not be the same in the 2 years, tax shares computed using the above method is scaled so that that the sum of the tax shares equals 1. 14 This is an estimate of the tax shares. If microdata is available, actual tax burdens can be computed by applying the new tax rules to individual tax returns. 15 This data was also collected from www.irs.gov/taxstats/indtaxstats. The table is Returns with Modified Taxable Income: Tax Generated – SOI Bulletin article – Individual Income Tax rates and Tax Shares, Table 2.
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Table 2 Overall K(I) and K(P) indices for the years 1995–2006. Year
Kakwani K(I) index
Kakwani K(P)nominal index
Kakwani K(P)real index
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
0.0320 0.0332 0.0331 0.0332 0.0343 0.0355 0.0343 0.0340 0.0300 0.0302 0.0307 0.0306
0.1997 0.1994 0.1957 0.1988 0.1983 0.1970 0.2070 0.2268 0.2222 0.2196 0.2162 0.2119
0.1997 0.1808 0.1571 0.1441 0.1285 0.1136 0.1370 0.1686 0.1575 0.1370 0.1207 0.1070
Comparing the K(I) values of income sources over the 12 year period, we find that S&W consistently produces equality gains vis-à-vis the after-tax income distribution (columns C and D of Table 3) while CG consistently produces equality losses (columns K and L of Table 3). The equality gains of the S&W distribution are more than offset by the equality losses of the CG distribution. S&W forms at least 50% of total income every year while the share of CG has more than doubled over the same period – from a low of 4.2% in 1995 to 9.6% in 2006. The increasing equality gains of S&W over the years and the increasing equality losses of CG over the years also indicate that (i) despite the doubling of CG’s share in total income, S&W not only continues to be the most important source of income to low-income taxpayers but its importance has been rising among them; (ii) the bulk of the increase in CG’s share in total income has been garnered by high-income taxpayers and (iii) the tax structure has not fully offset the equality losses caused by the unequal distribution of CG. This is likely the result of CG being taxed at a preferential lower rate. Because long-term capital gains are taxed at a maximum 15% rate, the tax paid on capital gains by higher income earners fall below the tax rate paid by many lower income earners whose incomes predominantly consist of salaries and wages and/or Schedule C income. This has the effect of pushing the after-tax income distribution away from the egalitarian line thereby increasing inequality. Note that increases in income inequality are correlated with performance of stock market returns. For example, large returns in the stock market during 1998, 1999 and the first half of 2000 (when the NASDAQ first reached 5000) coincide with large increases in inequality due to CG. In contrast, low or negative returns (during 2001 and 2002) coincide with relatively modest inequality increases due CG. As shown in Fig. 6, inequality reduction of S&W is offset by the inequality increase of CG every year. Dividend income results in inequality increase every year. The inequality increases are more pronounced after 2003 when qualified dividends began to be taxed a lower tax rate. Like CG, dividend income is unequally distributed to high-income taxpayers and the unequal distribution is not fully offset by the tax structure. The impact of dividend income is modest because of its low relative share in total income. Dividend income forms about 2% of total before-tax income each year. Despite its low share in total income, its impact on income inequality is rather large; about 10% before qualified dividend change in 2003 and about 15% (17.5% in 2006) after 2003. This also supports the findings of Chetty and Saez (2005) that the large tax rate cut on individual dividend income in 2003 was followed by an unusually large number of firms initiating dividends or increasing dividends to shareholders. The change was particularly pronounced in firms with strong principals whose tax incentives changed (i.e., high income taxpayers). The effects of Schedule C income are rather modest for most years and generally lead to inequality reduction. The modest inequality reduction due to Schedule C income may be attributed to a more equal distribution of Schedule C income vis-à-vis after-tax income and its taxability as ordinary income using the regular graduated tax rate schedule.
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(A)
(B)
Fig. 5. A K(I) index values from 1995 to 2006. B K(P)nominal and K(P)real index values from 1995 to 2006.
4.3. Progressivity effects About 85–90% of the overall progressivity is explained by S&W (see columns C and D of Table 4). S&W is the largest component of total income. It is also more equally distributed than total before-tax income. Also, the tax on S&W is based on the regular graduated tax rate schedule. Consequently, S&W has the greatest impact on progressivity. In contrast, CG reduces progressivity every year (about 3–6%;
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Year
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
Salaries and wages
Interest
A Value
Overall B %
C Value
D %
E Value
F %
G Value
Dividends H %
I Value
Sch C income J %
K Value
Capital gain L %
M Value
All other sources N %
0.0320 0.0332 0.0331 0.0332 0.0343 0.0355 0.0343 0.0340 0.0300 0.0302 0.0307 0.0305
100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00
0.0013 0.0039 0.0104 0.0140 0.0160 0.0167 0.0047 0.0006 0.0060 0.0161 0.0264 0.0296
4.02 11.87 31.32 42.04 46.56 47.08 13.7 1.76 20.09 53.41 85.92 97.00
0.0001 0.0001 0.0002 0.0004 0.0005 0.0011 0.0009 0.0004 0.0005 0.0009 0.0019 0.0028
0.48 0.27 0.71 1.10 1.39 3.16 2.86 1.04 1.65 3.13 6.16 9.18
0.0032 0.0035 0.0041 0.0037 0.0037 0.0039 0.0029 0.0025 0.0030 0.0041 0.0044 0.0053
10.02 10.45 12.31 11.27 10.73 11.13 8.58 7.23 10.05 13.69 14.26 17.45
0.0024 0.0014 0.0008 0.0005 0.0003 0.0001 0.0003 0.0001 0.0009 0.0013 0.0013 0.0019
7.42 4.15 2.39 1.54 0.97 0.33 0.04 0.02 3.25 4.46 4.27 6.35
0.0142 0.0199 0.0251 0.0293 0.0327 0.0349 0.0208 0.0164 0.0194 0.0272 0.0337 0.0352
44.36 59.76 75.72 88.14 95.32 98.54 60.45 48.19 64.83 90.07 109.59 115.12
0.0111 0.0124 0.0133 0.0133 0.0131 0.0123 0.0144 0.0154 0.0140 0.0154 0.0185 0.0188
34.65 37.23 40.19 39.98 38.15 34.58 41.85 45.34 46.81 50.99 60.18 61.60
Note: Equality gains are expressed in bold characters. Also note that index and percentage value of each component sums to the overall value and overall percentage respectively for each year (each row).
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Table 3 Decomposition of the K(I) index for 1995–2006.
Year
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
Salaries and wages
Interest
Sch C income
Capital gain
A Value
Overall B %
C Value
D %
E Value
F %
G Value
Dividends H %
I Value
J %
K Value
L %
M Value
All other sources N %
0.1997 0.1994 0.1957 0.1988 0.1983 0.1970 0.2070 0.2268 0.2222 0.2196 0.2162 0.2119
100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00
0.1731 0.1747 0.1747 0.1782 0.1783 0.1775 0.1807 0.1945 0.1919 0.1943 0.1955 0.1923
86.67 87.61 89.25 89.67 89.90 90.15 87.30 85.75 86.36 88.51 90.41 90.79
0.0084 0.0081 0.0330 0.0070 0.0063 0.0059 0.0065 0.0058 0.0044 0.0035 0.0033 0.0037
4.20 4.07 3.79 3.54 3.18 3.02 3.14 2.56 1.99 1.58 1.52 1.73
0.0019 0.0018 0.0014 0.0012 0.0015 0.0013 0.0016 0.0019 0.0015 0.0011 0.0010 0.0006
0.95 0.88 0.70 0.62 0.75 0.67 0.77 0.82 0.68 0.50 0.47 0.26
0.0071 0.0078 0.0079 0.0082 0.0080 0.0081 0.0086 0.0097 0.0104 0.0106 0.0104 0.0106
3.54 3.90 4.03 4.13 4.05 4.09 4.17 4.28 4.70 4.82 4.82 5.00
0.0049 0.0072 0.0087 0.0102 0.0116 0.0125 0.0076 0.0052 0.0068 0.0095 0.0115 0.0119
2.44 3.62 4.47 5.14 5.86 6.33 3.65 2.31 3.05 4.32 5.31 5.63
0.0141 0.0143 0.0131 0.0143 0.0158 0.0166 0.0171 0.0202 0.0207 0.0196 0.0175 0.0166
7.08 7.16 6.69 7.17 7.99 8.42 8.28 8.90 9.30 8.91 8.10 7.86
Note: Progressivity Losses are expressed in bold characters. Also note that index and percentage value of each component sums to the overall value and overall percentage respectively for each year (each row).
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Table 4 Decomposition of the K(P) index for the years 1995–2006.
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Fig. 6. Percentage of K(I) of source of income to overall K(I) for 1995–2006.
see columns K and L of Table 4). The reduction in progressivity may be attributed to a top heavy capital gain distribution and being taxed at preferential rates. The negative effect of net capital gains was the highest in the 3 years 1998 through 2000 and again in 2005 and 2006 indicated by the high negative numbers during those years. As mentioned earlier, these periods coincide with the high equity return, resulting in large gains to high-income earners that were preferentially taxed. Fig. 6 shows that while S&W contributes overall progressivity (above the x-axis, positive values), CG reduces progressivity (below the x-axis, negative values). The contribution of dividend income to progressivity is rather modest due to its low share in total income. Additionally, contribution of dividend income to progressivity reduces significantly after the 2003 tax change of taxability of dividend income (see Fig. 7). Tables 3 and 4 (columns C and D) show that the source that causes the greatest inequality reduction also contributes the most to progressivity and vice versa (columns K and L). For instance, the greatest inequality reduction was achieved by S&W in 2006 (97%). In the same year S&W contributed the most to progressivity (91%). Likewise, the smallest decrease to progressivity due to capital gains occurred in 2002 (2.3%). In the same year, capital gains led to the smallest inequality reduction (48%). The decomposition method allows us to examine each individual source separately and obtain intuitive explanations for the equity impacts of a tax system. The decomposition method pinpoints how much each source contributes to reduction (or increase) in inequality and progressivity. Consequently, policy makers can assess the marginal impact of changes in sources of income and how each source is taxed on overall progressivity and income inequality. 4.4. Separating the effects of long-term capital gains and qualified dividends Long-term capital gains and qualified dividends were subject to special rates during 1995–2006. To fully measure the impact of such income on K(I) and K(P), we computed separate K(I)s and K(P)s for such ‘‘special income’’ and the remaining ‘‘regular income.’’ Results are provided in Table 5. Note that the K(I) and K(P) values for regular income are almost the same as the overall K(I) and K(P) values (in many cases they are even higher). In contrast, the K(I) and K(P) values for special income are close to zero. These values indicate that while tax on regular income is progressive and
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Fig. 7. Percentage of K(P) of source of income to overall K(I) for 1995–2006.
Table 5 K(I) and K(P) indexes for regular tax rate items and special tax rate items for the years 1995–2006. Year
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
Overall index
Index for regular tax rate items (all income except long-term capital gains and qualified dividends)
Index for special tax rate items (long-term capital gains and qualified dividends)
K(I)
K(P)
K(I)
K(P)
K(I)
K(P)
0.0320 0.0332 0.0331 0.0332 0.0343 0.0355 0.0343 0.0340 0.0300 0.0302 0.0307 0.0305
0.1997 0.1994 0.1957 0.1988 0.1983 0.1970 0.2070 0.2268 0.2222 0.2196 0.2162 0.2119
0.0308 0.0316 0.0326 0.0336 0.0349 0.0365 0.0346 0.0297 0.0306 0.0315 0.0325 0.0325
0.1982 0.1979 0.2001 0.2071 0.2081 0.2087 0.2126 0.2254 0.2286 0.2322 0.2327 0.2296
0.0001 0.0001 0.0061 0.0061 0.0059 0.0055 0.0053 0.0052 0.0070 0.0052 0.0046 0.0044
0.0001 0.0001 0.0216 0.0254 0.0245 0.0228 0.0222 0.0218 0.0433 0.0314 0.0276 0.0263
reduces before-tax income inequality, the tax on special income is almost proportional and does not significantly impact before-tax income inequality. Indeed, the smaller overall K(P) values as compared to the K(P) values of the regular income indicate that distribution of special income and special tax contributes to a decrease in overall progressivity. Similarly, the tax on regular income mitigated before-tax income inequality, while the tax on special income had little or no effect on income inequality. Clearly, high income taxpayers with large long-term capital gains and qualified dividends are able to shield much of their total income from the graduated tax rate structure. The relative effects of regular income and special income for 2006 are illustrated in Fig. 8.
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Fig. 8. Distribution of regular tax income and special tax income for 2006.
5. Summary, conclusion and limitations 5.1. Summary In this paper, we analyzed the progressivity and income inequality effects of the US income tax system for the years 1995–2006 using two commonly employed Kakwani indices. Income inequality increased during this period accompanied by a decrease in real progressivity. While nominal progressivity exhibited an increasing trend during this period, the increase was due to changing income distribution: higher income taxpayers getting an increasing share of before tax income. Inequality increase and real progressivity decrease resulted because progressive tax rates applied to only certain sources of income, salaries and wages, interest, schedule C income; yet, those income sources diminished in importance as compared to capital gains. Using a graphical, Lorenz curve based method to decompose the Kakwani indices, we show that salaries and wages contributed to the greatest increase in progressivity and the biggest reduction in income inequality. However, the treatment of net capital gains contributes to a decrease in progressivity and more than negates the inequality reduction achieved by salaries and wages. 5.2. Discussion and conclusion Vertical equity is an important criterion in evaluating a tax system. The two main culprits increasing inequality and decreasing progressivity are the distribution of capital gains and dividend income along with the tax incident on them. Not only are capital gains concentrated at the high end of the income scale, they are also taxed preferentially. Not only does CG make the before-tax income unequal, it also renders the after-tax income even more unequal since high-income taxpayers with large capital gains are less impacted by the graduated rate structure. Consequently, we observe the dual effect of inequality increase as measured by the K(I) index but also a real progressivity loss as measured by the K(P)real index. That is, the distribution of pre-tax capital gains and the preferred rate on capital gains provides substance to the oft repeated statement that the ‘‘rich are becoming richer’’ vis-à-vis the middle income and lower income taxpayers.
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Changes to the existing tax structure seem imminent as Congress grapples with alternatives to deal with the growing budget deficit. Most of the discussion in popular press is centered on how high the tax rates ought to be for different income groups and how the tax burden ought to be distributed. What we show in this paper is that, it is important to focus on how different types of income are distributed and how each type of income is taxed. For instance, the equity effect of raising the tax rates on ordinary income is likely to be very different than raising the tax rates on capital gains. Vertical equity can be enhanced, for instance, by (i) subjecting capital gains to a graduated rate structure the same or similar to ordinary income; and/or (ii) making the rate structure on other income even more progressive by raising tax rates on high income earners. The first choice is likely to face very stiff political opposition from very high income taxpayers who derive a large percentage of their income from capital gains. The second choice is likely to face very stiff political opposition from a larger group of high but still less-high income taxpayers who derive a large percentage of their income from salary and wages. Both groups have significant political influence. The former, in part because of their wealth, and size of political contributions. The latter, in part because of their number of potential votes. Nevertheless, there are limits to how much a tax system can address the issue of pre-tax income inequality when (i) inequality of pre-tax incomes continue to rise and (ii) certain sources of income are protected from progressive taxation and (iii) and wealth is protected by favorably inheritance tax exemptions. We believe that the current discussion on tax reform must be expanded to explicitly consider how income from different sources is distributed and how income from each source is taxed. Our decomposition method allows policy makers to pinpoint what sources increase (or decrease) overall progressivity and how each source impacts income inequality. Although this study did not consider the impact of payroll taxes, it can only be expected to (i) reduce the progressivity of the system even further and (ii) increase the inequality of the after-tax income even more. The negative vertical equity effects of the payroll tax may be attributed to the following: Payroll taxes are imposed primarily on wage income. Consequently, the payroll tax will reduce the progressivity of the salaries and wages source (the most progressive source of income). Likewise, the payroll tax will also mitigate the income inequality reduction caused by salaries and wages (the source that contributes the most to reduction in income inequality). Additionally, income subject to the payroll tax is also capped (for instance the maximum earnings subject to OASDI tax was $94,200). Consequently, any income in excess of the ceiling is treated as special income not subject to the 6.2% payroll tax. Obvious beneficiaries are high income taxpayers. That is, although the payroll tax rate is a proportional rate, the OASDI tax ceiling renders it as a regressive tax resulting in an overall reduction in progressivity and increase in income inequality. 5.3. Limitations As with studies of this nature, there are several caveats: First, our study is based on aggregate data publicly available from the Internal Revenue Service Statistics of Income Bulletin. All the limitations of the data source apply to this study. Having micro data on individual tax returns would enhance analysis, if they were available, but are not. An important caveat with respect to the decomposition method is that the Gini indices expressed for the different source of income are bounded by the Gini of the total pre-tax income distribution. That is, they are not unbounded but are scaled based on their share in total income, and consequently, the Gini of different sources will add up to the overall Gini of the pretax income distribution. Also, this study considers only the reported income tax after credits and ignores all other taxes including social security taxes, sales taxes and excise taxes. Furthermore, we also do not consider nontaxable sources of income in our analysis. Finally, it is important to note that we consider only the equity dimension of tax law. However, we do not intend to imply that other dimensions (administrative, efficiency, behavior, social) are less important. What may seem unjustified from an equity standpoint may be justified based on efficiency or sound social policy. However, policy makers must consider income source distribution and income source taxability if they want to address the equity dimension of a tax system.
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