DOI: 10.17573/ipar.2016.1.01 1.01 Original scientific article Observations from the U.S. Federal Income Tax to Distinguish Between Measures of Progressivity and Redistributive Capacity Timothy Mathews Dept. of Economics, Finance, and Quantitative Analysis, Coles College of Business, Kennesaw State University, USA tmmathews@gmail.com ABSTRACT This study provides insights on the attributes of a tax that are measured by two different classes of progressivity indices - those defined by Kakwani (1977), Suits (1977), Stroup (2005), and Mathews (2016) and those defined by Musgrave & Thin (1948) and Reynolds & Smolensky (1977). Index values are determined for the U.S. Federal Income Tax from 1929 through 2010. These values illustrate that the indices of Kakwani, Suits, Stroup, and Mathews gauge the progressivity of the tax, while those of Musgrave & Thin and Reynolds & Smolensky measure the redistributive capacity of the tax. In the early 1940s the progressivity of this tax significantly decreased at the same time when the redistributive capacity of the tax significantly increased. Since the mid-1970s this tax has (i) been more progressive than it was from the early 1950s through the mid-1970s and (ii) redistributed income to a greater degree than it did from the early 1950s through the mid-1970s. Keywords: income taxation, progressivity measures, progressivity indices, income redistribution, U.S. tax policy JEL: H20, H24, D31 1 Introduction In order for governments to function, it is necessary for them to raise revenues. Thus, both scholars and practitioners of Public Administration must be concerned with government revenue generation. In most developed countries, the bulk of government revenues presently comes from income taxes. For example, in the U.S. in 2013, 91% of Federal Government revenues were attributed to income taxes and payroll taxes.1 The primary importance of income taxation for government revenue holds even for countries 1 See Office of Management and Budget (2015; p. 7). Mathews, T. (2016). Observations from the U.S. Federal Income Tax to Distinguish 11 Between Measures of Progressivity and Redistributive Capacity. International Public Administration Review, 14(1), 11-35. Timothy Mathews which have Value Added Taxes. In Slovenia as of 2013, 60% of government revenues resulted from income taxes and social security contributions.2 In recent decades, the levels and structures of taxation in many countries have changed dramatically. Focusing on income taxes, the common trend has been for countries to reduce Marginal Tax Rates (MTR, defined as the percentage of the next dollar earned that must be paid in taxes) while broadening the tax base. As argued by Lazovic-Pita (2015), this change in policy reflects a shift toward efficiency (over equity) in income taxation. A reduction of MTRs, particularly at the high end of the income scale, makes a tax less progressive and ultimately results in a distribution of income with greater inequality, A tax is progressive if the Average Tax Rate (ATR, defined as the amount paid in taxes divided by income) increases as income increases. While there has long been agreement on this basic definition of progressivity, scholars have yet to settle on an accepted measure of the degree of progressivity of a tax, Consider the U.S. Federal Income Tax. From an inspection of either MTRs or the resulting ATRs of different segments of taxpayers, this tax has always been a progressive tax.3 However, it is not clear when this tax was "most progressive." Further, different measures of progressivity yield conflicting insights, often because they are measuring different attributes of the impact of a tax. The present study contributes to this ongoing discussion by arguing that two well established and widely used indices of progressivity are in fact better thought of as measures of the redistributive capacity of a tax. Kiefer (2005) offers an insightful discussion of the numerous approaches used to measure the degree of progressivity of a tax. The present study focuses on indices which Kiefer calls "distributional" indices, the value of which depends on both the tax rate structure and the distribution of income within the population subject to the tax.4 More precisely, the present study considers distributional indices defined in terms of "concentration curves" (such as the well-known Lorenz Curve). Two of the earliest measures of this type were developed by Musgrave and Thin (1948) - the index of "effective progression" - and Reynolds and Smolensky (1977). These two distinct measures are each defined as a function of the pre-tax and post-tax values of the Gini-Coefficient. Thus, the dependence of each index on the pre-tax and post-tax Lorenz Curves is clear. Subsequently, several other tax progressivity indices based on the relation between 2 This figure is exactly equal to the OECD average, although the breakdown between these three revenue categories differs between Slovenia and the OECD as a whole. See OECD (2014). 3 Tax Foundation (2009a) reports relevant MTRs for each year over the entire history of this tax; the final table in Tax Foundation (2009b) summarizes realized ATRs for different income groups for each year from 1980 to 2008. 4 In contrast, the value of a "structural" index depends upon only the tax structure but not upon the distribution of income. Musgrave & Thin (1948) examine common structural indices, including measures of "average rate progression", "marginal rate progression", "liability progression", and "residual income progression." 12 International Public Administration Review, Vol. 14, No. 1/2016 Observations from the U.S. Federal Income Tax to Distinguish Between Measures of Progressivity and Redistributive Capacity an "income concentration curve" and a "tax concentration curve" were defined by Kakwani (1977), Suits (1977), Stroup (2005), and Mathews (2016).5,6 Recognize that a progressive tax (i) places a disproportionate amount of the burden of paying the tax on high income individuals, thereby (ii) making the final distribution of income more equal. Any distributional progressivity index essentially gauges the impact of the tax with respect to these two closely related outcomes. As noted by de Sarralde, Garcimartin, and Ruiz-Huerta (2013), Kakwani's index and Reynolds & Smolensky's index measure fundamentally different attributes of a tax: Kakwani's index quantifies the "progressivity" of the tax by computing the "disproportionality of tax payments relative to pre-tax incomes", whereas Reynolds & Smolensky's index quantifies the "redistributive capacity" of the tax by measuring "the difference between pre- and post-tax income distributions" (p. 326). Using this observation by de Sarralde et al. (2013) as motivation, the aim of the present study is to clearly illustrate how different progressivity indices measure distinct characteristics of a tax. Numerical values of various indices are computed for the U.S. Federal Income Tax from 1929 through 2010. Observing index values over such a long period of time (during which there were significant changes in both the fraction of the population subject to paying the tax and total taxes paid as a percentage of societal income) allows us to gain insight into what is actually being measured by each index. Based upon observed values, it is argued that while the indices of Kakwani, Suits, Stroup, and Mathews gauge "progressivity", the indices of Musgrave/Thin and Reynolds/Smolensky are better thought of as measures of "redistributive capacity". This is not to say that the indices of Musgrave/Thin and Reynolds/Smolensky are not useful. On the contrary, which class of indices is more insightful depends upon what questions one would like to address (i.e., what aspects of policy one is trying to assess). For example, someone who wants to gauge how the burden of financing government spending is spread over different segments of the population could look at the values of the measures of Kakwani, Suits, Stroup, and Mathews to make this assessment. Alternatively, someone who thinks that tax policy should reduce income inequality 5 Two other measures of this type were developed by Khetan and Poddar (1976). But, as explained within Mathews (2016), one of Khetan and Poddar's measures can be expressed as a monotonic transformation of Suits' index while the other can be expressed as a monotonic transformation of Stroup's index. 6 Additional alternative approaches for assessing progressivity have been offered by: Baum (1987) who develops the notion of "relative share adjustment" to measure how a tax alters the share of income realized by different segments of society; Allen & Campbell (1994) who examine the difference in average tax rate between very high income households and moderate income households; and Piketty & Saez (2007) who examine and compare levels of average tax rate across groups of taxpayers with different levels of income, paying particular attention to individuals at the high end of the income scale. In contrast to the indices examined in the present study, these alternative approaches do not make any attempt to construct a single dimensional progressivity measure. Mednarodna revija za javno upravo, letnik 14, št. 1/2016 13 Timothy Mathews could look to the measures of Musgrave/Thin and Reynolds/Smolensky to see if the tax is indeed helping to achieve their desired objective, The remainder of the paper is structured as follows, A brief overview of the six indices which serve as our focus is presented in Section 2, A discussion of the computation of numerical values of these indices is offered in Section 3, Index values for the U.S. Federal Income Tax from 1929 through 2010 are examined in Section 4, The observations made within this discussion support the claim that while the indices of Kakwani, Suits, Stroup, and Mathews gauge "progressivity", the indices of Musgrave/Thin and Reynolds/Smolensky are better thought of as measures of "redistributive capacity". Section 5 briefly concludes, 2 Definitions and Previously Observed Values of Indices A detailed discussion of the definitions and relations between the four indices of Kakwani (K), Suits (S), Stroup (St), and Mathews (M) is provided within Mathews (2016). Each of these four indices is defined as a ratio of areas in relation to plots of an "income concentration curve" (which summarizes how incomes are allocated over the population, ordered from lowest income earners to highest income earners) and a "tax concentration curve" (which summarizes how tax payments are allocated over the population, ordered from lowest income earners to highest income earners), The antecedent in each index (i.e., the first term in the ratio) is a weighted difference between income and taxes paid over the population being taxed, For K and St different segments of the population are weighted equally, while for S and M different segments of the population are weighted by their marginal contribution to cumulative income, For S and St the consequent (i,e,, the second term in the ratio) is a similarly weighted value of income, while for K and M the consequent is a similarly weighted value of population,7 As defined, each index can range in value between 0 and 1, with a larger value corresponding to taxation outcomes that are more progressive, Both Musgrave & Thin's index (MT) and Reynolds & Smolensky's index (RS) are direct functions of the pre-tax and post-tax values of the Gini coefficient.8 Letting Gj denote the initial (i.e., pre-tax) value of the Gini coefficient and Gf denote the final (i.e., post tax) value of the Gini coefficient, Reynolds & Smolensky's index) is simply RS = Gj - GF and Musgrave & Thin's index is simply MT = (1 - Gj) /(1 - Gf), Under a progressive tax individuals with higher incomes have higher Average Tax Rates, This results in a reduction in income 7 For a graphical depiction of these curves and a more detailed discussion of these definitions, see Mathews (2016), 8 The Gini coefficient is the most widely used measure of income inequality. It is defined in relation to the income concentration curve with respect to population (i,e,, a curve which illustrates the relation between cumulative fraction of population and their corresponding cumulative fraction of societal income) as the ration of the area between this concentration curve and the 45°-line to the entire are below the 45°-line. The value of the Gini coefficient ranges between 0 and 1, with a smaller value revealing less income inequality, 12 International Public Administration Review, Vol. 14, No. 1/2016 Observations from the U.S. Federal Income Tax to Distinguish Between Measures of Progressivity and Redistributive Capacity inequality and is reflected by a decrease in the value of the Gini coefficient, Consequently, for a progressive tax: GF < Gp implying RS > 0 and MT > 1. In order to have values of these two indices which are on a comparable scale, consider a simple additive transformation of Musgrave & Thin's index: MT = MT - 1, Note that MT = RS/(1 - G¡), from which it is apparent that the value of both RS and MT is positive for a progressive tax, Numerical values of St, S, K, and M for the U.S. Federal Income Tax have previously been determined by numerous researchers, including: Kakwani (1977) using his measure for 1968, 1969, and 1970; Suits (1977) using his measure for 1966 and 1970; Stroup (2005) using his measure for 1980 through 2000; Mathews (2016) using all four measures for 1987 through 2010; and Mathews (2014) using all four measures for 1929 through 2009.9 The Congressional Budget Office (2012) reports values of K and RS for both the U.S. Federal Income Tax and all federal taxes from 1979 through 2009, Stroup (2005), the Congressional Budget Office (2012), and Mathews (2014 and 2016) each present evidence to support a claim that the U.S. Federal Income Tax has become more progressive in recent decades, But while the Congressional Budget Office analysis does suggest that the U.S. Federal Income Tax became more progressive between 1979 and 2009, it also reveals that the progressivity of all federal taxes has either increased less substantially (based upon Kakwani's index) or not changed much at all (based upon Reynolds & Smolensky's index) over this time (see Congressional Budget Office (2012), Supplemental Table 9). This final observation is important because it begins to reveal how the distinct measures of Kakwani and of Reynolds & Smolensky can yield observations on changes in the degree of progressivity over time which appear to be at odds with one another, In addition to determining values of his index for the U.S., Kakwani (1977) computes values for Australia (for 1968 through 1972), Canada (for 1968 through 1970), and the United Kingdom (for 1964 through 1967). His results suggest that during these years income taxation in these four countries was least progressive in the U.S. and most progressive in the U.K. Khetan and Poddar (1976) determine numeric values of two different indices (one is a monotonic transformation of Suits' index and the other is a monotonic transformation of Stroup's index) for Canada from 1961 through 1971. Their results suggest that federal income taxation in Canada became less progressive during these years. More recently, Verbist and Figari (2013) 9 It is important to stress that the present study focuses solely on the U.S. Federal Income Tax and does not encompass other federal taxes (e.g., payroll, estate, and corporate taxes). Clearly, the overall progressivity of all federal taxes could differ from that of the Federal Income Tax. Piketty and Saez (2007) argue that the U.S. Federal tax system as a whole became less progressive between 1960 and 2004, due to an increased significance of fairly regressive payroll taxes and a diminished significance of highly progressive corporate and estate taxes. But, it is important to recognize that Piketty and Saez do not consider any of the four income/ tax concentration based distributional indices which are the primary focus here. Rather, they present a broad, general discussion of trends over time in average tax rates and the after tax position of different segments of the population (with an emphasis on subsets at the high end of the income scale, such as the "top 1%", "top 0.1%" and "top 0.01%"). Mednarodna revija za javno upravo, letnik 14, št. 1/2016 13 Timothy Mathews compute values of Kakwani's index for the EU15 in 1998 and 2008. Their analysis reveals tremendous variation in tax progressivity across these 15 countries, with the most progressive outcomes found in Ireland and the least progressive outcomes found in Denmark and Sweden, 3 Computations of Index Values Focusing on the U.S. Federal Income Tax, numerical values of St, S, K, M, MT, and RS are determined for every year between 1929 and 2010. In order to compute these values, it is necessary to construct various concentration curves.10 The bulk of the data used to construct these curves was obtained from the Internal Revenue Service's "Statistics of Income" report for each relevant year." Each report summarizes the number of tax returns filed, the amount of income represented on the filed tax returns, and the amount of taxes paid (broken down by taxpayer income levels). For example, the data reported in Table 3 on Pages 68-70 of the "Statistics of Income for 1932" show that in this year 3,877,430 returns were filed, and that the people filing these returns collectively had a combined net income of $11,655,756,678 and collectively had to pay $329,962,311 in Federal Income Taxes." As an example of how this data is further broken down by taxpayer income levels, Table 3 of the "Statistics of Income for 1932" further reveals that in this year people with net incomes of $2,000 or less collectively filed a total of 1,849,277 returns, had a combined net income of $2,376,974,549 and had a combined tax obligation of $12,357,186. When constructing the relevant concentration curves, it is necessary to define (either explicitly or implicitly) the population over which the index values are to be determined. If the population of interest is simply those people filing tax returns, then the curves can be constructed and the index values determined from solely the data in the "Statistics of Income" reports. This is the approach taken by Kakwani (1977), Suits (1977), Stroup (2005), Congressional Budget Office (2012), and Mathews (2016). However, if the true desire is a measure of the degree of progressivity over the entire population, then focusing on only those individuals filing returns has shortcomings. First, if individuals with incomes below a certain level are not even required to file a return (as has always been the case for the U.S. Federal Income Tax), then this approach ultimately understates the degree of progressivity at each point in time. Second, if the fraction of adults required to file a return changes dramatically, 10 To compute K, S, St, and M it is necessary to construct a "tax concentration curve with respect to population", an "income concentration curve with respect to population", a "tax concentration curve with respect to income", and a "population concentration curve with respect to income" for each year. Similarly, to compute RS, and MT it is necessary to additionally construct a "post tax income concentration curve with respect to population". 11 All reports can be accessed through http://www.irs.gov/uac/Tax-Stats-2. For example, "Statistics of Income for 1932" is available at http://www.irs.gov/pub/irs-soi/32soirepar.pdf. 12 Table 1 (presented in the Appendix of the paper) provides a summary of these values (along with the values of several other variables of interest) for the time period under consideration. In the interest of brevity, these values are reported for only every other year between 1929 and 2010. 12 International Public Administration Review, Vol. 14, No. 1/2016 Observations from the U.S. Federal Income Tax to Distinguish Between Measures of Progressivity and Redistributive Capacity then focusing only on this restricted population could give misleading results when examining how the degree of progressivity has evolved over time, Using additional data from the Bureau of Economic Analysis and the U.S. Census Bureau, Mathews (2014) constructed concentration curves and computed index values over the entire adult population. This is the first study to truly gauge the progressivity of the U.S. Federal Income Tax over the entire population, and not over just people filing tax returns. A similar approach is used in the present study, For each year from 1929 through 2010, data on total Personal Income for the U.S. were obtained from the Bureau of Economic Analysis and estimates of the total adult population in the U.S. were obtained from the U.S. Census Bureau.13 These figures are reported for every other year between 1930 and 2010 in the columns labeled "Total Societal Income" and "Total Adult Population" in Table 1 (presented in the Appendix of the paper). It is worth noting that the present study uses data on Personal Income collected after the comprehensive revision of national income accounts which was undertaken by the Bureau of Economic Analysis in 2013, whereas Mathews (2014) used data on Personal Income collected before this comprehensive revision. As a consequence, the numerical values of St, S, K, and M which are obtained differ between the two studies. Returning attention to the "Statistics of Income Reports," the total number of adults represented on all filed tax returns was determined in each year (see "Adults Represented on Returns" in Table 1). From here, the percentage of all adults represented on a filed tax return was computed for each year (see "Percentage of Adults on Returns" in Table 1). Following an approach first used by Suits (1977), each of the five relevant concentration curves for each year is constructed as a piecewise linear function passing through each relevant pair of values and the implicit endpoints of (0,0) and (1,1). For the resulting piecewise linear concentration curves, the relevant areas between the various curves each consist of a collection of triangles and trapezoids. As was done in Mathews (2014), when constructing the concentration curves which depend upon income the income not represented on filed tax returns (i.e., the residual income of society) is allocated equally across the total adult population. As an example, in 1944 a total of 46,919,590 tax returns were filed for 71,270,340 adults. The total adult population in this year, based upon U.S. Census Bureau estimates, was 97,153,352. Thus, roughly 26.64% of the adult population was not represented on a filed tax return and, therefore, 13 The former figures were obtained from http://www.bea.gov/iTable/index nipa.cfm, and the latter figures were obtained from http://www.census.gov/popest/data/historical/index.html Mednarodna revija za javno upravo, letnik 14, št. 1/2016 13 Timothy Mathews did not pay any income taxes.14 Consequently, the starting point for the tax concentration curve with respect to population is the point (0.2664, 0). Those individuals filing tax returns had a combined net income of $116,714,736,000, whereas total societal income was $169,700,000,000. Thus, the residual income of society was $52,985,264,000, roughly 31.22% of total societal income. Allocating this residual income equally over the entire adult population, it follows that the 26.64% of the population not represented on a filed tax return accounted for approximately 0.2664 x 0.3122 = 0.0832 of total societal income. Consequently, the first segment of the income concentration curve with respect to population extends from the origin through the point (0.2664, 0.0832). Following this approach, each relevant concentration curve is constructed for each year. From here, it is straightforward to determine numerical values of St, S, K, M, MT, and RS in each year from 1929 to 2010. 4 An Examination of Index Values For each year from 1929 through 2010, the resulting values (determined using the data and approach described in Section 3) of St, S, K, and M are reported in Table 2 and plotted in Figure 1. Similarly, values of MT and RS are reported in Table 3 and plotted in Figure 2" 4.1 Observations on St, S, K, and M Focusing first on St, S, K, and M, an inspection of Table 2 and Figure 1 reveals general trends in the degree of progressivity which are very similar to those discussed in Mathews (2014).16 For example, just as in Mathews (2014), St identifies 1929 and S, K, and M each identify 1931 as the year of most progressive taxation outcomes, while all four indices identify 1969 as the year of least progressive taxation outcomes over this period. Additionally, there is a consistent trend toward taxation outcomes that are increasingly more progressive from the late 1960s up to the present day. As a consequence, taxation outcomes in recent years are more progressive than at any point in time post World War II. In 2009 the value of: St was greater than in every year from 1942 onward; S was greater than in every year from 1943 onward; K was greater than in every year from 1943 onward; and M was greater than in every year from 1944 onward. Furthermore, for each index, the second largest value over this same time period was realized in 2010. 14 Since some people who file a tax return but do not ultimately have a positive tax burden, the percentage of the total population that paid no income tax would be greater than 26.64%. That is, this figure of 26.64% represents the minimum percentage of the population that paid no income taxes. 15 Tables are presented in the Appendix of the paper. 16 This should not be surprising, since the only difference between the values of St, S, K, and M in Mathews (2014) and the present study is that the latter were computed using data on Personal Income collected after the Bureau of Economic Analysis' most recent comprehensive revision of national income accounts. As a result, while the obtained numerical values of St, S, K, and M differ between the two studies, for the most part the differences are minimal. 12 International Public Administration Review, Vol. 14, No. 1/2016 Observations from the U.S. Federal Income Tax to Distinguish Between Measures of Progressivity and Redistributive Capacity These results are qualitatively consistent with Mathews (2016) which finds that over the period from 1987 through 2010, the U.S. Federal Income Tax was most progressive in 2009 (according to each of these four indices). Recall, however, that Mathews (2016) - as well as all other studies cited, with the exception of Mathews (2014) - effectively computes index values over only taxpayers (as opposed to over the entire population). Consequently, the index values reported in Mathews (2016) are numerically smaller than those reported here.17 Similarly, the resulted reported here are qualitatively consistent with those of Stroup (2005), where values of St were computed for each year from 1980 through 2000. Over this time period, both the present study and Stroup identify 1981 as the year of least progressive taxation and 2000 as the year of most progressive taxation. Furthermore, according to the findings of both studies, there was a sizable jump in the degree of progressivity between 1992 and 1993, causing all outcomes from 1993 through 2000 to be more progressive than all outcomes between 1980 and 1992. Finally, the present results are broadly consistent with those of the Congressional Budget Office (2012) study, which, based upon computed values of K, finds that taxation outcomes became more progressive between 1979 and 2009, Figure 1: Indices of Progressivity 1.00 0.90 0.80 Z> •5 0.70 | 0.60 c > 0.50 I 0.40