Historical trends in the degree of federal income tax

progressivity in the United States

Timothy Mathews1

Abstract

This study examines how the degree of progressivity of the U.S. Federal income tax evolved between 1929 and 2009. Data from the Internal Revenue Service, U.S. Census Bureau, and Bureau of Economic Analysis is used to construct annual tax concentration curves and income concentration curves. Numerical values of four tax progressivity indices are determined. These values suggests that: (i) the degree of progressivity has varied greatly over time, (ii) taxation outcomes have become more progressive over the past four decades, (iii) the period from the early 1950s through 1974 was one of relatively low progressivity, whereas the period from 1975 through 2009 was one of relatively high progressivity, (iv) the most progressive outcomes of the last 67 years have been realized within the past decade, and (v) recent outcomes are much less progressive than were outcomes before 1942. Keywords: income taxation; progressivity measures; U.S. economic history. JEL classification: H20; H24; N42.

                                                            1 Department of Economics, Finance, and Quantitative Analysis, Coles College of Business, Kennesaw State

University, 1000 Chastain Rd., Kennesaw, GA 30144-5591, U.S.A.; (678) 797-2072; tmmathews@gmail.com. This

paper was presented at the 2011 Western Social Sciences Association conference in Salt Lake City, UT and the 2011

Western Economic Association International conference in San Diego, CA. I am thankful to participants of these

conferences for their helpful feedback. I would also like to thank Ruth Schwartz of the Internal Revenue Service,

Statistics of Income Division for making some of the data used in this study publicly available and, finally, Scott

Carson and two anonymous referees for helpful comments and suggestions which greatly improved the paper.

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1. Introduction

This study provides insights on how the degree of progressivity of the U.S. Federal

income tax has changed since 1929. It builds upon existing theoretical studies that focus on

alternative approaches to measuring tax progressivity. Defining average tax rate (ATR) as the

ratio of taxes paid to income, a progressive tax is one for which ATR increases as income

increases. As noted by Kiefer (2005), while there is general agreement on this definition of

progressivity, there is no such consensus regarding how to measure the degree of progressivity.

For example, consider the U.S. Federal income tax. From inspecting either marginal tax rates or

the resulting ATRs of different segments of taxpayers, this tax has always been a progressive

tax.2 However, it is not clear when this tax was most progressive. This issue is addressed by

calculating numerical values of four previously defined income/tax concentration based

progressivity indices for the U.S. Federal income tax for each year between 1929 and 2009.

In contrast to previous studies that focus only on the population of individuals filing tax

returns, the degree of tax progressivity over the entire population are calculated. Results indicate

that the degree of progressivity has varied greatly over time. Furthermore, taxation outcomes

have become increasingly progressive over the past four decades. The period from the early

1950s through 1974 was among the least progress, whereas the period from 1975 through 2009

was the most progressive. However, recent outcomes are much less progressive than were

outcomes before 1942.

                                                            2 Tax Foundation (2009a) reports relevant Marginal Tax Rates for each year over the entire history of this tax; the

final table in Tax Foundation (2009b) summarizes the resulting Average Tax Rates for different income groups for

each year from 1980 to 2008.

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2. Federal US income taxation

Two of the more important reasons social scientists are concerned about the degree of tax

progressivity are how taxes spread the burden of financing government activities and the extent

to which taxes alter the distribution of societal income.

When assessing tax equity or fairness, it is common to apply the ability-to-pay principle,

which states that tax payments should be based on an individual’s capacity to pay. Vertical

equity refines this principle by requiring individuals with greater economic capacity to have

greater tax burdens, which means that individuals of greater financial means bear a greater

burden of paying taxes. If economic capacity is equated to income and tax burden is equated to

ATR, then vertical equity justifies progressive taxation3 because progressive taxation puts a

disproportionate amount of the tax burden, relative to income, on individuals with high incomes.

Two different taxes that each adhere to vertical equity can differ in regard to how much of the

burden of paying the tax is borne by different segments of the population. Depending upon its

definition, a measure of tax progressivity sheds light on which segments of the population are

bearing the burden of taxes.

In market economies, the distribution of income/wealth influences the distribution of

consumption goods across households. As a result, a more equal distribution of consumption is

realized by imposing a tax which reduces income inequality. Alternative theories of justice have

been proposed by scholars over the years, offering various arguments either in favor of or against

                                                            3 Note however that if tax burden is instead equated to dollars paid in taxes, then even a regressive tax (that is, one

for which ATR decreases as income increases) does not immediately violate the notion of vertical equity.

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income redistribution,4 and depending upon its definition, an index of tax progressivity sheds

light on how a tax alters the distribution of income.

2.1. Quantifying tax progressivity

So, “How progressive should income tax be?” Atkinson (1973) set out to provide insight

on this matter in an article by this very name. However, he does not make any “attempt to

provide a definite answer to the question posed in [his] title” since “such an answer cannot be

given without further clarification of social objectives” (Atkinson 1973, p. 90). The present

inquiry is in the same spirit. No attempt is made to offer normative insights on tax progressivity.

Rather, what is presented is a positive analysis of various tax progressivity indices. Any such

index can be thought of as a yardstick to use to measure the degree of tax progressivity. Kiefer

(2005) summarizes the varied approaches used to quantify the degree of tax progressivity. The

focus of the present study considers indices which Kiefer termed “distributional” indices, the

value of which depends upon both the tax structure and the distribution of income over the

population being taxed.5 Thus, the realized value of a distributional progressivity index depends

on not only tax policy but also on income levels and distribution.

The current focus is on distributional indices defined in terms of concentration curves,

such as the well-known Lorenz Curve. Two of the more widely used progressivity measures of

                                                            4 See Konow (2003) for a survey of the prominent and diverse notions of justice articulated by individuals such as

Bentham, Marx, Mill, Nozick, and Rawls.

5 In contrast, the value of a “structural” index depends upon the tax structure, but not on the distribution of income.

Musgrave & Thin (1948) discuss common structural measures such as “average rate progression,” “marginal rate

progression,” “liability progression,” and “residual income progression.”

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this type were developed by Musgrave and Thin (1948) and by Reynolds and Smolensky (1977),

each of which is defined as a function of the pre-tax and post-tax values of the Gini-Coefficient.

Subsequently, several tax progressivity indices defined as the relation between an income

concentration curve and a tax concentration curve were developed by Kakwani (1977a), Suits

(1977), and Stroup (2005). Mathews (2013) fully characterizes the relationships between these

different measures and develops a fourth previously undefined, closely related index. When

determining progressivity index values, it is necessary to define the population over which the

values are calculated. Should the income concentration curves and tax concentration curves be

constructed over all adults in society or over all taxpayers? If only a relatively small fraction of

the population pays the tax, then dramatically different numerical values result from focusing on

all adults in society versus all taxpayers. Considering this issue over time is important if there is

considerable change in the fraction of the population subject to the tax, which over time, has

been the case for the U.S. Federal income tax. In previous studies, index values were obtained

focusing on the population of “all taxpayers,” whereas in the present study index values are

computed for both the population of “all taxpayers” and “all adults in society.” Our primary aim

is to determine how the degree of progressivity of the U.S. Federal income tax over the entire

adult population has changed over the past century. By first obtaining values calculated over

only taxpayers, we illustrate how this approach understates the degree of progressivity.

2.2. Previous observations on numerical values of progressivity indices

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Numerical values of these four distributional progressivity indices for the U.S. Federal

income tax have been determined previously.6 A general theme of these prior observations is

that the U.S. Federal income tax has become more progressive in recent decades.7 The present

study uses data from the U.S. Internal Revenue Service, Bureau of Economic Analysis, and U.S.

Census Bureau to calculate values of each index for the U.S. Federal income tax in each year

between 1929 and 2009. No previous study has determined these values over such a long time

period – so, the present study creates unique insights into the historical evolution of the degree of

tax progressivity over a long time horizon.

Observing values since 1929, the changes in the degree of progressivity are complex.

The outcomes before the early 1940s are the most progressive of the period under study, and

during the early 1940s, the scope of the income tax expanded, associated with a large decrease in

the degree of progressivity. Taxation outcomes became gradually less progressive between the

early 1940s and late 1960s, followed by an the increase in the degree of progressivity beginning

around 1969. The period from the early 1950s through 2009 can be divided into two periods: an

                                                            6 By: Kakwani (1977a) 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; Congressional Budget Office (2012) using Kakwani's

measure for 1979 through 2009; and Mathews (2013) using all four measures for 1987 through 2010. Further,

Congressional Budget Office (2012) reports values for both Kakwani’s index and Reynolds & Smolensky’s index

for both the U.S. Federal income tax and all federal taxes from 1979 through 2009.

7 Stroup (2005), Congressional Budget Office (2012), and Mathews (2013) each present evidence to support this

claim. Similarly, McBride (2012) presents a detailed discussion of how tax burdens and progressivity evolved from

1979 through 2009. Based upon the CBO’s computed values for the Kakwani index, McBride observes that

outcomes from the Federal income tax were more progressive in 2009 than in any other year since 1979.

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initial period of relatively low progressivity from the early 1950s through 1974, followed by the

more recent period of relatively high progressivity from 1975 through 2009.

3. Income/tax concentration based indices

3.1. Indices definition

To calculate the degree of tax progressivity, taxpayer populations are ordered from

lowest income to highest income.8 Denoting an arbitrary cumulative portion of this population

by , let represent the cumulative portion of income, and let represent the

corresponding cumulative portion of taxes paid. Alternatively, letting denote the cumulative

portion of income earned by individuals with the lowest incomes, we can let represent

the cumulative portion of taxes paid by individuals, and represent the corresponding

portion of the population.

By slightly adapting terminology developed by Kakwani (1977b), these functions are

easily defined. When is plotted on the horizontal axis, is the income concentration curve

with respect to population, and is the tax concentration curve with respect to population.

Likewise, with on the horizontal axis, is the tax concentration curve with respect to

income, and is the population concentration curve with respect to income. Finally, the

population concentration curve with respect to population and the income concentration curve

with respect to income are each a 45°-line.

                                                            8 The overall presentation in this section draws heavily upon the discussion in Mathews (2013).

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For a progressive tax, for all ∈ 0,1 , and for all ∈ 0,1 .

Figures 1 and 2 illustrate these four curves. In Figure 1, is the area between the “population

concentration curve with respect to population” and the “income concentration curve with

respect to population”. is the area between the “income concentration curve with respect to

population” and the “tax concentration curve with respect to population”. is the area below the

“tax concentration curve with respect to population”. In Figure 2, is the area between the

“income concentration curve with respect to income” and the “tax concentration curve with

respect to income”. is the area below the “tax concentration curve with respect to income”.

is the area between the “population concentration curve with respect to income” and the “income

concentration curve with respect to income”.

The measures of Kakwani (1977a), Suits (1977), Stroup (2005), and Mathews (2013) are

defined in terms of these areas. Kakwani’s measure is , which is the ratio of the area

between the income concentration curve with respect to population and the tax concentration

curve with respect to population to the entire area below the population concentration curve with

respect to population. Suits’ measure is , which is the ratio of the area between the

income concentration curve with respect to income and the tax concentration curve with respect

to income to the area below the income concentration curve with respect to income. Stroup’s

measure is , which is the ratio of the area between the income concentration curve with

respect to population and the tax concentration curve with respect to population to the entire area

below the income concentration curve with respect to population”. Mathews’ measure is

and is the ratio of the “area between the income concentration curve with respect to

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income and the tax concentration curve with respect to income” to the “entire area below the

population concentration curve with respect to income”.

3.2. Relations between and properties of indices

These four indices are related to one another. Table 1 summarizes the relationships

between these measures. Each index is a ratio in which the antecedent, or first term in the ratio,

is the weighted difference between cumulative portion of income and cumulative portion of taxes

paid ( ) to a similarly weighted consequent, or second term in the ratio. Two

different approaches are taken regarding the choice of the consequent. and each focus on

the ratio of the weighted value of this difference ( ) to a similarly weighted value of

cumulative portion of income over the population, , while and focus on the ratio of the

weighted value of this difference ( ) to a similarly weighted value of population, .

Furthermore, two different approaches are taken regarding how to weight each term in this ratio:

and are constructed by placing equal weight on each segment of the population, while

and are constructed by weighting each segment of the population according to that segment’s

marginal contribution to cumulative portion of income, ′ .

All four indices exhibit common properties, which allows for similar interpretations. For

example, under a proportional tax and , so that 0. As a result,

the value of each index is zero. In contrast, for a progressive tax and , so

that 0 and 0. This makes the value of each index strictly positive.

Furthermore, for each index, a larger value indicates more progressive taxation. Fixing

the distribution of income, and increase if and only if increases while and increase if

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and only if increases.9 An increase in or is consistent with the gap between cumulative

portion of income earned and cumulative portion of taxes paid becomes larger, which intuitively

accords with taxation that is more progressive. For example, when the income distribution is

fixed, consider a change in tax structure which does not alter the total amount of tax revenue

generated, but results in a reduction of total tax dollars paid by some arbitrarily chosen group of

taxpayers and an increase in total tax dollars paid by a group of people with higher incomes.

Intuitively, this change makes the tax structure more progressive. Since the distribution of

income is unaltered, this change does not have an impact on or , but does lead to a

decrease in both and . Furthermore, both and increase, while , , ,

and each remain constant. This increases the value of each index.

4. Method for calculating numerical values of indices

For the U.S. Federal income tax, numerical values for , , , and are determined for

each year between 1929 and 2009. To conduct this analysis, 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. The bulk of the

                                                            9 In practice, the distribution of income also changes over time, so that two measures may possibly move in opposite

directions from one time period to the next. For example, when focusing on and , Formby, Seaks, and Smith

(1981) note how “inconsistent rankings can emerge when the distribution of pre-tax income is not fixed,” an

observation illustrated by their empirical finding that “in three instances and move in opposite directions,”

prompting them to state “the Suits and Kakwani indices, although identical in intent, are fundamentally different

measures of tax progression” (pp. 1018-1019).

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data used to construct these curves is from the Internal Revenue Service’s “Statistics of Income”

report for each relevant year.10 These reports contain data summarizing 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 summarized in Table 3 on

Pages 70-71 of the Statistics of Income for 1933 show that 3,723,558 returns were filed in 1933,

and that individuals filing these returns collectively had a combined net income of

$11,008,637,754 and collectively paid $374,120,469 in Federal income taxes.11 When

constructing concentration curves, it is necessary to define the population over which the index

values are to be determined. If the population of interest is those people filing tax returns, then

the curves and index values are determined from the available data in the Statistics of Income

reports. This is the approach taken previously by Kakwani (1977a), Suits (1977), Stroup (2005),

Congressional Budget Office (2012), and Mathews (2013). However, if the desire is a measure

of the degree of progressivity over the entire adult population, then focusing on only those

individuals filing returns has some shortcomings. First, if individuals with incomes below a

given level of income are not required to file a return, then this approach understates the degree

of progressivity at each point in time. Furthermore, if the portion of adults filing returns changes

significantly over time, then focusing only on this restricted population can produce misleading

results when examining how the degree of progressivity changes over time.

                                                            10 All reports can be accessed through http://www.irs.gov/uac/Tax-Stats-2. For example, “Statistics of Income for

1933” is available at http://www.irs.gov/pub/irs-soi/33soirepar.pdf.

11 Table 2 in the present study provides a summary of these values (as well as 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 2009.

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To determine the degree that such concerns are an issue and to construct index values

which measure progressivity over the adult population, additional data are acquired. Data on

Personal Income is obtained for each year from the Bureau of Economic Analysis.12 Estimated

values of the adult population of the U.S. in each year are obtained from the U.S. Census

Bureau.13 Returning attention to the “Statistics of Income Reports,” the total number of adults

represented on all filed tax returns and the percentage of all adults represented on a filed tax

return was determined in each year. From Table 2, the value of this latter figure changed

dramatically over time. Before 1937, less than 10% of adults were represented on a filed tax

return, whereas the corresponding figure has been over 75% since 1945.14 If our aim is to

accurately determine how the degree of progressivity has changed over this entire time period,

we cannot focus solely on individuals filing tax returns, since a comparison between years in

which there was a significant difference in the fraction of adults represented on tax returns could

potentially be misleading.

Following the approach used by Suits (1977), each of the four annual concentration

curves is constructed as a piecewise linear function passing through each relevant pair of values

and the endpoints of 0,0 and 1,1 . For the resulting piecewise linear concentration curves,

Areas , , , , , and each consist of a collection of triangles and trapezoids. It is then

straightforward to determine annual numerical values of , , , and .

5. Numerical values of indices

                                                            12 See Table 2.1 of the reports at http://www.bea.gov/national/nipaweb/SelectTable.asp?Selected=N.

13 These figures were compiled from reports available at http://www.census.gov/popest/data/historical/index.html.

14 Although not reported in Table 2, the “Percentage of Adults on Returns'” was 8.99% in 1936 and 73.36% in 1944.

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We first construct relevant curves and determine index values by focusing only on tax

filing individuals. Next, progressivity is calculated for the adult population. Comparing these

two sets of results illustrates how the degree of progressivity is understated by focusing only on

the population of adults filing tax returns, as opposed to the entire general adult population (both

filers and non-filers).

5.1. Index values computed over adults filing returns

Index values calculated for only adults filing tax returns are reported in Table 3 and

plotted over time in Figure 3. From these values, , , and identify 1969 and identifies

1970 as the year in which the U.S. Federal income tax was least progressive. Furthermore, all

four measures identify 1969 and 1970 as the two years in which outcomes were least

progressive. There is less agreement by the four measures regarding when taxation outcomes

were most progressive. identifies 1929; identifies 1931; and and each identify 1940 as

the year in which the U.S. Federal income tax was most progressive. However, each of the four

measures reveals a striking difference by the degree of progressivity before and after 1942. For

each index value between 1929 and 1941, the lowest value is greater than the highest value

between 1942 and 2009.

Consistent with many previous studies, there was a trend toward greater progressivity

during the last several decades. The numerical values indicate that the trend toward more

progressive taxation began in the late 1960s and that the most progressive taxation outcomes of

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the past half century occurred in recent years. Focusing on the period from 1951 onward, each

progressivity index achieved its largest value in 2009.

5.2. Index values computed over entire adult population

To calculate index values for the total adult population, additional data are needed, in

order to construct concentration curves over the entire adult population. When constructing the

, , and concentration curves that depend upon income, the residual income of

society or income not represented on filed tax returns is allocated equally across the total adult

population of society. As an example, in 1943, there were a total of 43,506,553 tax returns filed

for 65,738,182 adults. Based upon U.S. Census Bureau estimates, the total adult population in

this year was 95,837,053. As a result, roughly 31.41% of the adult population was not

represented on a filed tax return and, therefore, did not pay income taxes.15 As a result, the

starting point for the tax concentration curve with respect to population, . is the point

.3141,0 . Furthermore, the individuals filing tax returns had a combined net income of

$99,209,862,000, while total societal income was approximately $152,100,000,000.

Consequently, the residual income of society was $52,890,138,000, roughly 34.77% of total

societal income. Allocating this residual income equally over all adults in society it follows that

the 31.41% of the population not filing tax returns accounted for . 3141 .3477 .1092 of

total societal income. As a result, the first segment of the approximated piecewise linear

                                                            15 Since some people 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 this figure of 31.41%. Thus, this figure of 31.41% simply

represents the minimum percentage of the population that we know paid no income taxes.

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function for the income concentration curve with respect to population, , extends from the

origin through the point .3141, .1092 . Following this approach, each of the four concentration

curves are calculated for each year.

Index values for the total adult population are reported in Table 4 and plotted in Figure 4,

and note that each value in Table 4 is greater than the corresponding value in Table 3. This

illustrates how the degree of progressivity over the entire population is understated if attention is

restricted to only individuals filing tax returns. Moreover, even though the results in Table 3

understate the true degree of progressivity, many insights similar to those acquired from the

results in Table 3 emerge from the results in Table 4. For example, from the results in Table 4,

each progressivity index identifies 1969 as the year of least progressive taxation. It is also worth

noting that the “Percentage of Adults on Returns” in 1969 is greater than in any other year

between 1929 and 2009. Furthermore, the general tendency of taxation outcomes becoming

increasingly more progressive after the late 1960s still holds and, in fact, is more pronounced

when focusing on index values calculated over the total population than when examining index

values calculated for only individuals filing tax returns (Figure 3).

Table 4 as plotted in Figure 4 indicates there was a transformation in the degree of

progressivity during the early 1940s. The value of each measure decreased considerably in 1941,

1942, and 1943. Furthermore, for each of the four indices, every value from 1942 onward is less

than the values between 1929 and 1941.16 This result indicates that according to each of the four

measures that the early 1940s is a point of demarcation, with all subsequent taxation outcomes

being less progressive than earlier taxation outcomes. This change in the early 1940s was driven

                                                            16 For each of the four indices a similar statement would hold with either 1940 or 1941 as the cut-off year instead of

1942, and for , , and a similar statement would hold with 1943 as the cut-off year.

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by the substantial increase in “Percentage of Adults on Returns” which occurred during the

1940s. Since some people file tax returns but do not have a positive tax burden, the percentage

of the total population that pays the income tax is not the same as the percentage of the total

population that files a tax return. However, the latter provides an upper bound for the value of

the former. That is, the percentage that pays the income tax cannot exceed the percentage who

file a return. For example, before 1937, since less than 10% of the population filed returns, there

was less than 10% of the population that paid Federal income taxes.

The most progressive taxation outcomes of the last 67 years were realized during the

most recent decade. Each of the four indices is larger in 2009 than in every year from 1943

onward. Comparing recent values of each index to their corresponding median values from 1929

to 2009 reinforces that recent outcomes are more progressive than average. , , and each

has a value above their respective median in every year from 2001 onward, while has a value

at or above its median in every year from 1991 onward.

The higher values from 2002 onward are partly due to the across the board reduction in

marginal tax rates brought about by the Economic Growth and Tax Relief Reconciliation Act of

2001 (EGTRRA) and the “Jobs and Growth Tax Relief Reconciliation Act of 2003” (JGTRRA).

While marginal tax rates were decreased for all taxpayers starting in 2002, the reductions were

proportionately larger at the low end of the income scale. The lowest marginal tax rate

decreased from 15% to 10%. In contrast, the highest marginal tax rate decreased from 39.6% to

35%. While the magnitude of these two reductions is similar, the reduction is proportionally

greater for the lowest marginal tax rate than for the highest. As a result, these changes in

marginal tax rates shifted the relative burden of paying the tax away from low income taxpayers,

making taxation outcomes more progressive. Furthermore, starting under EGTRRA and

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continuing under JGTRRA the child tax credit was increased from $500 to $1,000. For a

married couple filing jointly, this credit gradually phases out between an income of $110,000 and

$130,000. As a result, this more generous credit provides no relief for taxpayers with incomes

above this latter level, but significantly reduces tax liability for many middle and low income

taxpayers. In sum, the child tax credit expansion shifted the relative tax burden away from low

income taxpayers, making taxation outcomes more progressive. The sizable jump in index

values between 2001 and 2002 is largely a reflection of these two changes.

Another jump in index values occurred between 2008 and 2009. This increase, which

contributed to making all four indices take on a larger value in 2009 than in any other year since

1943, was partly due to the Making Work Pay tax credit which was in place for low and middle

income taxpayers in 2009 and 2010.

Finally, values in Table 4 indicate the extent to which the degree of progressivity of this

tax has varied over time. The largest reported value of is 2.30 times greater than its smallest

reported value, of is 2.95 times greater than its smallest reported value, of is 3.08 times

greater than its smallest value, and of is 3.45 times greater than its smallest value.

6. Summary and conclusions

The present study considers how the degree of progressivity of the U.S. Federal income

tax has changed over time. After reviewing the construction of four previously developed

distributional indices defined in terms of income concentration and tax concentration curves,

annual progressivity indices are calculated for the U.S. Federal income tax from 1929 to 2009.

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Several studies show that the U.S. Federal income tax has become more progressive in

recent decades. However, no previous study determines progressivity index values over the

longer time period considered here. The primary results indicate that this trend toward greater

progressivity began in the late 1960s, at a time when taxation outcomes were less progressive

than at any other time since 1929. Furthermore, the period from the early 1950s through 2009

are divided into two periods: one period from the early 1950s through 1974 of relatively low

progressivity, followed by a period of relatively high progressivity from 1975 through 2009.

While taxation outcomes are more progressive in the past decade than at any other time since the

early-1940s, the degree of progressivity is not at an all-time high. Income taxation was more

progressive before 1942 than it is today, and during the 1930s, two of the four indices have

values close to their upper bound. Finally, the variation in the value of each index since 1929

indicates the extent to which tax progressivity has changed over time. Many of these

observations cannot be made without calculating index values over the extended period

considered here.

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(Nominal and Inflation-Adjusted Brackets). Retrieved October 2013, from

19  

http://taxfoundation.org/article/us-federal-individual-income-tax-rates-history-1913-

2013-nominal-and-inflation-adjusted-brackets

Tax Foundation. (2009b). Summary of Latest Federal Individual Income Tax Data, 1980-2008.

Retrieved October 2013, from http://taxfoundation.org/article/summary-latest-federal-

individual-income-tax-data-1980-2008

20  

Table 1 Summary of relations between the four different indices.

Equally by marginal contribution to cumulative income [ )( px ]

Income [ )( px ]CB

BSt

ED

DS

Population [ p ]CBA

BK

FED

DM

Each segment of the population weighted…

 Ratio of the difference between income and

taxes paid to…

21  

Table 2 Characteristics of entire population and taxpayers.

Year Number of

returns

Adults represented on returns

Total adult population

Percentage of adults

on returns

Income represented on

returns (millions of $)

Total societal income

(millions of $)

Total taxes paid (millions

of $)

Taxes paid as percentage of

societal income

1929 4,044,327 5,901,926 78,619,000 7.51 24,800.74 84,900 1,001.94 1.18 1931 3,225,924 4,635,290 81,209,172 5.71 13,605.00 65,200 246.13 0.377 1933 3,723,558 5,494,891 83,392,142 6.59 11,008.64 46,800 374.12 0.799 1935 4,575,012 6,675,038 85,698,080 7.79 14,909.81 60,300 657.44 1.09 1937 6,350,148 9,132,970 87,876,551 10.39 21,238.57 74,100 1,141.57 1.54 1939 7,570,320 10,894,018 90,311,164 12.06 22,938.92 72,900 890.93 1.22 1941 25,770,089 39,908,842 93,135,825 42.85 58,527.22 96,000 3,815.42 3.97 1943 43,506,553 65,738,182 95,837,053 68.59 99,209.86 152,100 16,974.23 11.16 1945 49,750,991 74,631,339 98,372,755 75.87 120,301.13 171,600 17,050.38 9.94 1947 54,799,936 81,288,966 100,723,315 80.71 150,295.28 190,900 18,076.28 9.47 1949 51,301,910 82,169,845 103,444,722 79.43 161,373.21 207,000 14,538.14 7.02 1951 55,042,597 87,545,182 106,048,368 82.55 203,097.03 257,900 24,438.74 9.48 1953 57,415,885 91,566,023 108,053,025 84.74 229,863.41 291,700 29,656.67 10.17 1955 57,818,164 93,115,608 110,192,874 84.50 249,429.18 316,000 29,613.72 9.37 1957 59,407,673 95,953,192 112,514,204 85.28 281,308.43 358,500 34,393.64 9.59 1959 59,838,162 96,798,855 114,779,195 84.34 306,616.92 392,300 38,645.30 9.85 1961 61,067,589 97,447,864 117,900,175 82.65 330,935.74 428,800 42,225.50 9.85 1963 63,511,244 101,007,468 120,822,242 83.60 370,270.62 479,500 48,203.58 10.05 1965 67,198,928 106,245,102 124,572,108 85.29 430,663.21 555,500 49,529.70 8.92 1967 71,282,524 111,784,150 128,784,895 86.80 506,641.75 648,100 62,919.96 9.71 1969 75,375,731 117,530,398 132,904,639 88.43 605,578.95 778,300 86,568.22 11.12 1971 74,146,785 116,610,979 137,852,263 84.59 676,334.16 903,100 85,397.55 9.46 1973 80,248,984 123,842,306 143,144,603 86.52 830,653.26 1,110,500 108,068.05 9.73 1975 81,585,541 125,342,139 148,805,353 84.23 954,089.43 1,334,900 124,511.77 9.33 1977 86,066,234 129,781,866 154,776,287 83.85 1,165,776.87 1,632,500 159,746.44 9.79 1979 92,152,198 136,745,013 160,950,041 84.96 1,474,781.37 2,059,500 214,424.05 10.41 1981 94,586,878 139,896,873 166,753,445 83.89 1,791,115.52 2,582,300 283,993.05 11.00 1983 95,330,713 141,152,582 171,741,042 82.19 1,969,599.86 2,952,200 274,055.71 9.28 1985 100,625,484 147,819,514 175,842,487 84.06 2,343,988.82 3,496,700 325,524.86 9.31 1987 106,154,761 153,441,887 179,747,130 85.37 2,813,727.90 3,924,400 369,046.18 9.40 1989 111,312,721 159,001,961 183,885,403 86.47 3,298,857.99 4,557,500 432,837.75 9.50 1991 113,804,104 162,091,174 188,184,628 86.13 3,516,141.52 5,031,500 448,348.65 8.91 1993 113,681,387 161,572,504 192,669,718 83.86 3,775,577.61 5,568,100 502,719.91 9.03 1995 117,274,186 165,941,734 197,093,059 84.20 4,244,607.26 6,200,900 588,331.07 9.49 1997 121,503,285 170,332,286 201,995,309 84.33 5,023,457.04 7,000,700 731,210.04 10.45 1999 126,008,974 175,484,446 207,348,336 84.63 5,909,328.56 7,910,800 877,292.22 11.09 2001 128,817,051 179,385,013 212,345,162 84.48 6,241,035.55 8,883,300 887,881.82 10.00 2003 128,609,786 179,567,821 217,068,101 82.72 6,287,586.38 9,378,100 747,938.91 7.98 2005 132,611,637 184,588,398 222,003,984 83.15 7,507,958.69 10,485,900 934,702.40 8.91 2007 141,070,971 194,565,001 227,239,768 85.62 8,798,500.33 11,912,300 1,115,661.33 9.37 2009 137,982,203 190,748,825 232,458,335 82.06 7,825,389.18 12,174,900 865,863.32 7.11

Source: “Number of returns,” “Adults represented on returns,” “Income represented on returns,” and “Total taxes paid” are from http://www.irs.gov/uac/Tax-Stats-2; “Total adult population” is from http://www.census.gov/popest/data/historical/index.html; “Total societal income” is from http://www.bea.gov/national/nipaweb/SelectTable.asp?Selected=N.

22  

Table 3 Progressivity indices, calculated over adults filing returns.

Year Year

1929 0.955 0.694 0.418 0.444 1969 0.298 0.224 0.161 0.154 1930 0.918 0.742 0.465 0.497 1970 0.301 0.223 0.166 0.154 1931 0.913 0.771 0.492 0.527 1971 0.331 0.244 0.182 0.169 1932 0.797 0.675 0.452 0.471 1972 0.343 0.253 0.187 0.174 1933 0.846 0.706 0.466 0.487 1973 0.328 0.240 0.178 0.165 1934 0.881 0.751 0.490 0.521 1974 0.321 0.235 0.173 0.161 1935 0.885 0.750 0.488 0.517 1975 0.362 0.263 0.196 0.181 1936 0.890 0.732 0.466 0.496 1976 0.373 0.273 0.201 0.187 1937 0.880 0.742 0.484 0.511 1977 0.390 0.283 0.210 0.194 1938 0.864 0.746 0.504 0.526 1978 0.374 0.270 0.201 0.184 1939 0.850 0.740 0.505 0.527 1979 0.375 0.271 0.201 0.185 1940 0.845 0.757 0.538 0.555 1980 0.363 0.260 0.193 0.177 1941 0.695 0.602 0.512 0.477 1981 0.345 0.245 0.184 0.167 1942 0.519 0.437 0.379 0.344 1982 0.349 0.248 0.186 0.169 1943 0.443 0.363 0.310 0.279 1983 0.360 0.257 0.189 0.174 1944 0.411 0.325 0.238 0.229 1984 0.364 0.261 0.190 0.177 1945 0.437 0.340 0.246 0.236 1985 0.368 0.263 0.191 0.177 1946 0.484 0.382 0.274 0.266 1986 0.393 0.280 0.199 0.187 1947 0.427 0.342 0.251 0.242 1987 0.385 0.264 0.187 0.174 1948 0.470 0.373 0.272 0.263 1988 0.384 0.250 0.179 0.163 1949 0.465 0.367 0.270 0.259 1989 0.369 0.239 0.173 0.156 1950 0.468 0.370 0.269 0.259 1990 0.368 0.238 0.173 0.156 1951 0.406 0.319 0.235 0.224 1991 0.379 0.250 0.180 0.164 1952 0.375 0.292 0.218 0.206 1992 0.401 0.263 0.188 0.172 1953 0.350 0.272 0.205 0.192 1993 0.421 0.284 0.197 0.185 1954 0.374 0.290 0.216 0.204 1994 0.423 0.284 0.198 0.185 1955 0.365 0.283 0.209 0.198 1995 0.431 0.287 0.198 0.186 1956 0.351 0.271 0.202 0.190 1996 0.442 0.289 0.198 0.186 1957 0.340 0.262 0.195 0.184 1997 0.442 0.281 0.194 0.180 1958 0.344 0.263 0.196 0.184 1998 0.455 0.286 0.197 0.182 1959 0.335 0.256 0.189 0.179 1999 0.465 0.288 0.197 0.182 1960 0.322 0.245 0.182 0.171 2000 0.467 0.282 0.194 0.179 1961 0.327 0.249 0.183 0.173 2001 0.464 0.294 0.204 0.188 1962 0.310 0.235 0.174 0.163 2002 0.496 0.323 0.223 0.209 1963 0.307 0.233 0.171 0.161 2003 0.491 0.316 0.219 0.203 1964 0.331 0.250 0.184 0.173 2004 0.503 0.313 0.216 0.199 1965 0.336 0.256 0.185 0.177 2005 0.515 0.309 0.213 0.195 1966 0.323 0.246 0.177 0.169 2006 0.514 0.301 0.208 0.189 1967 0.322 0.244 0.174 0.168 2007 0.514 0.296 0.205 0.185 1968 0.316 0.239 0.170 0.163 2008 0.520 0.315 0.216 0.199

2009 0.557 0.359 0.243 0.230

Minimum 0.298 0.223 0.161 0.154 (Year of minimum) (1969) (1970) (1969) (1969)

Maximum 0.955 0.771 0.538 0.555 (Year of maximum) (1929) (1931) (1940) (1940)

Median 0.401 0.283 0.201 0.186

23  

Table 4 Progressivity indices, calculated over entire adult population.

Year Year

1929 0.998 0.910 0.716 0.709 1969 0.435 0.322 0.258 0.229 1930 0.996 0.937 0.767 0.761 1970 0.450 0.332 0.271 0.237 1931 0.997 0.950 0.795 0.790 1971 0.481 0.356 0.288 0.254 1932 0.990 0.918 0.768 0.750 1972 0.487 0.361 0.291 0.258 1933 0.993 0.927 0.768 0.755 1973 0.477 0.352 0.288 0.252 1934 0.994 0.937 0.766 0.763 1974 0.473 0.349 0.286 0.250 1935 0.994 0.934 0.758 0.756 1975 0.525 0.391 0.320 0.281 1936 0.993 0.921 0.728 0.727 1976 0.530 0.397 0.323 0.285 1937 0.991 0.921 0.723 0.725 1977 0.548 0.409 0.333 0.294 1938 0.989 0.925 0.735 0.736 1978 0.535 0.398 0.326 0.286 1939 0.985 0.911 0.697 0.705 1979 0.534 0.398 0.325 0.286 1940 0.961 0.875 0.584 0.628 1980 0.532 0.394 0.324 0.283 1941 0.835 0.720 0.487 0.508 1981 0.525 0.387 0.324 0.280 1942 0.672 0.565 0.431 0.416 1982 0.539 0.398 0.334 0.289 1943 0.596 0.492 0.393 0.367 1983 0.555 0.412 0.344 0.299 1944 0.580 0.451 0.345 0.321 1984 0.556 0.416 0.348 0.303 1945 0.599 0.466 0.358 0.332 1985 0.557 0.415 0.347 0.301 1946 0.603 0.477 0.354 0.338 1986 0.575 0.427 0.349 0.306 1947 0.537 0.424 0.314 0.300 1987 0.560 0.400 0.325 0.282 1948 0.576 0.456 0.335 0.321 1988 0.557 0.381 0.311 0.264 1949 0.574 0.452 0.333 0.319 1989 0.551 0.378 0.314 0.264 1950 0.573 0.452 0.332 0.318 1990 0.555 0.384 0.321 0.270 1951 0.518 0.403 0.305 0.286 1991 0.567 0.399 0.333 0.283 1952 0.491 0.379 0.292 0.270 1992 0.595 0.419 0.347 0.296 1953 0.465 0.358 0.280 0.256 1993 0.613 0.441 0.361 0.312 1954 0.494 0.379 0.293 0.270 1994 0.617 0.444 0.364 0.315 1955 0.481 0.369 0.285 0.262 1995 0.620 0.442 0.360 0.312 1956 0.467 0.357 0.279 0.254 1996 0.628 0.441 0.356 0.308 1957 0.460 0.351 0.276 0.251 1997 0.623 0.426 0.342 0.293 1958 0.478 0.362 0.287 0.259 1998 0.630 0.426 0.340 0.292 1959 0.464 0.350 0.274 0.248 1999 0.631 0.419 0.329 0.283 1960 0.458 0.345 0.274 0.246 2000 0.635 0.414 0.326 0.279 1961 0.468 0.349 0.274 0.247 2001 0.644 0.445 0.359 0.308 1962 0.457 0.339 0.269 0.240 2002 0.673 0.482 0.389 0.339 1963 0.450 0.334 0.265 0.236 2003 0.675 0.480 0.389 0.337 1964 0.466 0.348 0.275 0.247 2004 0.681 0.470 0.378 0.325 1965 0.471 0.353 0.277 0.250 2005 0.686 0.458 0.363 0.311 1966 0.457 0.342 0.269 0.242 2006 0.685 0.450 0.359 0.305 1967 0.455 0.339 0.267 0.240 2007 0.676 0.436 0.348 0.294 1968 0.451 0.335 0.264 0.237 2008 0.700 0.480 0.390 0.333

2009 0.730 0.531 0.429 0.376

Minimum 0.435 0.322 0.258 0.229 (Year of minimum) (1969) (1969) (1969) (1969)

Maximum 0.998 0.950 0.795 0.790 (Year of maximum) (1929) (1931) (1931) (1931)

Median 0.567 0.416 0.333 0.294

24  

Figure 1. Concentration curves with respect to population.

Figure 2. Concentration curves with respect to income.

p ,  )( px ,  )( pw  

0 

0 

p

B

1  

1

)(gz ,  g ,  )(gy  

0 

0 

g

1  

1

A

C

p

)( px  

)( pw  

g

)(gz  

)(gy  

E

F

D

Income concentration curve w.r.t. population

Tax concentration curve w.r.t. population

population concentration curve w.r.t. income

tax concentration curve w.r.t. income

25  

Figure 3. Progressivity indices, calculated over adults filing returns.

Figure 4. Progressivity indices, calculated over entire adult population.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1929 1939 1949 1959 1969 1979 1989 1999 2009

Ind

ex V

alu

e Stroup

Suits

Kakwani

Mathews

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1929 1939 1949 1959 1969 1979 1989 1999 2009

Ind

ex V

alu

e Stroup

Suits

Kakwani

Mathews