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; [email protected]. 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.
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.
1 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.
2 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.”
3 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
4 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.
5 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
corresponding cumulative portion of taxes paid. Alternatively, letting
represent the
denote the cumulative
portion of income earned by individuals with the lowest incomes, we can let
the cumulative portion of taxes paid by individuals, and
represent
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,
with respect to population, and
is the income concentration curve
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).
6 For a progressive tax,
∈ 0,1 , and
for all
Figures 1 and 2 illustrate these four curves. In Figure 1,
for all
∈ 0,1 .
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”.
“tax concentration curve with respect to population”. In Figure 2,
is the area below the
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
7 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.
the ratio of the weighted value of this difference (
cumulative portion of income over the population,
weighted value of this difference (
and
each focus on
) to a similarly weighted value of
, while
and
focus on the ratio of the
) to a similarly weighted value of population, .
Furthermore, two different approaches are taken regarding how to weight each term in this ratio:
and
and
are constructed by placing equal weight on each segment of the population, while
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
the value of each index is zero. In contrast, for a progressive tax
that
0 and
0. As a result,
and
, so
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
8 increases while
and
increase if
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
decrease in both
and
and
. Furthermore, both
and
or
, but does lead to a
increase, while ,
,
,
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, (
respect to population, (
), an income concentration curve with
), a tax concentration curve with respect to income, (
population concentration curve with respect to income, (
), and a
), 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).
9 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.
10 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.
11 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
12 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, .3141,0 .
. is the point
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
total societal income.
.3477
.1092 of
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.
13 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.
14 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.
,
has a value above their respective median in every year from 2001 onward, while
, and
each
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.
15 Furthermore, starting under EGTRRA and
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
reported value, of
is 2.30 times greater than its smallest
is 2.95 times greater than its smallest reported value, of
greater than its smallest value, and of
is 3.08 times
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.
16 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.
References:
Atkinson, A.B. (1973). How Progressive Should Income Tax Be? In M. Parkin & A.R. Nobay
(Eds.), Essays in Modern Economics (pp. 90-109). London: Longman.
Congressional Budget Office. (2012). The Distribution of Household Income and Federal
Taxes, 2008 and 2009. Washington, D.C.: Congress of the United States. Retrieved
October 2013, from http://www.cbo.gov/publication/43373
Formby, J.P., Seaks, T.G. & Smith, W.J. (1981). A Comparison of Two New Measures of Tax
Progressivity. The Economic Journal, 91(364), 1015-1019.
17 Kakwani, N.C. (1977a). Measurement of Tax Progressivity: An International Comparison. The
Economic Journal, 87(345), 71-80.
Kakwani, N.C. (1977b). Applications of Lorenz Curves in Economic Analysis. Econometrica,
45(3), 719-727.
Kiefer, D.W. (2005). Progressivity, Measures of. In J.J. Cordes, R.D. Ebel, & J.G. Gravelle
(Eds.), The Encyclopedia of Taxation and Tax Policy (pp. 304-307). Washington, D.C.:
The Urban Institute Press.
Konow, J. (2003). Which is the Fairest One of All? A Positive Analysis of Justice Theories.
Journal of Economic Literature, 41(4), 1188-1239.
Mathews, T. (2013). Insights on Measurements of and Recent Trends in Tax Progressivity.
Applied Economics Research Bulletin, forthcoming.
McBride, W. (2012). CBO Report Shows Increasing Redistribution in the Tax Code Despite No
Long-term Trend in Income Inequality. Tax Foundation: Fiscal Fact, July 25, 2012.
Musgrave, R.A. & Thin, T. (1948). Income Tax Progression, 1929-48. The Journal of Political
Economy, 56(6), 498-514.
Reynolds, M. & Smolensky, E. (1977). Public Expenditures, Taxes, and the Distribution of
Income: The United States, 1950, 1961, 1970. New York: Academic Press.
Stroup, M.D. (2005). An Index for Measuring Tax Progressivity. Economics Letters, 86(2),
205-213.
Suits, D.B. (1977). Measurement of Tax Progressivity. The American Economic Review, 67(4),
747-752.
Tax Foundation. (2009a). U.S. Federal Individual Income Tax Rates History, 1862-2013
(Nominal and Inflation-Adjusted Brackets). Retrieved October 2013, from
18 http://taxfoundation.org/article/us-federal-individual-income-tax-rates-history-19132013-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-federalindividual-income-tax-data-1980-2008
19 Table 1
Summary of relations between the four different indices.
Each segment of the
population weighted…
Equally
Ratio of the difference Income [ x ( p ) ]
between income and
taxes paid to…
Population [ p ]
B
BC
B
K
A BC
St 
20 by marginal contribution to
cumulative income [ x ( p ) ]
D
S
DE
M 
D
DEF
Table 2
Characteristics of entire population and taxpayers.
Number of
returns
4,044,327
3,225,924
3,723,558
4,575,012
6,350,148
7,570,320
25,770,089
43,506,553
49,750,991
54,799,936
51,301,910
55,042,597
57,415,885
57,818,164
59,407,673
59,838,162
61,067,589
63,511,244
67,198,928
71,282,524
75,375,731
74,146,785
80,248,984
81,585,541
86,066,234
92,152,198
94,586,878
95,330,713
100,625,484
106,154,761
111,312,721
113,804,104
113,681,387
117,274,186
121,503,285
126,008,974
128,817,051
128,609,786
132,611,637
141,070,971
137,982,203
Year
1929
1931
1933
1935
1937
1939
1941
1943
1945
1947
1949
1951
1953
1955
1957
1959
1961
1963
1965
1967
1969
1971
1973
1975
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
2007
2009
Adults
represented
on returns
5,901,926
4,635,290
5,494,891
6,675,038
9,132,970
10,894,018
39,908,842
65,738,182
74,631,339
81,288,966
82,169,845
87,545,182
91,566,023
93,115,608
95,953,192
96,798,855
97,447,864
101,007,468
106,245,102
111,784,150
117,530,398
116,610,979
123,842,306
125,342,139
129,781,866
136,745,013
139,896,873
141,152,582
147,819,514
153,441,887
159,001,961
162,091,174
161,572,504
165,941,734
170,332,286
175,484,446
179,385,013
179,567,821
184,588,398
194,565,001
190,748,825
Total adult
population
78,619,000
81,209,172
83,392,142
85,698,080
87,876,551
90,311,164
93,135,825
95,837,053
98,372,755
100,723,315
103,444,722
106,048,368
108,053,025
110,192,874
112,514,204
114,779,195
117,900,175
120,822,242
124,572,108
128,784,895
132,904,639
137,852,263
143,144,603
148,805,353
154,776,287
160,950,041
166,753,445
171,741,042
175,842,487
179,747,130
183,885,403
188,184,628
192,669,718
197,093,059
201,995,309
207,348,336
212,345,162
217,068,101
222,003,984
227,239,768
232,458,335
Percentage
of adults
on returns
7.51
5.71
6.59
7.79
10.39
12.06
42.85
68.59
75.87
80.71
79.43
82.55
84.74
84.50
85.28
84.34
82.65
83.60
85.29
86.80
88.43
84.59
86.52
84.23
83.85
84.96
83.89
82.19
84.06
85.37
86.47
86.13
83.86
84.20
84.33
84.63
84.48
82.72
83.15
85.62
82.06
Income
represented on
returns
(millions of $)
24,800.74
13,605.00
11,008.64
14,909.81
21,238.57
22,938.92
58,527.22
99,209.86
120,301.13
150,295.28
161,373.21
203,097.03
229,863.41
249,429.18
281,308.43
306,616.92
330,935.74
370,270.62
430,663.21
506,641.75
605,578.95
676,334.16
830,653.26
954,089.43
1,165,776.87
1,474,781.37
1,791,115.52
1,969,599.86
2,343,988.82
2,813,727.90
3,298,857.99
3,516,141.52
3,775,577.61
4,244,607.26
5,023,457.04
5,909,328.56
6,241,035.55
6,287,586.38
7,507,958.69
8,798,500.33
7,825,389.18
Total societal
income
(millions of $)
84,900
65,200
46,800
60,300
74,100
72,900
96,000
152,100
171,600
190,900
207,000
257,900
291,700
316,000
358,500
392,300
428,800
479,500
555,500
648,100
778,300
903,100
1,110,500
1,334,900
1,632,500
2,059,500
2,582,300
2,952,200
3,496,700
3,924,400
4,557,500
5,031,500
5,568,100
6,200,900
7,000,700
7,910,800
8,883,300
9,378,100
10,485,900
11,912,300
12,174,900
Total taxes
paid (millions
of $)
1,001.94
246.13
374.12
657.44
1,141.57
890.93
3,815.42
16,974.23
17,050.38
18,076.28
14,538.14
24,438.74
29,656.67
29,613.72
34,393.64
38,645.30
42,225.50
48,203.58
49,529.70
62,919.96
86,568.22
85,397.55
108,068.05
124,511.77
159,746.44
214,424.05
283,993.05
274,055.71
325,524.86
369,046.18
432,837.75
448,348.65
502,719.91
588,331.07
731,210.04
877,292.22
887,881.82
747,938.91
934,702.40
1,115,661.33
865,863.32
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.
21 Taxes paid as
percentage of
societal
income
1.18
0.377
0.799
1.09
1.54
1.22
3.97
11.16
9.94
9.47
7.02
9.48
10.17
9.37
9.59
9.85
9.85
10.05
8.92
9.71
11.12
9.46
9.73
9.33
9.79
10.41
11.00
9.28
9.31
9.40
9.50
8.91
9.03
9.49
10.45
11.09
10.00
7.98
8.91
9.37
7.11
Table 3
Progressivity indices, calculated over adults filing returns.
Year
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
Year
0.955
0.918
0.913
0.797
0.846
0.881
0.885
0.890
0.880
0.864
0.850
0.845
0.695
0.519
0.443
0.411
0.437
0.484
0.427
0.470
0.465
0.468
0.406
0.375
0.350
0.374
0.365
0.351
0.340
0.344
0.335
0.322
0.327
0.310
0.307
0.331
0.336
0.323
0.322
0.316
0.694
0.742
0.771
0.675
0.706
0.751
0.750
0.732
0.742
0.746
0.740
0.757
0.602
0.437
0.363
0.325
0.340
0.382
0.342
0.373
0.367
0.370
0.319
0.292
0.272
0.290
0.283
0.271
0.262
0.263
0.256
0.245
0.249
0.235
0.233
0.250
0.256
0.246
0.244
0.239
0.418
0.465
0.492
0.452
0.466
0.490
0.488
0.466
0.484
0.504
0.505
0.538
0.512
0.379
0.310
0.238
0.246
0.274
0.251
0.272
0.270
0.269
0.235
0.218
0.205
0.216
0.209
0.202
0.195
0.196
0.189
0.182
0.183
0.174
0.171
0.184
0.185
0.177
0.174
0.170
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
0.444
0.497
0.527
0.471
0.487
0.521
0.517
0.496
0.511
0.526
0.527
0.555
0.477
0.344
0.279
0.229
0.236
0.266
0.242
0.263
0.259
0.259
0.224
0.206
0.192
0.204
0.198
0.190
0.184
0.184
0.179
0.171
0.173
0.163
0.161
0.173
0.177
0.169
0.168
0.163
Minimum
(Year of minimum)
Maximum
(Year of maximum)
Median
22 0.298
0.301
0.331
0.343
0.328
0.321
0.362
0.373
0.390
0.374
0.375
0.363
0.345
0.349
0.360
0.364
0.368
0.393
0.385
0.384
0.369
0.368
0.379
0.401
0.421
0.423
0.431
0.442
0.442
0.455
0.465
0.467
0.464
0.496
0.491
0.503
0.515
0.514
0.514
0.520
0.557
0.298
(1969)
0.955
(1929)
0.401
0.224
0.223
0.244
0.253
0.240
0.235
0.263
0.273
0.283
0.270
0.271
0.260
0.245
0.248
0.257
0.261
0.263
0.280
0.264
0.250
0.239
0.238
0.250
0.263
0.284
0.284
0.287
0.289
0.281
0.286
0.288
0.282
0.294
0.323
0.316
0.313
0.309
0.301
0.296
0.315
0.359
0.223
(1970)
0.771
(1931)
0.283
0.161
0.166
0.182
0.187
0.178
0.173
0.196
0.201
0.210
0.201
0.201
0.193
0.184
0.186
0.189
0.190
0.191
0.199
0.187
0.179
0.173
0.173
0.180
0.188
0.197
0.198
0.198
0.198
0.194
0.197
0.197
0.194
0.204
0.223
0.219
0.216
0.213
0.208
0.205
0.216
0.243
0.161
(1969)
0.538
(1940)
0.201
0.154
0.154
0.169
0.174
0.165
0.161
0.181
0.187
0.194
0.184
0.185
0.177
0.167
0.169
0.174
0.177
0.177
0.187
0.174
0.163
0.156
0.156
0.164
0.172
0.185
0.185
0.186
0.186
0.180
0.182
0.182
0.179
0.188
0.209
0.203
0.199
0.195
0.189
0.185
0.199
0.230
0.154
(1969)
0.555
(1940)
0.186
Table 4
Progressivity indices, calculated over entire adult population.
Year
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
0.998
0.996
0.997
0.990
0.993
0.994
0.994
0.993
0.991
0.989
0.985
0.961
0.835
0.672
0.596
0.580
0.599
0.603
0.537
0.576
0.574
0.573
0.518
0.491
0.465
0.494
0.481
0.467
0.460
0.478
0.464
0.458
0.468
0.457
0.450
0.466
0.471
0.457
0.455
0.451
0.910
0.937
0.950
0.918
0.927
0.937
0.934
0.921
0.921
0.925
0.911
0.875
0.720
0.565
0.492
0.451
0.466
0.477
0.424
0.456
0.452
0.452
0.403
0.379
0.358
0.379
0.369
0.357
0.351
0.362
0.350
0.345
0.349
0.339
0.334
0.348
0.353
0.342
0.339
0.335
0.716
0.767
0.795
0.768
0.768
0.766
0.758
0.728
0.723
0.735
0.697
0.584
0.487
0.431
0.393
0.345
0.358
0.354
0.314
0.335
0.333
0.332
0.305
0.292
0.280
0.293
0.285
0.279
0.276
0.287
0.274
0.274
0.274
0.269
0.265
0.275
0.277
0.269
0.267
0.264
Year
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
0.709
0.761
0.790
0.750
0.755
0.763
0.756
0.727
0.725
0.736
0.705
0.628
0.508
0.416
0.367
0.321
0.332
0.338
0.300
0.321
0.319
0.318
0.286
0.270
0.256
0.270
0.262
0.254
0.251
0.259
0.248
0.246
0.247
0.240
0.236
0.247
0.250
0.242
0.240
0.237
Minimum
(Year of minimum)
Maximum
(Year of maximum)
Median
23 0.435
0.450
0.481
0.487
0.477
0.473
0.525
0.530
0.548
0.535
0.534
0.532
0.525
0.539
0.555
0.556
0.557
0.575
0.560
0.557
0.551
0.555
0.567
0.595
0.613
0.617
0.620
0.628
0.623
0.630
0.631
0.635
0.644
0.673
0.675
0.681
0.686
0.685
0.676
0.700
0.730
0.435
(1969)
0.998
(1929)
0.567
0.322
0.332
0.356
0.361
0.352
0.349
0.391
0.397
0.409
0.398
0.398
0.394
0.387
0.398
0.412
0.416
0.415
0.427
0.400
0.381
0.378
0.384
0.399
0.419
0.441
0.444
0.442
0.441
0.426
0.426
0.419
0.414
0.445
0.482
0.480
0.470
0.458
0.450
0.436
0.480
0.531
0.322
(1969)
0.950
(1931)
0.416
0.258
0.271
0.288
0.291
0.288
0.286
0.320
0.323
0.333
0.326
0.325
0.324
0.324
0.334
0.344
0.348
0.347
0.349
0.325
0.311
0.314
0.321
0.333
0.347
0.361
0.364
0.360
0.356
0.342
0.340
0.329
0.326
0.359
0.389
0.389
0.378
0.363
0.359
0.348
0.390
0.429
0.258
(1969)
0.795
(1931)
0.333
0.229
0.237
0.254
0.258
0.252
0.250
0.281
0.285
0.294
0.286
0.286
0.283
0.280
0.289
0.299
0.303
0.301
0.306
0.282
0.264
0.264
0.270
0.283
0.296
0.312
0.315
0.312
0.308
0.293
0.292
0.283
0.279
0.308
0.339
0.337
0.325
0.311
0.305
0.294
0.333
0.376
0.229
(1969)
0.790
(1931)
0.294
Figure 1. Concentration curves with respect to population.
p , x ( p ) , w( p ) 1 p
x( p )  Income concentration curve
A
w.r.t. population
B
w( p )  Tax
concentration curve
C
w.r.t. population
p
0
1
0
Figure 2. Concentration curves with respect to income.
z ( g ) , g , y ( g ) 1 z ( g )  population concentration curve
w.r.t. income
g
F
y ( g )  tax concentration curve
D
w.r.t. income
E
g
0
1
0
24 Figure 3. Progressivity indices, calculated over adults filing returns.
1.0
0.9
0.8
Index Value
0.7
0.6
Stroup
0.5
Suits
Kakwani
0.4
Mathews
0.3
0.2
0.1
0.0
1929
1939
1949
1959
1969
1979
1989
1999
2009
Figure 4. Progressivity indices, calculated over entire adult population.
1.0
0.9
0.8
Index Value
0.7
0.6
Stroup
0.5
Suits
Kakwani
0.4
Mathews
0.3
0.2
0.1
0.0
1929
1939
1949
1959
1969
25 1979
1989
1999
2009