The Right Way to Measure Tax Changes by Income Group

July 12, 2018

The Tax Foundation and other prominent tax policy groups typically focus on the percent change in after-tax income to measure how different proposals impact the distribution of the tax burden. This measure is preferred because it creates an accurate representation of the change in the distribution of the tax burden.

Other methods tend to overstate, or understate, the distributional effects of certain policies. Probably the most prominent example of this is measuring the “share of a total tax change.” Using this metric as a guidepost of progressivity and regressivity of a single tax change can imply some odd things about policy.

To show how, let’s take an example economy with 100 people with a distribution of income similar to taxpayers here in the United States (Table 1). The average income ranges from \$7,807 in the bottom 20 of income earners to \$1.5 million for the top earner in the economy. The share of income by income group in unequal. The bottom 20 percent earns 2.2 percent of all income, the third twenty earns 11.4 percent, and the top 1 percent earns 22.4 percent of all income.

In this mini economy, the federal government raises revenue with a flat income tax of 20 percent on all income, meaning that every individual pays 20 percent of their income in taxes. The total tax bill ends up being exactly 20 percent of each group’s total income and the share of the total tax burden is identical to its share of income. This is what you call a “proportional” tax. It is neither progressive nor regressive.

Table 1: Distribution of Tax Burden by Income Group
Average Income Total Income Share of Total Income Total Tax Bill Share of Tax Burden

Source: Tax Foundation Taxes & Growth Model, 2018

First Twenty     \$7,807.70 \$156,154.10 2% \$31,230.82 2%
Second Twenty     \$22,712.17 \$454,243.43 6% \$90,848.69 6%
Third Twenty     \$40,273.84 \$805,476.81 11% \$161,095.36 11%
Fourth Twenty     \$67,785.34 \$1,355,706.71 19% \$271,141.34 19%
Next Ten     \$103,339.13 \$1,033,391.32 15% \$206,678.26 15%
Next Five     \$148,445.62 \$742,228.12 11% \$148,445.62 11%
Next Four     \$260,154.90 \$1,040,619.59 15% \$208,123.92 15%
Top One     \$1,581,089.46 \$1,581,089.46 22% \$316,217.89 22%

Now let’s say the government decides that, because it is running a budget surplus, it will reduce the flat tax rate from 20 percent to 19 percent. Before going into the numbers, it’s worth thinking about what this will mean. The overall distribution of the burden will remain the same, even though the overall burden will be slightly lower than before. In other words, we don’t think the tax system will be any more progressive or regressive than it was before.

Below is a table showing how two methods (percent change in after-tax income and share of total tax change) measure a reduction in a flat 20 percent tax on income to 19 percent. The first column shows what this tax cut looks like in terms of a percent change in after-tax income for each group. Under this measure, each income group sees an equal increase in after-tax income of 1.25 percent. This means that everyone’s after-tax income went up in proportion—every group is seeing the same percent increase in their ability to consume goods and services. Most importantly, this proportionate increase of after-tax income is reflecting the fact that the distribution of the tax burden remained the same after thetax change—flat—even though the overall burden declined. That’s a useful feature of the “percent-change in after-tax income” metric. When there is a proportional change in taxes, it clearly indicates that with equal changes for each income group.

The measure “share of total tax change” looks a lot different. Under this measure, the first twenty taxpayers are only seeing 2.2 percent of the total tax change, while the fourth quintile sees 18.9 percent and the single highest income earner gets 22.1 percent. In stark contrast to “percent-change in after-tax income,” this measure implies that this tax cut was regressive, meaning that the new tax system is less progressive than it used to be. But we know, intuitively, that this is false: the tax rate went down from 20 percent to 19 percent, but it is still a flat, proportional tax on all income. Overall, this metric is just showing us what the distribution of income is, not the distribution of the new tax system.

Table 2: Effect of Reducing a Flat Tax on Income from 20 Percent to 19 Percent
Percent Change in After-Tax Income Share of Total Tax Change

Source: Tax Foundation Taxes & Growth Model

First Twenty          1.25% 2.2%
Second Twenty    1.25% 6.3%
Third Twenty    1.25% 11.2%
Fourth Twenty    1.25% 18.9%
Next Ten    1.25% 14.4%
Next Five    1.25% 10.4%
Next Four    1.25% 14.5%
Top One    1.25% 22.1%

By no means are these the only two methods by which one could measure the impact of tax change on income groups. Other methods include measuring the average tax change in dollars, the percent change in tax burden, and the percentage point change in the share of the tax burden. All these measures can tell us about how a tax change impacts different groups of people. However, when looking to see how a tax change impacts the distribution of the tax burden, “percent change in after-tax income” is the most informative.

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