Unexpectedly Intriguing!
April 15, 2008

Corner of IRS Form 1040 Why does the U.S. government hate people earning between $30,650 and $45,115 so much?

We asked this question yesterday when we took a closer look at the changes in tax rates between 1954 and 2006, finding that the people represented by this income range saw just a 4% reduction in their marginal tax rates, while virtually all income earners saw at least double-digit tax rate percentage reductions. These other percentage reductions in marginal tax rates from 1954 to 2006 ranged from 17% to 50% over the adjusted gross income spectrum covering $0 through $100,000 for households in inflation-adjusted, constant 2006 U.S. dollars.

As we'll show you next, and as our post title states, the reason the people and households who fall within this income range have never had their tax rates lowered very much in the U.S. is because they earn more income than any other group in the U.S. Those individual and household personal income tax filers within this $30-$45,000 range also provide the most stable source of tax collections for the U.S. government from personal income taxes, upon which the U.S. government relies to fund its massive levels of spending.

Our first step in answering the question was to find the distribution of income for income tax filers. The most recent figures we could obtain were from 2005, and the key assumption in our analysis is that the distribution of income within the households represented in the IRS' statistics of income did not change significantly from 2005 to 2006.

We took the 2005 data for the accumulated size of adjusted gross income for tax returns filed by all households for that year, adjusted the various adjusted gross income levels to be in constant 2006 dollars.

From there, we took the inflation-adjusted adjusted gross income data and the accumulative number of tax returns filed in 2005 and used ZunZun's 2-D function finder to fit a curve to the data.

We selected the second-ranked option provided by ZunZun's results, as it represented an ideal combination of low error and a minimal number of factors, which was given by the NIST MGH09 distribution:

Approx. Number of Returns = a * (x2 + b*x) / (x2 + c*x + d)

where "x" is given by adjusted gross income.

To get the distribution of income, we next used this equation and the fitted coefficients given by ZunZun to find the approximate number of returns for each $100 adjusted gross income interval between $0 and $100,000. This number is given by the difference between the values obtained by solving our distribution equation at the high end of the income interval and the low end. The results are provided in the chart below:

Approximate Number of Personal Income Tax Returns in 2005

We next approximated the accumulated adjusted gross income earned for each $100 interval represented by this distribution of personal income tax returns (for both individuals and households). We did this using a quick-and-dirty technique that involves simply multiplying the mid-range of the $100 interval by the approximate number of returns filed given for the interval by the distribution. The following chart shows our results:

Approximate Aggregate Amount of Adjusted Gross Income in 2005

The aggregate amount of Adjusted Gross Income (AGI) in the chart above is provided in 2006 U.S. dollars.

And so, we confirm using our back-of-the-envelope analysis that those individuals and households filing personal income tax returns in the income range of $30,650 to $45,115 do, in fact, earn the highest amount of income, which accounts for why these people have never had their marginal tax rates significantly lowered.

We believe this inflation-adjusted income range represents something of a sweet spot for personal income tax collections for the U.S. government, as those with lower incomes can be expected to move up into this range in good years, while those with higher incomes might be expected to move down into this range in bad economic years.

As a result, the U.S. government seeks to capitalize on the stability provided by those individuals and households within the $30-$45,000 income range and maximize its personal income tax collections by sustaining the highest marginal tax rates possible.

And that's why the government hates people earning between $30,650 and $45,000 (in constant 2006 U.S. dollars), as demonstrated by its unwillingness to provide those falling within this income range with significant tax rate cuts.

Have a happy Tax Day!

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