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Last month, the CBO released a report on historical effective tax rates. I ran through the data with an odd goal in mind. I wanted to see if I could replicate the existing tax burden with a simple flat tax. I don’t mean to say that I’m a flat tax advocate. I simply wanted to look at what Americans actually pay and see if I could mimic the real thing with the simple rules of a flat tax.

The answer is, not really, at least not very accurately. The CBO report only gave me eight data points to work with. Still, this type of analysis has value. In fact, there are emerging fields of study, like Chaos Theory, that look to find simple rules that lie beneath highly complex structures.

Here’s what I was able to come up with. The graph below is my Faux Flat Tax going back to 1979. The blue line follows the left scale and is the flat tax rate. The black line follows the right scale and is the standard household deduction. The deduction is in 2005 dollars.

For 2005, I come up with a tax rate of 31.85% and a deduction of $35,725. So every penny a household makes under that, is completely tax free. Every penny above it is taxed at 31.85%. That includes everything—income taxes, social security, Medicare, corporate taxes, the whole shebang. And most importantly, we can abolish the IRS (wait for applause).

I realize these aren’t quite the numbers that most flat taxers have in mind, but my goal is mimicry. I took the current tax code "as is" and tried to be revenue neutral. Obviously, if I had more data points I could be more accurate.

Looking at the table does reveal some interesting information. When the two lines rise, the tax code becomes more progressive (higher taxes on the rich and less on the poor). When both lines fall, the reverse happens.

What I find interesting is that despite using just eight data points, there seems to be some continuity through the years. So even if I had many more data, I think this is a reasonable approximation of what a clear-the-table flat tax would look like.

Notice, for example, how the two lines tended to track each other for most of the 1980s and early 90s. So there was some method to the madness. I’ve scaled the graph so when the lines follow each other, the tax changes had minimal impact on a household making about $80,000. I’m sure no one planned it that way, but that relationship held up for several years and a few tax overhauls. The relationship only broke down over the past few years as we’ve seen larger deductions and lower tax rates.

One of the drawbacks of my flat tax is no matter how impressive my R-square is (.9994 in 2005), any small deviation can be rather unpleasant for certain taxpayers. That’s the messiness of using a simple model to replace a complex one. The flat tax doesn’t quite capture the right “bend” of the current tax burden. For example, under my flat tax, households making $123,500 would have a tax hike of nearly $3,000. I don’t think they would be terribly impressed by my stab at being revenue neutral.

As a general rule, my flat is close to the current burden but it tends to be slightly more progressive. The major reason is due to social insurance taxes. Since so many lower income workers are completely exempt from any taxation under my theoretical flat tax, it’s made up for with higher taxes at the upper end. The Top 1% pays about 30% more taxes while the other groups in the Top 20% pay about 5% to 10% more taxes.

Let me explain how I got my numbers. I apologize but this is going to get mathy. In the data files of the CEO report, Table 1A has the effective tax rates and Table 1C has the pre-tax income for eight subsections; the five income quintiles, plus the highest 10%, 5% and 1%.

Since those last three groups are included in the Top Quintile, I used some basic math to extrapolate four new subgroups; the highest 1%, 1% to 5%, 5% to 10% and 10% to 20%. So now I have a grand total of eight data points with which to replicate 114 million households. Here goes.

If you run a scatter plot with the X-axis being the eight income points and the Y-axis being the tax paid (income times effective tax rate), you get this:

That's for 2005. Using the trend line function, I added a linear trend line and the linear equation is also included. In the equation, y = mx + b, m is our flat tax rate and b/m is the deduction. As you can see, that's how I got 31.85%.

Here's a spreadsheet I used for the computations. Columns B through I have the effective tax rates for the eight income groups. Columns K through R have the household incomes (note that the definition for household income changed in 1986). Columns T through AA are the taxes paid. In column AC, I used the LINEST function to get "m" which is the flat tax rate. Column AD has "b," and Column AE has the deduction (AD/AC).

Source: What if We Had a Flat Tax?