Dullroar

For our purposes, there are three main differences between a progressive and flat tax: First, the tax rate is lower with a flat tax. Much lower. And second, the theory goes that because people are going to have much lower taxes, they'll invest some amount of their additional income (and proceeds from those investments will generate more tax revenue). Third, because the tax code is dramatically simpler with a flat tax, the assumption is that there will be less tax evasion.

To start off, I've tried to use the simplest model of taxation that I could get away with: total revenue (R) is equal to the average tax rate (T) multiplied by the average income (I). For the progressive tax, R_prog = T_prog*I, where the "_prog" suffix denotes we're talking about the progressive tax. What's the flat tax equation look like then?

R_flat = T_flat * (I + (T_prog - T_flat)*I*ROI)

Which means that the revenue from the flat tax is equal to the flat tax rate multiplied by the average income (of course), along with the amount of taxes that come from investing the money they saved by not paying a progressive tax. That second term is the amount of money saved (I times the difference in tax rates) multiplied by the rate of return on that saved money (ROI), which finally is multiplied by T_flat again to compute the tax revenue. This is actually much less complicated than it looks.

So I wondered: at what point does R_prog equal R_flat? In other words, for a given progressive tax rate and a given flat tax rate, what does the typical ROI have to be for a flat tax to raise just as much money as a progressive tax? A bit of algebra later, I had this:

ROI = (T_flat + T_flat * T_prog + T_prog) / (T_flat * T_flat)

For instance, if the average progressive tax rate was 30% and the flat tax rate was 15%, the ROI would have to be... 400%. That means that if the rich people who save scads of money from going to a flat tax were to just quadruple their money by investing it, we'd be even. That sounds impossible, but in fact it's not if you're patient. Historically, the stock market has earned about 10% per year (on average), which means that an investment in the market will double every 7 years. Two doublings (or 14 years) later, you've got your 400% return. And after those 14 years were up, hey, the flat tax would pull in more revenue than the progressive tax!

At this point, I was pretty amazed: It looked like this flat tax could work. Sure, the government would have to borrow some money for the first 14 years or so, but eventually, the flat tax would be sustainable. (Actually, the government would have to pay maybe 5% interest on the money it's borrowing, so in fact maybe the period of government borrowing would have to last more like 30 years.) Still, in government terms, a few decades is nothing. A blink of the proverbial eye.

Except I found a bit of a problem with my model: I assumed that all of those tax savings would go toward investments. What would happen if people invested less? It seemed as long as they invested enough money in the market to stay ahead of the interest payments on the government borrowing, the math would work. In this case "enough" turns out to be 50%. Ok. So how much do people save, anyway?

Finally, we come to the part of the story where I do real research, sort of. I refer you to page 26 of this Federal Reserve study from 2001. Optimistically, people save 10% of their income on average. Unfortunately for the flat taxers, the people least likely to save are those in the highest income brackets (the very ones we most need to save in order to make the flat tax work). Even worse, as this 2001 study shows, if you dump a bunch of money on people (as happened during the boom in the late 1990's), those in the highest tax brackets save less not more.

So all of this was a long-winded way of saying: According to my highly dubious back of the envelope calculations, a flat tax just won't work.