Data to Virtue

"Wisdom is to know what to do next; virtue is doing it." -- David Starr Jordan, American Naturalist -- Observation collects data from which we build knowledge. Wisdom makes sense of that knowledge. However, it is not enough to merely develop wisdom, we must act on what we know. That is virtue--and the purpose of this blog--from data to virtue.

Sunday, August 06, 2006

GDP and Taxes

In the figure below I have plotted several effective tax rates and the per capita gross domestic product (GDP) by year going back to 1979. (Click on the figure for a larger view.)

There is absolutely NO correlation between a change in the tax rate (up or down) and the growth of the per capita GDP over this time frame.

If there were a correlation between the tax rate and the GDP, then the wiggles in the GDP curves would either be offset by a year or two or three from the wiggles in the effective tax rate or mirrored for an inverse correlation. Let me state this another way, a reduction in the effective tax rate for everyone, or the top 10%, or the top 1% of incomes does not have any correlation to the growth of the GDP. The republican mantra that reducing taxes stimulates the economy is not based in data, but in the typical telling of a half truth. It's cherry picking the data, "Look we lowered taxes and the GDP went up." Of course it did, it always go up. They never also say, "Looked we raised taxes (or kept them the same) and the GDP went up." The GDP always goes up. It's like saying, "Every year there's a blue moon the GDP goes up." Well not only does it go up when there is a blue moon, but also in years when there is not a blue moon. Maybe the phases of the moon have nothing to do with the GDP. Similarly, the small tweaks to taxes that we make in the modern era don't have a statistically significant effect on the GDP. I guess if you say something enough times, people believe it to be true even when it is not.

Note that I'm not advocating that we increase taxes. I'm only saying the argument that lowering taxes increases the GDP is a statistically invalid myth propigated to foster an agenda of greed at worst and a half truth at best. For more discussion on tax rates, see my post on tax rates and revenues at:

Point out this data to people who tell you that reducing taxes helps the economy. Don’t vote for candidates that make this a major part of their platform; they clearly don’t know how to look at data. What else are they missing?

I didn’t take it back further because I didn’t have the tax rate data before 1979, but I also want to stress I don’t have any interest in returning to the exceedingly high rates of 40 years ago where large change in tax rates could be made. This is the modern era, so let’s compare apple to apples. Bringing up how things worked before that time is literally ancient tax history and has no revelvance to today.

I should also say I’ve done further analysis trying to find any correlation between a change in the effective tax rate and the slope of the growth rate of the GDP and can say with confidence that there is no statistically valid correlation. I looked at this for one, three, and five years out in case there is a delayed benefit, but found no statistically valid correlation. The tax doesn’t affect the economy nearly as much as we’d like to think. The economy grows because people go to work, work hard, produce, are creative, make new products, and the masses have enough money to buy those products. Putting more and more of the GDP into the hands of a very small number of people does not make a vibrant economy. Let’s stop this political grand standing and let the government do what it should do; leading toward appropriate technologies and social responsibility.

The effective tax rates are arrived at by taking the difference between the pretax income and the post-tax income for the respective set of returns and dividing it by the pretax income. This is the tax rate that each income group actually pays, not their tax bracket. A tax cut, or tax increase, cannot be sorted out by the bracket alone due to all the possible deductions and credits. The bottom line is what people actually pay, labeled the effective tax rate on the bottom set of curves. There are three sets of data here, one for all returns filed, one for top the 10% of incomes filed, and one for the top 1% of incomes filed. This data is from

The per capita GDP (the amount each individual contributes to the GDP) is in the top set of data in the figure. The blue curve is in the respective year dollars while the red curve is the same data adjusted for inflation, to 2000 dollars. The figure is similar in taking the actual GDP rather than the per capita GDP, but it makes more sense to normalize out the population growth. In otherwords, what is illustrated is the amount each person contributes to the GDP. This data is from and the US Census Burbeau.

Saturday, August 05, 2006

Tax Rates and Revenues

Below I plotted several tax related items as a function of the adjusted gross income (AGI) of individual US taxpayers. Note that the bottom axis is on a log scale to keep all the data from being squished up against the left axis. (Click on the figure for a larger view.)

First, the effective tax rate is already quite progressive and doesn’t need a lot of tweaking. This is a good thing. This is seen in the red curve in frame B which represents an "average" tax rate for a given AGI.

Second, all AGI groups pay, on average, below the tax bracket for their level of AGI.

Third, the use of a flat tax, applied equally to all tax brackets clearly shifts the tax burden to lower and middle income wage earners. I believe a progressive tax, similar to what we have now, is more ideal for a civilized nation.

While the way taxes revenues are obtained progressively is a good thing, it accomplished through an extremely sophisticated set of tax codes and regulations. Why not just have a straight progressive tax and simplify taxes. You make X, you pay the rate of the green curve in set B); no deductions for this, credit for that, etc. The way things turn out in what US individuals actually pay in taxes is not far off from a good structure, it's not completly broke. The problem is it's so cumbersome to get there.

On a slight side note, the agrument that it's so critical to the economy to lower taxes for the wealthiest 1% is a bunch of hooey. What supporters of these tax cuts would like you to believe is that it brings that money back into the economy and thus builds it. First of all, the few billion dollars lost to the treasury aren’t that significant in the big pictures of things. The 2002 Bush tax cuts resulted in a reduction of tax revenue of $64B that could boost the economy. This was in a GDP of almost $11T; that is less than a 0.6% shot in the arm. Besides, why are those billions better than somebody else’s billions? Is all that matters that rich people reinvest money into the economy? Does this imply that poor and middle income people take their money and bury it in the backyard or burn it in the fireplace? I guess when people spend their money on food, clothing, and shelter that’s bad for the economy. Secondly, it implies that if the government gets a dollar, none of it ends up back in the economy. Apparently government workers don't spend their money, nor does the government buy goods and services. Clearly is ridiculous to think that only money in the hands of the rich helps the economy. Thirdly, it’s clear that no AGI grouping pays close to what their tax bracket would require. Why not just have a true progressive tax through to the highest 1% of incomes? Why does the effective rate go down above an AGI of $1M and go down with increasing AGI the most for the most wealthy? It’s clearly a “favor” for the most wealthy sold on the premise it helps the economy. The recent move to hold an increase to minimum wage hostage to another tax break for the most wealthy is unconscionable.

Urge your representatives to approve tax simplification and a true progressive tax through all incomes (not a flat tax nor one that "turns back down" at the highest income levels). Also urge them to stop giving breaks to the wealthiest individuals. Let’s establish a set and simple tax schedule like the green curve in frame B), get rid of the linear feet of tax codes, and get on with life. People that are paying more than the average for their AGI should be in favor of such tax simplification. People that are paying less might even be able to set their own financial interests aside for making their life easier.


The bottom curve, A), is the number of tax returns filed in a range of AGI. As expected, it clearly shows that most returns are filed by those with low and mid incomes.

The next set of curves up, B), are three different tax rates and the tax brackets for 2003.
- The red curve is the 2003 effective tax rate for each range of AGI. This is calculated by taking the total tax revenues generated for a given range and dividing it by the cumulative AGI for that range. This makes it the rate that each particular range actually paid, not their bracket. In other words, it’s the effective tax rate, or what people actually paid in taxes, after deductions, credits, etc. for each AGI.
- The green curve is my proposed progressive tax rate. It generates the same tax revenues as the actual data.
- The blue line is the flat rate applied to everyone that would generate the same tax revenues as the actual data (11.9%).
- The black lines are the tax “brackets” (marginal tax rates) for various AGI. The range varies depending on the type of filing, single, married-jointly, married filing signally, head-of-household, etc.

The next set of curves up, C), are the distributions of the tax revenues generated by each of the tax rates described above. It shows the tax revenues generated, in billions of dollars, by each AGI range.

The top set of curves, D), are the cumulative revenues generated by each of the tax rates described from B). In other words the revenues generated, in billions of dollars, for a range of AGI added to the previous and to the previous all the way to the highest AGI range.

Actual data is from the IRS SOI Tax Stats - Individual Income Tax Returns Publication 1304, Table 1.2--2003; the most recent year available.