9-9-9 Nonsense

Herman Cain is a Republican candidate for President. He came up with a plan for taxes that is very simple, and simply ridiculous. He calls in 9-9-9. It consists of 9% personal income tax, 9% corporate income tax and 9% national sales tax.

In an interview, Cain said that he came up with the plan this way:

"Here is how we arrived at it. I had some of the best economists in this country help me to develop this plan. You know, my background is mathematics. It was a simple regression analysis. We took the government data and looked at how much tax revenue from personal income tax, how much tax revenue came from corporate tax, how much revenue came from capital gains tax, how much revenue from the death tax. We added them all up and you do a simple regression analysis and say in order to reduce this much on corporate income, personal income and national sales tax, what should that number be if we equally break up those three buckets. It was a simple regression analysis. "

(source: http://www.foxnews.com/on-air/fox-news-sunday/2011/09/18/rep-paul-ryan-rips-obamas-jobs-plan-herman-cain-defends-his-999-tax-proposal#ixzz1YKPUrJ7Y)

Here, Herman Cain proves that he is either a liar or a fool.

First Herman Cain says "Some of the best economists ....", he doesn't name them, so they can't be asked. But he's trying to argue from authority. "An expert said it!". Cain continues this with "my background is in mathematics". His background IS in mathematics. That makes it worse. If his background was in something else, he might just be confused.

Next, Cain says "it was a simple regression analysis". Well, regression analysis CAN be simple - it's one of the first statistical techniques you learn in a course on statistics. But regression analysis is only simple when you are trying to model something simple. If you want to model the relationship between, say, the height of parents and the height of children, it's pretty simple. The United States economy is a lot of things, but simple isn't one of them.

But it gets worse! Because if you wanted to do what Cain says he did, you would NOT need regression analysis, you'd just need some very elementary algebra (really, more like arithmetic). You would need to solve this:
d = (a + b + c)*x

Where d is the total revenue and a, b and c are personal income, corporate income and total sales. No regression needed.

The problem is that this assumes that a, b and c will be constant over time. They won't. Historically, all three grow over time, but not smoothly. Herman Cain knows this. Pretty much everyone knows this. So, maybe this is where the 'simple regression analysis' comes it?

Well, no. If you want to model how things are going to change over time, you ought not use simple regression analysis. You need time series models, which account for the fact that the data are not independent (if you want to know more about what that means, see this article). Time series analysis is complicated. It's a subspecialty within statistics. Herman Cain may not know this. Having a degree in math doesn't mean that he ever studied statistics at all. But economists DO know this. Applying time series analysis to economic data is a field called econometrics. Economists are not all econometricians, but they all know the field is out there.

9-9-9 is nonsense. If Herman Cain knows this, he's a liar. If he doesn't know it, he's a fool.