# Taxes and Growth Rates and Plenty of Charts

What's the most famous thing ever drawn on a dinner napkin?

I would say it's probably the Laffer Curve. While the idea had previously existed, it was at a dinner with Donald Rumsfeld, Dick Cheney and somebody named Jude Wanniski when Arthur Laffer drew a relation between tax rates and the amount of tax collected. Most famous, perhaps, but I would also say the "most incorrect" or at least "most mis-used."

The concept of the Laffer Curve is simple: as tax rates decrease, people have more incentive to work, and therefore they work more. As they work more, the economy grows, and therefore the government takes in more revenue. By this theory, **cutting** tax rates will, lead to an **increase** in government revenues.

This has entered our politics; it is often stated that tax cuts pay for themselves (or at least partially). The Federal Government collects around 25% of GDP in taxes. To pay for themselves, each $1 of tax cuts would therefore have to create around $4 of growth. This seems unlikely. But it is taken almost as a given that tax cuts create economic growth. Let's ask the question: how much growth do tax cuts create?

Now, I'm not the first person to look into this. But given that we've been talking about taxes, it's a good time to consider it. It will also allow me to address the criticism that we don't have enough charts and graphs here at L7. If you are reading this, there is a 50-50 chance that you know a bit about regression analysis. If so, **please** skip 2 paragraphs. I'm going to do some really bad math.

A regression is a mathematical attempt to see if one thing is caused by another thing. If we regressed rain against clouds, we would see that the relationship is strong. We can then infer that it is very likely that rain is caused by clouds. Regressions can also give spurious results. For example, if you weren't careful, you might find a strong relation between umbrellas and people closing car sunroofs. But closing sunroofs doesn't cause people to use umbrellas. Both of them are caused by a third factor.

There are a lot of fancy regression techniques and terminologies, the only one you need to know to read this is "R-squared." R-squared is a statistical tool that tells you how good a model fits a set of data. It varies between zero and one. If the R-squared for a regression is 1, then the model fits the data very well. If it is zero, the model tells us nothing. You could say that there is no relationship.

So let's have some fun with some basic regression analysis. I assume this is what you also do in your spare time. Fortunately, we have good data sets for all the relevant economic data. Let's use 1961-2015 as the period for our analysis. We'll look at just U.S. numbers, but please feel free to run your home country and send me the results. We'll start with a simple one, a regression of the top marginal tax rate vs. real GDP growth. If Arthur Laffer was right, we should see a strong negative relationship:

Well...that's not good. The relationship is weak (R-squared = 9%), but even worse, it shows that higher tax rates are associated with **higher growth**. I know what you are saying - the complex incentive effect in play here takes some time to work its way into the economy. Let's look at tax rates against GDP growth the following year:

That's no better. Against the average GDP growth for the 5 following years?

This is getting bad. An R-squared of 30% is not very strong. But if anything almost seem that higher tax rates are correlated with strong growth. But, hey, GDP growth isn't everything - what people really care is if they have a job. Let's regress against unemployment. I'm using U-3, but trust me the broader unemployment definition of U-6 gives similar results.

Well, at least it isn't going the wrong way any more. But an R-squared of 2% shows there is no relationship at all. Let's try our lagged method?

I won't push my chart posting luck with the 5-year average but trust me, it's no better. If you think about it, comparing unemployment rate to top marginal rates doesn't make a low of sense. One applies to top earners, the other to people who currently have limited personal income. Let's try total US tax collection (normalized as a % of GDP). First against GDP growth:

Wow. Another R-squared of zero. You'll trust me that lagging doesn't help either. Let's try unemployment against total collections:

OK! We've gotten somewhere, found one economic variable that correlates negatively with one measure taxation! Not a strong relationship, but at least it's something. But there is a problem when we bring in the lag:

That's really not good - if it were real, the effect should persist. And I have worse news - look at tax collections against unemployment the **previous **year (lagging the other direction):

You might have heard the saying that "correlation doesn't equal causation"? All of these relationships ar