# Tax Rates, Real GDP Growth Rates, and an Apology

I like to post data, and I like to make my spreadsheets available to anyone who wants them. It keeps me honest. It also means that sometimes my mistakes get caught. Sure, there’s egg on my face, but hopefully I learn something from it.

Reader M. Jed has pointed out that at times I’ve been using straight averages of percentage growth rates when I should be using the geometric mean. It’s a stupid mistake, and I apologize for it. As time permits, I’ll go back to old posts and make corrections where necessary.

But I would like to focus on the post where M. Jed pointed out the error. It looked at growth rates in real gdp per capita following tax cuts, tax hikes, and years in which tax rates remained the same. If I haven’t made a mistake (insert very nervous chuckle), using data beginning in 1981, when Reagan took office, the average of the geometric mean growth rate after x years following a cut, hike, or no change in the highest personal marginal rate:

_________________tax hike___tax unchanged_tax cut
year 0______________-0.07______2.79______0.87
year 0 to year + 1______2.30______5.08______2.51
year 0 to year + 2______1.81______3.57______2.66
year 0 to year + 3______2.08______3.07______2.45
year 0 to year + 4______2.13______2.82______2.26
year 0 to year + 5______2.25______2.61______2.33
year 0 to year + 6______2.42______2.47______2.35
year 0 to year + 7______2.46______2.36______2.36

In other words, the year of a tax cut, growth rate averages 0.87%, and in the year of a tax cut through 7 years later, growth rates average 1.77%.

To summarize, the year of a tax cut, through as many as 6 years later, keeping taxes unchanged outperforms tax cuts and tax hikes. Hiking taxes outperforms keeping taxes constant and cutting taxes between any given year and 7 years later, and hiking taxes outperforms cutting taxes in the last two out years.

Results are similar using data beginning in 1978. Using data beginning in 1984, tax hikes outperform tax cuts starting four years out. And results are similar using medians of the geometric means rather than averages.

Conclusion… For the range of taxes we have observed over the past 25 years or so, over the short run, a tax cut will lead to faster growth than a tax hike (though both are outperformed by keeping taxes constant). Over a longer period, the tax cut does not lead to faster growth than tax hikes.

What’s the mechanism? Well, here’s my guess… Cutting taxes provides some stimulus (apparently not very well, since keeping taxes constant outperforms tax cuts), but mean either less government spending today or more borrowing. In either case, that means less government spending, either today or in the future, which means less government spending, either today or in the future. Government spending on public goods is necessary for the long-term growth of the country, and has few private sector substitutes. Thus, cutting taxes today leads to slower growth in the future.

Put another way… cutting taxes today means reducing growth rates in someone else’s administration. Not surprisingly, Presidents that are willing to impose costs of tax cuts on their successors are willing to compound the problem by increasing spending quite a bit at the same time.

As always, my spreadsheets are available to anyone who wants them.

Update – “Over a longer period, the tax cut does not lead to faster growth than tax hikes” now reads correctly.