Peter Diamond, Emmanuel Saez, Paul Krugman and Me!! Looking at Optimal Tax Rates

by Mike Kimel

Peter Diamond, Emmanuel Saez, Paul Krugman and Me!! Looking at Optimal Tax Rates

Via Paul Krugman, I learned of this paper by Peter Diamond and Emmanuel Saez. Diamond, of course, is a Nobel Laureate. I will be shocked if Saez isn’t one too in ten or fifteen years.

Long story made very short, Diamond and Saez jump through a lot of hoops and find that the optimal top marginal income tax rate (all in, that is, including federal, state and local), which they define as maximizing social welfare, is about 73%.

Now, long time readers may recall I’ve been doing this sort of analysis for years, though of course I’ve been looking at tax rates that maximize real GDP growth. Simply put, you cannot maximize long run social welfare if you aren’t maximizing economic growth.

My approach is much simpler than that followed by Diamond and Saez. I like to think its much more intuitive and easier to explain. I note that US data shows a simple quadratic relationship between real GDP growth from one year to the next and tax rates:

growth in real GDP, t to t+1 = f(top marginal tax rate, top marginal tax rate squared, other variables)

One recent post on the topic is here. (Unlike the Laffer curve, the coefficients come out statistically significant and with the right signs.)

I mention all this to note that no matter what I throw into the equation, I find that the top marginal tax rate that maximizes economic growth is somewhere around 65%. Of course, I’ve focused only on federal tax rates… add in state and local it comes pretty close to what Diamond and Saez have found.

As I noted above, my approach is somewhat simpler, and easier to follow than that of Diamond and Saez. Part of the reason is that they come at it from a point of view of elasticities. But with all due respect to my betters (Diamond and Saez, and Krugman as well considering the explanation in his post) I think this is the wrong way to consider the problem. It requires all sorts of assumptions and generalizations about people’s behavior, some of which are both false and create resistance from folks on the right.

For example, there is a notion that raising tax rates will reduce people’s willingness to work… which is only true above certain thresholds. (That threshold, of course, varies per individual.) As anyone who has ever had a business will tell you (when they’re not busy demanding tax reductions), you don’t pay taxes on income from the business if you turn around and reinvest that income. (An accountant would talk to you about decreasing your tax liability by increasing expenses which amounts to the same thing.) You only pay taxes on that income you take that income out, presumably for consumption purposes.

So to simplify, consider an example…. is a successful businessperson more likely to take money out of the business if his/her tax rate is 70% or if its 25%? In general, a person is more likely to take that money at 25%, as there’s less of a penalty. At 70% tax rates, there is more of an incentive to reinvest in the business, creating more growth in the business in subsequent years, and more economic growth thereafter. 70% tax rates are more likely to generate faster economic growth than 25% tax rates precisely because people are self-interested and the higher tax rates induce people to continue investing in things they do well.

(Of course, tax rates can get too high. At 95%, people will reinvest almost every dime… even if they have exhausted every good investment opportunity they have. Thus, to avoid taxes they’ll be making lousy investments which in turn slow economic growth.)

Still, its gratifying to see others who are more, er, credentialed doing similar work. If I might end on a digression, though, I can think of a number of examples of work being done on blogs by people who are essentially hobbyists which is somewhat ahead of the academic literature. However, to a large extent, if something wasn’t published in the academic literature, for all practical purposes it didn’t happen. Which is a shame, because most of us who aren’t academics don’t have time or the resources required for such publication (such as access to econlit). That inevitably slows economic development three ways:

1. the lack of recognition discourages hobbyists who have the potential and otherwise would have the willingness to improve on the existing literature
2. should such hobbyists persist and do the research, that research will not be widely disseminated even if it is an improvement over the academic literature
3. it maintains an insular attitude among those who are not hobbyists. As smart as Diamond, Saez, and Krugman all are, none of them are thinking the way someone running a business thinks of they’d have realized immediately how people who are running a business react to higher and lower tax rates. I have read a lot of academic papers on taxation and have yet to stumble on one that gets it right.

Thanks to Steve Roth of Asymptosis and Jazzbumpa of Retirement Blues for notifying me of Krugman’s post.

And since I always offer… if anyone wants any spreadsheets showing the quadratic relationship between tax rates and economic growth or anything else I’ve done, drop me a line. I’m at my first name (mike) then a period then my last name (kimel – with one m only!!!) at

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