Not long ago, economics textbook magnate Greg Mankiw excerpted some analysis and featured a simple bit of math on his blog related to the magnitude of marginal tax rates that would apply for a person seeking to move from the bottom to the middle quintile of the income distribution. Since the original post is short, here it is excerpted in full:

Interesting numbers from Phil Gramm and Robert B. Ekelund Jr.:

The bottom quintile earned 2.2% of all earned income in 2013, but after adjusting for taxes and transfer payments, its share of spendable income rose to 12.9% — six times its proportion of earnings. The second quintile’s share more than doubled, rising from 7% of earned income to 13.9% of spendable income. For the third quintile, middle-income Americans, the increase was much smaller, from 12.6% to 15.4%.

To put it another way, the effective marginal tax rate when a person moves from the bottom to the middle quintile is 1 - (15.4-12.9)/(12.6-2.2), or 76 percent.

That math matters because these kinds of effective marginal tax rates affect how people behave. The following less-than-a-minute-and-a-half video from PolicyEd explains why:

In doing that math, Mankiw simple math illustrates how moving from the bottom tier of the income distribution to the middle comes with a large effective income tax penalty.

But David Tufte has taken that math a step further. After reviewing the jump from the bottom to the middle quintiles of the income distribution that Mankiw described, he went on to calculate the effective marginal taxes that anyone would face whenever they might have the opportunity to move from one quintile of the income distribution up into the next higher quintile, and in doing so, uncovered a really perverse feature built into the U.S. tax code.

A better way to assess this would be to figure out the effective marginal tax rates for all upward shifts. So, it’s 79% to go from lowest to second lowest, and then 73% to make the jump from second lowest to the middle quintile, 59% to go one step further, and then 44% to go from the second highest to the highest quintile. Now we’re getting somewhere. Our system as it currently stands punishes everyone for working more, harder, and better. But don’t forget that this is OK: it means we’re all chipping in to help the less fortunate. The thing is, we punish the poor who work more, harder, and better more than we punish the upper middle class who choose to do that. Is it any wonder that there’s a perception that the upper middle class has more strivers?

Taken further, it's also a potential reason why the poorest people often see playing the lottery or pursuing professional sports careers as a more viable way to get ahead than taking more incremental, achievable steps toward boosting their incomes, since the outsized gains that might be realized from these low probability of success pursuits would overcome the barrier of the effective marginal tax rates they face in moving up the income ladder.

In any case, the math is very straightforward, so we've built a tool so that anyone armed with the relevant data can do it for themselves. If you're reading this article on a site that republishes our RSS news feed, please click through to our site to access a working version of the tool. The default data would apply for an individual seeking to move up from the lowest quintile into the next higher income quintile.

Now that we have the tool to replicate the results of Mankiw's and Tufte's math, what can we do with it?

Tufte has a very interesting tax reform proposal. He advocates reallocating the U.S. welfare system and tax code so that the effective marginal tax rate faced by people moving up from each quintile rung of the income ladder to the next higher is equal at all levels (emphasis ours):

How could we do better? Let’s start with not punishing poor people who try to improve their lots more than richer people who try and improve theirs.

[Click through to see Tufte's table showing revised shares of spending]

With the shares on the right, no matter which quintiles you move up from, and no matter how many steps you go up, the effective marginal tax rate is always 60%. That’s right in the middle of the four rates noted above. Do note the calculations show that the FINAATT share of the lowest quintile should go up ever so slightly, but not by enough to round up to the next digit.

There’s something for almost everyone here. Democrats/Progressives will be happy to see that more is redistributed away from the highest quintile. Republicans/Conservatives will be happy to see that we’ve already helped the poor “enough”. And (at least in word) everyone likes to help the middle class (generally understood to be the middle three quintiles), and these numbers show that they need some help: in the range of a 10% improvement in their share. That’s $5-10K more per year for tens of millions of households across the country: in the range of a car payment, tuition, or a sweet family vacation.

This result is ironic. There are duel concerns about whether we help the poor the right amount, and whether the poor have appropriate incentives to improve their lot. It turns out that getting the incentives right for the poor is mostly about making the middle class more attractive.

This also goes some way towards explaining what some view as capriciousness on the part of middle-class voters. Many are perplexed at the numbers of the middle-class who voted both for Trump in 2016, and Obama in either of the two previous elections (and maybe even showed an interest in the maverick or third-party campaigns of Dean, Nader, McCain, Buchanan, Perot, or even Anderson). They say they’re hurting, but it’s been difficult to pin down how that could be. Now we know.

It's an important point that should be considered in any serious reform of any nation's tax and welfare system. It's time that the needs of the middle class stop being ignored by professional politicians.