Paul Krugman, “The Economics of Soaking the Rich,” The New York Times, 01/05/2019.
Peter Diamond and Emmanuel Saez, “The Case for a Progressive Tax: From Basic Research to Policy Recommendations.” Journal of Economic Perspectives, Vol. 25, #4 (Fall 2011): 165-190.
The resurgence of the Democratic Party in the 2018 elections is encouraging more discussion of some progressive policy ideas. One of those is a more progressive income tax, as some Democrats advocate higher taxes on the wealthy in order to fund liberal programs like early childhood education and assistance for college tuition.
Paul Krugman’s column calls attention to both the political debate over progressive taxation and the relevant economic research, in particular the work by Peter Diamond and Emmanuel Saez. They make a strong case that a higher top tax rate is in the public interest.
The problem
The top federal bracket is now 37%, which applies to income over $510,300 for individuals and $612,350 for married couples filing joint returns. Is 37% too low, too high, or about right?
Advocates for a higher rate argue that once people reach a certain level of wealth, no one derives much benefit from their additional consumption. Society would benefit from some redistribution of wealth from those who have enough to those who have too little, either through direct spending on the needy or general spending on public goods like good roads or good schools. On the other hand, advocates for a low rate argue that high taxes reduce people’s incentive to earn income by making useful contributions to the economy. When taxes get too high, public revenue can actually drop because the tax base shrinks.
The optimal tax theory presented by Diamond and Saez acknowledges the effects of taxes on both social welfare and personal incentive. Optimal taxation requires some trade-off between the two.
Social welfare is larger when resources are more equally distributed, but redistributive taxes and transfers can negatively affect incentives to work, save, and earn income in the first place. This creates the classical trade-off between equity and efficiency which is at the core of the optimal income tax problem.
The social welfare effect
The idea that money received by very high earners could be put to better use through taxation and public spending is based on the “marginal utility of consumption.” That is the idea that how much you value an additional dollar you get to spend depends on how many dollars you already have. Each increment of income matters more to a poor person than a rich person, and so the marginal utility of consumption declines dramatically as income increases. Taxing the highest incomes in order to spend for the benefit of the less affluent majority should contribute positively to the general good.
The potential positive effect of taxing the rich can be easily calculated by first computing the tax revenue obtained from the highest bracket. For example, if the highest bracket begins at $500,000, and the average taxpayer in that bracket makes $1.5 million, then $1 million is taxable at the highest rate. A 37% rate raises an average of $370,000 from each top-bracket taxpayer, in addition to whatever is collected from the income falling into lower brackets.
The potential effect on the public good is offset by the loss to rich people of their benefit from private consumption. But since the marginal utility of consumption declines so dramatically as income increases, this offset is very small. Diamond and Saez ignore it in order to simplify their mathematical presentation, but make an adjustment for it before they are finished. One estimate is that marginal utility for people in the top 1% is only 3.9% of the marginal utility of the median-income family.
The potential social welfare effect of taxing the rich is only achieved if the revenue is spent usefully, as opposed to foolishly or wastefully. But that is more of a political problem than a problem of economic theory.
The behavioral effect
How much do high taxes reduce incentives to earn high incomes? That depends on what the authors call “behavioral elasticity,” which they define as the “percent increase in average reported income…when the net-of-tax rate increases by 1 percent.” If the tax rate is r, then the net-of-tax rate is 1-r, the portion of top-bracket income you get to keep. The more you get to keep, the greater incentive you should have to earn.
The paper’s formulas and charts are confusing for us non-economists, so here’s a concrete example with simple numbers. Let’s start with the average wealthy taxpayer described above, earning $1.5 million and paying top-bracket rates on $1 million (the portion falling over the $500,000 threshold). Say that a future Congress is considering raising the top bracket rate from 40% to 45%. If income remained the same, that would generate additional revenue of $50,000 (5% of $1 million) per wealthy taxpayer. But now income goes down some because of reduced incentive, in response to the change in the net-of-tax rate. Reducing it from 60% to 55% is a percentage decline of 5/60 or 8.3%. Research on behavioral elasticity has found that the effect on income is about one-quarter of the percentage change in the net-of-tax rate, in this case about 2.1%. So the estimated decline in income is 2.1% of $1.5 million, or $31,500, leaving $1,468,500 to be taxed, $968,500 of it at the top rate. Top-bracket tax revenue from this taxpayer still goes up, but only from $400,000 (40% of $1 million) to $435,825 (45% of $968,500). The behavioral effect is significant, but it is not enough to offset all the additional revenue from the tax hike.
Suppose, however, that we start from a much higher initial rate, and consider increasing the top rate from 75% to 80%. Starting from the same taxpayer earning $1.5 million, the potential increase in revenue is the same, $50,000, but the effect on the incentive to earn is in theory much larger. With the net-of-tax rate for top-bracket income only 25% to begin with, taxing away another 5% has a greater proportional impact. The reduction from 25% to 20% is a percentage decline of 5/25 or 20%. The estimated effect on income is again one-quarter of that or 5%. The estimated decline in income is $75,000, leaving $1,425,000 to be taxed, $925,000 at the top rate. Top-bracket tax revenue from this taxpayer now goes down, from $750,000 (75% of $1 million) to $740,000 (80% of $925,000). Raising the top bracket further when it is already so high is counter-productive.
The optimal top tax rate
These examples demonstrate the general principle that when the top rate is relatively low, raising it can generate additional revenue to be used to enhance general social welfare. But when the top rate is already relatively high, trying to raise it further can be counter-productive.
Diamond and Saez use the same mathematical relationships to calculate the sweet spot where revenue is maximized. The optimal top rate comes out 73%. Rates below that sacrifice revenue and overlook an opportunity to increase the general welfare. Rates above that reduce revenue by reducing the incentive to earn high incomes.
Three additional points are worth noting:
- The analysis to this point does not take into account the loss of consumption utility for the wealthy taxpayer. However, the marginal utility of consumption for the rich is so low that incorporating it into the analysis only lowers the optimal tax rate by about one percentage point.
- The optimal rate should take into account all taxes based on income, not just federal income taxes. At the time the authors were writing, other taxes added about 7.5% to the total tax burden, after federal deductions for state taxes were considered. So a total top rate of 73% implies a federal top rate of no more than 65.5%.
- The case for raising middle-class taxes would be much weaker, because of their much higher marginal utility of consumption. The more that people are already spending their income on essentials, the less government can enhance the common good through taxing and spending.
The politics of taxation
The United States has been in a relatively low-tax era since the “Reagan Revolution” of the 1980s. From the 1950s to 1970s, the top federal rate was in the 70-90% range. Since the 1980s, it has dropped from 50% to today’s 37%. According to the Diamond-Saez analysis, 90% is too high, but 37% is far too low.
During this era, achieving lower taxes, especially for the wealthy, has been the highest domestic priority for Republicans. They have pursued this goal almost without regard for the fiscal consequences, advocating lower taxes whether they can be matched by spending cuts or just result in larger deficits. Their rhetorical arguments have gone far beyond what economists know, belittling the benefits of public spending and exaggerating the deleterious effects of high taxes on earning incentives and economic growth. They have become the party of hostility to government and affection for those who feather their own nests.
The public benefits of high taxes on the rich may–like climate change–be one of those inconvenient truths that too many of our leaders choose to ignore. Rather than dismissing advocates of higher taxes as lunatics, economist Paul Krugman would like us to base tax policy more on facts and reasoned analysis. For example, he points out that the economy grew at a somewhat faster rate during the postwar era of high tax rates than it has grown lately.
Republicans almost universally advocate low taxes on the wealthy, based on the claim that tax cuts at the top will have huge beneficial effects on the economy. This claim rests on research by. . .well, nobody. There isn’t any body of serious work supporting G.O.P. tax ideas, because the evidence is overwhelmingly against those ideas.
Beneath the Surface 