Just after President Obama won reelection four years ago, he and Congress increased taxes abruptly on the wealthiest Americans. In response, the rich paid up — and then went on with their lives as before, according to a new working paper.

Economist Emmanuel Saez estimated that, in the three years since the tax hike took effect, strategies used by the rich to reduce their reported income eliminated about 19 percent of the revenue the government could have collected from the tax increase had the wealthy not changed their behavior. This relatively small figure suggests the 2013 tax hike didn't significantly affect rich Americans' drive to make money, and Saez's analysis of tax data shows the reported incomes of the wealthiest Americans, as a share of all Americans' incomes, has continued to rise.

That finding is particularly timely as the presidential campaign ends, given that Hillary Clinton and Donald Trump have diametrically opposed views on tax policy.

The Republican nominee has promised that major reductions in taxes, largely for the rich, would encourage Americans to work harder, invest more and stimulate the economy. His allies have argued that his Democratic rival's plan, which would increase taxes on corporations and the wealthy, would have the opposite effect, discouraging wealthy households from working and saving with negative economic consequences for everyone else.

In response to a question about claiming a $916 million loss to avoid paying income taxes, Donald Trump said, "Of course I do. And so do all of her donors." (The Washington Post)

However, there's limited evidence that the rich significantly changed their behavior in response to Obama's tax increase, writes Saez, who is based at the University of California at Berkeley.

As a percentage of all income before taxes, the incomes of the wealthiest 1 percent of families increased to 22 percent last year, Saez found, extending a trend toward greater inequality in free-market incomes that has continued for decades.

The share of income claimed by the extremely rich — the wealthiest 0.1 percent of families — also increased, to 10.9 percent.

The increased taxes, which took effect in 2013, included a new surtax of 3.8 percent on income from investments for the very wealthy that helped to pay for Obama's Affordable Care Act. Also, the president and Congress allowed tax relief enacted by President Bush to expire for the wealthiest households, resulting in an increase in the tax on capital gains from 15 percent to 20 percent and an increase in the top marginal rate on ordinary income from 35 percent to 39.6 percent.

Anticipating these changes, many wealthy taxpayers — especially the very richest — claimed as much income as they could on their returns in 2012 to avoid the increased rates that the following year would bring. That resulted in an increase in the apparent share of income claimed by the rich in 2012, but in 2013, the figure promptly returned to the previous level of about 20 percent, the same share recorded in 2010 and 2011.

In the following years, some wealthy taxpayers might have spent less time working or saved less of their money because they would have to pay more of what they received from doing so. Others might simply have found ways of shifting their income to avoid the increased taxes. As a result, their share of reported income might have increased more slowly than it would it would have otherwise, but the effect is difficult to discern in these figures in any case.

Saez estimated how much revenue the government lost out on from the wealthiest taxpayers by comparing the overall trend in their incomes with the data for taxpayers who were not quite as wealthy and not as severely affected by the increases in 2013 — that is, those in the 90th through the 98th percentiles of income.

It is a speculative estimate, because it is impossible to know for certain what decisions wealthy taxpayers would have made about work and saving since 2013 had their taxes not increased.

Meanwhile, as far as the rest of the country is concerned, overall economic conditions depend not only on the decisions of the very rich, but also on many other factors that taxes can influence one way or another.

Rather than expanding the economy by encouraging Americans to save and invest, for instance, Trump's plan to reduce taxes on the wealthy could actually hamper the economy over the long run if he instead borrowed the money needed to run the government, according to a recent projection from the nonpartisan Tax Policy Center.

That forecast relies on the assumption that increasing federal borrowing would also increase rates of interest. With investors buying more Treasury bonds, on this analysis, they would have less available to loan to the rest of the economy — for businesses to hire and expand and for consumers to buy big-ticket items such as cars and houses.

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