President Obama identified economic inequality as “the defining issue of our time.” (Carolyn Kaster/AP)

Zachary Goldfarb says that President Obama “has reduced inequality.” Timothy Noah says “inequality has gotten worse” under Obama. They’re both right.

Part of the apparent disagreement is a matter of focus. Goldfarb mostly assesses the impact of Obama’s tax policies, while Noah argues that “taxes and transfers don’t do all that much” to affect inequality and looks instead at “market” incomes (before taxes and transfers are taken into account).

However, the more profound source of disagreement between Goldfarb and Noah is a matter of perspective. For Goldfarb, “reduced” is a relative term, implying that we have less inequality due to Obama’s policies than we otherwise would. Noah concedes that point: “Relative to an imaginary Republican president, Obama has reduced income inequality. That’s something to be grateful for.” But in absolute terms, inequality is still increasing. For example, the income share of the top 1 percent and the Gini index (a broader measure of inequality) were both higher in 2012 than they were in 2009.

I think it is crucial to keep both of those contrasting perspectives clearly—and simultaneously—in sight.

The Census Bureau’s tabulations of annual family income show that the real incomes of poor families declined by about 1 percent per year from 2009 to 2012, while the real incomes of affluent families (up to the 95th percentile of the income distribution) declined by about half as much. Thus, by this measure, too, inequality has (so far) “gotten worse” under Obama. (These tabulations exclude government benefits and taxes, and they miss substantial increases in real income above the 95th percentile.)

As Noah notes, the fact that inequality has increased during Obama’s time in the White House represents a significant break with previous experience under Democratic presidents. He cites data on income growth since the late 1940s from my 2008 book, “Unequal Democracy,” as “evidence that Republicans are the party of the rich and Democrats the party of the middle class and the poor.” Those data (updated here through 2012) show that income growth under Democratic presidents has generally been robust and relatively equal (in percentage terms) across the income spectrum, while growth under Republican presidents has been substantially lower for middle-class families and minimal for poor families.

By that historical standard, the pattern of income growth over Obama’s first few years in office is indeed dismal. According to Noah, however, that is “not really Obama’s fault,” because “economic forces at work since 1979, hugely exacerbated by decades of conservative government policies” have made inequality “extremely difficult to reverse.”

A comparison of partisan income growth rates since the Reagan era illustrates both the “economic forces at work since 1979” and the continuing significance of government policies that exacerbate or mitigate those forces. Overall income growth rates were substantially lower in this era than in the earlier post-war period, and middle-class and poor families experienced somewhat lower growth rates than affluent families even under Democratic presidents. Nevertheless, they clearly fared much better under Democrats (Clinton and Obama) than under Republicans (Reagan, Bush, and Bush). The difference amounts to about 1.5 percent per year for poor families and 0.8 percent per year for middle-class families—substantial sums when they are compounded over decades.

In recent years, “economic forces” have become even bleaker. Obama took office in the midst of the Great Recession, the largest shock to the American economy since the Great Depression. Thus, it is even more than usually difficult to gauge how the economy, and income inequality, would have evolved with “an imaginary Republican president” in the White House. One obvious benchmark is how things went under the last Republican president, George W. Bush. Middle-class and poor families experienced even larger income losses in the last few years of Bush’s presidency than they did in the first few years under Obama. For poor families the difference is substantial—almost a full percentage point per year. (These losses are not solely attributable to the Great Recession; even in 2007, the real incomes of poor families were lower than they had been when Bush took office.) For middle-class families the difference is about half as large.

Of course, short-term comparisons of this sort can be quite misleading, especially in turbulent times. Still, this may be the best basis we have at the moment for assessing Obama’s impact on the broad economic fortunes of ordinary American families. In absolute terms that impact looks disastrous. But in the context of the times it seems roughly consistent with the broader historical pattern: whereas middle-class and (especially) poor families have generally experienced much more income growth under Democratic presidents than under Republicans, in recent years they have suffered smaller income losses. That is certainly no cause for celebration. Nevertheless, insofar as it reflects the impact of the administration’s policies—perhaps most importantly, the much-maligned 2009 stimulus package—it is a real and important achievement.

In the longer term, Obama’s impact on income inequality may depend as much or more on reshaping taxes and redistribution as on changing patterns of “market” income growth. Historically, Noah is right that “taxes and transfers don’t do all that much to alter income distribution in the United States.” But that could change—as his reference to experience from other comparable nations makes clear.

That is where Goldfarb’s analysis comes in. He summarizes a new study by the Tax Policy Center estimating that the 2013 after-tax incomes of households in the bottom four-fifths of the income distribution were about $150 higher under Obama’s tax policies than they would have been under George W. Bush’s, while the incomes of households in the top fifth of the distribution were about $4,000 (1.8 percent) lower, and those in the top 1 percent were about $78,000 (6.5 percent) lower, under Obama’s policies than they would have been under Bush’s policies.

The impact of Obama’s policies in coming years will be even greater, as those increased taxes on affluent households begin to pay for substantial new subsidies for health insurance under the Affordable Care Act, substantially boosting the future economic well-being of poor and middle-class households.

According to Goldfarb, that means that “inequality will shrink further” in coming years. But then, “shrink” is another relative term. Whether inequality will actually decline anytime soon is far from clear. As Noah concludes, inequality is “extremely difficult to reverse, even for a president who’s made reversing it a top priority.”

The Sisyphean nature of that challenge was nicely, though perhaps unintentionally, captured in a recent remark by Jason Furman, chairman of the Council of Economic Advisers. “Just the tax changes we made in this administration undid about half a decade of the increase in inequality,” Furman said. “If you add in the Affordable Care Act, it’s more than a decade of inequality that was undone.”

If a once-in-four-decades policy shift undoes a decade of increasing inequality, it is going to take a very long time to get this rock to the top of the hill. But that’s no reason to stop pushing.