In the best-loved holiday fable of them all, Ebenezer Scrooge raises his tardy clerk's salary on the morning of the day after Christmas — and then invites long-suffering Bob Cratchit out for a bowl of hot punch after work, the better to talk over additional ways Scrooge can "assist [his] struggling family."

This ever-pleasing portrayal of moral reformation in a "covetous old sinner," like many vignettes in Charles Dickens' "A Christmas Carol," raises social and economic questions that continue to trouble us 179 years after the great novella's publication.

Dickens was haunted by inequality and its causes. Scrooge is a "morose" capitalist "rich enough" to be merry, in his festive nephew's view. Having finally had "the cold within him" thawed, Scrooge sets forth at his story's end to combat the literally Dickensian poverty that dwells all around him, but to which he was cruelly indifferent before his Christmas Eve visitations ("Are there no prisons?").

What's notable is that Scrooge departs from his miserly course in two quite distinct ways. He commits himself to income "redistribution" (as in the largesse to be planned over punch) and also to what economists sometimes call "pre-distribution" (as in Cratchit's pay raise).

Today, as in the 1840s, both approaches have a role to play in improving the well-being of the less affluent — both efforts that increase the earned incomes of lower-paid workers as well as public and private transfers of resources to those left in need.

But which approach is more effective and important?

Scholars from the World Inequality Lab at the Paris School of Economics take on this riddle in an illuminating new paper, (Here's a freely accessible working paper version) "Why is Europe More Equal than the United States?" brought to my attention by the always outstanding Conversable Economist blog.

Disputing conventional wisdom, Thomas Blanchet, Lucas Chancel and Amory Gethin argue that "Contrary to a widespread view ... Europe's lower inequality levels cannot be explained by more equalizing tax-and-transfer systems. ... [T]he U.S. redistributes a greater share of national income to low-income groups than any European country."

They assert that "'pre-distribution,' not 'redistribution,' explains why Europe is less unequal than the United States."

The conventional analysis, these researchers note, concludes that "if high ... inequality countries (like America) were to increase redistribution to its level observed in less unequal countries, they would get significantly closer to the inequality levels observed in the latter. Our results challenge this claim. ... If anything, taxes and transfers reduce inequality more in the U.S. than in Europe."

It's far too simple to say, in response to this, that it's more important to find ways of raising Cratchit's earnings than to buy him a prize turkey for Christmas dinner or make other "slight provisions for the poor." But in economic policy terms, that's the direction this research points.

The key difference between the old world and the new, these researchers say, is that "Europe has been much more successful than the U.S. at ensuring that its low-income groups benefit from relatively good-paying jobs."

The difficulty in understanding inequality is that there are so many different but defensible ways of measuring income and the benefits of government programs. Blanchet, Chancel and Gethin believe that their methods yield particularly comprehensive, consistent and comparable data, "allowing us to compare the dynamics of inequality and redistribution ... in great detail" between the U.S. and 26 European nations.

Details in the "dynamics of inequality" are worth attention, as they were in Dickens' time. For all the focus on Bob Cratchit's hardships in "A Christmas Carol," he is far from the bottom in Scrooge's London. The depths of that era's destitution are represented by the starving, "wolfish" wretches who hide beneath the robe of the Ghost of Christmas Present.

As an accountant, Cratchit is a skilled information worker of his era, and with his famous 15 shillings a week he is able to provide a roast goose Christmas feast for his family of eight (albeit "such a small goose," in Scrooge's estimation). Pinched as their life is, the Cratchits hail from the middle class of their time.

Today, middle-class Americans compare more favorably with their European counterparts than do the poorest in the U.S. Using 2017 data, the Paris school researchers show that in "pretax income" (before taxes and government transfers), Americans overall have higher average incomes than residents of all European nations except Norway and Luxembourg. But the poorest half of the U.S. population has lower average pretax income than their counterparts in 18 European countries.

Worse, the poorest 20% of Americans earn less than a third of the average pretax income of their peers in Northern Europe, about half that in Western Europe.

As for the literal middle class, the middle 40% of populations, Americans in this group on average are slightly better off than Northern Europeans, more than a third richer than Western Europeans and have twice the average pretax income of Eastern Europeans.

And the rich, morose or otherwise? America's top 10% in pretax income — today's information workers, professionals, etc. — are substantially more prosperous than European peers. Incomes of the super rich in the U.S. — the top 1%, top one-tenth of 1%, etc. — all but go off the charts.

People can and do differ about whether the rich being too rich is a moral blight, or whether kingly incomes for some is a price worth paying for an intensely dynamic economy that produces prosperity for many — including the middle class. But it's hard to deny that America's society and marketplace still produce an underclass that is too poor.

For this reason it's comforting to learn from Blanchet, Chancel and Gethin that "the US tax-and-transfer system appears to be unequivocally more progressive" than the European. They explain that while it's true European nations tax at significantly higher levels than the U.S., and have larger government transfers overall, the American system taxes more progressively and directs more net resources to the poor.

Specifically, they show that the bottom 50% in pretax income in America receive a net transfer of more than 6% of national income through total government taxation and spending. This compares with less than 4% in Northern and Western Europe and less than 3% in Eastern Europe.

Nonetheless, America remains more unequal in the end. After all taxes and transfers are accounted for, the richest 1% of Europeans collect 9% of income, say these researchers. In America, in 2017, the figure was 16%. Redistribution, in short, is less powerful than pre-distribution.

This makes the challenge facing America more daunting. If reducing poverty and inequality really were merely a matter of emulating European welfare state policies, we at least would know what choices we needed to make. But matching European success in helping low-income groups thrive in the pre-distribution economy would require solving more complicated and elusive social and political problems — from educational failure to family fragmentation to labor market inequities and much more.

Let's get started, right after Christmas.