Many of the world’s most celebrated stories are tales of upward mobility. There’s Arthur, the orphan who becomes king after yanking a sword from a rock; Aladdin, the street urchin who wins fabulous wealth from a magic lamp; and Cinderella, the bullied girl who marries a prince after a footwear-related meet-cute.

In each of these stories, the characters succeed mostly by fate or luck. But in the late 1800s, during a time of rising inequality and hardening social hierarchies, an American named Horatio Alger became famous for telling a different kind of tale, one in which poor people ascended to the upper class by dint of their own hard work and sterling morals. By Alger's formula, crossing class lines didn’t require a genie or a fairy godmother — only gumption.

Although many scholars now say we’ve misunderstood Alger’s message, he still is remembered for spreading a distinctly American fantasy of self-made success. A new study out of Harvard shows how Alger’s legacy continues to steer our perceptions of the economy. Unlike Europeans, Americans vastly overestimate the likelihood of moving up the economic ladder, according to economists Alberto Alesina, Stefanie Stantcheva and Edoardo Teso.

And Alger — or at least, the way we’ve misread him — is partly to blame.

“We find that this idea of the American Dream, going from rags to riches, is really salient in people’s minds,” Stantcheva said. “In the U.S., people are too optimistic about intergenerational mobility, particularly about the chances of making it from the very bottom to the very top.” Such perceptions — or misperceptions, as the case may be — are important because they may influence how we think about government programs such as the social safety net or public education.

This chart from the paper illustrates how people responded when they were asked to guess the trajectories of children who grew up in the lowest-earning households. On average, Americans thought that 12 percent of children from the bottom fifth would end up among the top fifth of earners — but only 7.8 percent do so in reality. “This is a big gap,” Stantcheva said. “It shows that Americans are overestimating upward mobility by 50 percent.” (A leap from the bottom 20 percent to the top 20 percent, in today’s terms, would be like moving from a household making less than $20,000 a year to a household making more than $112,000 a year.)

To put it another way: If you just went by what Americans believed about the chances of children at the bottom, the picture wouldn't look like the United States at all. You would think they were describing a country like France.

Europeans are also mistaken, but in the opposite way. According to the study, people from the United Kingdom, Italy, France and Sweden are overly pessimistic about upward mobility in their countries. (Each of those nations, in fact, offers its children a better shot at reaching the upper class than the United States does.)

Impressions of upward mobility are tangled up in people’s values, as well their beliefs about the government’s role in private lives. It’s no coincidence that European countries, where people are more concerned about the opportunities afforded to the poorest, have more vigorous policies to combat inequality. The study finds that individuals who believe it’s difficult to ascend the economic ladder are more likely to support taxing the 1 percent and boosting public spending on social services. Naturally, there’s also a partisan divide. In the United States, conservatives particularly overestimate levels of upward mobility, while liberals' perceptions are a little closer to reality.

It’s hard to tell where these beliefs are coming from. Does a rosy view of upward mobility cause people to adopt conservative beliefs? Or do conservatives embrace rags-to-riches stories to defend their other opinions about shrinking government and lowering taxes? Likewise, could it be that some Europeans play down upward mobility in their countries to justify their generous welfare policies?

To help answer those questions, the researchers followed up with an experiment. At random, they told some subjects that upward mobility was relatively rare: “Only very few kids from poor families will ever make it and become rich.”

This nudge caused both conservatives and liberals to lower their expectations about upward mobility in the United States. But only liberals also adjusted their political views — they became even more likely to support government interventions to increase opportunities for poorer children. Conservatives, on the other hand, remained skeptical of any policies to combat inequality.

Ever since Thomas Piketty’s book “Capital in the Twenty-First Century” hit American shores, there has been a lot of concern about intergenerational mobility, but little done to address it. Political gridlock is one reason. The Harvard study suggests that confronting this issue only serves to polarize people. It emboldens liberals, but doesn’t change how conservatives think about government programs, even if both sides agree that there have been troubling trends in inequality.

The Harvard experiment shows that perceptions of opportunity are not completely rooted in reality; among many Americans, there remains a stubborn faith in the power of self-determination.

There’s irony in all of this. Alger’s stories were never really about entrepreneurialism. Alger was a Unitarian minister; his novels were moral parables designed to teach young boys the virtues of honesty and honest work.

“The original Alger hero was not a poor boy who became a millionaire by dint of honest enterprise and patience, but a poor boy who rose to bourgeois respectability as a reward for his filial piety,” University of New Mexico English professor Gary Scharnhorst writes in the introduction to a new volume of Alger’s stories.

In most of Alger’s tales, upward mobility occurs only when the hero chances upon a benevolent mentor who helps him break into the upper class. “The character has to be noticed somehow,” said Carol Nackenoff, a political science professor at Swarthmore College who has studied Alger’s role in American history. “There’s always this accidental encounter where the hero shows his mettle, his willingness to take risks, to rescue somebody or to stop a robbery.”

As Scharnhorst puts it, “The typical Alger hero, therefore, improves his station as much by a stroke of luck . . . as by dint of hard work. He may deserve his good fortune, but he does not entirely earn it.”

So why, then, do so many people still think of Alger as the bard of the American Dream? One reason is that we don’t read his stories anymore — his bestseller “Ragged Dick” was pulp fiction for teenage boys. Instead, Alger's legacy has been shaped by a kind of willful misremembering — from the novelist F. Scott Fitzgerald, who parodied Alger’s themes in novels such as “The Great Gatsby,” to the propagandists of the 1940s, who saw in Alger's work a patriotic set of stories about Americans rising up in society. “Each generation between the Civil War and World War II discovered its own usable past in Alger by reinventing him according to the milieu of the moment,” Scharnhorst argues.

Today, Alger’s plight illustrates a deeper truth about politics: The stories we tell are often more important than the underlying facts. In part, our misunderstandings about Alger's work, like our misunderstandings about the true levels of intergenerational mobility, stem from a belief that the United States is a nation where opportunity exists for all. It's unclear how long that optimism will persist. The most recent presidential election showed that many think the American Dream has faded — although we still disagree about how to bring it back.