You’ve probably seen a picture like this before, incomes corrected for inflation measuring how much stuff people can buy and how that changes over time.

The rich get richer. And the poor get poorer. The middle class barely gets ahead.

But when someone says the rich get richer, what does that really mean?

It could mean that the richest people in 1980 were 50% richer by 2014, the poor people of 1980 never got a raise. And as for the middle class, they got crumbs—a crummy 10% gain over 34 years.

The studies that use numbers like these create a lot of outrage and reasonably so—it sure looks like the rich get all the gains from economic growth. It’s why Nobel Laureate Joseph Stiglitz can claim that the US economy is rigged in favor of the rich. Why Nobel Laureate Paul Krugman can say wages for ordinary workers have been stagnant since the 1970s. And why New York Times columnist David Leonhardt can say that “the very affluent, and only the very affluent, have received significant raises in recent decades.”

But this picture doesn’t actually doesn’t tell you that.

Almost all the gloomy evidence that people use showing the rich getting all the gains –like this chart–take a snapshot each year and compare the snapshot today with one from the past to see how people have been doing.

But it’s not the same people in the snapshots. The economy’s dynamic. People move up and down. They have good years. And bad ones. People leave school and start working. People retire. Some die.

Some of the people in the top 20% today weren’t rich to start with. Some of the people at the top today, weren’t even born in 1980. Like NBA superstar Stephen Curry or Google founders Larry Page and Sergey Brin.

Some of the ones in the middle today used to be at the top.

So it isn’t necessarily true that the rich got richer.

Maybe the people in the past who weren’t rich, became rich. And they ended up richer than the rich who were rich yesterday. So they show up in the snapshot of the the top 20% in 2014 and because they’re richer today than the rich people of the past, it looks like the rich captured all the gains.

Same with the poor falling behind. Maybe those who are poor now are younger and less skilled than the poor of the past. That will make it look like poor people are losing ground. But maybe the poor of the past actually got ahead and aren’t poor anymore. And today’s poor will get ahead, too.

So which story is right? Who has prospered in America? Just the rich? Or has prosperity been widely shared?

To answer those questions, you can’t use a series of snapshots. You need to follow the same people over time, like a movie.

And when you do that, you find that a good chunk of the gains go to the poor and the middle class. And sometimes the rich are the ones whose incomes are stuck in place or falling.

A Brookings study Julia Isaacs for the Pew Foundation looked at how people did as grown-ups compared to their parents. What happened to kids whose parents [in the late 1960’s] were in the bottom 20% with median income of just over $20K? When those kids entered the workforce—did they make more than their parents or were they stuck in place making no progress? It turns out, they did a lot better—twice as well in absolute terms. The kids who grew up in the richest households—the top 20% whose parents had median income of $100K—ended up with the same income as their parents. The children who grew up in the middle made 27% more than their parents. The poorest children had the biggest absolute and percentage gains when they grew up.

That’s partly due to what’s called regression to the mean—if your parents had bad luck and that’s part of the reason they ended up poor you’re more likely to have average luck and do better. Similarly, if your parents are rich partly because they had especially good luck, you’re not as likely to have good luck yourself so you’re not as likely to do as well as they did.

But that doesn’t change the reality, that over the last three decades of the 20th century, kids from poorer families gained more ground relative to their parents than kids from richer families. In the gloomy pictures, there’s no regression to the mean. Only the rich make progress and everyone else is treading water. But it’s not true. The passage of time narrowed the gaps between the top and the bottom.

Here’s a different study that follows the same people over time using tax data.

It looks at people 35-40 years old in 1987 and the percentage change in their income 20 years later.

The biggest percentage gains? The people who started in the lowest quintile. Their income doubled over the 20 years just as it did in the Brookings study.

The people who started in the middle quintile gained 27% just like in the Brookings study.

The people who were in the top quintile in 1987 were actually 5% worse off 20 years later.

In a recent working paper [“Growth, Inequality and Absolute Mobility in the United States, 1962-2014”], Yonatan Berman of the Paris School of Economics and the London Mathematical Laboratory found that in recent decades, the poorest workers were more likely to gain income than the richest ones in the aftermath of a recession or a recovery.

I asked him to look at a longer period of time and to look at how young workers have done over time as their careers advance.  Do the young people who start off at the top get all the gains as they grow older? Or did the rest of the work force also see substantial progress?

This is labor income for young workers in 1980. It averages over a four year period to reduce measurement error and transitory effect. It excludes taxes, government payments and income from investments. It only measures the money you earn from working–how the economy rewards you.

Let’s follow the young people were at the bottom in 1980 and see what happened to their incomes toward the end of their careers 32 years later, corrected for inflation.

How’d they do?

Some stay at the bottom. Others moved up to higher quintiles over time.

What was the median income for that same group of people three decades later? It more than doubled.

Let’s say that for each group of young workers in 1980. Follow each group to three decades and see how they ended up doing over their carrers.

The people from the top two quintiles in 1980 did very well but the people that were in the bottom 60% in 1980 also made steady progress over their working lives.

The rich weren’t the only ones getting healthy raises and these numbers understate the absolute gains. They don’t include fringe benefits, which are much larger today than in the past.

The bottom line snapshots of quintiles produce gloom and doom.

For alot of the same people, it’s a lot sunnier. The portrait of the American economy from the snapshots isn’t telling the whole story.

People across the economy have been getting raises and they’re pretty large.

Of course it’s not all sunshine even when you follow the same people over time. Not everyone has an equal chance to get to the top—in all of these studies, the richest Americans were still sitting pretty as time passed. People from all parts of the income distribution are getting ahead. But they don’t easily get ahead of people who start out ahead of them.

And these results don’t justify the status quo. There’s plenty to fix. Too many cronies get special treatment from the government and there’s too little opportunity for the least skilled among us. You can still argue that there’s too much inequality if that’s your concern.

But the economy isn’t rigged to favor just the rich. The poor and the middle class have made progress. The death of the American dream is greatly exaggerated.