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Instead of offering a salutary lesson in how to reduce inequality, the country turns out to be an illustration in just how devilishly difficult that is. Stephanie Nolen reports from Rio de Janeiro.

Nivea Caridade, 39, holds her daughter Sofia, 4, who has special needs. Ms. Caridade lost her job as a clerk in a construction firm in 2016, a few months after her husband lost his.

Of all the things her family lost, what Nivia Caridade misses most is hope.

Over the past decade, she got out of the habit of mistrusting good fortune, and allowed herself the luxury of optimism. That, it turns out, was a mistake.

Today, Ms. Caridade, 39, wonders how she will feed and clothe her family, how she will buy medication for her severely disabled four-year-old daughter, what her teenage kids will ever make of themselves with just a basic education from a semi-functional public school. She wonders if they will all survive from one week to the next, as a low-grade civil war wages in their neighbourhood on the periphery of Rio, one almost entirely abandoned by the bankrupt state government. Her family is back where they started when she was a teenager herself, she thinks – maybe worse.

Ms. Caridade has had her security and her sense of optimism snatched away by Brazil's vicious recession, and the ongoing political crisis that impedes a recovery. The country is seeing sharp reversals of key gains from the prosperous first 15 years of this century. The World Bank says as many as 3.6 million people have fallen below the poverty line of $54 (U.S.) a month since the start of 2016 (some 16 million were already living below the line) while millions more have slid back precariously close to that line.

Brazil went from growth of 7.5 per cent in 2010 to contracting by almost the same amount in the past two years.

It's not a full-on return to the Brazil of old – people aren't starving to death, for example (the country was removed from the Global Hunger Index in 2011). But with unemployment staying stubbornly over 12 per cent, and a steep decline in social spending, the swell in the number of those who are poor was predictable, and contributes to the profound unpopularity of the government of President Michel Temer.

In the good years, when commodity prices boomed and the government was flush, an estimated 30 million Brazilians, including Ms. Caridade and her family, moved out of poverty and into a new lower middle class.

And there was more: in addition to reducing the number of poor, Brazil was believed to have reduced inequality, for the first time ever while the country was experiencing growth. The Workers' Party (the PT, in its Portuguese acronym), in power from 2003-16, claimed the achievements; its co-founder, the former president Luiz Inacio Lula da Silva, leads the current polls to be re-elected to the presidency next year.

Amid an intensified global interest in inequality and how it shapes politics and people's lives, Brazil stood out as a rare country where the gap was shrinking. It was a spectacular achievement that brought researchers here from as far away as Bangladesh and Tanzania to study the changes.

Brazil’s economy began to shrink in 2014 as commodity prices fell and the government doubled down on a bad set of policy choices.

Now, however, in addition to the personal pain of families such as Ms. Caridade's, there is new evidence that in fact, inequality did not fall after all – in fact, concentration of income in the hands of the richest actually increased. Instead of offering a salutary lesson in how to reduce inequality, Brazil turns out to be an illustration in just how devilishly difficult that is.

There is no question that poverty fell in Brazil. The economic expansion of the 2000s pulled a huge number of low-skilled workers out of the informal sector and into jobs in services and construction where they had much stronger bargaining power, explains Laura Carvalho, an expert on economic inequality at the University of Sao Paulo. At the same time, the PT raised the minimum wage by more than 50 per cent while it was in power.

Meanwhile, the government was investing in social programs such as the Bolsa Familia, or family grant, a cash grant every month to women whose children were in school and vaccinated. The average grant is just $70 (Canadian) a month, too little for anyone to survive on, but the Bolsa Familia played a key role for individual families, buying them breathing space when there was a health problem or other crisis.

Ms. Caridade's trajectory through the boom years was a typical one: she comes from a family where women have always done domestic work – the standard for Brazilian women of limited education – and grew up thinking she would likely do the same. But in 2000 she got her first office job, as a clerk in a construction firm. She worked her way into a job doing accounts that paid $1,200 (U.S.) a month. Her husband Vinicius Duque, 42, had a stable job with good benefits as a telecom technician that paid $750 a month. They bought a car, and they started talking about putting money aside for a house of their own. "It seemed within reach," she said. Their children were checking out college courses and talking about careers. And Ms. Caridade herself enrolled in night school for an accounting degree – the classes thrilled her, because no family member before her had even made it out of high school.

Brazil was removed from the Global Hunger Index in 2011.

The family was firmly in the demographic of new consumers – of the consumer goods, such as televisions and cellphones that became a symbol of the new lower middle class – but also of education, a change that seemed to herald a shift in the historic pattern of wealth (and power) distribution in Brazil.

"But we have to separate the absolute and the relative," says Marcelo Medeiros, one of Brazil's most prominent researchers on inequality, who is currently teaching at Yale University – and who has, of late, had to revisit years of his own academic work arguing that Brazil reduced inequality. "Poverty is absolute, but inequality is relative." And it can grow even as poverty falls, as it has in China. Initially that seemed like it might not be the case here. As wages rose for those in the lowest-paid jobs, the gulf between them and the top began to shrink – and many studies, by government and academics, looking chiefly at the labour market, concluded that inequality was falling.

But a series of new analyses – most recently from the World Wealth and Income Database in Paris, headed by the economist Thomas Piketty – argues that inequality not only did not fall, it actually grew.

A study by Marc Morgan, a scholar at the institute, found that while the least-wealthy 50 per cent of Brazilians increased their share of national income from 13 per cent to 14 per cent between 2001 and 2015, those in the top 10 per cent also grew their share – from 54 per cent to 55 per cent – and of course this share was substantially bigger to begin with.

"What we see in the data, after careful combination, is that concentration of income at the top, before taxes, grew," Mr. Morgan said. "So inequality between the top and the rest widened. But also within the top we see increased inequality, between the top 1 per cent and the bottom 9 per cent of the top 10. Inequality did seem to fall among the bottom 90 per cent – because the bottom 50 increased their share, while the middle 40 per cent saw their share fall."

While labour income inequality did fall – no question – that wasn't enough to offset the growing concentration of resources in the hands of the elite.

The previous analyses of Brazilian inequality have looked at wage data, explains Prof. Medeiros, and household survey data (something similar to Canada's long-form census.) But rich people often dodge those surveys, and when they do take them, they understate the level of their wealth. The new analyses add in government accounts and income tax data. The penchant of Brazilian politicians for Swiss bank accounts notwithstanding, it is much harder to lie about income levels on tax returns. (Researchers, he notes, knew the problem with the survey data – but once he got the recently released tax data for these years and reran his analyses, he was stunned by how it shifted the findings.)

Mr. Morgan's analysis looks at what economists call " pre-tax, post-replacement national income," including interest payments, dividends, rent, pensions, salaries and unemployment insurance. (So it does not include government redistribution policies such as the Bolsa Familia.) He found that the wealthiest 10 per cent of Brazilians received the benefit of 61 per cent of economic growth. In other words, that boom? The poor got a bit of it. The richest 10 per cent got most of it. Oxfam calculated that six people – six individual Brazilians – now have a share of wealth equal to that of the poorest one half of citizens.

In the good years, when commodity prices boomed and the government was flush, an estimated 30 million Brazilians moved out of poverty and into a new lower middle class.

"It was that concentration of income at the top that we were missing by just using surveys – concentration at the top is very high and very persistent," Mr. Morgan says.

Tereza Campello, a former PT minister of social development, gave a lecture recently in which she criticized these analyses for looking only at income levels and leaving out all the other ways she says the government levelled the playing field – by, for example, strengthening the public health and education services on which the poor rely. These studies do not count the huge change in the profile of university students, after the PT brought in affirmative action for black and mixed-race students, who were historically nearly absent from the public postsecondary system, and for students from low-income backgrounds, she said.

Mr. Morgan says Ms. Campello is correct on many counts: The shift in access to higher education in particular is a change that will have a long-term impact, he said. But his goal was to investigate the role of capital income, and he found it was far greater than anyone realized.

Prof. Medeiros says the new findings matter because they make clear what the causes are. "Our policies to reduce inequality need to be revised. There are new players in the game, and they are heavy players, like wealth, inheritances, profits and capital gains … A very large part of inequality in Brazil will not be affected by anything that affects the labour market – such as education. That doesn't affect taxation or inheritance."

Demonstrators take part in a protest calling for Brazil’s President Michel Temer to step down in downtown Rio de Janeiro in June, 2017. An unemployment staying stubbornly over 12 per cent contributes to the profound unpopularity of the Temer government.

Brazil's economy began to shrink in 2014 – as commodity prices fell and the PT doubled down on a bad set of policy choices. Brazil went from growth of 7.5 per cent in 2010 to contracting by almost the same amount in the past two years. Jobs were lost fastest among those who had only recently joined the formal employment market, Prof. Carvalho noted. The Temer government tried, with limited success, to stimulate new investment with an austerity program that slashed health and education spending. "Wage inequality is up again, and the expenditures being cut affect the poor disproportionately," she said. The social mobility that occurred in the boom proved to have been limited, and fragile.

In early 2016, Mr. Duque was laid off when the service contractor he worked for went out of business. A few months later, Ms. Caridade lost her job when the construction firm shut down. She hunted for other clerical jobs – but all the competition was closed, too. They sold the car. She registered with agencies for domestic workers, but got no calls.

She shelved her dream of finishing her degree – tuition was $700 a month, far more than the whole family is living on now. "Do I dream of finishing?" she asks. "Of course. I dream about degrees for my children, too. But I can't afford the private classes they would need to go to, to get into college. What's the future for my children without an education in this country?"

They receive a disability pension of $360 for Sofia, 4, which covers her diapers and her food supplements. It doesn't pay for therapy – or for the $12 a day in medication she needs, which the family used to receive free from a city health clinic, now closed. The family has fallen so far they now qualify for the Bolsa Familia: They get $50 a month. Mr. Duque brings in about $15 a day driving a motorbike taxi and Ms. Caridade has found cleaning jobs a couple of days a month. "Today it's not about what you want to be – it's about anything you can be," she says.

Ms. Caridade wonders how she will feed and clothe her family and how she will buy medication for Sofia.

The family is better off than they would be, of course, if Brazil had no social programs. But they're struggling without access to health services for Sophia; there are no books in the kids' school, which half the time is closed because of shootings. Rio has also slashed its policing budget. She says it would cost them at least double their current rent of $175 to live somewhere that was safer – something that simply isn't possible.

"It's not simple to reduce inequality in an environment like this, when 0.1 per cent of the population – almost the amount that would fit in a football stadium – controls 10 per cent of the income of the country. They control more than the poorest half of the population," Prof. Medeiros says. "You're talking about very different groups with very different powers. Very high concentration of income which translates to very high concentration of political power – it decides political outcomes." A couple of social policies aren't going to fix that any time soon, he said.

The Bolsa Familia made a big difference for many poor families – but with a budget of just 0.5 per of GDP, it was never a significant redistribution of resources. And the PT shied away from a change that might have made a big difference: an overhaul of Brazil's profoundly regressive tax system (which includes a vast array of tax breaks for the super rich and relies heavily on consumption taxes of which the poor pay proportionately more than the rich). In the current Congress, dominated by wealthy conservatives, tax reform isn't on the agenda; slashing pension benefits is.

Ms. Caridade's daughter Julia, 14, dreams of a 15th birthday bash, the kind that the family used to think that, of course, she would have – in a rented hall, with fancy sweets and an extravagant dress. Now, she says, a little tearful, she has had to tell Julia bluntly to stop dreaming about the party, because it isn't going to happen.

"I think it's a false impression that inequality fell – I don't see it," she said. "This country is the same as it's always been."