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Pedro and Denise Magalhaes with their two children.

Each weekday morning, Pedro and Denise Magalhaes wake in their whitewashed bungalow on the southern outskirts of Sao Paulo, make a quick espresso, check the headlines on the web, drag their two teenagers away from their TVs and computers and usher them off to school, and open the front gate to begin their drive to work. As they back their Peugeot sedans into the street, Pedro glances across the road to a spot he has spent his entire life watching: a small park in the middle of their boulevard, one of the few scraps of green in this extremely dense neighbourhood. These days it is occupied only by a lone drunk, an old school friend of Pedro's who fell on hard times and sleeps on one of its benches.

Two decades earlier, when Pedro attended the secondary school at the top of the street, he would pass this park each Monday morning and frequently see that at least one bullet-punctured corpse had been dumped there, very often the bodies of his schoolmates, sometimes one of his friends. For a number of years this was almost a weekly occurrence.

Murder, for everyone living here, was a staple of daily life, and horrific poverty and isolation its backdrop. In 1996 Jardim Angela became known as the most violent community on earth. This was the wider world's confirmation of something that had been evident to residents of this favela for years.

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In 1976 it was empty parkland with a few migrants' shacks strung along its snakelike main street. By the end of the century, this hilly strip of land had a population exceeding 250,000 and an astonishing 309 homicides per year. Almost all the victims were teenagers, caught up in local gang struggles. Its murder rate, which was the highest in Brazil through the 1990s and peaked at 123 per 100,000, made it more deadly than most war zones. Some of the killings were carried out by warring teenage gangs. Others were conducted by the military police, who staged raids every few months, shooting up parties, capturing and torturing teenagers, and conducting clandestine assassinations. There were also private-sector death squads, made up of current and former police hired by local businessmen to kill troublesome gang members.

Property values were below zero: the neighbourhood was a degraded pile of shacks, almost uninhabitable after most shops and services moved out and crime became the main business. Drug abuse and alcoholism were default modes of coping, and the infant-mortality rate was one of the highest in the country. Jardim Angela was synonymous with dangerous slum life.

Pedro Magalhaes was caught in its centre, in his most vulnerable years, with a dead father, an impoverished family, a pregnant teenage girlfriend and no useful education. It seemed certain that he would become one of the lost arrivals.

Pedro was born in 1971, the youngest son of a farming family in the poor north of the inland Minas Gerais state, just as Brazil's great migration was approaching its peak. In 1976, his family abandoned the village and took advantage of the father's seasonal-migration links to Sao Paulo to participate in a land invasion on the city's far southern boundary. It was a risky move. The land was near the edge of one of two lakes that provide most of Sao Paulo's drinking water, and the city had a history of violently evicting squatter communities from water-supply areas. But Brazil's military dictatorship was under stress and had few resources to fight urban battles.

The sheer mass of people converging on the city made a sustained resistance unlikely.

Pedro's family cobbled together a wood hut, pressed tightly against its neighbours, on the lower slope of the favela's main hill, on far less desirable land than their current residence. Although his family's wood shack would be bulldozed by Sao Paulo authorities more than once in the land battles of the 1970s, they were able to stay, penned in by a city that would neither completely evict them nor formalize their ownership, leaving them in a limbo with neither services nor official citizenship.

In its earliest years, there was a mood of optimism in Jardim Angela. It was far better than the village, and there was work. "It was quite a deserted place then," Pedro told me. "Lots of empty spaces, big areas for kids to run around." And jobs for the adults, in the local metalworking industry and a big bicycle plant. There was pirated electricity, but no water, sewage, paved streets, bus service or any other connections to the urban surroundings, and the city did not recognize ownership of the favela huts.

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In 1976, just as Pedro's family was arriving, Oliveira Viana Municipal School opened, a one-room classroom at the top of the little park. For the next 20 years, the school would be the only permanent face of government in the favela.

In 1982, Pedro's own life took a difficult turn when his father died, and his mother was forced to work as a dinner lady at the school, a job that provided hardly enough to support her three sons. And as their family life foundered, the fast-growing neighbourhood seemed to collapse around them.

The great 1970s wave of rural-urban migration had been built around an industrial economy controlled and usually owned by Brazil's military dictatorship in a closed economic system. In the 1980s, this all fell apart. The artificial economy collapsed in simultaneous currency, fiscal, inflation and banking crises just as the military regime was launching a stumbling transition to democracy. For the entire decade, Brazil had very little economic activity and no government with the fiscal resources to support an emerging urban community. It was a time of decay.

For Jardim Angela and hundreds of other new-formed favelas and squatter enclaves around Sao Paulo and Rio de Janeiro, this proved a disastrous combination. The new migrants, who had just begun to build their houses, often using money they'd borrowed, suddenly found themselves without any means of employment or any resources with which to start their own companies. The communities had not yet become linked to the larger city in even the most rudimentary way, so there was no way for the suddenly jobless migrants to find work outside the favela.

"It became very bad very quickly - we had the fathers unemployed, so mothers had to become the primary breadwinners," says Jucileide Mauger, who was a schoolteacher at Oliveira Viana in those years.

"The dads started drinking, and we could only give kids four hours of school a day, so the second-generation kids were unsupervised, with nothing to do, and they were becoming teenagers. There became a huge problem with poverty, and there was no government at all to help. Kids would come to school without having eaten, with no uniforms; we had to provide for them. The families were falling apart, everyone was unemployed, and the situation kept getting a lot worse."

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Pedro Magalhaes was one of those kids. He watched his classmates turn to crime. At first, it was mainly theft: they would rob the drivers of trucks that delivered water and fuel to the neighbourhood - just about the only outsiders to enter the favela.

Then, by the end of the '80s, it became more serious: the older teenagers formed gangs inspired by American movies, the Bronx and the Ninjas, and they got involved in cocaine and went to war with one another. It became increasingly brutal. They were strictly local gangs, without links to international cocaine trafficking, and perhaps because of this they were both less organized and more violent than the big gangs.

They would, and often did, kill for an outstanding debt worth a few dollars. "For a number of years, starting in 1992, we had kids killed every week, sometimes every day - their bodies would be dumped out in that square, and I'd see that they were our students," says Ms. Mauger, who became head teacher of what was a 2,500-student school at the height of the violence shortly after her predecessor lost her teeth in a beating by gang members inside the school.

"One family with seven brothers, five of them were killed one year. I knew something had to be done. I'd keep the school open in the evenings so they could play in the courts. … I thought just keeping them in the building was important - never mind keeping them in classes, never mind what we were teaching, it was a matter of having them in here and not out shooting one another. The government wasn't present, the police weren't present, it was just us."

Pedro hovered on the edge of the gangs, never quite joining, but tempted. One morning on the way to school, his friend Chico approached him, feverish and excited: "I had a dream," Chico said, "I'm going to kill Carlos." Chico had become a paid killer. He murdered Carlos, and dropped his corpse in the small park. He killed 30 more people in the next year, mostly classmates, before he too wound up in the park. As the violence reached world-record levels, Pedro repeated a year of school because of bad grades and, he says, incompetent teaching. Then, at 18, he learned that his girlfriend, Denise, was pregnant.

He was unemployable, without any prospects. He was about to drop out of school. The only possible source of employment was the Bronx gang. "I didn't want to join," he says. "I'd have to kill for them and they were all on drugs, but it was the only thing there was. They were trying to recruit me, and I didn't have any choices."

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Pedro and Denise recounted this story to me one Saturday morning as they drove their family, crammed into the back seat of her Peugeot, from their house in the middle of Jardim Angela to the nearest indoor shopping mall. It has become a family custom to spend Saturday mornings shopping at the mall's department stores, then to have lunch in the food court. Their daughter, Kassia, 17, a freshman at a private college who wants to major in fashion design, gets her lunch from Panda Express. Vitor, 14, enrolled in a private high school, eschews the usual McDonald's for heartier Brazilian fare. They practise their English, learned from private tutors, on me, discussing their favourite brands of mobile phones and preferred social-networking sites. Tuition for the two of them costs $800 a month, eight months a year. Denise talks about the family's next big move: she and Pedro have just put a one-third down payment on a $63,000, three-bedroom condominium on the eighth floor of an 18-storey building beside this mall, on the edge of the favela cluster that includes Jardim Angela.

The development contains government-funded "favela rehousing" apartments, squat turquoise-painted blocks with small windows, as well as large flats like theirs, in modern glass-walled towers with broad balconies, marketed to people who want to stay in their original favela surroundings, near their friends and relatives and businesses, but with modern amenities and more security. For the next few months, they will continue to live in the whitewashed shantytown house on the edge of the park, which belongs to Denise's mother. There is a property boom taking place within Jardim Angela, as the people at the top of the favela move into new apartments and people living lower on the hill purchase their vacated houses. The proceeds of this boom are financing business start-ups.

Pedro is a member of Brazil's new arrival-city middle class. For the past decade, he has owned and run an information-technology consulting firm, based out of Jardim Angela, which currently provides network-hardware services to a multinational branding company.

His earnings, combined with his wife's pay, amount to between $30,000 and $35,000 a year - a comfortable middle-class income by the standards of the developing world. It is a salary that allows them to send both their children through private education, to have two cars and all manner of modern appliances, clothes, toys and a broadband connection, and to save enough money to become property owners.

Like many arrival-city dwellers, they managed this by moving in with relatives during their child-rearing years to save housing costs.

I have not chosen Pedro and Denise because they are rare and miraculous exceptions, but because they are fairly characteristic of a sizable minority of people in Jardim Angela today. In the years since the favela's collapse into violence, a thriving middle class has emerged; depending who you believe, between a fifth and a third of the neighbourhood's population have "made it" enough to become homeowners.

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It remains a poor neighbourhood, with most of its population employed informally as delivery drivers, domestic servants, builders or call-centre operators (there is little unemployment), and drug abuse remains a visible problem in some quarters. But there is a fundamental change now. The main street, once a strip of forlorn drinking establishments, now teems with furniture and appliance stores, restaurants, ice-cream parlours and home-improvement outlets.

Households here have an average of 1.5 televisions each, and a third have DVD players; half have cellphones; a third have family cars; and 14 per cent own computers, half of them with broadband Internet. All the houses are now made of brick; two-thirds have invested in expanding or improving their houses, and about a third have stuccoed, painted exteriors (stucco and paint are worldwide badges of disposable income).

Beneath all this are more important changes. First, violent crime and gangs are no longer dominant features. Between 1999 and 2005, Jardim Angela's homicide rate fell by 73.3 per cent, and continued to plummet to levels comparable to a South American middle-class neighbourhood. The Bronx and Ninja gangs have by all accounts faded into irrelevance. While a larger statewide gang has taken control of the city's entire cocaine trade, reducing gang rivalries, most informed observers believe the disappearance of gangs from this neighbourhood is a direct result of economic development.

Cellphone theft and armed robbery are now the prevalent crimes, and the major cause of teenage mortality is motorcycle accidents.

Second, the neighbourhood is today tightly linked into the city, with bus services running through the favela to a nearby commuter-train link, as well as offices of numerous government agencies.

Third, since 2003 the people here have legally owned their homes, thanks to a forward-looking Sao Paulo mayor who made land-titling a priority. As a result, almost-two-thirds have invested in improvements.

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Fourth, there are now the means to start and run a small business, and the neighbourhood is packed with shops, department stores, credit agencies and small workshops. People here remain poor, and there remains a large population of young people (mainly male high-school graduates) who are stuck in a netherworld of casual employment. But a notable and sustainable middle class is emerging within the favela, turning it into a much better neighbourhood and improving the living conditions of even the poorest residents.

The process of arrival, dramatically interrupted in the 1980s and '90s, has returned.

It is worth examining Jardim Angela's transformation closely, for it offers answers to a key question of our age:

What does it take to make the journey from a rural shack to the centre of middle-class urban life within a generation? Or, for that matter, even in two generations?

This is, after all, the core function of the arrival city, the sole objective of all those hundreds of millions of journeys from village to city. It is a wonder, then, that we know so little about how this can be accomplished. It is clear, from our tour of the world's arrival cities, that this transformation often does not take place within a generation, and that grim and violent repercussions can take place when it doesn't. Yet it should also be clear that rural migrants consider this transformation to be the norm. In fact, they expect it.

In Jardim Angela, we can see what obstacles can block their path, and what can be done to remove them.

In 1996, there did not seem to be any paths at all. Jardim Angela, built by soy farmers and sugar-cane planters to be a platform for their dreams, had turned into a deadly, isolated antechamber for their children.

The second generation had no purchase in urban life, and no connection to the village. They were culturally city-dwellers, with a standard of living and expectations far higher than those of their parents, but they were trapped in a world that treated them as no more than the unwanted offspring of villagers. Lost, and without support, they consumed one another.

"There wasn't a day that would go by, when I walked around the parish, that I wouldn't step across two or three bodies," says Father Jaime Crowe, the favela's priest, who found himself with the task of burying an entire generation.

"To step over a body in front of a door with a newspaper thrown over it to have a drink - you'd think nothing of it. Children, small children, would tell me that their life was not worth living. It had to stop."

To most Brazilians, it seemed as if some evil had overtaken Jardim Angela, as if its people were genetically predestined to violence, poverty and inactivity.

Yet it was becoming abundantly clear to a group of committed people living in Jardim Angela that this was not its natural or inevitable state. They had the desire and the will to do better, but there was nothing to provide the capability. As the violence peaked in 1996, and with no sign of an improvement, people began to meet, and came to a shared conclusion: that Jardim Angela's problem wasn't the presence of evil; it was the absence of normal city institutions and functions.

Pedro Magalhaes learned this earlier than most. At 18, with Denise pregnant and his school career jeopardized, he teetered on the edge of gang life. He had no interest in crime - in fact, it inspired a moral revulsion - but he would do anything to secure his daughter's future, and no other options were presenting themselves in the barren economy of Jardim Angela.

Then his oldest brother stepped in with an offer: a job cutting hair in his barbershop, which he had opened in the better years and was one of the few arrival-city businesses still standing (in large part because haircutting requires little capital and no links to the city outside).

"That job saved me," Pedro says. "It allowed me to keep out of trouble, and it gave me enough savings that I could borrow the money to study computers."

Through the dense network of mutual connections that defines the arrival city, Pedro was able to weave a new sort of life, one built on education, financial credit and entrepreneurship. He found his pathway to the middle class, and it led through the middle of the arrival city.

Was it possible that all the residents of Jardim Angela were attempting something similar? That was the question the favela's community leaders began asking as the violence peaked and they began holding emergency meetings at the school to talk about the neighbourhood's grisly problems. After having been ignored for years by the larger municipal, state and national entities outside, the favela developed its own grassroots municipal government, at first as an emergency response to the deaths of hundreds of children, and then as a larger, more potent institution.

The meetings at the school became known as the Forum for the Defence of Life. As the favela became infamous for its violence, these meetings were first attended by school officials, some police and Father Jaime (who was the first to organize the meetings); then by members of international aid organizations, which took up the favela cause as news of the violence spread; and, finally, by representatives from municipal and state governments.

Soon, hundreds of residents were attending. The citizens of Jardim Angela were unanimous in their descriptions of the neighbourhood's needs: first security, then education, then a proper link to the larger city, physically and economically.

"The school became the first really neutral territory, the first public space," says Jucileide Mauger. Before, her school had offered four hours per day of the most basic sort of teaching - like many arrival-city schools, which are either private or minimal, it offered few handholds for social mobility. Lobbying the government and the aid organizations for funds, they engineered a school better attuned to arrival-city needs.

"We had to cultivate the idea that the school is a government body, that it's an authority, that you have to come and follow rules. We made it part of the community. Then we started evening classes for adults and older teenagers with a seventh- or eighth-grade education who wanted a new start."

These were so successful that the school had to open all 15 classrooms at night.

Education proved popular, not just to the kids who wanted to avoid the life of gangs and drugs, but to those who lived that life.

"Many kids had dropped out, started drug dealing at 12 or 13 - then, at 20 or 21, realized that it's not such a good living, so they come back here looking for a future."

Most dramatic and visible, and most often praised by Jardim Angela residents, was the change in security. Before, the police had literally been heavily armed military platoons travelling in armoured vehicles invading from fortress-like bases outside, treating the entire neighbourhood as "enemy territory" and the whole population as potential combatants. They would raid at night, arrest, kill, then leave. Drug crime was their only priority. The police were feared as much as the gangs - often more so, since at least the gang's killers were neighbours and relatives.

There were good reasons to distrust them: in the early 1990s, hundreds of military police were implicated in thousands of revenge slayings and contract killings in the favelas.

As the violence peaked, some of the favela-born members of the police began to feel that they were partly responsible for the poverty and isolation. By treating the arrival city as a quarantined zone subject to periodic invasions, they were pushing the neighbourhood inward, against itself.

In 1998, after years of pressure from the Forum for the Defence of Life, the police embarked on a truly bold experiment. They built a station inside Jardim Angela, with big windows and an open door, reduced their vehicle count to two cars for 200 officers, and devoted themselves to foot patrols, going door to door in the style of beat cops - something Brazil had never seen before.

They developed a philosophy of "community-based policing," a worn catchphrase in the wealthy world but a very new idea in Brazil.

"For my first 15 years as a cop, I approached crime in an aggressive manner, because that's all I knew," says Davi Monteiro da Conceicao, known to everyone here as Sergeant Davi, a former military police strongman who began attending the Forum for the Defence of Life meetings in the 1990s, became captivated by the ideas circulating, and now commands the Jardim Angela community force.

"There were many confrontations - I took part in the exchange of gunfire. … But I changed the way I acted. Now I have more involvement with the people around me. They still don't completely trust us, so we have to keep things at the personal level. We need to go into their houses and explain to them that the police aren't just for beating up and being violent, which is all we'd done before, but that there are other uses for police - it's slow going."

It was too late for most members of Pedro's generation, but his children's neighbours and classmates have entered a very different world, one in which Jardim Angela is an integral part of Sao Paulo.

The years of political organizing within the favela changed things, as did the realization by more enlightened city and state governments that these neighbourhoods were an important investment. It helped that Sao Paulo passed a comprehensive gun-control law in 2003, which the Jardim Angela community police enforce aggressively. It helped that a farsighted mayor the same year recognized the social and economic value of giving the outlying favelas comprehensive bus and commuter-train service, and an affordable transit pass for poor workers. It helped that medical clinics and street lighting were installed. It helped that micro-credit agencies established themselves here and offered loan guarantees, and that small-business laws were liberalized, making it easier for favela-dwellers to use the value in their real estate to start a company. And it helped that entrepreneurs and agencies built venues to popularize and profit from the music and dance that had been an underground part of the favela's culture.

For the arrival city's third generation, there were suddenly reasons to stick around and improve the place.

"The second generation grew up without a past - they didn't have their parents' rural backgrounds, and they didn't have futures, either," says Bruno Paes Manso, a Sao Paulo scholar and writer who has analyzed the economics behind favela violence.

What he discovered in his investigations was that Sao Paulo's dramatic reduction in crime rates during the 2000s was due not primarily to police enforcement or gang organization but to economic development. The emergence of legitimate jobs in the favelas encouraged thousands of gangsters to abandon the life.

"They went into crime, but there was an attitude of 'I don't want this destiny for my son.' You never had an ideology of maintaining this way of life -it was just a circumstance the second generation found itself forced into. It felt like a prison for them. There was no self-valorization. The third generation is much more integrated into the economy and the culture of the city. The transportation, the jobs in the city, the hip hop music movements - these gave them a past and a tradition, an ability to talk about their roots and their future. You always hear them saying, 'I come from village roots, I come from slaves, native communities, and I have no interest in dying before I'm 25, because I'm a Paulista' [Sao Paulo citizen] They're creating a new identity."

The children of Pedro and Denise Magalhaes have no sense of fear or desperation: they are aspirational teenagers of Sao Paulo, attached to the music and culture of Jardim Angela but utterly unconcerned with the economics or folkways of migration, or the battle that was required to give them normal lives. Looking over the string of apartment towers that she will soon call home, I ask 17-year-old Kassia about the prospect of living in a high-tech castle of former neighbours, eight storeys up: Does she look forward to the view?

"No," she tells me, "it's not such a great view. There's a park, but there are favelas in the way."

This is fundamentally a book about social mobility. The move from village to city, we have seen, is always a calculated effort to raise a family's living standard, income and quality of life, using the arrival city as its main instrument. Urban poverty, despite its crowding and frequent humiliations, is an improvement on rural poverty, and no arrival-city resident considers poverty anything but a temporary necessity. But the creation of an arrival city is only the first step in a journey planned carefully by the migrant. Nobody invests their entire life, and a generation's income and peace, simply to move from one form of poverty to another. The residents of arrival cities do not consider themselves "the poor" but rather successful urbanites who happen to be passing through a period of poverty, perhaps for a generation.

The arrival city, if it is to function at all, must create members of a middle class: families with enough earnings and savings to start businesses and employ others, to own and improve dwellings, to send children to university, to have a sustainable quality of life capable of moving them, and their neighbours, beyond merely surviving. An arrival-city middle class is important for a number of reasons. It creates social and political stability, because the middle class ties the neighbourhood to the institutions of the wider city and thereby opens a pathway to something other than crime, marginal informal economy employment and dependency.

The presence of an arrival city middle class shows new arrivals and their children that the process of migration is not a journey into perpetual injustice, that sustainable prosperity is available to those willing to study and invest.

It tends to generate employers and political leaders within the arrival city, improving the quality of life for others. And research has shown that the presence of a middle class raises living standards for those neighbours who remain poor.

The economist Steven Durlauf has shown that a middle class, even a small one, within a poor community can generate "neighbourhood feedback effects" in which investments in the higher education of children become a behavioural norm.

And, significantly, the presence of a middle class within the arrival city helps improve the standards of living in the originating villages, financing non-agricultural industries in rural areas and creating a parallel rural middle class. By equalizing village and city, the middle-class arrival city puts an end to rural-urban migration.

Middle-class status is not an unrealistic expectation for rural arrivals: it has been the historic norm. It is what occurred in the cities of Europe and North America throughout the late 19th and 20th centuries. As we have seen, it is widely attainable in the more successful Western arrival cities today. And it can be observed in the arrival cities of the developing world. Turkish gecekondu neighbourhoods have cultivated a new, internal middle class that now dominates the nation; former shack-town favelas like Rio de Janeiro's Rocinha district have evolved into desirable middle-income enclaves, and their Sao Paulo cousins have spawned a consumer and industrial boom and a new form of national politics.

The more established slums of Mumbai, like Dharavi, now have internal economies worth hundreds of millions of dollars, and within their labyrinthine walls I have encountered slum-based factories employing 40 or 50 people and financing computer-science educations for extended families.

Jardim Angela today is a good example of just such a middle-class arrival city. According to the five-band Brazilian measure of household wealth and consumption, in which band A are the country's wealthiest 20 per cent and band E the poorest fifth, at least 14 per cent of people living in the favela district encompassing Jardim Angela now fall into the comfortably middle-class B band, and only 31 per cent into the second-poorest D band, with more than half the favela's population living within band C, the lower bounds of the middle class, a massive change from the 1990s. It is a pattern repeated across the arrival-city favelas of Sao Paulo. You can see it in the colourful array of shops, services and small businesses that fill the streets.

Still, these places remain the global exception rather than the rule. Many arrival cities are failing to give members of their second generation, no matter how hard they work or school themselves, the chance to enter the middle class. And that is jeopardizing economic growth and political stability in many countries.

David Rothkopf, a scholar with the Carnegie Endowment for International Peace, described this neglect as a large-scale mistake: "With the notable exceptions of India and China and a few others, which show some heartening middle-class growth, we are doing a very bad job of building the middle classes, which are the foundation of stability and the antidote to the boom-bust cycles that bedevil much of the emerging world."

To explain the nature of this challenge, it is important to understand what we mean - and what rural-to-urban migrants mean - by "middle class." One way to define a middle class is by identifying the middle income range: you pick out those families that earn between 75 per cent and 150 per cent of a country's median income.

The economist Branko Milanovic did this for the entire world, dividing all 6.7 billion people into a "lower class" - which turned out to be those whose annual family incomes were below $4,000 annually, the median income of Brazil - and an "upper class," those families with more than $17,000 a year, the median income of Italy. The lower class made up 78 per cent of the world's population, the upper class 11 per cent, and the worldwide middle class, those families living on between $4,000 and $17,000 a year, another 11 per cent.

The middle class can also be identified by their role and self identification. Even if much of the "middle class" today are better-paid factory workers and computer operators rather than the traditional bourgeoisie, an important identifying characteristic is their ability to deploy savings and investments to alter their future status. The middle class, by almost universal consensus, are those who can easily take care of all their food, housing and transportation needs in a sustainable way across generations and who also have a consistent ability and willingness to borrow (and repay) money for investments in future growth, to accumulate savings and capital, to put their children through any level of education, and to gather enough resources to start a business, expand a house or buy a vehicle without sacrificing living standards.

As it happens, in the developing world this level of security and comfort tends to be attained at almost exactly the income level defined by Milanovic in his study. With regional variations, somewhere between about $5,000 and $15,000 per year in family income is the gateway to the middle class.

The middle class should have grown a lot more in the two decades after the economic crises of the 1980s and the liberalization of the world's economies. Based on the extraordinary economic growth of that time, along with the increases in per capita incomes and boosts in living standards that occurred in those years, there should have been far more social mobility.

In 2006, economists working for MasterCard predicted a "deluge" of a billion new middle-class consumers, with family incomes of more than $5,000 annually, emerging from Asia, with 650 million such consumers appearing in China and 350 million in India by 2020. At the time, there were exactly 12 million people with such incomes in India and 79 million in China, so the projected growth was exponential, with equivalent rewards to industry: "As soon as income exceeds the $5,000 threshold, marginal expenditures shift quickly to discretionary spending such as dining out, personal travel, auto purchases, etc., and these have a huge business and economic impact," the MasterCard report claimed. The estimate has been echoed in similar studies.

Something went wrong, though. While living standards did improve, especially for the very poor, many who had sat on the brink of the middle class at the beginning of the long boom ended it, 20 years later, still sitting on the brink, unable to get in. These frustrated people were, overwhelmingly, the children of rural arrivals.

In one of the most important studies of the middle class in the developing world, three economists from prominent U.S. think tanks examined large banks of income statistics from around the world and found that the turn to market economics had been generally positive for income groups on the extremes - the poor and the very rich saw their fortunes rise dramatically in the 1990s and early 2000s (the poor, in large part, because of urbanization). But they concluded that "the middle has had very mixed rewards: increased upward mobility for some sectors … but increased uncertainty and downward mobility for others."

In Latin America, for example, liberalization brought income gains for most people, but "increasing economic insecurity for middle-income households." It described large segments of the middle class - broadly those without post-secondary education or family connections (that is, the arrival-city second generation) as "stalled in the jam."

In too many places, this "stalled" condition has left a large part of a generation out of the middle class. In his study of social mobility in Mumbai, the geographer Jan Nijman found that "the upper-middle income classes have grown relative to the total, the lower-middle income classes have shrunk, and that the ranks of the poor have expanded slightly" during the 1990s - that is, the numbers entering the middle class in that decade were smaller than the numbers of poor people entering the city every year.

His detailed examination of new home buyers found "little upward mobility"- in other words, the majority of home buyers were children of homeowners, not children of migrants. People who should have been stepping into the middle class, those earning $5,000 to $8,000 a year, were finding themselves barred from home ownership.

Entry to the middle class, in India and elsewhere, had become difficult in a time when other forms of growth were widespread. The problem had little to do with markets and much to do with the way governments responded. At the precise moment when governments should have been stepping in to help the newly secure poor find entry points to middle-class success, many governments seemed to vanish from the scene.

It was a vast fiscal miscalculation. In the aftermath of the 1980s, when countries opened to markets, many adopted exceedingly tight spending policies - sometimes because these were required by international lending agencies as conditions for bailout loans, in many more cases because the countries were opening themselves to international capital markets for the first time and wanted to demonstrate their macroeconomic discipline. In either case, the result was that a large part of the world was failing to invest in the development of its middle class (and the functioning of its rise from poverty through arrival cities). They would pay the price well into the 21st century.

"These societies ignored a couple key dimensions of middle-class development," says Sherle Schwenninger, the U.S. economist who co-authored a major study in 2007 that found that the global middle class had stagnated.

"They'd been slow to develop home mortgage markets that would have helped develop middle entrepreneurial industries; they have ignored state spending on infrastructure," he told me. "Too much of the economy was ignored, partly under the pressures to pay attention to public finances."

The parts of the economy that were being ignored by these governments were precisely those that had their locus in the arrival city. In analysis after analysis, the site of failed mobility turned out to be the institutions and functions that are most needed to make the arrival city work.

Janice Perlman, whose work with South American rural-urban migrants in the early 1970s was the first to recognize the economically central and dynamic nature of the arrival city, returned to revisit her subjects and their children.

"The move from an illiterate rural life in agriculture (or fishing) to a literate urban life in manual labour was a great leap in socio-economic mobility for the original interviewees or their parents," she concluded, and "there have been major improvements in collective consumption of urban services and in individual consumption of household goods over 35 years." But, while "significant gains were made in education by the children of the original interviewees … these gains are not fully reflected in better jobs."

Notably, she found "a striking lower rate of return to educational investment" for those living in arrival cities: paying to send your kid to a private secondary school or college, as the Magalhaes family are doing in Sao Paulo, does not guarantee that they will enter the middle class. Perlman did find that large numbers of children of Brazilian rural migrants are becoming middle class, but only by leaving the arrival city behind. Of the original migrants, 34 per cent are now living outside the arrival city in "legal" homeowner neighbourhoods that would qualify as middle-class, and 44 per cent of their children and 51 per cent of their grandchildren are.

In order to break out of the types of jobs their parents held, though, they needed university educations, and few were able to get them.

Another large-scale study, directed by the U.S.-based Council on Foreign Relations, found that those developing countries that experienced middle-class growth had done so because they had stable currencies and had attracted long-term capital flows, but also because they had cultivated a number of things directly aimed at the arrival city: financial institutions capable of supporting small businesses, plus "access to reasonably priced, long-term credit" for poor consumers to finance home ownership, post-secondary education and infrastructure development.

Even more significantly, a United Nations study of earnings in the developing world, which examined the factors behind failed middleclass growth in this century's first decade, found that developing countries are investing in post-secondary education at the expense of primary and secondary schools for the poor, causing educational benefits to be biased toward the existing middle class, thereby cutting off migrant families and reducing social mobility. And it found that the primary and secondary schools for the poor were not delivering the same results: the best teachers and educational resources were outside the arrival city.

It was the economist Amartya Sen who first recognized that poverty is, fundamentally, not the dearth of money or a lack of possessions or a shortage of talent or ambition, but the absence of capacities - the lack of tools or opportunities needed to function as a full citizen. This concept has become widely used in the field of development, but it finds its most pointed and obvious truth in the arrival city. For it is here, where there is the most will to reach out for betterment, that people are most dangerously deprived of capacities, those knobby handholds in the otherwise smooth vertical face of the economy.

As we've seen, most needed are the capacity to start a business and the capacity to be educated: when these are provided, a whole new class can develop. Those capacities suddenly materialize, as they did in Jardim Angela, when people have effective self-government, when they have good security and access to credit and urban amenities, when the government takes an active involvement in the neighbourhood. And in the eyes of arrival-city residents and many observers, another key to realizing these capacities lies in the full ownership of the land beneath your feet.

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