Huge streams of migration flow from the countryside villages to the cities in the Third World, in hopes for a better life. Poverty awaits the new migrants in the cities in shanty-towns, but the urban poverty is less than the rural poverty from which they have escaped, and so the magnet still operates to draw them in. (They don’t come simply because they are misinformed about the urban poverty; information spreads efficiently and reliably through kinship and friendship networks.)
While on the land, they may have owned small plots of land or been tenants or share-croppers or farm workers. In any of these situations, they needed large families to help work the land. The move to the city still maintained the social traditions of large families for a time, but gradually the children became a burden and not a help, as the family breadwinners moved from subsistence on the land into the money economy – perhaps first to the informal sector, but eventually into wage employment, even if part-time, temporary or seasonal. If they managed to move up in the social scale and into better housing, the children would go to school rather than labour in the fields or beg in the streets, and in the next generation even the mothers would have an education (at least be literate), and perhaps outside employment. Then they would begin to have fewer children.