I doubt your 'statistical truth'. Other 'third-world' areas of the 60s and 70s, including India and Central/South America, haven't seen living standards fall after life expectancy increases.
Sometimes population declines, like after the plague in Europe, can improve the lot of survivors by freeing up resources and increasing the returns for labor. But the reverse -- that population growth makes things worse -- doesn't necessarily follow. It depends on a lot of other factors, and in most of the world, including most of the third world, lower death rates and improved living standards have gone hand-in-hand.
Sometimes population declines, like after the plague in Europe, can improve the lot of survivors by freeing up resources and increasing the returns for labor. But the reverse -- that population growth makes things worse -- doesn't necessarily follow. It depends on a lot of other factors, and in most of the world, including most of the third world, lower death rates and improved living standards have gone hand-in-hand.