Even in countries not classed as 'developed', birth rates are in decline. India and China for example. The Chinese really didn't need the 'one child policy', as birth rates would soon have declined without it. Now they are encouraging women to have more children!
Africa is the only exception, but within a decade or two, the same thing will also happen there. Female education and work opportunities are a huge factor. When women have the chance to complete their education and work outside the home, they will start having children later, or perhaps not at all. Unfortunately this isn't the case yet in much of Africa, hence birth rates as high as 7 per woman in some countries.