the most important factor here is that it is agrarian, poorly educated and patriarchal societies that reproduce well.
Of course that's the trend. As soon as women know how to prevent pregnancy and have the means to do it thay usually start to opt for less kids.
However I do agree with Maf that rather than simply giving money the better option is childcare, job security, housing conditions and more equal share in household chores ( although the last one is of course outside of the system and between the partners). Money are good but only as a safety net so the parents know they won't starve if something happens