Do welfare payments for children incentivise having children?
For example, "Assessing the Impact of the Maternity Capital Policy in Russia" (2014):


  Starting in 2007, the federal government has pursued an ambitious pro-natalist policy. Women who give birth to at least two children are entitled to "maternity capital" assistance ($11,000). In this paper we estimate a structural dynamic programming model of fertility and labor force participation in order to evaluate the effectiveness of the policy. We find that the program increased long-run fertility by about 0.15 children per woman.


Of course, the impact varies by country and incentive. See references and citations of this paper for more research.