Compared to two centuries ago, today's world is much different, as the standard of living has dramatically increased, along with population. This has been in strong contrast with previous history, characterized by growth close to zero in both population and the standard of living. During this period, there has been a very strong demographic change, called Demographic Transition, with a large decrease in mortality followed by a decrease in fertility. This has implied that every country that went (or still goes) through this transition has a period of high population growth while mortality is low and fertility has not yet declined. Such major shift in demographics have large implications, but it is also important to understand what triggered the Demographic Transition, especially as some countries are now just at the start of it.
Oded Galor tries to disentangle to various triggers that have been proposed. As this is a dynamic process, obviously some triggers are going to be more important at different stages of the transition. There is too discussion in the paper about the various theories and the quantitative evidence for and against them for me to summarize it efficiently here. Galor concludes that the following theories hold water when plunged into the data: First there is the theory that the higher demand for human capital during industrialization lead to a decline in fertility as parents concentrated more on the quality of their children rather than their quantity. Second, as the wage gap between females and males decreased, the increase in female labor force participation and the associated higher opportunity cost of having children for mothers reinforced the decrease in fertility.
What is important here are the theories that did not passed the test of the data according to Galor: the theory that the emergence of financial markets made in less necessary for parents to have been adult children to support them in old age; the theory that a decline in mortality lead to a too high number of surviving children; and the theory that the general increase in income lead to a rising opportunity cost of raising children.