So lots of people are debating the economic side of things, here's an actual study from South Korea and it looks like lack of income/housing security DOES play a role in the low birthrates.
Here I'll copy-paste the conclusion:
Results from discrete-time hazard models provide evidence of substantial socioeconomic differentials in fertility. For instance, the husband’s higher education and better employment status (e.g., college education, standard employment) are positively associated with having a first and second childbirth. Also, those who can secure enough money to purchase a house or to deposit a lump-sum for a Jeonse lease have a higher likelihood of having first and second births than those who rent by the month (Weolse).8 At the same time, it is important to note that the association between socioeconomic status and fertility often varies across indicators and gender. In general, higher socioeconomic status seems to be conducive to the transition to parenthood and second birth; however, employed wives are less likely than housewives to have a first child. This reflects the difficulty of combining work and motherhood due to gender norms emphasizing women’s domestic responsibilities and a family-unfriendly work culture (e.g., long work hours and after-work social gatherings) (Brinton 2001; Choe, Bumpass, and Tsuya 2004). While women’s labor force participation is negatively associated with childbirths, the underlying reasons for delaying births may differ by employment status. For example, women in nonstandard employment, who in light of a strong preference for status homogamy in Korea are likely to have husbands with insecure jobs, might delay (or give up) childbearing for economic reasons. On the other hand, women with standard jobs might postpone childbearing for career reasons, since the opportunity costs of leaving standard employment are high in the Korean labor market, where it is almost impossible for married women to find standard employment upon reentry (Brinton 2001). Indeed, the likelihood of making the transition to a second birth is the lowest among wives in standard employment (Model 7, Table 3). A recent qualitative study on highly educated Korean women provides supporting evidence for this possibility by documenting that those who continue working full-time consider having only one child (Brinton and Oh 2019).
In addition, fertility differentials by husbands’ employment status are worth taking into consideration. Women have a lower likelihood of giving birth if their husbands hold nonstandard jobs compared to those whose husbands work in standard employment or self-employment. As discussed above, employment status is not only an indicator of one’s current labor market status but also of one’s future career trajectory in a rigidly segmented Korean labor market. In this context, married couples may postpone having their first child or subsequent children if the husband is not in secure standard employment (or does not run his own business), reflecting the persistent malebreadwinner norm. These findings are consistent with the finding that deteriorating employment prospects for young men are linked to declining marriage and fertility rates (Cherlin 2014; Karabchuk 2020; Ruggles 2015; Yeung and Yang 2020). By considering employment types of both husband and wife, this study also finds that the role of employment in fertility may differ depending on whose labor force participation is examined. Given that prior studies on fertility have often focused only on one spouse’s employment (e.g., including wife’s employment status without considering the effect of husband’s labor market status) (e.g., Kim 2014; Ma 2016), the results of this study show that it is important to understand fertility decisions by looking at the dynamics of couples’ employment status.
Another important finding of this study is the role of homeownership in fertility behaviors. For both first and second births, those with Weolse (monthly rent) are least likely to make the transition to parenthood.9 With skyrocketing home prices and the lack of affordable housing, securing ‘key money’ becomes a challenge and is causing rising household debt in Korea (Sohn 2019). Therefore, policies to help relieve the burden of high housing costs for young couples need to be implemented and expanded as a measure to boost fertility. For instance, Seoul Metropolitan Government provides newlyweds with low mortgage rates and public housing (Seoul Metropolitan Government 2020).
TL/DR: If the husband has a great education, a high-paying job, a stable, secure job, or the couple owns a home they are the most likely to have a kid earlier. But if the husband has less education, a lower-paying job, a non-standard job, or the couple rents their place, they are less likely to have a kid earlier. And they are less likely to have a kid if the woman works, especially if the lower or nonstandard husband income requires the woman to work.