I believe birthrate is tied to culture, which is influenced heavily by the economy.
In a developed economy skilled labor is almost expected. A developed economy also attracts immigrants from less developed economies. This causes two things to occur; The bar for what is considered "skilled labor" is constantly on the rise and unskilled labor is continuously devalued.
These cause young adults to either spend their youth in training or to compete in a glutted unskilled labor market. Neither of which are conductive to encouraging family starting.
There's also women in the workforce to consider. In your granddaddy's day it wasn't uncommon for women to be housewives and to keep the home and care for all five kids while the husband provided for all of that thanks to his labor being more valued than yours. I still cannot imagine why you'd want to work instead of staying home with your kids, I'd be a househusband in a heartbeat.
>welfare and social security
Developed economies generally have various forms of welfare. Even if you're not a bleeding heart it's just practical for the economy's sake for the better off to support the less off. This causes an increase in birthrate for the unskilled labor market while drains away at the resources of everyone else, resources typically used to raise their families.
Social security, or anything that allows an adult to feel secure in their financial future, further reduces the reason to have kids. Because they feel that they can support themselves without the need of their potential children's help.
Unhealthy old farts just aren't dying. With the age of the average first time parent getting older that means that the age gap between children and grandparents is getting larger.
Why does this matter? Because children are spending their childhoods watching their parents take care of not only the parent and child generations, but the grandparent generations as well, causing kids to see future children as an added hassle on top of their parents will be. This has an added effect of effectively removing any chance of grandparents meaningfully assisting in the raising of the next generation.
A successful economy tends to offer a smorgasbord of entertainment.
A lot of said entertainment is solo focused, meaning people are interacting more and more with entertainment alone and less with others (potentially of the opposite sex). A lot of entertainment options also means people aren't fucking for fun as much as they used to. Ask your parents and grandparents how much they fooled around back in the day. If they're honest and not prudes chances are their old sex lives blows your's the fuck out.
>cost of living and luxuries
The more developed an economy is the more resources it costs to maintain a person's status quo. You've got automobile expenses (initial costs, gas, maintenance and repair, and insurance), living space costs, food & hygiene, the list goes on.
Then we've got luxuries. Subscriptions for cable, internet, and phone. On top of those there's the multi-billion video game, movie, and music industries constantly siphoning wealth, wealth that those in less developed economies would invest into their families.
To top it all off inflation continues to rise while wages stagnate, meaning that the odds and ends it takes to get through the day not only cost more in terms of wealth, but cost more in terms of time spent gathering said wealth.
>security and stress
I'm going to go out on a limb here and assume the majority of nations/demographics suffering a declining birthrate are democracies. Democracies are awful for one's sense of security, constant elections trying to convince you why everything is awful, how they're going to fix it, and how all the other guys are baby eating demons. With elections comes unexpected policies and laws out of the blue and flipflopping on other matters. Also, no one knows when their government will decide to start/join another war because some backwards people just don't have enough FREEDOM
The chaotic nature of democracies breeds apprehension and stress in it's inhabitants. Even more so for those considering planning a family and questioning what kind of lives their children will be able to lead.