They do indeed have a common cause. It is the exploitation of non-organic energy, that is, fossil fuels. Without them the English industrial revolution would have come to a stop around 1850, or earlier.
Why do kids mean more economic growth? Current thinking is that of Oded Galor.[3] More people, more ideas, so more one-in-a-billion great ideas that improve everyboy's lives.
1. Energy and the English Industrial Revolution https://www.cambridge.org/core/books/energy-and-the-english-...
2. Ayres and Warr 2005, "Accounting for Growth: The Role of Physical Work" (pdf) http://113.212.161.150/elibrary/Library/Structural_Change/Ay...
3. https://en.wikipedia.org/wiki/Unified_growth_theory