|A lone child playing with a ball. It's symbolic, trust me.|
But of course that the causation could easily be the other way around: Better economic conditions and smaller families free up resources for things like electricity and television sets. And the TV networks probably follow their customers; they build out their networks once there's enough women with enough free time to enjoy daytime dramas, and enough income to buy the items advertised on them.
We humans are great at finding spurious correlations, then making up plausible-sounding just-so stories to connect the dots we seem to have found. How about this explanation: Increasing wealth makes better indoor lighting available. With more light, people spend their evenings reading, working and playing. That gives people less time and energy for sex, which results in fewer children.
That idea is also sort of plausible-sounding, I think, but unlikely to be true of course. The old expression that "correlation is not causation" sounds like a dull platitude, but is really a strong warning; we are so predisposed to think that correlation is causation that we are reluctant to give it up even in the face of overwhelming evidence to the contrary.
And it's easy to find evidence against this idea. For instance, we should not forget that this is not the first wave of declining birth rates. European nations went through the same shift from large to small families one to two centuries ago, well before mass media was widespread and accessible enough to cause such a shift. And it's by far most likely the same factors are driving the shift in India, south American and African societies today.
So, the connection to soap operas is an interesting idea. It may well add a marginal contribution to the rate of current demographic shifts. But it's very unlikely to be one of the main factors.