It all started some 2 weeks ago with the post about overpopulation.

Although the sources were legitimate and according to the common narrative, I have seen that applied statistics was just a shallow rubbish.

In the comment section, the debate turned a bit with the rising question: are GDP per capita and Level of education only relevant parameters?

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My standing point was that it is true, but only for the extreme cases of poverty and illiteracy. After passing into the advanced society, the religion and cultural views take control.

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Unfortunately, I had no numbers, and I spoke only from my previous experience (read: street smart).

Now I found the data I needed and done the analysis to prove my points. @sco thank you for the suggestion:

Data:

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It was relatively easy to obtain all relevant data:

• Total fertility rate for every country originates from United Nations forecast 2015-2020
• List of countries by GDP (PPP) per capita comes from CIA, Central Intelligence Agency (1993–2017). This list contained the largest number of countries and I found it more precise because it provides the "average" over the reasonable time span
• Data about religion came from here. It's probably not perfect, but it's certainly good enough
• And the last parameter was Education Index, also provided by the UN (Human Development Report 2016)

Workflow:

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After the alignment and cross-comparison, it was possible to extract the data for 176 countries.
The list was filtered to obtain separate tables for each dominant religion. The cutoff was set to 70% (I did it arbitrarily).

• Christian + Irreligious, 105 countries in total
• Muslim, 39 countries in total
• and the list of countries that can be considered as Western. The list includes European countries, ANZAC and USA with primarily Christian + Irreligious population above 70%

After the data are plotted, there are several solutions that could be applied to see the trends:

• we can apply some function, but it's bad because it presumes some behaviour
• some smoothing spline, but the smoothness parameter is subjective
• moving window is great and common. We can use just a simple moving average (MA), weighted MA, or Savitzky-Golay if we feel funky and want to impress our colleague. (tested - doesn't work)
• or, we can apply some sort of histogram-style logic, where we take the group with similar GDP (ex. 10-20k $), and calculate the average for GDP and Education index. Average can be weighted according to the percentage of religious people but the differences were negligible in comparison with the simple average. In order not to make it complicated, I used just a simple average.

First question, where is the limit when GDP becomes irrelevant to Fertility rate?

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All the countries:

Ok, yes, there is the fall, but where is the breaking point?

Up to 15k $, there is a power function:

Linear break occurs at about 10k $. After 15k $, there is no trend.

Or, if you prefer, here is the moving average:

Zoom:

In conclusion, the Total fertility rate is related to GDP only for the countries poorer than the poorest European countries.

Second question, where is the limit when GDP becomes irrelevant to Education index?

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Similar results:

After passing 20k $, there is no relation between the education and total fertility rate.

And the third question: is there a relation between the total fertility rate and education

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Just to clarify:

• basic literacy, 4 years in school = 0.25
• elementary school, 8 years = 0.49
• high school, 12 years = 0.73 (Western countries are all above 0.7)

After the 0.7 mark, it becomes irrelevant

Now, does the religion plays it's role if we exclude the GDP as the factor?

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In this case, I used the average of following GDP values (<10k, 5-15k, 10-20k, 15-25k, 20-30k, 25-50k, 40-80k).
Overlap was taken to obtain the proper sampling, and the breaking points were taken into account.

I'm not implying that anything is good or bad, right or wrong, I'm only pointing out the differences in way of life according to religion!!!

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In all the cases, Muslim countries have TFR > 2. Western countries never go above 2.

Concerning the education:

Again, no, matter how poor, Western countries always have Education index > 0.725 (MOL, ARM).
And with the growth of GDP, it goes >0.8 (Georgia, Croatia, Russia).
Switzerland, Canada, Slovenia, USA, Netherlands are about 0.9.
And the top ranking >0.92: GER, NOR, DEN, AUS, NZE.

Top Muslim countries are ex-Soviet countries (about 0.7-0.75, KAZ (0.80), KYR, UZB, AZB), Pakistan (0.77).
What we don't see is the coefficient >0.8.
North African countries are in range between 0.50 and 0.65.

Finally, Education and Fertility:

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In all the countries, once the average education becomes the highschool, the total fertility rate drops to 2:

Bonus, Educattion vs TFR

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No connection in Muslim countries, 2-3 children is normal:

And no connection in Western countries, 1-2 children is normal:

Conclusion:

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Both education and family planning are purely guided by religion/culture/ lifestyle once the basic education and income are provided.