Baby Money Index - Reader Comments

My previous post on the Baby Money Index was picked up by Marginal Revolution and some interesting questions have come in. My thoughts:

1) Why is TFR squared?

Though there is a technical reason for squaring Total Fertility Rate (see appendix), really squaring was necessary so that BMI wouldn't become yet another indicator of limited value due to a high correlation with GDP.

Below is a table of how BMI correlates to GDP per capital (PPP) when various exponents (n) are used in a formula BMI = GNI × TFRⁿ:

You can see that to have no more than a moderate correlation (r = 0.6 to 0.4), n must be at least 2.

A possibility would be to fine tune to some decimal exponent between 2 and 3, but the added precision seems less valuable than the simplicity of BMI = GNI × TFR². Also, people mostly seem to complain that TFR is overweighted, not underweighted, and n = 2 while large, is straightforwardly defensible.

(In fact, the other BMI, i.e. weight/height², also finds that an exponent of 2.5 might be better, but we continue to use 2 for simplicity.)

2) A Commenter Says North Korea is Actually the Worst :

the real lowest BMI country is actually North Korea

Reliable data on North Korea is hard to come by, from what I can tell for GDP per capita there's a range from ~$600 (nominal) to $1800 (PPP). That last number is from 2015, but it doesn't seem that the North Korean economy has grown in the past decade, so it may still apply.

My World Bank data set did have North Korea's TFR for 2022, listed as 1.78. The commenter alleges that this is too high, but ultimately doesn't affect its ranking because even using the official TFR and the higher GDP figure, North Korea's BMI is only 5.7 kiloChads.

This puts it far behind Jamaica's 19 kiloChads to make the probable, if not official, lowest BMI country on earth.

(North Korea seems like an out-of-sample prediction, and I find its low ranking validating for the metric.)

3) Cost of Living Compensation

What about adjusting for Cost of Living in different places?

In fact, all my numbers use the Gross National Income at Purchasing Power Parity (PPP), so this is already accounted for.

4) Why is Israel Both Rich and Fertile?

Israel is a clear outlier, and many have mused why. I don't know enough to make specific claims, other than to refute the notion that it's only because of fertility rates among the highly religious Haredi:

Even among Jewish women who self-identify as secular and traditional but not religious, the combined TFR exceeds 2.2, making it higher than the TFR in all other OECD countries.

Appendix: Math Why Squaring TFR is Reasonable

Regarding the footnote about "the GNI already being divided by a population term", this is to deal with the fact that when you have higher fertility rates, you have more people, and thus your GDP per capita (i.e. per person) will be lower. Of course if all these people were working this wouldn't matter, but above-replacement fertility rates results in a true population pyramid: there will always be more younger than older people at any given age.

As an example, let's consider computing the GNI of an idealized country, where everyone is either a man, woman or child (e.g. no double counting).

Total Fertility Rate (TFR):

\( \text{TFR} = \frac{\text{Children}}{\text{Woman}} \)

Therefore:

\( \text{Children} = \text{Women} \times \text{TFR} \)

Total Population:

\( \text{Population} = \text{Men} + \text{Women} + \text{Children} \)

Income per Capita:

\( \text{Income per Capita} = \frac{\text{GNI}}{\text{Population}} \)

\( \text{Income per Capita} = \frac{\text{GNI}}{\text{Men} + \text{Women} + \text{Children}} \)

Substitute in: \( \text{Children} = \text{Women} \times \text{TFR} \)

\( \text{Income per Capita} = \frac{\text{GNI}}{\text{Men} + \text{Women} + \text{Women} \times \text{TFR}} \)

As TFR becomes larger, the Men and Women population terms become insignificant:

\( \text{Income per Capita} = \frac{\text{GNI}}{\text{Men} + \text{Women} + \text{Women} \times \text{TFR}} \)

\( \lim_{\text{TFR} \to \infty} \text{Income per Capita} = \frac{\text{GNI}}{\text{Women} \times \text{TFR}} \)

In the limit, a country's income per capita has TFR in the denominator. Therefore in the limit, to have a positive effect on BMI, the TFRⁿ exponent must be n > 1.

Of course no country has a fertility rate outside the single digits. This is just to demonstrate how the higher the fertility rate, the more income per capital is effectively divided by TFR.