Do Fertility rate and Inequality-adjusted HDI go together across countries?

Across 167 countries the link before adjusting for anything is r = -0.84, on a scale from -1 (opposite) to +1 (in step). A version that uses only each country's rank gives -0.84.

Does the link hold within countries over time, not just across countries?

Comparing each country only with itself across 2010-2023, and setting aside what happened worldwide in each year, the link is +0.004 (166 countries, 2,131 country-years). Using year-to-year changes, it is +0.044.

Does Fertility rate cause Inequality-adjusted HDI?

This analysis cannot answer that. It shows only that the two go together. A link between two country measures, adjusted or not, does not show that either one changes the other. Country figures also say nothing about individual people.

Fertility rate vs. Inequality-adjusted HDI

Fades after adjusting for income

Across 167 countries, Fertility rate and Inequality-adjusted HDI rise and fall together at r = -0.84 (on a scale from −1 to +1, where 0 means no link). Comparing only countries with similar income (GDP per person) shrinks it to -0.26, which could easily be chance (q = 0.29, allowing for the many pairs tested, and allowing for countries in the same region being alike). So the first figure mostly shows richer countries differing from poorer ones, not a link between these two things. Caution: direction is not consistent across regions.

Comparing countries across the middle half of inequality-adjusted hdi, 0.434 to 0.771 points, fertility rate is 1.82 births per woman lower at the top of that range than the bottom. Comparing only countries with similar national income, the gap is 0.862 births per woman.

Link before adjusting (r)-0.838p = 3.3e-45 · 167 countries

After adjusting for national income-0.264p = 0.001 · likely range [-0.40, -0.12]

p, allowing for regions0.059standard error 0.114 · 7 regions

Check for luck (q)0.292across 12,497 pairs

How to read these.r runs from −1 (one goes up as the other goes down) to +1 (they rise together), and 0 means no link. Adjusting for national income means comparing countries with the same GDP per person, so differences in wealth can’t explain the link. Income is used in percentage terms, since an extra $1,000 means more to a poor country than to a rich one. p is how likely a link this strong would be if there were really none. Below 0.05 means it is unlikely to be chance. Very small values are written in short form: 1.1e-32 means a decimal point followed by 31 zeros and then 11, so very close to zero. The likely range is where the true figure probably lies, and a range that crosses zero means the link could easily be chance. Countries in the same region tend to resemble each other, so the third figure allows for that, which gives a fairer p. The standard error is the typical size of the error in r. Finally, testing this many pairs means some will look strong by luck alone. A q below 0.05 means this link is unlikely to be one of those.

Fertility rate · births per womanlink with income -0.81 · proxy

Inequality-adjusted HDI · index, 0 to 1link with income +0.94 · proxy

Both of these rise and fall closely with national income, so a strong link between them before adjusting was close to certain. Read the adjusted figure, not the first one.

“Link with income” is how closely each measure tracks GDP per person across countries, from −1 to +1.

Every country as a dot

best-fit line line after adjusting

Four ways to measure the link

Method	r	p	Countries
Standard (Pearson), not adjusted	-0.838	3.3e-45	167
By rank (Spearman), not adjusted	-0.841	8.4e-46	167
Standard (Pearson), adjusted for national income	-0.264	0.001	167
By rank (Spearman), adjusted for national income	-0.215	0.005	167

The rank version uses only each country’s place in line, from lowest to highest, so a few extreme countries count for less. The adjusted and unadjusted versions use the same 167 countries: those that report both measures and GDP per person. So the gap between them comes from the adjustment, not from a change in which countries are counted. Drop in the size of r after adjusting: +0.574 (a minus sign means it grew).

How solid is it?

Leaving out one country at a time, r ranges from -0.286 (without BTN) to -0.229 (without AGO). The bar above shows that range on a scale from −1 to +1, with the solid line at the full result. The single country that moves r most: AGO (+0.035).

Fragile: this link may not hold up.

direction is not consistent across regions

Within each region

Countries are not separate, unrelated cases, and neighbors share a lot. A link that holds inside each region is far more believable than one that shows up only when comparing regions.

	n	r
East Asia & Pacific	29	+0.17
Europe & Central Asia	47	+0.01
Latin America & Caribbean	22	-0.18
Middle East, North Africa, Afghanistan & Pakistan	16	-0.00
Sub-Saharan Africa	45	-0.46

By income third

If the link shows up only in the richest third of countries, it is a feature of rich countries, not a general pattern.

	n	r
Poorest third	56	-0.43
Middle third	55	-0.30
Richest third	56	-0.15

By largest religious group

Countries grouped by a label they share, such as main religion, rather than by a number. Groups of fewer than twelve countries are not shown. These groups differ in income, region and history all at once. So a gap between them is a place to start asking questions, not an answer.

	n	r
Christians	100	-0.25
Muslims	41	-0.41

By last european coloniser

	n	r
France	24	-0.43
Never a European colony	18	-0.08
Spain	18	-0.49
United Kingdom	51	-0.10

Without outliers (countries far outside the middle half of countries on either measure, by more than one and a half times the width of that middle half): r = -0.252 after dropping 1 countries.

Two series, one country

Both measures over the years for one country you pick. The two charts are stacked so they share only the years along the bottom.

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Over time, within countries

Everything above compares countries with each other at one moment. This section compares each country only with itself over 14years. So a link here can’t come from anything about a country that stays the same, such as its history, geography, institutions or culture.

Within countries over time, there is no link that is clearly more than chance (r = +0.004, comparing each country only with itself over the years, and each year only with the same year elsewhere). Whatever the cross-country picture shows, countries whose fertility rate moved did not tend to see their inequality-adjusted hdi move with it.

Across countries (adjusted)-0.264for comparison

Within countries-0.540each country vs itself

…and vs the same year elsewhere+0.004q = 0.967 · 166 countries

Year-on-year changes+0.044q = 0.198

Read with care.

Almost all of this indicator's variation is between countries, not within them, so the within-country estimate rests on a small part of the data.
Much of the within-country association disappears once shared global year effects are removed, which points to a common worldwide trend rather than a country-level relationship.

2,131 country-years (one country in one year), 166 countries, 2010–2023, about 13 years each on average. Share of the variation that happens within countries over time: 1% for Fertility rate, 3% for Inequality-adjusted HDI. The margins of error allow for each country appearing many times, and for each year’s value being close to the year before.

Year-to-year changes are a cautious test, not a final answer. Looking only at changes from one year to the next removes each country’s own trends. But it also makes measurement mistakes louder, which pulls the results toward zero. A near-zero result here is weak evidence of no link, not proof.

With one measure years behind the other

Same year (lag 0): +0.004. A peak away from zero does not show which comes first. These series change slowly — this year’s value is close to last year’s. That makes the curve smooth and nearly symmetric, whatever produced the data. Even a sharp peak at one lag (a gap of some years) would not prove that one measure changes the other.

This curve peaks at the edge of the window (lag +10), so it is still drifting where the search stops. That pattern usually reflects a slow trend left over in the data, not a link with real timing. The peak value should not be read as the “true” link at the right lag.

The data

	births per woman	index, 0 to 1	Years
Chad TCD	6.03	0.252	2024, 2023
Somalia, Fed. Rep. SOM	6.01	0.229	2024, 2023
Congo, Dem. Rep. COD	5.98	0.341	2024, 2023
Central African Republic CAF	5.95	0.253	2024, 2023
Niger NER	5.93	0.265	2024, 2023
Mali MLI	5.51	0.281	2024, 2023
Angola AGO	5.05	0.36	2024, 2023
Burundi BDI	4.79	0.286	2024, 2023
Afghanistan AFG	4.76	0.321	2024, 2023
Mozambique MOZ	4.69	0.297	2024, 2023
Mauritania MRT	4.63	0.374	2024, 2023
Tanzania TZA	4.54	0.391	2024, 2023
Benin BEN	4.48	0.316	2024, 2023
Nigeria NGA	4.38	0.379	2024, 2023
Sudan SDN	4.26	0.328	2024, 2023

World Bank, World Development Indicators
United Nations Development Programme, Human Development Report 2025

Sources

Fertility rate

Fertility rate, total (births per woman)

World Bank · CC BY 4.0 · updated quarterly

Inequality-adjusted HDI

Inequality-adjusted Human Development Index

United Nations Development Programme, Human Development Report Office · via Our World in Data · CC BY 3.0 IGO · updated annual · comparable from 2010 only

The HDI marked down for how unequally each of its three parts is spread within the country. The gap between this and the HDI is what inequality costs, and that is the number worth reading. The level itself is the HDI again, with its parts flagged the same way.

How this was computed

Data used: most recent value in 2010-2025; values come from 2015–2024. To adjust for income, each measure is first predicted from GDP per person (in percentage terms, on a log scale) with a straight-line fit. Only what is left over is then compared. This is called a partial correlation. The line is drawn the standard way (ordinary least squares), which picks the line that comes closest to all the countries at once. The error margins allow for countries in the same region resembling each other, using 7 World Bank regions. The q-value corrects for testing all 12,497 pairs at once, using the Benjamini–Hochberg method. Underlying data last updated DYB 2024. How the country data works · explore Fertility rate and Inequality-adjusted HDI

This page shows that two measures go together. It does not show that Fertility rate changes Inequality-adjusted HDI, or the reverse. These figures also describe countries, not individual people. See the ecological fallacy.