Do Capital per worker and HDI go together across countries?

Across 166 countries the link before adjusting for anything is r = +0.78, on a scale from -1 (opposite) to +1 (in step). A version that uses only each country's rank gives +0.92.

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

Comparing each country only with itself across 1990-2023, and setting aside what happened worldwide in each year, the link is -0.166 (168 countries, 5,339 country-years). Using year-to-year changes, it is -0.037.

Does Capital per worker cause 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.

Capital per worker vs. HDI

Fades after adjusting for income

Across 166 countries, Capital per worker and HDI rise and fall together at r = +0.78 (on a scale from −1 to +1, where 0 means no link). Comparing only countries with similar income (GDP per person) shrinks it to -0.01, which could easily be chance (q = 0.96, 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: sign flips when a single country is removed.

Comparing countries across the middle half of capital per worker, $76,293 to $427,471, HDI is better by 0.169 points at the top of that range than the bottom. Comparing only countries with similar national income, the gap reverses, to 0.00139 points the other way.

Link before adjusting (r)+0.782p = 1.6e-35 · 166 countries

After adjusting for national income-0.014p = 0.863 · likely range [-0.17, +0.14]

p, allowing for regions0.922standard error 0.132 · 7 regions

Check for luck (q)0.958across 18,622 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.

Capital per worker · 2021 international $ per workerlink with income +0.93 · proxy

HDI · index, 0 to 1link with income +0.96 · 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	+0.782	1.6e-35	166
By rank (Spearman), not adjusted	+0.916	4.4e-67	166
Standard (Pearson), adjusted for national income	-0.014	0.863	166
By rank (Spearman), adjusted for national income	+0.165	0.034	166

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 166 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: +0.769 (a minus sign means it grew).

How solid is it?

Leaving out one country at a time, r ranges from -0.034 (without TJK) to +0.098 (without BRN). 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: BRN (+0.112).

Fragile: this link may not hold up.

sign flips when a single country is removed
correlation moves sharply once outliers are trimmed
sign flips once outliers are trimmed
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	18	-0.55
Europe & Central Asia	48	+0.30
Latin America & Caribbean	27	-0.17
Middle East, North Africa, Afghanistan & Pakistan	20	-0.03
Sub-Saharan Africa	45	+0.30

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	+0.42
Middle third	55	+0.15
Richest third	55	-0.12

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	99	+0.21
Muslims	46	-0.17

By last European coloniser

	n	r
France	25	+0.42
Never a European colony	20	+0.46
Spain	19	-0.30
United Kingdom	50	-0.24

By official ideology

	n	r
Nationalist	25	-0.24
No strong official ideology	109	+0.20

By party system

	n	r
A few parties banned	25	+0.51
No parties banned	115	+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 = +0.163 after dropping 3 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 34years. So a link here can’t come from anything about a country that stays the same, such as its history, geography, institutions or culture.

The link shows up within countries over time (r = -0.166) but mostly disappears in year-to-year changes (r = -0.037). That points to slow trends particular to each country, not the two measures moving together from year to year.

Across countries (adjusted)-0.014for comparison

Within countries+0.511each country vs itself

…and vs the same year elsewhere-0.166q = 0.012 · 168 countries

Year-on-year changes-0.037q = 0.080

The direction flips. Comparing each country only with itself gives +0.51. Also taking out what happened to the whole world each year gives -0.17. So the first figure was picking up a trend both measures share with worldwide progress, not a link between them.

Read with care.

Almost all of the second indicator's variation is between countries, 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.

5,339 country-years (one country in one year), 168 countries, 1990–2023, about 32 years each on average. Share of the variation that happens within countries over time: 20% for Capital per worker, 10% for 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): -0.166. 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.

The data

	2021 international $ per worker	index, 0 to 1	Years
Brunei Darussalam BRN	$1,365,080	0.837	2023
United Arab Emirates ARE	$960,197	0.94	2023
Qatar QAT	$955,762	0.886	2023
Ireland IRL	$916,129	0.949	2023
Belgium BEL	$788,016	0.951	2023
Italy ITA	$772,186	0.915	2023
Norway NOR	$771,357	0.97	2023
Switzerland CHE	$713,606	0.97	2023
France FRA	$697,343	0.92	2023
Austria AUT	$691,757	0.93	2023
Hong Kong SAR, China HKG	$667,472	0.955	2023
Finland FIN	$666,233	0.948	2023
Iceland ISL	$663,692	0.972	2023
Singapore SGP	$659,201	0.946	2023
Bahrain BHR	$656,018	0.899	2023

Feenstra, Robert C., Robert Inklaar and Marcel P. Timmer (2015), "The Next Generation of the Penn World Table", American Economic Review, 105(10), 3150-3182, www.ggdc.net/pwt. Data: Penn World Table version 11.0, Groningen Growth and Development Centre, doi:10.34894/FABVLR.
United Nations Development Programme, Human Development Report 2025

Sources

Capital per worker

Capital stock per person engaged, at current PPPs (Penn World Table)

Groningen Growth and Development Centre, University of Groningen · via DataverseNL · CC BY 4.0 · updated irregular (new versions every few years)

The value of a country's buildings, machines, roads and other equipment, divided by the number of people working. It is in dollars adjusted for what money buys in each country, and it is best for comparing countries in the same year. The Penn World Table builds it by adding up past investment and taking off wear and tear, so it is linked to the investment share by construction. Where it is used for adjusting, it is measured in percentage terms (on a log scale), like income. No "better" direction is set.

HDI

Human Development Index

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

The geometric mean (a kind of average that multiplies the parts together) of three parts: income per person (GNI per capita), life expectancy, and schooling (expected years and average years). All four inputs are on this site, and each is flagged. So a link between the HDI and any of them is shown for what it is: the index matching a part of itself. For the same reason it is kept out of this site's own topic scores. Those already contain its parts, and adding it would count each twice. It is the most-cited development index there is. It is here mostly so its parts can be read separately.

How this was computed

Data used: most recent value in 2010-2025; values come from 2023. 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 18,622 pairs at once, using the Benjamini–Hochberg method. Underlying data last updated V-Dem v16; V-Party v2. How the country data works · explore Capital per worker and HDI

This page shows that two measures go together. It does not show that Capital per worker changes HDI, or the reverse. These figures also describe countries, not individual people. See the ecological fallacy.