Do Human capital (PWT) and PISA science go together across countries?

Across 78 countries the link before adjusting for anything is r = +0.71, on a scale from -1 (opposite) to +1 (in step). A version that uses only each country's rank gives +0.73.

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

Comparing each country only with itself across 2006-2022, and setting aside what happened worldwide in each year, the link is +0.296 (55 countries, 324 country-years). Using year-to-year changes, it is —.

Does Human capital (PWT) cause PISA science?

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.

Human capital (PWT) vs. PISA science

Holds up after adjusting for income

Across 78 countries, Human capital (PWT) and PISA science rise and fall together at r = +0.71 (on a scale from −1 to +1, where 0 means no link). Comparing only countries with similar income (GDP per person) shrinks it to +0.42 (q = 0.033, allowing for the many pairs tested). Much of the first figure is that both measures rise with national income, but a moderate positive link remains.

Comparing countries across the middle half of PISA science, 410 to 493 PISA points, human capital (PWT) is better by 0.507 points at the top of that range than the bottom. Comparing only countries with similar national income, the gap is 0.338 points.

Link before adjusting (r)+0.713p = 2.4e-13 · 78 countries

After adjusting for national income+0.417p = 0.000 · likely range [+0.21, +0.59]

p, allowing for regions0.003standard error 0.063 · 5 regions

Check for luck (q)0.033across 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.

Human capital (PWT) · index (1 = no schooling)link with income +0.82 · proxy

PISA science · PISA pointslink with income +0.78 · high

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	+0.713	2.4e-13	78
By rank (Spearman), not adjusted	+0.735	1.9e-14	78
Standard (Pearson), adjusted for national income	+0.417	0.000	78
By rank (Spearman), adjusted for national income	+0.517	1.5e-6	78

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 78 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: +0.296 (a minus sign means it grew).

How solid is it?

Leaving out one country at a time, r ranges from +0.387 (without QAT) to +0.450 (without MAC). 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: MAC (+0.033).

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	15	+0.50
Europe & Central Asia	37	+0.29
Latin America & Caribbean	15	+0.32

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	26	+0.36
Middle third	26	+0.04
Richest third	26	+0.58

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	51	+0.46
Muslims	13	-0.11

By last European coloniser

	n	r
Spain	14	+0.07
United Kingdom	14	+0.56

By official ideology

	n	r
No strong official ideology	59	+0.45

By party system

	n	r
No parties banned	64	+0.36

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 = +0.417 after dropping 0 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 17years. 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 = +0.296) but mostly disappears in year-to-year changes (r = —). That points to slow trends particular to each country, not the two measures moving together from year to year.

Across countries (adjusted)+0.417for comparison

Within countries-0.013each country vs itself

…and vs the same year elsewhere+0.296q = 0.014 · 55 countries

Year-on-year changes—q = —

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.

324 country-years (one country in one year), 55 countries, 2006–2022, about 6 years each on average. Share of the variation that happens within countries over time: 5% for Human capital (PWT), 9% for PISA science. 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): +0.296. 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

	index (1 = no schooling)	PISA points	Years
Israel ISR	3.99	465	2023, 2022
Slovak Republic SVK	3.89	462	2023, 2022
Korea, Rep. KOR	3.87	528	2023, 2022
United Kingdom GBR	3.85	500	2023, 2022
United States USA	3.83	499	2023, 2022
Croatia HRV	3.81	483	2023, 2022
Czechia CZE	3.78	498	2023, 2022
Canada CAN	3.77	515	2023, 2022
Norway NOR	3.75	478	2023, 2022
Switzerland CHE	3.75	503	2023, 2022
Germany DEU	3.71	492	2023, 2022
Denmark DNK	3.67	494	2023, 2022
Japan JPN	3.66	547	2023, 2022
Slovenia SVN	3.66	500	2023, 2022
Australia AUS	3.61	507	2023, 2022

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.
OECD databases as named on each indicator: PISA, Social Expenditure Database (SOCX), Income Distribution Database, Development Assistance Committee statistics, Family Database, Government at a Glance, Corporate Tax Statistics, employment and environment statistics

Sources

Human capital (PWT)

Human capital index, from years of schooling (Penn World Table)

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

"Human capital" means the skills and knowledge workers bring to their jobs. This index measures it from schooling alone. It starts from how many years adults spent in school, then counts the early years for more than the later ones, following studies of how much higher pay tends to be with each extra year. A score of 1 means no schooling; the US is about 3.8. It uses the same schooling figures as mean years of schooling, so the two are close by construction. For that reason it is left out of the education score, which already counts years of schooling.

PISA science

PISA mean science score

OECD · via Our World in Data · CC BY 4.0 (OECD terms and conditions) · updated annual, except the snapshots noted per indicator

How this was computed

Data used: most recent value in 2010-2025; values come from 2015–2023. 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 5 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 Human capital (PWT) and PISA science

This page shows that two measures go together. It does not show that Human capital (PWT) changes PISA science, or the reverse. These figures also describe countries, not individual people. See the ecological fallacy.