Human capital (PWT) vs. Pupil-teacher ratio
Holds up after adjusting for income
Across 134 countries, Human capital (PWT) and Pupil-teacher ratio rise and fall together at r = -0.75 (on a scale from −1 to +1, where 0 means no link). Comparing only countries with similar income (GDP per person) shrinks it to -0.23 (q = 0.033, allowing for the many pairs tested). Much of the first figure is that both measures rise with national income, but a weak negative link remains. Caution: direction is not consistent across regions.
Comparing countries across the middle half of human capital (PWT), 2.2 to 3.31 points, pupil-teacher ratio is better by 15.9 pupils per teacher at the top of that range than the bottom. Comparing only countries with similar national income, the gap is 4.93 pupils per teacher.
Link before adjusting (r)-0.751p = 1.5e-25 · 134 countries
After adjusting for national income-0.231p = 0.007 · likely range [-0.39, -0.06]
p, allowing for regions0.003standard error 0.047 · 7 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
Pupil-teacher ratio · pupils per teacherlink with income -0.83 · 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 | -0.751 | 1.5e-25 | 134 |
| By rank (Spearman), not adjusted | -0.746 | 4.9e-25 | 134 |
| Standard (Pearson), adjusted for national income | -0.231 | 0.007 | 134 |
| By rank (Spearman), adjusted for national income | -0.188 | 0.030 | 134 |
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 134 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: +0.520 (a minus sign means it grew).
How solid is it?
Leaving out one country at a time, r ranges from -0.268 (without CAF) to -0.192 (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 (+0.040).
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 | 18 | +0.06 | |
| Europe & Central Asia | 40 | +0.04 | |
| Latin America & Caribbean | 20 | -0.30 | |
| Middle East, North Africa, Afghanistan & Pakistan | 14 | -0.21 | |
| Sub-Saharan Africa | 36 | -0.15 |
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 | 45 | -0.23 | |
| Middle third | 44 | -0.17 | |
| Richest third | 45 | +0.02 |
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 | 82 | -0.33 | |
| Muslims | 31 | -0.36 |
By last European coloniser
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 | ||
|---|---|---|---|
| France | 18 | +0.19 | |
| Never a European colony | 15 | -0.32 | |
| Spain | 17 | -0.06 | |
| United Kingdom | 40 | -0.03 |
By official ideology
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 | ||
|---|---|---|---|
| Nationalist | 18 | -0.04 | |
| No strong official ideology | 92 | -0.26 |
By party system
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 | ||
|---|---|---|---|
| A few parties banned | 18 | -0.66 | |
| No parties banned | 98 | -0.20 |
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 = -0.284 after dropping 5 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 30years. 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 = -0.069, 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 human capital (PWT) moved did not tend to see their pupil-teacher ratio move with it.
Across countries (adjusted)-0.231for comparison
Within countries-0.412each country vs itself
…and vs the same year elsewhere-0.069q = 0.385 · 141 countries
Year-on-year changes-0.022q = 0.345
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.
2,874 country-years (one country in one year), 141 countries, 1990–2019, about 20 years each on average. Share of the variation that happens within countries over time: 6% for Human capital (PWT), 10% for Pupil-teacher ratio. 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): -0.069. 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
index (1 = no schooling) | pupils per teacher | Years | |
|---|---|---|---|
| Israel ISR | 3.99 | 12.1 | 2023, 2016 |
| Slovak Republic SVK | 3.89 | 15.5 | 2023, 2017 |
| Korea, Rep. KOR | 3.87 | 16.3 | 2023, 2017 |
| United Kingdom GBR | 3.85 | 15.1 | 2023, 2017 |
| United States USA | 3.83 | 14.2 | 2023, 2017 |
| Croatia HRV | 3.81 | 13.5 | 2023, 2016 |
| Czechia CZE | 3.78 | 18.9 | 2023, 2013 |
| Norway NOR | 3.75 | 8.59 | 2023, 2017 |
| Switzerland CHE | 3.75 | 9.93 | 2023, 2017 |
| Germany DEU | 3.71 | 12.3 | 2023, 2017 |
| Denmark DNK | 3.67 | 10.7 | 2023, 2014 |
| Japan JPN | 3.66 | 15.7 | 2023, 2017 |
| Slovenia SVN | 3.66 | 13.8 | 2023, 2016 |
| Finland FIN | 3.6 | 13.7 | 2023, 2017 |
| Estonia EST | 3.58 | 11.3 | 2023, 2017 |
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.
World Bank, World Development Indicators
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.
Pupil-teacher ratio
Pupil-teacher ratio, primary
UNESCO Institute for Statistics · CC BY 4.0 · updated quarterly
The World Bank's copy stops at 2019.
How this was computed
Data used: most recent value in 2010-2025; values come from 2010–2023. 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 Human capital (PWT) and Pupil-teacher ratio
This page shows that two measures go together. It does not show that Human capital (PWT) changes Pupil-teacher ratio, or the reverse. These figures also describe countries, not individual people. See the ecological fallacy.
More links with Human capital (PWT) or Pupil-teacher ratio
- Adult literacy vs Human capital (PWT) before +0.84 → after adjusting +0.59
- Birth rate vs Pupil-teacher ratio before +0.84 → after adjusting +0.50
- Basic water access vs Pupil-teacher ratio before -0.80 → after adjusting -0.49
- Primary completion vs Pupil-teacher ratio before -0.78 → after adjusting -0.45
- Fertility rate vs Pupil-teacher ratio before +0.81 → after adjusting +0.45
- Human capital (PWT) vs PISA reading before +0.72 → after adjusting +0.44
- Electricity access vs Pupil-teacher ratio before -0.76 → after adjusting -0.43
- Birth registration vs Pupil-teacher ratio before -0.72 → after adjusting -0.43