Capital per worker vs. Regulatory quality
Fades after adjusting for income
Across 170 countries, Capital per worker and Regulatory quality rise and fall together at r = +0.73 (on a scale from −1 to +1, where 0 means no link). Comparing only countries with similar income (GDP per person) shrinks it to +0.22, which could easily be chance (q = 0.14, 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 capital per worker, $77,621 to $435,583, regulatory quality is better by 0.94 points at the top of that range than the bottom. Comparing only countries with similar national income, the gap is 0.3 points.
Link before adjusting (r)+0.730p = 1.4e-29 · 170 countries
After adjusting for national income+0.225p = 0.003 · likely range [+0.08, +0.36]
p, allowing for regions0.032standard error 0.081 · 7 regions
Check for luck (q)0.139across 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
Regulatory quality · index (approx. -2.5 to 2.5)link 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 | +0.730 | 1.4e-29 | 170 |
| By rank (Spearman), not adjusted | +0.757 | 8.3e-33 | 170 |
| Standard (Pearson), adjusted for national income | +0.225 | 0.003 | 170 |
| By rank (Spearman), adjusted for national income | -0.107 | 0.167 | 170 |
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 170 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: +0.505 (a minus sign means it grew).
How solid is it?
Leaving out one country at a time, r ranges from +0.214 (without BDI) to +0.251 (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 (+0.027).
Fragile: this link may not hold up.
- direction is not consistent across regions
- much weaker within income groups than across them (mostly a gap between richer and poorer countries)
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 | 19 | -0.34 | |
| Europe & Central Asia | 48 | +0.12 | |
| Latin America & Caribbean | 29 | -0.11 | |
| Middle East, North Africa, Afghanistan & Pakistan | 20 | +0.22 | |
| Sub-Saharan Africa | 45 | -0.11 |
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 | 57 | -0.11 | |
| Middle third | 56 | -0.13 | |
| Richest third | 57 | +0.04 |
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 | +0.31 | |
| Muslims | 46 | +0.26 |
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 | 25 | -0.40 | |
| Never a European colony | 20 | +0.16 | |
| Spain | 19 | -0.27 | |
| United Kingdom | 50 | +0.07 |
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 | 25 | +0.15 | |
| No strong official ideology | 109 | +0.29 |
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 | 25 | -0.07 | |
| No parties banned | 115 | +0.32 |
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 = +0.251 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 28years. 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 = -0.010, 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 capital per worker moved did not tend to see their regulatory quality move with it.
Across countries (adjusted)+0.225for comparison
Within countries+0.080each country vs itself
…and vs the same year elsewhere-0.010q = 0.915 · 174 countries
Year-on-year changes+0.003q = 0.928
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.
4,313 country-years (one country in one year), 174 countries, 1996–2023, about 25 years each on average. Share of the variation that happens within countries over time: 16% for Capital per worker, 6% for Regulatory quality. 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): -0.010. 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
2021 international $ per worker | index (approx. -2.5 to 2.5) | Years | |
|---|---|---|---|
| Brunei Darussalam BRN | $1,365,080 | 0.963 | 2023, 2025 |
| United Arab Emirates ARE | $960,197 | 1.17 | 2023, 2025 |
| Qatar QAT | $955,762 | 0.998 | 2023, 2025 |
| Ireland IRL | $916,129 | 1.62 | 2023, 2025 |
| Belgium BEL | $788,016 | 1.21 | 2023, 2025 |
| Italy ITA | $772,186 | 0.598 | 2023, 2025 |
| Norway NOR | $771,357 | 1.59 | 2023, 2025 |
| Switzerland CHE | $713,606 | 1.68 | 2023, 2025 |
| France FRA | $697,343 | 0.989 | 2023, 2025 |
| Austria AUT | $691,757 | 1.07 | 2023, 2025 |
| Hong Kong SAR, China HKG | $667,472 | 1.62 | 2023, 2025 |
| Finland FIN | $666,233 | 1.63 | 2023, 2025 |
| Iceland ISL | $663,692 | 1.07 | 2023, 2025 |
| Singapore SGP | $659,201 | 2.11 | 2023, 2025 |
| Bahrain BHR | $656,018 | 1 | 2023, 2025 |
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.
Kaufmann, D. and A. Kraay, Worldwide Governance Indicators, World Bank
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.
How this was computed
Data used: most recent value in 2010-2025; values come from 2023–2025. 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 Regulatory quality
This page shows that two measures go together. It does not show that Capital per worker changes Regulatory quality, or the reverse. These figures also describe countries, not individual people. See the ecological fallacy.
More links with Capital per worker or Regulatory quality
- Liberal democracy vs Regulatory quality before +0.68 → after adjusting +0.51
- Regulatory quality vs Women's political empowerment before +0.62 → after adjusting +0.49
- Civil liberties (FH) vs Regulatory quality before -0.62 → after adjusting -0.46
- Participatory democracy vs Regulatory quality before +0.62 → after adjusting +0.45
- Electoral democracy vs Regulatory quality before +0.61 → after adjusting +0.44
- Age at childbearing vs Capital per worker before +0.63 → after adjusting +0.43
- Political rights (FH) vs Regulatory quality before -0.59 → after adjusting -0.43
- Price level vs Regulatory quality before +0.70 → after adjusting +0.39