Capital per worker vs. Public social spending
Fades after adjusting for income
Across 42 countries, Capital per worker and Public social spending rise and fall together at r = +0.56 (on a scale from −1 to +1, where 0 means no link). Comparing only countries with similar income (GDP per person) shrinks it to +0.35, which could easily be chance (q = 0.15, 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.
Comparing countries across the middle half of public social spending, 17% to 24.5% of GDP, capital per worker is $140,833 higher at the top of that range than the bottom. Comparing only countries with similar national income, the gap is $59,824.
Link before adjusting (r)+0.558p = 0.000 · 42 countries
After adjusting for national income+0.346p = 0.027 · likely range [+0.04, +0.59]
p, allowing for regions0.027standard error 0.101 · 5 regions
Check for luck (q)0.149across 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
Public social spending · % of GDPlink with income +0.44 · moderate
“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 | +0.558 | 0.000 | 42 |
| By rank (Spearman), not adjusted | +0.545 | 0.000 | 42 |
| Standard (Pearson), adjusted for national income | +0.346 | 0.027 | 42 |
| By rank (Spearman), adjusted for national income | +0.358 | 0.022 | 42 |
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 42 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: +0.212 (a minus sign means it grew).
How solid is it?
Leaving out one country at a time, r ranges from +0.300 (without FRA) to +0.427 (without IRL). 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: IRL (+0.081).
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 | ||
|---|---|---|---|
| Europe & Central Asia | 30 | +0.40 |
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 | 14 | +0.42 | |
| Middle third | 14 | +0.52 | |
| Richest third | 14 | +0.06 |
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 | 35 | +0.38 |
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 | ||
|---|---|---|---|
| No strong official ideology | 37 | +0.32 |
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 | ||
|---|---|---|---|
| No parties banned | 41 | +0.33 |
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 = +0.346 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.
Loading…
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.
Within countries over time, there is no link that is clearly more than chance (r = +0.061, 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 public social spending move with it.
Across countries (adjusted)+0.346for comparison
Within countries+0.524each country vs itself
…and vs the same year elsewhere+0.061q = 0.767 · 42 countries
Year-on-year changes+0.038q = 0.367
Read with care.
- 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.
1,265 country-years (one country in one year), 42 countries, 1990–2023, about 30 years each on average. Share of the variation that happens within countries over time: 17% for Capital per worker, 48% for Public social spending. 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): +0.061. 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 | % of GDP | Years | |
|---|---|---|---|
| Ireland IRL | $916,129 | 14.4% | 2023, 2024 |
| Belgium BEL | $788,016 | 28.6% | 2023, 2024 |
| Italy ITA | $772,186 | 27.6% | 2023, 2024 |
| Norway NOR | $771,357 | 24.1% | 2023, 2024 |
| Switzerland CHE | $713,606 | 16% | 2023, 2024 |
| France FRA | $697,343 | 30.6% | 2023, 2024 |
| Austria AUT | $691,757 | 31.6% | 2023, 2024 |
| Finland FIN | $666,233 | 31.4% | 2023, 2024 |
| Iceland ISL | $663,692 | 19.2% | 2023, 2024 |
| Spain ESP | $645,774 | 25.9% | 2023, 2024 |
| Luxembourg LUX | $630,742 | 24% | 2023, 2024 |
| Denmark DNK | $624,134 | 26.4% | 2023, 2024 |
| Australia AUS | $588,436 | 17.1% | 2023, 2022 |
| Sweden SWE | $568,885 | 26.1% | 2023, 2024 |
| Latvia LVA | $567,433 | 19.7% | 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.
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
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.
Public social spending
Public social expenditure
OECD · via Our World in Data · CC BY 4.0 (OECD terms and conditions) · updated annual, except the snapshots noted per indicator · comparable from 1980 only
All public social spending, as a share of GDP: pensions, health, family, unemployment, housing and the rest. The figures before 1980 are stitched together from older OECD tables and from Lindert's historical estimates, so they are left out. The OECD's social spending database (SOCX) itself starts in 1980. The four spending areas below are parts of this total and are flagged as such.
How this was computed
Data used: most recent value in 2010-2025; values come from 2021–2024. 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 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 Capital per worker and Public social spending
This page shows that two measures go together. It does not show that Capital per worker changes Public social spending, or the reverse. These figures also describe countries, not individual people. See the ecological fallacy.
More links with Capital per worker or Public social spending
- Public social spending vs Redistribution before +0.73 → after adjusting +0.69
- Median age vs Public social spending before +0.65 → after adjusting +0.59
- Public social spending vs Under-5 mortality before -0.65 → after adjusting -0.52
- Infant mortality vs Public social spending before -0.65 → after adjusting -0.52
- Public social spending vs Slum share of urban population before -0.63 → after adjusting -0.50
- Population 0-14 vs Public social spending before -0.56 → after adjusting -0.48
- Family benefits spending vs Public social spending before +0.53 → after adjusting +0.44
- Age at childbearing vs Capital per worker before +0.63 → after adjusting +0.43