Do Inequality-adjusted HDI and Productivity (TFP) go together across countries?

Across 112 countries the link before adjusting for anything is r = +0.70, on a scale from -1 (opposite) to +1 (in step). A version that uses only each country's rank gives +0.74.

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

Comparing each country only with itself across 2010-2023, and setting aside what happened worldwide in each year, the link is +0.159 (112 countries, 1,494 country-years). Using year-to-year changes, it is +0.079.

Does Inequality-adjusted HDI cause Productivity (TFP)?

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.

Inequality-adjusted HDI vs. Productivity (TFP)

Fades after adjusting for income

Across 112 countries, Inequality-adjusted HDI and Productivity (TFP) rise and fall together at r = +0.70 (on a scale from −1 to +1, where 0 means no link). Comparing only countries with similar income (GDP per person) shrinks it to -0.21, which could easily be chance (q = 0.24, 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. Productivity (TFP) and Inequality-adjusted HDI share a building block (undp mys), so part of this link is mechanical: they are bound to match to some degree.

Comparing countries across the middle half of productivity (TFP), 0.463 to 0.81 ratio to the US, inequality-adjusted HDI is better by 0.208 points at the top of that range than the bottom. Comparing only countries with similar national income, the gap reverses, to 0.0324 points the other way.

Link before adjusting (r)+0.701p = 7.3e-18 · 112 countries

After adjusting for national income-0.207p = 0.030 · likely range [-0.38, -0.02]

p, allowing for regions0.078standard error 0.097 · 7 regions

Check for luck (q)0.236across 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.

Inequality-adjusted HDI · index, 0 to 1link with income +0.94 · proxy

Productivity (TFP) · ratio to the US (US = 1)link with income +0.79 · 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.

Built from the same numbers. Productivity (TFP) and Inequality-adjusted HDI share a building block (undp mys), so part of this link is mechanical: they are bound to match to some degree.

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	+0.701	7.3e-18	112
By rank (Spearman), not adjusted	+0.735	2.7e-20	112
Standard (Pearson), adjusted for national income	-0.207	0.030	112
By rank (Spearman), adjusted for national income	-0.207	0.029	112

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 112 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: +0.495 (a minus sign means it grew).

How solid is it?

Leaving out one country at a time, r ranges from -0.242 (without NGA) to -0.176 (without SWZ). 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: NGA (-0.036).

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	14	+0.34
Europe & Central Asia	40	-0.13
Latin America & Caribbean	19	+0.14
Sub-Saharan Africa	27	+0.13

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	38	-0.43
Middle third	37	-0.27
Richest third	37	+0.30

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	75	-0.19
Muslims	21	-0.32

By last European coloniser

	n	r
France	12	-0.36
Spain	18	-0.04
United Kingdom	29	-0.00

By official ideology

	n	r
Nationalist	14	-0.41
No strong official ideology	81	-0.18

By party system

	n	r
A few parties banned	15	-0.67
No parties banned	90	-0.09

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 = -0.207 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 14years. 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 = +0.159, 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 inequality-adjusted HDI moved did not tend to see their productivity (TFP) move with it.

Across countries (adjusted)-0.207for comparison

Within countries+0.013each country vs itself

…and vs the same year elsewhere+0.159q = 0.199 · 112 countries

Year-on-year changes+0.079q = 0.035

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.

1,494 country-years (one country in one year), 112 countries, 2010–2023, about 13 years each on average. Share of the variation that happens within countries over time: 7% for Inequality-adjusted HDI, 1% for Productivity (TFP). 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): +0.159. 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 largest value on this curve (+0.24 at lag -4) is higher than the same-year one by 0.08. That gap is not a finding. It is the largest of 20 closely related estimates, and picking the biggest of many tests always makes it look bigger. That is exactly why nothing on this site is ranked or chosen by lag.

The data

	index, 0 to 1	ratio to the US (US = 1)	Years
Iceland ISL	0.923	0.908	2023
Norway NOR	0.909	1.08	2023
Denmark DNK	0.909	0.929	2023
Switzerland CHE	0.894	0.985	2023
Netherlands NLD	0.892	0.987	2023
Finland FIN	0.891	0.772	2023
Belgium BEL	0.891	0.916	2023
Germany DEU	0.89	1.02	2023
Sweden SWE	0.886	0.876	2023
Ireland IRL	0.886	1.04	2023
Slovenia SVN	0.885	0.665	2023
Australia AUS	0.873	0.847	2023
United Kingdom GBR	0.869	0.834	2023
Czechia CZE	0.867	0.617	2023
Canada CAN	0.867	0.809	2023

United Nations Development Programme, Human Development Report 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.

Sources

Inequality-adjusted HDI

Inequality-adjusted Human Development Index

United Nations Development Programme, Human Development Report Office · via Our World in Data · CC BY 3.0 IGO · updated annual · comparable from 2010 only

The HDI marked down for how unequally each of its three parts is spread within the country. The gap between this and the HDI is what inequality costs, and that is the number worth reading. The level itself is the HDI again, with its parts flagged the same way.

Productivity (TFP)

Total factor productivity level, compared with the US (Penn World Table)

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

Total factor productivity (TFP) is how much a country produces compared with what its workers, their schooling, and its machines and buildings would be expected to produce. It is the part of GDP that those inputs do not account for, such as better technology or better organisation. The US is set to 1 in every year, so 0.5 means a country gets about half as much output from the same inputs as the US. It is worked out from GDP, capital, the number of workers, their schooling and the labor share, so it is linked to each of them by arithmetic. It is left out of the economy score: being built from GDP, it would turn that score back into GDP per person.

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 Inequality-adjusted HDI and Productivity (TFP)

This page shows that two measures go together. It does not show that Inequality-adjusted HDI changes Productivity (TFP), or the reverse. These figures also describe countries, not individual people. See the ecological fallacy.