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How UN manipulates the Gender Development Index

I think that UN manipulating it's own index is not culture wars even if the index is related to gender. Let me know if I am wrong.

Human development

The Gender Development Index (GDI), along with its more famous sibling Human Development Index (HDI) is a an index published annually by UN's agency, the United Nations Development Programme (UNDP). Whether an index is manipulated or not can be judged only against a precise definition of what the index claims to be measuring. So how do you measure human development? Whatever you do, you will never capture all nuances of the real world - you will have to simplify. The UNDP puts it this way:

The Human Development Index (HDI) was created to emphasize that people and their capabilities should be the ultimate criteria for assessing the development of a country, not economic growth alone.

So the UNDP defines the Human Development Index as a geometric mean of three dimensions represented by four indices:

Dimension Index
Long and healthy life Life expectancy at birth (years)
Knowledge Expected years of schooling (years)
Mean years of schooling (years)
Decent standard of living Gross National Income (GNI) per capita (2017 PPP$)

Source: https://hdr.undp.org/data-center/human-development-index#/indicies/HDI

Gender Development

So far so good. Next, on it's website the Gender Development Index (GDI) is defined like this:

GDI measures gender inequalities in achievement in three basic dimensions of human development: health, measured by female and male life expectancy at birth; education, measured by female and male expected years of schooling for children and female and male mean years of schooling for adults ages 25 years and older; and command over economic resources, measured by female and male estimated earned income.

Source: https://hdr.undp.org/gender-development-index#/indicies/GDI

While in the actual report HDI it is simply defined as a ratio of female to male HDI values:

Definitions - Gender Development Index: Ratio of female to male HDI values.

Source: https://hdr.undp.org/system/files/documents/global-report-document/hdr2021-22pdf_1.pdf

Let's look, for instance, at the Gender Development Index of United Kingdom. The value 0.987 means that despite longer life and more education, in UK, females are less developed than males.

Dimension Index Female value Male value
Long and healthy life Life expectancy at birth (years) 82.2 78.7
Knowledge Expected years of schooling (years) 17.8 16.8
Mean years of schooling (years) 13.4 13.4
Decent standard of living Gross National Income (GNI) per capita (2017 PPP$) 37,374 53,265

Source: https://hdr.undp.org/system/files/documents/global-report-document/hdr2021-22pdf_1.pdf

Wait, what?? What does it mean that females in UK have command over economic resources of post Soviet Estonia (GNI Estonia=38,048) while males in UK have command over economic resources of EU leader Germany (GNI Germany=54,534)?

The manipulation

The UNDP calculates separate command over economic resources for females and males, as a product of the actual Gross National Income (GNI) and two indices: female and male shares of the economically active population (the non-adjusted employment gap) and the ratio of the female to male wage in all sectors (the non-adjusted wage gap).

The UNDP provides this simple example about Mauritania:

Gross National Income per capita of Mauritania (2017 PPP $) = 5,075

Indicator Female value Male value
Wage ratio (female/male) 0.8 0.8
Share of economically active population 0.307 0.693
Share of population 0.51016 0.48984
Gross national income per capita (2017 PPP $) 2,604 7,650

According to this index, males in Mauritania enjoy the command over economic resources of Viet Nam (GNI Viet Nam=7,867) while females in Mauritania suffer the command over economic resources of Haiti (GNI Haiti=2,847).

Let's be honest here: this is total bullshit. There are two reasons why you cannot use raw employment gap and raw wage gap for calculating the command over economic resources:

Argument 1

Bread winners share income with their families. This is a no brainer. All over the world, men are expected to fulfil their gender role as a bread winer. This does not mean that they keep the pay check for themselves while their wives and children starve to death. Imagine this scenario: a poor father from India travels to Qatar where he labours in deadly conditions, so that his family can live a slightly better life. According to UNDP, he just became more developed, while the standard of living his wife is exactly zero.

Argument 2

Governments redistribute wealth. This is a no brainer too. One's command over economic resources and standard of living is not equal to ones pay check. There are social programs, pensions, public infrastructure. Even if you have never earned a pay check yourself, you can take a public transport on a public road to the next public hospital. Judging by the Tax Freedom Day, states around the world redistribute 30% to 50% of all income. And while men pay most of the taxis (obviously, they have higher wages) women receive most of the subsidies (obviously, they have lover wages). But according the UNDP, women in India (female GNI 2,277) suffer in schools and hospitals of the war-torn Rwanda, while men in India (male GNI 10,633) enjoy the infrastructure and social security of the 5-times more prosperous Turkey.

Don't get me wrong, the employment gap and pay gap are not irrelevant for the standard of living and command over economic resources. Pensions and social security schemes mostly do not respect the shared family income and as a result the partner doing less paid work - usually a women - gets lower pension, unemployment benefit etc. What's worse, the non-working partner is severely disadvantaged in case of divorce or break up. But while this has an impact on each gender's standard of living it certainly does not define 100% of that value.

Argument 3

You may argue that the command over economic resources measured by estimated earned income is some kind of proxy for all other disadvantages women face in society. But do you remember what I said in the beginning?

Whether an index is manipulated or not can be judged only against a precise definition of what the index claims to be measuring.

The HDI measures "people and their capabilities" and the GDI is a ratio of these capabilities measured separately for men and women. The economic dimension of the GDI is supposed to be standard of living or command over economic resources - neither of which can be represented by earned income alone.

The taboo

Wikipedia says: "For most countries, the earned-income gap accounts for more than 90% of the gender penalty." (I have not verified this.) This is important, because when we look at the other two dimensions it becomes clear that while men have shorter and less health lives they also increasingly fall behind in mean and expected years of schooling. Without the misrepresentation of the command over economic resources value, the index would show something very uncomfortable: that according to UN's own definition of Human Development men are the less developed gender.


PS: Is there a way to give those tables some borders and padding?
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I think the answer is ‘maybe, maybe not, but he can almost certainly get away with it for a while and it’s cold comfort to an Indian housewife who has to send her children to the sweatshops because of her husband’s gambling addiction that she’ll eventually start getting some portion of his checks’.

Sure, he can maybe get away with it for a while, but the point is that the standard assumes he can get away with it forever. In reality women truly do have practical, legal power over their husbands' salaries.

the standard assumes he can get away with it forever.

This is little more than a suggestion that the index would be more accurate if it discounted a woman's earned income somewhat in order to account for the possibility that a woman with no earned income might recover from her husband. A fine suggestion, but the index's failure to do (assuming it indeed fails to do so) hardly delegitimizes the entire endeavor.

This is little more than a suggestion that the index would be more accurate if it discounted a woman's earned income somewhat in order to account for the possibility that a woman with no earned income might recover from her husband.

You keep talking about how any problems with the index are just inaccuracies. I wonder if you'd accept that excuse for something on the other political side. "Yes, we're exaggerating the number of third trimester abortions, but that's just inaccurate". This kind of inaccuracy is deceptive. It's not excusable just because it's an inaccuracy that doesn't call the whole thing into question--at some point, inaccuracy does call the whole thing into question.

  1. I don't know why you think there are "sides" on this particular issue. But this is pretty rich, since it sure seems that most of the objections seem to be that commenters fear that it says something that commenters don't want to hear.
  2. The problem with your analogy to abortion numbers is that false numbers are just that: false. And true numbers are true. In contrast, as I have repeatedly noted, an index like this one is inherently less than perfectly accurate, And, an index, unlike an abortion statistic, can not be said to be either "false" or "true." So, it is not enough to say, as people have, that it is not perfectly accurate. It might be so inaccurate that is "call[s] the whole thing in question," but neither you nor I nor anyone else here has any idea how "inaccurate" it is (ie, the degree to which it does not reflect what is actually happening on the ground). None of us even knows the precise methodology used. The only one who has posted any description of the methodology is yours truly.

Again, the original claim was that the index is invalid simply because it is not perfect. That is a claim a failure to understand the nature of that which is being critiqued.

The claim is that the UN agency drawing up this index had already written the bottom line of "we don't want to say that Western countries are currently biased in favour of women", due to feminism, and chose what to correct and not correct (note the "women should live 5 years longer than men" thing mentioned above) such that all classic Western countries would come out below 1 (I checked; there are some classic Western countries extremely close to 1 but none above it).

"This agency is running a bottom-line-first algorithm" is a significantly-more-damning criticism than "this agency's index is not perfect". Ignoring a propagandist's numbers is not the ideal strategy, but it does better than taking them at face value (the ideal strategy is to pull apart how their numbers were derived, and derive better ones, but that's significantly harder). And if the agency is ideologically captured, it is not likely to improve its index in the future on metrics relevant to the bottom line, at least absent some effort to change its institutional incentives.

chose what to correct and not correct (note the "women should live 5 years longer than men" thing mentioned above) such that all classic Western countries would come out below 1 (I checked; there are some classic Western countries extremely close to 1 but none above it)

When you calculate the GDI using "equal lifespans is gender parity" instead of "women having 5 years longer lifespan is gender parity", I can confirm that a supermajority of countries listed as "very high human development" end up above 1 (i.e. women are favored), with the gaps comparable to the male-favorable ones in the current index.

Thanks for running the numbers; I was too lazy to do it myself.

Yes, but the problem is that that is all it is: A claim, with no evidence.

And, it is hardly surprising that few countries are above 1. In how many countries does the average female income exceed that of men? (Note that that is an empirical question, not a normative one, and not a commentary on the causes of any differences).

All you do here is start with a vague premise "Western countries are currently biased in favour of women", then simply assume that every data point that you incorrectly believe* seems to refute that assumption must have been manipulated.

*The GDI is not a measure of bias, and it does not measure 90% of the types of things that make up the pro-female bias that is commonly complained of.

you

Explaining a position is not the same as taking it*. In this particular case I'm not entirely convinced. Conspiracy to keep the Western numbers below 1 doesn't make a lot of sense since the numbers being barely below 1 is now but the metric hasn't AIUI been revised in decades (and indeed it's been partially superseded by the Gender Inequality Index). Also, the UN isn't fully a Western organisation, and non-Western countries would object to explicit fiddling to make women look worse off than they are. Don't get me wrong, the "women ought to live 5 years longer than men" thing does strike me as a bit of a double standard, but you don't need to be an explicit conspirator to run a double standard; you just need to have a mindset where it seems normal.

*Fine, whatever, I feel like kind of a prick now for not explicitly signposting this even though I didn't actually intend it as bait and it's not like I actually lied.

"women ought to live 5 years longer than men" thing does strike me as a bit of a double standard,

Well, it does seem that woman naturally live a big longer than men, all else being equal. Certainly life expectancy at birth tends to be lower for men, in part because of a greater propensity for risk-taking among young men and resulting higher rate of accidental death, and in part because of that pesky exposure to added risk from recessive genes because of the whole Y chromosome thing.

So, if you are looking at a country and trying to assess the effects of policy/society/culture/whatever, on life expectancy by gender, of course you are going to control for the natural tendency of women to live longer.

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The index's problems make it seriously misleading for its intended purpose.

You're trying to understate this.

Neither you nor I have any idea of the extent of its problems; I also suspect that you do not know what its intended purpose is.

I think the index is broadly designed to advance certain goals, in particular goals to get women out of childrearing and into the workplace, at the expense of women. Rather than actually measure women's wellbeing, they choose to lump very ideological and unnatural goals such as "women should be in the workplace just as much as men, despite their different inclinations and reproductive schedules" in with much more broadly agreed-upon measures such as life expectancy. Obviously a difference in life expectancy should matter way more than how many women choose to enter the workforce, but the measure puts them on the same level.

One way to attack such behavior without being dismissed as a partisan crank is to highlight the differences between the activist organization's claimed goals and their actions. Things like power over household finances, likelihood of getting abused, and ability to survive/feed children after a divorce are far better indications of women's wellbeing, and men's societal treatment towards them, than any gender pay gap could be, since the latter is caused mainly by women's choices.

I grew up in a very conservative subculture. My sisters and female friends were still very embarrassed to admit they wanted to be stay at home mothers. Even in our subculture, women are heavily pressured to enter the workforce, so I'd argue that in some cases a narrowing gender pay gap is actually indicative of rising misogyny, at least if you define "pressuring women into making decisions they don't want to make" as misogyny.

It’s the UN. Decreasing fertility and economic growth through getting women into the workplace are explicit goals.

But I don’t see how that delegitimizes the whole index- it’s a measure and like all measures is somewhat imperfect. That the imperfections are there because of biases in the people that developed it is ultimately irrelevant; it’s the kind of measure that’s going to have a bias built in.

That the imperfections are there because of biases in the people that developed it is ultimately irrelevant; it’s the kind of measure that’s going to have a bias built in.

Agreed with the first half, though that's pretty much a non-sequitur because I never said its creators' biases were relevant anyways. The only thing that matters is the bias of the measure itself. Sure, maybe some kinds of measures have biases built in, but the extent to which they're biased still varies and matters quite a bit. You can't just lump all measures into either the "biased" category or the "unbiased" category.

Your first sentence:

But I don’t see how that delegitimizes the whole index- it’s a measure and like all measures is somewhat imperfect.

Makes me think you're trying to reduce this down to just the two categories, "perfect" and "imperfect", or that you think I'm trying to do so. I'm not and never said anything of the sort. I am arguing that this measure is more imperfect than most people think, and that attitudes towards it should be updated accordingly.

Obviously a difference in life expectancy should matter way more than how many women choose to enter the workforce, but the measure puts them on the same level

Why is it so obvious? To take an extreme example, the life expectancy of slaves in the US was probably higher than that of free whites in the Caribbean during the same time period, but I dare say that few would argue that slaves were better off. It certainly isn't obvious that they were. Re women, one can certainly argue, "your life sucks, but at least you live a long time," but it does not seem to me to be obvious that everyone must agree.

Things like power over household finances, likelihood of getting abused, and ability to survive/feed children after a divorce are far better indications

  1. That might be true, but you are ignoring an important factor: It is difficult, if not impossible to quantify and accurately measure those things, especially across all the countries of the world. A metric that cannot be measured is less than useless.

  2. The ability survive/feed children after a divorce is almost certainly one of the things that the earned income measurement is meant to proxy for, so this seems to be an argument in favor of the index.

Obviously a difference in life expectancy should matter way more than how many women choose to enter the workforce, but the measure puts them on the same level

Why is it so obvious? To take an extreme example, the life expectancy of slaves in the US was probably higher than that of free whites in the Caribbean during the same time period

I very much doubt slaves lived longer than free whites in the Caribbean. Regardless, though, I didn't even mention income, which your example implicitly compares. What I mentioned was workforce participation. If women were paid 50% of what men were paid for the same jobs, that would be an enormous problem. If women choose to participate in the workplace at 50% of the rate that men do, that's hardly a problem at all, but it's considered equivalent by the GDI.

Re women, one can certainly argue, "your life sucks, but at least you live a long time," but it does not seem to me to be obvious that everyone must agree.

Sure, one can argue that, but not me. That's nothing at all like what I'm arguing. It conflates happiness with income. What I'm arguing is more like "You earn only 99% of what men earn, but at least you live six years longer. I'd trade 1% of my income for an extra 6 years of life, wouldn't you?

That might be true, but you are ignoring an important factor: It is difficult, if not impossible to quantify and accurately measure those things, especially across all the countries of the world. A metric that cannot be measured is less than useless.

The ability survive/feed children after a divorce is almost certainly one of the things that the earned income measurement is meant to proxy for, so this seems to be an argument in favor of the index.

The first two things are already measured across all countries. The third isn't really an objective measurement per se, but there are much better proxies available (I mean come on, just measure income post-divorce) than female earned income.

Workforce participation is a bad measure. The only reason to use it, rather than something better like "average wage of full-time workers", is if you are implicitly privileging the conclusion that men and women are identical, and women entering the workforce at greater rates is just as important as women living longer. Should a woman choose to stay out of the workforce and raise children instead, that's implicitly treated the same on the GDI as if she died at 25 while her male counterpart lived to 80.

I very much doubt slaves lived longer than free whites in the Caribbean.

I think you are underestimating how low life expectancy was in the Caribbean at the time

What I mentioned was workforce participation. If women were paid 50% of what men were paid for the same jobs, that would be an enormous problem. If women choose to participate in the workplace at 50% of the rate that men do, that's hardly a problem at all, but it's considered equivalent by the GDI.

That is an entirely different point than the one I was responding to, which was that life expectancy is obviously more important than the other metrics in the index.

If women were paid 50% of what men were paid for the same jobs, that would be an enormous problem. If women choose to participate in the workplace at 50% of the rate that men do, that's hardly a problem at all,

Why, if the issue is the degree to which women have income independent of the man in their life?

Sure, one can argue that, but not me. That's nothing at all like what I'm arguing. It conflates happiness with income. What I'm arguing is more like "You earn only 99% of what men earn, but at least you live six years longer. I'd trade 1% of my income for an extra 6 years of life, wouldn't you?

That is precisely my point: Life expectancy is NOT obviously more important, among other things because it depends on the relative levels of the various factors.

The first two things are already measured across all countries.

I notice that you seem to assume that we are talking about first-world countries. We are not. Do you think that "power over household finances" and "likelihood of getting abused" are measured in Burundi? In Myanmar? In Sri Lanka? I sincerely doubt that there is data on either of those in more than 20 countries in the world. Especially since "power" of any kind is difficult to measure objectively.

I mean come on, just measure income post-divorce.

Again, how many countries measure that? How many have an incentive to measure it accurately? Not to mention that is ignores post-separation/abandonment/death income. Compare that with income per se, which all countries with an income tax have an incentive to measure. Which measure is more likely to be complete and accurate? Note that Wikipedia has data on divorce rates for only 105 countries and this UN document on divorce includes almost no African countries. And please don't argue that the UN data is from 10 years ago; a metric that only has recent accurate data is of limited utility, because knowing about change over time is important.

Workforce participation is a bad measure. The only reason to use it, rather than something better like "average wage of full-time workers", is if you are implicitly privileging the conclusion that men and women are identical, and women entering the workforce at greater rates is just as important as women living longer.

But, the GDI does not include a measure of workplace participation. It includes a measure of earned income.

And as for "and women entering the workforce at greater rates is just as important as women living longer," so what? I understand that you, personally, value longer life differently than they do (or, more accurately, than how you understand them to value them), but that does not, in itself, make their measure illegitimate or fraudulent. They are just measuring different things.

I think you are underestimating how low life expectancy was in the Caribbean at the time

Put up some numbers then. When I looked it up slaves had a life expectancy of 22 years. I couldn't find statistics for the Caribbean but I doubt for free white people it was lower than that.

Obviously a difference in life expectancy should matter way more than how many women choose to enter the workforce, but the measure puts them on the same level.

What I mentioned was workforce participation. If women were paid 50% of what men were paid for the same jobs, that would be an enormous problem. If women choose to participate in the workplace at 50% of the rate that men do, that's hardly a problem at all, but it's considered equivalent by the GDI.

That is an entirely different point than the one I was responding to, which was that life expectancy is obviously more important than the other metrics in the index.

If you read what I said, my point was much more about how unimportant workforce participation is. The only time life expectancy was brought up was in comparison to workforce participation.

That is precisely my point: Life expectancy is NOT obviously more important, among other things because it depends on the relative levels of the various factors.

This is literally how prioritization in general works. I believe life expectancy is more important than money, in general, given reasonable amounts of each. Saying "health is more important than money" is a perfectly reasonable statement. At the same time, I would gladly take a billion dollars over a year of life. Does this prove I was lying or mistaken? No, it's just that the statement "health is more important than money" does not necessarily imply "health is infinitely more important than money." What I have consistently argued is that wage should not be weighted the same as the other measurements. It perhaps deserves a place in the index, but should be deweighted so that differences in education and life expectancy matter more. This means it takes a very large difference in average income to overcome a difference in life expectancy, and is the common-sense interpretation of what I have been saying.

If women were paid 50% of what men were paid for the same jobs, that would be an enormous problem. If women choose to participate in the workplace at 50% of the rate that men do, that's hardly a problem at all,

Why, if the issue is the degree to which women have income independent of the man in their life?

"Gender development" implies all sorts of things from gender equality to independence. If the claim was actually that the GDI measured gender independence alone, I would be fine with workforce participation being weighted as heavily as it is.

I notice that you seem to assume that we are talking about first-world countries. We are not. Do you think that "power over household finances" and "likelihood of getting abused" are measured in Burundi? In Myanmar? In Sri Lanka? I sincerely doubt that there is data on either of those in more than 20 countries in the world. Especially since "power" of any kind is difficult to measure objectively.

Yes, absolutely, I know they're measured in those countries. Here's abuse rates in Myanmar. Here's Myanmar power over household finances by gender, plus this includes another study on abuse rates. Here's abuse rates in Sri Lanka. Here's household purchasing power in Sri Lanka. A study on abuse rates in Burundi is referenced on this site though I unfortunately couldn't find the study itself online. This page includes a study on household purchasing power by gender in Burundi.

I agree "power" is hard to measure objectively, but in the end all survey results are heuristics anyways, and existing measurements do come pretty close. They are more useful and more relevant to gender development than workforce participation is, imo.

These statistics already exist because people are very interested in them, and people are very interested in them because they are good heuristics for actual gender development.

Again, how many countries measure that? How many have an incentive to measure it accurately? Not to mention that is ignores post-separation/abandonment/death income. Compare that with income per se, which all countries with an income tax have an incentive to measure. Which measure is more likely to be complete and accurate? Note that Wikipedia has data on divorce rates for only 105 countries and this UN document on divorce includes almost no African countries. And please don't argue that the UN data is from 10 years ago; a metric that only has recent accurate data is of limited utility, because knowing about change over time is important.

Alright, so post-divorce income is a bad measure, but there are still ways to improve the existing measurement. The best way IMO would be to simply discount workforce participation, and measure male vs female incomes based on the income of those who are actually working. Another way would be to weigh income as less important relative to the other two factors. Both easy ways that don't rely on some hard-to-find fourth measure, though I think I've established there are other legitimate fourth measures (with statistics available in just about every country) which could be used.

Workforce participation is a bad measure. The only reason to use it, rather than something better like "average wage of full-time workers", is if you are implicitly privileging the conclusion that men and women are identical, and women entering the workforce at greater rates is just as important as women living longer.

But, the GDI does not include a measure of workplace participation. It includes a measure of earned income.

That's the problem. Since it includes everyone in its average, including those who are not working, it is essentially a workplace participation measure pretending to be a wage gap measure. The semi-official site Human Development Reports describes this measure as "command over economic resources" which I find highly inaccurate, since many of those not working do have lots of command over economic resources.

And as for "and women entering the workforce at greater rates is just as important as women living longer," so what? I understand that you, personally, value longer life differently than they do (or, more accurately, than how you understand them to value them), but that does not, in itself, make their measure illegitimate or fraudulent. They are just measuring different things.

So it is a lie. It portrays itself as an objective measurement of gender equality, but relies on assumptions (such as the assumption that men and women should be identical) which are incorrect. Women will never enter the workforce at the same rate as men, but this doesn't mean there is gender inequality, as this measure implies. Men will never live as long as women (well, in both cases I assume no vast technological advances or societal changes that upend all of our assumptions) and that doesn't mean there's gender inequality either. They have correctly adjusted for that latter fact, but incorrectly (imo deliberately) not adjusted for the other.

Also, just to be clear once again, it's not that I care about longer life specifically, it's that I don't care about workforce participation. I care about the actual wage gap, I care about longevity, and I care about education rates by gender, just workforce participation specifically should not be put on the same pedestal as those three.

This is literally how prioritization in general works. I believe life expectancy is more important than money, . . . Does this prove I was lying or mistaken?

Dude, no one said you were lying or mistaken. The point is that you claimed that your position is obviously the correct one. It isn't, because it depends on how you value the two elements. As I said, "it does not seem to me to be obvious that everyone must agree." And as you say, "this is literally how prioritization works" -- people prioritize different things.

Yes, absolutely, I know they're measured in those countries.

But, how many countries measure all of those things, and for how long? And how accurately? The Sri Lanka study says data was first collected in 2019. And it is based on a survey, which have all sorts of inherent challenges, and are of dubious value as a cross-country metric if the same survey is not used in every country. Moreover, this World Bank report says this about its data on gender-based violence: "When a country did not have any eligible data between 2000 and 2018, their rates were estimated based on countries with similar characteristics, and these estimates were fed into the regional averages." It does not sound to me as if that data is particularly easy to obtain.

but there are still ways to improve the existing measurement.

Yes, I am sure there are. But that is not really the issue; the issue is the OP claim that the existing metric is invalid.

The best way IMO would be to simply discount workforce participation, and measure male vs female incomes based on the income of those who are actually working.

I guess I don't understand; isn't that what the current practice is? It uses data on earned income.

Since it includes everyone in its average, including those who are not working, it is essentially a workplace participation measure pretending to be a wage gap measure.

I don't see how it is "essentially a workplace participation measure." For example, it captures differences between countries where women work, but are excluded from certain occupations, and those where they are not. A pure workplace participation measure does not include that. A measure of earned income is in essence a composite of labor force participation and wages. Would it be nice to measure them separately? Yes. But, again, 1) accurate measures of wages, rather than income; might be difficult to obtain; 2) once again, the fact that the GDI is imperfect does not mean that it is useless; 3) it is perfectly possible that your suggestion was tested, and it was found that it did not materially improve the performance of the index. 4) most importantly, this indicates that the GDI might actually be doing pretty much what you suggest. It says:

Nevertheless, estimates of average male and female per capita GDP are included in the GDI. The restricted availability of sex-disaggregated income data leads the UNDP to use female and male shares of earned income to indicate gender disparities in the standard of living. The female (or male) income share is computed by multiplying the ratio of the female (male) wage to the average wage by the female (or male) share of the economically active population.7 Multiplying the HDI figure for average GDP per capita by the harmonic mean of the male and female income shares adjusts the HDI (downwards, as the male income share is largest for all countries) so that it reflects gender disparities in earned income

So it is a lie. It portrays itself as an objective measurement of gender equality, but relies on assumptions

The GDI employs objective data, but it is an index; of course it relies on certain assumptions, and makes certain decisions about what to include and how to weigh each element of the index. No one claims otherwise. That is the nature of indexes. The GDI is not even the UN's only measure of gender inequality; there is at least one other. It is AN index of gender inequality, not THE index.

Women will never enter the workforce at the same rate as men, but this doesn't mean there is gender inequality, as this measure implies.

Of course it means that there is gender inequality; there is inequality in the labor participation rate. Just as there is inequality in rates of breast cancer. What it does not necessarily mean is that there is unjust gender inequality. But, how are you going to know if a given inequality is unjust, if you don't measure it, and see if it has changed, or whether it is different in different countries. I am sure that back in the early 1960s, when the female labor participation rate was under 40%, people assumed that that was just natural and normal. But then it changed. So now we have reason to think that the rate in the early 1960s was possibly the result of unjust restrictions on women.

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