# Understanding minimums in the calculation of Human Development Index

In the calculation of HDI, three indices are involved. One of them is the GNI index. In calculating this index, there's some scaling done. Quoting from the UNDP Technical notes

The low minimum value for gross national income (GNI) per capita, $100, is justified by the considerable amount of unmeasured subsistence and nonmarket production in economies close to the minimum, which is not captured in the official data. I don't understand what this justification means. Isn't \$100 too low? The index goes on to put an upper cap at $75000 which makes sense - because beyond that income there's not much impact on the standard of living. The calculation of this index is fairly straightforward:$Dimension\ index = \frac{actual\ value – minimum\ value}{maximum\ value – minimum\ value}$• sorry for the wrong tag. I couldn't find an appropriate tag and can't create a new tag.. – yathish Sep 27 '17 at 17:35 • Would it make sense to change the title to "Understanding minimums in the calculation of Human Development Index"? – JoaoBotelho Sep 29 '17 at 14:11 • @JoaoBotelho thanks for the suggestion. Updated. – yathish Sep 29 '17 at 15:06 ## 2 Answers This means that if a country would have most of its population living out of subsistence farming, which in practice could be registered as zero income, this would lead to an estimated/assumed GNIpc equivalent to \$100 per year per capita, which no country would ever go below. Having this value makes sense when reading the starting notes of that section:

Minimum and maximum values (goalposts) are set in order to transform the indicators expressed in different units into indices on a scale of 0 to 1. These goalposts act as the “natural zeros” and “aspirational targets” (...)

Said in other words, having this minimum means that \$100 would be the GNI per capita that would provide the lowest or minimum standard of living possible. Answering to the "isn't \$100 too low":

For income, it is set at \$100 per capita GNI, which is lower than the lowest value attained by any country in recent history (Zimbabwe in 2008). Should any country’s per capita GNI fall close to or below$100, the minimum will be changed accordingly.

I can recommend to read the source from UNDP, gives interesting inputs on the other dimensions too.

There are mathematical reasons to chose a low minimum

It is also convenient to choose minimums that make the dimensions non-zero, or not too close to zero even for countries which would score close to the minimum. Since the HDI is all about the combination of several aspects, and the formula is:

$HDI = (I_{health} \cdot I_{education} \cdot I_{income})^\frac13$

If any country would score a zero in any dimension this would dominate the whole HDI (make it zero), which defeats the purpose of the index. The index aims at acknowledging average human development balancing the three aspects.

• Isn't it far more sensible to set the minimum as $280 based on the minimum observed in actual data rather than bring in the arbitrary$100? Doing so would intrinsically compensate for some income that gets missed out. I still find it confusing.. Because I'm thinking of how these minimums were chosen for health and education indices (which are rational). – yathish Sep 29 '17 at 15:18
• Side comment: you can write a \ (bash) before the dollar sign to avoid getting your text changed to Mat text ;) – JoaoBotelho Sep 29 '17 at 15:29
• I'm familiar with LaTeX. Didn't use bash because it shows $sign just fine without bash (on android phone) – yathish Sep 29 '17 at 15:36 • It's hard to say what is the source/idea they chose for the minimum, they don't mention anything. My guess is that they've done it in the early 2000's, when Burundi had a GNIpc of \$140and chose \$100 as an indicative value for the minimum, close to the lowest GNIpc available, and haven't changed it since. – JoaoBotelho Sep 29 '17 at 15:38 • No country would actually go below the minimum \$100, something that is intended and common to other indicators like the life expectancy (minimum is 20, lowest country in the world is Sierra Leone at 50). I am adding some extra mathematical reasons to my answer above in a second. – JoaoBotelho Sep 29 '17 at 15:51

If anything the $100 is too high. There are many people in rural communities within which they earn 0 income given the fact that they are subsistence farmers and don't hold a job. The $100 per year minimum is to state that it is impossible for anybody to subsist on 0 per day and that if someone in official statistics is recorded with an income of 0 per day then in all likelihood there is unrecorded income from subsistence farming and non-market activity.

The $100 a year salary isn't all that unreasonable considering the kind of poverty many people live in. Nearly 1.1 Billion people live in absolute poverty (Income <$1.90 / day) which annualized is a salary of $700. It's quite reasonable to assume that some large percentage of those individuals make less than that which means there are millions who live on less than $.3 per day which the $100 annual income would imply. • I'm confused. In the health index, the minimum is 20 years. This is to scale that every person should have a minimum life expectancy of 20 years. Any additional life expectancy (beyond 20 years) is accounted for, in the health index. Similarly, here$100 minimum would mean a person needs a bare minimum of $100 for living. But how can an individual live with$100 a year? – yathish Sep 27 '17 at 19:29
• There are some very poor individuals in the world. 1.1 billion live on less than $365 per year. It's not a stretch to think that some people live on less than 100. – TheSaint321 Sep 27 '17 at 20:06 • I wouldn't say that \$100 is necessarily too high. When you live out of your own subsistence farming, if you would sell all your yearly production in the market, would this give you less than \\$100 per year? The fact that you do not earn any income and live almost outside of the market doesn't mean that your production is zero. – JoaoBotelho Sep 28 '17 at 2:03
• Even if we ignore simply poor people a rich person with a lot of wealth who chooses not to work has an annual income of 0. Income is not a measure of consumption. Income is a measure of the economic value of what your produce annually. It is assumed in economics that even when income = 0 consumption != 0. – TheSaint321 Sep 28 '17 at 19:01
• Yes, we're clear on consumption =! income. But would you say that income must always come from a transaction? I was suggesting that when you are a subsistence farmer you have an income from the land that you farm, even if no money is ever exchanged. – JoaoBotelho Sep 29 '17 at 13:23