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So as we saw earlier, the first step is to see what other dimensions we want to

Â include in this index.

Â The human development index has three dimensions.

Â One is, the first one is health, the second one is education, and

Â the third one is decent life, which is going to be proxyed by income,

Â but I'll come to that later.

Â So we have three dimensions, health, education, and living conditions.

Â So the next step is what are the indicators that describe well-being or

Â that reflect well-being in these three dimensions?

Â As far as health, they have chosen one indicator, the UNDP.

Â And in fact it's an office which is called a Human Development Report Office,

Â HDRO, that publishes these indices, that publishes these index annually for

Â all countries of the world for which there is data available.

Â And in fact, every year they publish,

Â not only this index, but also other indices for different countries.

Â And they kind of, the report contains information

Â on the general information on how the world is doing in terms of well-being.

Â The different countries or the different regions of the world,

Â how are they varying in terms of well-being?

Â But also, every report concentrates or gives particular

Â attention to a particular theme, like for example, gender equality or

Â environmental sustainability or work well-being and so on.

Â So every year there is a particular focus given to a certain theme.

Â So let's come back to the index.

Â So it has three dimensions, health, education and living conditions.

Â Health, there is one single indicator which is the life expectancy at birth.

Â For education, we have two indicators, mean years of schooling and

Â expected years of schooling.

Â For the living decent life or living conditions dimension,

Â the per capita gross national income is take as relevant indicator.

Â So let's start with health.

Â Health life expectancy at birth, what is life expectancy at birth?

Â I'll just simply put, it's just simply the average number

Â of years that a child born in country is expected to live.

Â So the average number of years of life of a child at birth.

Â That's the life expectancy, so the unit of measurement is years.

Â Let's say, for example, 80 years, or 65 years, or 95 years.

Â So it's an indicator which is measured in years.

Â Then we go to education, there are two indicators for this dimension,

Â mean years of schooling and expected years of schooling.

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Here maybe it may be important to note that

Â when you have different number of indicators per dimension,

Â it is all the more important to have this multi-level or two level reasoning.

Â As to what are the dimensions which we want to include, and

Â what are the indicators.

Â If you don't have this two level reasoning,

Â you run the risk of giving undue importance to one dimension, for

Â which you may have more indicators than others.

Â So it's better to allocate the weights of cross dimensions first, and then to look

Â at indicators within a dimension and distribute the weights within a dimension.

Â So in education we have two indicators, mean years of schooling.

Â Again mean years of schooling is simply the average years of education of

Â the adult population in a country.

Â And the expected years of schooling is the average years of education that

Â a child enrolled in school is expected to have at the completion of his or

Â her education based on the current enrollment rate.

Â So based on the current enrollment rate, how many years of education

Â will a child have after completion of education, on average.

Â So that's again these two indicators are in years.

Â One can imagine that the first one, that the mean years of schooling is not, or

Â education, is not going to be moving very fast because normally,

Â the adult population in the country has already completed its education.

Â And so that's not going to be changing unless the generations get renewed.

Â So that is why they also added the other indicator, which is the expected years of

Â schooling, which will move faster because at more and more children

Â get enrolled in school that is a likely to move faster than the first one.

Â That's also these two indicators are also in years.

Â And then we have the third indicator dimension for

Â which there's one single indicator, which is the gross national income per capita.

Â And that is measured in dollars, US dollars and in PPP US dollars, that is

Â purchasing power parity US dollars, which is basically a kind of currency,

Â I mean conversion of all currencies into comparable US dollars.

Â That is in such a way that we can compare

Â the per capita income of different countries in this PPP US dollars.

Â So now we have for three dimensions and four indicators.

Â We need to combine them, for the two dimensions for

Â which there is only one indicator, there's nothing to be done.

Â But we notice that we have three indicators in terms of

Â years as unit of measurement and the last indicator which is the per

Â capita national income in terms of PPP US dollars.

Â So how do we combine something which is in years with something which is dollars?

Â So first ting we need to do is to convert them into a same

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unit of measurement so that we can combine them at a later stage.

Â So how do we do that?

Â This process is called a normalization process.

Â And the normalization that is chosen or

Â that is used in the construction of the HDI is as follows.

Â So you take for, so the index, the normalized index if you want is given by

Â the value of the indicator minus a minimum value divided by maximum minus minimum.

Â So what are these maximum and minimum values, or where are they coming from?

Â So for each indicator, we need to set minimum and a maximum.

Â So what is this minimum?

Â The minimum is that level of achievement at which or

Â below which the country is supposed to be at zero level of achievement.

Â And the maximum is that level of achievement at which, or

Â above which, the country is supposed to be at a maximum,

Â having attained the maximum level of achievement.

Â So let's take life expectancy for example.

Â The minimum and maximum have been set at 20 and 85 respectively.

Â So if a country is at level of 20 or

Â below 20, then it hasn't had any achievement in this dimension, so

Â the achievement will be zero.

Â And if for a countries at 85 or above 85, it considered to have achieved

Â the maximum level of achievement for this indicator, so that'll be one.

Â So this normalization process basically what is does is to project

Â the value onto a scale, a zero one scale.

Â So maximum achievement being set at one, and

Â the minimum achievement set at zero for the normalized value.

Â For the mean years of schooling, this maximum is set.

Â There are natural minimum and maximum possible for these indicators.

Â For example, years of schooling, obviously the minimum is zero and

Â the maximum is set at 15 for the mean years of schooling.

Â Which is the years of schooling, average years of schooling of

Â the adult population as I said, let's say of the older generation.

Â And the expected years of schooling has a minimum also at zero but

Â a maximum of 18 because is the years of schooling

Â supposed to reflect the years of schooling of a younger population.

Â Who are normally, if you go in overtime, we expect that

Â the younger generations have higher levels of education than the older generations.

Â And the last indicator, per capita income, the minimum is set at $100 PPP,

Â and the maximum at $75,000 PPP dollars.

Â These are the major steps involved in the construction of a multi dimensional index.

Â Now let's see how this normalization works and

Â what is the meaning of this normalization.

Â So we set for each indicator, we set a minimum and a maximum.

Â So let's say the minimum is here and the maximum is here.

Â So remember that this is a level of achievement at which or

Â below which the country is supposed to be at a zero level of achievement,

Â zero level for the index normalized value.

Â And the maximum value is that level at which are above it,

Â the country is at a level of one maximum achievement.

Â Now, so this is the maximum possible achievement for any country.

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at what is the percentage of achievement that the country is at

Â compared to the maximum possible achievement that it could have.

Â So if you take this A, So

Â the A is basically value minus the minimum value.

Â The value for that country minus the minimum is the length A, and

Â if you look at the length B, it's simply the maximum minus the minimum.

Â So where is this country compared to the maximum level of achievement that it

Â can have?

Â So that is the normalized value of every indicator.

Â And this normalized value as you can see goes from zero to one

Â because anything at the minimum or below the minimum is zero.

Â Anything at he maximum or above the maximum is one, and

Â any other value is between zero and one.

Â So we are projecting this value onto a scale which goes from zero to one.

Â So that we do it for each indicator.

Â So the life expectancy is converted into an index, a normalized index in this way.

Â The education dimension has two indicators we set, the mean years of schooling and

Â the expected years of schooling.

Â And each indicator has its own maximum and minimum.

Â So we'll do the same operation for each of these indicators, and so

Â we get two normalized indices for the education dimension, and

Â the overall education index is taken to be a simple average and

Â arithmetic mean of these two indices.

Â The income index is also normalized,

Â the per capita national income is also normalized in the same way,

Â but using the log of the value rather than the value itself.

Â And I'll come to that in slightly

Â in a short while to say why we use the log value.

Â So we have now after this normalization procedure we have one index for

Â health, one index for education which is in already an arithmetic mean of

Â the two sub-indices if you want.

Â And then one index for income.

Â And the human development index is simply constructed as

Â the geometric mean of these three indices.

Â So the formula is that we do the product of these three indices and

Â raise it to the power one-third, that's called a geometric mean.

Â So we saw different types of means are being used in this process,

Â one is an arithmetic mean and one is a geometric mean.

Â And that has to do with the degree of substitutability that we want to have

Â among the different elements that make these means.

Â So an arithmetic mean normally allows for perfect substitutability, and a geometric

Â mean for much less substitutability among the different dimensions.

Â So the overall HDI is the geometry coverage of the three dimensional indices.

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