BOX 3N
THE UNDP HUMAN DEVELOPMENT INDEX

Compiled by Bedrich Moldan

In the 1990 issue of the UNDP's Human Development Report¹, it was suggested that the measurement of human development, the Human Development Index, should focus on the three essential elements of human life-longevity, knowledge and decent living standards.

For the first component, longevity, life expectancy at birth is the indicator. The importance of life expectancy lies in the common belief that a long life is valuable in itself and in the fact that various indirect benefits (such as adequate nutrition and good health) are closely associated with higher life expectancy. This association makes life expectancy an important indicator of human development, especially in view of the present lack of comprehensive information about people's health and nutritional status.

For the second key component, knowledge, literacy figures are only a crude reflection of access to education, particularly to the good quality education so necessary for productive life in modern society. But literacy is a person's first step in learning and knowledge-building, so literacy figures are essential in any measurement of human development. In a more varied set of indicators, importance would also have to be attached to the outputs of higher levels of education. But for basic human development, literacy deserves the clearest emphasis.

The third key component of human development, command over resources needed for a decent living, is perhaps the most difficult to measure simply. It requires data on access to land, credit, income and other resources. But given the scarce data on many of these variables, we must for the time being make the best use of an income indicator. The most readily available income indicator, per capita, has wide national coverage. But the presence of nontradable goods and services and the distortions from exchange rate anomalies, tariffs and taxes make per capita income data in nominal prices not very useful for international comparisons. Such data can, however, be improved by using purchasing-power-adjusted real GDP per capita figures, which provide better approximations of the relative power to buy commodities and to gain command over resources for a decent living standard.

A further consideration is that the indicator should reflect the diminishing returns to transforming income into human capabilities. In other words, people do not need excessive financial resources to ensure a decent living. This aspect was taken into account by using the logarithm of real GDP per capita for the income indicator.

In the 1996 issue of the Human Development Report², the following methodology was applied:

For the construction of the index, fixed minimum and maximum values have been established for each of these indicators:

• Life expectancy at birth: 25 years and 85 years 
• Adult literacy: 0% and 100% 
• Combined enrolment ratio: 0% and 100% 
• Real GDP per capita (PPP$): PPP$ l00 and PPP$l00 and PP$ 40,000.

For any component of the HDI, individual indices can be computed according to the general formula: 

Index  = Actual x_i value - minimum x_i value /  Maximum x_i value - minimum x_i value

If, for example, the life expectancy at birth in a country is 65 years, the index of life expectancy for this country would be :  

Life expectancy index = 65- 25 / 85- 25 = 40 / 60 = 0.667

The construction of the income index is a little more complex. The average world income of PPP$,711 is taken as the threshold level (y*), and any income above this level is discounted using the following formulation based on Atkinsons formula for the utility of income: 

W(y)= y* for 0 y y* 
        = y* + 2 ( y -y*) 1/2 for y* y 2y* 
        = y* + 2(y*^1/2 ) +3(y = 2y*)^1/3 for 2y* y 3y*

To calculate the discounted value of the maximum income of PPP40,000, the following form of Atkinsons formula is used: 

W(y) = y* +2 (y*^1/2) +3 (y*^1/3) +4 (y*^1/4) +5 (y*^1/5) + 6 ( y*^1/6) + 7 (y*^1/7) + 8( 40,000 -7y*)^1/8

This is because PPP$40,000 is between 7y* and 8y*.

With the above formulation, the discounted value of the maximum income of PPP$40,000 is PPP$6,040.

The construction of the HDI is illustrated with two examples - Greece, an industrial country, and Gabon, a developing country. 

Life expectancy index

Greece = 77.7- 25  / 85 -25 = 28.7 / 60 = 0.938  

Gabon = 53.7- 25 / 85- 25 = 28.7 / 60 = 0.478 

Adult literacy index

Greece = 93.8 - 0 / 100 -0 = 93.8 /100  = 0.938  

Gabon= 60.3 - 0 / 100 -0 = 60.3 / 100 = 0.603 

Combined primary, secondary and tertiary enrolment ratio index

Greece = 78- 0 / 100- 0 = 0.780   

Gabon= 47- 0 / 100-0 = 0.470

Educational attainment index

Greece = [2 (0.938) + 1 (0.780) ] / 3 = 0.885 

Gabon = [2 (0.603) + 1 (0.470) ] / 3 = 0.558

Adjusted real GDP per capita (PPP) index

Greece's real GDP per capita, at PPP8,950, is above - but less than twice - the threshold. Thus, the adjusted real GDP per capita for Greece would be PPP5,825 because5,825=5,711+2(8,950-5,711)1/2.

Gabon's real GDP per capita, at PPP3,861, is less than the threshold, so it needs no adjustment.

The adjusted real GDP per capita (PPP) index for Greece and Gabon would be: 

Greece = 5,825 -100 / 6,040- 100 = 5,725  / 5,940  =  0.964    

Gabon = 3,861-100 / 6,040- 100 = 3,761 / 5,940 =  0.633 

Human development index

The HDI is a simple average of the life expectancy index, educational attainment index and the adjusted real GDP per capita (PPP) index. It is calculated by dividing the sum of these three indices by 3. The Hill values for Greece and Gabon are calculated using this formula: 

The values of the Human Development Index, published in 1996, are found in Table 1.

REFERENCES

¹ UNDP (1990) Human Development Report 1990. Oxford University Press, New York, Oxford.

² UNDP (1996) Human Development Report 1996. Oxford University Press, New York, Oxford.