The HDI is based on three indicators: longevity, as measured by life expectancy at birth; educational attainment, as measured by a combination of adult literacy (two-thirds weight), and the combined gross primary, secondary and tertiary enrolment ratio (one third weight); and standard of living, as measured by real per capita GDP (PPP$).

Fixed minimum and maximum values
To construct 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 rate: 0% and 100%
• Combined gross enrolment ratio: 0% and 100%.
• Real GDP per capita (PPP$): $100 and $40,000.
For any component of the HDI, individual indices can be computed according to the general formula:

Index =	Actual xivalue - minimum xivalue
	Maximum xi value - minimum xi 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	=	40	= 0.0667
	85 - 25		60

Treatment of income
Constructing the income index is a little more complex. Over the years the Human Development Report has used a particular formula to do this, explained below. This year a thorough review of the treatment of income in the HDI was done, based on the work of Anand and Sen (1999).

Income enters into the HDI as a surrogate for all the dimensions of human development not reflected in a long and healthy life and in knowledge - in a nutshell it is a proxy for a decent standard of living. The basic approach in the treatment of income has been driven by the fact that achieving a respectable level of human development does not require unlimited income. To reflect this, income has always been discounted in calculating the HDI. The issue is, how should it be discounted, and at what level?

In previous years the practice was to discount income above the threshold level of the world average income, using the following formula:

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*

Where y is the actual per capita income in PPP$ and y* is the threshold per capita income (PPP$) at the world average income in the year for which the HDI is constructed. The world average income was taken as the threshold income on the premise that each person should have the income that the world on average enjoys.

To calculate the discounted value of the maximum income of $40,000 (PPP$), the following formula was used:

W(y) = y* + 2(y*1/2) + 3(y*1/3) +4(y*1/4) + 5(y1/5) + 6(y*1/6) + 7[(40,000 - 6y*)1/7]

This is because $40,000 (PPP$) is between 6y* and 7y*. With the above formula, the discounted value of the maximum income of $40,000 (PPP$) is $6,311 (PPP$).

The main problem with this formula is that it discounts the income above the threshold level very heavily, penalising the countries in which income exceeds the threshold level. It reduces the $34,000 (PPP$) between the threshold and maximum level of income to a mere $321 (PPP$). In many cases, income loses its relevance as a proxy for all dimensions of human development other than a long and healthy life and knowledge.

This year's refinement in the treatment of income attempts to rectify this problem by putting the methodology on a more solid analytical foundation. The rationale and the formula adopted in the refinement are discussed in detail in Anand and Sen (1999). To summarise, in the construction of this year's HDI, income is treated using the following formula:

W(y) =	log y- log ymin
	log y max - log ymin

There are several advantages to this formula. First, it does not discount income as severely as the formula used earlier. Second, it discounts all income, not just the income above a certain level. Third, as figure TN1 shows, the asymptote starts quite late, so middle-income countries are not penalised unduly: moreover, as income rises further in these countries, they will continue to receive recognition for their increasing income as a potential means for further human development.