# Calculating the HDI Sheet 1

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1 1 Calculating the HDI Sheet 1 Four values go into calculating the human development index (HDI) for a particular country. One value is life expectancy at birth. Two other values are related to education. The first is the adult literacy rate that is, the percentage of adults in the country who are literate. The other measure of education is the combined primary, secondary, and tertiary (that is, post-secondary) education enrollment as a percentage. This is the percentage of all people in the appropriate age groups for primary, secondary, and post-secondary school who are actually enrolled in school. The final value that goes into computing a country s HDI is the gross domestic product (GDP) per capita at purchasing power parity, given in U.S. dollars. This is the value of all new final goods and services produced within a country in that year divided by the average population for the same year. The term at purchasing power parity means that the gross domestic product value is adjusted to account for differences in the prices of goods and services in the various countries. This activity introduces you to the calculations involved in the HDI. Data for Kuwait are used to illustrate the calculations. Then you are asked to perform the calculations using Brazil s data. The 2004 data used here are available in the United Nations 2006 report at hdr.undp.org/hdr2006/statistics. For Kuwait, the life expectancy at birth is 77.1 years, the adult literacy rate is 9.%, the education enrollment ratio is 7%, and the gross domestic product is \$19,84. For Brazil, the life expectancy at birth is 70.8 years, the adult literacy rate is 88.6%, the education enrollment ratio is 86%, and the gross domestic product is \$8, Before making any calculations, how do you think these two countries will compare if we use these measures to come up with a single HDI for each country?

2 2 Calculating the HDI To calculate the HDI, first combine the two measures of education using a weighted average, with a two-thirds weight for the adult literacy rate (ALR) and a one-third weight for the education enrollment ratio (EER). The formula for the weighted average to give the education percentage (EP) as a measure of education is EP = 2 ALR + 1 EER. Kuwait s EP is EP Kuwait = 2 9.% + 1 7% 86.5%. 2. Use the formula to find the EP for Brazil. To calculate a single numerical measure of human development, the HDI, we want to combine the measure of health, which is in years, with the measure of education we just found, which is given as a percentage, with the measure of economic well-being, which is given in U.S. dollars.. Explain why we cannot combine these values directly with different units (like years, percent, and dollars) into a single measure.

3 Calculating the HDI One way to combine these values is to convert each of them to an index number with no units associated with it. We can then average these three numbers to obtain the HDI. To convert life expectancy values to a life expectancy index number, we first identify a reasonable minimum and maximum for each of these values. The United Nations uses 25 as the minimum and 85 as the maximum. Then the life expectancy value (LEV) is converted to a life expectancy index (LEI) using the equation LEI = LEV Explain why an index number defined this way will be between 0 and 1 and will not have any units (like years) associated with it. For Kuwait, with life expectancy of 77.1 years, LEI Kuwait = Find the life expectancy index for Brazil.

4 4 Calculating the HDI In fact, a value given in any units can be converted to an index using this same approach: First identify a reasonable minimum (min) and maximum (max) for these values and then convert the value to an index using the equation Index = Value min max min. The result is an index with no units associated with it. In a similar way, the education percentage (the weighted average of the adult literacy rate and the education enrollment ratio you computed in question 1) is converted to an index value by using a minimum of 0 (percent) and a maximum of 100 (percent). This gives the education index (EI) in terms of the education percentage (EP) as EI = EP = EP 100. Kuwait s EI is EI Kuwait = = = Find the EI for Brazil.

5 Calculating the HDI 5 For the final conversion to an index value, we convert the gross domestic product per capita in US\$ (GDP) to an index value. This is done a bit differently than the previous conversions. Here base-ten logarithms are used so that the effect of a larger GDP value is diminished. (Natural logs may be used as well.) The minimum and maximum values used by the United Nations for the GDP are 100 and 40,000, respectively, and the equation to calculate the GDP index value (GDPI) from the GDP is GDPI = log(gdp) log(100) log(40,000) log(100). Kuwait s GDPI is GDPI Kuwait = log(19,84) log(100) log(40,000) log(100) Find Brazil s GDPI. Finally, to obtain the HDI for a country, we take the mean or average of the three index values: the LEI, the EI, and the GDPI. That is, we add them and then divide by. Kuwait s HDI is HDI Kuwait = Find Brazil s HDI and compare it to Kuwait s HDI. Was your prediction in question 1 correct? 9. What other values (other than life expectancy at birth, adult literacy rate, education enrollment ratio, and gross domestic product) might be appropriate to include in an index designed to measure the wellbeing of people?

### Calculating the HDI Sheet 1

1 Calculating the HDI Sheet 1 Four values go into calculating the human development index (HDI) for a particular country. One value is life expectancy at birth. Two other values are related to education.

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