Human Development Index
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Three dimensional plot showing the values of the geometric mean. In mathematics, the geometric mean is a type of mean or average , which indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the n th root (where n is the count of numbers) of the product of the numbers. For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product; that is 2 √ 2 × 8 = 4 . As another example, the geometric mean of the three numbers 4, 1, and 1/32 is the cube root of their product (1/8), which is 1/2; that is 3 √ 4 × 1 × 1/32 = ½ .
Each year since 1990 the Human Development Report has published the Human Development Index (HDI) which was introduced as an alternative to conventional measures of national development, such as level of income and the rate of economic growth. The HDI represents a push for a broader definition of well-being and provides a composite measure of three basic dimensions of human development: health, education and income. Between 1980 and 2012 Uruguay's HDI rose by 0.4% annually from 0.664 to 0.792 today, which gives the country a rank of 51 out of 187 countries with comparable data. The HDI of Latin America and the Caribbean as a region increased from 0.574 in 1980 to 0.741 today, placing Uruguay above the regional average.
A few days back I wrote a post claiming that “for all the work that goes into the Human Development Index, it just doesn’t tell you much that you wouldn’t learn from simple comparisons of G.D.P. per capita.” Subsequently, Francisco Rodriguez , who heads research at the UN Human Development Report Office , touched base to tell me that he thought I hadn’t told the whole story. Francisco is a terrific macroeconomist (in fact, he was the TA when I took my graduate macro classes at Harvard), and so he kindly agreed to write a guest post filling in the missing pieces.