How to Combine Income and Life Expectancy into an Index of Wellbeing-Becker
Modern national income accounts developed about 75 years. Although a sterling achievement that won Richard Stone a Nobel Prize in economics, even pioneers like Stone and Simon Kuznets recognized that these accounts had serious limitations as measures of wellbeing. Among the major oversights that remain to this day are that these accounts neglect the value of time spent in households at housework and other activities, they do not attempt to measure investments in human capital, they fail to adjust for the environmental damages due to pollution, and they take no account of improvements in the quantity and quality of life.
The UN's Human Development Index recognizes some of these defects in income accounts, and attempts to correct them by combining percentage changes (or percentage levels) in per capita incomes with percentage changes in life expectancy, and percentage changes in education levels. However, as Posner points out, the weights attached to these different changes (1/3 weight to each) are completely arbitrary. Moreover, there is substantial double counting since much of the value to increased education results from its effects on raising incomes and lower mortality, and these are counted separately.
The UN Index ignores modern research that provides a method that is well grounded in economic analysis to combine changes in national income with changes in various types of mortality risk. This method calculates the "statistical value of life", which essentially measures how much individuals are willing to pay for various improvements in mortality rates. To get a measure of the per capita change in what has been called "full" income, one simply adds the per capita change in real income to the value placed on the improvements (or deterioration, as in some African countries due to Aids) in mortality risks. One can divide this change by the initial level of per capita real income to obtain a measure of the percentage changes in full income. These full income measures combine changes in life expectancy and in ordinary income not in some arbitrary way, but by extending the willingness to pay concept that is used in national income accounting to valuations of changes in life expectancy.
Hundreds of estimates of statistical values of life have been made for different countries. They are derived from evidence on how consumers and workers value various types of risks to their life. The most common type of study determines how much individuals need to be paid to choose occupations, like construction, that involve relatively large risks of fatal accidents. Other studies use the speed of cars under different circumstances, recognizing that after a point greater speed raises the risk of a deadly accident. Still others examine the willingness of individuals to pay for expensive drugs that are believed to reduce the probability of dying from different major diseases.
There is a range of estimates even for a given country, but the central tendency of estimates for young Americans is that they require some $500 to take on a risk that adds about 1/10,000 to their annual risk of dying. So the statistical value of a typical young American life in this case would be $5,000,000=$500/1/10,000. Based on similar calculations for a number of countries, a rough approximation is that young persons in other countries would have statistical values of life that multiply the American value of life by the ratio of per capita income in that country to the American per capita income.
In a paper I published with Tomas Philipson and Rodrigo Soares in the American Economic Review, March 2005 called "The Quantity and Quality of Life and the Evolution of World Inequality", we apply this method to estimate the relative changes in full income from 1960-2000 in about 100 countries. A common finding on income growth is that the usual measures of per capita incomes grew only a little more rapidly during this period of time in poor and less developed countries than in richer countries. Even that slight degree of income convergence is found only when income changes in each country are weighted by its populations since the two largest countries with about 40 per cent of the world's population, China and India, experienced unusually rapid growth in per capita incomes.
That conclusion about little change in inequality among countries is altered quite significantly when changes in full incomes are compared. Since mortality declined more rapidly in poorer countries than richer ones, adding the value placed on declines in mortality to get measures of changes in full incomes affect the calculations for poor countries more than for rich countries. In fact, the percentage increases in full incomes are on the average much more rapid in poorer countries than in richer ones, which imply a sizable convergence in full incomes across nations during the past several decades. The main reason for this convergence was the transfer of antibiotics and other drugs and medical knowledge from rich to poor countries.