December 15, 2007
How to Combine Income and Life Expectancy into an Index of Wellbeing
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.
The UN's Human Development Index: A Critique--Posner
When nations are ranked by gross national income per capita, the United States comes in sixth, after Luxembourg, Norway, Switzerland, Denmark, and Iceland, confirming one's general impression that the United States is the wealthiest large country; none of the countries ranked ahead of the U.S. have more than a fortieth of the U.S. population (Switzerland, the most populous of the group, has a population of 7.5 million). But when countries are ranked by the United Nations' Human Development Index, which rates 177 of the world's 193 countries, the United States falls to 12, Denmark to 14, and Luxembourg to 18; and among the nations promoted above the United States are Australia, Canada, Sweden, Japan, the Netherlands, France, Finland, and Spain (in that order).
The composition of the Index reflects dissatisfaction with income as a measure of well-being. And of course it is a limited measure; income is not the only argument in a person's utility function. The Human Development Index is an attempt to develop a better measure of well-being. It is a composite of three indexes: GDP per capita (computed on a purchasing power parity basis, to correct for distortions introduced by using currency exchange rates); life expectancy at birth; and a combination of the adult literacy rate and the combined primary, secondary, and college/university enrollment rate, with the adult literacy rate being weighted twice as heavily as the enrollment rate. For each component index, the value of 0 is assigned to the minimum level of the development indicator (income, life expectancy, and enrollment) and 1 to the maximum, and each country's score is the percentage of the maximum level that it achieves. A country's Human Development score is the simple average of its scores on the three indexes.
I cannot myself see the value of the Human Development Index. Not that per capita income, life expectancy at birth, and level of education as proxied by adult literacy and school enrollments are unimportant; a ranking of each of these aspects of human development might be a good first step in identifying areas of weakness that a society might wish to devote additional resources to improving. It is the combining of the indexes and announcing that the combination offers a ranking of nations by the degree of their "human" as distinct from narrowly defined "economic" development that strikes me as dubious, and indeed as senseless. The obvious objection is to the equal weighting of the three indexes, and to the omission of a host of other important dimensions of development, such as housing quality, pollution, tax rates, adult life expectancy, crime rates, unemployment, inflation, quality and variety of goods and services, economic growth, and quality of education--though including them would exacerbate the weighting problem, and some involve serious measurement problems.
A less obvious objection, but a general problem with rankings, is that from a sensible evaluative standpoint the distance between ranks is more important than the number of ranks that separate two countries. The wealthiest nation has a per capita income twice as great as that of the 20th wealthiest nation. That is a big difference. But now consider life expectancy at birth. Japan is number 3 with a life expectancy at birth of 82 years; the United States is only number 44, with a life expectancy at birth of 78. A four-year difference in life expectancy is not trivial by any means; but compare it to the difference in per capita income between the third richest country, Switzerland, and the 44th, Palau: the Swiss income per capita is almost eight times as great as the per capita income of Palau.
If a country devotes resources to improving life expectancy, it has to give up some other good. It is hard to say that the United States is making a mistake in not spending more resources on extending life expectancy; many Americans think that we spend too much on health care already. One reason (though by no means the only one) that the United States ranks only 44th in life expectancy is that our large black population has an abnormally high death rate; the average life expectancy of black male Americans is only 69. This shockingly high death rate reflects deep-seated problems of American blacks that would probably cost an enormous amount of money to solve. The political will to expend those resources does not exist. This may be a misfortune, a tragedy, or even a sin, but to use it to push the United States down in an index of human development is a political judgment, rather than anything determined by neutral social science.
The Human Development Index is an example of ranking mania that has the United States tightly in its grip, so maybe Americans shouldn't complain about the Index. One cannot generalize about the value of rankings. There are pluses and minuses. The major plus is that a ranking is an economical method of presenting information. The related minus is that it often presents it in a misleading way--that is my earlier point that the distance between ranks is more important than the number of ranks that separates the persons (nations, etc.) being ranked. The more compressed a distribution--of ability, health, income, etc.--the less meaningful rank ordering is.
But the more serious problem with rank ordering is the arbitrariness of weighting different quality measures to come up with a composite ranking. It is well illustrated by the college, law school, and business school rankings done annually by U.S. News & World Report. Unlike the UN, the editors of that magazine do not rank the different measures they use (such as SAT or LSAT scores and ratio of applicants to admits) equally; but the weightings are just as arbitrary. They are worse in one respect than the Human Development Index: they are manipulable. A school can (and many schools do ) increase its ratio of applicants to admits by blurring its admission criteria or reducing its application fee, thus increasing the number of applicants without increasing the number of admits. It is unlikely that a nation would try to improve its ranking in the Human Development Index by reallocating resources to activities that influence the rankings.