Economics is often referred to as "the dismal science." This refers not to its practitioners, but to the accuracy of their results. Economics inevitably involves making forecasts. Since there are many ways in which a forecast can be wrong and only one way in which it can be right, a high miss rate seems inevitable.

There is always talk of "improved economic models," but in a sense those models are no more than window-dressing designed to disguise the real problem. Before you can make an economic prediction, you are forced to make assumptions about the future of the world. Your results are likely to be highly sensitive to those assumptions. I want to illustrate this by focusing on projections of world population, which is a driving force for every large-scale economic model of the future.

It takes no great insight to propose certain key variables that radically affect population estimates. One is the number of children per family that survive to an age at which they can produce the next generation. I will simply call this the "family size," remembering that it excludes the parents and is always going to be less than the number of live births per family. A second important variable is human life expectancy. A third is the age at which parents have children. At the moment, most children are born to mothers between the ages of fifteen and thirty-five. A significant extension of female fertility could change this, but I don't think many women would approve. A fourth factor is the current age distribution of the world's population. A fifth is the way in which death rates vary with age. Average life expectancy is not a very useful concept. It is often badly skewed because of high infant mortality rates, and in the past large-scale wars have killed off a disproportionate fraction of the young men.

It turns out that the first two factors are the most important ones when we try for long-term predictions, which I will define as more than fifty years. Given these two, and assuming that they hold constant (a dangerous assumption), in the long run the age distribution of the population tends to a limit that is not dependent on the initial age distribution.

However, as John Maynard Keynes famously remarked, in the long run we are all dead. He might have added, as the most famous economist of his time, that we are thereby relieved of the burden of accurate forecasts since we will not be around to be embarrassed by them. Comforted by that thought, I will now examine the combined effects of changes in longevity and changes in family size.

I am going to make one more assumption; namely, that increased longevity in the coming century will arise mainly from a reduction in deaths by disease in youth and middle age. It will not arise from a major change in maximum human life span. Anyone who has read earlier columns will know that such an assumption may prove horribly wrong. However, I suspect that for the next several generations the beneficiaries of such techniques as telomere modification will be drawn from the ranks of the very wealthy.

Now, after all that preamble, I want to employ a model containing the assumptions I have described. As a sanity check, let me first note that with two children as the family size, and actual life span equal to average life expectancy, the model tends over time to a constant population with the same number of people in each age group. That population, however, will not equal today's population of about six billion. The present skew toward younger ages produces a future population bulge, which peaks around 2040 at a little over eight billion people.

However, the average isn't two children per family, and has not been for a long time. A century ago in this country, and more recently for much of the world, families of seven or more children were common. So, unfortunately, were high death rates. From 1800 to 1930, when the population grew from one billion to two billion, the average family size was 2.3 children per family. From 1930 to the present, the family size has been 3.0 children.

Which one should be used to model the future? We don't know, although the huge swell in population for the past seventy years came because of a great drop in infant mortality rates. However, we can readily calculate the consequences of any particular family size.

At a family size of 2.3, the population in 2060 would be 9.6 billion and growing. At 3.0, the 2060 population would be a terrifying 15.4 billion, and growing even faster. However, the present trend in many countries is toward smaller family size, dipping well below two. Suppose that the family size for this century went as low as 1.5. Then the population would peak between 2020 and 2030 at just over seven billion, and by 2060 it would be down to five billion.

To those of you who feel overcrowded, the last projection may sound attractive. However, the age distribution of the population may make you think again. With a family size of 3, the most numerous group, at 23 percent of total, would be children under ten. Only 5 percent of the people in 2060 would be over sixty years old - although there would be close to a billion of them. However, in the case where the family size is 1.5, only 10 percent are young children, while 17 percent are over sixty-five and another 19 percent are between fifty-five and sixty-five.

This is the well-known problem of a "graying population." With a decline in family size, the increasing fraction of old people who no longer work must be supported by the decreasing fraction of younger ones who do. Will children under the age of ten form part of the work force? In agricultural and early industrial societies, they certainly do and did. But whether they will in the future calls for yet another assumption. If they do not, they too must be supported by the shrinking work force.

The study of possible futures should be of great concern to anyone attempting long-term planning, although there is little evidence that the country or the world does much of that. Maybe people just turn off when confronted by the kind of numbers given here.

How about you? Are you still reading, or have you long ago given up? I did say it was called the dismal science.

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