(FORTUNE Magazine) – For thousands of years people measured the weight of precious stones by comparing them to a qirat, the Arabic word for the weight of four grains. Sound like a vague measure? Well, it used to be, but over the centuries the unit has become more precise: Today's carat is equal to one five-thousandth of a kilogram. Yet there are a lot of things that are as much trouble to measure today as the weight of a ruby in distant times. What is the economic value of a piece of software? Of the Internet? Or of better health and increased life expectancy? These questions are not just the stuff of philosophy: They carry real-life consequences. The difficulty in measuring the output of, say, an office worker affects everything from the consumer price index (and hence billions in benefits) to the stock market valuations of companies in new industries to the fundamental question of whether productivity in America has really been going up this decade--and thus how fast the economy can grow in the future.

As the sources of wealth migrate away from natural resources and capital toward information and highly skilled people, traditional economic yardsticks look as old-fashioned as a slide rule. To have an accurate idea of how fast productivity or living standards are changing, there needs to be a way to measure changes in output, adjusted for inflation. For old industries--such as steel or color televisions--figuring that out is not difficult. The trouble comes with products that enjoy fast and dramatic changes in quality, like computers, or with products and services that never existed before, like mobile phones. In these cases, the statisticians at the U.S. Bureau of Labor Statistics and other bean counters are flailing, because the way they are accustomed to measuring the economy cannot keep pace with the economy itself.

For example, if a personal computer with a Pentium III processor were sold today for exactly the same price as one with an 8086 processor 20 years ago, that would not mean that the output of personal computers has been stagnant for two decades: The new computer is far more powerful and efficient than the old one. Yet it is impossible for official statistics to adjust quickly or accurately for the new and the better. The problem of how to measure the New Economy is so intractable that in the 1970s and early 1980s, the U.S. government's assumption in its output calculations was that the quality of computers, the fastest-improving good in history, never changed. As late as 1990, the government made routine quality adjustments in its statistics for only two items, computers and housing.

Such assumptions can be spectacularly distorting. A Yale professor, William Nordhaus, compared the price of lumens (a standard unit of measurement for light) over time. In 1750 b.c., the average Babylonian, relying on lamps fueled by sesame oil, had to work 350,000 hours to buy as many lumens as the average American could buy with one hour's work in 1992. The amount of light Thomas Jefferson could buy for $100 in 1800 cost just 3 cents (in constant dollars) in 1992.

Why does that matter? Because according to the standard consumer price index calculation, the price of light has increased three to five times since 1800. By Nordhaus' reckoning, then, for lighting, Americans are about 1,000 times richer than the official figures indicate. The reason for the colossal discrepancy is that the usual CPI calculation is based on the price of inputs in the form of purchased goods, such as kerosene, gas, or electricity. Nordhaus instead calculated the price of the service--in this case, light--delivered to the consumer. This method was able to take into account improvements in quality and efficiency. Correcting the CPI for light alone adds perhaps 7% to the total growth of real wages in America between 1800 and 1992--making American incomes about $275 billion higher in 1992 than the traditional figure has it. Extending this analysis to consumption across the board, Nordhaus suggests that real wages have risen not 13-fold since 1800, as conventionally measured, but at least 40 times.

Does it matter if GDP is being measured accurately? After all, the things that make up the economy are there even if they are not properly measured. But tell that to Alan Greenspan, who spends most of his time making decisions on the basis of statistics like these, which may well be inaccurate. Ditto for investors. If the information is not good, decisions will be flawed. And although it is a matter of hot dispute among economists, there is a school of thought that holds that the problem of measuring output accurately has worsened over the past couple of decades as new product and service development has accelerated and the knowledge-based component of the new things has become more important.

Over the past century, Nordhaus cautions, there have been probably no more than 20 goods or services that have had the kind of effect on living standards that electric lighting has had (the internal combustion engine is another, and penicillin probably a third). A commission chaired by Michael Boskin, a Stanford UniversIty professor who had been President Bush's head of the Council of Economic Advisers, reported in 1996 that the CPI as then constructed probably understated quality improvements by 0.6% a year. If that figure is right, on the basis of quality improvements alone over the past century, America's real output and real wages today may be twice as big as the government has reckoned. That is one reason the Bureau of Labor Statistics made several big changes in late October to the way it calculates GDP. Among other things, software will now be counted as investment--incredibly, it used to be counted as consumption--and ATMs will be recognized as contributing to the productivity of banks.

As innovation accelerates, it is increasingly difficult to measure the sources of wealth. The three biggest measurement headaches are human capital, health care, and computers.

Human capital is essentially the power of people to generate economic output through the application of their education and skills. The difficulties with measuring human capital mount as the Information Age waxes: More and more, value is produced not by real assets like factories and capital, but rather by people thinking and working together. The discrepancies between company balance sheets and stock market valuations--particularly among software and Internet firms--have prompted much debate about whether accounting rules need to be changed to reflect the ability of the people in a company to generate earnings for it. When Microsoft passed a market capitalization of $500 billion in July, the market was valuing the company at about 24 times book value, or ten to 20 times higher than the average blue-chip ratio between 1930 and 1990. For the companies in the Dow Jones industrial index as a whole, the stock price per book value per share has gone up sixfold since 1980. The implication is that as the market sees it, a firm's value depends less and less on physical capital and more and more on human capital.

The Federal Reserve publishes a balance sheet of the American economy, which showed in 1998 that the U.S. was worth about $40 trillion in tangible and financial assets. Michael Milken, the former junk-bond impresario who now invests in education and health-care enterprises, has done an entertaining parallel calculation. Using some concepts developed by Gary Becker, a Nobel Prize-winning economist at the University of Chicago, Milken used a discounted cash-flow analysis of earning power over people's probable lifetimes as a way of coming up with the asset value of their human capital. Including this in USA Inc.'s balance sheet, Milken estimated that the assets of the U.S. were between $180 trillion and $1 quadrillion in 1998, and that human capital accounted for at least three-quarters of the total worth.

Today's main income-producing assets--people interacting with one another in corporations--are hard to judge with the accounting tools of the age of steel. It's not just that it's easier to measure how much it will cost to replace a steel mill than a software genius. The point is that the balance sheet is supposed to reflect the value of a firm's assets if it were broken up--and of course you can't own human "assets." So while it is possible to measure human capital, it's very hard to "capture" it, in both a literal and a figurative sense. Human capital can walk out the door--and worse, go to work for the competition--making it impossible to assign a constant value to it. That creates more problems for stock valuations.

Because humans are so uniquely valuable, keeping them fit and healthy poses the second big headache for economic statisticians. Health traditionally enters the national accounts only through the cost of medical care rather than the value of outputs, such as better health and longer, more productive lives. As in the case of light, the traditional valuation may thus be far off the beam.

Nordhaus has done another piece of research that suggests the value of increased life spans has added at least as much to the increase in living standards in America this century as the growth of all other consumption goods and services combined. More concretely, he figures that all the wonderful products of this century--cars, television, planes, highways, computers, and so on--did not add as much to the increase in American incomes as penicillin, vaccination, improved workplace safety, and better diagnostic and surgical techniques.

Two other economists, Kevin Murphy and Robert Topel from the University of Chicago Business School, are trying to quantify the benefit of longer lives. Their preliminary reckoning is that higher life expectancy added $2.8 trillion per year (in 1992 dollars) to the American economy from 1970 to 1990. They also estimate that a 20% cut in deaths from either heart disease or cancer, America's two biggest killers of people in their productive years (ages 20 to 70), would generate $10 trillion in economic value--or about a year's worth of American GDP.

Humans have always been mystifying creatures, but computers are proving only slightly less so. Specifically, while it seems obvious that computers have to have boosted productivity, proving that they have has been impossible. The bluntest exponent of the view that the computer revolution is mostly bunk--"a pipsqueak among revolutions," he calls it--is Robert Gordon, an economics professor at Northwestern University near Chicago. Gordon doesn't dismiss the impact of computers. By his reckoning, price declines in computers and telecoms have been reducing American CPI by one percentage point a year during the 1990s, a huge contribution to the Goldilocks economy. That, however, is a different question from whether computers have been raising productivity and hence the long-run growth potential of the economy. Gordon's view is that they have not. "Computers have to interact with humans," he concludes, "and humans have a limited quantity of time to combine their unique talents (thinking, typing, planning) with the computational and information-gathering resources of computers."

This is where the measurement problems crash into the great debate about whether American productivity slowed badly in the 1970s and 1980s, and is now reviving strongly. Official productivity figures show both the slowdown and the revival, but both are controversial. One argument is that the slowdown was illusory because, in the 1970s, economic activity began shifting rapidly into services and information technology. Output in those sectors is inherently more difficult to measure. But that has always been true of new things. Unless the economy suddenly became significantly more difficult to quantify in the 1970s, the relative change should not have happened.

Gordon's view is that productivity did indeed slow down in the 1970s. More radically, he argues that it has not improved at all. The official reckoning is that productivity has revived substantially since 1994, after slumping since the early 1970s. He reasons that the entire apparent spurt in productivity came from the better measurement of inflation and a normal speedup associated with the economic cycle, combined with a rise in manufacturing productivity in the making of computer hardware--one of the only items in which productivity improvements are constantly taken into account.

To Gordon, computers are a relatively minor economic innovation compared with things like electricity, the car, drugs, aviation, or the telephone. The productivity effects of these great innovations had trailed off by the 1970s. That is why productivity growth slowed then and, in Gordon's view, has not picked up since. Most economists agree with Gordon. As Brad De Long, a Berkeley economist, puts it, "A technological revolution is not an economic revolution"--and evidence for the latter is scant.

Yet the stock market flatly disagrees. The most striking proof is the valuation that the market has been putting on investment in computers compared with other capital equipment. Traditionally, the thinking has been that a company's balance sheet should just about equal the market capitalization. Detailed sampling of firms done between 1987 and 1994 by Erik Brynjofsson and Shinkyu Yang at MIT's Sloan School of Management, however, shows that the value for companies' investment in computers was reckoned at ten to 30 times as valuable, even while the ratio for investment in other kinds of capital stayed close to one. According to the MIT men, the market is factoring in all sorts of highly productive intangibles--new systems, new organizational structures, new ways of doing business--that successful companies create when they introduce computers in the right way.

As people and information become ever more significant in the economy, the answer to the question on everyone's mind--is this market a gigantic bubble waiting to burst, or is it just starting to grow?--probably lies in that interaction between new and little-understood income-producing assets and old balance sheets. If only we could measure it.