[An updated version of this article can be found at Economic Growth in the 2nd edition.]
Compound Rates of Growth
In the modern version of an old legend, an investment banker asks to be paid by placing one penny on the first square of a chess board, two pennies on the second square, four on the third, etc. If the banker had asked that only the white squares be used, the initial penny would double in value thirty-one times, leaving $21.5 million on the last square. Using both the black and the white squares makes the penny grow to $92,000,000 billion.
People are reasonably good at forming estimates based on addition, but for operations such as compounding that depend on repeated multiplication, we systematically underestimate how fast things grow. As a result we often lose sight of how important the average rate of growth is for an economy. For an investment banker the choice between a payment that doubles with every square on the chess board and one that doubles with every other square is more important than any other part of the contract. Who cares whether the payment is in pennies, pounds, or pesos? For a nation the choices that determine whether income doubles with every generation, or instead with every other generation, dwarf all other policy concerns.
Growth in Income Per Capita
Starting at one-third the level in the United States, income per capita in Japan grew at the rate of 5.8 percent per year from 1960 to 1985. Starting at one-fifteenth of the level in the United States, income per capita in India grew at the rate of 1.5 percent per year. Because income per person grew at an annual rate of 2.1 percent in the United States, Japan was catching up and India was falling farther behind.
You can figure out how long it takes income to double by dividing the growth rate into the number 72. If growth in the United States continues at the annual rate of 2.1 percent, income per capita will double every 34 years (72/2.1 = 34). In 102 years, income will increase eightfold. This increase is large, but not unprecedented.
In the United States, income per person grew by about this factor over the last 100 years. At the Japanese rate of 5.8 percent, income will double every 12 years. If this were sustained for 96 years, average income in Japan would increase by a factor of 256.
One reason Japan grew so fast is that it started from so far behind. Rapid growth could be achieved in large part by copying industrial practices in the leading countries of the world. The interesting question is why India did not manage the same trick (see Third World Economic Development). As Japan catches up with the leading countries, growth will inevitably slow. [Editor's note: that is exactly what happened] Over the course of the next century, an increase by a factor of 8 in per capita income is believable, but an increase by a factor of 256 is not.
After correcting for the cost of living, North America is still the most prosperous region in the world, but it may not remain so for long. Even if growth in Japan slows dramatically, Japan may still take the lead, just as North America surpassed England at the beginning of this century.
Suppose that the rate of increase in Japan is 2.6 percent, half a percentage point higher than the recent rate in the United States, and suppose that the rate in North America falls by half a percentage point to 1.6 percent. In a hundred years income per person would be more than twice as large in Japan as it is in North America.
Growth and Recipes
Economic growth occurs whenever people take resources and rearrange them in ways that are more valuable. A useful metaphor for production in an economy comes from the kitchen. To create valuable final products, we mix inexpensive ingredients together according to a recipe. The cooking one can do is limited by the supply of ingredients, and most cooking in the economy produces undesirable side effects. If economic growth could be achieved only by doing more and more of the same kind of cooking, we would eventually run out of raw materials and suffer from unacceptable levels of pollution and nuisance. Human history teaches us, however, that economic growth springs from better recipes, not just from more cooking. New recipes generally produce fewer unpleasant side effects and generate more economic value per unit of raw material (see Natural Resources).
Every generation has perceived the limits to growth that finite resources and undesirable side effects would pose if no new recipes or ideas were discovered. And every generation has underestimated the potential for finding new recipes and ideas. We consistently fail to grasp how many ideas remain to be discovered. The difficulty is the same one we have with compounding. Possibilities do not add up. They multiply.
In a branch of physical chemistry known as exploratory synthesis, chemists try mixing selected elements together at different temperatures and pressures to see what comes out. Several years ago, one of the hundreds of compounds discovered this way was found to be a superconductor at temperatures far higher than anyone previously thought possible. This discovery may ultimately have economic implications that are as far-reaching as the discovery of the transistor.
To get some sense of how much scope there is for more such discoveries, we can calculate as follows. The periodic table contains about a hundred different types of atoms, so the number of combinations made up of four different elements is about 100 × 99 × 98 × 97 = 94,000,000. A list of numbers like 1, 2, 3, 7 can represent the proportions for using the four elements in a recipe. To keep things simple, assume that the numbers in the list must lie between 1 and 10, that no fractions are allowed, and that the smallest number must always be 1. Then there are about 3,500 different sets of proportions for each choice of four elements, and 3,500 × 94,000,000 (or 330 billion) different recipes in total. If laboratories around the world evaluated 1,000 recipes each day, it would take nearly a million years to go through them all. (In fact, this calculation vastly underestimates the amount of exploration that remains to be done because mixtures can be made of more than four elements, fractional proportions can be selected, and a wide variety of pressures and temperatures can be used during mixing.)
Even after correcting for these additional factors, this kind of calculation only begins to suggest the range of possibilities. Instead of just mixing elements together in a disorganized fashion, we can use chemical reactions to combine elements such as hydrogen and carbon into ordered structures like polymers or proteins. To see how far this kind of process can take us, imagine the ideal chemical refinery. It would convert abundant, renewable resources into a product that humans value. It would be smaller than a car, mobile so that it could search out its own inputs, capable of maintaining the temperature necessary for its reactions within narrow bounds, and able to automatically heal most system failures. It would build replicas of itself for use after it wears out, and it would do all of this with little human supervision. All we would have to do is get it to stay still periodically so that we could hook up some pipes and drain off the final product.
This refinery already exists. It is the milk cow. And if nature can produce this structured collection of hydrogen, carbon, and miscellaneous other atoms by meandering along one particular evolutionary path of trial and error (albeit one that took hundreds of millions of years), there must be an unimaginably large number of valuable structures and recipes for combining atoms that we have yet to discover.
Objects and Ideas
Thinking about ideas and recipes changes how one thinks about economic policy (and cows). A traditional explanation for the persistent poverty of many less developed countries is that they lack objects such as natural resources or capital goods. But Japan had little of either in 1950 and still has few natural resources, so something else must be involved. Increasingly, emphasis is shifting to the notion that it is ideas, not objects, that poor countries lack. The knowledge needed to provide citizens of the poorest countries with a vastly improved standard of living already exists in the advanced countries. If a poor nation invests in education and does not destroy the incentives for its citizens to acquire ideas from the rest of the world, it can rapidly take advantage of the publicly available part of the worldwide stock of knowledge. If, in addition, it offers incentives for privately held ideas to be put to use within its borders (for example, by protecting foreign patents, copyrights, and licenses, and by permitting direct investment by foreign firms), its citizens can soon work in state-of-the-art productive activities.
Some ideas from the developed world are rapidly adopted by less developed countries. For example, oral rehydration therapy now saves the lives of hundreds of thousands of children who previously would have died from diarrhea. Yet governments in poor countries continue to impede the flow of many other kinds of ideas, especially those with commercial value. Even automobile producers in North America recognize that they can learn from ideas developed in the rest of the world. But car firms in India operate in a government-created protective time warp. The Hillman and Austin cars produced in England in the fifties continue to roll off production lines in India today. India's commitment to closing itself off and striving for self-sufficiency has been as strong as Japan's commitment to acquiring foreign ideas and participating fully in world markets. The outcomes—grinding poverty in India and opulence in Japan—could hardly be more disparate.
For a developing country like India, enormous increases in standards of living could be achieved merely by letting in the ideas held by companies from industrialized nations. But leading countries like the United States and Canada, and new leaders like Japan, cannot stay ahead merely by adopting ideas developed elsewhere. They must also offer incentives for the discovery of new ideas at home, and this is not easy to do. The same characteristic that makes an idea so valuable—everybody can use it at the same time—also means that it is hard to earn an appropriate rate of return on investments in ideas. The many people who benefit from a new idea can too easily free-ride on the efforts of others.
After the transistor was invented at Bell Labs, for example, many applied ideas had to be developed before this basic science discovery yielded any commercial value. By now, private firms have developed improved recipes that have brought the cost of a transistor down by a factor of 1 million. Yet most of the benefits from those discoveries have been reaped not by the innovating firms, but by the users of the transistors. Just a few years ago, I paid a thousand dollars per million transistors for memory in my computer. Now I pay less than a hundred per million, and yet I have done nothing to deserve or help pay for this windfall.
If the government confiscated most of the oil from major discoveries and gave it to consumers, oil companies would do much less exploration. Some oil would still be found serendipitously, but many promising opportunities for exploration would be bypassed. Both oil companies and consumers would be worse off. The leakage of benefits such as those from improvements in the transistor acts just like this kind of confiscatory tax and has the same effect on incentives for exploration. For this reason most economists support three government policies designed to encourage the production, transmission, and implementation of ideas: universal subsidies for education, competitive grants for basic research, and patents and copyrights, which offer temporary monopoly profits on ideas. Economists also recognize, however, that such policies may not provide adequate incentives to discover the many small applied ideas needed to convert a basic idea such as the transistor into a product such as computer memory, or to convert a new product such as the videocassette recorder (which was first produced in the United States) into an inexpensive consumer good.
Stimulated in part by the dramatic and continuing success of the Japanese in catching and then surpassing North American firms in many areas of manufacturing, policymakers in the United States are now considering additional ways to stimulate the production of ideas. Proposed changes range from increased funding for basic science to antitrust exemptions for research consortia, from cuts in capital gains tax rates to an explicit "industrial policy" whereby a government agency directly subsidizes specific industries. We should not attempt to transplant institutions from Japan into the very different social and political climate of North America, but we should learn from Japan's experience.
Through a complicated and poorly understood combination of practices that we would not want to copy—practices that seem to include collusion between firms, bid rigging, systematic exclusion of foreigners, arm twisting by the government, the isolation of managers from any effective control by shareholders, and the pursuit of growth in firms that takes precedence over shareholder returns—the Japanese have achieved a far higher level of research and development by firms than exists in the United States. In the construction industry, for example, Japanese firms spend more than five times as much on research as comparable firms in the United States. All of the top six construction firms in Japan maintain major research laboratories with facilities, budgets, and coverage of disciplines that exceed those of the largest university- or government-based construction-oriented laboratories in the United States. None of the top North American firms maintains a similar institute. In a further contrast with the United States, very little of the research done by firms in Japan is funded directly or indirectly by the government or conducted in universities. As just one indication of the success of their system, the Japanese share of the worldwide construction market has been increasing and the North American share has been falling.
The usual retort to this kind of comparison is that universities in Japan are weak and that the quantity and quality of basic research are much higher in the United States. From the perspective of our national interest, this response is doubly misleading. The benefits of pure basic science in the United States can be captured by any country in the world. For the price of a journal subscription, Japanese firms can learn the latest recipe for high-temperature superconductors. In addition, because construction is a very large fraction of GNP—9 percent in the United States and 18 percent in Japan—even small improvements in construction techniques can have effects on national income that are large compared with more exciting basic science discoveries.
The lesson from the Japanese experience is clear: mundane forms of applied research, such as design work or product and process engineering, can have large cumulative benefits for the firm that undertakes them and even larger benefits for society as a whole. Moreover, the gains from applied research are largest not when it is dictated by government agency priorities or academic interests, but instead when it is closely integrated into the operations of a firm and motivated by the problems and opportunities that the firm faces.
Perhaps the most important ideas of all are meta-ideas. These are ideas about how to support the production and transmission of other ideas. The British invented patents and copyrights in the seventeenth century. North Americans invented the agricultural extension service in the nineteenth century and peer-reviewed competitive grants for basic research in the twentieth century. Japanese economic policy has been remarkably successful in the last three decades, but a growing number of scandals involving bribe-taking politicians warns us not to blindly imitate their institutions. The Japanese are learning the same lesson we should have learned when members of Congress intervened in the supervision of savings and loans: if the government has important discretionary power over economic affairs, members of the government can all too easily divert that power from its intended public purpose and put it to private use. The challenge facing all of the industrialized countries, including Japan, is therefore to invent new institutions that support a high level of applied, commercially relevant research in the private sector. These institutions must not impose high efficiency costs and, most important, must not be vulnerable to capture by narrow interests.
We do not know what the next major idea about how to support ideas will be. Nor do we know where it will emerge. There are, however, two safe predictions. First, the country that takes the lead in the twenty-first century will be the one that implements an innovation that supports the production of commercially relevant ideas in the private sector. Second, new meta-ideas of this kind will be found.
Only a failure of imagination, the same one that leads the man on the street to suppose that everything has already been invented, leads us to believe that all of the relevant institutions have been designed and that all of the policy levers have been found. For social scientists, every bit as much as for physical scientists, there are vast regions to explore and wonderful surprises to discover.
Paul M. Romer is the STANCO 25 Professor of Economics in the Graduate School of Business at Stanford University and a Senior Fellow at the Hoover Institution.
"A survey of India." The Economist, May 4, 1991.
"Exploring the New Material World." Science 252 (May 3, 1991): 644-46.
Japanese Technology Evaluation Center. "Construction Technologies in Japan." National Technical Information Service report no. PB91-100057. 1991.
North, Douglass C. Institutions, Institutional Change, and Economic Performance. 1990.
Romer, Paul. "Increasing Returns and New Developments in the Theory of Growth." In Equilibrium Theory and Applications: Proceedings of the 6th International Symposium in Economic Theory and Econometrics, edited by William Barnett et al. 1991.
Rosenberg, Nathan. Inside the Black Box: Technology and Economics. 1982.
World Bank. The Challenge of Development: World Development Report 1991.