We all do a primitive form of growth accounting every time we talk about labo productivity; in so doing we are implicitly distinguishing between the part of overall national growth due to the growth in the supply of labor and the part due to an increase in the value of goods produced by the average worker. Increases in labor productivity, however, are not always caused by the increased efficiency of workers. labor is only one of a number of inputs, workers may produce more, not because they are better managed or have more technological knowledge but simply because they have better machinery a man with a bulldozer can dig a ditch faster than one with only a shovel, but he is not more efficient; he just has more capital to work with. The aim of growth accounting is to produce an index that combines all measurable inputs and to measure the rate of growth of national income relative to that index to estimate what is known as "total factor productivit So far this may seem like a purely academic exercise. As soon as one starts to think in terms of growth accounting, however, one arrives at a crucial insight about the process of economic growth: sustained growth in a nation s per capita income can only occur if there is a rise in output per unit of input 2 At first, creating an index of all inputs may seem like comparing apples and oranges, that is, trying to add together noncomparable items like the hours a worker puts in and the cost of the new machine he use How does one determine the weights for the different components? The economists answer is to use market returns. If the average worker earns $15 an hour, give each person-hour in the index a weight of $15; if a machine that costs $100,000 on average earns $10,000 in profits each year(a 10 percent rate of return), then give each such machine a weight of $10, 000; and so on 3 To see why, let's consider a hypothetical example. To keep matters simple, let's assume that the country has a stationary population and labor force, so that all increases in the investment in machinery, etc, raise the amount of capital per worker in the country. Let us finally make up some arbitrary numbers Specifically, let us assume that initially each worker is equipped with $10, 000 worth of equipment; that each worker produces goods and services worth $10,000, and that capital initially earns a 40 percent rate of return, that is, each $10,000 of machinery earns annual profits of $4, 000. Suppose, now, that this country consistently invests 20 percent of its output, that is, uses 20 percent of its income to add to its capital stock How rapidly will the economy grow? Initially, very fast indeed. In the first year, the capital stock per worker will rise by 20 percent of $10,000 that is, by $2,000. At a 40 percent rate of return, that will increase output by $800: an 8 percent rate of But this high rate of growth will not be sustainable. Consider the situation of the economy by the time that capital per worker has doubled to $20,000. First, output per worker will not have increased in the same proportion, because capital stock is only one input. Even with the additions to capital stock up to that point achieving a 40 percent rate of return, output per worker will have increased only to $14,000. And the rate of return is also certain to decline-say to 30 or even 25 percent. (One bulldozer added to a construction project can make a huge difference to productivity. By the time a dozen are on-site, one more may not make that much difference. The combination of those factors means that if the investment share of output is the same, the growth rate will sharply decline. Taking 20 percent of $14,000 gives us $2, 800; at a 30 percent rate of return, this will raise output by only $840, that is, generate a growth rate of only 6 percent; at a 25 percent rate of return it will generate a growth rate of only 5 percent. As capital continues to accumulate, the rate of return and hence the rate of growth will continue to decline4 We all do a primitive form of growth accounting every time we talk about labor productivity; in so doing we are implicitly distinguishing between the part of overall national growth due to the growth in the supply of labor and the part due to an increase in the value of goods produced by the average worker. Increases in labor productivity, however, are not always caused by the increased efficiency of workers. Labor is only one of a number of inputs; workers may produce more, not because they are better managed or have more technological knowledge, but simply because they have better machinery. A man with a bulldozer can dig a ditch faster than one with only a shovel, but he is not more efficient; he just has more capital to work with. The aim of growth accounting is to produce an index that combines all measurable inputs and to measure the rate of growth of national income relative to that index to estimate what is known as "total factor productivity."2 So far this may seem like a purely academic exercise. As soon as one starts to think in terms of growth accounting, however, one arrives at a crucial insight about the process of economic growth: sustained growth in a nation's per capita income can only occur if there is a rise in output per unit of input.3 2 At first, creating an index of all inputs may seem like comparing apples and oranges, that is, trying to add together noncomparable items like the hours a worker puts in and the cost of the new machine he uses. How does one determine the weights for the different components? The economists' answer is to use market returns. If the average worker earns $15 an hour, give each person-hour in the index a weight of $15; if a machine that costs $100,000 on average earns $10,000 in profits each year (a 10 percent rate of return), then give each such machine a weight of $10,000; and so on. 3 To see why, let's consider a hypothetical example. To keep matters simple, let's assume that the country has a stationary population and labor force, so that all increases in the investment in machinery, etc., raise the amount of capital per worker in the country. Let us finally make up some arbitrary numbers. Specifically, let us assume that initially each worker is equipped with $10,000 worth of equipment; that each worker produces goods and services worth $10,000; and that capital initially earns a 40 percent rate of return, that is, each $10,000 of machinery earns annual profits of $4,000. Suppose, now, that this country consistently invests 20 percent of its output, that is, uses 20 percent of its income to add to its capital stock. How rapidly will the economy grow? Initially, very fast indeed. In the first year, the capital stock per worker will rise by 20 percent of $10,000, that is, by $2,000. At a 40 percent rate of return, that will increase output by $800: an 8 percent rate of growth. But this high rate of growth will not be sustainable. Consider the situation of the economy by the time that capital per worker has doubled to $20,000. First, output per worker will not have increased in the same proportion, because capital stock is only one input. Even with the additions to capital stock up to that point achieving a 40 percent rate of return, output per worker will have increased only to $14,000. And the rate of return is also certain to decline-say to 30 or even 25 percent. (One bulldozer added to a construction project can make a huge difference to productivity. By the time a dozen are on-site, one more may not make that much difference.) The combination of those factors means that if the investment share of output is the same, the growth rate will sharply decline. Taking 20 percent of $14,000 gives us $2,800; at a 30 percent rate of return, this will raise output by only $840, that is, generate a growth rate of only 6 percent; at a 25 percent rate of return it will generate a growth rate of only 5 percent. As capital continues to accumulate, the rate of return and hence the rate of growth will continue to decline