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/ Will slower population growth lead to more capital per worker; thereby increasing per worker output and consumption? Production of economic goods and services requires the use of various factors in a technical process. One type of factor is physical capital,* including social infrastructure (roads, communications, dams), machinery, buildings, and inventories. Another factor is labor, and it is often important to distinguish between the number of workers and the characteristics that may affect the* usefulness in production, often referred to as 'human capital." When production processes exhibit constant returns to scale, in He sense that increasing all inputs by a given proportion increases total output in just that proportion, the average productivity of each worker depends on his or her human capital and the average amount of other factors with which he or she works, but not on the number of workers or the overall amount of any other factor. In this situation, when more of any single factor is used, total production increases but the average output per unit of Be increased factor declines, while the average productivity of all other factors increases. When the grown of the population and labor force is rapid, We grown of the stock of physical and human capital must be equally rapid if a decline in their average quantity per worker, known as "capital dilution," is not to occur. If, in the absence of technical change, capital stocks do not increase in proportion to We grown of the labor force, Men real wage rates will decline and per capita income growth may slow or reverse. Conversely, if capital accumulation outpaces the growth of the labor force, wages will *In this chapter, "physical capital" is sometimes abbreviated to "capital" when Mere is no possibility of confusion with human capital. 40

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WORKER OUTPUT AND CONSUMPTION 41 increase, and per capita income will also probably increase. However, if investment were too high, consumption might fall because of the high rate of saving required to maintain the level of capital per worker. Technological change may offset the effects of capital dilution; this possibility is discussed in the next section. For the present, however, the possibility of such offsetting change is ignored. It seems useful to put the role of physical capital accumulation in economic growth in perspective. Physical capital accumulation is sometimes viewed as the critical ingredient for growth, and it is the most easily quantifiable and analyzable of all sources of growth. But its contribution may be quite modest. Denison (1974), for example, found that capital accumulation accounted for only 15 percent of the growth in total income in the United States from lg29 to 1969 and only 11 percent of the growth in per capita income. While some of the balance can be explained by growth in other measured inputs, such as education, much of it (about one-half for total income and about four-f~fths for per capita income) remains unexplained and is attributed to such categories as growth in knowledge and returns to scale. Conditions in today's developing countries differ from the historical U.S. context, and Denison's analysis is not necessarily generalizable. However, it illustrates that one should not assume that physical capital accumulation is the principal source of economic growth. Simple algebra shows that if new workers are to have the same amount of physical capital to work with as those already in the labor force, then the net investment rate, s, must equal the rate of growth of the labor force, n, times the capitaVoutput ratio, e-that is, s = ne-which is typically about 3. If the net investment rate exceeds this amount, as it generally does, then the excess is available for increasing the amount of capital per worker ("capital deepening"), Hereby raising per capita output. The conceptually separable portion of investment going to meet He needs of new workers (ne) is sometimes called demographic investment, and it is one form of "capital widening" (World Bank, 19743. A stationary labor force would require no demographic investment; one growing at 3 percent annually would require (assuming a capitalloutput ratio of 3) demographic investment equal to about 9 percent of total annual output. Demographic investment generally forms a far higher proportion of total investment in developing counties than in developed counties because of Heir more rapid population growth rates and frequently lower rates of savings, although there is much intercount~y variation (World Bank, 1974~. If the net investment rate does not change, what is the effect of an increase in the rate of population grown? Initially, net savings would be inadequate to provide new workers with as much capital as existing workers had, so the average amount of capital per worker would fall, leading to

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42 POPUl~lON GROWN AND ECONOMIC DEVE=PME~ lower output and lower per cotta income. After a time, however, capital per worker would have fallen sufficiently low to be just sustained by the savings rate, given the growth in the labor force, and no further decline in income would occur. Thus, the population growth rate, acting through capital dilution, should have no further effect at all on the growth rate of per capita income, and any income growth will then depend solely on the rate of technological progress (Solow, 1956; Phelps, 1968~. To the extent that counties' economies resemble this theoretical concept, there is no reason to expect any correlation between the population growth rate and the rate of growth of per capita income across countries (Phelps, 1968~. Indeed, many empirical cross-national studies have confimned the absence of such a correlation (see Simon, 1977, for a review). The theory does not lead one to expect a negative effect of population growth rates on the rate of change of per capita income in the long run. However, if rates of net investment and technological progress are unchanged, it does suggest that more rapid population growth rates will lead to less capital per worker, thereby depressing Me level of per capita income. The magnitude of this effect can be easily calculated: per capita income in a population "Towing at 3 percent per year would be only 13 percent lower than in one growing at 1 percent per year. In both cases, per capita income would be growing at the rate of technological progress.* This calculation reflects the effect of capital dilution alone and is by no means intended to indicate even approximately the entire effect of population growth operating through all channels. So far, the rate of capital formation has been assumed to be constant or to be adjusted in some exogenous way when the population growth rate changes. But there are a number of reasons to expect that different demographic situations will themselves lead to changes in the rate of capital formation; some of these changes would be expected to exacerbate the problem of capital dilution rather Man mitigate it. Tithe calculations are based on results in Keeley (1976:25~5) and assume technological progress at 2 percent annually, depreciation at 3 percent annually, and a constant-retun~- Scale Cob~Douglas production function with a capital coefficient of 0.3 and a labor coefficient of 0.7, and a savings rate that is independent of the population growth rate. The economy takes 15 years to adjust halfway to Me new steady-state capital labor ratio following a change in the population growth rate. If instead of requiring the savings rate to be constant, one assumes it to be at the optimal level (i.e., to maximize consumption) for each population growth rate, the results would be unaltered in the Cobb Douglas case considered here, but more generally, the adverse effects of more rapid population growth would be mitigated. Technological change in this calculation was assumed to be labor augmenting; for the case of embodied capital-augmenting technical progress, see Phelps (1968.499).

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WORKER OUTPUT AND CONSUMP170N 43 It is sometimes argued that more rapid population growth and a younger age structure reduce investment in physical capital by diverting scarce funds to human capital expenditures, such as health and education expenditures, which are argued to have a more delayed effect and a lower rate of return (Coale and Hoover, 1958~. However, it is not clear that governments actually do devote a greater share of the* gross national product (GNP) to such expenditures in countries whose populations have younger age distributions or more rapid growth rates (see, e.g., Schultz, 1985~. But if one supposes that savings must be used to equip each new worker with both human and physical capital, then even if their rates of return were equal, the effects of population growth could be considerably stronger Han the calculation above suggests (Kuznets, 1967). For example, if capital, when broadly construed to include human as well as physical forms, is responsible for one-half rather than one-third of output, then the negative effects of population grown, operating through capital dilution, would be twice as large as in the above example. Domestic savings are an important source of funds for physical capital fonnation. It is often argued that higher fertility and younger age distributions in a population will increase consumption relative to savings, since each adult will have more children to support. A more sophisticated argument views savings and asset accumulation as a strategy for smoothing individual consumption over the life cycle, including old age, taking into account the greater need for total household consumption when children are present (Mason, 1985; Tobin, 1967~. This approach generates two opposite effects. On the positive side, more rapidly growing populations (if the difference is due to fertility) have a smaller proportion of older people who are dissevers relative to younger workers who are saving for retirement; therefore, such populations will generate positive net savings in the aggregate, even though He average individual dies without a penny. This positive effect of fertility on savings rates is called the rate-of-grow effect and occurs equally when per capita income is growing over time (Mason, l9SS). At He same time, higher fertility also has a negative effect, because having more children to support shifts the average timing of household consumption to an earlier age of the head of household and thereby postpones the timing of saving for retirement; it may even lead to a period of dissaving in He early to middle years of the household life cycle (Mason, 1985; Arthur and McNicoll, 1978~. Bow these effects are stronger when per capita income is increasing more rapidly. On the basis of theory alone, one cannot predict either a negative or a positive effect of fertility on the aggregate saving rate, although there are clearly good reasons to expect some effect. Differences in mortality also directly affect the population grown rate, but Hey have only weak effects

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44 POP Ul~lON GROWTH Ad ECONOMIC DEVELOPMENT on the age distribution. Nonetheless, the net effect of mortality and fertility changes on savings should be similar since lower mortality increases life- cycle saving for old age. These arguments concern the motivations for individual or household saving, but much saving is done by governments and corporations, which calls into question the relevance of household-level theories. To the extent that governments and corporations respond to the preferences of their citizens and stockholders, public and corporate savings will reflect the same demographic influences as do direct household savings. Households may also adjust their private savings to compensate for perceived over- or undersavings by governments or corporations; this possibility would lend further plausibility to the hypothesized links between household preferences and aggregate savings. But these assumptions about the behavior of governments, corporations, and households may not hold in all countries, developed or developing. There have been a number of empirical investigations of the effect of age composition, represented by ratios of dependent to working-age groups, on aggregate national savings rates. The first and best known was due to Left (1968), who used a cross-national data set and found that both child and old-age dependency ratios depressed savings rates. Subsequent research has questioned his results, win most commentators claiming Hat the effect was weaker or nonexistent, but some also claiming that the eject should actually be stronger (Mason, 1985~. In a more carefully derived model, Mason (1985) found negative effects of dependency on savings and positive effects of population growth rates on savings, with the net effect of higher fertility being positive when He growth rate of per capita income is zero and negative when it is as high as 4 percent, win a nonmonotonic relationship in the middle range. Hammer (1984) sees fertility and savings as being alternative forms of provision for old age in developing counties, with the development of financial institutions inducing a switch from fertilibr to savings; in dais case, high fertility would accompany low savings, but not cause it. There have also been a number of household-level studies. These tend to show either no effect of child dependency on savings or a negative effect, for both developed and developing countries (Mason, 1985). Some studies have found that children bow reduce the proportion of income saved and lead to an increase in household income, with He two effects offsetting each other so that household savings are substantially unaltered (Kelley, 1973~. In interpreting these household studies, it must be remembered that a change in fertility also alters the distribution of households by age of head, leading to effects that may tend to offset effects within households. A consensus view has not yet emerged from the aggregate and household-level research, and one might most safely say that research to date, while sometimes revealing

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WORKER OUTPUT AND CONSUMPT70N 45 negative effects of higher fertility and younger age distributions on saving rates, does not yet provide a compelling case for such a relationship. In addition to affecting the age distribution, changes in the population growth rate redistribute income between groups with different savings propensities. Population growth tends to raise returns to land and to capital, and recipients of such income are believed to be wealthier and to have higher savings rates than recipients of labor income. This tendency suggests that if slower population growth boosts wages and decreases rents and profits, the result may be a lower aggregate savings rate. In the preceding discussion, we have emphasized the savings rate as the chief determinant of investment. In theory, the amount of resources devoted to investment is jointly determined by the supply of savings (chiefly from households) and a demand for investment funds (chiefly by businesses). Current demand for investment funds is linked to the expected future profit rate, which is believed to be positively linked to the rate of growth of GNP. More rapid growth implies a greater fixture need for capital equipment and a business environment more conducive to experimentation with new techniques. If investors think that population growth promises GNP growth, investment demand will be stimulated. In turn, an increase in investment demand could raise the interest rate, possibly eliciting additional savings and thereby increasing the proportion of output devoted to investment. However, recent empirical work (based on aggregate savings rates in seven Asian countries over the period 19641980) suggests that the supply of savings is relatively insensitive to the interest rate (Giovannini, 1983), which in turn suggests that a change in investment demand would affect the interest rate but not He realized quantity of investment. In sum, the link between population growth and realized investment via increased demand for investment funds is hypothetical and tenuous. However, population grown may directly improve the average quality or effectiveness of the capital stock. Population growth could increase the rate of growth of the capital stock, decreasing its average age. If new technology is embodied in new capital, then capital may on average be somewhat more productive, partially offsetting the effects of capital dilution.* (Ihe issue of productivity gains from population-induced economies of scale is discussed under Question 5.) It should also be noted that domestic saving is not He sole source $The average age of capital stock, in a steady state, equals the inverse of the rate of population growth plus that of technology plus depreciation. If technological progress is 2 percent per year and depreciation is 3 percent, then with a population growth rate of 3 percent, the average age of capital would be 12.5 years; with 2 percent, it would be 14.3 years; and with 1 percent, it would be 16.7 years (Phelps, 1962).

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46 POPUI~ION GROWTH AND ECONOMIC DEVELOPMENT of domestic capital connation; international capital flows may also be an important source. Thus, at early stages of a country's development, when its capital endowment relative to labor is relatively small, it can borrow from abroad (or foreigners may invest in its economy) until the domestic rate of return to capital is equal to the foreign rate of return. Rapid population growth may encourage these inflows by boosting the domestic rate of return to capital, thus making investment more attractive. If a country's economy is large relative to that of the rest of We world, it cannot expect to lend or borrow any amount at an unchanging rate of interest; see Deardorff (1985) for a relevant analysis of this case. Whether the country can expect to raise its steady-state per capita consumption above its self-suff~cient level by recourse to foreign lending or borrowing will depend, among other things, on its rate of growth of population relative to that of the rest of the world. CONCLUSIONS Slower population growth can be expected to increase the ratio of capital to labor, which in turn will increase the level of per capita income. The fist link~etween population and the capitaVlabor ratio-has two components. First, holding constant the growth rate of investment in physical capital, theoretical arguments indicate that slower population grown will directly increase the capitalllabor ratio. Second, slower population growth could change the rate of saving and investment and thereby change the growth rate of physical capital. While the direction of this effect is indeterminate, there is no evidence to suggest that slower population grown would significantly decrease the savings rate, and some evidence actually suggests a positive effect. Thus we would expect slower population growth to have a net positive effect on the capital/labor ratio. An increase in this ratio, in turn, will increase the level of per capita output, though theory and limited empirical evidence suggest that this effect may be relatively modest. Thus, while capital deepening does appear, at least in theory, to be a genuine positive consequence of reduced population growth, such growth by no means appears to be a decisive influence.