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OCR for page 40
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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.
Representative terms from entire chapter:
capita income
