APPENDIX C REFERENCES

1. Ritchie Reed and Susan McIntosh, "Costs of Children" (paper prepared for the Commission on Population Growth and the American Future, 1972). The basic source of the data underlying the calculations in this paper are the U.S. Department of Agriculture, 1960-61 Consumer Expenditure Surveys.

2. See Glen G. Cain, "Issues in the Economics of a Population Policy for the United States," Discussion Paper 88-71 (Madison, Wisc.: Institute for Research on Poverty, University of Wisconsin, 1971), Appendix. (The paper, without the appendix, is published in American Economic Review, May 1971.)

3. Sara A. Sohn, "The Cost of Raising a Child” (Institute of Life Insurance, Division of Research and Statistics, 1970, mimeographed). This report draws on six budget studies using data from U.S. Department of Labor, "Three Budgets for an Urban Family of Four Persons-Preliminary Spring 1969 Cost Estimates," 1969; Community Council of Greater New York, Annual Price Survey-Family Budget Costs, October 1968; U.S. Bureau of Labor Statistics, Consumer Expenditure Survey: 1960-61, Report 237-38, Supplement 3, Part A, 1964; and U.S. Department of Agriculture, Agricultural Research Service, "Cost of Raising a Child" (speech given by Jean L. Pennock at the 47th Annual Agricultural Outlook Conference, Washington, D.C., February 18, 1970).

4. U.S. Bureau of the Census, Current Population Reports, Series P-60, No. 75, December 14, 1970.

5. William G. Bowen and T. A. Finegan, The Economics of Labor Force Participation (Princeton: Princeton University Press, 1968).

6. Ibid., p. 101.

7. Ibid., p. 102 (table).

8. Ibid., p. 676.

9. Ibid., p. 682.

APPENDIX D

The Relation Between a Decrease in the Age of Childbearing and the Rate of Population Growth

A decrease in the ages at which women have children (parity progression), whether stemming from a decrease in age at marriage or just a more rapid bunching of childbearing in the years after marriage, has several separable effects on population growth. For convenience, I will refer here to the whole range of possibilities of changes in the age at marriage and in parity progression by the single expression, mean age of childbearing.

For a given intended or desired number of children, the speedup in timing will leave more years of risk from the time of the birth of the last child to menopause. With existing historical data it is difficult to tell when a higher (lower) level of cohort fertility was causally related to an earlier (later) marriage age (or other sources of a lowering (raising) of the mean age of childbearing) from situations in which other factors were causal to both phenomena. If, for example, an economic depression led to a decline in desired family size and a postponement of marriage, it would be misleading to interpret the latter event as causal to the lower actual completed family size. We can say, with some certainty, that the causal connection between the mean age of childbearing and total number of children born has been, and will be, weakened by advances in birth control. Indeed, the advent of "perfect contraception" would eliminate the causal connection between the age at marriage and completed family size.

A decline in mean age of marriage will show up in an increase in period fertility rates. This can be easily seen if we imagine that, in any given year, the cohort about to commence marriage and childbearing were to decrease by one year its mean age of childbearing (that is, each child in the parity progression is born when the wife is one year younger than the prevailing age fertility pattern). We assume that no change in completed family size is desired or achieved-only in the timing. All births from the previous cohort of wives will be doubled up with those of the current cohort, and in year t the birth rate will rise. This will be offset by decline in year t + 1, since all that has happened is a change in timing of the same (by assumption) number of births per woman. This change in mean age of childbearing will, however, affect both the rate of population growth and the amount of population growth; but these effects will be relatively minor, as shown below.

Consider first the effect on the stable (or intrinsic or Lotka) growth rate of the population. It is this rate

(whether actually stable or stable in some reasonable "average" sense) that gives rise to the possibilities of geometric and even astronomical growths of population, so it may be considered most critical for the determination of population size. A decline in the mean age of childbearing will affect the stable growth rate, r, of the population as revealed by the following formula:1

where

T

n

q

= the length of a generation (~≈ the mean age of childbearing)

= the number of years by which T changes

= the proportion of women surviving from age T to T + n.

Some plausible values for the terms are: that q equals 1, since death rates for women in the childbearing years are negligibly different from zero; n equals -3 years (a quite sizeable decrease, so the effects reported are probably overstated); T equals 31 (its approximate value in 1964 in the U.S.). For given values of r, we find the change in r.

a society like the modern-day United States. Decisions about the timing of marriage and of the first and second births after marriage may have some effect on completed cohort family size. If these events take place earlier in the life cycle then, depending on the rate of contraceptive failures in the additional years of exposure, the long-run growth rate will be higher because of larger completed family sizes. A change in the mean age of childbearing, by itself, would have to be fairly large, say more than three years, to have a large effect on the rate of population growth in the United States.

REFERENCE

APPENDIX D

1. Taken from A. J. Coale and C. Y. Tye, "The Significance of Age-Patterns of Fertility in High Fertility Populations," Milbank Memorial Fund Quarterly, October 1961, pp. 631-646.

(*Approximate values of r for the current U.S. population.)

These may be judged rather small increases, and it was the judgment of Coale and Nye that the effects of a change in T on low mortality/low fertility populations would be small.

A one-time or one-period increase in population stemming from the decline in mean age of childbearing, as illustrated above, will affect the long-run population size, although by a much smaller relative magnitude than in the short run. The long-run effect results in part from the small increase in r as noted above and in part from the new r operating on a larger base population in year t; thus, by the time year t + 1 arrives, the population will be larger by a factor of rt. It should be obvious that a given positive r will create a larger number n years hence if the base population is 101 instead of 100.

Thus, the main source of the effect of fertility increases on population growth are the increases with respect to completed cohort fertility. Timing decisions, per se, constitute a second-order effect in the context of

The Effect of Income Maintenance Laws on