Griffith Feeney's Demography Website

Time-plotting Children Ever Born Data for the United States

May 31, 2009

Table 1 shows mean children ever born for US native white women age 45 years and over for the censuses of 1910 and 1940-1980.

Table 1: Children Ever Born Data for Native White Women,
United States Censuses of 1910, 1940, 1950 1960, 1970 and 1980

Children ever born data for the United States

The 1980 values are from 1980 Census of Population, Volume 1, Characteristics of the Population, Chapter D, Detailed Population Characteristics, Part 1, United States Summary, table 270, page 1-104, top left; 1970 values from 1970 Census of Population, Subject Reports, Women by Number of Children Ever Born, table 4, page 14; 1960 values from U.S. Census of Population: 1960, Subject Reports, Women by Number of Children Ever Born, table 4, page 10; 1950 values from 1950 United States Census of Population, Special Report P-E, No. 56, Fertility, table 1, page 5C-17; 1940 and 1910 values from 16th Census of the United States: 1940, Population, Differential Fertility, 1940 and 1910, Fertility for States and Large Cities, table 3, page 13, for 1940, table 4, page 15-16, for 1910. The table above shows all available values five year age groups.

Time Plotting the 1970 Data

The first step in time-plotting the data is to calculate the time at which the mean children ever born value for the youngest age group is to be plotted. It will be assumed here that the mean age at child bearing is 30 years for all cohorts.

The women in the 45-49 age group are age 42.5 years, on the average, and these women reached the mean age at child bearing 12.5 years prior to the census. The census reference date is April 1, which corresponds to time 1970.25. Subtracting 12.5 from 1970.25 gives 1957.75. Rounding to one place after the decimal gives 1957.8. Plotting to a precision of tenths of a year is sufficient. Expressing times to tenths of a year makes it clear that the numbers refer to points in time rather than to calendar years.

Times for each older age group may be obtained by subtracting 5 years from the next younger age group. The calculation and its results are shown in the table at the top of the following page, followed by the time plot.

The plot shows a steady decline in completed fertility from 2.8 children per woman (c/w) in 1923 to 2.17 c/w in 1943, followed by a show and then rapid rise to 2.6 c/w in 1958. The slight acceleration in rate of decline after 1928 is plausible explained by the onset of the Great Depression. The rise following 1943 is of course the post-war baby boom.

Interestingly, the rates of decline and increase are similar: a decline of 0.40 c/w/decade from 1928 to 37 versus an increase of 0.42 c/w/decade from 1948 to 1958.

Table 2: Time-plot Data for the 1970 Census

Time plotting CEB data for the US

Figure 1: Time-plot of Children Ever Born Data, 1970 US Census

Time plot of 1970 CEB data for the US


How accurate a picture is this of total fertility in United states for the half century 1923-1958? Comparison with estimates based on civil registration is appropriate, but it must be recognized that estimating period from cohort statistics imposes a strong smoothing. The time-plotted series should be a sensible smoothing of the annual civil registration estimates, but these annual estimates may fluctuate widely about the time-plotted series.

Another approach to assessment is to compare time plots for multiple censuses. This has the advantage of being possible when accurate statistics from birth registration are not available (much of the world today and most of the world less than a century ago). Comparisons of series are also facilitated because all are period estimates based on cohort data. Comparison of time plots of children ever born data from multiple censuses is in fact one of the most effective ways of assessing the quality of children ever born data for older women. The reader is invited to make comparisons using the data shown above.


Feeney, Griffith. 2009. “Time-plotting Life Cycle Events.”