University of Colorado March 3, 2015 Support for this research was provided by the U.S. National Institute of Child Health and Human Development. Family Size of Women and Children during the Demographic Transition David Lam University of Michigan Letícia Marteleto University of Texas

Family size and cohort size This paper is a sequel to previous papers looking at family size and cohort size during the demographic transition: David Lam and Letícia Marteleto, “Stages of the Demographic Transition from a Child’s Perspective: Family Size, Cohort Size, and Children’s Resources,” Population and Development Review, June 2008, 34(2): David Lam and Letícia Marteleto, “Small Families and Large Cohorts: The Impact of the Demographic Transition on Schooling in Brazil,” in The Changing Transitions to Adulthood in Developing Countries, National Academies Press, Washington, DC, 2006, pp We showed that family size declines while cohort size increases during a long period of the demographic transition – 20 to 30 years in most countries. During this period competition for resources within families is declining, while competition with cohort members is increasing.

David Lam and Letícia Marteleto, “Stages of the Demographic Transition from a Child’s Perspective: Family Size, Cohort Size, and Children’s Resources,” Population and Development Review, June 2008.

Purpose of this paper How are changes in the family size of children related to changes in fertility during the demographic transition? This is important if children are competing for resources with siblings. While it may seem obvious that children’s family size will fall when fertility declines, they do not need to fall at the same rate or even change in the same direction. We expand on Preston (1976) and study a large number of countries during the demographic transition. We also look at the inequality in family size, extending Preston’s results.

Distribution of family size for women Number of children surviving to women aged 45-49, Brazil 1960

Children’s family size as a function of women’s family size

Mean family size of women and children Number of children surviving to women aged 45-49, Brazil 1960

Sam Preston, Family Sizes of Children and Family Sizes of Women,” Demography 1976

Fertility can decline without a decrease in mean family size for children 50% of women have no children50% of women have 6 children Mean family size for women = 1/2*2 +1/2*6 = 4.0 Mean family size for children = 2/8*2 + 6/8*6= = % of women have 6 children50% of women have 2 children Mean family size for women = 1/2*0 +1/2*6 = 3.0 (decrease of 1) Mean family size for children = 6.0 (increase of 1) Case 2: After fertility decline Case 1: Before fertility decline

Implications of Preston’s result Mean children’s family size is always greater than mean women’s family size, as long as there is any variance in fertility Fertility decline and family size: –If CV goes up while mean fertility declines, children’s family size will decline more slowly than women’s family size Comparing subgroups: –If a group with higher fertility also has a higher CV, then the difference in family size of children will be larger than the difference in family size of women.

Preston’s analysis of U.S. data Preston found exactly these two patterns in historical U.S. data for women aged Women’s family size fell 54% from , but children’s family size fell only 37% Due to rising CV Nonwhite women had 19% higher family size than white women, but nonwhite children had 50% higher family size than white children Due to larger CV for nonwhites

Implications for family size during demographic transition “These patterns are a disconcerting precedent for those concerned with issues of population quality in less developed countries; the pace of reductions in family size for children can be expected to lag behind that for women in the process of fertility transition” (Preston 1976: 108). One purpose of this paper is to test this prediction across a wide range of countries.

We extend Preston’s results to look at the standard deviation of children’s family size

Number of children surviving to women aged 45-49, Brazil Distribution becomes more skewed as fertility declines

Surviving family size of children of women aged 45-49, Brazil This distribution also becomes more skewed as fertility declines, but is shifted to right compared to distribution for women.

Distribution of surviving family size for women aged and children of women aged 45-49, Brazil Note that bottom figure is a reweighted version of the top figure Women’s family size Children’s family size

Distribution of family size for women aged and children of women aged Thailand 1970 and 2000 Mean for women=6.53 Mean for children=8.21 (ratio 1.26) Mean for women=2.55 Mean for children=3.47 (ratio 1.36)

Empirical Analysis We use IPUMS-International census data and Demographic and Health Surveys We use 101 countries, 310 total data sets, including high-income countries with fertility data Scatterplots include both cross-sectional variation across countries and time series variation within countries We show estimates of OLS regression and Fixed Effect (FE) regression using only within-country variation over time.

Summary of datasets with children ever born variable

Coefficient of variation in women’s family size, by mean family size, children ever born to women aged Slope= (0.003) b(FE)= (0.005) N=310 (101 countries) CV rises as fertility falls

Coefficient of variation in women’s family size, by mean family size, children ever born to women aged Slope= (0.003) b(FE)= (0.005) N=310 (101 countries) CV rises as fertility falls

Skewness in women’s family size, by mean family size, children ever born to women aged Slope= (0.010) b(FE)= (0.017) Skewness is negative at high fertility levels, increases to highly positive at low fertility levels

Mean children’s family size by mean women’s family size, children ever born to women aged Slope=1.041 (0.017) b(FE)=1.191 (0.029)

Standard deviation in children’s family size, by mean number of children ever born to women aged Slope= (0.022) b(FE)= (0.036) Standard deviation of children’s family size rises slightly with falling fertility, in spite of the large decline in the mean

Multipliers for mean and standard deviation

Ratio of children’s mean family size to women’s mean family size, by mean family size of women aged 45-49, children ever born Slope= (0.004) b(FE)= (0.006) Preston was right that children’s family size falls more slowly than women’s family size South Africa 2007, 2001, 1996

Ratio of children’s mean family size to women’s mean family size, by mean family size of women aged 45-49, children ever born Mexico 1960 and China 1982 had similar fertility levels, but mean family size of children was 37% higher in Mexico (2.4 extra siblings)

Ratio of children’s mean family size to women’s mean family size, by mean family size of women aged 45-49, surviving children Slope= (0.006) b(FE)= (0.005) Pattern using surviving children is very similar to pattern using children ever born N=266 (87 countries)

Implications for children’s resources Suppose some fixed resource, like mother’s time, is divided by the number of children. Suppose women’s family size falls from 8 to 2. If children’s family size also fell to 1/4 its original size, then resources per child would go up 4 times. Alternatively, suppose the ratio of children’s family size to women’s size increases from 1.2 to 1.5 (children’s family size falls from 9.6 to 3.0). Resources per child increase by 3.2 times instead of 4 times. The increase is 20% smaller than it would have been if children’s family size had fallen as fast as women’s family size.

Ratio of children’s mean family size to women’s mean family size, by mean family size of women aged 45-49, children ever born Increase in ratio from 1.2 to 1.5 when fertility falls from 7 to 2. This implies a 20% smaller increase in resources per child than if ratio remained constant. (1.2/1.5=0.8)

“Leakage” in resources per child

“Leakage” in resources per child – Regression of log(k) on log(children ever born)

Family size of school-aged children The children of women aged are not necessarily an interesting group. –Many of them are not children –They span a large age range. We may be more interested in a particular age range of children, say school-age children. We will focus on children aged 10 (or 9-11). We show empirically that the following is a good approximation for describing the mean family size of ten-year old children:

Family size of school-aged children Calculate the family size of children aged 9-11: –Match them to their mothers in the censuses and DHS surveys –Take the number of surviving children of their mothers Generate the surviving family size of women using the same reweighting used above A comparison shows that these distributions are very similar in all countries. Children aged 9-11 are roughly representative of the children of women aged 25-49

Family size of children aged 9-11 and children of women aged 25-49, Brazil 1960

Mean family size of children aged 9-11 and children of women aged 25-49

Cumulative distribution of family size for women aged and children aged 9-11, Brazil, Ecuador, and Costa Rica Large families are much more common for children than for women.

In Brazil 80% of women aged had less than four surviving children in 2000; Only 58% of children were in families with less than four surviving children in 2000, similar to the proportion for women in 1960.

In Ecuador in 2001 only 3.2% of women were in a family with 8 or more children, but 10.6% of children were in a family with 8 or more surviving children.

Inequality in children’s family size Women’s standard deviation falls at slightly lower rate than the mean As a result, children’s mean falls at slightly lower rate than women’s mean But children’s standard deviation falls much more slowly – it tends to stay roughly constant due to increase in skewness in women’s family size These imply that the coefficient of variation in children’s family size must increase as mean family size declines In general there is a substantial increase in inequality in children’s family size as mean family size declines

Coefficient of variation of surviving family size of children by mean family size of women age Coefficient of Variation of children’s family size increases as fertility declines Slope= (0.005) b(FE)= (0.005)

Brazil: 90 th percentile fell from 9 to 7 from 1960 to th percentile fell from 2 to 1. So 90/10 ratio rose from 4.5 to 7 If there are fixed resources in families, the 10 th percentile child goes from getting 4.5 times as much as the 90 th percentile child to getting 7 times as much. This is in addition to inequality in the amount of the fixed resource between small and large families.

Ecuador: 80 th percentile fell from 8 to 6 from 1974 to th percentile fell from 4 to 2; 80/20 ratio rose from 2 to 3

90/10 and 80/20 ratios for children’s surviving family size, by mean family size of women Slope= (0.026) b(FE)= (0.030) Slope= (0.097) b(FE)= (0.082)

Conclusions Mean family size of children tends to fall more slowly than mean family size of women as fertility declines. The ratio of mean children’s family size to mean women’s family size rises from about 1.2 to 1.5 as fertility falls, the result of an increase in the coefficient of variation in women’s family size. There is roughly a 20% smaller increase in resources per child during the demographic transition than would be implied by fertility decline alone. Inequality in children’s family size tends to increase with the decline in fertility, the result of increasing skewness in women’s family size. The gap in resources per child between large and small families increases as fertility declines.