Memorandum

Memorandum DATE: June 7, 1996

TO: SEAFERT TEAM

FROM: Charles Hirschman and Sara Curran

RE: Adjusting Fertility

Notes on the Adjustment of Children Ever Born Data to Include Infant Deaths

Background

The dependent variable is the number of births that occurred in the 36 months prior to the interview in the census. This is measured by the number of "own children" ages 0,1,2 of women who survived to the date of the census. This variable is adjusted to include a correction for the number of unmatched children by multiplying each woman's "own children" by the 1 plus the ratio of (total children)/(matched children) for each year.

Next, we wish to adjust the "own children" index of fertility to include an estimate of the number of births that did not survive to the date of the census. This is done in two steps: 1) estimate the number of births that did not survive to the census date for each province, and 2) distribute these "deaths" to women in each province who would be most likely to have experienced an infant death in the preceding 36 months.

Methods

1.Estimation of infant and child deaths in each province.

We want to estimate all births between 1978 and 1980 (B78-80). From the census data we know the number of children surviving until the census date, age 0,1,2 . This is defined as P0 + P1 + P2 = 3P0.

Using the Far Eastern Model Life Table from: Model Life Tables for Developing Countries by the United Nations, p. 257 and also attached to this memo we will choose:

l0 - radix of life table = 100,000

L0 - mid year population at age 0 = .3 l0 + .7 l1

1L1 - midyear population at age 1 = .4 l1 + .6 l2

1L2 - midyear population at age 2 = .5 l2 + .5 l3

The ratios for these equations are from Barclay, George W. 1958 Techniques of Population Analysis ( New York, NY: John Wiley and Sons). See attached for a copy of the pages from that volume used as a reference.

For each province we:

a) pick the model life table with the 1q0 closest to the infant mortality rate for that province.

b)solve for L0, L1, L2

c) compute: 1. B78-80 = l0 /(L0+ L1+ L2) * 3P0

2. Infant deaths, 3d0 = B78-80 - 3P0

2. Allocation of infant deaths in each province to individual women

For each province:

Wd= women who have a non-surviving child

Wt=all women in sample

B78-80 = total births in province

3d0 = infant deaths in province

3P0 = surviving children in province

For each province and for each woman in the population with an infant death (CD>0):

bir3= bir2 *(1+ 3d0/ Wd)

For all other women,

bir3=bir2

Comments:

By adjusting proportionately to the number of births in the last three years we have widened the absolute differences in fertility. This adjustment will serve to increase the variation across provinces in fertility rates. Some caution should be used in interpreting results from the multilevel analytic models. Significant provincial level coefficients may be the result of explaining infant mortality or whether or not a woman has experienced a child death rather than fertility.

Other references:

Cho, Lee Jay. 1973. "The Own-Children Approach to Fertility Estimation: An Elaboration." International Union for the Scientific Study of Population, International Population Conference, Lige Vol. 2

location of files:

this memo:

I:\user\seafert\thailand\memos\fert.mmo

excel files used to calculate IMR adjustment:

I:\user\seafert\thailand\papers\fert7859\fert03.xls

I:\user\seafert\thailand\papers\fert7859\imr.xls

program files used to calculate the number women and the number of births at each by province

csde unix /csde/seafert/thai/papers/fert789/women.sps

csde unix /csde/seafert/thai/papers/fert789/fert03.sps

resulting spss data files as zipped portable files (changed 9/4/01, PJG):

csde unix /csde/seafert/thai/papers/fert789/fert03_70

csde unix /csde/seafert/thai/papers/fert789/fert03_80