Data and Programs used in ‘Variance Effects in the
Bongaarts-Feeney Formula,’ Demography, 38(1), 1-16
Hans-Peter Kohler* Dimiter Philipov†
February 21, 2001
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Abstract
Bongaarts and Feeney (1998) have recently proposed an adjusted total fertility rate
to disentangle tempo effects from changes in the quantum of fertility. We propose an
extension to the Bongaarts and Feeney formula that includes variance effects, i.e.,
changes in the variance of the fertility schedule over time. If these variance effects
are ignored, the mean age at birth and the adjusted total fertility rate are biased.
We provide approximations for these biases, and we extend the TFR adjustment to
fertility schedules with changing variance. We apply our method to the Swedish baby
boom and bust and show that variance effects are important for evaluating the relative
contributions of tempo and quantum effects to the fertility change from 1985 to 1995.
Back to [ Hans-Peter Kohler] [ Data and Programs]
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Below we provide the data and programs used in Kohler and Philipov (2001), henceforth KP, for
the calculation of Variance Effects in the Bongaarts-Feeney Formula subject to our disclaimer.
All calculations are preformed using S-plus version 4.0 / 4.5 and the respective steps to
reproduce our results are given below. (The files listed below are also available in a single zip
file)
The data for Sweden were obtained from the Eurostat (1998) New Cronos database. The
age-specific fertility rates are calculated from the number of births by order and age of mother
and the mid-year population in the respective years. The files se-nfx-1.txt, se-nfx-2.txt,
se-nfx-3.txt, se-nfx-4.txt and se-nfx-all.txt contain the respective age-and-parity specific
fertility rates for first, second, third, 4+, and all births.
The following commands read these files into S-plus and define some auxiliary objects (alternatively
to typing these commands, you can source the script file bfvariance-dataread.ssc).
# determine year and age range of the data
se.yrs_ 75:96
se.age_ 15:49
# read in the age-specific fertility rates obtained
# from the New Cronos (1998) database
se.nfx.1_as.matrix(read.table("se-nfx-1.txt",header = T, sep = "\t"))
se.nfx.2_as.matrix(read.table("se-nfx-2.txt",header = T, sep = "\t"))
se.nfx.3_as.matrix(read.table("se-nfx-3.txt",header = T, sep = "\t"))
se.nfx.4_as.matrix(read.table("se-nfx-4.txt",header = T, sep = "\t"))
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The script bfvariance-functions.ssc defines several functions that calculate the adjustment of
the total fertility rates according to Bongaarts and Feeney (1998), henceforth BF, and
additionally with the adjustment for variance effects provided in KP. These functions are loaded
into S-plus by sourcing the script bfvariance-functions.ssc as
source("bfvariance-functions.ssc", echo=T)
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The main functions defined in this script are
- F.bf.calc(nfx, age, years) which calculates the adjusted TFR with and without
variance effects for a single birth order on the basis of the age-specific fertility rates
(nfx) across the time and age range specified in age and years. The function returns
a list including the elements (all pertain to births of a given parity)
- $years: years for which calculations are performed
- $tfr: observed total fertility rate
- $tfr.s: observed total fertility rate (smoothed)
- $mab: observed mean age at birth
- $mab.s: observed mean age at birth (smoothed)
- $vab: observed variance of the fertility schedule
- $vab: observed variance of the fertility schedule (smoothed)
- $r.bf: tempo measure according to BF derived from difference in the observed
mean age at birth
- $tfr.adj.bf: adjusted TFR for a given parity according to BF
- $r.bf.biascorr: a one-step correction of the BF-tempo according to Result 11 in
KP
- $gamma: tempo measure g in KP derived from the mean age of the adjusted
fertility schedule
- $delta: variance effect measure d in KP derived from the change of the variance
of the fertility schedule
- $mab.adj.var: mean age at birth of the adjusted fertility schedule (corresponds
to
(t) in KP)
- $vab.adj.var: variance of the adjusted fertility schedule (corresponds to s2(t) in
KP)
- $tfr.adj.var: adjusted total fertility rate with variance effects for a given parity
according to KP
- F.allorder(nfx.tot, age, os.result) combines the order-specific results calculated by
F.bf.calc across different birth orders. The function takes as arguments a matrix with the
age-specific fertility rates of all orders (nfx.tot), the age-range (age) and a list os.result
with the order-specific results calculated by F.bf.calc (see below for an example how to
generate this list with the order-specific results). The function F.allorder returns a list
including the elements
- $years: years used for analysis
- $tfr: total fertility rates for all birth orders (not smoothed)
- $tfr.s: total fertility rates for all birth orders (smoothed)
- $mab: observed mean age at birth across all birth orders (not smoothed)
- $mab.s: observed mean age at birth across all birth orders (smoothed)
- $vab: observed variance of the fertility schedule across all birth orders (not
smoothed)
- $vab.s: observed variance of the fertility schedule across all birth orders
(smoothed)
- $tfr.adj.bf: adjusted TFR across all birth orders according to BF
- $tfr.adj.var: adjusted TFR across all birth orders with variance effects according
to KP
The parity-specific adjustment of the total fertility rates with and without variance effects is
then performed as
se.os.res <- list(
first.births = F.bf.calc(se.nfx.1,se.age,se.yrs),
second.births = F.bf.calc(se.nfx.2,se.age,se.yrs),
thrid.births = F.bf.calc(se.nfx.3,se.age,se.yrs),
fourth.births = F.bf.calc(se.nfx.4,se.age,se.yrs)
)
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where se.os.res is a list that contains the order-specific results produced by F.bf.calc in the
elements $first.births, $second.births, etc. These order-specific results are then combined across
all birth orders via
se.all.res <- F.allorder(se.nfx.all, se.age,se.os.res)
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Figures 1, 3 and 4 in KP are then generated by sourcing bfvariance-figures.ssc
as
source("bfvariance-functions.ssc", echo=T)
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and Figure 2 is generated by sourcing bfvariance-intuition.ssc as
source("bfvariance-intuition.ssc", echo=T)
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Back to [ Hans-Peter Kohler] [ Data and Programs]
References
Bongaarts, J. and G. Feeney (1998). On the quantum and tempo of fertility. Population
and Development Review 24(2), 271–291.
Eurostat (1998). New Cronos Database - Population and Social Conditions. Brussels:
Eurostat.
Kohler, H.-P. and D. Philipov (2001). Variance effects in the Bongaarts-Feeney formula.
Demography 38(1), 1–16.