1. Old Insights and New Approaches: Fertility Analysis and Tempo Adjustment
Hans-Peter Kohler

2. Birth rates Crude birth rate (CBR) = …
General fertility rate (GFR) = … CBR = GFR * 35C15F where 35C15F is proportion of PYL in pop by females 15 to 50 years old
Age-specific fertility rates = …
TFR, GRR, NRR
Decomposition of birth rates (CBR, TFR, etc)
Births as “repeatable events”
Period vs cohort fertility
Parity, birth order and fertility rates

3. Cohort Fertility

4. A demographer’s “problem”

5. Tempo effects are not connected to behavior
Why adjust for tempo?
Individual Fertility:
How many?
When?
Observed Fertility:
Influence of the number of women in age-parity categories
Tempo effects
Tempo effects are not connected to behavior

6. Ryder (1980): The fundamental flaw in research based on the period mode of temporal aggregation is simply that changes in cohort tempo are manifested as changes in period quantum

10. Bongaarts-Feeney adjustment
TFR = (1 – r) TFR*

15. Problems interpretation of adjusted TFR
inconsistent treatment of parity
not a “pure” period measure
biases in the inference of tempo changes

16. Tempo Adjustment TFR based Fertility Intensity based
adjusted TFR: “Total Fertility that would have been observed in a given year had there been no change in the timing of births during that year” (BF)
Problems:
Shape of fertility schedule (KP)
Use of rates of the second kind: Affected by parity composition (KO)
potentially erroneous inference of tempo changes
Fertility Intensity based
Not affected by compositional changes.
Allows mean and variance changes
Parity Progression Rates can be computed with a clearer interpretation in terms of cohort fertility
Can it be used for projections of cohort fertility when childbearing is delayed

17. Childbearing intensities versus incidence rates
fj(a): incidence rates (rates of the second kind)
mj(a): childbearing intensities (rates of the first kind or occurrence-exposure rates)
Bj(a) and Ej(a): births to and exposure of women at parity j

18. Adjusted period fertility rates
BF-adj. incidence rates:
KO-adj. childbearing intensities:
KO-adj. incidence rates:
tempo change rj(a) is calculated from mean and variance of the incidence rate or intensity schedule
same tempo effect at all ages (as in BF)
allow for variance effects (as in KP): tempo change depends on age

19. Intensities vs. incidence rates, Italy 1995

20. Mean and variance changes, 1995

21. Life-Table Measures of Fertility
Goal:
describe fertility behavior of a synthetic cohort
pure period measure
eliminate tempo effects
avoid influences of past fertility behaviors that affect period parity distribution
building block for further analyses, including
cohort completion
forecasting
Fertility Tables
columns for (1) parity distribution, (2) births by parity, (3) age-specific parity progression probabilities

22. Fertility Measures
parity distribution at age a: Dj(a), for parity j = 0, 1, 2, …, J
conditional parity progression probability:
between age a and a+1:
between age a0 and a1:
recursion for births and parity distribution:

23. Fertility Measures, cont’d
births between age a0 and a1 of order j1+1 to j2+1:
period fertility index (PF):
equal to the total fertility in synthetic cohort that experiences tempo-adjusted period childbearing intensities
free of tempo and distributional distortions
measure of period quantum

24. Fertility Table, Italy 1995

25. Parity Distribution in Synthetic Cohort Italy and Czech Republic 1995

26. Period Fertility Analysis
separate factors contributing to the number of births in a calendar year
age composition
parity distribution
tempo effects
quantum of fertility
total fertility rate:

27. Building Blocks for Period Fertility Analysis
KO-adjusted TFR:
mean tempo effect:
parity distribution effect:
quantum of fertility:
mean generation size Gt

28. Decompositions of Period Fertility
Total fertility rate
Number of births in a calendar year

29. Application to Italy and Czech Republic

31. Brazil: TFR and Mean Age at Birth

33. Cohort Completion: Bridging the Gap between Period and Cohort Fertility
utilize past cohort fertility as “starting point”
utilize recent period fertility to predict remaining cohort fertility
predict future period and cohort fertility patterns
use age-parity model to calculate future quantum and tempo
postponement stops scenario
postponement continues
can obtain predictions of all future period measures
obtain predictions of cohort fertility pattern

34. Postponement stops scenario
Remove tempo distortions at time T and calculate
tempo-adjusted period fertility measures

35. Postponement continues scenario
Reference year T
Slope is
mean change
Assume future postponement with
mean change gjs and variance change djs
Remove tempo distortions in T
using mean change gj(T) and variance change dj(T)

36. Cohort completion, Italy after 1996

37. Cohort completion, Czech R. after 1996

38. Brazil after 2010

40. R Scripts
## calculate adjusted TFR br.data <- ko.add.tfr.adjustment(br.data) ## TFR decompososition br.tfr.decomp <- ko.tfr.decomp(br.data) ko.plot.adj.tfr.comp.1(br.data,br.ppr.comparison,key.pos=c(1982,.8)) ko.plot.adj.tfr.comp.all(br.data,br.ppr.comparison,key.pos=c(1990,3.7))

41. Conclusions
integration of various fertility measures, all based on a common age-parity model, with
tempo-adjustment
life-table measures of fertility
methods for cohort completion/projection
if available, use of childbearing intensities (occurrence-exposure rates) is preferable
decomposition of period fertility influences in
period quantum
parity distribution effect
mean tempo effect
versatile “tool-kit” for period fertility analyses and projection