Interesting enigmas in the demography of fertility: examples from Switzerland

1. Interesting enigmas in the demography of fertility: examples from Switzerland Dr Marion Burkimsher Affiliated to the University of Lausanne and the University of Geneva

2. Glaciology Demography Snow Births Immigr-ation Emigr-ation Glacier Population Meltwater Deaths Sublimin-ation

3. 3 puzzles • If an average woman in Switzerland goes through her full reproductive life when the average fertility rate (TFR) is 1.5, how does she end up with an average of 1.7 children? • How can it be that the TFR of foreigners is higher that that of the native Swiss, yet they have smaller families? • If spacing between children has remained constant, how is it that the difference in mean age of successive birth orders has declined?

4. 3 puzzles • If an average woman in Switzerland goes through her full reproductive life when the average fertility rate (TFR) is 1.5, how does she end up with an average of 1.7 children? • How can it be that the TFR of foreigners is higher that that of the native Swiss, yet they have smaller families? • If spacing between children has remained constant, how is it that the difference in mean age of successive birth orders has declined?

5. What is the TFR? • “The average number of children a women would have assuming that current age-specific birth rates remain constant throughout her childbearing years” Population Reference Bureau

6. In the 2000 Swiss census, each person was asked how many children they had had. • For women born in 1960 - who were, therefore, aged 40, and so approaching the end of their childbearing years - the mean number of children they had had was 1.71 • But the mean TFR for the period 1980-1999 was 1.53! • Why the big difference between 1.53 and 1.71?

7. Possible reasons for mismatch between • period fertility rates and cohort fertility rates • Data errors: • Birth registrations • Population totals by age • “Sampling” errors in the census • Change in population between years of birth and census • Differential mortality • Immigration and emigration • Postponement of childbearing

8. Trends in fertility rates

9. Age-specific fertility rates, birth order 1 1966 cohort (partial) and 1996 period rates highlighted

10. Fertility curves for 1st births Age-specific fertility rates, birth order 1 CTFR1 = 0.80 TFR1 = 0.71

11. Fertility curves for 1st births Age-specific fertility rates, birth order 1 CTFR1 = 0.83 TFR1 = 0.73

12. Trend in mean age at 1st birth1969-2015

13. Bongaarts-Feeney correction Tempo-adjusted TFR, TFR*, takes into account the change in age at childbearing: TFR* = Raw TFR (1-rp) where rpdenotes the rate of change in the period mean age at childbearing in year t. Gives an indication of underlying cohort fertility rates. Needs to be applied to each birth order separately because each birth order may be affected by postponement at different times and to differing degrees! Used a 5 year moving average of delays for each birth order

14. Trends in TFR and children/mother 1969-2015

15. Why the difference between the period TFR and cohort TFR? • Because of postponement a month’s worth of babies are delayed and moved into the following year’s births and are ‘missing’ in that year’s birth statistics, and this is ongoing. • As a woman goes through her reproductive life, the ‘norms’ of childbearing (and age-specific fertility rates) are constantly changing. In her 20s then there was a higher likelihood of her having a child at that age than there is today. But now there is a higher likelihood of having a birth in her 30s than there was when she first entered her reproductive life. • The cohort curve is wider than the period fertility curve because of this effect.

16. What is the TFR? • “The average number of children a women would have assuming that current age-specific birth rates remain constant throughout her childbearing years” Population Reference Bureau • But they don’t!!!

17. 3 puzzles • If an average woman in Switzerland goes through her full reproductive life when the average fertility rate (TFR) is 1.5, how does she end up with an average of 1.7 children? • Answer: Because of postponement, cohort fertility rates are greater than period rates • How can it be that the TFR of foreigners is higher that that of the native Swiss, yet they have smaller families? • If spacing between children has remained constant, how is it that the difference in mean age of successive birth orders has declined?

18. 3 puzzles • If an average woman in Switzerland goes through her full reproductive life when the average fertility rate (TFR) is 1.5, how does she end up with an average of 1.7 children? • How can it be that the TFR of foreigners is higher that that of the native Swiss, yet they have smaller families? • If spacing between children has remained constant, how is it that the difference in mean age of successive birth orders has declined?

19. TFR of foreign women and Swiss women 1971-2015 Swiss Federal Statistical Office

20. Average number of children per woman Proportion childless Average number of children per mother

21. Defining the discrepancy • If the TFR of foreigners is higher than for Swiss women, how is it they have (seem to have) smaller families? • Is it a mismatch (or errors) of data? • Are there selection effects of who immigrates, who stays, who emigrates, who becomes naturalised? • Is it another example of the fundamental difference between period and cohort fertility? • Can both statistics be logically reconciled?

22. What is the TFR? • “The average number of children a women would have assuming that current age-specific birth rates remain constant throughout her childbearing years” Population Reference Bureau • In reality it is a measure of the intensity of childbearing amongst a specific population of women living in a specific place in a given year • -> How does an influx of young adults affect the TFR? • -> What about the changing denominator of the ASFR calculations?

23. Female population by age, Switzerland 2015

25. Foreign women by age 2000-2014

26. The Big Question • Can we ‘correct’ the raw TFR of foreigners to more accurately forecast their cohort TFR? • Yes….? • If we use as the denominator in the ASFR calculations the maximum foreign population(for all ages up to the age at which there is the maximum foreign population) • This, in effect, includes in the calculation women who have not yet arrived in the country, but are going to do so. They are currently childless and living in another country, but we are forecasting, going on current trends, that they will arrive in the coming years

27. Calculation of TFR1 using estimated maximum population (2014 data) • TFR1 raw: 0.9989 • TFR1 using max. pop. 0.7929

28. Fertility curves TFR1 2014 TFR1 Swiss = 0.6713 Foreign (raw) = 0.9989 Foreign (corrected) = 0.7929

29. There is a different distortion happening to Swiss fertility rates • Postponement deflates the period TFR with respect to • cohort fertility • This can be corrected by the Bongaarts-Feeney method

30. Total fertility rates of foreign and Swiss women after applying corrections Just mothers 2.08 1.97 1.58 1.56 All women

31. Conclusions • TFR1 is higher for immigrants than Swiss nationals – lower incidence of childlessness • But parity progression rates are lower for foreigners than Swiss • Hence, Swiss nationals who have at least one child have bigger families on average than foreigners • Corrected TFR for both Swiss and foreign women is now very similar and close to 1.57 • …

32. …conclusions • Foreigner fertility rates are distorted (too high) because too low a population estimate is used as the denominator for ASFR calculations • Can correct for this (approximately) • Swiss native fertility rates are distorted (too low) because of ongoing postponement • Can correct for this • Swiss native fertility rates could also be distorted (too low) by Swiss women emigrating and having their children elsewhere. They are included in the denominator for the early part of their reproductive life but have then ‘disappeared’ when they actually have children • => Impossible to correct for this?

33. Implications for other countries • Countries with high net immigration are likely to see a boost to their period fertility rates (assuming most women arrive in the country in their 20s and are childless) • Countries with net emigration of young women – are also likely to have their fertility rates distorted. The women who leave the country are included in the denominator of the TFR calculation before they emigrate. That depresses the TFR. A ‘correction’ could be made by using the minimum population to calculate the ASFRs

34. 3 puzzles • If an average woman in Switzerland goes through her full reproductive life when the average fertility rate (TFR) is 1.5, how does she end up with an average of 1.7 children? • How can it be that the TFR of foreigners is higher that that of the native Swiss, yet they have smaller families? Answer: TFR is a period measure; family size is a cohort measure • If spacing between children has remained constant, how is it that the difference in mean age of successive birth orders has declined?

35. 3 puzzles • If an average woman in Switzerland goes through her full reproductive life when the average fertility rate (TFR) is 1.5, how does she end up with an average of 1.7 children? • How can it be that the TFR of foreigners is higher that that of the native Swiss, yet they have smaller families? • If spacing between children has remained constant, how is it that the difference in mean age of successive birth orders has declined?

36. Assertion Spacing≠ difference in mean age of successive birth orders (Age at birth childx+1 – Age at birth childx) ≠ (MABx+1– MABx) This is counter-intuitive!

37. What is birth spacing? • The mean gap between births of successive children • It is, by definition, a cohort measure • It is a very skewed distribution: mode<median<mean • In Switzerland the mode is almost always a 2 year gap, median is higher and mean spacing higher still • The likelihood of progressing on to a further child has changed much more than the interval between births

38. Probability distribution of 2nd child after 1stby period when 1st child born Life table analysis, Swiss census 2000

39. Probability distribution of 3rd child after 2nd by period when 2nd child born Life table analysis, Swiss census 2000

40. Probability distribution of 4th child after 3rdby period when 3rd child born Life table analysis, Swiss census 2000

41. Summary on spacing • Very small variations in birth spacing over time • No trend towards wider or narrower birth spacing

42. Mean age of mother at 1st, 2nd, 3rd, 4th birth • This can be calculated from birth registration records: period measure • Can calculate the difference between mean age at 1st birth and mean age at 2nd birth, etc. (MAB2-MAB1….)

43. Mean age at 1st, 2nd, 3rd and 4th births (MAB4-MAB3) (MAB3-MAB2) 1969-2015 Increase in MAB1: 5.6 years Increase in MAB2: 4.5 years Increase in MAB3: 3.0 years Increase in MAB4: 2.0 years (MAB2-MAB1) Swiss birth registration (BEVNAT)

44. Difference in mean age of successive birth orders Swiss birth registration (BEVNAT)

45. Standard deviation in mean age at 1st, 2nd, 3rd, 4th births Increases 1980-2008 Stddev MAB1: 0.8 Stddev MAB2: 0.5 Stddev MAB3: 0.2 Stddev MAB4: 0 Swiss birth registration (BEVNAT)

46. Summary of empirical observations • From 1950s-1990s (using census 2000 data): • Spacing between all births has stayed ~constant • Median spacing between births ~3 yrs (mode=2yrs) • From 1969 to 2015 (using birth registration data) • (MAB2-MAB1) declined from 3yrs to 2 yrs • (MAB3-MAB2) declined from 2.8 to 1.2 yrs • (MAB4-MAB3) declined from 2.4 to 1.2 yrs • How to reconcile these 2 sets of observations…?

47. Scenario 1: 4 women, having 1, 2, 3 and 4 children respectively ~1969 28 31 34 25 Age Mean age at 1st birth: 25 Stddev 0Mean age at 2nd birth: 28 Stddev 0 Mean age at 3rd birth: 31 Stddev 0 Mean age at 4th birth: 34 Mean spacing between all birth orders: 3 years Mean age at last birth: 29.5 (MAB4-MAB3) = (MAB3-MAB2) = (MAB2-MAB1) = 3yrs

48. Scenario 2: 4 women, having 1, 2, 3 and 4 children respectively ~2015 35 32 26 29 Age Mean age at 1st birth: 30.5 Stddev 3.9Mean age at 2nd birth: 32 Stddev 3.0Mean age at 3rd birth: 33.5 Stddev 2.1Mean age at 4th birth: 35 Mean spacing between all birth orders: 3 years Mean age at last birth: 35 (MAB4-MAB3) = (MAB3-MAB2) = (MAB2-MAB1) = 1.5yrs

49. Why the difference between spacing and ΔMABx? • Because they relate to different subsets of women! • Women who start their family younger in life have a greater likelihood of having a larger family, and v.v. • Why the trends in ΔMABx post-1969? • ‘All’ women used to have their 1st child around the same age: since 1970 there has been a divergence of behaviour • Transition from Scenario 1 to Scenario 2

50. 3 puzzles • If an average woman in Switzerland goes through her full reproductive life when the average fertility rate (TFR) is 1.5, how does she end up with an average of 1.7 children? • How can it be that the TFR of foreigners is higher that that of the native Swiss, yet they have smaller families? • If spacing between children has remained constant, how is it that the difference in mean age of successive birth orders has declined?Answer: spacing is a cohort measure; mean age at each birth order is a period measure