“On the quantum and tempo of fertility.” Population and Development Review, 24(2), 271-291.

The main advantage of the period TFR is that it measures current age-specific fertility and therefore gives up-to-date information on levels and trends

-In addition, it is simple to interpret

Main disadvantage is that it doesn’t reflect the actual experience of any cohort of women

- Although the cohort TFR has the advantage of representing the actual fertility experience of a group of women, it has the disadvantage of representing past experience because women currently age 50 did most of their childbearing decades ago

The purpose of this paper is to develop a measure of the period TFR that is free of tempo effects (distortions due to changes in the timing of births)

- This will measure just the quantum component of the TFR (the TFR that would have been observed in the absence of changes in the timing of births)

- New measure called the tempo-adjusted tempo-adjusted TFR

- The main problem to be dealt with is that a decreasing mean age at childbearing artificially inflates the TFR, whereas an increasing mean age at childbearing automatically deflates the TFR

- Bongaarts and Feeney derive the tempo-adjusted TFR by dividing the observed TFR at parity i by (1-r_i) where r_i is the change in the mean age at childbearing at order i during the year

- The tempo-adjusted TFR (TFR*) simply equals the sum of the parity-specific TFRs

- If the mean age at childbearing increases by 0.2 years, the number of births in year t will be 20% lower than they would have been in the absence of this change

- Likewise, if the mean age at childbearing decreases by 0.2 years, the number of births will by 20% higher

- It is easy to distinguish between tempo and quantum effects because tempo effects involve a change in the mean age at childbearing whereas quantum effects do not

Advantages of this method

- Only need data from one period

Challenges of method

- Need to be able to discern birth parity

Assumptions of this method

- Women of all ages bearing children in year t defer or advance their births to the same extent, regardless of age or cohort identification

- This assumption is likely violated during periods of war, famine, etc. when fertility changes rapidly from one year to the next and cohort effects are not negligible

In other words, period effects, rather than cohort effects, are the primary force in fertility change

Coale and Trussel (1974; 1978) model of marital fertility

- The Coale and Trussel model expresses marital fertility at age ‘a’ r(a) as a function of:

M, the ratio of actual marital fertility at age ‘a’ r(a) to expected marital fertility at age ‘a’ in the absence of parity-related limitations n(a), and

m, a measure of the extent to which parity-related limitation affects age-specific marital fertility rates

- Lower values of m indicate less of an effect of parity-specific measures on the reduction of marital fertility, whereas higher values of M indicate less of an effect of parity-specific measures on reduction of marital fertility

“Model fertility schedules: Variations in the age structure of childbearing in human populations.” Population Index, 40(2), 185-258.

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Coale-Trussell Model of Fertility

- Coale and Trussell aim to examine the nature of the roots of a set of fertility functions expressing the full variety of fertility experience found in large human populations, and attempt to create a family of model fertility schedules encompassing the full range of human experience

- Express fertility as a function of the proportion married at each age and the age specific fertility rates within marriage

f(a) = G(a) * r(a)

- Multiplying together these two model subschedules (proportions even married at each age and proportion of married women at each age experiencing a live birth) should result in the age specific fertility rate

2 parameters necessary to calculate the age structure of the proportion ever married (ie, the G(a) function)

1. These are the age of initiation of first marriage and

2, The pace of first marriage relative to a standard (in this case, nineteenth century Sweden)

- The ultimate proportion ever married is important for determining the level, but not the age pattern, of nuptiality

- The ratio of observed marital fertility to natural fertility is a function of this ratio at one particular age (M) (Coale and Trussell recommend using the age group 20-24) and a scalar that expresses contraceptive prevalence (or the difference between observed and natural fertility) at each age (m)

 In other words:

r(a) / n(a) = Mexp(m*v(a))

- v(a), like n(a) is observed empirically, and expresses the tendency for older women in populations using contraception to effect particularly large reductions in fertility

The age pattern of fertility is therefore given by the following equation

                       f(a) = G(a)*n(a)*e^m*v(a)

Coale and Trussell also argue that these models can account for fertility outside of marriage, by simply adjusting the parameters to account for an earlier age of onset of sexual activity or additional contraceptive prevalence at ages with high rates of divorce

 “The Decline of Fertility in Europe since the Eighteenth Century as a Chapter in Demographic History.” In The Decline of Fertility in Europe.  Edited by Ansley J. Coale and Susan Cotts Watkins.  Guildford, Surrey: Princeton University Press.  Ch. 1.

Summary of the historical context of fertility decline that prompted the Princeton Fertility Project

- For the majority of human history, growth rates were near zero

- Since 1750, growth rates have increased dramatically; only since about 1970 have the begun decelerating

- Coale believes that various homeostatic mechanisms have kept birth rates roughly in line with death rates throughout human history

- Malthus proposed various positive checks to population growth, such as more contagion, more contamination, and less adequate nutrition

- Although some demographers have postulated that pre-transition fertility rates must have been quite high to offset death rates, Coale finds that fertility rates at this time were actually quite moderate (in the realm of TFRs of 4-6)

- What factors contributed to moderate fertility in pre-transition populations?

- Henry (1961) distinguishes between non-parity specific fertility measures (measures that serve to reduce births but are unrelated to number of prior children) and parity specific fertility measures (measures used to reduce births after desired number already born)

- Coale argues that non-parity specific measures—specifically low proportions of married women—contributed to moderate fertility in pre-transition populations

- In contrast, reduction in fertility during the transition was due to parity specific measures, including abstinence w/in marriage, birth control, and abortion

- Uses the Coale and Trussel (1974; 1978) model of marital fertility to provide evidence for this argument

- The Coale and Trussel model expresses marital fertility at age ‘a’ r(a) as a function of M, the ratio of actual marital fertility at age ‘a’ r(a) to expected marital fertility at age ‘a’ in the absence of parity-related limitations n(a), and m, a measure of the extent to which parity-related limitation affects age-specific marital fertility rates

- Lower values of m indicate less of an effect of parity-specific measures on the reduction of marital fertility, whereas higher values of M indicate less of an effect of parity-specific measures on reduction of marital fertility

- Coale recognizes, however, that select pre-industrial populations were using parity-specific measures to reduce fertility (for instance, the nobility in France, England, and Italy, the Jews in Italy, and the rural population in France)

- While pre-industrial populations exhibit a decent amount of variation in fertility rates, fertility rates in developed societies are much more similar

- Differing marriage rates explain most of the variation in fertility amidst pre-transition societies

- Marriage acts as a sort of homeostatic mechanism to regulate population size in good and bad times

“Timing effects and the interpretation of period fertility.” Demography, 41(4), 801-819.

Develops the average cohort measure (ACF) of fertility, which measures period fertility adjusted for timing effects

- Norman Ryder argued that fertility change should be analyzed from a cohort perspective

- In contrast, Bongaarts and Feeney take a period perspective with their tempo-adjusted TFR

- As a way to combine these perspectives, Schoen’s measure examines the fertility behavior of a period and assesses the extent to which that period has a disproportionate share of cohort fertility

- Develops a timing index (TI) to assess the extent to which the cohort fertility of women childbearing during year t occurs in year t

- If TI(t) =1 no timing effects are occurring

- If TI(t) < 1 year t contains disproportionately small amount of cohort fertility and

- If TI(t) >1 year t contains disproportionately large amount of cohort fertility

The average cohort fertility in year t ACF(t) = TFR(t) / TI(t)

- One major limitation of this method is that it requires knowledge of completed cohort fertility, which often isn’t available until long after women have children

- Schoen argues that the ACF performs better than Bongaarts and Feeney’s TFR* because the TFR* has the tendency to amplify some period behavior while at other times failing to capture the level and direction of fertility timing effects

TFR* performs better when there are long, gradual changes in the mean age at childbearing

Argues there are advantages of period measure of fertility  

Period measures vary with time which is what fertility does

period measures also better because allow for moving target

flaw of cohort fertility-- it forces a fixed fertility target

Pollak 1986