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

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

Cohort Fertility

A demographer’s “problem”

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

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

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

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

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

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

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

Intensities vs. incidence rates, Italy 1995

Mean and variance changes, 1995

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

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:

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

Fertility Table, Italy 1995

Parity Distribution in Synthetic Cohort Italy and Czech Republic 1995

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:

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

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

Application to Italy and Czech Republic

Brazil: TFR and Mean Age at Birth

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

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

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)

Cohort completion, Italy after 1996

Cohort completion, Czech R. after 1996

Brazil after 2010

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))

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