Tempo Effects in Fertility

Definition

Tempo effects in fertility are distortions in the period Total Fertility Rate (TFR) caused by shifts in the timing of births. When women postpone births (mean age at birth rises), the TFR is mechanically depressed below the true completed fertility level (quantum), because births are being delayed out of the observation window. Conversely, anticipation of births (mean age falling) inflates the period TFR. The TFR is a quantum measure — a period integral of birth rates — and is therefore vulnerable to timing distortions in a way that period life expectancy (a timing measure) is not. See Tempo Effects in Mortality for the contrasting negative result for $e_0$ .

Key Ideas

Quantum vs. tempo: Quantum is the completed fertility level (average lifetime births per woman). Tempo is the timing of those births. Period TFR measures quantum but is contaminated by tempo because it counts births falling in a given year; when births shift later, fewer land in any given year.
Bongaarts-Feeney (B-F) (1998) tempo adjustment: $\text{TFR}^*(t) = \text{TFR}(t) / (1 - r(t))$ , where $r$ is the rate of change in the mean age at birth. Bongaarts (1999) applied this adjustment to 7 developed countries (1985–89 avg), finding adjusted TFR $= 2.03$ vs. observed $1.78$ ( $+0.25$ gap); France and Netherlands showed the largest distortion ( $+0.40$ ), the US the smallest ( $+0.08$ ). Survey evidence on expected family size across 15 countries reinforces that reproductive preferences remained near replacement throughout the apparent fertility collapse. This removes the timing artifact, yielding a tempo-adjusted TFR closer to quantum. For parity-specific adjustment: $\text{TFR}^*_j(t) = \text{TFR}_j(t) / (1 - r_j(t))$ , using parity-specific mean age shifts.
Compositional bias in B-F: B-F estimates $r$ from mean ages derived from incidence rates (births at age $a$ / all women age $a$ ). But incidence rates at parity $j$ depend on the parity distribution of women — how many women are currently at parity $j-1$ — which is a legacy of past fertility. A fall in first-birth quantum years earlier leaves fewer young women at parity 1, causing the mean age at second birth to rise even if second-birth timing behavior is unchanged. B-F would falsely register this compositional shift as a tempo effect.
Kohler-Ortega (K-O) refinement: Estimate $r$ from mean ages derived from intensities (occurrence-exposure rates using parity- $j-1$ exposure only). Intensity-based mean ages reflect only current timing behavior, holding the parity distribution fixed at a uniform counterfactual. This eliminates compositional bias. The adjusted intensity rates are: $f^*(a) = f(a) / [1 - r(a)]$ , with age-and-parity-specific $r(a)$ .
Period Fertility Index (PF): The tempo-adjusted parity-age total fertility rate (PATFR) (from adjusted intensities). This is the pure behavioral quantum measure, free from both timing shifts and parity-composition effects. PF can be interpreted as the fertility level that would be observed if timing were stable and the parity distribution were in equilibrium with current behavior.
Three-way decomposition (Ortega and Kohler 2002):

$\text{TFR} = (1-r)(1+d)\cdot\text{PF}$

where $r$ = tempo effect (fraction of births "missing" due to postponement; positive when births are being deferred), $d$ = parity distribution effect (positive when composition favors high fertility), and $PF$ = Period Fertility Index (pure quantum). Adding the mean generation size $G$ yields the four-factor births decomposition (Kohler and Ortega 2004): $B = G \times PF \times \frac{1}{1-r} \times \frac{1}{1+d}$ , linking the behavioral quantum directly to the annual birth count.

B-F over-adjustment relative to K-O (Kohler and Ortega 2004): Applying both methods to Italy and Czech Republic 1995, B-F-adjusted TFR exceeds K-O-adjusted TFR by $\approx 7\%$ in Italy and $\approx 17\%$ in Czech Republic. The larger discrepancy in Czech Republic reflects a more severe parity-composition distortion caused by a rapid quantum decline combined with onset of postponement in the early 1990s.
Czech Republic 1985–1995 decomposition: Underlying quantum (PF) fell only $17\%$ ; observed TFR fell $35\%$ . The remaining 18 percentage point (pp) gap is explained by a tempo effect of $17.7\%$ and a parity distribution effect of $-6.7\%$ emerging by 1995 — quantifying exactly why the TFR collapse appeared catastrophic while the behavioral quantum decline was more modest.
Cohort completion scenarios (Kohler and Ortega 2004): "Postponement stops" — no further tempo change after the reference year — vs. "postponement continues" — reference-year tempo pace persists indefinitely. Applied to Italian and Czech cohorts not yet done in 1996/1999: tempo-distorted observed intensities project $\approx 28\%/25\%$ ultimate childlessness; K-O "postponement stops" projects $\approx 20\%/13\%$ . The gap reveals how badly tempo distortion inflates apparent childlessness in cohorts observed during a rapid postponement wave.
Fertility ageing effect: If postponement continues beyond the reference year, it does not merely delay births timing-neutrally — it also reduces higher-order parity transitions, because women who begin childbearing at older ages are exposed to the risk of second and third births at ages where those transition probabilities are already low. This is distinct from the quantum effect, and it means ongoing postponement has a cumulative additional cost to completed cohort fertility beyond what tempo adjustment alone reveals.

How It Works

The mechanism of tempo distortion: births of order $j$ by women of age $a$ in year $t$ = intensities $\times$ (share of women at parity $j-1$ at age $a$ ). When first-birth rates fall (reducing cohort sizes entering parity 1), there are fewer women eligible for second births at young ages in subsequent years. The incidence rate for second births at age $a$ then changes not because second-birth behavior changed, but because the pool of eligible women shrank and aged. This is the compositional contamination that K-O removes.

Intensity-based mean age: Computed as if every woman of childbearing age were at every parity — a hypothetical uniform distribution. Formally: $\mu_I = \sum_a [a \times m_j(a)] / \sum_a [m_j(a)]$ , where $m_j(a)$ is the parity- $j$ intensity. This mean age can differ from the incidence-rate-based mean age, and can produce counterintuitive results: the mean age at third birth can be lower than at second birth if older women disproportionately remain at lower parities.

Application: Sweden 1990 vs. 1998

Component	1990 (peak)	1998 (trough)
TFR	high	low
Tempo effect (r)	$\approx 11\%$	—
Parity distribution effect (d)	positive (offset)	—
Period Fertility Index (PF)	$\approx 0.89$	much lower

The 1998 fertility collapse was genuine behavioral decline (PF fell sharply across all parities), not a tempo or compositional artifact. The 1990 peak overstated quantum due to favorable composition, but PF in 1990 was still near 0.9 — real fertility behavior was already below TFR.

Why It Matters

Demographic diagnosis: Distinguishing postponement-driven TFR depression from true quantum decline is essential for forecasting and policy. A country with $\text{TFR} = 1.3$ driven by postponement (high $r$ , stable PF) has very different prospects than one with $\text{TFR} = 1.3$ from genuine quantum reduction ( $\text{PF} = 1.3$ ).
Lowest-low fertility: Much of the TFR collapse in Southern and Eastern Europe in the 1990s ( $\text{TFR} < 1.3$ ) reflected tempo effects amplified by social interactions (Kohler, Billari, and Ortega 2002). Without tempo adjustment, these countries' fertility appeared catastrophically low; after adjustment, quantum was less alarming (though still below replacement). Kohler, Billari, and Ortega (2006) further show that in low work-family compatibility settings, postponement also reduces quantum permanently via reduced higher-order parity transitions — making tempo adjustment a necessary but not sufficient diagnosis. See Lowest-Low Fertility.
Forecasting: The K-O framework allows cohort completion by separately projecting quantum (adjusted intensities) and tempo (mean-age scenarios), yielding more structurally coherent projections than direct TFR extrapolation.
Contrast with mortality: The tempo-distortion logic applies to fertility (a quantum measure) but not to period life expectancy $e_0$ (a timing measure). See Tempo Effects in Mortality.

Developing-World Application

Bongaarts (2002) notes that tempo effects from rising age at first marriage and first birth likely depress period TFR below quantum in many developing countries, but defers full analysis. This means observed period TFR declines in developing-world transitions may partly overstate the true behavioral (quantum) decline — particularly in countries experiencing rapid marriage postponement. The B-F adjustment formula $\text{TFR}^*(t) = \text{TFR}(t)/(1-r)$ applies in principle to developing-country transitions, but parity-specific register data for clean K-O estimation is rarely available outside Scandinavia, making the magnitude uncertain. The practical implication is that some apparent Fertility Stalling in period TFR data may partly reflect tempo deceleration rather than true quantum plateaus.

Open Questions

How sensitive is the PF measure to the choice of intensity-based vs. incidence-rate-based mean ages in practice? For most countries, the difference may be modest.
Can the K-O framework be applied reliably when parity-specific register data is unavailable? Most countries lack the Scandinavian-quality data needed for clean intensity estimation.
Has the postponement wave of the 1990s–2000s substantially ended in Europe? If mean ages have stabilized, $r \to 0$ and $\text{TFR} \approx \text{PF}$ — the tempo correction becomes less critical.