Ortega and Kohler 2002 — Measuring Low Fertility

Summary

Max Planck Institute for Demographic Research (MPIDR) Working Paper WP 2002-001 (January 2002). A methods paper rethinking demographic measurement of low fertility in the context of widespread postponement across Europe. The central contribution is the Kohler-Ortega (K-O) framework: a refinement of the Bongaarts-Feeney (1998) tempo-adjustment procedure that uses parity-specific fertility intensities (occurrence-exposure rates) rather than incidence rates. This removes compositional bias from tempo estimates. The paper also introduces the Period Fertility Index (PF) — a pure behavioral measure of fertility quantum free from both tempo distortions and parity-distribution effects — and a three-way total fertility rate (TFR) decomposition: $\text{TFR} = (1-r) \times (1+d) \times \text{PF}$ .

Key Claims

Fertility rates can be computed with two denominators: incidence rates (all women of age a) or intensities (women of parity j−1 only, i.e., those at risk of a birth of order j). Intensities are theoretically preferable for parity-specific analysis because they reflect the instantaneous birth probability for women actually at risk.
Incidence rates at a given parity conflate fertility behavior with the parity distribution of the population — a legacy of past fertility levels. When quantum or timing of first births changes, the parity distribution of older ages shifts in subsequent years, causing apparent tempo effects in higher-order births even with no behavioral change.
The Bongaarts-Feeney (B-F 1998) tempo-adjustment procedure estimates r from mean ages at birth derived from incidence rates. These mean ages are compositionally polluted and can register spurious tempo effects. K-O replaces them with intensity-based mean ages (computed as if the parity distribution were uniform across women), which reflect only current timing behavior.
The parity-specific tempo-adjusted rates are: $f^*(a) = f(a) / [1 - r(a)]$ , where $r(a)$ is an age-and-parity-specific intensity-based tempo effect.
The Period Fertility Index (PF) is the tempo-adjusted PATFR (parity-age TFR computed from adjusted intensities). It is the pure behavioral measure of quantum, free from both timing shifts and parity-composition effects.
The three-way decomposition: $\text{TFR} = (1-r) \times (1+d) \times \text{PF}$ , where $r$ = tempo effect (% of births "missing" due to postponement), $d$ = parity distribution effect (positive when composition favors high fertility), and PF = Period Fertility Index (pure quantum).
Sweden application: In 1990 (TFR peak), $r \approx 11\%$ and $d > 0$ (composition favored high fertility), but $\text{PF} \approx 0.89$ — true quantum below TFR. In 1998 (trough), PF was much lower across all parities — the fertility collapse was genuine behavioral decline, not a tempo or composition artifact.
For cohort completion: quantum (adjusted intensities) and tempo (mean age at birth scenarios) can be projected separately, yielding demographically coherent cohort fertility projections.

Concepts Introduced or Extended

Entities Mentioned

Quotes

"The adjusted PATFR is a pure index of fertility in the sense that it is free from tempo and compositional distortions; it is called the Period Fertility Index, PF."

"In searching for an explanation of fertility trends, one should concentrate on explaining the appropriate summary fertility measures that are free from tempo and compositional effects."

My Take

A technically demanding paper that resolves a genuine methodological problem. The key insight — that B-F's use of incidence-rate-based mean ages introduces compositional bias from past fertility history — is correct and important. The K-O intensity-based approach is the right solution. The PF decomposition is particularly useful as a diagnostic tool: it separates the "demographic noise" (postponement, parity-composition inertia) from the behavioral signal. Limitation: intensities require parity-specific exposure data, which is rarely available from vital statistics alone; the paper relies on Scandinavian register data. The working paper predates the final published K-O papers and is partly a methodological synthesis rather than a primary research contribution. The applied example (Sweden 1990 vs. 1998) is clear and convincing.