Coale-Trussell Model

M is a scale parameter: it sets the overall level of marital fertility relative to the natural-fertility standard at the youngest reproductive ages, before deliberate control takes hold. m is the control parameter: it measures how strongly the schedule bends below the natural pattern at older ages, which is the signature of parity-dependent stopping. A population with little control has m near zero and a marital fertility curve that simply tracks a scaled natural standard.

The Hutterites, an Anabaptist communal group in North America, historically practiced essentially no deliberate fertility limitation and had detailed, high-quality records, making their age-specific marital fertility a clean empirical benchmark for natural fertility. Coale and Trussell anchored the natural standard n(a) on such non-controlling populations so that any downward departure at older ages could be attributed to deliberate control.

Not well. The control function v(a) is specifically shaped to capture parity-dependent stopping, where couples cease childbearing after reaching a desired family size. Birth spacing and postponement produce different age signatures that the model can confound with stopping, so a high m should not be read as evidence of stopping alone. Researchers studying spacing typically supplement Coale-Trussell with birth-interval and parity-progression analyses.