MPIDR Working Paper

Calibrated spline estimation of detailed fertility schedules from abridged data

Schmertmann, C.
MPIDR Working Paper WP-2012-022, 22 pages.
Rostock, Max-Planck-Institut für demografische Forschung (Juli 2012)
Open Access


I develop and explain a new method for interpolating detailed fertility schedules from age-group data. The method allows estimation of fertility rates over a fine grid of ages, from either standard or non-standard age groups. Users can calculate detailed schedules directly from the input data, using only elementary arithmetic.

The new method, the calibrated spline (CS) estimator, expands an abridged fertility schedule by finding the smooth curve that minimizes a squared error penalty. The penalty is based both on fit to the available age-group data, and on similarity to patterns of 1fx schedules observed in the Human Fertility Database (HFD) and in the US Census International Database (IDB).

I compare the CS estimator to two very good alternative methods that require more computation: Beers interpolation and the HFD's splitting protocol. CS replicates known 1fx schedules from 5fx data better than the other two methods, and its interpolated schedules are also smoother.

The CS method is an easily computed, flexible, and accurate method for interpolating detailed fertility schedules from age-group data.

Data and R programs for replicating this paper’s results are available online at
Das Max-Planck-Institut für demografische Forschung (MPIDR) in Rostock ist eines der international führenden Zentren für Bevölkerungswissenschaft. Es gehört zur Max-Planck-Gesellschaft, einer der weltweit renommiertesten Forschungsgemeinschaften.