Calibrated spline estimation of detailed fertility schedules from abridged data
OBJECTIVE<br> 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.<br> <br> METHODS<br> 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 <sub>1</sub>f<sub>x</sub> schedules observed in the Human Fertility Database (HFD) and in the US Census International Database (IDB).<br> <br> RESULTS<br> 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 <sub>1</sub>f<sub>x</sub> schedules from <sub>5</sub>f<sub>x</sub> data better than the other two methods, and its interpolated schedules are also smoother.<br> <br> CONCLUSIONS<br> The CS method is an easily computed, flexible, and accurate method for interpolating detailed fertility schedules from age-group data.<br> <br> COMMENTS<br> Data and R programs for replicating this paper’s results are available online at <a target="_blank" href="http://calibrated-spline.schmert.net">http://calibrated-spline.schmert.net</a>
