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Calibrated spline estimation of detailed fertility schedules from abridged data¹

Estimadores spline calibrados para tasas detalladas de fecundidad a partir de datos agrupados por edad

Estimadores splines calibrados: estimativas de taxas detalhadas de fecundidade a partir de dados agrupados por idade

I develop and explain a new method for interpolating detailed fertility schedules from age-group data. The method allows estimation of fertility rates over any fine grid of ages, from either standard or non-standard age groups. The new method, called 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 1f x schedules observed in the Human Fertility Database (HFD) and in the US Census International Database (IDB). I compare the CS estimator to a very good alternative method that requires more computation: Beers interpolation. The results show that CS replicates known 1f x schedules from 5f x data better, and its interpolated schedules are also smoother. The conclusion is that the CS method is an easily computed, flexible, and accurate method for interpolating detailed fertility schedules from age-group data. Users can calculate detailed schedules directly from the input data, using only elementary arithmetic.

Fertility; Interpolation; Splines; Penalized least squares

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