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Grigoriev, Pavel; Michalski, Anatoli I.; Gorlishchev, Vasily P.; Jdanov, Dmitri, A.; Shkolnikov, Vladimir M. (2018)
MPIDR Working Paper WP-2018-001. Rostock
Background and Aim Occasionally, there is a need to split aggregated fertility data into a finegrid of ages. For this purpose, several disaggregation methods have been developed. Yet thesemethods have some limitations. We seek to identify a method that satisfies the following criteria: 1) shape – the estimated fertility curves should be plausible and smooth; 2) fit – the predictedvalues should closely trace the observed values; 3) non-negativity – only positive values shouldbe returned; 4) balance – the estimated five-year age group totals should match the input data;and in case of birth order data 5) parity – the balance by parity has to be maintained. To ourknowledge, none of the existing methods fully meets the first four criteria. Moreover, no attempthas been made to extend the restrictions to criterion (5). To address the disadvantages of theexisting methods, we introduce two alternative approaches for splitting abridged fertility data:namely, thequadratic optimization (QO) method and theneural network (NN) method. Data and Methods We mainly rely on high-quality fertility data from the Human Fertility Database (HFD),Additionally, we use a large and heterogeneous dataset from the Human Fertility Collection(HFC). The performance of the proposed methods is evaluated both visually (by examining ofthe obtained fertility schedules), and statistically using several metrics of fit. The QO and NNmethods are tested against the current HFD splitting protocol (HFD method) and the calibratedspline (CS) method. Results The results of thorough testing suggest that both methods performwell. The main advantage – and a distinguishing feature – of the QO approach is that it meetsall of the requirements listed above. However, it does not provide afit as good as that of the NNand CS methods. In addition, when it is applied to birth order data, it can sometimes produceimplausible shapes for parity 1. To account for such cases, we have developed individualsolutions, which can easily be adapted to account for other cases that might occur. While theNN method does not satisfy thebalance andparitycriteria, it returns better results in terms offitthan the other methods.ConclusionsTheQO method satisfies the needs oflarge databasessuch as the HFD and the HFC. While this method has very strict requirements, it returnsplausible fertility estimates regardless of the nature of the input data. The NN method appearsto be a suitable alternative for use in individual cases in which the priority is given to thefitcriterion.