世代和年代生育率、死亡率模型的比較

臺灣婦女生育率下降快速，近年來屢創新低，堪稱全球生育率最低的國家，總生育率自民國89年1.68、降為民國98年1.03，民國99年甚至降至0.90以下，提升生育率成為政府施政的重要課題。因為資料限制，生育率大多以總生育率(Total Fertility Rate)表示，而非較能反映婦女一生生育總數的世代完成生育率(Completed Cohort Fertility Rate)。這兩者間存有不少差異，以生育率下降的臺灣為例，總生育率會因生育時機遞延而低估世代生育率，以總生育率詮釋生育率可能有瑕疵。有鑒於此，本文以比較「世代」及「年代」兩者的差異，以生育率及死亡率為研究對象，探討較適宜描述臺灣特性的模型。 由於世代生育率會有資料不足的問題，本文使用外推法(Extrapolation)補足年齡較高（如35歲以上）的婦女生育率，並以四種模型估計年代生育率與世代生育率，包括Gamma模型、Gompertz模型、主成份分析(Principle Component Analysis)與單一年齡組個別估計法，希望找出適合預測臺灣世代完成生育率的模型。除了台灣資料，也用日本、法國與美國的世代生育率資料，比較各國世代生育率模型的異同。另外，本文也以世代及年代兩種觀點，類似生育率的探討方式，比較常用死亡率模型的優劣。 不論是生育率或是死亡率資料，配適模型結果皆以世代資料可得到較好的估計結果，生育率以單一年齡組個別估計法為最佳的模型，死亡率則以Gamma模型、主成份分析、單一年齡組個別估計法為較佳的模型。

Taiwan’s fertility rates have been declining radically in recent years, much faster than most countries in the world. For example, the total fertility rate (TFR) is 1.68 in 2000, 1.03 in 2009, and even reduces to 0.90 in 2010. Therefore, one of the top priorities for Taiwan government policies is to enhance the willingness of having children. Due to the data availability, the TFR is used more often, although the completed cohort fertility rate (CFR) is a more reasonable measurement. However, previous studies showed that the TFR is likely to be influenced by the deferring (i.e., tempo effect) of childbearing and produces misleading results. In order to measure the effect of deferring childbearing, this study focuses on exploring the difference of measures in the view of cohort and period (especially the CFR vs. TFR) and evaluates which fertility and mortality model is more appropriate for Taiwan. Because there are fewer complete cohort fertility data, we use extrapolation to make up the higher age-group fertility data (such as aged 35 and above). We consider four fertility models in this study, including Gamma model, Gompertz model, principal component analysis, and individual group estimation. We use the data from Taiwan, Japan, France and United State data to evaluate these fertility models. The results indicate that the parametric models (Gamma and Gompertz) have the worst performance, probably due to the rapid change of fertility behaviors. In addition, similar to evaluating the fertility models, we compare the performance of frequently used mortality models using the cohort and period mortality data. The result shows that using cohort data to estimate fertility and mortality is better than period data. Also individual group estimation is the best model to fit fertility; the better models to fit mortality are Gamma model, principle component analysis and individual group estimation.