Tempo and Quantum : Comparison between Ryder Index and a Simple Method

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  • テンポとカンタム : Ryder指標と簡易法の比較
  • テンポ ト カンタム Ryder シヒョウ ト カンイホウ ノ ヒカク

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Abstract

For the better observation of fertility trend, it is necessary to analyze Total Fertility Rate(TFR) in tempo and quantum aspect. The former indicates the changes in childbearing timing and the latter shows the changes in the number of children of a woman in her life. There exist different methods to decompose TFR in tempo and quantum factors and among them, so called Ryder Index posed by N. Ryder in his pioneer works is the most popular. However, one needs all the Cohort Total Fertility Rates(CTFRs) in reference to the age-specific fertility rates from 15 years to 44 years to calculate the Ryder Index in a one year period. Thus, due to the limitation of available data, the tempo index(TI) and the quantum index(QI) could be obtained mostly in only limited periods of time. To solve this problem, the author developed the new brief method(named Simple Method) to use only TFRs and CTFRs time series data without detailed age-specific fertility rates. In this paper, we introduced this Simple Method in methodological detail compared with Ryder's Method and explained mathematically the possibility to obtain almost same values with Ryder Index. Then, using time-series and periodical age-specific fertility rates in Switzerland 1932-1996 and in Germany(former West and East Germany), Austria, Switzerland, the Netherlands and Japan after World War II, we calculated the tempo and the quantum by both methods and attested the results. Trends of TI and QI were identical and the RMSPE : the root mean square percentage error(RMSPE) were usually 1%-2% and 5%-6% at most.

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