臺灣的死亡率步調效果：步調調整後的平均餘命

「步調效果」(tempo effect)的研究首度出現在生育率上，之後逐漸擴展至其他時期率的討論，尤其是初婚率與死亡率。所謂的「步調效果」是指慣用的「時期」測量，其多種率與平均餘命會受到「步調」影響，產生偏誤的情形(Bongaarts and Feeney 2006)。有鑑於此，去除年齡改變所造成的扭曲，估計「實際」的趨勢變化已成為長久以來學界努力的目標。一般均接受生育步調改變會對時期別生育率產生影響，但對於死亡率的步調效果則有較大爭議。另一方面，臺灣目前僅有生育率與初婚率步調效果的研究，對於死亡率步調的討論與經驗研究尚付之闕如。因此本研究乃針對死亡率步調作系統性的討論，進一步探究臺灣死亡率的步調效果，瞭解死亡率下降的過程中，平均餘命受步調效果的影響與實際變化趨勢。研究結果發現，臺灣成人死亡率的變化同於其他高平均餘命國家，更接近邏輯斯模型(logistic model)而非Gompertz模型。此外，在當時條件(current conditions)的觀點下，調整過後的平均餘命與生育率一樣，為去除步調效果後的時期測量。當去除死亡的步調效果後，慣用的平均餘命有高估的現象，且女性大於男性，平均的步調效果各為2.3與2.1，女性的步調效果高於瑞典、美國、德國、丹麥、英格蘭與威爾斯，原因可能是臺灣死亡率下降的速度較快，造成步調效果偏高的情形。再者，兩性在調整過後平均餘命之差異上，一路呈現平滑的上升趨勢，但在時期別指標之差異上卻受到步調效果影響，分成兩階段的變化，期間上下波動，這也顯示使用調整過後的平均餘命比未調整的平均餘命可能更可以反映當時的死亡率條件。

關鍵字

步調效果；平均餘命；時期率；邏輯斯模型； Gompertz死亡率改變模型

並列摘要

The tempo effect was first discussed and applied to fertility studies, before being extended to other fields such as marriage and mortality. The tempo effect means that the period quantum and tempo of conventional life tables are impacted by tempo, which results in bias (Bongaarts and Feeney 2006). Therefore, the goal of recent studies has been to adjust this tempo distortion, which results from a rise or fall in the mean age at which an event occurs, and to estimate the actual period measure of longevity. In general, the fertility tempo effect is widely accepted, but the mortality tempo effect remains controversial. Studies of the tempo effect on fertility and first marriage have been examined thoroughly in Taiwan. For this reason, our research focuses on the mortality tempo effect, and explores unadjusted and adjusted life expectancies in Taiwan. Our results show first, that the observed adult mortality rate fits the logistic model better than the Gompertz model, as in other countries with high life expectancy. On the other hand, tempo adjusted life expectancy measures current conditions, as does fertility. Second, when the tempo effect on mortality is excluded (thus the value of average life span is increased), the conventional life expectancy has a positive bias, with women having a higher life expectancy than men, and the average tempo effect is 2.3 and 2.1 years respectively. Finally, the tempo effect on women in Taiwan is higher than that in Sweden, the U.S., Germany, Denmark, England and Wales. The reason might be that mortality in Taiwan has decreased more sharply than other countries, causing the tempo effect to be higher. We conclude that the adjusted life expectancy is more accurate than the unadjusted one.