How mortality inprovement increases population growth (Q2725674)

This paper presents the estimation of mortality improvement on population growth. Over the past century, most of the momentous increase in world's population has been fueled by increased survival. Birth rates have tended to fall, often sharply, but death rates have decreased even faster. As a result, the population of the world has multiplied. The primary interest of the authors are often called the population growth rate \( \bar\rho (y) \), and the intensity of improvement in mortality \(\dot\mu (x,y)\). NEWLINENEWLINENEWLINEThe focus study is on how \( \mu (x) \) affects \( \bar\rho (y)\). NEWLINE\[NEWLINE \mu (x,y)= \frac{-dN(x+a,y+a)da} {N(x,y)} NEWLINE\]NEWLINE where \( N(x,y) \) denotes the population surface over age \( x \) and time \( y \). As was shown by \textit{G. B. Preston} and \textit{A. J. Coale} (1982), NEWLINE\[NEWLINE N(x,y)=B(y)S(x,y)R(x,y) , NEWLINE\]NEWLINE where \( B(y) \) denotes the number of births at time \( y\), \(S(x,y) \) is the period survival function and NEWLINE\[NEWLINE R(x,y)=e^{-\int_0^x \rho (a,y) da}. NEWLINE\]NEWLINE To understand how population growth is related to changes in the number of births, to improvements in mortality, and to the cohort-period adjustment, the general result NEWLINE\[NEWLINE \bar\rho (y)= \dot B (y)+ \dot e_o (y) +R^ \star (y) NEWLINE\]NEWLINE permits the decomposition of the current population growth rate into NEWLINENEWLINENEWLINE(1) the current intensity of change in births, NEWLINENEWLINENEWLINE(2) the current intencity of change in period life expactancy (which captures the impact of current mortality change), and NEWLINENEWLINENEWLINE(3) a residual term that reflects the influence of historical fluctuations that have resulted in a population size and structure that is different from the stationary population size and structure implied by current mortality and birth. NEWLINENEWLINENEWLINEThe authors prove that a constant rate of mortality improvement will continue to increase life expectancy by about the same absolute amount; on the other hand as life expectancy increases, the relative rate of improvement will fall. NEWLINENEWLINENEWLINEConsidering the relationship between the total fertility rate and the intensity of change in the number of births, the authors show that NEWLINE\[NEWLINE \rho (y)=\dot B (y)+ \dot e_o (y)=0,0004. NEWLINE\]NEWLINE where \( e_o (y)=\int_0^w S(x,y) dx \) and \( \dot e_o (y) \approx \frac {e_o (y+1)-e_o (y)} {e_o (y)} \).NEWLINENEWLINEFor the entire collection see [Zbl 0956.00059].