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I was reading a report on population projection using cohort component method. There the authors have only stated their assumptions regarding the TFR (total fertility rate) and life expectancy at birth (they are working with five year age groups). It seems from their write up that, say, if someone assumes that the TFR is 2.1 in next 5 years and the life expectancy at birth is 76 years, then somehow they can get the projected population given the base year's population using cohort component method.

But with my little knowledge in Demography, I know that one needs ASFR (age specific fertility rates) and age specific death rates (here age-group specific...) to get projected population. Can someone tell me how assumptions about TFR and life expectancy at birth be used to get the projected population?

NB: They have also talked about UN model life table. If I do use the age-group specific probability of death/mortality rates, then how is the assumption on life expectancy at birth helping here? Could anyone kindly explain (or give reference to) the whole mechanism?

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For cohort component projection model, age-specific birth,death and migration rate is essential as the TFR, life expectancy and net migration rate. As you know, TFR is the sum of age-specific fertility rate (sum(ASFR)*5/1000). You can link the TFR with ASFRs. the simplest way is to assumed constant proportion of given ASFRs (in the base year) over the projection period and produced the ASFRs with associated TFR. For mortality, you have to produced life table for life expectancy at birth. In many cases, demographers link the life expectancy at birth with UN model life table and adopted the corresponding life table survival function. Population Hand book-PRB. For cohort component projection methods, please read thoroughly this Cohort Component Methods. There is also some nice free software avaialbe to execute the population projection, e.g. Spectrum by futur-groups. I hope this will help you. Please let me know the if you need any further help.

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