The IFs demographic model captures the mechanical or accounting effects of mortality on population.  A key pathway passes from mortality through adult age population to labor supply (including aging-related lags). ^[1]   Similarly, IFs captures the mechanical effect of mortality on fertility through the death of women of childbearing age. 

The most important non-mechanical linkage is almost certainly the relationship between child mortality and fertility. IFs forecasts fertility as a relationship with infant mortality, the log of educational level of those aged 15 and older (neither the education of women alone nor the education of those 15-24 work as well), and the percentage use of modern contraception.  Adding the rate of infant mortality boosted the overall adjusted R-squared to 0.84.

R-squared = 0.8345; other terms and algorithmic specifications modify the relationship, most importantly a term that slowly shifts TFR over time and the specification of a minimum level toward which the function slowly converges if it overshoots on the downward side.