Development accounting is the manipulation of a production function to examine whether cross-country income differences arise from differences in total factor productivity (TFP), or due to factor accumulation. It is useful to find this information out so that we can correctly inform policy decisions and let developing countries know if they need to simply increase quantity of factors of production (i.e. promote higher fertility, immigration, labour market inclusion and capital appreciation), whether they need to increase the quality of the factors of production (better education and more efficient use of investment funds) or if they need to increase efficiency and technological adoption.
We may be interested in understanding fertility decisions, because it is generally believed that population growth is detrimental to economic development (c.f. the Solow growth model and lessons from the British Industrial Revolution) and so we would advise policymakers to try and reduce population growth. The death rate has been falling across the globe since the 1960s (by 50% according to Schultz) as a result in medical advancements and the cheapening of drugs (as well as globalisation which meant this knowledge could diffuse across the world more easily), yet many LDCs have not followed the same transition path with respect to birth rates as developed countries did. By understanding why a couple decide to have a child (at the margin) we may be able to reduce these incentives, so as to limit population growth.
The most important macro externality that high fertility can have is its effect on economic development. If high fertility leads to more rapid economic growth and development then we may consider the externality positive, if not we would say it is negative. This works if we consider the mortality rate to be below high fertility, such that high fertility means high population growth.