Is population growth irrelevant with respect to per capita GDP growth In Solow's growth model the growth rate of the output or GDP of a country is denoted by $g$. In the model this can be decomposed to
$$
g = g_l + g_k,
$$
where $g_l$ is the growth rate of the effective labor force and $g_k$ the growth rate of capital. If you calculate the growth rate of per capita GDP population growth will not play a role. (Per capita growth is 'kind of' like $g_k$, but not quite, as technological advancements  are factored into the growth rate of effective labor.)

Does historical data support the statement that the effect of population growth on per capita GDP growth is zero?

I did some limited searching and it seems that while US growth is sometimes set as an example to other western countries, the real difference is in population growth, not per capita GDP growth.



Source



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Am I being too superficial in my examination? Are there more subtle effects, such as a lagged effect due to the pension and elderly care systems?
Indeed, there is branch of literature about semi-endogenous models (Jones, 1995, Segerstrom 1999 etc.). They were basically arguing that there was a scale effect in endogenous growth models, which means that when population increases, by default, growth increases (it is due to the fact that there would be more researcher in society, this is the scale effect.) and this branch of literature shows that growth rate at the long run is equal to the growth rate of population, which is an exogenous term. It is why they called it as "semi-endogenous".

This was challenging endogenous models but the empirical literature states that that the semi-endogenous model does not fit to data.

Some empirical references are : 

Ha and Howitt (2007) 

http://onlinelibrary.wiley.com/doi/10.1111/j.1538-4616.2007.00045.x/full

and 

Madsen (2008) 

http://link.springer.com/article/10.1007/s10887-007-9024-0