￼￼Time to update this, as my thinking on a bunch of issues has changed over the past sixteen years. But first, as I think about how to so, let me reprint it...
I construct estimates of world GDP over the very long run by combining estimates of total human populations with largely-Malthusian estimates of levels of real GDP per capita.
I take my estimates of human population from Kremer (1993), but it would not matter if I had chosen some other authority. All long-run estimates of human population that I have found are quite close together (with the exception of estimates of population around 5000 BC, where Blaxter (1986) estimates a population some eight times that of other authorities). Note that ￼￼￼this does not mean that the estimates are correct—just that they are roughly the same.