I wrote a draft of this paper half a decade ago:
Estimating World GDP: Angus Maddison (1995) has constructed estimates of real GDP per capita for the world from 1820 to 1992. His estimates are best thought of as Laspeyres purchasing power parity estimates in 1990 international dollars. That is, they:
- Compare income levels across countries not using current exchange rates, but instead trying to change one currency into another at rates that keep purchasing power constant ("purchasing power parity").
- Value goods in relative terms using the prices found in a country in the middle of the world distribution of income ("international"). Calculate a value for 1990 GDP per capita in the United States equal to U.S. current-dollar GDP per capita in 1990 ("1990 dollars").
- Do not take explicit account of the benefits of the introduction of new goods and new types of goods, but instead calculate GDP per capita in the past by valuing the commodities produced in the past at recent prices--and not making any correction for the restricted range of choice enforced by limited production possibilities ("Laspeyres").
All of these save the last are reasonable--are in fact vastly preferable to the alternatives. I will return to the last of these later. But first I want to extend Maddison's estimates backward before 1820.
If you plot the rates of world population growth against Maddison's estimates of world GDP per capita, you find a very high and significant correlation between the two from the early nineteenth century until roughly World War II. After World War II the demographic transition has begun to take hold in large parts of the world, but before World War II the higher is world GDP per capita, the faster is population growth--with a 1 percentage point per year increase in population growth associated with an increase in average world GDP per capita of $1,165 (with a t-statistic of 7.4 and an adjusted-R2 of 0.84).
If you are enough of a Malthusian to believe that this tight relationship before World War II is not coincidence but instead reflects a near-linear dependence of the rate of human population growth on the margin between actual production and bio-cultural subsistence, then you can use the fitted relationship between population growth and Maddison-concept GDP per capita to backcast estimates of world GDP per capita before 1820....
Now I'm looking for a URAP to help me finish it for real.