Understanding and reconciling the two real GDP series in Maddison Project 2018

Imagine you have several stopwatches. You start them all at the same time, but when you come back after several days, you find them all to be displaying different numbers. So you set them to the same time, and check back a few days later again. The figures diverge again, in a completely different way from the way they did the last time. You find it impossible to predict whether a stopwatch will go too slow or too fast. A stopwatch may be too fast at one day, too slow on another, and at the right speed at yet another time. But it’s nearly certain the figures the stopwatches show will diverge from each other over long periods of time if not periodically reset. You have a decision: allow each stopwatch to stay consistent within itself, and thus allow inconsistency between stopwatches to creep in, or sacrifice internal consistency by resetting the stopwatches from time to time in order to maintain consistency between the stopwatches.

This parable is of the difficulty of deriving GDP (PPP) estimates. Every five years or so, the purchasing power parity weights seem to change significantly, with no regard for measured within-country growth over years. And, yet, if one does not re-weigh one’s GDP per capita estimates over long periods of time, you are certain to have nonsensical results like Switzerland and the Netherlands being richer than the United States in the 1860s, when literally no contemporary evidence suggests this, and the resulting implied price levels from these countries would be absurdly low.

The Maddison Project has thus made the unusual decision to produce two GDP series. One series (rgdpnapc) is purely within-country, with the international price comparisons being done only once (2011). The other (cgdppc) coerces the GDP data to fit every international price comparison the Maddison Project has on record, no matter how ridiculous (e.g., the 1985 ICP, which obviously overstated the relative price levels in India, Japan, and other key economies). The base country for the cgdppc growth estimates (i.e., the one whose rgdpnapc and cgdppc series is the same) in the Maddison Project is the United States. The cgdppc series shows faster growth for Western Europe than the within-country series, as well as more insane variation as we get closer to today, due to the greater frequency of international price comparisons these days as opposed to earlier times. An example:

Code here

The upper lines are estimated GDPs per capita for the U.K.; the lower lines are for India. The red and magenta lines are the rgdpnapc series; the blue and cyan lines are the cgdppc series. As you can see, using cgdppc series creates a bizarre Indian Great Contraction during the first few post-independence decades. As A. Karlin pointed out, this seems rather inconsistent with the facts on the ground.

My first attempt to reconcile those series is to weigh the rgdpnapc series more in years closer to 2011 and the cgdppc series in years further away from 2011, as thus:

Code here

The other option would be to create a trendline for the cgdppc data, create another trendline for the rgdpnapc data, subtract the two, and add that difference to the rgdpnapc data. However, my first solution better deals with the fact within-country real GDP estimates become more accurate over time and always imperfect international comparisons simultaneously become more frequent.