First, in the long term, GDP - life expectancy correlation is ridiculously high - just look at gapminder.

Now back to the main subject.

With Korea it's not much of a natural experiment - it involves two extreme outliers in their camps, so every explanation should also explain why North Korea was so much less successful than almost every Communist country, and why South Korea was so much more successful than almost every Capitalist country.

Anyway, Germany. It is comparable enough to work as a "natural experiment" - but then:

• West Germany got plenty of money from USA, while East Germany was looted by Soviets and forced to pay reparations
• West Germany traded with rich countries, while East Germany traded with poor countries, and by argument of regional convergence mentioned in the paper we should expect West Germany to do much better.
• East Germany was actually the richest Communist country, due to its atypically high starting point.

And the big argument. According to data I've been able to find - almost all of the difference comes from very early time - in 1950 West Germany to East Germany GDP per capita ratio was 2.04:1.00. In 1989 it was almost identical 2.14:1.00. So 40 years hardly widened the gap, and 1950 gap can be easily blamed on harshness of Soviet occupation and reparations.

German "natural experiment" provides very little support for Capitalism vs Communism economy. On the other hand it seems to show quite well (together with Japanese / South Korean etc. examples) that American/British occupation is much better thing to happen to you than Soviet occupation.