I've heard it's 33% during the Qing dinasty. 4% during cultural revolution. Now it's climbing up steadily to 11%.
Where can I see the table of those actually tracking those numbers?
What were the causes?
Well, at least the drop during the "Cultural Revolution" is easily explained. Setting hordes of young, largely semi-literate, thugs to torture and maim the productive and educated members of society will do wonders for the economy. Here is a long quote from wikipedia:
The ten years of the Cultural Revolution brought China's education system to a virtual halt. The university entrance exams were cancelled after 1966, and were not restored until 1977 under Deng Xiaoping. Many intellectuals were sent to rural labour camps, and many of those who survived left China shortly after the revolution ended. Many survivors and observers[who?] suggest that almost anyone with skills over that of the average person was made the target of political “struggle” in some way. According to most Western observers as well as followers of Deng Xiaoping, this led to almost an entire generation of inadequately educated individuals. The impact of the Cultural Revolution on popular education varied among regions, and formal measurements of literacy did not resume until the 1980s. Some counties in Zhanjiang had illiteracy rates as high as 41% some 20 years after the revolution. The leaders of China at the time denied any illiteracy problems from the start. This effect was amplified by the elimination of qualified teachers—many of the districts were forced to rely upon chosen students to re-educate the next generation.
Han dynasty (206 BC–220 AD)
GDP per capita: $450, 26%
Tang Dynasty 618 – 907 AD GDP per capita:$480, 58% of world GDP
Song Dynasty 960-1279 AD GDP per capita:US$2,280, 80% of the world’s GDP
Yuan Dynasty 1271-1368 A estimated to account for about 30% -35% GDP
Ming Dynasty 1368–1644 AD GDP per capita:US$600, 55% of world GDP
Qing Dynasty 1644-1922 AD GDP per capita:US$600 Qing Dynasty accounted for 35% -10% of the World GDP
People’s Republic of China 1949- GDP per capita:US$5414, 9.48 percent of the world economy. See also Wikipedia for this period.
There is also another article at Wikipedia: Economic history of China before 1912
Maybe you can find hint to other sources there.
The ChinaWhisper article doesn't seem to give sources, and its numbers are implausible, particularly having per capita GDP be several times bigger under the Song dynasty than before or after.
A big compilation of historical population and GDP estimates was done by the late economist Angus Maddison, who among other things wrote extensively on China's economic history, and this work is being continued as the Maddison Project. His book The World Economy: A Millennial Perspective can be downloaded; Table B-20 (p. 263) gives estimated historical GDP percentages by country (in "1990 international dollars").
A graph of his estimates for China's share of world GDP is available on Wikipedia. While it does not resolve all the dynasties, China's share of global GDP stays in the 20% to 35% range until the mid-19th century, at which point it starts dropping, to around 4% under Mao. Now it is back up to 17%.
What is China has changed over time, as have the number of people in China, as has China's level of per capita output (GDP prior to capitalism is an anachronistic imposition if measured in a current value expression), as has the number of people not-in-China, as have the level of per capita output in places not-China.
The assumption that China's proportion of world output would remain static is a less tenable hypothesis than that all proportions of long lasting cultural nexuses of output would vary.
What you're really asking is "Was Needham right?" http://en.wikipedia.org/wiki/Joseph_Needham#The_Needham_Question
And there's a great deal of literature about prefigurative forms of capitalism in China out there. I'd suggest you start by reading the review articles on the Needham Question, because scholarly discontent with the failure of China, a large high productivity advanced feudal society*1 to cement the prefigurative forms of capitalism into actual capitalism continues.
*1 Marxist use in relation to circulation of prestige, status, and direct extraction techniques; not a claim of infeudation.