Simon Kuznets only came up with the GDP in the 1930's and he was not particularly happy with the measure he created. GDP for any time before that, therefore, is more of an estimate as economists need to reverse engineer what they can from census data and similar statistical information.
German GDP in 1913 is established as by Myszczyszyn in 'Use of econometric modelling to evaluate the impact of the railways on economic growth of German reich (1879–1913)'. I am not fully convinced as these numbers don't make sense. I'm also not sure about the reference to "1956".
Overall GDP grew much faster than per capita; in 1879 it amounted to 18.08 bln marks (M), while being 845 bln M in 1913–1956. The average annual GDP growth rate during that period was 3.01%, which meant the product doubled within approximately 24 years.
GDP per capita, which is a better measure for determining social welfare, grew much slower; it was 475 bln M in 1879 and it reached 873.76 bln M in 1913, the average annual growth rate was 1.73%. That was due to rapid population growth in Germany.
When I try the same geometric progression from 1879 to 1913 for the GDP, I get a 1913 value of ℳ 51.0 bln. Even extending this to 1956 only gives a total of 177 bln. The GDP per capita geometric progression makes sense (I get the same value), but the "bln M" claim is preposterous. These numbers should, therefore, be treated with the uttermost care!
Alternatively, the net national product (NNP) is estimated as a compromise value of ℳ 53.7 bln by Burhop and Wolff in 'A Compromise Estimate of German Net National Product, 1851-1913, and Its Implications for Growth and Business Cycles'. However, the NNP is a wildly different measure to the GDP and not very helpful in determining the other.
How the Great War affected German GDP is a tough question and the answer doesn't seem to be clear-cut. Baten and Schulz estimated that the GDP in 1917 was 69% of the 1913 value. 1918 would have reduced this further and the territories lost in the peace treaty would have had a similar effect.
Most of the other research that comes up only cites relative values -- percentage of the Net Domestic Product compared to 1913. As such, we also have:
The oft-cited work by Hoffman is 'Das deutsche Volkseinkommen 1851-1957', and nearly all values are quoted with respect to this. I suspect it may contain better numbers, but it only seems to be available on paper as well as in German.
If we take the above estimates of 1919 NDP being about 72% of the 1913 values (quite close agreement!) and assume that the NNP, GDP, and NDP went through similar declines through the war period (I'm already able to guess what some of the below comments are going to say...), we get a value of ℳ 38.6 for the NNP in 1919 (in 1913 Goldmark).
The original Versailles' Treaty value of ℳ 226 is nearly six years' worth of NNP, while the reduced ℳ 132 bln is 3.5 years' NNP. I speculate that the ratio might hold even if the actual GDP is different. Better economists than me can point out how wrong this comparison is.
Lastly, a note on Goldmark conversion from the Bundesbank:
The Goldmark is a special case insofar as it was neither a legal unit of currency nor legal tender, but a short name for the monetary value (price) of a given amount of fine gold payable in monetary tokens of the relevant official currency, ie the Mark from 1876 to 1924, and the Reichsmark from 1924 to 1948. Generally speaking, a Goldmark corresponded to the price of 1/2790 kilogram of fine gold.
Up to the outbreak of the First World War, the legal gold parity at the time meant that one Goldmark was equivalent in value to one Mark. When the Reichsbank suspended the exchange of banknotes for gold on 31 July 1914, the value of the Goldmark in paper Mark increased with rising inflation according to developments in the US dollar exchange rate. On 20 November 1923, the Mark’s exchange rate against the Goldmark and the US dollar, which was likewise on a gold standard, was stabilised. Subsequently, and until the introduction of the Reichsmark on 11 October 1924, the Goldmark had a consistent value of 1 trillion Mark.
The accompanying 'Purchasing power equivalents' notes (alongside "major uncertainty") that ℳ 1 in 1913 would have been worth €5.40 in 2019 on PPP while ℳ 1 in 1919 would have been worth €1.10 though in the above research, most people took care to reference the 1913 Goldmark.
