To start, in 1976 economic historian Paul Bairoch made estimates to the historical GDP of a country and conveyed them using a scale of measurement called PPP (purchasing parity power).

An important preface is that I am not an economic historian, or even really that familiar with economics to begin with. As far as I understand it, PPP is a way to compare the relative strength of a currency to another currency. In his case Bairoch uses the value of the American Dollar in 1960 as the baseline for historical economies. Of course, this comparison is not perfect, as apparently using PPP works better for undeveloped economies than it does for the fairly complex ones in question.

Introductions aside, here is the data presented by Bairoch in his 1976 article "Europe's Gross National Product: 1800–1975" published in Volume 5 of the Journal of European Economic History on pages 273 to 340. It puts Germany's 1913 PPP at $49,760,000,000 (1960 USD), or about $398,301,677,645.95 in 2014. Immediately this raises red flags as the PPP of the United States in 2012 is listed as being half of what Germany is supposed to have had after conversion. Another red flag is the obvious question of where Bairoch got these figures and if they are at all accurate. My feeling is they are not, though it is very possible I am not interpreting or converting the figures properly.

I searched through Holger Herwig's The First World War: Germany and Austria-Hungary 1914-1918, the Longman Companion to the First World War, and Gerard J. De Groot's The First World War to try and find the sort of GDP figures we are familiar with today. What I found were measurements of industrial imports and exports, but no hard data on the GDP of European nations. However, I did find one source that lists GDP figures in modern terms that is worth a look.

This paper by Stephen Broadberry and Mark Harrison puts the German GDP at $250.7 billion in 1990 USD on page 25 which converts to $471,491,872,385.58 in 2014. This would make 1914 Germany the 27th biggest economy in the world today, between Argentina and Austria. However, the essay these figures are taken from the League of Nations Statistical Yearbook 1926 and may not be entirely accurate.

While this whole answer may seem fairly unsatisfying, hopefully someone much better qualified than me can fill in the gaps.

*edits were to fix some wording and a broken link