Lets say you a country where the official government debt (not adjusted for who owns the debt) is 30% of GDP. The official government debt consist of 50% government bonds and the central banks owns 40% of these government bonds. Since the government finance the centralbank we have to adjust the official government debt and remove the 40% of the government bonds that the centralbank own to get the real government debt expresed as % of GDP. In my initial calculation I simply did like this:
Real government debt expressed as % of GDP = 0.3*(1-0.4) =18%
However, that such number does not take into consideration that the official government debt is only made up of 50% government bonds. I tried to play around with different types of equations but I found none that makes any logical sense and provides me with a reasonable number. I would expect the real government debt to around 23% of GDP. This might be a simple question but I must admit I am stuck and I am not making any progress. Any help would be appreciated.