Letting a sandbox S/L lose money

 Getting at this idea that the central bank can effect the economy by insuring NGDP growth. LOook at the non profit automated S/L first.

Normally an S/l currency emitter might have a zero loss function, but an upper and lower limit, say half a point. It is the variance that counts, not the level.  I can show that for any contracted loss or gain function, the traders make a one time shift in deposits to loans to compensate, and the system reverts back to managing the variance interval, which is constant. I will do that below, later.

If this applied to central banking, which is never will, then we again end up with a direct inflation rate which varies with the productivity rate within those upper and lower bounds. The economy should otherwise be unaffected. Low productivity means high inflation and versa versa when the currency banker has a loss function uncorrelated to productivity.