In the case of fiat currency, the supply of money is based primarily on 1) Increases/Decreases in the loans provided by banks and to a lessor extent 2) a central banks balance sheet.
I don't believe it's possible to add to the supply of bitcoins simply by loaning them into existence vs. fiat currency. That is, there isn't a closed-loop system similar to the banking system that allows for this elasticity of bitcoin units.
I'm not advocating that this is a requirement or even desirable, it's just a limitation that I don't see often discussed.