Could you explain how do you define this "natural interest rate"?
As for 0% interest rates not causing inflation. Well I guess that would depend, but it certainly causes more inflation than higher rates (assuming that the production remains the same, which is a fair assumption in the long run). And that means you can't do as much open market operations. I am not sure whether I would like the banks or the government to have this printed money.
The size of deficits should be viewed from the desirability of the non-government sector to net save in dollars. If the deficit is too small, and unemployment increase, we know that spending wasn’t sufficient to cover the spending gap.
Deficits add to bank reserves and result in reserve surpluses within the banking system. The excess reserves will result in competition in the interbank market for banks looking for better returns than the FED can offer.
It would be more logical not provide for a support rate at all. Under this scenario, net spending will shift the overnight rate to zero since interbank competition can’t remove the surpluses in the banking system. All of these transactions would net to zero, and there wouldn’t any destruction of net financial assets.
If we consider full employment as part of the natural setting, fiscal policy will shift the short-terms interest rates to zero. In the even the FED desires a positive short term rate, it would have two options in its policy tool box: drain the excess reserves by issuing bonds or offer a substantially better rate of return on excess reserves.
Personally, I rather zero rates and no bonds sales. The would put fiscal policy in the driver’s seat where it belongs.
In terms of inflation, $$$$ creation, simply doesn’t result in inflation. Spending, taken in isolation, cannot cause inflation. A continuous rise in the price level is a result of demand outpacing the capacity of the economy to expand through increased production. The only way for this to occur is if government spending outpaces the desire of the non-government sector to save at close to full employment. You then end up in a scenario where energy, materials, and labor are bid up. We can also see inflation result from supply shocks.
We can never prognosticate about inflation by simply looking at $$$$ creation/government spending apart from demand as it pertains to supply.