I want to do some very back-of-the-envelope calculations. (I will probably get the arithmetic wrong.)
A bond-financed deficit is where the government prints bonds to finance a deficit. A money-financed deficit is where the government (or the central bank it owns) prints money to finance the deficit. They are different for two reasons:
1. Money is the medium of exchange and unit of account.
2. Money usually pays lower interest rates than bonds.
Here I want to concentrate on that second reason. To keep it simple, I will assume that the money the government prints is currency that pays 0% nominal interest. I will ignore the cost of paper and ink.
Assume that the demand for currency is 5% of Nominal GDP. (That's normally ballpark correct for Canada.)
1. If the central bank targets NGDP, then 0% of a deficit will in fact be money-financed. Because a deficit has no effect on NGDP, by assumption, and so has no effect on the stock of currency, by assumption. (And if I relaxed my assumption that currency demand is a fixed percentage of NGDP, and assumed it is negatively related to the rate of interest on bonds, for standard opportunity cost reasons, and if the deficit increased the rate of interest on bonds, then a negative percentage of the deficit would in fact be money-financed.)
2. Suppose a temporary deficit causes a temporary change in NGDP. It will then cause a temporary change in the stock of currency. Assume the fiscal multiplier is one. A deficit of 10% of NGDP for one year will cause the stock of currency to rise by 0.5% of NGDP for one year then return to its original level. If the interest rate on bonds is 5%, the government will pay 0.5% x 5% = 0.025% of NGDP less interest than if it were wholly bond-financed. 0.025%/10% = 0.0025 = 0.25%. This means that 0.25% of every $1 in debt (or $0.0025 of every $1 in debt) would be covered by the interest saved due to temporary money-finance. It's peanuts. We can ignore it, like I ignored the costs of paper and ink. We would need to assume a fiscal multiplier of 10 to get even 2.5 cents money-finance on the dollar of debt.
3. Suppose a temporary deficit causes a permanent change in NGDP. Assume a multiplier of one per year of deficit. So a 10% deficit for one year causes a permanent 10% increase in NGDP, and a permanent increase in the stock of currency equal to 0.5% of NGDP. And that causes a permanent reduction of interest payments of 0.5%x5%=0.025% of NGDP. If the same deficit were wholly bond-financed, the annual interest payments would be 5%x10%=0.5% of NGDP. 0.025%/0.5% = 0.05 = 5%. This means that 5% of the annual interest payments from the deficit would be covered by the interest saved due to permanent money-finance. That's not peanuts, but it's not very big either.
I don't trust my arithmetic, for good empirical reasons. So somebody please check it.
But if my arithmetic is right, you need to assume that a very short temporary deficit will have a very big and permanent multiplier (some sort of multiple equilibrium thing?) in order to say that money-finance makes a big difference to the costs of servicing the debt.
Otherwise, we can ignore money-finance of deficits to a one order-of-magnitude approximation.
And you could instead simply tell the central bank to target a higher level of NGDP to ensure that some of the existing stock of debt from past deficits will in fact be money-financed.
4. But would this conclusion change if I assumed that NGDP is growing at (say) 4% a year, and a temporary deficit caused a permanent change in the level of NGDP, and that it would continue to grow at 4% per year thereafter, but would be permanently 10% higher than it otherwise would be? That's what I can't figure out. But it should be standard arithmetic. Over to you.