One of the side effects of Quantitative Easing programs is a positive impact on the fiscal situation. The central bank buys government bonds. Interest payments go from the government to the central bank and are then remitted back as part of the central bank’s profit dividend to the government. This has a positive fiscal impact even if QE purchases don’t reduce the interest rates on new government bond issues.

To give an example of the size of this effect in previous programs, figures from the Fed show it earned $116 billion in interest payments last year from the securities it acquired via QE. This allowed the Fed to distribute $99 billion back to the US Treasury. $116 billion is 0.67 percent of US GDP (i.e. two-thirds of one percent). That’s not huge but it’s a nice interest break for the US taxpayer

You could imagine a QE program that also had a big fiscal effect in Europe. For example, Eric Lonergan presents the following figures:

“Consider Italy, which is probably the major beneficiary. Italy currently has a budget deficit of around 3% of GDP. But its primary balance (i.e. the budget balance before interest payments) is close to 2% of GDP. Interest payments therefore account for approximately 5% of GDP. Consider what happens if the ECB, or the Bank of Italy, buys 30% of Italian bonds financed by creating new bank reserves in the Eurosystem? Italy’s interest bill falls by 30%, and its budget deficit falls by 50% from 3% of GDP to 1.5% of GDP.”

Indeed, Italy is projected to spend 4.5 percent of its GDP on interest payments this year. The Euro Area as a whole will spend 2.7 percent of GDP. on interest payments. So on the face of it, a European QE program could have a nice positive fiscal impact based on national central banks (who are the institutions buying almost all the sovereign bonds) remitting money back to their governments.

Alas, it won’t.

In a fantastic “QE manual” from the Bruegel think tank, Gregory Claeys, Alvaro Leandro and Allison Mandra do the sums. They reckon Italy will only get a budget boost of 0.07 percent of GDP (i.e. less than one tenth of one percent) from the Banca d’Italia purchases of its sovereign bonds, while (by my calculations based on their paper) the boost for the Euro area as a whole would be only 0.04 percent of GDP. That’s puny.

There are three reasons why these figures are so small.

1. A Small Program

The Fed has purchased bonds equivalent to about 25 percent of US GDP. At the moment, the ECB’s QE program is projecting to be much smaller. The national central banks will buy about €730 billion in sovereign bonds if the program finishes in September 2016, which is the current plan. That’s about 7 percent of euro area GDP, so the fiscal effect will be comparably smaller than in the US.

2. Capital Key Weighted Purchases

The €730 billion in sovereign bond purchases by the national central banks will be equivalent to about 7.5 percent of the face value of the public debt of euro area members. The amount of QE purchases for each country’s bonds will be in proportion to the corresponding ECB “capital key” which is determined by GDP and population. So for a country like Italy, which has more debt relative to GDP than other members, the total value of bond purchases relative to the face value of its debt will be smaller. The Banca d’Italia will spend an amount equivalent to 6.7 percent of total Italian public debt.

The fact that purchases are capital-key-weighted (and so will include lots of German bonds) also means the average interest rate on the QE purchases will be lower than the average rate on Euro area public debt as a whole.

3. Low Bond Yields

But the key issue (which has received little or no coverage so far as I can tell) is the low average yield on Euro area debt in financial markets.

These low yields mean European central banks will be purchasing bonds at market values well above their original par values. The Bruegel manual states the market value of the debt that could be purchased in the ECB’s program is €5.3 billion, even though the face value of this debt is €4.3 billion. In other words, the market value of this debt is about 23 percent higher than its par value.

This means the Euro Area QE program is even smaller than the figures above had suggested. The €730 billion being spent by the national central banks may be equivalent to 7.5 percent of the face value of the public debt of euro area members but it is not going to buy 7.5 percent of the stock of debt. If these bonds are purchased at a 23 percent premium relative to par value, then these central banks will only be acquiring about 6 percent of the stock of public debt.

For those not familiar with the various pieces of bond-related terminology I’m using here, you should know when the price of a bond goes up in financial markets, the purchasing investors get a lower rate of return (a smaller yield) even though the stream of coupon payments on the bond has not changed. So higher bond prices mean lower bond yields for those purchasing the bonds.

I’ve made a spreadsheet that explains the link between interest coupon payments, bond prices and bond yields. The first tab describes a situation in which a government issues bonds with a face value of €100 that pay an annual interest payment of €2.85 per year. It illustrates the situation where bond yields in the market are 2.85%, which means the market price of the bonds of all maturities will be €100. The figure of 2.85% is chosen because this is the average interest rate on outstanding euro area debt (based on comparing the 2.7% of GDP projected to be spent on interest payments this year with the 95% projected debt-to-GDP ratio.)

The second tab shows what happens when the yield on these bonds drop to 0.23 percent. The price for bonds of all maturities go up, with larger increases the longer the maturity. The ECB is buying bonds with an average maturity of 9 years. A yield of 0.23 percent is required to bid the price of a 9-year bond with an annual coupon payment of 2.85% up to 23 percent over par value, consistent with Bruegel’s calculations and the average maturity of the bonds being acquired. See below for these calculations.