# Wealth effect from OMO

In a paper by Eric Leeper he says:

For example, a contractionary open-market sale of government bonds raises nominal interest rates, including yields on government bonds. If the higher debt service is permitted to flow in to more rapid growth in nominal debt with no prospect of eventually higher taxes – or primary surpluses, more generally – then bond holders will perceive that their wealth has increased and seek to convert that wealth in to purchases of goods. This higher aggregate demand will ultimately raise the price level.

On a theoretical level I seem to understand what he is saying but I do have some questions regarding the operation from practical perspective.

Say in period $t-1$ I own some government bonds. In period $t$ the central bank performs the contractionary OMO. So they lower the price of government bonds but raise its yield. This will increase the debt service cost for the government and if they decide to fund it by selling more bonds, I will experience a positive wealth effect.

I think I'm confused because I don't quite understand the specifics of bond trading. So the bonds that I own in period $t-1$, is their yield flexible? I.e, once the CB performs the OMO and raises yield, will the bonds I already own also receive this new, higher yield?

Also, in period $t-1$, when I bought the bonds, I paid a certain price. Then the CB starts selling bonds, thus lowering its price while raising yield. The higher debt service cost results in the government issuing more bonds, surely this lowers the bond prices further? So when I eventually sell the bond, I should have lost money?

What am I missing here?

I've changed order slightly, for ease of explanation.

I think I'm confused because I don't quite understand the specifics of bond trading. So the bonds that I own in period t−1, is their yield flexible?

In the real world (and more complex models) certainly - otherwise bond trading would be rather boring.

During the day, bond traders exchange bonds at various prices, and the yield is essentially the implied internal rate of return (modulo quote convention effects) corresponding to those prices if the bond is held to maturity. That is, if you hold to maturity, you are guaranteed that internal rate of return (IRR) - absent default - although total return depends upon coupon reinvestment. Otherwise, your profit/loss depends upon what price you sell at (and coupon income during your holding period).

Dynamic economic models quite often diverge from this reality in two ways.

1. All bond trading during a period occurs at one price. Therefore, you cannot have gains/losses during a single accounting period.
2. In many models, "bonds" mature in the next period. ("Bills" would be a better label.) Since there are no intermediate time periods, you cannot suffer a capital loss on bonds in such a period. The only way to have capital gains/losses on bonds is to allow for multi-period maturity bonds (or perpetuals), which complicates the model mathematics.

I.e, once the CB performs the OMO and raises yield, will the bonds I already own also receive this new, higher yield?

If you are investing in one period bills, your existing bill matured, and you would invest in a new bill at a higher yield.

If you hold multi-period bonds, their projected internal rate of return would rise. However, the effect on your wealth is mixed. The way that bond yield conventions work is that you would receive the running yield of the bond (+), but you would get a capital loss (-) which roughly equals the modified duration of the bond in the next period, times the yield change. For long maturity bonds, the capital losses are typically much larger than the running yield. In other words, you would likely experience a short term capital loss, but that is made up by higher projected returns. After all, if you hold to maturity, you get the initial yield as an IRR.

Say in period t-1 I own some government bonds. In period t the central bank performs the contractionary OMO. So they lower the price of government bonds but raise its yield. This will increase the debt service cost for the government and if they decide to fund it by selling more bonds, I will experience a positive wealth effect.

Leeper's text is phrased in a somewhat confusing way. It refers to a model of a representative household, who effectively owns all government liabilities. In a world with multiple households, if you bought a long-term bond at t-1, you could easily have less wealth in period t; the increased interest could be received by other households who held 1-period bills that matured, and did not have a capital loss.

That is, he is really writing about the household sector, and not individual bond owners.

Also, in period t−1, when I bought the bonds, I paid a certain price. Then the CB starts selling bonds, thus lowering its price while raising yield. The higher debt service cost results in the government issuing more bonds, surely this lowers the bond prices further [1]? So when I eventually sell the bond, I should have lost money [2]?

Sub-question [2] is covered by the above; your gain/loss depends upon the trade-off between the running yield and the capital loss.

As for [1], the effects of supply on bond yields is controversial. In a simplified model where there is no term premium, bond yields depend only upon the expected path of interest rates. If the increased interest payments do not cause the central bank to raise interest rates (over the lifetime of the bond), bond yields are unaffected.

In the real world, there presumably is a term premium, which might be affected by the amount of bond issuance. Even so, it is clear that the effect is not that large: we have had plenty of rate hike cycles, and bond yields did not enter a positive feedback loop of ever-rising yields.

• Dr. Romanchuk, thank you so much for the detailed answer, it helped me immensely. Could you recommend any academic literature where I can learn more about bonds and their effect on the economy? I'm an undergrad trying to learn about FTPL and the most confusing part for me thus far has been understanding the mechanisms of bond trading. Apr 22 '17 at 13:55
• I am a post-Keynesian, so I am partial to "Monetary Economics" by Godley and Lavoie. The mathematics is much simplier than DSGE macro, so it's easier to follow. Won't help you with the FTPL, but it discusses portfolio/wealth effects. I write about bonds, and the problem with "bond trading" is that it is either too simple, or too complex. No mass market in bond analysis, unlike stocks. I would try central bank web sites as a first step, they have a lot of material that explains academic research. Apr 22 '17 at 14:09