Convertible Indexed Consols

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Consols. Low transaction costs and safe nominal flow.

Indexed. Safe real flow.

We could index them to different consumption bundles, and even account for international differences.

Convertible. There is still one big risk with the indexed consols: the risk that the government will rig the index. If the index used is the CPI or the GDP deflator, that index is defined by an agency of the U.S. government, the same government you are lending to. What is to stop the government from solving its debt service problem by telling the agency to change the index formula so that the CPI rise this year is not 15%, which when added to the base of 1% makes the consol yield 16% this year, but 0%, or even -5%, so the consol yields 0% this year? Since the asset in question is a consol, this does more than solve the debt service problem: it solves the debt problem completely. Once the nominal interest is reduced to zero, that does the job, since there is never any principle to repay.

The solution is to make the consol convertible. It must include a clause saying that the holder may, at his option, convert a $1,000 indexed consol into a $1,000 unindexed consol--- an escape hatch.

Situation (1). Each day, the government issues a $1,000 indexed consol paying 2% plus the CPI, and also unindexed consols at whatever interest rate makes the consol sell for $1,000 that day. Suppose that interest rate is 2% forever; the real interest rate never changes. You own an indexed consol you bought ten years ago. We make it convertible, so you can trade it in any day for one of the freshly issued unindexed consols. Will this work?

This will solve the problem of the government extremely abusing the CPI, because you will convert if they try that. But will you convert even if they don't abuse the CPI, because chance can cause the unindexed consol to have a higher market value?

No. We must think about the market price of the indexed consol. Will it be $1,000? If it is, then everything works fine. Both the indexed and the unindexed consol yield a real rate of 2% at par, but they are different assets because they are different with respect to inflation risk. The indexed bond is safer with respect to real returns, but riskier with respect to nominal returns. Note that we *cannot* just say it is safer, and hence its market price will be higher than $1,000. It depends on supply and demand. Most people like safe real returns, to be sure, to hedge their consumption or their investment purchase of real goods. Some people, though, have more in the way of nominal needs, either locked-in prices for real goods, or nominal liabilities such as fixed-rate mortgages and loans they've taken out. Those people would prefer the unindexed consols. So the market price could go either way, depending on how many people there are of each type and --- crucially--- how many consols of each type the government supplies. If the government issues enough indexed consols, it will flood the market and their price will have to fall below $1,000 because the marginal buyer will prefer an unindexed consol.

So let's suppose the government issues enough of each type of consol to keep the market price of indexed consols equal to $1,000. Now we're OK, I think. You will only trade in your indexed bond if the government abuses the CPI, not just to arbitrage prices. (I will start using the word "bond" instead of "consol" because I like it better, and you'll understand by now the kind of bond I mean. "Bond" is germanic-- Old Norse bonda for peasant-- and just one syllable, and everyday English, and doesn't end with the sentence slowing sound "l")

Situation (2). Now suppose the government only issued the unindexed bonds once, ten years ago when you bought yours.

Why does lack of daily issue make a difference? --because the government might have read the game theory literature on repeated tit for tat and realize that it doesn't support a cooperative equilibrium in the infinitely repeated game. That's my way of thinking, but for most people it needs to be put differently. The government can't competely expropriate your bond anymore by setting the CPI to -20% each year, because you'd convert. Suppose, though, it says, "We are going to set the CPI to -20% for this year, but we're going back to being fair after that," and this is true? (the government's incentives get us into heavy game theory, I think, as to whether this *can* be true, so just suppose it can commit to that). You have a choice: trade in the bond, and lose the indexing that you like and is the reason you bought it originally, or take a small hit for one year. The government can choose the hit to be just small enough that you accept it, and so the escape hatch doesn't work.

If indexed bonds are issued daily,

There's a caveat: what if the government commits to abusing for only one year, and you really prefer having the indexed consol?)

Call abel bonds, for indexed bond  artile. This would be bad in a debt crisis.  Should there be bond covenants for government bonds?