Economics and similar, for the sleep-deprived

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Friday, February 07, 2003

Rubinomics Redux

I still don't know what the word "redux" means, despite someone telling me a while ago, but they use it all the time in Slate so it must still be fashionable.

There has been much mud (and indeed shit) thrown around the economic policy community over the question "Do deficits raise interest rates"? I thought I'd throw in my couple of penn'orth. Recent visitors, do feel free to summarise the following in a sarcastic one-liner; it may turn out long.

Brad DeLong's argument is pretty simple; he tries to explain it in terms of supply and demand. If you increase the deficit, you increase the supply of bonds, so you drive down their price, and one minus the reciprocal of the bond price is the interest rate. It's a simple, plausible argument and I hate it.

Why? OK, first up, a couple of economics concepts.

I admitted in comments a few stories below that although I act like I do, I don't actually have an advanced degree in economics. My degree is in Finance, a closely related but separate discipline. To my way of thinking, the chief difference between finance and economics is that in finance, supply-and-demand arguments are generally treated with suspicion and no-arbitrage arguments are the standard method of proof, while in economics, things are the other way around.

Definition: A "no arbitrage" argument is a piece of economic reasoning which proceeds by showing that, under assumptions, a financial claim must have a particular price, because any other price would allow a speculator to make unlimited riskless profit by following a particular trading strategy. For example, the correct price of a 3-month S&P500 future is the value of the S&P today, discounted by the 3 month interest rate. If the future is any dearer than this, you short the future and borrow three month money to buy the S&P today; if it's any less, vice versa.

I'm assuming that you guys can work out what "supply and demand" arguments are.

Economists tend to distrust no-arbitrage reasoning because it looks too much like an analytical free lunch, because they often make restrictive assumptions which are not too bad when the context is a financial market but ludicrous in other contexts, and because they are "ketchup reasoning" - they tell you that a quart of ketchup costs the same as two pints, when you want to know the price of ketchup given the cost of tomatoes.

Finance theorists tend to distrust supply-demand arguments because in the first place, they are often used as a dodge to get out of some difficult maths, and because the elasticity of substitution of financial assets is extremely high. For example, if a big fund tries to sell a huge chunk of GE stock, should it push the price down? Well, not really. If the price drops as a result of the new supply, then somebody might as well sell some of their Boeing to buy GE; since all they care about are cashflows and exhypothesi the supply-induced drop in GE means that GE cashflows are cheaper than anyone else's, people would step in to iron out the discrepancy.

Obviously it's horses for courses. The question is, are US Treasury bonds more like GE stock, or are they more like the sort of commodities for which supply-demand arguments are appropriate?

It depends how you model it. Implicit in Brad's argument, and I wish he'd made it explicit, is something like the following model of the bond market.

Bonds are claims on the productive resources of an uncertain future. Longtime readers of this blog will recall that neoclassical economics doesn't deal with time and uncertainty very well at all; they deal with it by flattening the future down into the past by means of "taking expectations". This is what Brad's model is implicitly doing, and it's the source of much of the confusion over what Glenn Hubbard said and what the evidence shows. Instead of thinking of the market as being one in which
the government decides every day on the supply of bonds and investors decide every day on their demand, we have to pretend that tomorrow the government is going to announce the net amount of bonds it wants to sell on every future date until the end of time, and investors are going to have to
say what price they would be prepared to pay for each of those future bond issues. Instead of a demand function for bonds, if we're going to use a supply-demand argument, we need a demand function over debt paths.

This makes the argument a bit more sophisticated at the cost of not much confusion, I think. A one-off big deficit this year wouldn't have much impact on the interest rate if we knew that it was matched at some future date by an equally big net repayment of bonds (if you doubt this, think
what the effect on ten year interest rates would be if the government announced that, just for fun, it was going to issue $1trn ten year bonds today and use the proceeds to buy them back tomorrow). This is why there is, to coin a phrase "no one-for-one relationship between deficits and interest rates" in the empirical literature - if you are just trying to match up today's deficit with today's interest rates, then you're ignoring expectations, and you shouldn't be surprised if you don't find a relationship between an interest rate based on an entire future path of deficit expectations, and today's single time-slice of that path. Brad's supply and demand argument is clearly one about a static demand function over debt paths, and the Bush deficits (and Clinton deficit reductions) work on interest rates through their effect on market expectations of future deficits out to the end of time (or in fact, out to thirty years, as that is, noncoincedentally, both the longest maturity of treasury bond and the point beyond which cash flows become really small when discounted back to today).

That's a supply-demand argument. I still don't like it, because even in its debt-path form, it assumes a constant, stable demand function over debt paths. I don't like this assumption, because I think that the willingness of the population to trade off current consumption for future will depend on a variety of factors which ought to change in historical time. I also don't like the use of the expectations operator because I think that we live in a nonergodic world (what was your expectation in 1995 of the fiscal
stance of the Bush government? Well, if you were pricing ten year government bonds at the beginning of Rubinomics, this model says that you had to have had one!).

How would a no-arbitrage version of the same argument go? Basically, this literature starts suprisingly recently in the 1970s with Vasicek's one-factor model of the yield curve. The idea is that, while GE stock probably isn't a good substitute for ten year Treasuries, nine year treasuries probably are. And eight year treasuries are a decent substitute for nine year, and so on ... until, by the (arguable) transitivity of the relation "is a good substitute for", we have the overnight repo rate as a
good enough substitute for ten year treasuries to get an arbitrage argument off the ground. Which isn't as unrealistic as it sounds; there's quite an intuitive appeal to the concept that it ought not to make a difference whether you buy a ten year bond and hold it to maturity on the one hand, or on the other, you take your money and invest it at the overnight rate every night for ten years.

Under Vasicek's model, the no-arbitrage price for a ten year bond is exactly that price at which the two strategies above have the same expected return (note that finance doesn't get away from using the expectations operator; below I argue that it does so in a less pernicious way). If the ten year is cheap relative to your expectation of the future of interest rates over ten years, then you borrow overnight money today and buy a ten year bond, then roll your debt over, every day borrowing overnight money to pay back the previous day's loan until you get your final payment on the ten year bond, which compensates you for the interest costs you have incurred over the previous ten years. Or equivalently, every ten year bond price is implicitly a forecast of the ten year path of overnight interest rates, and the price of government debt in general should, under conditions of strict no-arbitrage, be equivalent to the market's expectation of the path of overnight rates until the end of time.

So, we've got a bit of a conundrum here. Under the supply-demand model, the ten year interest rate is determined by the market's preferences over future debt paths. Under the Vasicek no-arbitrage model (there are more complicated ones which incorporate time and risk premia, but give me a break), the ten year interest rate has to be identically equal to the market's expectations of overnight interest rates. There is some quite severe over-determination here. Are the market's expectations of overnight
rates determined by the market's expectations of future debt paths and preferences of debt paths? We can't rely on this being the case, because the one thing that we do know are that the market for overnight money is not composed of the same individuals as the market for ten year money -- one of these markets provides liquidity to the other, so the one thing we know about the two investor bases is that they don't have similar views about liquidity, so why would their expectations and preferences
necessarily coincide?

I think that this antinomy has to be resolved by dropping the supply-demand model of government deficits and the yield curve. I believe this for the following reason; the use of the expectations operator in the two models is not symmetrical. Note that in the supply-demand model, the market is being asked to do two things; to form an expectation of the future debt path based on today's information, and to decide on the terms on which it is prepared to provide ten year money given that debt path. In the Vasicek model, the epistemological demands on the market aren't so great. Participants aren't asked to make any guesses about the future of the world at all; they're just asked to give a snap judgement of what terms they see themselves providing money going forward. Obviously, the objection to this is that the terms on which they will provide money going forward will depend on the state of the world in the future, so the position is symmetrical, but I think that there is a difference. Basically, it all comes back to ergodicity. The future debt path is nonergodic; there's destabilising feedback on all sides, and just isn't possible to have sensible expectations ten years out. But ten years out, the money market will be about the same as it is today. The mean of the spread of market expectations of the overnight rate ten years' out is likely to be much more informative than the mean of expectations of the deficit, because the interest rate has much more structure; it's anchored in the region 0-20% for practical purposes, can't be negative, etc. The market expectation of the overnight rate ten years out might not be right; it might not even be an unbiased or efficient predictor, but I don't need that. All I'm saying is that it's more plausible to assume that this future price quote exists, than that a coherent expectation of future debt paths exists.

So, given this interpretation, what effect do deficits have on interest rates? Well, do you know, I think it comes down to animal spirits in the end. The important thing about Rubinomics wasn't really deficit reduction, it was that there was a coherent story to tell. People didn't bid down ten year treasuries because they thought that ten year treasuries were going to be incredibly scarce in future; they did so because they thought that we'd entered a new environment of lower interest rates. And similarly, when Glenn Hubbard tells fibs about deficits, it's the fibs that will have the effect on long term interest rates, not the deficits. This is the kind of economics that they don't teach you in universities, but that you pick up quite naturally on the job. It's an intrinsically nonmathematical way of looking at the fundamental drivers of a very mathematical model (try solving the Vasicek one day). It's something we ought to learn about from the sociologists. It's all about telling a story.

If you care about this sort of thing, Nicholas Dunbar's Inventing Money is a very good book. It's not quite such a thrilling account of the Long Term Capital Management disaster as Lowenstein's "When Genius Failed", but it doesn't dumb down the finance theory.
0 comments this item posted by the management 2/07/2003 11:12:00 AM

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