Elsewhere

I have added the blog of some economists at the University of Missouri-Kansas City to my blogroll. That blog is more policy-oriented than this. Bill Mitchell blogs from Australia, also more about policy than I do. Grupo Lujan-Circus seems like a blog of interest to me, but I can read only the names. The same remark applies to the blog of the Italian Association for the History of Political Economy.

Occasionally I stumble across curious articles in Wikipedia. The one on Surplus economics references Paul Baron and Paul Sweezy. It doesn't describe their ideas very well, and could do with some reference to Sraffa too. The entry on Newtonian time in economics seems to have been written by Austrian fanboys who, typically, know about neither Joan Robinson's distinction between logical and historical time nor Paul Davidson's attack on the Austrian school.

By His Bootstraps

1.0 Introduction
One can hold savings in various forms of assets. In effect, savings is a time machine for transferring purchasing power into the future. A debt, when purchased - that is, a bond - is one such asset in which one can store savings. The relationships between bonds of various maturities and the existence of well-developed markets in which to trade bonds allows the determination of interest rates without relying on the theory of time preference, a theory which is a lot of utter hogwash anyhow.

The point of this post is to explain how, under certain institutions for selling second-hand debt, a relatively stable long-term interest rate can be maintained by beliefs in its stability. No need arises to call on the forces of thrift and productivity. This post might even be relevant to current events in the USA.

2.0 Institutions Providing a Setting in Which a Second Decision Must be Made
The model I outline here is based on Keynes' account of the two decisions a saver must make:

"The psychological time-preferences of an individual require two distinct sets of decisions to carry them out completely. The first ... determines for each individual how much of his income he will consume and how much he will reserve in some form of command over future consumption. But this decision having been made, there is a further decision which awaits him, namely, in what form he will hold the command over future consumption which he has reserved, whether out of his current income or from previous savings." -- J. M. Keynes, The General Theory of Employment, Interest and Money (1936): p. 166

Assume that the debts of the best quality available for purchase consist of Treasury bills (T-bills) that mature in three months, T-bills that mature in a year, and Treasury notes (T-notes) that mature in 10 years. These are all available in the U.S.A., along with T-bills, T-notes, and T-bonds of other maturities. In this exposition, I abstract from the existence of these other maturities. By including debts of these three maturities, the model incorporates the decision to hold money, assets that pay the short-term interest rate, or assets that pay the long-term interest rate.

In describing three-month T-bills as money, I again follow Keynes:

"...we can draw the line between 'money' and 'debts' at whatever point is most convenient for handling a particular problem. For example, we can treat as money any command over general purchasing power which the owner has not parted with for a period in excess of three months, and as debt what cannot be recovered for a longer period than this; or we can substitute for 'three months' one month or three days or three hours or any other period; or we can exclude from money whatever is not legal tender on the spot. It is often convenient to include in money time-deposits with banks and, occasionally, even such instruments as (e.g.) treasury bills." -- J. M. Keynes, The General Theory of Employment, Interest and Money (1936): p. 167

Suppose, contrary to fact, that the short term interest rate, r, was known to be constant for the next ten years, where 100 r is stated as an annual percentage. Then the long term interest rate would be established in the market at the start of the year as 100 [(1 + r)¹⁰ - 1] percent for 10 years, and the interest rate on money would be 100 [(1 + r)^1/4 - 1] percent for three months. A higher price on a bond corresponds to a lower interest rate. For example, the price of a T-bill with a face value of $1000 to be paid in a year is 1000/(1 + r) dollars.

3.0 The Individual
In this model, federal authorities set the interest rate on money. The short term interest rate provides a market consensus on monetary policy is likely to be over the next year. If the annual interest rate embodied in the price of one-year T-bills is higher than the annualized interest rate on money, the market price of T-bills is predicting a tightening of monetary policy. The individual allocates his savings partly on his opinion of this consensus. If he thinks, for example, that the monetary authority is not going to tighten that much, he would sell three-month T-bills and buy one-year T-bills, so as to make a profit from speculation when the price of the latter rises.

The individual, one assumes, has some idea of what is a normal long-term interest rate. He expects that over a long enough period, the federal authority's monetary policy will average out, thereby achieving this normal rate. The individual expects the price of T-notes to eventually rise when the current long-term interest rate is above that normal long-term rate and to fall when the current long-term rate is below that normal rate. Here, too, the possibility for speculative gains influences the individual in his allocation of his savings between T-notes and T-bills.

3.0 Markets
Consider a range of the price of T-notes. For a high enough price, those who are bears on this market (who expect the long term interest rate to rise) would dominate the bulls (who expect the long term interest rate to fall). More would be selling than buying, and the price would fall. The opposite is true for a low enough price. The equilibrium price at an instant of time balances bulls and bears:

"In the Treatise [Keynes] pictures the Bulls and Bears of the gilt-edged market going into and out of bonds as they individually come to think that the next price movement will be up or down. In this speculative market the price of bonds and thus their yield, the interest rate, can only settle if opinion is divided, so that those who wish to sell for fear of a fall find their offers matched by the bids of those who wish to buy in hope of a rise. It is thus, as Keynes says, a variety of opinion in the gilt-edged market which gives stability to the interest rate and some control over it to the monetary authorities." -- G. L. S. Shackle, "Simplicity in Keynes's Theory of Money and Employment", The South African Journal of Economics, v. 51, n. 3 (1983): 357-367

Elsewhere Shackle talks about equilibrium in such a speculative market as inherently restless.

4.0 Conclusions and a Policy Implication
I suppose one could express the above model in mathematics, if one were so inclined. One might start with some distribution of agents' beliefs about the conventional long term interest rate, and allow each agent to slowly update their view, maybe with the addition of random noise. (One might draw on Shackle's "The Bounds of Unknowledge" (in Beyond Positive Economics (ed. by J. Wiseman) Macmillan, 1983) in specifying this updating.) And the agents would decide on the distribution of their savings based on their views. Maybe the model should have more types of assets. One would want a model in which a diversity of opinion is maintained among agents, and in which time series for stock equilibria exhibit hysteresis and non-ergodicity. It wouldn't surprise me if somebody has already published such a model.

Keynes had something to say about policy based on this sort of analysis:

"Thus a monetary policy which strikes public opinion as being experimental in character or easily liable to change may fail in its objective of greatly reducing the long-term rate of interest... The same policy, on the other hand, may prove easily successful if it appeals to public opinion as being reasonable and practicable and in the public interest, rooted in strong conviction, and promoted by an authority unlikely to be superseded." -- J. M. Keynes, The General Theory of Employment, Interest and Money (1936): p. 203

An Experiment Protocol

1.0 Introduction
The point of the experiment described here is to offer empirical evidence for the importance of the distinction between uncertainty and risk, as put forth by Frank Knight and by John Maynard Keynes. People are not "rational", as "rationality" is defined by neoclassical economists.

As usual, I don't claim much originality except, maybe, in details. Daniel Ellsberg described the experiment below, as well as another. He references Chipman as having conducted experiments much like these. (Although Ellsberg's paper is oft cited and has been republished, Daniel Ellsberg is probably best known for having leaked The Pentagon Papers to the New York Times and others. Nixon's "plumbers" illegally broke into and searched Ellsberg's psychiatrist's office.)

2.0 The Protocol
The experimenter shows the test subject two urns, urn I and urn II. The test subject is shown that urn 1 is empty. The experimenter truthfully assures the test subject that urn II contains 8 balls, with some or none of them red and the remainder black. The test subject sees the experimented put one red and one black ball in urn II. The experimenter also puts in five red and five black balls in urn I in the test subject's presence. The urns are shaken.

So the test subject knows that urn number I contains 5 red and 5 black balls. Urn number II contains 10 balls. All are either red or black. At least one is black, and at least one is red.

The experimenter flips two coins so as to offer a gamble to the test subject. The coin flipping ensures the probability of offering each gamble is one in four. The gambles are described to the test subject:

• Gamble A: You pay $5 for a draw from urn number I. You choose before the draw whether to play red or black. If a ball is drawn of your color, you receive a payout of $10.
• Gamble B: You pay $5 for a draw from urn number II. You choose before the draw whether to play red or black. If a ball is drawn of your color, you receive a payout of $10.
• Gamble C: You pay $5. You choose urn number I or urn number II. A ball is drawn from the urn you selected. If the ball is red, you receive $10.
• Gamble D: You pay $5. You choose urn number I or urn number II. A ball is drawn from the urn you selected. If the ball is black, you receive $10.

Each test subject goes exactly once, and no test subject is able to observe previous plays by other test subjects (so urn number II cannot be sampled by a test subject).

The hypothesis is that in gambles A and B, statistically equal numbers of people will choose each color, while in gambles C and D, people will prefer to choose urn nmber I.

3.0 To Do

• Demonstrate mathematically that no assignments of probability in urn number II are compatible with the hypothetical behavior.
• Decide on a sample size. Perhaps a sequential test can be defined in which the sample size is not known beforehand.
• Read Craig and Tversky (1995) and Chipman (1960). Where else is Ellsberg referenced?

References

• J. S. Chipman, "Stochastic Choice and Subjective Probability", in Decisions, Values and Groups (edited by D. Willner), Pergamon Press (1960)
• Daniel Ellsberg, "Risk, Ambiguity, and the Savage Axioms", Quarterly Journal of Economics, V. 75, N. 4 (Nov. 1961): 643-669
• Craig R. Fox and Amos Tversky, "Ambiguity Aversion and Comparative Ignorance", Quarterly Journal of Economics, V. 110, N. 3 (1995): 585-603