Interview with Kenneth Arrow
By Darrell Duffie
On April 6, 2006
Note: The transcript has been edited for clarity and readability. In addition, footnotes have been added to clarify names or documents.
Duffie: The American Finance Association is conducting a series of interviews with founding contributors to the field of finance. Today we are at Stanford University for an interview with Professor Kenneth Arrow.
Good morning Kenneth.
Arrow: Good morning.
Duffie: I want to get right to what I think of as the key id ea for today’s discussion. That is the notion of state-contingent consumption cited in your 1972 Nobel Prize. In your speech for the Nobel Prize, you referred to your 1953 paper in which you developed the idea that general equilibrium theory covers uncertainty through its treatment of state-contingent consumption of a commodity, (just) like any other commodity. If you would not mind, could you take us back and tell us how you developed that idea?
Arrow: Of course. When I talk about developing ideas, I find that the roots are not exactly linear or even easily describable. When I think about a question, I think about it one way. Then I think about it another way. Suddenly some synthesis pops into my mind. I t’s like doing a crossword puzzle. You look at it, and look at it. Then suddenly you see, oh yes, of course.
The fact that general equilibrium theory did not well incorporate uncertainty, was sort of known among those people who were concerned with this. The state of general equilibrium theory at this period was really defined by
J.R. Hicks ’ Value and Capital , published in 1939. The novelty of that book, apart from the fact that it was a beautiful synthesis in general, was the treatment of
1

time and particularly the idea that commodities at different points of time are really just commodities except they have a different time subscript.
If you looked back at what capital theory was, say in the hands of people like Frank Knight or Frederick Von Hyak, it was mysticism. Those two argued very vehemently with each other, but many of us could not understand what the question was. (laugh) They would tell parables with some simple examples and argue in those terms but not in terms of a general theory.
Hicks made the very simple argument that if you are planning to provide for the future, whether it is as somebody who is worried about consumption in the future, or as somebody who is building up capital in real terms, - you are not buying capital goods with the idea that they would yield future product
, that’s the investment side - all this could be done by planning for a consumption vector which includes dated commodities. Or, if I am a firm, I am planning for an input/output mix with dated values. Suddenly, something that had been mystical became very simple. In fact, the standard general equilibrium, let’s say as has been sketched by Leon Walrus or Gustav Cassel, could be now restated in the same form. I don’t mean there weren’t problems. That was not the end of the story, but it certainly was the beginning.
Hicks was aware that when you are dealing with the future, you are likely to have uncertainty. He rather explicitly introduced a device, but I won’t bother going into what he did, which he knows is imperfect. So therefore, the problem of how you incorporate uncertainty into a general equilibrium theory was known to be a problem. As I say, Hicks discusses this with some specifics.
As for my own training, we may come back to this in more detail, I really started as a statistician. I studied mathematical statistics and gradually moved into economics. So I was well acquainted with ideas of uncertainty and the things to be done about it. And what was to be done about it in this case was investigate further, take samples. That was a strategy for dealing with uncertainty. So after I had done some other work, my attention was drawn to it, because this was in my field.
S omewhere, probably in the fall, I’m not even sure of the date, but somewhere around the fall of 1951, I was considering this. Now at this point, there was literature developed, not on the general equilibrium theory of
2

uncertainty, but just how to handle unc ertainty. I don’t want to go into too much historical detail, but there had been, of course, the expected utility theory of choice, which had been developed by Daniel Bernoulli and was published in
1738. It’s quite ancient. This had been kind of undermined because avant garde economic theorists with whom I studied, like Harold Hotelling, sai d utility can’t be cardinal. Utility is simply an ordering. Well, if you don’t have numerical utility, then you can’t take an expected value. So the Bernoulli theory was coming under criticism. Then, von Neumann and Morgenstern stated, in the first edition, actually they printed the proof in the second edition in 1947, of their book, Theory of Games & Economic Behavior , an argument that even though you start from what you might call an ordinal point of view, nevertheless, if you make some assumptions about what you mean by rational choice under uncertainty, you can construct a utility function whose expected value determines choice.
This was very shocking, and everybody in this group was writing refutations. Paul Samuelson, for example, was writing refutations, and so forth.
It took a few years for people to be convinced that it really was right (laugh). The next step was a further formalization to which the name Leonard J. Savage, known as Jimmy Savage, is especially associated. The idea was that probabilities need not be some objectively given fact, they could reflect subjective evaluations of uncertainty. The primitive concept was that there could be a number of possible states of the world, and if you took an action, what that meant is you would get a certain outcome under each possible state of the world. Now this fitted in with the general way probability was formulated, especially by people like ??? in the 1930s, that a random variable was a function over states of the world.
Duffie: Savage got into that?
Arrow: Did he formulate it that clearly? Maybe he did. It was explicit in probability theory, and I think Savage made it clear. At any rate, Savage brought it to the attention of those interested in decision making.
I began to think about how to incorporate uncertainty. The usual thing is you started with probabilities, and you had a utility function over the mean and
3

variance. There were papers by people like Marshak, who had written a couple of papers in the late ‘30s, and even applied it to things like portfolio selection.
But means and variances are particular ways to describe probabilities. There could be probability distributions that didn’t have means and variances, like the
Cauchy distribution. So somehow it didn’t seem very fundamental. It seemed like a way of talking which might be useful. Marshak even said that maybe the third moment counts in your evaluation. But there didn’t seem any particular way of just talking about it.
So I was brooding about it.
I knew of Hick’s device of dating commodities, and suddenly
, it was like the fall of ’51, it finally came to my mind that the way to think about it is that a consumption vector could be thought of as consumption at particular states of the world, just as you had consumption at a particular time.
Consumption of a particular commodity in a particular state of the world is analogous to Hick’s consumption at a particular point of time. Then it struck me that ordinary securities are sort of that thing. Y ou don’t write them out that way, but it is obvious in the case of a common stock that what the company pays out is a function of the state of the world.
Duffie: The notion of general equilibrium had been out there. I mean, the rigorous mathematical structural had been in place. Had no one attempted to treat uncertainty in some other way?
Arrow: The idea that there was uncertainty in the world and that it should be treated is certainly in much of the earlier writing. If you go back to Stanley
Jevons in 1871, he didn’t have a true general equilibrium point of view, but if you try to express his ideas carefully, you would have come to that conclusion because while he didn’t quite have it, he almost did. He discusses the fact that consumption might be uncertain. He worries about consumption over time, and he explicitly dated commodities. He had something like that. He discusses a ship which is provisioning itself for a trip, and things of that kind. He mentions there is uncertainty, such as what your needs are going to be, and he refers to
Bernoulli. Marshall, 30 years later, or 20 years later, also refers to Bernoulli, but it is just a reference.
4

Roughly speaking, there was a theory out there which needed to be developed. They recognized the need for it. The references to Bernoulli, I think, were kind of pro forma. If you look at it carefully, a man named Isaac Todd
Hunter wrote a history of the theory of probability, in about 1865 or so. These mathematically inclined economists all knew about it. It is quite clear to me they took their discussion of Bernoulli, not from the original, which hadn’t been translated into any modern language at that time, but from Todd Hunter
’s summary, which was okay but not exactly very full. He has a big book, and he is terribly detailed. But they knew there was this question. Even Fisher refers to uncertainty in his book on a capital market, I forget the title. I t’s about 1910 or
1907 or so, and he refers to uncertainty. But he does not identify a question.
Nobody had really integrated uncertainty. Walras does not even refer to uncertain ty, I don’t believe. I won’t swear that there’s no reference, but there is certainly no useful reference in the whole book, the two volumes. Casell, who gave a summary of it in 1903, again does not refer to uncertainty at all, if I am correct. There was a lot of this. Of course , in the ‘20s people were writing on uncertainty. T he famous one is Frank Knight’s doctoral dissertation, Risk,
Uncertainty and Profit. But he really talks in terms of individuals facing an uncertain issue.
Duffie: As opposed to a market?
Arrow: As opposed to markets. I think there is some qualitative discussion of things like common stocks as a risk shifting device. Hicks took up the subject in the ‘30s, by the way, not only (in) Value and Capital , but in some other papers.
But it doesn’t really lead to a systematic interpretation. That’s why anybody who thought about it knew this need was (there). It was perceived by people like
Marshak, but there was a gap. T hat’s about the best you can say. Hicks does address the question in Value and Capital , but he addresses it in a (limited way).
He says people behave as if there is a price (of risk), which presumably is being interpreted as a price discounted for uncertainty. But how you do it? And what
(should) the price would be? Indeed, I was accustomed to the argument that there is behavior, just as a statistician, that there are things you do which you
5

would not do with any certain price. The idea of a certain(ty) equival ent doesn’t really make any sense, because you would actually do things, (like hold) inventories, or something like that, which you would not do If you knew for certain what was going to happen. If you knew for certain what was going to happen, you would never hold inventories. You would hold exactly enough to meet the demand. So it was the idea that there is behavior under uncertainty that really could not be explained by (existing) models.
Duffie: I, among others, think that key ideas in your 1953 paper were probably the foundation of modern asset pricing theory. You mentioned a moment ago that one of the innovations in that paper was (that) of statecontingent consumption, treating it just like any other commodity. Another innovation in that paper was an alternative mechanism for achieving an allocation of state-contingent consumption. Rather than a security that pays one bushel of wheat at a particular point in time in a particular state of the world, (you had) a security that pays a certain amount of units of account, dollars if you will, or wealth. In the event that (a) contingent state of the world actually occurs, you could use the proceeds from the sale of that security, or claims to that security, to purchase commodities directly.
So there are two different ways of thinking about getting claims to consumption, one direct and one indirect. You pointed out the differences.
What prompted that kind of alternative which, by the way, didn’t appear e ven in Debreu’s work Une Economie de l’Incertain which (also) followed your paper on statecontingent consumption, but didn’t get into securities whose cash flows would then be used to purchase consumption. So you had these two different ways of doing it. What prompted that?
Arrow: Well, I guess I knew enough about the world to know that securities usually didn’t pay commodities (laugh). There were futures contracts. So there was some set of markets where you actually delivered goods. But I knew that most securities did not, and it struck me that this reduced the number of markets.
Therefore if you think of a world in which markets are costless, but still somehow reducing them for markets wasn’t the (laugh), a good thing. So there (is) an
6

efficiency, due to the fact that securities are paid in money, which you then translate and I realized and the answer is no, very trivial. (laugh) It’s a question of stating it. Anything you say there is obvious once stated. The problem is to state it.
Duffie: You probably know that those state-contingent wealth claims are now known as Arrow securities, and we still teach it that way in graduate school. (Or) so I have heard.
Arrow: Yeah.
Duffie: Going back to Debreu
’s paper, I mentioned a minute ago that he develop(ed) this notion of state contingent consumption claims.
(However he) did not develop the notion of a security whose cash flows could then be used to purchase consumption, and, as you say, create some efficiencies. Yet his paper was written (a) year after yours. Did you have a chance to discuss this with him?
Arrow: No, I never did.
Duffie: It never came up?
Arrow: All the discussions we had, I guess (were on) other topics. I never asked him why he didn’t follow that up.
Duffie: One of the big ideas for which you won the Nobel Prize was your collaboration with G
érard Debreu, which not only formalized this notion of general equilibrium, but actually proved that an equilibrium exists. Yet in that famous 1954 paper with Debreu, after both of you had written about state-contingent consumption
, you really didn’t get into that at all in that 1954 paper. I t wasn’t even mentioned, that I could tell.
7

Arrow: The truth is, I’m not very clear. I can’t really answer why it didn’t happen. But what actually happened is (that at) the same time I was thinking about incorporating uncertainty, I had this idea in the fall of ’51 (that) I have to work it out. For some reason I started working on it, and I seemed to find a dif ficulty. I don’t know now what the difficulty could have been, (but) somehow I was thinking it was slightly wrong. (There) seem(ed) to be a little bit of a problem. Meanwhile, I thought about the question of (the) existence of (an) equilibrium. I saw it based, essentially, on reinterpret ing Nash’s work, (and) seeing that it is applicable to general competitive equilibrium.
Duffie: The fixed point part?
Arrow: Once you saw the fixed point, you could see (it). What I actually did was invent a game. (That) is not quite the way it shows up, but it’s not too different (from) the way it was published. The way I (originally) came to it was, I thought of an artificial game whose equilibrium is (a) competitive equilibrium. I won’t try to describe it here. I worked it out to get all the details right. There were problems because (the) equilibrium was not a mechanical application.
These ac tion spaces weren’t compact, and they weren’t bounded. You have to provide for that. So it took a little gadget??, and I spent the fall of 1951 on that.
Actually a funny story happened then. I had applied for and gotten a traveling fellowship to study statistical problems in economic planning. All
European countries were doing planning. And, of course, what was the statistical basis of this and the concept? To tell you the truth, I did it in order to do some tourism. (laugh) I spent nine months of very enjoyable tourism. I was collecting a lot of stuff, but I never finished the project. All the raw materials, which probably have historical significance, seemed to have disappeared. But I
(made) a lot of contacts.
The first place I went to was Rome. This was in January, and I figured I would go to the southern most and work my way up with the seasons. My wife and I went on this trip, and (in) those days, mail went through American Express.
If you want(ed) to send communication, you would send it to American Express.
So (I went) down to the American Express office, (and) there was a big
8

manuscript from G érard. It seems he had been working on the existence question also, and he had gotten a preprint I had circulated with ??? Sulty. So I had it, but he just thought he would send me the manuscript to show what he had done, and he realized I had scooped him. I was going to look at it, (but the) next day I get another letter (that says) no, you made a mistake. I am going to distribute my copy because you have an error.
Duffie: (The letter was from) G
érard?
Arrow: Yeah, a letter from Gérard. And he explains the mistake. (But) it wasn’t a mis(take). I was sure it was not a mistake. (The) next day (he says) no,
I’m sorry, I’m wrong. You were quite right. (Then around) the third day, I (get) another letter (that says) you made a different mistake. (laugh) That (one) was a mistake. At this point I thought, well, how did he avoid this problem, because there was a real counter example. It wasn’t just a mistake in the proof. So I then
I looked at his paper, and it turns out that he had made essentially the same mistake, in a different form. I could see (that) the counterexamples really were counter example(s for) his result as well as mine. So I said, why don’t we c ollaborate and try to see if there’s some way of making another assumption which would cover this case. Then we sort of corresponded. My point is that when we started this collaboration, the uncertainty thing had not been written up.
He was not aware of it at all, I believe.
Duffie: Well , he didn’t start working on that until the year after your paper.
Arrow:
Yeah, (not) until ’53. So, as I am working my way through Europe we are having correspondence (laugh) on ways of repairing this thing. So (my) mind wasn’t on the uncertainty thing.
Duffie: And you were simultaneously getting ready for this meeting?
9

Arrow: Well, what happened was this. I was traveling to Italy, France,
(and) England. And (when) I was in England, I got a communication, let’s say
(in) March or April, maybe March, that the (CNRS) 1 was holding a conference on uncertainty. I forget the title.
2 You have probably looked at it more recently than
I have.
Duffie: title myself.
I looked at it just before we came in, but I don’t remember the
Arrow: It was being organized by Pierre Massé, 3 who has been director of research for Electricité de France, and… one of his… one of his— That, and
??? Marshak, and Ma rshak had recommended…
Duffie: Jacob Marshak?
Arrow: Jacob Marshak. Oh yes, I had started at the Cowles Commission for Research in Economics in 1947. Marshak was the director, and then he was succeeded shortly by Koopmans . I’d been there at the Cowles Commission. (It) is not part of the University of Chicago, but (it is) located physically there.
Marshak and Koopmans were professors at the university, and I was (at Cowles) for two years, a little over two and a half years, roughly. So I was in very close contact with Marshak. In fact, in the summer of ’51, I had collaborated with him on a paper on inventory theory. So I was in contact with Marshak. Marshak apparently had written to ??? and had been invited, and (he) invited me.
Although I had actually done nothing, he believed I’d probably have something to say. And I have the statistical background. So then I very hurriedly had to take these extremely v ague ideas (laugh) and put them into a paper. That’s the reason why the paper is so short (laugh), and a little cryptic
. I don’t dwell on, on things (that were) mostly were pretty clear.
1 This is Centre National de la Recherche Scientifique.
2 This meeting was the “Colloque International d’Econométrie” held May 12 to 17, 1952 under the title “Fondements et Applications de la Théorie du Risque en Econométrie” (a reasonable translation is: “Foundations and Applications of the Theory of Uncertainty in Mathematical
Economics”) .
3 The official organizers were G. Darmois, M. Allais, R. Roy, and M. Fréchet.
10

Duffie: It was very clear.
Arrow: It was at that moment that I worked out this idea (about) securities payable in money. I started (by) taking this old idea, and it turned out (that) the difficulty I thought I had didn’t seem to exist. So I was able to (do it) in a very elementary fashion just by re-identifying variables. I was a little worried about the fact that securities pay money. I thought well, this could be done (with) exactly the same result. And within a couple of weeks, I guess, I wrote this paper.
Duffie: In French?
Arrow: No, no.
Duffie: That’s not true?
Arrow: That’s not true. No, I sent it in English. In fact, I had it typed it at the Office of Naval Research. I had an Office of Naval Research contract. So I went to the Office of Naval Research and they —
Duffie:
Arrow:
They translated it?
No, they just typed it up.
Duffie: Oh.
Arrow: Then it was sent to France, and the Institute, the ??? Appliqué translated it. I did some correcting of the translation. I have always found that translation offers problems. The only language in which I really can correct the translation was French. I know a little bit of German, a little bit of Spanish, but not enough to proof read. But French I can (laugh). I have never seen a translation that did not have errors in it, and it always worries me when I read
English translations. Anyway, it was translated. I did see it, and (I) had a chance
11

to correct it. The conference was not until June. So at that point I went back to
France. I had been in France before. And this conference was held just outside of Paris somewhere.
Duffie: (At) some mansion I read.
Arrow:
Duffie:
Yeah it was (the) Chateau something or other.
That’s correct yeah, (the) Chateau … (de Gif)
Arrow: The French group was extremely impressive.
Duffie: Yeah, I looked at the list of participants in that conference. I mean not only the French, the French had ??? Then, in addition to yourself, there were ??? Milton Friedman, Paul Samuelson, Ragnar Frisch,
Gebrat, Savage, Weyl and Harold Wold.
Arrow: Oh, Herman Wold. Yeah, (he) is Swedish. Well, I don’t think they were all there. I don’t really remember Samuelson being there.
Duffie: It was a five day conference.
4
Arrow: The food was very good. (laugh) (And) there were some very good papers. (Of) course, probably the biggest thing at the conference was the arguments between Allais and Savage. Allais did not
—
Duffie:
Didn’t like the Savage (theory)?
Arrow: Did not like the Savage (theory).
4 The remarkable list of official participants is: M. Allais, K. Arrow, M. Boiteux, A. Cacquot, G.
Darmois. G. Dessus, F. Divisia, H . Eyraud, B. de Finetti, M. Fréchet, M. Friedman, R. Frisch, R.
Gibrat, G.Th. Guibaud, R. Hutter, W. Jaffé, H. Lavaill, G. Létinier, J. Lhomme, E. Malinvaud, J.
Marscahl, J. Marschak, P. Massé, R. Mercier, J. Milhau, G. Morlat, A. Nataf, F. Perroux, Ch. Rist,
V. Rouquet la Garrigue, J. Rueff, P. Samuelson, L. J. Savage, G. L. S. Shackle, J. Ullmo, G. van
Dantzig, J. Ville. J. Weyl, and H. Wold.
12

Duffie: Well, that came through historically (laugh).
Arrow: And well, what he did was get us to take quizzes. It was one of the first experiments. (We) were asked to make choices, (laugh) and most of the people, including Savage, fell into the Allais paradox.
Duffie: Really?
Arrow: For some reason, he didn’t publish that for 15 years or so, but he kept on referring to it. Finally it was published 15 or 17 years later. He really did have the empirical evidence. (laugh) But no, Savage was defending his theory.
Friedman, I guess, presented his paper explaining the fact that people gamble and take insurance by (assuming) a convex-concave utility function. Allais had a paper incorporating general uncertainty and general equilibrium. I don’t remember the detail, but I thought it was definitely based on mean and standard deviation for some reason or, it was if you took the standard deviation (instead of) the variance it should… be the same thing, but it turns out if you (make the) usual (assumptions about) differentiability and continuity, you really get some very funny results for that. But in any case, it didn’t seem to be a way of incorporating general equilibrium, because you had some uncertainty in the system somewhere, but by the time you filter it through the economics the, the distribution (could) be anything. You don’t want to start out by assuming that you know that everything is normal. (I am) pretty sure that some of it is not. So I’ve never felt it was a good contribution. Well, he published it, I think in ??
So… the proceedings 5 came out.
Duffie: Your paper was published in French in those Proceedings.
Did that slow down the dissemination.
5 The proceedings of this CNRS meeting were published as Econométries, Volume XL, Paris,
CNRS, 1953. Arrow’s and Allais’ contributions were published in the proceedings. Allais’ chapter was later expanded and published in 1955 as a monograph under the same title, by Imprimerie
National. Arrow’s chapter was subsequently published in English in different versions.
13

Arrow: Oh, it certainly did. You know for some reason, I was wondering about the ethics of publishing a paper twice.
Duffie: Once in French (and) once in English?
Arrow: Once in French and once in English. I kept on feeling that I want(ed) to get this thing out in English because nobody is going to read it in
French. It wasn
’t even in the journal. It was in a Proceedings. So I should get it out, and I kept on dithering about it. Finally, the editor of the Review of Economic
Studies, I think it was Peter Newman at the time, s aid why don’t we publish an
English version. (laugh) So of course, I took my original manuscript and sent it to him. (laugh) The so-called translation was in fact the original version. But that was not until ’61 (or) ’62 I think.
Duffie: That was in the early ‘60s. Then you published a revised version in your book, Essays in The Theory of Risk, which did have a little bit more in it.
Arrow: Yeah, when I reread (it), I added comments at some places.
Duffie: I think it was a Swedish, or at least a Scandinavian series of lectures that you gave.
Arrow: Well I gave some lectures in Finland, where I went over some of this material, but by that time I was on to other things. I did that too, but by that time, I was onto other things, and the stress was something else. I, now, and now there, so the result is somehow that work with G
érard was on a different track than…
Duffie: So you were thinking about both things at the same time.
Arrow: Yeah. But we completed our work. The paper had not been published, but we wound up our joint work (at) the end of ’52.
14

Duffie: It was presented at the December meetings of the AEA.
Arrow: The AEA yeah. Well, probably the Econometrica society, (but) maybe it was AEA.
Duffie: of the year.
It was at the an nual meetings anyway. They’re still at the end
Arrow: I think it was one of the Econometrica society sessions. We were working on that, but somehow we never incorporated uncertainty which was about all we could have done. Because the emphasis (was) on the existence, which was true no matter which interpretation you gave to it.
Duffie: Yeah. I t’s a bit ironic because the brilliance of the ’53 paper, which you had presented in ’52 was that you don’t have to do anything other than add the word(s) “state contingent”.
Arrow: (laugh) Well, so there. I have no really good explanation of why it didn’t occur. Gérard spent the year of ’53, some part of the year, (I) forget which, in France, and he started (extending) this. He made two very important contributions. One was the extension to the firm. I think you could find a statement that the extension to the firm is easy. The other (contribution), which was not easy, was going to more than one time period. But you have to look at the whole sequence. It was essentially a filtration as we would call it today. I had not worked on that, and that struck me as really clarifying it. It made it complete
(for an) arbitrary (number of) time periods, whereas I had only considered the single time period.
Duffie: We mentioned (your book), Essays in the Theory of Risk. The version of the ’53 paper you rewrote for (the book) included what was then a very minor kind of paragraph near the end of the paper (about) what is now known as the idea of risk-neutral probabilities. Maybe you should
15

explain the idea of risk-neutral probabilities, because now they are basically the foundation of modern financial engineering.
Arrow: I didn’t realize how important it was going be. It struck me when you got through (that) if you use the idea of money securities then, as a price to the security… I’m sorry, (I need to) back up a little bit. One of the (features??) was that any real security could be thought of as a bundle. (A) real security pays so much at state one, a different amount at state two, (and) a different amount at state three. You can think of that as a bundle of, as you say or what somebody calls Arrow Securities. W ell you take the unit is a… essentially paying $1.00 if state (occurs)
… and nothing otherwise. The, now that’s not with market price, cause price has gotta add to one, if, especially if you think of arbitrage with holding money. And they act like probabilities (laugh). So (I) made this remark without fully thinking of the consequences.
Actually, I was teaching in the early ‘60s, (and) I used to give a course on the economics of uncertainty. I was trying to explain material from Markowitz and Tobin, and all this. I went back to the foundation, to this idea of counting?? probability theory from actions, as in Savage, and really there had been earlier work by Ramsey, (and) by Bruno de Finetti. De Finetti ’s argument was well, supposing that you start… the wealthy, you think of bets, and think of all possible bets, including conditional bet s… you know I bet, how much you bet on A if it is known that B occurs with the assumption that B doesn’t occur the whole thing is off. And it… you have a whole vast number of bets. These bets however have to be coherent in a sense that nobody can make a —
Duffie: No arbitrage.
Arrow: Yeah. (You) cannot offer a series of bets which would, which you lose for certain. It turns out, of course, those bets have to obey the axioms of probability theory even though they are prices. T hey don’t start out being probabilities. It struck me (that), suppose you start out initially with a (level of) wealth which itself depends on the state of nature. The same argument would go
16

through. These certainly would not be probabilities as we ordinarily understand it. They would be probabilities times marginal (utilities), essentially.
Duffie: Right.
Arrow: I never published that. It seemed to be just an observation. And it wasn’t until later (when) I started reading the literature (that) I realized how important the observation was.
Duffie: Yeah.
Arrow: And when I saw it later, I said, oh yes. (laugh)
Duffie: Did (that) follow the idea that was taken up in finance that you could reinterpret these state-contingent prices as probabilities.
Arrow: Yes.
Duffie: It does (provide) dramatic simplification. You can use
Martingale theory and ??? theory to ???
Arrow:
Duffie:
But (it) still gets translated, eventually, back into regular …
Well, if you are only interested in pricing, which a lot of the literature is, you really only have to deal with risk-neutral probabilities, and you never have to come back. It’s when you’re doing statistical work that you need to look at both sets of probabilities at the same time. By the way,
(Jacques) Dr
èze seems to have independently, or at least he was writing a kind of an analysis of your 1953 paper, sometime in the late ‘60s, and he seems to have also made this observation that you could reinterpret these state-contingent prices, the prices of Arrow securities after normalizing for
(the) time value of money, as probabilities. But if you look in the modern finance literature, the trail back to risk-neutral probabilities, where it came
17

from, it doesn’t seem to pick up on the fact that you and Drèze had this idea.
Arrow: I see. Well, it probably came (from) … (I’m) not sure.
Duffie: Okay. As I mentioned, a lot of us think of that 1953 paper as the foundation of modern asset pricing theory. Maybe you could give us a sense of the implications of that for how we think about financial markets,
(or) how an investor would implicitly use that idea. Of course, it comes down through applications, but what are the implications of that?
Arrow: Well, there are several. The idea really can be looked at as a way
(or providing) insurance. The ordinary insurance policy… well I can have a high risk… risk of a large loss let’s say. In fact this goes back to, in a way to some of
Bernoulli ’s observations in 1738, and it was one of the (… one of the) interesting parts of the paper is the discussion of marine insurance. The example Bernoulli gave, by the way, is very frightening. He suggests that the chance that a ship will sink on a voyage is 10 percent . (laugh). Maybe he wasn’t being realistic. I hope not. If a ship owner loses the ship, it’s a big loss. So he can insure, and marine insurance existed at this point. The expected value of this insurance will be negative.
Duffie: For the purchaser of the insurance?
Arrow: Negative for the purchaser of the insurance. The seller of the insurance was making a profit, (and) has costs possibly. It was assuming that the purchaser of the insurance, the ship owner is going to be paying a premium which is greater than the expected value of the ship. So that seems irrational.
Why would he do it? The answer is that you have to look at it as from (the) point of view of the utility of his total wealth. If his wealth is diminished by a large amount, he has lost a lot because he’s now in the realm where he is poor.
Therefore, the value of an additional dollar, or mark, or florin is, is greater. There is an opportunity for trade. The insurer may be wealthier or, because of the law
18

of large numbers, (the insurer may) be able to achieve a degree of certainty which the individual ship owner cannot. So there is a market for risk sharing. In fact, the title of my paper was “The Optimal Allocation of Risk Bearing,” or I’m sorry, “The Role of Securities in the Optimal Allocation of Risk Bearing.” That is, by shifting risks, you can make everybody better off. Just as there is a trade in goods, there can be a trade in the willingness to take risks. The purpose of this
(article) was to show how, by issuing securities, which securities mean things you can buy in multiples. You can buy in any scale.
An individual will buy this… on any scale commensurate of course with their, with his or her income, or wealth.
And you… by, by buying things and at, at a scale that you choose and others are selling it, a scale that they choose. You can achieve an allocation risk bearing, which makes everybody better off.
Duffie: Not only better off, but from your 1951 paper, optimal.
Arrow: It is strictly speaking an optimum (in that) there is no way in which everybody can be made better off. I pointed out that, in the paper, in very short sentences, that there are a large number of devices available in the world for doing this. (The) one where I think I mentioned most frequently in that paper was common stocks. I pointed out that bonds typically are risky because there is a probability of default so that the typical corporate bond at least is not a riskless security. So there i s risk. These all evolved ways of paying… the bond has to be thought of something that in some states pays nothing, or pays us less than its face value. In many states will pay its face value, but the payoff is still a function of the, of the states, and it’s a way by which corporations can shift risks to others more willing to bear them. That was the real theme of the paper. The competitive equilibrium which for many ways is identified with a Pareto optimum will in fact operate in the field of uncertainty as it does in the field of production of more conventional goods.
Duffie: Or goods from one state for goods in another state?
19

Arrow: Another state. And that was the, and that sort of linked … these portfolio theories where, which still actua lly hadn’t been fully developed.
Duffie: Markowitz was active in the late ‘40s, but he hadn’t been dealing with market equilibrium right. He was dealing in the late —
Arrow:
Was it late ‘40s, I thought it was early ’50. Am I wrong?
Duffie: We will have to check the record on that one.
6
I thought Markowitz was a little later, but I could be wrong. Arrow:
Duffie: But he wasn’t looking at market equilibrium?
Arrow: He was not looking at markets, he was looking was the behavior of a single investor.
Duffie: By the way did you know Markowitz back in the early’50s?
Arrow: Yes. He was at Rand. He came to Rand somewhere along there, I do n’t remember exactly when. I used to be a summer consultant to the Rand
Corporation. We got to know each other then. But of course, I was on the
Cowles mailing list. No, it was after the Cowles Foundation moved to (Yale).
That’s where I used to get these, and that was ’54. So it must have been in the middle ‘50’s that Markowitz started writing. And he was just looking at the individual behavior of an individual in the market, which of course was a building block in general, but not yet an equilibrium concept. There were a lot of problems in those days, (and) we worried about algorithms for solving it. But everybody knew it was important contribution.
6 M arkowitz’ theory was first published in 1952.
20

Duffie: Maybe we should go back now, much earlier, to the beginning of your career as an academic. If y ou wouldn’t mind, kind of set up a circumstances by which you entered into the field of academics and then eventually into economics.
Arrow: My interest in probability theory does correspond to the fact that I really believe the world is full of chance. My own career, I think exemplifies it.
There was just one random event after another. (laugh) It is easy to see where things could have gone differently. I was a good student, bright. So it is like systematizing. I went beyond what I was being taught. I tr(ied) to organize (and) connect things from different fields.
Duffie: Why am I not surprised to hear that?
Arrow: It was just a part of my character (as a) student. My family was at that point very badly off.
Duffie: This was in New York?
Arrow: New York. I lived in New York City, and my father was (in) very bad (shape) during the Depression. He had been pretty well off in the ‘20s, but not (in the) ‘30s. So I went to City College, which was free, and I could live at home. I was a little worried (about) how I (was) going to make a living. Given the economic circumstances, economic security ranked very high. There was one fairly obvious solution, which is to be a high school teacher. And that was what I ha d said…
Duffie: It was very safe?
Arrow: Well actually, I think it was safe once you became a high school teacher of math, (and) I was majoring in mathematics. But it turned out there was one problem. I went through education. In fact a fair fraction of my curriculum was spent taking courses in education because to be a teacher you
21

had to have so many credits. I even had practice teaching. In my senior year, I taught for a high school. In fact, maybe the best teaching experience I ever had in my life was teaching a group of people who had done badly in geometry, but still might be allowed to take the Regents ’ (exam). They took it as a voluntary class, and I was coaching them. Probably, say, two-thirds of them took the regents (exam). I had the right to say who was going to take it, and they all passed (laugh). The Regents
’ (exam) is a state-wide examination in New York for high school students. Since they were not required to take this course, discipline was not an issue (laugh), and attention was not an issue.
There was one problem. This was the Depression, and I was not the only one had the idea of being a high school teacher. (laugh) An examination had been given in, I don’t know 1933, and there were people who had passed that examination (but had) not yet got(ten) jobs. Until that list was used up, they would not give another examination. So it became rather clear (that there) was a big risk I would not have a chance (laugh) to be a high school teacher of mathematics. Some people get shocked when I give this economic interpretation of my career, but as an economist I don’t see why. (laugh)
(Then I learned there was) something called statistics. The math department had somebody teaching a course in probability and statistics.
Duffie: At City College?
Arrow: City College . He didn’t know much. I can tell you. But he did have a few elementary things, and there were a few references to textbooks, (or) to books, not textbooks really. I was eagerly reading. I finally wound up reading current literature in statistics, and (I) found it absolutely fascinating. I graduated college. There is no examination for a high school teacher of math. (So what was I) to do? (I) came from a family which regarded education as extremely important. And more education was better, although my father assumed I would like to become a business man. But the idea of going (for) more education was perfectly compatible then. I decided to try to study statistics. The trouble was it wasn’t a recognized field. There was no degree in statistics anywhere. And it was given usually by some professor who was affiliated in some other
22

department. I looked around, and I realized the leading statistician in the United
States was a professor at Columbia, Harold Hotelling. There were a couple of other well known ones, but he was clearly the leading mathematical statistician.
And he was at Columbia, which meant I could live at home.
Duffie: Which department at Columbia was he (in)?
Arrow: He was in the econ omics department. And … how this happened that the economics department was so progressive (was) because, some(where) around 19??, they had a man (who) was a pioneer in applying statistical economics. (His name was) Henry Moore. Moore evidently went insane and was confined to an asylum. They had a vacancy, and I felt they would appoint somebody like Moore. They looked around, (and) they found this young fellow at
Stanford who had published some papers in economics, and also was a rising statistician, although his Ph.D. was in mathematics and his dissertation was on topology.
Duffie: This is Hotelling?
Arrow:
Duffie:
Hotelling.
Was he already a faculty member at Stanford?
Arrow: He was a faculty member at Stanford. He came to the Food
Research Institute actually, but apparently he’s listed, according to the catalogs, as being in the mathematics department as well as the Food Research Institute.
I’m still not very clear as to how this all happened, but his faculty advisor, who was Thorstein Veblein’s nephew, (laugh) knew the head of the Food Research
Institute. He was a chemist in those days. Anyway, Hotelling was plucked from
Stanford to be a professor of economics.
What (Hotelling) did was create an enclave, in which he taught a series of courses called statistics. It was actually a label in the catalog. Statistics 206, and things like that. But there was no department corresponding to that. And he
23

had no help except (from) the Carnegie Corporation, which had given him a grant to hire a research assistant. He used it, essentially, to get bright young statisticians to teach.
When I got there, there was this refugee named Abraham Wald, and
Hotelling and Wald were the teachers in statistics. Hotelling (was) famous, but I did not know (who) Wald was. It was obvious (from) the first lecture I went to that
I was in the presence of a first rate mind. They were great teachers, both of them, but especially Wald.
Hotelling also gave a course on mathematical economics. Out of curiosity
I took the course. My interest began to move from that point on. The economics department, (as a) matter of fact, was not a very good department at that point.
(It was) nothing (like) places like Harvard or Chicago or Princeton, oh no,
Princeton was later. Harvard and Chicago were the leading places. Yale was pretty good too. Nevertheless, I got along well with the professors and got the scholarships I needed to continue.
The war broke out, so I had a little bit of (an) interruption. And this is how… I took a lot of statistics, but I didn’t…. I took economics but it was very atheoretical. The department, outside of Hotelling, was really very much against theory basically. They didn’t have a course in price theory. It’s hard to believe
(laugh). And of course in the history of price theory, which was given by John
Morris Cark (who) really was quite good and one of the best people there.
Maybe (even) the best. By the way he was a dreadful lecturer. He was boring, the most boring thing that I ever heard, although he could write beautifully. He was a beautiful writer, but a terrible lecturer.
I’m not sure, (but) I think I may have answered more than you intended.
Duffie: From this experience at Columbia, you left essentially as a statistician but with (an) interest in economics. How did you eventually make the transition to become an (economist)?
Arrow: No, let me sa y, it’s a little more than that. By the time I completed my studies, my coursework, which were the first two years, I was convinced I was going to write something econometric. Or, that it wasn’t yet in the (laugh), I
24

wasn ’t yet a theorist, … but I felt there was a need to develop theory as a basis…
I was influenced of course by the whole tradition of statistics, which is: You construct a model and then you fit it. But, it means you have to have a model which is… you knew was going on up to a number of parameters.
There had been this major study of business cycles conducted by
(Ohlin???) for the League of Nations. It was a big model of the United States economy. Now there were statistical problems with it. You know I was a little worried about the fact that… (you( had a whole system and somehow you’re fitting it one at a time.
I didn’t come to… work (on it), but I, at least I had that on my agenda as a problem (laugh). The, the n there… the economics of the… individual relations… as kind of shaky, on some of them, some of them looked very good, some of them seemed, didn’t seem so reachable to me… I was gonna, so I had some idea of rethinking this all through… using theory to build up, course … it was a ridiculously, you know, grandiose scheme and I had no, no… reality. At that point I had enlisted in the Army and I was called up and spent the next, from it was like from October ’42, or September 40, October ’42 I guess to January ’46 in the, in the Army as a weather forecaster, weather officer.
It was fascinating but not very …, although I got my first published paper out of that actually.
Duffie: (On) meteorology?
Arrow: Yes. Well, it was not actually on meteorology, it was on … how to optimally use wind in o rder to track … (an)… airplane, so (that) it’s to get there in the shortest length of time. It wasn’t so much the Army was interested in getting there -- the Air Force was part of the Army then -- it wasn’t so much that they wanted to get there fast, but you wanted to use up as little gasoline as possible.
… I worked. I even did calculations and showed that you could save about an hour. Remember
, the … trans-Atlantic trip was like 12 hours in those days, it was, and I went over a lot of actual days into the past and showed you could save an hour. And, 12 hours roughly on the average, but … nothing ever happened to it. But of course the paper (appeared in) the Journal of Meteorology
25

after the war… there was some follow up on… So I got a paper out of that, but it really had very little to do with (my) subsequent work. So I returned to study.
And I was really very frustrated because I began to concentrate on the theoretical side. I was going to redo Hicks properly. I could see all sorts of problem, even as much as I admired Hicks, I could see… theory… (of the) firm was it was very… what happens when firms have a number of owners and, and uncertainty and then I wanted to bring in this whole same instance stability theory.
See what the stability, you know the, that you wanted the stability conditions and well I didn’t get very far. In fact, I really spent several years not really making any, very much, progress. Although I was thoroughly committed to this… to the field. But I spent… till the summer of ’48—
Duffie: (The) development of finance and economics were more or less along parallel but not integrated tracks at that time. They eventually merged, and you were there during that process. Can you describe who the people were that made that happen?
Arrow: I think Paul Samuelson was more responsible than any other one person. One thing that (what) attracted a lot of peoples ’ attention was the statistical work of Maurice Kendall. Kendall was a statistician, not an economist.
(He) was interested in developing methods for analyzing time series (data).
That meant finding hidden cycles. You would try to estimate things called periodograms, and things like (the) stock market would be a great place to apply it. (But if you) applied it, (you) could get nothing. (laugh) There were no periods.
Yet you look at this graph, and you see ups and downs. The question is, how could this be? Well, he talked with some economists and the economists said, oh yes, of course. If it were predictable, there would be the arbitrage. (So it) can’t be predictable. Well, Paul picked that up, and I guess wrote first some papers (about) why prices have to vary randomly. Then he got (into) the theory
(of) warrant pricing. I think (that) is what stimulated Black, Merton and I guess
Scholes too. It seems to me that his bringing stochastic processes into
(consideration), and emphasizing the martingale idea of unpredictability, is really the start of modern financial theory, more than any(thing) else.
26

Duffie: That is certainly true on the asset pricing side. What about on the corporate finance side where (there were) really economists (like)
Modigliani and Miller?
Arrow: That paper really re-started me. Then after awhile I thought, oh, if I only (had) applied my contingent price theory, it would have come out immediately (laugh). Of course, it would affect actually their argument was almost… they talk about… classes.
Duffie:
That’s how it’s taught today, using contingent-claim theory.
Arrow: Yeah. They have an argument which in fact had some element that was put a different way (about) things of equivalent risk classes. So really that was stopping (the result that) there must be an optimal (financial structure). In fact, even in my sketches for this Hicks revision, one of my problems was optimizing the financial structure of firms. There is no optimal (structure). (laugh)
All financial structures are equivalent. It was (laugh) not something expected at all. Therefore I was startled by the result. I had a very high view of Modigliani in general, and this sort of confirmed (it).
Duffie: (Modgiliani and Miller were) working in the field of economics at the time. Did they work from the viewpoint of moving the finance literature forward, or it didn’t matter at that point? Did you know them at the time?
Arrow: Franco had visited the Cowles Commission in Chicago for a year.
We had become very friendly. But he was at Carnegie Mellon, I think, when he wrote that paper. Yeah, he was Carnegie Mellon. And, you know, I wasn
’t in daily touch with him.
Arrow: How about Bill Sharpe
, did you know him back in the 1960’s?
27

Arrow: No , I only got to know him after I got to Harvard. I don’t remember where I met him, but I read his work. His (work) was (closer to mine) than Harry
Markowitz’s work, because it was on (the) equilibrium concept. He and Lintner had similar models. I thought this was the first (work on asset) pricing which
(takes) some of this rather abstract formulation, (and) makes it concrete model even though you obviously had to simplify a lot of things.
Duffie: As you said, (your) 1953 paper was in French, and it may not have had (the) initial impact it might have had (if) it been in English, (but) it was eventually translated into English. Could you see the process by which your approach to modeling financial markets was having an impact on financial economics? Could you watch that happen?
Arrow: Well,
I don’t think I really know all the steps. I started out with a somewhat different (problem). There are these theories of markets where you take the security structure as given. And of course, (that is) a good deal less rich than what I postulated in my markets. (As for) all these problems that really restrict the markets (for) the possibility of getting good theorems under special circumstances, I followed them, but I wasn’t really involved in it. After awhile, I began to see (a) more general literature, which drew (on) us. The original
(model) could be translated into a state-contingent language, but it really wasn’t state-contingent language at the time.
Duffie: On a more personal level, can you take us back to the day that you found out that you won the Nobel Prize? I’m sure it’s an interesting story.
Arrow: Well, it was a little fascinating. I was on th e board of directors of…
… Associates while I was still at Stanford. I then moved to Harvard. (But) from
(one of the) board of directors meetings, I got an invitation from the State
University of Binghamton to give a lecture there. Somebody I knew was there in health economics, which (I had) worked on. I flew to Binghamton to give my lecture. The next morning I get to the airport, and the clerk looks a little funny.
28

He says, I guess we (had) better get started. There have been several calls to you. I couldn’t imagine what was going on (laugh). The only thing that occurred to me, frankly, (was that) my mother had not been very well. There might be something about her, but several calls didn’t seem very (likely). One call yes, but several calls d idn’t seem to make any sense. What was going on? I picked up the phone, and (it was) the ABC News Service or something like that. I think it was ABC. Well, then I knew immediately.
Duffie: You guessed.
Arrow: They informed me, and I stammered out some kind of statement.
(laugh) (Then) my poise improved, and I made a much smoother statement
(laugh) that expressed my joy at sharing it with John Hicks, (who) meant so much to me as a graduate student. Then my wife gets on the phone. (laugh) She had been awakened a couple of hours earlier (laugh), or (an) hour earlier by the call.
I think the first call was actually from (a) news service. I think the Swedes called about two hours later. But the first (call) was the news service. Because of the time difference, they announce it earlier here. Very shortly, reporters swarmed into the house, (and) started interviewing my 7-year old son (laugh). Luckily he answered very well. (laugh) But I didn’t know what (my son) was going to say,
(and) my wi fe didn’t know what he was going to say. So this was very dramatic.
I then took a plane that made three stops. There were reports after me, and by the time I got here, my friends had organized a welcome party. So it couldn’t have been done better. I mean, if I (had been) home, (it) would have been less drama tic. I didn’t,… you know,… frankly. This was the fourth year of the Prize, and I really was not expecting (it).
Duffie: It strikes me that this tremendous recognition for your work can’t have been all positive. I mean, this and one honor after another --- just recently you got the National Medal of Science --- surely this must be somewhat distracting in terms of getting your work done. Have you ever found that all the public appearances and the requests for comments
—
29

Arrow: Yeah. You get that. Requests for signing statements is probably the biggest part of the story. Well , I don’t think it has actually in my case. I don’t go to places where I’m invited (just) because I’ve got a Nobel. (laugh) I don’t want to decorate anybody. So I try to keep on working. On the whole, I think it can happen, (but) I thin k it hasn’t happened in my case. I think I’ve, I’ve kept pretty much …. And the things that I have gotten as a result of it, on the whole, have been things I liked to go to, and I simply turned down things that I’m not interested in. So
I don’t think it’s been a strongly negative matter at all.
Dufie: It has worked for you. (What) advice (do you have) for a young graduating economist. (What) lessons can he or she draw from what you have done?
Arrow: Well, as I said earlier, I consider chance to have played a major role. I happened to go to work with Hotelling, who happened to be interested in economics as well as statistics. Then I went to the Cowles Commission, which
(was) a very formative period. But I tell you (that) one of things that (was) a plus in my case, (but) which I am not sure I would want to recommend to other people, is that I am easily distracted. I get into a question, and somebody asked me a question, and instead of saying oh no, no I’m busy, I’ve got the, I’ve got this big research project… I’m gonna have to take it seriously, and sometimes it turns out to be much more important, much more fruitful. That was true in the social choice; it’s true in my health economics. So, I’m not sure that following what I think is the most interesting lead at the moment, even though it may mean dropping something I’ve spent some time on, will work for other people.
Most people seem to work better by concentrating. And certain kinds of work can only be done that way, historical work, statistical work.
So I’m not sure
I would like to give advice. (All I) care about is that, if in the course of your work you come across a problem, don’t try to smooth over it. If there is a real problem there, that may be what is really interesting. (laugh)
30

Duffie: The main audience for this interview is going be people interested in financial markets. (What are) your impressions of where the new research is headed, or should be headed?
Arrow: Well, let me make a general statement, which is by no means new.
The biggest thing that (has) happened in this field, and in economics in general to my mind, after this work, is the emphasis on asymmetric information. Some people know something that other people don’t know, and other people know
(that some) people knowing something they don’t know. (laugh) In my case, I came to it through an interest in health economics. (This) [asymmetric information]… seems to be an utterly basic matter in financial markets, and in corporate finance, and corporate governance, which (is not) identical with corporate finance, but the two obviously have some close relationship. I think is one of the biggest developments in economics in its history, in my opinion. It plays an utterly important role in finance, for example. One of the arguments against the (Modigliani) Miller indifference idea (for) corporate structures is that some of them give better incentives to managers than others. I think what has
(been done) so far is a little superficial. But I think the question is the right question. I think there is plenty more to understand.
Then, of course, one of the things that’s recognized in public policy is you have all these requirements of revelation. But there is an intrinsic limit to that. I mean, not just tha t it’s being resisted, but that you can’t??, a lot of analogous tacit??, and you can’t convey it. So I think the questions of, for example, or excuse me. You know one of the reasons why financial markets (are) so much more limited than the require(ments of) the Arrow securities, is the fact that ---
Roy Radner was the first one to give a good explanation of this --- how can two people make a contract (that) is contingent on something occurring when only one of them knows whether it occurred or not. So (there are) all these revelation problems (about) transfer(ing) information, some which it’s almost impossible imagine it will ever be trans(ferred). So instead, we have a whole literature on the incentives, on the assumption that you are not going to, (and) so using the observables to an extent. It seems to me that this puts great pressure on the concept of information (and) who knows what.
31

Of course, who knows what can’t be taken as a given? If you assume it’s a given, you can go through the principle-agent theory to (find) optimal incentives
(of) one kind of another. But you must recognize that (there) is a big incentive
(problem) to acquire information. Maybe it will be acquired. It leaks. It may be acquired even without deliberate effort. (Or), it may be acquired with deliberate effort. This shows up in all sorts of economic realms, (such as) in the theory of growth, particularly the question of total factor productivity, the residual. There was a question of how an innovation spreads. Well, in the same way, you know, it can spread through the market by licensing, (and) things like (that). (Or) it can spread in lots of other ways.
You (can) try to model why the stock market fluctuates so much. After all, if people make errors. (But) why aren’t they randomly distributed, and why don’t they sort of cancel out? How can you get something like the whole market chang(ing by) one or two percent? And t oday that’s sort of nothing. Yet that’s huge. I mean, our estimate of the future wealth of the country has changed by two percent in one day. That’s an amazing statement. The problem is that these information flows somehow are correlated. O r at least that’s one way of looking at it. If X has an idea that somehow spreads to other(s), you are going to get some kind of – I have never seen this fully (developed). I mean I have seen a number of models, (but) I have never seen anyone that really catches it.
Duffie: There is a development called “behavioral finance” that attempts to explain some of these fluctuations, not from going back to what I would call super rational viewpoint from your early papers on financial markets, but violations of sort of standard choice axioms.
Arrow: I think we have to take that stuff very seriously. I would like to explain it, but you know there are problems about the limits of rationality too. In fact, if you push the logic back far enough, you have some problems because information has to be processed. As I learn something, it has some implications.
And it takes time to draw the implications. So time comes into the picture. (As for) rationality, assume you have information (that) you know instantaneously,
(and you) know all its implications. The fact that mathematics is an open subject
32

(laugh) means that not all the implications from a pretty small set of axioms have been found in hundreds of years of work by smart people.
So we have the question of what fills that gap. And that is where the behavioral people (fit), I think. Facts they have unearthed, the generalizations, are raw material for something else. I think this is extremely prominent in asset markets more than it is in flow markets because you close the market, you start over again, and maybe you have learned something. I mean, there may be carry over in information even in flow market. But in asset markets, when the whole future is at stake, the implications of information flow (are greatest). It seems to me somehow that the spread of information, the willingness to acquire it, and to spend resources acquiring and using it are key problem(s) in many areas of economics, and I think in financial markets most especially.
The other (issue) with the corporate-governance problem is (the question of) what induces managers to behave? The idea (that) the board of directors represents stockholders and gives (appropriate) incentives (to mangement is) --- having been on boards of directors --- well (maybe) it is 5-percent correct. There is something to it. But it is a long, long way (from perfection) because the board of directors (is) the creature of the present. So the whole question of corporate governance, which in turn reflects itself in corporate finance, I think somehow we are not really (understanding fully). All these rational considerations are relevant
(laugh), but there is a lot more that is relevant. We are not getting this power, and that is where game theory should, in principle, be applicable.
Duffie: It’s an evolving product of human endeavor. … Do you imagine that we could do better?
Arrow: Well, it’s easy to imagine. I am certainly not prepared to give you concrete things. For example, I may be wrong what
I’m about to say because I do not know this in depth. But at an early stage I was a strong advocate of increasing derivative market(s), on the grounds that they enrich the functions of the original stock, and they increase the space that is spanned by securities.
Duffie: Getting more towards optimal allocation risk bearing?
33

Arrow: Exactly. The trouble is, for various reasons I am disturbed because their behavior is not compatible in some cases.
Duffie: What do you mean by that?
Arrow: The volatility of the derivative markets, at least (for) some derivative(s), (and) I think particularly (in) the foreign exchange market, is so great that it doesn’t seem explicable in terms of people hedging. For example, the textbooks tell you that you have foreign exchange markets or forward exchange markets because, say you’re engaged in a commercial transaction and there is a lag between the time you make the contract and time delivery is made, and you want to be hedged against foreign exchange fluctuations. That would explain that (volume in) the foreign exchange might be of the order of magnitude of trade. I think (volume) is something like 300 times the order of trade. So it’s clear that (the foreign exchange market) is being used for speculative purposes.
There (are) other pieces of evidence. I have seen something about commodity futures where they seem to be used in ways (in) which the risks are increased, not decreased. The commodity markets are easier to relate to the underlying (assets) than the stock markets. I think there is a relation in the stock market and the underlying reality, but it is more complicated. So it is a little harder to analyze.
These problems suggest to me that the derivatives are not necessarily improving the allocation of resources. I’m sure some are. And I may be wrong, but I am a little worried when the volumes and the volatility get so big, that (it) doesn’t seem to (be) serving what is conceptually the function of improving the allocation of risk bearing.
Duffie: I think we have covered the ground that we wanted to cover today. I am very pleased about how this has gone. Thank you very much.
Arrow: I enjoyed it very much. Thank you.
34

Duffie: Thank you Kenneth.
35