require using the overlapping-generations structure, although we built

on one of the properties of the overlapping-generations model, the friction

you get by restricting participation on certain markets. Much later we wrote

a paper showing that there™s another aspect of the overlapping-generations

model, that somehow the open-endedness of time also plays a role. We

constructed an example where there were complete markets and unre-

stricted participation”it is something like the following. This is basic-

ally an overlapping-generations model where the uncertainty is all in the

¬rst period, you either get an alpha or a beta, and you can buy insurance

against that, but because of the in¬nite structure of the model, you

would still have sunspot equilibria. So there are two causes for sunspot

equilibria: One of them has to do with the time structure of overlapping

generations; the other has to do with not having enough access to asset

markets.

MD: Didn™t Jim Peck pick up on the second thing in his thesis?

Cass: Yeah, yeah, that™s right. I haven™t thought much about sunspots,

especially in the overlapping-generations model, for quite a while, but he

develops a generalization about nonstationary sunspot equilibria in the

OLG model. I think sunspots are really interesting, but even when Karl

and I wrote that JPE paper, my interests had already diverged to thinking

the way I did on the general equilibrium problem, in which you can

actually do a ¬nite-dimensional model. Of course, we have this simple

but important theorem which says that if you have all the hypotheses

that are necessary, stated and unstated, to get the First Welfare Theorem,

then you can™t have sunspots. Then we have what Karl used to call the

Philadelphia Pholk theorem, which is that if you violate any of these

hypotheses you can get sunspot equilibria. It™s not quite true, because

all it is saying is that if you have a theorem that says A, B, and C imply

D, it™s likely to be the case that if you drop one of the assumptions

the conclusion is not going to be true. But, of course, it may be that it

An Interview with David Cass 51

can still be true. I guess that is where Karl and I diverged on this a little,

but he™s gotten very interested in the absence of convexity. Now, his

examples are perfectly okay, but it is not quite true to say that if you

have some nonconvexity then you have sunspots, because”as Heracles

Polemarchakis and I pointed out”you can have nonconvexity in produc-

tion and, since pro¬t maximization is relative to a hyperplane, you can

substitute everything under the hyperplane and call that the production

set, and you get the ¬rst welfare theorem back.

The JPE example is a real simple example where there are two states

of the world and we interpret it, in the structure of the overlapping-

generations model, as two classes of households. One class can trade

assets against the state of the world, while the other can™t because it is

born later, so it has to trade just on the spot market. That is one kind of

example. But I got interested in constructing other examples of sunspot

equilibria. In particular, in the early 1980s, I went to spend a year in

Paris, and the ¬rst project I wanted to work on was to construct a sunspot

example where there was a missing market. Somehow I decided the way

to do that was in a model where you had assets, and not enough assets to

span the states of the world. That™s how I got interested in incomplete

markets. That™s another paper I like a lot, “The Leading Example”

paper. I had real trouble getting it published because I wrote it precisely in

the JPE style, a kind of a followup to the ¬rst paper but, to the Chicago

mind, sunspots are irrelevant, just not interesting. Ironic as holy hell.

MD: In the famous Kareken and Wallace volume, one thing Cass and

Shell say is that by de¬nition the overlapping-generations model is the

only dynamic disaggregated model, which one may take to mean it is

the only interesting macro model.

Cass: I have to get back now to the train of thought about the

overlapping-generations model. I got interested in the overlapping-

generations model because of sunspots. And then Okuno and Zilcha”

this may have even been at the same conference at Squam Lake”

presented a paper which was an attempt to prove that if you introduced

money into the overlapping-generations model, then equilibrium where

money had a nontrivial price would necessarily be Pareto optimal. There

was a ¬‚aw in their proof.

MD: Neil Wallace was always inclined to say that in Minnesota.

Cass: Their work was based on trying to verify formally what Neil

believed. I saw their proof, read their proof very carefully, and it had an

error in it. I decided that it probably wasn™t true, depending on some

characteristics of the utility functions, and so on, so I decided to work on

a counterexample. Basically, I constructed a lot of counterexamples, where

you can introduce money and, for one reason or another”heterogeneity,

52 Stephen E. Spear and Randall Wright

nonstationarity, and so on”you will not get Pareto optimality. I got

interested in the overlapping-generations model again. Karl and I really did

believe in it, and we started working more generally on the overlapping-

generations model after we™d worked on sunspots. We really did believe

at that time that it was the only serious model where money played a

role. Of course, subsequently you have some very famous papers which

present other basic paradigms in which money plays a basic role.

MD: Although mathematically those structures maybe aren™t so different?

Cass: Well, I was going to talk about that. The Kiyotaki“Wright model

I like a lot, but as I have pointed out to you, Randy, I think that the

ultimate principle in both of those models is that the horizon is inde¬nite.

If you truncated your search model, you wouldn™t get a role for money

either. So even though we didn™t have the imagination to think of another

model, and this, for example, would be your model with search, in which

there would be an in¬nite horizon, I think you were right in asserting

that the underlying time structure of the overlapping-generations model

is what provides a reason for having money. I still think that the ultimate

thing is that money has value because people believe it is going to have

value, and the only way they™ll consistently believe it will have value is if

they™re never forced to put up. And that™s common to Kiyotaki“Wright

and the overlapping-generations model.

MD: Well, it™s interesting, because there are some in¬nite horizon

models in which money has no role. So the in¬nite horizon isn™t a suf-

¬cient condition.

Cass: Just the in¬nite horizon does not necessarily give you a role for

money. In addition, you have to have some type of imperfection, some

violation of the hypotheses of the ¬rst welfare theorem, like restricted

participation (overlapping generations), or noncompetitive behavior (the

search model).

MD: Do you agree that there are still many issues in monetary eco-

nomics that are yet to be sorted out?

Cass: Oh absolutely. It would be nice but probably impossible to have

a consistent model where we could get away from having to have an

inde¬nite future to give value to money, but it is hard to conceive of how

you would do that. John Geanakoplos has a model, it™s an incomplete

markets model with money and cash-in-advance constraints, where he

gets value for money because money is issued by a bank and you have to

repay the bank. But, ultimately, the bank is just throwing money away at

the end of the day, and somehow the model is not really closed. It™s a

little unsatisfying.

MD: What are the issues with an in¬nite horizon?

Cass: I changed my mind sometime in the 1980s about the in¬nite

horizon. I suppose ultimately the reason that I object to it relates to

An Interview with David Cass 53

rational expectations, although I would de¬ne rational expectations in a

more general equilibrium than a macro way. I de¬ne rational expecta-

tions to mean that you have a well-de¬ned state space, and that in those

states every individual has common beliefs about the prices that will prevail.

For those beliefs about future prices, today™s markets will clear, and when

tomorrow™s state rolls around, given the plans, one equilibrium in the

realized spot market will be at the prices that they forecast. Now there™s

a little problem in that there could be other equilibria. No equilibrium

model that I™m aware of has a sensible process for actually achieving

equilibrium prices, so it™s not clear why the particular prices they forecast

are going to be the ones that occur. Getting back to the issue, I can kind

of understand why I might want to use rational expectations as a bench-

mark when the predictions that we™re making are not too far ahead. But

this is generally a question of assuming that you know what the structure

of the world is. There™s a big difference in my mind between that and

assuming implicitly that you know this forever. I have become very un-

comfortable with that.

MD: Is your view that for some relevant questions it may be more

appropriate to use a short-run model?

Cass: I think you can use a short-run model, but the objection there

is exactly the motivation behind the overlapping-generations model, that

when you reach a certain period, if you reach that period, then it is

reasonable for people to expect that there will be a period to follow.

It™s sort of like an induction argument. You can™t cut the world off because,

in the last period, people are still going to be looking ahead one period.