Figure 2.2 A conference at Carnegie Mellon University in honor of Dick

Cyert, September 11, 1993. Pictured (from left to right) are Dave Cass,

Robert Lucas, Dick Cyert, Allan Meltzer, Edward Prescott, and Timothy

McGuire.

rule capital stock, and get a consumption bonus and have higher con-

sumption ever after that. Being at the upper point you still have compet-

itive prices, they are just not ef¬ciency prices. If you look at those

competitive paths, you can rule out the ones that are inef¬cient if you

impose the transversality condition. So the transversality condition is a

suf¬cient condition for ruling out capital overaccumulation.

I found this to be a very interesting problem: What is a necessary and

suf¬cient condition? The transversality condition is a suf¬cient condition

for ef¬ciency, but is not necessary. The golden-rule path itself is a coun-

terexample, as I said earlier. The golden-rule path is ef¬cient, and for

some criterion is also Pareto optimal, but there the transversality condi-

tion is not satis¬ed since the interest rate is identically zero. Manny Yaari

and I had started working on this problem two years before, and we got

one solution for it that was in terms of a condition that wasn™t that

interpretable. Now I know why I didn™t like the condition. I wanted a

condition on the price path itself that was necessary and suf¬cient, so I

worked all year in Japan on that and got a complete solution. I really like

that paper.

So I spent a year in Japan working on that problem, and then I wrote

a couple of other papers on things I wanted to write about. One of them

44 Stephen E. Spear and Randall Wright

was actually very much Solow-like. I took the Wicksellian model, the point-

input/point-output model and analyzed competitive equilibrium. I like

that paper a lot, too, but it™s very specialized. I doubt anyone has ever

read it. And Joe and I ¬nished our paper on portfolio choice that year.

The biggest stumbling block for that was that in the paper itself there are

computations for speci¬c parametric forms and neither Joe nor I was that

excited about, or that careful sometimes, dealing with parametric forms.

So we really had a hell of a lot of trouble agreeing upon what was the

correct way to write down these examples to illustrate our theorem. In

the ¬nal version of that paper there were still algebraic errors; somehow

neither of us took the responsibility for proofreading it.

Then I kind of ¬shed around for a while. I worked more on growth

theory. I got interested in the general problem, which was then very

unfashionable because it was at the tail end of the neoclassical growth

period, of the stability of competitive dynamical systems more generally.

Karl and I produced a paper that I like a lot, although it might have been

a little archaic even then, on this problem.

MD: Was that the ¬rst time you worked with Karl?

Cass: That was the ¬rst time Karl and I really worked together on a

paper. Karl was at Penn at that time. Anyway, back at Carnegie I wrote

some minor papers, like on the Hamiltonian representation of ef¬cient

production, a paper on duality; these were not major papers. Probably

I got to talking with programmers and got back to doing things with

programming at Carnegie. The guy I really talked to a lot was”I remem-

ber him well, in fact he died some years ago”a guy named Bob Jeroslow,

who was really a mathematical logician turned programmer. He was

extraordinarily clever. The big thing in programming then was integer

programming, ¬nding algorithms that would solve integer programming

problems. There were lots of algorithms but people didn™t have any idea

of why they worked, and Bob was really good at constructing for any

algorithm a counterexample that would never converge. I used to talk to

him a lot. He started to get interested in economics and I got interested

in programming again, so I wrote some programming papers.

After that, Karl and I got into the stability thing, which we spent a

couple of years ¬nishing up. Then at some point”I don™t now how this

should appear in this interview”the Dean, Cyert, became President and

we had to hire a new Dean. At Carnegie the faculty was very involved in

this process, and we actually talked a lot about the kind of person we

wanted. For some reason we settled on Arnie Weber, who was a Chicago

Business School labor economist. That turned out to be, from Carnegie™s

viewpoint and my own viewpoint, a disaster, because the guy had no feel

for the Carnegie tradition at all. He did not understand the fact that

Carnegie was quantitative, and that the quantitative emphasis was on

An Interview with David Cass 45

economics, and that meant that you were going to have a lot of econom-

ists around. An example of this, a personal example, is that very early on

Arnie called me into his of¬ce for some reason, and I had an interview

with him. He told me that I was a luxury good and that I didn™t do

business. I did theoretical economics and it wasn™t something that busi-

ness schools could really support, and he did it in a very obnoxious way

that really pissed me off. And I said “f” you, Arnie.”

MD: Literally?

Cass: Yeah, I said “f” you,” and I decided that since I was working

with Karl it might make sense to come to Penn, even though I had a few

reservations about Penn because I knew it was very econometric-model

oriented. But they made me a good offer so I couldn™t turn it down.

MD: Could we stay on your time at Carnegie for a while?

Cass: Yeah, we could do that.

MD: Okay. Ph.D. students: One of the prominent ones you worked

with there was Finn Kydland.

Cass: Finn Kydland, yeah, I was on his committee, and actually worked

with him a lot on one or two chapters, but not most of his thesis. His

thesis was all programming. Another one was Bill Barnett. I don™t remem-

ber if I was formally on Barnett™s committee. I know I talked to him a lot

but I may have left before he ¬nished or he may have just drifted off. The

main group I worked with includes people who came my ¬rst year at

Carnegie, such as John Donaldson and Bob Forsythe. Those two stand

out in my mind.

MD: Kydland™s work with Ed Prescott began the development of real

business-cycle theory, and the workhorse model in real business-cycle

theory is the Cass“Koopmans model. Did you and Finn ever talk about

growth theory?

Cass: No, as I said, Finn when he was a graduate student was doing

programming.

MD: Let™s talk about Lucas™s use of the overlapping-generations

model.

Cass: I™ll tell you, that is an interesting paper we™re talking about, in

Journal of Economic Theory, an interesting paper. I wasn™t so interested in

the macro, but what struck me, and this is related to some of my later work,

was the assumption that Bob made to solve for equilibrium, that the

state variables were obvious (that is actually the ¬rst time that I thought

about the sunspot idea). Bob and I had some long discussions, and I

would say, “Well Bob, why is this the actual state space in this model?”

That question came up”and now I am jumping ahead”after I came

to Penn. At some point Karl and I started talking about that and we

developed what we called the idea of sunspots. But the initial impetus

toward that for me was talking to Lucas.

46 Stephen E. Spear and Randall Wright

MD: Also, technically, Lucas™s paper was one of the ¬rst uses in

economics of contraction mappings.

Cass: Well, Bob was very ¬xated on using contraction mappings to

get ¬xed points. I think maybe he always uses that technique. I don™t think

he even knows Brouwer™s Theorem! No, actually he does. He just likes

contraction mappings. Anyway, the view in capital theory, as I understood

it, was that you could treat, from a fundamental state space, uncertainty

as well as time. So a commodity index could represent time, uncertainty,

and commodity characteristics like location, whatever you wanted. But

the viewpoint in growth theory is precisely that equilibrium is just prices

that depend on the underlying state space. Bob went a step further and”

I™m not even sure how I would say it”it is more like a function of the

underlying state variables, or to put it more accurately, the state space

itself is generated via some underlying process through observed vari-

ables. So that™s what the state space itself is, for instance, money and

some actual random shocks. Money is one of the state variables, though

it™s actually de¬ned on the underlying state space. The states of the world

are described by money and a random variable that has to do with island-

speci¬c shocks.

The ultimate question is, “What is a state space?”

MD: Brock and Mirman was another seminal paper.

Cass: Brock and Mirman was kind of a milestone because they focused

on introducing uncertainty into the neoclassical model. Where did I

meet Buzz Brock? Somehow, Buzz was a student at Berkeley and I think

his thesis had to do with optimal growth in a multisector model. That is

probably when I ¬rst met him. Our careers overlapped in several dimen-

sions, for instance, when Jan and I spent the year later visiting Cal Tech