On the pleasures and gains of collaboration.

Baumol, William J.

I was very grateful for the invitation to write this piece about those with whom I have collaborated over the years, because it gives me the opportunity to go beyond the usual meager introductory footnote or the brief book preface to express my appreciation and my deep and abiding affection for my coauthors. Yet the writing of this piece is also frustrating because it requires me, almost arbitrarily, to focus upon only a small selection of my partners in crime. Lack of space forces me to refer only briefly to other collaborators who have a profound place in my career and affections, and to omit altogether others of my nearly sixty coauthors with whom my association was fleeting. For my coauthors have ranged from some as close as my wife and very dear friends to others with whom I communicated only by telephone or by mail and never actually met. I have even had one coauthor who was no longer alive.

It must be admitted at once that the attitudes reported here are unlikely to be typical of joint ventures in writing and research. A dispassionate observer may well consider my experience to be somewhat outre, if not a bit pathological. The telltale symptom is the fact that, in more than 40 years of collaboration, harsh words were spoken on only one occasion. But even then matters were not quite as they might have been expected. Lester Chandler, with whom I had several weeks earlier finished the hard work of writing a rather thick volume, was discussing with me some economic issue quite unrelated to the book, when suddenly we found ourselves shouting. This lasted perhaps a minute or two, when suddenly we realized what we were doing, and both of us burst into laughter. Of course, we remained good friends until his death.

I. My Coauthors - A Quick Survey

Before turning to a few of my collaborations in greater detail, let me first indicate who my coauthors were. Twenty of them have been colleagues in my departments at the LSE, Princeton and NYU. Sixteen were students, two of them undergraduates at the time. Of those sixteen, fourteen went on to become professors, two became Presidents of Princeton University (Bill Bowen and Harold Shapiro), one was awarded the Nobel Prize (Gary Becker) and one is today a member of the House of Lords (Maurice Peston). There have been eight women with whom I served as coauthor, five fellow consultants and three mathematicians.

Let me first discuss collaborations that grew out of dire need rather that convenience or happen-stance. It is well-known to some that I have a propensity to flit from field to field, often entering arenas in which ignorance was my prime qualification (indeed, I embarked on my years of study of productivity growth when the president of the Committee for Economic Development suggested that they wanted me to conduct such a study for them primarily because my mind was not preconditioned by knowledge of the subject). Consequently, I have often had to rely with some degree of desperation on others who were working in the area, and who actually knew what they were talking about. This was emphatically true of my work on industrial organization, for which I had to lean heavily on Elizabeth Bailey, Gerald Faulhaber, Janusz Ordover, John Panzar and Robert Willig. I will speak of my collaboration with this group later in somewhat greater detail. Similarly, when econometric analysis was required, it was necessary to turn that part of the task over to others, and my colleagues Richard Quandt, Stephen Goldfeld and, now, Edward Wolff, have enriched my working life and acted as ideal partners over the years. I have been a coauthor with a number of mathematicians. First, though not a coauthor, there was Solomon Lefschetz, then the grand old man of differential equation theory, who spurred me on to write a piece on nonlinear difference equations. Also in the background was Albert Tucker who was instrumental in arranging partnerships with a number of others, including Michel Balinsky, Ralph Gomory (about whom more anon), Harold Kuhn and Philip Wolf. This was a period of intense research on mathematical programming, and as new developments emerged I served as coauthor on several articles discussing the economic implications of such things as the nonlinear dual, decomposition and integer programming. My good friend Tibor Fabian, then president of our consulting firm, MATHEMATICA, also participated in this collaboration. There were other fields in which I have had to rely on others to protect me from my ignorance. The one that most needs mentioning is corporate finance, in which Burton Malkiel has been my dependable rescuer (as well as my partner in the consumption of quantities of most delicious, cholesterol-laden cuisine, offset by excellent red wine).

I want very much to single out several of the women with whom I have been a coauthor. Proceeding alphabetically, with one exception that will be obvious, I first mention my former student and very dear friend, Elizabeth Bailey, whose subsequent distinguished career is widely known. She participated in the discussions and research leading to the theory of contestable markets, about which more will presently be said, and in the process exercised her genius in stimulating the creative efforts of others. Sue Anne Batey Blackman has been my research associate and occasional coauthor for more than twenty years, and has contributed to all of my writings throughout that period. Her ingenuity in digging up information and in extracting unpublished data is extraordinary. The accuracy of her work underlies anecdotes that should be told if space permitted. Most important, of course, are the ideas she has contributed to the work we have done together and on which I am counting for work we have projected. Peggy Heim (now Nelson) is another coauthor with whom I became a close friend. We labored happily together for about a decade at the Association of American University Professors, carrying out a national survey of faculty salaries, both for the sake of research and as a bargaining instrument on behalf of faculty in negotiations with college and university administrations. We also carried out two studies of academics' contracts with publishers, in the second of which we were joined by another enduring friend, Martin Shubik. Our long collaboration produced an extraordinary understanding of the ways in which one can study remuneration of academics and contributed to the quality of our product. Helen Makower worked with me when I was a junior faculty member at the LSE and she was very senior. I frankly do not remember any details of our work together, aside from recalling it as another pleasant experience. Mary Oates provides another example of a coauthor who contributed indispensable knowledge from another field (as well as a good deal more). We had a marvelous time writing on the economics of the Renaissance theater in London, she being a specialist in English literature, and I having recently completed a similar effort on the theater of ancient Athens. My most enduring collaboration with a member of the other sex is, of course, with my wife of 53 years, with whom I first began to work on the economics of the performing arts some three decades ago. That, too, is a tale to which I will return, but I must mention here that over the years she has contributed in a number of ways: with ideas when I was stuck, by editing and carrying out substantial research and, above all, by continuing to tolerate the partnership.

Let me end this survey with a few words on several of the others with whom the partnership was particularly close, though lack of space prevents more extended accounts. I have already mentioned Gary Becker, who was one of my two undergraduate coauthors. He, as a matter of fact, was senior author of our piece on monetary theory, I having merely contributed the portion on doctrinal history that, though clearly needed in the article, was a secondary issue. The other undergraduate coauthor was Ralph Turvey, who wrote a chapter on the Swedish contribution for my Economic Dynamics, though he continues to insist that he took greater pride in correcting my misspellings. He recently cooked a magnificent dinner for my wife and me and Frank and Dorothy Hahn on the occasion of Ralph's sixtieth birthday. I must not omit Jess Benhabib, with whom I wrote an introductory paper on chaos theory, he supplying the knowledge while I attempted to write up the material so clearly that even I could understand it. I have also profited over the years in a number of collaborations with David Bradford who was able to take suggested ideas that I understood only dimly, showing in each case that there was much more to the matter than I had seen. Alvin Klevorick and I spent several years completing a paper on the Averch-Johnson thesis, one that seems to have brought the discussion to an end. The reason it took so long to complete was the constant flood of ideas pouring out of New Haven, he just having joined the Yale faculty after completing his graduate studies at Princeton. Last, I must not forget Wallace Oates, with whom I wrote two books on environmental economics. Gentle, kind, reliable and hard-working, the task of completing a book with him was a constant pleasure.

II. Bill Bowen and Arts Economics - Birth of a Small Industry

Our entry into the performing arts arena in about 1962 was almost happenstance. John D. Rockfeller the third and August Heckshire, then president of the Twentieth Century Fund, had decided that the propitious moment had arrived for an assault on Congress and the Administration on behalf of funding of the performing arts, and had decided to sponsor a study to investigate appropriate measures. Various economists had been consulted, and someone had mentioned to the group to which the task of organizing the endeavor had been assigned that there was an economist at Princeton who was heavily involved in artistic activity. I was invited to appear before the group, and explained to them that my activities in sculpture and painting offered me little insight into the economics of the performing arts. However, I pointed out that my consulting experience had taught me ways of approaching the study of industries about which one initially knew nothing, and that a useful study of the subject in which they were interested would be most effective if the arts were treated dispassionately, as a product like beer or breakfast cereal, in which observation was not clouded by sentiment. Something I said that day must have struck a spark, because the next day I received a telephone call saying they had decided to offer me the project. I declined politely because of other pressing obligations. This seemed only to enhance their desire to have the study carried out in the manner I had described, and I finally agreed to do it if I could induce a young colleague - Bill Bowen, then an assistant professor - to join me in a partnership. Our fate for the next four years was sealed.

The undertaking turned out to be larger than we had imagined. We recruited colleagues. Our wives joined the enterprise. Undergraduates fanned out throughout the country to survey audiences. A fine subsidiary study was carried out in England by Muriel Nissel. All of this was organized and overseen by Bill with dedication and panache. He tolerated no malingering by anyone, though always with diplomacy. Every day, without fail, we would receive a telephone call at 8 AM. Every day it had a different subject, but the real purpose was clear. It was to ensure that we were up and about attending to our duties.

Bill took charge of the data planning, collection and analysis, while I focused on the more theoretical side of the subject. He would constantly come up with surprising and illuminating observations and conclusions. As an example, I remember the excitement when he found a near perfect inverse correlation between the size of an orchestra's annual budget and the proportion of women among its musicians. In most collaborative work I usually end up doing most of the writing on the basis of outlines supplied by my colleagues. This case was no exception, but Bill's outlines were extraordinary-logically organized, optimally detailed, full of insights, with clear signposts at every point where there was any likelihood that I might go wrong. His outlines were models of planning for the production of a book, and I have many times regretted their disappearance, because I have so often wanted to show them to others.

Careful planning by August Heckshire, with his journalistic experience, yielded publicity that I have never obtained before or since. We made the front page of The New York Times, The Washington Post, The London Times and Pravda. Pravda recounted that in our book two respected Princeton economists had documented conclusively how capitalism destroys the arts.

Bill went on to apply our analytic approach to higher education, while I used it to discuss municipal services, health care and other activities which we said to be infected with what we called the "cost disease". Meanwhile, other talented investigators that have gone further into the economics, of the arts, have formed an association devoted to the subject and published a fine journal in the arena. At the 30th anniversary of the publication of our book, the association held meetings in celebration, for which we are deeply grateful.

III. Alan Blinder and the Principles Textbook

Alan Blinder was another of the brilliant Princeton undergraduates who had majored in economics - the group included Gary Becker, Otto Eckstein and Richard Quandt. Thus he, too, had been one of my students and, like the others in this group, had taken my graduate microeconomics course while still an undergraduate. He had gone to MIT for his formal graduate work and returned to Princeton as a junior faculty member.

At the time he returned I had accepted a nominal consulting position with Harcourt Brace Jovanovich as advisor on its economics list. The head of the enterprise, a very pleasant person (Robert Styron), had dreamed of creating an economics principles text, and had put together a team of three of the nation's most noted economists (no names will be mentioned) who had agreed to produce the volume, but who seemed unwilling to get started. I was induced to join the group but, still, nothing happened. It soon became clear to all of us that nothing was likely to occur, and I assumed, perhaps somewhat relieved, that the project was dead. Then Styron's successor, he himself having retired, called me and announced that he had looked into the project and decided it was too promising to abandon. My reaction was that this was a view to be expected from a publisher, until he told me that he had spoken to a young colleague of mine who had agreed to undertake the task provided I would participate. Knowing Alan's ability in writing and his extreme reliability (very similar to that of Bill Bowen), an undertaking that has so far produced seven editions had been launched.

Since, in textbook publishing, financial issues are more than a little pertinent, it should be noted that, except in a few special cases, the compensation arrangement with my coauthors has always been equal sharing. I believe any other arrangement must threaten to remove much of the pleasure a collaboration can offer.

Like Bill, Alan would stand for no nonsense from me. More than once I have hinted that a chapter was good enough and needed no further work, to be informed, gently but firmly, that it required drastic revision. While each of us took responsibility for half the chapters, I was expected to go over those assigned to Alan without reservation or mercy, and the favor was reciprocated. My trouble was that when Alan offered a criticism of something I had done, it was almost invariably right. I never could think of a good counter-argument. While there was for each of us a core of chapters that were never shifted, an interchange of a number of chapters would occur from one edition to the next to reduce the chance that we or the book would become stuck in a rut.

There are few incidents to report here. After all, the care and feeding of a text is no laughing matter. We have had many pleasant evenings with Alan's delightful wife, Madeline, an indispensable member of the group, and we have worked together on such profound literary efforts as the faculty skits for the departmental Christmas party. We have had occasion to collaborate during his period on the Council of Economic Advisers, but work on the text remains so serious an undertaking that we begin work on the next edition with some foreboding. Incidentally, Alan's recent position as Vice Chairman of the Federal Reserve Board imposed another responsibility upon me. More than once I received a call from a reporter that finally got to the question, "How will Dr. Blinder vote on interest rates next week?" The answer has been easy: don't know, and if I did, I wouldn't tell anyone!"

IV. The Birth of Contestability Theory

Among my collaborative efforts I must describe the design of contestability theory. It all started when I was asked by persons at the National Science Foundation to sum up the case for governmental intervention in support of technical publications. I expected to provide a routine discussion of the role of externalities, imperfect competition and the other usual suspects, but my exposition unexpectedly bogged down when writing about a multiproduct firm such as the publisher of a number of journals. There did not seem to be a readily available story on what constituted a natural monopoly in that case - scale economies just did not seem to do the trick. Other related matters also proved to be less cut-and-dried than I had suspected. Elizabeth Bailey, then head of the economic research group at Bell Laboratories, was also teaching part-time at New York University, where l, too, had also recently joined the faculty. She being an ex-student of mine, we had grown close, and I was delighted when shortage of space made it convenient for her to share my office on her weekly visit. We began to discuss the issues avidly, and elements of the solution to the puzzles that had baffled me, concepts such as trans-ray convexity in output space began to emerge. It then transpired that two of her colleagues at Bell Laboratories, John Panzar and Robert Willig, had been struggling with related issues. It also soon emerged that significant contributions had been made some three years earlier by Gerald Faulhaber, then a graduate student at Princeton on leave from Bell Laboratories. It is ironic that I had been Faulhaber's thesis supervisor, and though I remembered his work, its pertinence to what our group was doing at first escaped me.

Elizabeth then assumed a double role. She and I worked together in exchanges, sometimes heated, on the evolving theory. At the same time she became our communications link, regularly reporting our latest results to John and Bobby, and transmitting their discoveries in the other direction. The race to be the first to solve the current week's conundrum became a cross between collaboration and friendly but avid competition. Each of us can claim our individual contributions, usually then taken up by the others and carried forward far beyond the relatively primitive original idea. For example, John and Bobby provided a set of necessary conditions for subadditivity of the cost function, while I arrived at a set of sufficient conditions. On the same day, independently, John and Bobby produced a workable criterion of incumbent prices sustainable against entry while Betsy and I came up with essentially the same concept.

There is one event that does not entail collaboration, but is sufficiently bizarre to be worth recalling. My wife and I were attending a performance at La Mama, an off-off-Broadway experimental theater that we frequented. That night was a benefit for a transvestite group, starring the most glamorous individuals in that realm, and we were waiting in line surrounded by bespangled and costumed individuals whose sex was not entirely obvious. Suddenly my wife looked concerned as I went silent and then looked at her with astonishment. I reported that out of nowhere there had flashed before me a theorem, complete with outline of the proof, indicating that for a monopoly with a subadditive cost function Ramsey prices must be sustainable against entry. After that, whenever we were stuck on some analytic point, my coauthors would direct me to attend a La Mama performance.

Months later Bobby and I, along with perhaps a dozen others, were asked to represent the National Science Foundation at a meeting in Leningrad with a counterpart Soviet organization. In the airplane we sat up all night and talked, and out of that talk the concept of a contestable market arose. Several years were to pass, and persons such as Dietrich Fischer and Thijs ten Raa were to contribute to the effort before the book finally emerged. There are tales to be told about the writing process, but I have already devoted an appropriate amount of space to the collaboration that resulted in the contestable market analysis.

V. Productivity Growth and the Surprising U.S. Performance

It was probably in 1981 that Robert Holland, president of the Committee for Economic Development, invited me to serve as director of its project on productivity policy. I took on the assignment with enthusiasm, and proceeded along the usual CED track, conducting research to a considerable extent by means of discussion among a group of experienced and knowledgeable persons. All of us were convinced of the correctness of the common wisdom at that time: that the United States was already beset by forces that had undermined its productivity growth and threatened its position as economic leader of the world. The evidence we examined seemed to support this position, and the only dispute that emerged among the members of the subcommittee engaged in the production of the CED statement on productivity was about the appropriate means to effect a rescue.

The limited time allotted to the project having passed, I had the time to go into the issues more deeply, with Kenneth McLennan (then vice president of CED)joining me in the initial follow-up steps. First, it seemed appropriate to delve into the long-term productivity record, Jacob Viner having long ago drilled into me the importance of considering the long period along with the short. My colleague, Ed Wolff, suggested some data sources to me and identified some of the most important contributions in the literature. Sue Anne Batey Blackman began to follow up. However, at first I did most of the analytic work by myself, and came up with statistical evidence based on Angus Maddison's 1982 sample of countries, indicating that over the past century there had been marked convergence among the industrial countries in terms of productivity growth and per capita incomes. Obviously, there had been earlier writers, notably Veblen, Gerschenkron and Abramovitz, who had pursued the convergence hypothesis. So far as I know, however, only Matthews, Feinstein and Odling-Smee had (very briefly) previously studied the statistical evidence directly. My subsequent article on the subject attracted considerable attention, elicited much follow-up work that still continues and, predictably, was met with some deserved criticism. In particular, Bradford de Long pointed out cogently that I had worked with a sample of countries that had proved, in retrospect, to have grown successfully. This, he argued persuasively, biased the result toward a finding that convergence had occurred.

At this point I turned to Ed Wolff for help, and we began to explore the subject more systematically and with the degree of econometric sophistication that he but not I could contribute. Our study spread to related issues, and we gradually and reluctantly were forced by the growing accumulation of evidence to conclude that reports of the demise of U.S. economic leadership were a bit premature. We found, for example, that this country had suffered a drastic decline in productivity growth by the early 1970s, but that declines had occurred in the other industrial countries at about the same time, with Japan's growth rate falling by about the same percentage as ours. We found also that while the U.S. was indeed moving toward a service economy, so was every other industrial economy, most of them at a pace considerably faster than ours. And the evidence of convergence confirmed that other countries were indeed outpacing the U.S. in terms of productivity growth rate, but that this was a necessary condition for their emergence out of relative poverty, with no evidence indicating that they were doing more than approaching our productivity level asymptotically.

Our study also indicated that in the course of a century productivity growth had made contributions to living standards so enormous (increasing them, perhaps, eightfold) that the change eluded intuitive comprehension. Ms. Blackman independently carried out a study of the concrete manifestations of the change in living standards that had occurred over a century, and succeeded far beyond what might have been hoped in giving to nineteenth century living standards a local habitation and a name. The result was our book that showed how much productivity matters in the long run, and documented how wrong I and my associates had been in accepting at face value the despairing view of the U.S. productivity record.

VI. Ralph Gomory and the Orderly Region of the Many Scale-Economies Trade Equilibria

One day in about 1958, when I had been a member of the Princeton faculty for nearly a decade, Albert Tucker, chairman of the Math Department at Princeton (and codiscoverer of the Kuhn-Tucker theorem), came by and suggested that there was a young man whom I ought to meet. "He has solved the integer-programming problem," Tucker told me (revealing to me for the first time that the problem had up until then evaded solution). The young man was Ralph Gomory, then assistant professor in the Math Department.

We did meet and he explained to me how one went about solving a maximization or minimization problem subject to the constraint, among others, that some or all of the variables be integer. As the discussion proceeded it offered hints of the properties of the dual of the original program, and its interpretation as the values of the constraining parameters - the incremental values in terms of superior achievement in the objective of a loosening of the constraint parameters. An example is the addition to a firm's maximum profits that is made possible by an addition to its warehouse space. In an integer programming case the usual interpretation requires obvious modification, because if packages to be stored come in a minimum size of, say, one cubic foot, then the addition of a cubic inch of space to that offered by the warehouse clearly is zero, meaning that the first derivative of profit with respect to the constraining warehouse space is also apt to be zero, even if more warehouse space is needed urgently. In that paper we also indicated that integer programming held some promise as a means to approach optimization in the presence of scale economies, where the usual facilitating concavity-convexity conditions are violated - an indication of things to come three decades later.

We both enjoyed our collaboration, and then Ralph left the academic world to rise to the position of Director of Research and Senior Vice President at IBM. A few years ago I heard that he had left IBM and had joined the Sloan Foundation as its president. I thought no more about it until a bit later when I received a telephone call from Ralph inviting me to join him in a project on the borderline between economics and mathematics. Despite my weak grounding in the field - international trade theory (but when had that stopped me before?) - I leaped at the invitation. The work was fascinating, and I could not resist renewing the pleasures of our previous work together. Aside from its trade orientation, it was a first for me in another respect, for it is the first time, as far as I can recall, in which I had entered a partnership with the other person already having made the breakthrough as well as the intellectual investment. Nevertheless, I flattered myself that before it was over I would be able to make a contribution sufficient to qualify as a legitimate junior partner.

The topic was equilibrium in the presence of scale economies or substantial startup costs. The subject had previously been explored by very capable economists who had, particularly in recent years, made profound contributions to the subject, on a number of which we were to build. For example, the underlying scenario, in which scale economies are external to the firm but internal to the industry within a nation, had already been used widely. Earlier studies showed that under scale economies equilibrium is not unique. Moreover, it was already known that in the theoretical case of universal scale economies, equilibria generally entail perfect specialization, with no product produced in more than one country. Ralph had been able to carry this reasoning several steps further. He had shown that in this model each and every perfectly specialized assignment among countries is an equilibrium, and one, moreover, that is stable locally. In addition, he showed that as the number of traded commodities grows, the number of equilibria grows astronomically, in the case of two countries and n goods, on the order of [2.sup.n], that is, the number of different ways of dividing up the specialized production of goods between two countries. Most exciting of all, he devised a workable calculation method which permitted representation of each equilibrium by a point in a graph, and showed that the region of equilibrium points is well-defined and that it always takes the same general shape, a shape with a very illuminating economic interpretation, notably that many of the equilibria are far from ideal, and that they constitute a newly recognized source of rivalry among trading countries.

Later, we were to show that part of the explanation is the fact that scale economies undermine the role of comparative advantage. We have just recently proved that in this case many equilibria violate comparative advantage, that an equilibrium that violates comparative advantage may nevertheless be efficient, and that many equilibria may be inefficient. We have described some of this work in the 1994 Lionel Robbins Lectures at the London School of Economics and are now engaged in writing various articles reporting the details of the analysis. Two books are currently expected to emerge from the work.

VII. Concluding Comment

What is to be said by way of peroration? Only that collaboration can be fun and profitable intellectually, provided that one selects only coauthors who are simpatico and very patient.