Koji Shimomura: A Memoir

On 24 February 2007, Koji Shimomura passed away at the age of 54, after a long and courageous struggle against illness. He was academically productive till the end of his life and published a number of excellent papers in leading journals. His death was a great loss to the economic profession, to his family, his friends, colleagues, and students. Koji left behind a wealth of brilliant contributions to economic theory, particularly in international trade theory and in the study of economic dynamics. Over a span of 24 years, after the completion of his PhD thesis at the University of New South Wales, Australia, he had published several research monographs and almost a hundred academic papers in professional journals and scholarly volumes. He had scores of co-authors, ranging from his thesis supervisor, Murray C. Kemp, friends and colleagues of various age groups, to his students. His articles appeared in well-known international journals, such as Journal of Political Economy, Journal of Economic Theory, International Journal of Economic Theory, International Economic Review, Economic Theory, Journal of Mathematical Economics, The Economic Journal, Journal of Economic Dynamics and Control, Review of Economic Dynamics, Review of International Economics, Journal of Public Economics, Oxford Economic Papers, Journal of Economic Behavior and Organization, Japanese Economic Review, Japan and the World Economy, Canadian Journal of Economics, Scandinavian Journal of Economics, German Economic Review, Economics Letters, Annals of Operations Research, and many others. In recognition of Koji's contributions to international economics and in particular to the Review of International Economics, for which he served as an associate editor for several years, Professor Kwan Choi, editor of Review of International Economics has kindly offered us an opportunity to put together a special issue in honor of Koji for RIE. Owing to the constraints of journal space, we humbly offer our apologies to many of Koji's friends, colleagues, co-authors, and graduate students, whom we could not invite to contribute in this issue. We would like to thank the authors and the referees of the contributions to this special issue. This article offers a brief outline of Koji's life and work, a summary of Koji's main contributions to economics, and a collection of personal remembrances written by some of Koji's friends, colleagues, students, and, most important of all, former teachers. Koji's career as an academic economist began when he obtained his Bachelor of Economics from Kobe University in 1975. He went on to pursue graduate studies at the same university, obtaining his Master of Economics in 1977, and taking PhD courses during the following three years, while being employed as a research assistant. In 1980, following the recommendation of Professor Uekawa, Koji applied for admission to the University of New South Wales as a PhD student, where Professor Murray C. Kemp, a great friend of Professor Uekawa's, was his thesis supervisor. In joining the University of New South Wales as a PhD student under Professor Kemp, Koji was following the footsteps of three other Japanese economists, Hideo Suzuki, Hiroshi Ohta, and Makoto Tawada, listed in chronological order. Koji did his research on the theory of optimal exploitation of renewable resources, such as fishery. The analysis of these types of problems requires a good command of mathematical techniques. He acquired the necessary skills over a short period, and completed his thesis within two years. The examiners of his thesis, Daniel Leonard, Ngo Van Long, and Hans-Werner Sinn, were sufficiently impressed with the quality of the work that they unanimously recommended the award of the PhD degree. One of them later became one of Koji's close friends and co-authors. Upon his return to Kobe in 1982, Koji became associate professor of economics at the Research Institute for Economics and Business Administration (RIEB) within Kobe University. In 1986, he was granted leave to return to Sydney to continue his collaboration with Professor Kemp. He was accompanied by his wife, Hiroko, and soon their first son was born in Australia. During this leave period, another achievement that he would later mention to his friends with pride was his passing of a Driver's Licence test in Sydney, which he found much harder than economic theory. In 1996, he visited the University of New South Wales for an extended period, and afterward was a visiting professor at McGill University for three months. In both places, he conferred positive externalities to his hosts and, in his usual style, did a minimum of sightseeing. Koji started his publications very early in his career. Three publications, of which two were single-authored, appeared in 1983–84. These papers, which dealt with various aspects of renewable natural resources, were based on his PhD thesis. Soon after that, he moved on to new directions: trade theory, labor union, dynamic general-equilibrium models, and differential games. In 1993, at the age of 40, he became full professor at RIEB. At that time, his 15 articles and three books had appeared in print, and many more were in the pipeline. After becoming full professor, Koji played a more active role in academic administration, while continuing to produce high-quality research papers. In January 1996, one year after the Kobe earthquake, he organized his first conference. The theme was The Welfare Economics of International Trade and Investment. Together with Professor Murray Kemp, Koji served as joint guest editor of a special issue of Japanese Economic Review in which selected papers of that conference were published. While continuing to do fundamental research at a steady pace, from 2003 Koji embarked on a new endeavor: to be a leader of Kobe University's 21st Century Center of Excellence Program. The theme of his research within the Center of Excellence (COE) was Analysis of International Trade under the Global Economy. He brought the Kobe University's COE to an eminent status in Japan. As a leader of the COE at Kobe University, Koji showed his talents in many facets. Carrying out his vision for the Center, Koji became heavily involved in detailed planning and administration. He had increasingly more guests to host, more conferences and workshops to organize, but he always generously gave his guests his precious time and courteous attention. Many international conferences and workshops in economics were held in Kobe under the auspices of the Center of Excellence. Well-known international researchers visited the Center to interact with Kobe University economists and graduate students, intensifying a fruitful two-way flow of ideas. With so many administrative duties, Koji's success in maintaining his research output at a high level was a marvellous achievement. In addition to his commitment to the Center, Koji took on the positions of president of the International Economics and Finance Society Japan in 2003, associate editor of the Review of International Economics in 2004, and member of the Executive Committee of Japan Economic Association in 2005. In October 2006, Koji was awarded the Kojima prize from the Japanese International Economics Association. While many of his economist friends think of him as an ingenious builder of abstract mathematical models, several of us had an opportunity to admire one of his less abstract models: he built a physical three-dimensional model, using chopsticks with bits of string. The result of this art work was an article in the International Economic Review, entitled A Geometric Approach to the Stolper–Samuelson Theorem. Figure 4 (p. 652) in that article is almost a photographic reproduction of Koji's famous chopstick model. Other evidences indicated Koji's artistic side: Koji loved classical music, and was an accomplished singer. Koji's research interests ranged from international trade to economic dynamics (which includes macroeconomics, growth theory, and differential games). He also wrote on various microeconomic themes, such as production function and public goods. In order to guide the readers through the multitude of Koji's papers, we have decided to classify his papers under three main headings: trade theory, economic dynamics, and microeconomics. Many of his papers deal with international trade in a dynamic context. In several cases it is somewhat arbitrary to decide if a paper should be classified under trade, or under economic dynamics. We have prepared as an appendix a list of selected papers of Koji's, catalogued under three separate headings. Papers that deal with trade theory, dynamic economics, and microeconomics are respectively numbered as T1, T2, . . . , D1, D2, . . . , and M1, M2, etc. His three books, each of which has direct contributions to all three subject areas, are referred to as B1, B2, and B3. Koji was perhaps the most determined economist to bring dynamical analysis to trade theory. He also made significant contributions to trade theory using the traditional static approach. These two approaches are complementary. Dynamical analysis of trade issues A recurring theme in Koji's research agenda is the conditions under which one could obtain some dynamic version of the various theorems and results in the traditional static theory of trade. In (T4) he proved that, in a two-country world, the country with a low rate of discount will, in the long run, be the exporter of the durable consumption goods. In (T18) Koji pioneered the analysis of tariff wars in a dynamic model of asset accumulation, where each country maximizes its welfare over an infinite time horizon. He showed that the bilateral optimal tariff rates reflect both the difference in endowments and the difference between the rates of discount. In (T24), in collaboration with Murray Kemp, Koji investigated the implications of costly factor re-allocation for a dynamic Heckscher–Ohlin model. Koji was keen to learn new techniques and concepts and to introduce them to trade theory. For instance, he learned about the theory of chaos, and wrote two papers on trading economies displaying chaos (T11, T12). More recently, he became interested in the theory of dynamic indeterminacy, and produced several excellent papers on trade with indeterminacy. In (T20), in collaboration with Kazuo Nishimura, Koji showed that for a small open economy, if there are both negative and positive production externalities such that the production functions exhibit constant returns both privately and socially, and if the rate of discount is increasing in consumption, one can find parameter values such that there is a unique steady state that displays indeterminacy of approach paths. In (T22), the same authors showed another type of indeterminacy in a dynamic two-country model: starting from an initial distribution of capital, one equilibrium path converges to a long-run equilibrium in which the initially capital-abundant country becomes the labour-abundant country, while another equilibrium path converges to a different long-run equilibrium, in which the initially capital-abundant country preserves its status. This implies that the long-run trade patterns cannot be predicted from the initial ranking of endowment ratios. Here again, the authors rely on production externalities. In (T29) Koji and his co-authors extended the Heckscher–Ohlin model to the case of human capital accumulation that generates endogenous growth, and showed that, with externalities in production, the multiplicity of balanced growth paths may arise. The pattern of trade in this model depends partially on the difference in psychic costs of investment in human capital. In another paper (T28), Koji and Kazuo Nishimura generated indeterminacy without relying on externalities, but they needed the assumption that interest rates differ across countries because of the assumed difference in the rates of depreciation and the lack of an international credit market. Together with Toru Kikuchi, Koji extended the dynamic two-country trade theory in other directions to take account of factors such as endogenous time preference or monopolistic competition (T30, T31). Static analysis of trade issues Koji extended the Heckscher–Ohlin theory to the case of oligopoly (T10, T26). In several papers, by relaxing standard assumptions, Koji, in collaboration with Murray Kemp, made significant contributions to the theory of international transfers and foreign aid (T21, T25) and the theory of gains from trade (T7, T14, T16). They also extended the theory of customs union to the case of increasing returns and oligopolistic competition (T17). Koji was particularly interested in the role of labor union. Together with Murray Kemp, he showed in (T1) that the folk theorem that labor union drives out capital is not generally valid: there are conditions under which the emergence of a labor union in one country will attract capital from the other country. In a co-authored book (B2), he explored further the problem of trade between countries where labor unions exercise market power. Koji offered a geometric approach to the Stolper–Samuelson Theorem (T8). He provided a pair of new equivalent conditions for a given square matrix of dimension n to satisfy the Stolper–Samuelson one-to-one relationship between factor prices and commodity prices. When n = 4, these conditions can be illustrated by using a tetrahedron. Koji's contributions to the study of economic dynamics can be grouped under three headings: differential games in economics, growth and distribution, and indeterminacy in dynamic general-equilibrium models. Differential games in economics Among Koji's most cited articles are two papers on differential games (D2, D5). In (D2), he analyzed a differential game between the capitalists and the workers, both using feedback strategies. He showed that if workers are the feedback Stackelberg leader, the outcome would be the same as in the feedback Nash equilibrium; this is in sharp contrast to the open-loop case. In a joint paper with Murray Kemp and Ngo Van Long (D5), he considered a game between the capitalists and a government that redistributes their incomes by means of capital income taxation. It was shown that open-loop equilibrium redistributive taxation may be cyclical, and that, in the case of the feedback equilibrium, contrary to the received wisdom, the optimal long-run capital income tax rate may be nonzero. These two papers were followed by a series of articles on differential games, some treating general properties of a class of games (D7, D10), some dealing with specific models, such as durable goods monopoly (D8), the private provision of a durable public good (D11), the equilibrium use of antibiotics in the presence of drug-resistant bacteria (D12), or the use of triggered strategies in a capitalists-versus-workers model (D13). Growth and distribution Koji had a longstanding interest in economic growth, in particular when economic agents are heterogeneous. In (D2, D3), he showed that the long-run distribution of wealth depends on the initial distribution and that poor families cannot catch up with rich ones. Twelve years later, he showed in (D15) that if agents care about relative status, under certain conditions, the poor can catch up with the rich. Another issue in growth theory is the role of self-fulfilling expectations. In a joint work with Been-Lon Chen (D6), Koji showed that given an initial condition, an economy may embark on different growth paths, depending on expectations. In (D9), he showed that the growth rate of an economy may depend on redistributive taxation policies, which act as partial insurance for failure. Indeterminacy in dynamic general-equilibrium models Economists have long noted the possibility that, starting from a given initial capital stock, or vector of capital stocks, an economy can move along different paths of consumption and investment, all of which may converge to the same steady state (transitional indeterminacy), or to different steady states (long-run indeterminacy). There are several distinct mechanisms that are capable of generating indeterminacy. In a series of joint papers, Koji and his co-authors identified various mechanisms. Some of their papers were in the context of international trade. Others were formulated in the closed-economy framework. In (D17), Koji, together with Kazuo Nishimura and Ping Wang, studied a class of models with many capital goods, set in discrete time, without the usual assumption of Cobb–Douglas production functions. They established conditions for the steady state to display a unique approach path, or non-unique approach paths, from a given initial stock. In (D16), together with Kazuo Mino and Ping Wang, Koji constructed an overlapping-generations (OLG) model in which occupational choice by agents with heterogeneous skills was the source of indeterminacy. They did not need complicated specifications of preferences and technology, nor the assumption that the consumption good is capital intensive, which were commonly made by previous authors who found indeterminacy in OLG models. In (D18) in a four-authored article, Koji and his co-authors showed that the necessary and sufficient conditions for indeterminacy in a class of endogenous growth models in continuous time are neither necessary nor sufficient in the corresponding discrete-time models. Koji's interests in economic issues were extended beyond trade theory and economic dynamics. He also wrote papers on production functions (M7), natural resources (M1, M2, M3), duality theory (M8), public goods (M9), and methodological or conceptual issues (M4, M5, M6). In (M8), together with Kazuo Nishimura and Ping Wang, Koji showed that in a general multi-sector model with sector-specific externalities, the price–output dual may fail to hold. The relationship between factor prices and commodity prices remains valid for factor intensity ranking from the social perspective (but not from the private perspective). In (M9), the famous result that the private contributions to public goods are invariant to small redistribution of wealth was shown to be invalid if agents realized that their contributions to the public goods have an impact on relative prices. In (M4), Murray Kemp and Koji argued that the simplifying assumption that individuals are identical would render some Nash equilibria unacceptable if one insists on full rationality. In fact, they maintained that identical of games would at the of the This would that in the standard they would the outcome that both to not than to Koji realized that the of in (M4, M5, was not as as academic are he was not of being In this we some of Koji's friends, colleagues, and to contribute each a of their with Koji and their on As it was not to invite all of Koji's friends, colleagues, and to because of the on journal space, we to who would have loved to to Koji's student at Hideo and have written about the and that them to Koji in early and The Kemp the of all During the there were many at which and with their Japanese and cannot much to the and of Hideo and has set about Hideo and Koji, two who under Hideo to almost as an economist by and and economic Koji, on the other to from Kobe University of and but less of a than Hideo and Koji were in that, at they had in an problem in economic theory. With his more Hideo this and soon had a article, his work and to be published in the Review of Economic Koji, on the other realized that he needed to his and set the of trade and the on theory. This he did very and, for a time, had that he should be in the of than in the of he had less in in economic theory and soon the research papers began to After his thesis, Hideo decided to in but could find an academic at where were to and his research interests were soon Koji, on the other to the RIEB. 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He loved his and It is a that we cannot his and more on first Koji at the Society held in Koji gave some on the paper at the After the he to a at his Research Institute We started to do joint visited to in workshops Koji or to do a joint research with Koji also visited at the several to in conferences or to do joint with As a Koji always very and was He was a and great economist and a good that learned a from did not have a in international trade. learned international trade when with In Kobe or we went out to had a to with him about other than him to at for a after Koji had When he he very Koji more in his took him to the a famous in We had a good In 2006, had a to Koji at Kobe University after he out the for a He had up to a paper the previous A Koji was It was he out of the this As a good Koji was always when visited from with him and him a great Koji's in research and is always in His direct an for to along the of research and The economic of individuals are not by but also by the and to which they and the economic of the they economic theory and that our economy of and the is an There is or to the life that the of and wealth or can him beyond the economic with and is for a under the that in his cannot through the of and with his this is not the case with a Koji Shimomura did not his life in of his welfare or His life was by his the for his to is a an the end of his Koji to have when he has to in the years, cannot the of Koji us to our research by many international The international conference he organized for the first time is the conference which was held at Kobe University on the first and at Kobe on the following two in January Koji, Makoto Tawada, Makoto and the of together in this conference. Koji organized many international Koji was the one us who could international conferences and us with the opportunity to close with foreign When Koji in the he and did not that passed that he was about research papers as he was of Koji is with an that when visited Kobe University in Koji the Stolper–Samuelson Theorem with One Koji showed us a which was made of He his for these chopsticks in the and made the at cannot Koji's at that Professor Shimomura his students, like his received of of first paper many he kindly not to be He to that paper was of and that one and new the of a professional When paper was at he and as if his son had passed an after many Professor Shimomura if had a to At that time, him that would for a while to all of time on he is and have to He his for his Professor Shimomura was a not on research and economics but also on think the first time Koji Shimomura was on a to Kobe University, the early Koji, of was not one of our students, but over time to him to both his interest and in economics and as a and On that early gave a of the theorem that Murray Kemp and International Economic provided to sufficient conditions for the Stolper–Samuelson Theorem did work for the case. This was by using a and with each of the a for the use of each Some on was to in the 4 4 case the conditions were not this would the use of a tetrahedron. did not and Koji went to obtain some chopsticks from his so that he could three an of the not with factors and he have the result in that He will be both in Japan and where good and economics is Koji was a of will and This have from his his he in

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