Prof CR RAO’s 90th Birthday, 10 September 2010
A long time ago I (Suresh) was told by a man who had more understanding than the wise that man is really born at the age of 60. Being not so wise as the wise man was and given your spirit and ongoing active contribution to knowledge we completely rely on his judgement. So as for as we see, you are only 30 years old. Please accept out heartiest greetings on your birthday and we wish you live 1,000 years and every year has 1,000 days in it. "Tum Jiyo Hajaron Sal, Sal Ke Din Hon Ake Hajar". [Photo 1: Suresh with Prof. Rao].
Last December we attended an International Conference in Hyderabad, India at CR Rao Advanced Institute of Mathematics, Statistics and Computer Science. This was the second occasion when I (Suresh) attended an international conference in honor of an International dignitary and doyen in the subject. Suresh's first conference was in honor of Professor Robert Aumann and to felicitate 1994 awarded of the Swiss Bank prize in economic science in honor of Alfred Nobel (also called a Nobel Prize in economics), Prof John Nash, Prof Reinhardt Selten and Prof John Harsanyi for their contribution to applica-tion of Game theory to economics. [Photo 2: Suresh & his lttile one with Prof Nash].
Photo 3; Suresh with Prof Harsanyi]. Profs Nash and Robert Aumann are more known as mathematicians than economists. In fact, Nash’s main work is in Differential Geometry, partial differential equations and work on Game theory was in passing. In 1948 when he was 19 year old, as a graduate student at Carnegie Mellon University, Pittsburgh he wrote a paper on economics of bargaining as a term paper for a course on international trade. Thus he went to Princeton where he worked on his equilibrium theory. According to him he was not certain that his work on game theory applied to economic problems would be recognized and received well for the award of doctoral degree in mathematics. Nash, therefore chose to work on differential geometry that was one of the main fields of distinguished research at Princeton in the forties and fifties with Herman Wyle and N.E. Steenrod. He, however, earned a doctorate in 1950 with a 28 page dissertation on non-cooperative games. The thesis, which was written under the supervision of Albert W. Tucker, contained the definition and properties of what would later be called the "Nash Equilibrium". These studies led to four articles: "Equilibrium Points in N-person Games", Proceedings of the National Academy of Sciences 36 (1950), 48–49. MR0031701, "The Bargaining Problem", Econometrica 18 (1950), 155–162. MR0035977, "Non-cooperative Games", Annals of Mathematics 54 (1951), 286–295. , "Two-person Cooperative Games", Econometrica 21 (1953), 128–140. MR0053471. In fact although he has not worked on Game theory or economics since his seminal paper on Nash Equilibrium recently he has been working on the concept of the need for a global currency.
He shared 1994 Nobel Prize with Harsanyi and Selten for their work on game of incomplete information and noncooperation and its application to economics. Of course, Game theory has never been a recognized subject until1980s, although the basic concept of equilibrium in a game can be found in the economic theory of duopoly and oligopoly enunciated by Augustus Cournot way back in 1838. [Photo 4: Suresh with Prof Selten].
[Photo5: Suresh & his little one with Prof Aumann].
“I know that you know, you know that I know, I know that you know that I know, and so on”, (See, Movie: Last Emperor of China's dialogue with his English Teacher).
My (Suresh) own PhD Thesis: A Study of Game theoretic Methods and Application to Takeovers, Advances in Econometrics (1989, 1991), Managerial Decision Economic (1994), International Review of Financial Analysis (1999), Journal of Management and Governance(2000), etc. There was a section on biblical origin of game theory and its application to finance published in Blackwell Internal Encyclopedia of Finance, Blackwell Co., 1996. Prof Rao was one of my (Suresh) thesis supervisors. I discovered then that two other students of Prof. C.R. Rao, Prof T Parthasarthy and Prof TES Raghavan, are well known Game theorists.
Prof. Aumann received the Nobel Prize in Economics in 2005 for his work on conflict and cooperation through game-theory analysis. He shared the prize with Thomas Schelling, an economist, President of American economic Association in late 1980s. [Photo 6: Prof TKKrishna Kumar].
If we keep these game theorists in the background and contrast with Prof CR Rao’s contribution to Econometrics, a well recognized branch of knowledge of economics (part of Ontology), it far exceeds the contribution of Nash & Aumann put together. He was appointed a Fellow of World Econometrics Society in 1972 and Journal of Quantitative Economics, a Journal of The Indian Econometric Society brought out a Special Issue in honor of Prof CR Rao. The author in the preface of the JQE commented: “One of the purposes of this special issue is to recognize Dr. Rao's own contributions to econometrics and acknowledge his major role in the development of econometric research….'' In fact, his statistical methodology continues to inspire and guide mainstream research in econometrics ranging from generalized inverse of a singular matrix, unified theory of linear models with fixed and mixed effects, MINQUE theory for estimation of variance components, extension of principal component analysis using covariates for studying trends of economic variables, characterization of probability distributions, score tests, etc. Further, weighting distribution, pooling and shrinkage, varying parameter methods, generalized spatial median and majorization are all examples of the new applications to econometrics. The length, breadth and dept of his contributions has long way to go. We perhaps see no other concepts used in econometrics as much as the asymptotic theory of statistical inference, the foundations of which were laid by Dr CR Rao. Likewise, one of the most popular concepts used in econometrics is the Lagrange multiplier test that was developed by Prof. C.R. Rao.
[Photo 7: Prof Rao's Family]
[Photo 8: Suresh, Mrs Jenny Mayo-Deman & Fareed with Prof Rao in Piitsburgh 1986]
A survey of literature published in Journal of Quantitative Economics (1991), in which Prof H. D. Vinod played a major role in coordinating the editorial wrok, shows Prof Rao's seminal paper on scoring was cited more than 130 times by leading econometricians and economists like, Amemiya, Brandt. Breusch, Chesher, Chow, Cox, Davidson, Durbin, Engle, Godfrey, Harvey, Hauman, Hendry Higgins, Judge, CG Khatre, Koenker, Kmenta, MacKinnon, Maddala, Newey, Neyman, Pagan, Pearson, Rothenberg, Sargan, Tauchen, Ullah, HD Vinod, Wald, Wallis, White, Woodridge, and others. CR Rao's reference in their papers appeared more than once in Econometrica, Journal of Econometrics, Advanced Econometrics, Australian Economic Papers, Review of Economic Studies, International Economic Review, Hand book of Econometrics, Econometrics Reviews. Journal of Economic Literature, Econometrics Theory, Econometric and Quantitative Economics, Proceedings of Econometric Society, Time Series Econometric Modeling, etc. In fact, many volumes of Handbooks on Econometrics published by North-Holland, econometrics journals and interviews attest to this. As a graduate student at the University of Pittsburgh I read a review of his book on the Linear Statistical inference and Its Applications, 1972 John Wiley, NY., which said, “it was one of the most widely cited book after the Bible”. One may see the interview of Prof. C.R. Rao published in Econometric Reviews. Late Prof DeGroot of Carnegie Mellor University devoted an entire issue of the journal Statistical Science 1986 on his interview with Prof Rao. He received a Ph.D. under Prof R. A Fisher and a Sc.D. on his published work from the University of Cambridge. Prof C R Rao supervised and produced over 50 PhD who in turn produced about 250 PhDs. He is the author of 14 books and about 350 research papers of which some in Econometric journals. Three of his books have been translated into several European and Chinese and Japanese languages. Prof Rao has been awarded 32 honorary doctorates from 18 countries from 7 continents. Times of India dated 31 Dec 1988 chose C.R. Rao as one of the 10 top scientists of India; the list includes the outstanding scientists, S.N. Bose, S. Ramanujan, Harishchandra, H. Khurana, C.V. Raman, S. Chandrasekhar and G.N. Ramachandran most of them already got the Noble Prize (see, http://www.stat.psu.edu/~crrao/bio.htm).
Prof Rao’s comments on the econometric problem posed by the founder of econometrics Ragnar Frisch plays a central role in characterization of how probability enters in econometrics. His contributions to estimability using the concept of Fisher information play a very central role in one of the most fundamental problems of econometrics, the identification problem. Prof. CR Rao founded the Indian Econometric Society in 1960. Several persons whose methodological contributions are so trivial compared to Prof CR Rao’s received the Swiss Bank prize. Although US President conferred on Prof CR Rao title of National Science Laureate and gave him a Gold Medal in 2002 we really don’t understand why Prof Rao was not nominated for the Swiss Bank prize in economic science in memory of Alfred Nobel for his contribution to econometric methods and theories. Alternatively, following Prof Stephen Hawkings’ recent article in Eureka rendering God irrelevant for the creation of the Universe, Professor Rao being a self creator of an institution of statistics also made the Nobel Prize irrelevant [Photo 9: Prof Hawkings & his admirers].
HAPPY BIRTHDAY PROF RAO
Prof. S. Deman, Hon Director, Centre for Economics and Finance, UNEP/UNCTAD & Employment Consultant, London, UK.
Professor Krishna Kumar, Guest Faculty, Indian Institute of Management, Bangalore and retired Professor, Indian Statistical Institute, Bangalore.