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Prasanta chandra mahalanobis.

[ Mahalanobis's ] analytical turn of mind manifested itself at a very early age and he was given to arguing things out with his friends and even with his superiors. Even at a very early age he came under the influence of Rabindranath Tagore who took a liking to young Mahalanobis, being particularly impressed by the combination in him of a love of literature with a flair for logical analysis.

He started reading the volumes on the boat during the journey, and continued to study and work out exercises on his own during spare time after arrival in Calcutta. He saw that statistics was a new science connected with measurements and their analysis, and as such capable of wide application. He tried to look for problems where he could apply the new knowledge he was acquiring. Fortunately, he found some extremely interesting problems in meteorology and anthropology, and started working on them. This was the turning point in his scientific career.

An Act to declare the institution known as the Indian Statistical Institute having at present its registered office in Calcutta to be an institution of national importance and to provide for certain matters connected therewith. ... the Institute may hold such examinations and grant such degrees and diplomas in statistics, mathematics, quantitative economics, computer science and such other subject related to statistics as may be determined by the Institute from time to time.

Those of us who are actively engaged in starting this journal are doing so because of our interest in statistics and our belief that a journal devoted to statistics will be useful in India. ... The spirit and outlook of 'Sankhya' will be universal, but its form and content must necessarily be, to some extent, regional. We shall keep the special needs of India in view without, however, restricting the scope of the journal in any way. We shall naturally devote closer attention to the collection and analysis of data relating to India, but we shall try to study all Indian questions in relation to world problems. A research journal serves that narrow borderland which separates the known from the unknown, and it is not always possible to see clearly the lines of future developments. We shall, therefore, invite papers of all kinds appraising them only on the basis of observational accuracy and logical reasoning. We shall publish carefully collected statistical materials irrespective of the subject even if they have not received any analytic treatment. We shall pay special attention to developments of the mathematical theory of statistics, and include abstracts and expositions of important papers published elsewhere. We shall try to help statistical researches on co-operative lines by bringing workers in different parts of India in contact, and by providing a medium for exchange of ideas. Bibliographies of Indian statistical publications, numerical tables tending to reduce the labour of computation, book reviews, and notes and comments on current topics are some of the ways in which we shall try to make 'Sankhya' useful to statistical workers in India. Knowing that our resources are small we shall seek guidance and help from other countries, and we shall welcome and thankfully receive papers from abroad. The study of modern statistical methods in its infancy in our country, and we do not expect to be able to achieve immediate results. We shall be satisfied if we can help by our humble efforts to lay the foundations for future work.

... for his contribution to science and services to the country.

The Professor, as Prasanta Chandra Mahalanobis was known in India, passed away on 28 June 1972 , three weeks after an abdominal operation in Calcutta. The death occurred one day before his 79 th birthday, when he was still active doing his research work, looking after the Indian Statistical Institute as Honorary Secretary and Director and helping the Government as Honorary Statistical Adviser. The 'Mahalanobis Era' in statistics which started in the early twenties has ended. Indeed it will be remembered for all time to come as the golden period of statistics in India, marked by intensive development of a new technology and its applications for the welfare of mankind.

References ( show )

A Rudra, Prasanta Chandra Mahalanobis: A Biography ( Oxford University Press, Oxford, 1996) .
Bibliography of Prasanta Chandra Mahalanobis, in A collection of articles dedicated to the memory of P C Mahalanobis, Sankhya Ser. B 35 (4) (1973) , 51 - 62 .
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S N Bose, Prasanta Chandra Mahalanobis, Current Science 65 (1) (1993) , 96 - 97 .
W E Deming, P C Mahalanobis (1893 - 1972) , The American Statistician 26 (4) (1972) , 49 - 50 .
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C R Rao, Statistics must have a purpose: the Mahalanobis dictum, Sankhya Ser. A 55 (3) (1993) , 331 - 349 .
C R Rao, The Professor, Economic and Political Weekly 7 (31 / 33) (1972) , 1461 - 1464 .
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A Roy, Two Famous Bengali Scientists: Some Personal Memories, Economic and Political Weekly 28 (17) (1993) , 796 - 797 .
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Additional Resources ( show )

Other pages about Prasanta Chandra Mahalanobis:

An entry in The Mathematical Gazetteer of the British Isles ,

Other websites about Prasanta Chandra Mahalanobis:

Mathematical Genealogy Project
MathSciNet Author profile
zbMATH entry

Honours ( show )

Honours awarded to Prasanta Chandra Mahalanobis

Popular biographies list Number 78

Cross-references ( show )

Other: Cambridge Individuals
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Father of Indian Statistics: Prof. Prasanta Chandra Mahalanobis

“statistics must have a clearly defined purpose, one aspect of which is scientific advancement and the other human welfare and national development.”.

By Indian Statistical Institute

Prasanta Chandra Mahalanobis (1950) Indian Statistical Institute

Father of Indian Statistics

Prof. Prasanta Chandra Mahalanobis is also known as the father of Indian Statistics. He was a physicist by training, a statistician by instinct and a planner by conviction. His contributions were massive on the academic side as the builder of the Indian Statistical Institute, organizer of the Indian statistical systems, pioneer in the applications of statistical techniques to practical problems, architect of the Indian Second Five Year Plan, and much more. Statistical science was a virgin field and practically unknown in India before the twenties. Developing statistics was like exploring a new territory. It needed a pioneer and an adventurer like him, with his indomitable courage and tenacity to fight all opposition, clear all obstacles, and throw open wide pastures of new knowledge for the advancement of science and society.

Prasanta Chandra Mahalanobis view about statistics Indian Statistical Institute

Prof. Prasanta Chandra Mahalanobis perceived statistics ‘as a universal tool of inductive inference, research in natural and social sciences, and technological applications’ and ‘as a key technology for increasing the efficiency of human efforts in the widest sense’.

Prasanta Chandra Mahalanobis at the age of two. (1895) Indian Statistical Institute

Prof. Prasanta Chandra Mahalanobis was born into a family well established in Calcutta (Kolkata), who were relatively wealthy and whose members were enterprising, adventurous, imbued with liberal Brahmo Samaj traditions, and active in all Bengali life.

210, Cornwallis Street, Calcutta, where Prasanta Chandra was born. Indian Statistical Institute

He was born on 29th June 1893 at 210 Cornwallis Street (his grandfather’s house) as the elder son among two sons and four daughters of Probodh Chandra Mahalanobis and Nirodbasini Devi.

Prasanta Chandra Mahalanobis at the age of seven. (1900) Indian Statistical Institute

The family background and the contacts he had with the great intellectuals and social reformers of Bengal cut him out for the active life he had to lead over the next seventy years.

Gurucharan Mahalanobis, Grandfather of Prasanta Chandra Mahalanobis Indian Statistical Institute

Prof. Prasanta Chandra Mahalanobis' actual surname was “Bandyopadhaya”. Possibly six generations before, Guru Charan Mahalanobis started using the surname Mahalanobis as he was appointed to keep the accounts of land and land revenue of Mahal of ancient Bengal. They knew him as “Nauvice”. In Persian “nauvice” means scribe of Mahal (A Mughual administrative unit), so his surname “Mahalanobis” came from the concept of “Mahal” and “Nauvice”. Prasanta Chandra Mahalanobis’s roots were in Panchasar village, now in Vikrampur, Bangladesh. Prasanta Chandra Mahalanobis's grandfather was Guru Charan Mahalanobis who was follower of Sadharan Brahmo Samaj.

His father was Probodh Chandra Mahalanobis, a pioneering entrepreneur, who successfully ran a dealership in sports goods, gramophones and records. Through this efforts, the first successful recording of Rabindranath Tagore’s voice was made in 1924.

Prof. Prasanta Chandra Mahalanobis's mother was Nirodbasini Devi, who was the sister of Dr. Nilratan Sircar, the eminent physician, educationist, and industrialist of that time.

Brahmo Boys’ School (1904) Indian Statistical Institute

He started his education at Brahmo Boys’ School, which was founded by his grandfather Guru Charan Mahalanobis in 1904.

Prasanta Chandra with his friends just before he left for England in 1913 (1913) Indian Statistical Institute

Prof. Prasanta Chandra Mahalanobis earned a Bachelor degree in Science with Honours in Physics from the Calcutta University under Presidency College in 1912, before he sailed to England and joined Cambridge University

The Indian Daily news, 23rd June, 1915 (1915-06-23) Indian Statistical Institute

He obtained Mathematics Tripos part I in 1914, and Physics Tripos part II in 1915 from Cambridge University.

Standing from right- H.O.William, W.I. Saxton, unidentified person, Prasanta Chandra Mahalanobis, F.B. Johnston, G.A.Lupton, A.W.Neal, E. H. Toulmin, and E.A.Cameau; Degree day, Kings College, Cambridge, 1915 (1915) Indian Statistical Institute

As a student, Prof. Prasanta Chandra Mahalanobis never confined himself in his subject books. He was very interested in various subjects like amateur astronomy, philosophy, architecture, and psychology. Around this time, Prasanta Chandra Mahalanobis met with pioneer of Mathematics Srinivasa Ramanujan in Cambridge. He had his initiation in Statistics in 1915 through Biometrika, the journal founded by Karl Pearson.

Prasanta Chandra Mahalanobis with Prof. Peake and others Physics Department, Presidency College, Calcutta Indian Statistical Institute

Early career

He first joined Presidency College in 1915 as a temporary Professor. In 1922 he became Asst. Professor of Physics and taught Physics for 33 years (1915-1948). He was also the Principal of Presidency College for a few years and held the post of Meteorologist in the Alipore Observatory in Calcutta from 1922 to 1926.

Prasanta Chandra Mahalanobis and his wife Nirmal Kumari Mahalanobis Indian Statistical Institute

Life companion

Prof. Prasanta Chandra Mahalanobis married Nirmal Kumari (nicknamed Rani), who was the daughter of Puritan Brahmo leader and educationist of Bengal Heramba Chandra Moitra.

Prasanta Chandra Mahalanobis and Nirmal Kumari Mahalanobis Indian Statistical Institute

Nirmal Kumari was the person who stood by the Prof. Prasanta Chandra Mahalanobis in all his struggles, helped him in all his endeavours and exercised a great influence on his life.

P.C.Mahalanobis and Mrs. Mahalanobis in Ankara, Turkey, November 1948 (1948) Indian Statistical Institute

She often accompanied Prof. Prasanta Chandra Mahalanobis on his frequent tours abroad. Their companionship lasted for 49 years until the death of Mahalanobis.

Prasanta Chandra, Nirmal kumari Mahalanobis with Rabindranath Tagore, 1925 (1925) Indian Statistical Institute

Influence of great minds

Rabindranath Tagore, Prof. Prasanta Chandra Mahalanobis, and Nirmal Kumari Mhahalanobis shared a unique relationship. Rabindranath Tagore used to take a keen interest in Prof. Prasanta Chandra Mahalanobis’s statistical work from the very beginning. Even his career in statistics was very largely influenced by the poet.

Brajendra Nath Seal, Prof. of Philosophy, University of Calcutta introduced Prasanta Chandra to actual statistical analysis for the first time. Indian Statistical Institute

When Prof. Prasanta Chandra Mahalanobis expressed his interest to work on Statistics, he approached Rabindranath Tagore for his kind opinion. Tagore sent him to meet with Dr. Brajendranath Seal (B.N.Seal). He was further encouraged to engage in statistical research by B. N. Seal who asked him to take up a certain statistical exercise with respect to the examination result of Calcutta University.

Statistical Laboratory, Presidency College, Calcutta. Indian Statistical Institute

Establishment of Indian Statistical Institute

At the time Prof. Prasanta Chandra Mahalanobis was a Professor of Physics at Presidency College, he was highly involved in the work of statistics. He set up the Statistical laboratory in the baker laboratory of Presidency College, Calcutta, in the early 1920s. In the initial phase, his statistical research was in anthropometry, in meteorology and in problems of flood control in North Bengal and Orissa.

Indian Statistical Institute Indian Statistical Institute

On 17th December, 1931, Prof. Prasanta Chandra Mahalanobis set up the Indian Statistical Institute for advanced research and training in statistics. Later during the 1950s, ISI shifted to the present premises at Baranagar, a suburb of Kolkata, West Bengal.

Pandit Jawaharlal Nehru viewing a model of the ISI building, 1953 (1953) Indian Statistical Institute

In 1932, the Institute was located in a small portion of the Physics Department of the Presidency College but by 1972 the Institute had several large building of its own to provide working space for research and training in diverse subjects such as: anthropometry, biochemistry, botany, computer science, crop science, economics, human genetics, precensus, psychometry, sociology, and statistics. The Institute's activities were not confined within Calcutta but spread all over the India.

Portrait of C.R.RAO Indian Statistical Institute

While Prof. Prasanta Chandra Mahalanobis struggled against many odds in his bid to develop statistics as a science in India, he was lucky to receive whole hearted cooperation and help from a number of people. He had a special ability for locating talents. From the very beginning of the Institute he was assisted by a number of young and talented researchers, namely Harish Chandra Sinha, Raj Chandra Bose, Samarendra Nath Roy, and Keshvan Raghavan Nair. In 1941 came Calyampudi Radhakrishna Rao. That Mahalanobis was not wrong in his selection of comrades-in-arms was evident from the fact that many of his early associates earned international fame for themselves and the Institute for their outstanding contributions to statistics.

J.B.S.Haldane speaking at the degree course opening ceremony at the Institute, 16th August, 1960 (1960-08-16) Indian Statistical Institute

Indian Statistical Institution started courses of study leading to the degrees of Bachelor of Statistics and Master of Statistics from July, 1960 and also made arrangement for the award of Degrees Ph.D. and D.Sc. in Statistics.

Academician A.N.Kolmogorov, S.N.Bose, Prasanta Chandra at a special convocation held to confer Honorary degree of Doctor of Science of the ISI to Kolmogorov Indian Statistical Institute

The First Convocation of the Indian Statistical Institute was held in the mango-grove of the Institute on 12 February 1962. The event of first convocation was marked with the conferment of Honorary Doctor of Science to five eminent people: Professor Satyendra Nath Bose, Sir Ronald Aylmer Fisher, Sri Jawaharlal Nehru, Academician Andrey Nikolaevich Kolmogorov and Dr. Walter Andrew Shewhart . During the first convocation, the Degree of Doctor of Philosophy was conferred to two students, Kalyanapuram Ranga Parthasarathy and Jayaram Sethuraman, and Master of Statistics Degree to Narasimha Sreenivasa Iyengar, Vasant Tukaram Korde, Tares Maitra, Manjula Mukhopadhyay, Ganesan Parthasarathy, Kadiyala Koteswara Rao, and Paras Nath Singh.

Mahalanobis Distance- the major tools widely used in taxonomical classification even today. Indian Statistical Institute

Contribution to the field of Statistics

The anthropometric studies led to the formulation of D2- Statistic, known in statistical literature as Mahalanobis Distance, which has proved to be a valuable tool not only in taxonomy but in many other fields including economics and geology. A rich field of research in multivariate analysis opened up; Sir Ronald Aylmer Fisher (R.A.Fisher) accepted this concept by giving it the name ‘Mahalanobis D-square’ or ‘Mahalanobis distance’,

Report on Rainfall and Floods in North Bengal (1870-1922) (1870) Indian Statistical Institute

Prof. Prasanta Chandra Mahalanobis was again called upon to tackle the problem of flooding after two devastating floods, one in North Bengal in 1922 and the other in Orissa in 1926. This led him to undertake extensive statistical studies of rainfall and floods in Bengal and Orissa covering a span of about sixty years. The studies yielded some of the basic calculations that were later used for the two hydro-electric and irrigation projects in Hirakud and Damodar Valley.

Prasanta Chandra’s first paper on statistics, published in the Records of the Indian Museum, Vol.23, 1922. (1922) Indian Statistical Institute

Prof. Prasanta Chandra Mahalanobis’ first systematic work was on a statistical study of the anthropometric measurements of Anglo-Indians in Calcutta and his first paper was on “Anthropological Observations on the Anglo-Indian of Calcutta Part-I Analysis of Male Stature’urt”, which was published in the records of the Indian Museum in 1922.

Sankhya- the Indian journal of Statistics started in 1933 (1933) Indian Statistical Institute

Sankhya, The Indian Journal of Statistics , founded by Prof. Prasanta Chandra Mahalanobis in 1933 is the official publication of Indian Statistical Institute. Prof. Prasanta Chandra Mahalanobis explained his reasons for choosing the name Sankhya . In his words: "We believe that the idea underlying this integral concept of statistics finds adequate expression in the ancient Indian word Sankhya. In Sanskrit the usual meaning is ‘number’, but the original root meaning was ‘determinate knowledge" He was the editor of Sankhya from 1933 to 1972.

Extraction of fiber from the jute bundles Indian Statistical Institute

Then came the epoch-making investigation on the technique of large scale sample surveys, with which Prof. Prasanta Chandra Mahalanobis’ name will always be associated. Systematic work on the surveying of agriculture crops began in 1937, which culminated in a large scale sample survey of the acreage and yield of jute crop in 1941. It covered the whole province of Bengal and was extended to all important crops in both Bengal and Bihar in 1943.

Worker collecting sample from the field Indian Statistical Institute

This was followed by sample surveys for collecting socio-economic data, such as public preference. A large number of surveys were conducted from 1937-1950 in Bengal for collecting information on crops and socio-economic data, which gave opportunities for improving the design of sample surveys and for gaining experience in the collection of data from the field.

Prasanta Chandra Mahalanobis with R.A.Fisher in Amrapali, 1945 (1945) Indian Statistical Institute

During the sample census on jute crop in Bengal, Prof. Prasanta Chandra Mahalanobis insisted on the use of sampling methodology. But the Government officials had no idea about sampling and the survey was on the verge of being abandoned altogether. At this juncture, R. A. Fisher came to India in 1938 and in a memorandum submitted to the Viceroy, he strongly recommended the use of sampling methodology in India. At last a large scale sample survey of the area under jute for the whole province of Bengal was undertaken in 1940.

Archival video of P.C.Mahalanobis's visit to an Indian village for a sample survey. Indian Statistical Institute

Several hurdles had to be crossed in convincing the administrators that gaps in national income statistics could be filled through data obtained by sampling, and that there would be a need for continuous collection of information to assess the progress of economic development and to make policy decisions. Prof. Prasanta Chandra Mahalanobis won the battle and the National Sample Survey was established in 1950 . It is a continuing survey in which information is collected year by year with the help of a whole time field organization, spread all over India, and which provides periodic estimates on social and economic factors affecting the nation economy.

Prasanta Chandra with Central and State statisticians during a reception at his New Delhi residence , 8, King George Avenue, 3rd December 1954 (1954-12-03) Indian Statistical Institute

A Central Statistical Unit was established by the Government of India in 1949 to work under the technical guidance of Prof.Prasanta Chandra Mahalanobis as Honorary Statistical Adviser to the cabinet. For more than two years this unit was entirely staffed from and run by ISI. After two years the Central Statistical Organizations was formed for coordinating all statistical activities of the Government.

P.C.Mahalanobis at the conference on standardization and Quality Control at ISI (Presidency College Premises) 08.02.1948 (1948-02-08) Indian Statistical Institute

After meeting with Dr. Walter Shewart, who was known as the 'Father of Statistical Quality Control', Prof. Prasanta Chandra Mahalanobis wrote to the Government of India in 1942 pointing out the advantages of using statistical quality control methods, particularly in the industries. As a consequence, the Indian Statistical Institute took initiative in spreading the use of quality control methods in industry by establishing Statistical Quality Control units in different parts of India since 1953.

Prasanta Chandra Mahalanobis delivering lecture on fractile graphical analysis, 1958 (1958) Indian Statistical Institute

Even when Prof. Prasanta Chandra Mahalanobis was working on his planning models, he had not stopped giving new ideas in statistical methodology. In 1958 he found a simple but very effective technique known as Fractile Graphical Analysis.

The first Electronic Analogue Computer designed by Samarendra Kumar Mitra and constructed by ISI in 1953. (1953) Indian Statistical Institute

Start of a new era: introduction of computers

Prof. Prasanta Chandra Mahalnobis was one of the first people in the country to recognize the importance of machines – mechanical, electrical as well as electronic – to make fast, accurate and complicated calculations with masses of figures. In the 1950s, Prof. Prasanta Chandra Mahalanobis arranged to have a large number of electromechanical data processing machines from IBM; the Hollerith and the Power Samas varieties were installed to process NSS data. Through his initiative in 1953, a small analog computer was designed and built in the Institute.

In 1956, Prof. Prasanta Chandra Mahalanobis arranged for the installation of a British made digital computer, the HEC-2M, Hollerith – Electronic Digital Computer, the first of its kind to be in operation anywhere in India.

During 1955, the USSR Government had offered the Institute a big electronic digital computer called URAL through the UNTAA (United Nations Technical Aid Administration). The URAL computer was received in March 1958 and installed on 20 December 1958 in the Institute for the processing of statistical data by the Soviet engineers who handed it over for use in February 1959.

By 1959-60, the Indian Statistical Institute became, for all practical purposes, a National Computer Centre for the country. It met the computational requirements for scientific problems in organizations like the Ministry of Defense, The Atomic Energy Commission, the Tata Institute of Fundamental Research, and the Meteorology Department.

The first solid state digital computer in India, ISIJU-1, was designed, developed and constructed by the engineers of the Institute in collaboration with the Jadavpur University in 1965.

Dinosaur Fossil at ISI. Indian Statistical Institute

Contribution of ISI: excavation of a dinosaur

In 1957, Prof. Prasanta Chandra Mahalanobis invited Dr. Pamela Robinson of the University College London to the ISI to set up the Geological Studies Unit. The team under the leadership of Dr.Pamela Robinson discovered for the first time in India the fossil bones of the giant prehistoric lizard; the largest animal that lived on the earth.

Prasanta Chandra, C.R.Rao, Pamela Robinson, Alec J. Smith (Prof. of University College, London) K.B.Madhava and others studying in front of fossil bone of Dinosaur excavated by ISI team. Indian Statistical Institute

Over ten tons of bone material were collected from the Pranhita–Godavari valley and brought to Calcutta. The bones were assembled and later mounted in 1976, in record time into a full length skeleton of the dinosaur in the Geological Studies Unit. The skeleton was named Barapasaurus tagorie.

Prasanta Chandra and Jawaharlal Nehru at Amrapali. Indian Statistical Institute

Contribution to national development

Prof. Prasanta Chandra Mahalanobis played an important role in Indian National Economic Planning. He took major responsibility in drafting the Second Five Year Plan for India. He believed in perspective planning and used simple logical ideas in deriving an economic model for planning in a under developed country, like India.

Jawaharlal Nehru inaugurating studies relating to planning for national development at the institute, 3rd November, 1954 (1954-11-03) Indian Statistical Institute

As a member of the Planning Commission, he sold the idea of making large investments in heavy industries, setting aside other sectors of development, a policy which helped the country considerably in rapid industrialization.

Satyendranath Bose, Prasanta Chandra and Norbert Weiner (Massachusetts Institute of Technology, USA) at Amrapali Garden, 1953 (1953) Indian Statistical Institute

Dignitaries at ISI

The growing importance of the Institute was reflected in the continuous inflow of visitors, over a thousand leading scientists of the world visited the Indian Statistical Institute. Many of these scientists spent long periods of time at the institute and often stayed with Mahalanobis at his residence.

J.D.Bernal , Nirmal Kumari Frederic Joliot- Curie, Madame Irene Joliot-Curie and Prasanta Chandra during a visit in January 1950. (1950) Indian Statistical Institute

From 1937 to 1967 about six hundred leading scientists and economists of the world came to the Institute, among them were J.B.S. Haldane, Abraham Wald, J.K. Galbraith, Frederic Joliot-Curie, Madame Irene Joliot-Curie, Norbert Weiner, Chou-en-Lai, Prime Minister of China, Ho-chi-minh, and President of the People's Republic of Vietnam to name a few.

Prasanta Chandra Mahalanobis delivering lecture at the Vatican City , Rome, 1963 (1963) Indian Statistical Institute

International liasions with ISI

As the Indian Statistical Institute started earning international fame, Prof. Prasanta Chandra Mahalanobis was becoming more and more preoccupied with assignments outside. Prof. Prasanta Chandra Mahalanobis worked for international understanding and collaboration in scientific research with foreign scientists.

Prasanta Chandra attending the United Nations Statistical Commission as Chairman, New York , 16th April- 3rd May, 1956 (1956-04-16) Indian Statistical Institute

Prof. Prasanta Chandra Mahalanobis started going abroad from 1946 in connection with the work at the United Nations Statistical Commission in various capacities: as member; Vice-Chairman and Chairman; as its representative on the Population Commission in 1948; and as a member of drafting committee at the Regional Meeting of Statisticians.

P.C.Mahalanobis delivering his lecture in International House of Japan. Indian Statistical Institute

Prof. Prasanta Chandra Mahalanobis attended all the sessions of the Statistical Commission from the Nuclear Session in February-June 1946, to the 16th session in October 1970—an unparalleled record.

Prasanta Chandra Mahalanobis at the International Symposium on Higher Education, Moscow,1962. (1962) Indian Statistical Institute

Prof. Prasanta Chandra Mahalanobis chaired the Conference of Statisticians of the United Nations Economic Commission for Asia and the Far East, ECAFE (now Economic and Statistical Commission for Asia and Pacific, ESCAP) in 1952.

P.C.Mahalanobis receiving an award (1959) Indian Statistical Institute

Awards and accolades

Prof. Prasanta Chandra Mahalanobis received a number of awards and honors in India and abroad for his outstanding and fundamental contribution to Statistics and Planning.

Prasanta Chandra Mahalanobis receiving the Mayor-of-Paris Award for exemplary work in Statistics, 1963. (1963) Indian Statistical Institute

He was elected as fellow of the: - Royal Society of London in 1945, - Chairman of the United Nations Sub- Commission on Statistical Sampling (five sessions- 1947-1951) - Fellow of International Econometric Society (1951) - Chairman of United Nations Statistical Commission (1954-1958) - President of National Institute of Sciences of India (1957 and 1958) - Fellow of American Statistical Association (1961) - Fellow of World Academy of Art and Science (1963).

Prasanta Chandra receiving the Bulgarian Science Academy award, 1962 (1962) Indian Statistical Institute

Prof. Prasanta Chandra Mahalaonbis was honored with several awards: -The Weldon Medal from Oxford University (1944), - Sir Devaprasad Sarbadhikari Gold Medal from Calcutta University (1957), - Gold Medal from Czechoslovak Academy of Sciences (1964), - Durga Prasad Khaitan Memorial Gold Medal from Asiatic Society (1968), - Srinivasa Ramanujam Gold Medal (1968), - Honorary Deshikottama from Visva Bharati University (1961).

Photograph of the Padmavibhushan Certificate (1968-04-16) Indian Statistical Institute

In 1968, he was awarded the Padma Vibhushan , the second highest civilian award by the Republic of India for his contribution to science and services to the country. He also received honorary doctorates from Calcutta University (1957), Sofi University (1961), Delhi University (1964) and Stockholm University (1966).

Prasanta Chandra Mahalnobis Indian Statistical Institute

Prof. Prasanta Chandra Mahalanobis viewed statistics not as a branch of mathematics but as a technology. Mathematics and probability theory are only the means to promote the use of statistical methods in the world of reality. He shaped Indian Statistical Institute as a beacon of knowledge with commitment for national development and social welfare. He is still being remembered for the Mahalanobis Distance, a statistical measure, and for his great contribution in the large scale sample survey. He continues to inspire statisticians in India and around the world.

P.C.Mahalanobis Memorial Museum & Archives; Reprography and Photography Unit; Library, Documentation and Information Science Division ISI Team Co-ordinator: Dr. Kishor Chandra Satpathy Photo Design & Restoration: Mr.Tapas Basu Research & Compilation: Ms. Keya Das & Ms. Kasturi Basu Special thanks to Dr. Sanghamitra Bandyopadhyay,Director and Dr. Dipti Prasad Mukherjee,Deputy Director of Indian Statistical Institute in making this online exhibit possible. Text References : 1. Biographical Memoirs of Fellows of The Royal Society,Volume 19,London,The Royal Society. 2. Prasanta Chandra Mahalanobis by A. Mahalanobis, National Book Trust India, New Delhi,1983. 3. Prasanta Chandra Mahalanobis A Biography by Ashok Rudra by Oxford University Press,1996

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P C Mahalanobis: India’s Numbers Man

AUTHOR Aditi Shah
PUBLISHED 29 June 2021

He was a physicist by training, a statistician by instinct and an economist by conviction. He founded one of the first institutes in the world dedicated to the subject of statistics and was instrumental in formulating India’s Second Five-Year Plan. Prasanta Chandra Mahalanobis, or ‘PCM’, as he was fondly referred to by his colleagues, wore many hats. Here’s the story of this man of numbers:

Mahalanobis was born on 29th June 1893 into a wealthy family of intellectuals and social reformers in the erstwhile Bengal Presidency. After graduating with honours in physics from Presidency College, Calcutta, in 1912, he moved to England to study physics and mathematics at the University of Cambridge. Here, he came across Biometrika, a peer-reviewed scientific journal with a focus on theoretical statistics that piqued his interest in the subject. Soon he started researching statistical problems relating to agriculture, biology, meteorology and anthropometry.

On his return to India in 1915, Mahalanobis started teaching physics at his alma mater, Presidency College. But alongside that, he started an informal group of people interested in statistics to pursue the subject academically. When Rabindranath Tagore, a friend of Mahalanobis, learnt of his interest, he introduced him to Brajendranath Seal, a scholar and educator who asked the 24-year-old Mahalanobis to analyse the exam records of Calcutta University.

Mahalanobis was very curious about racial biometrics and anthropometry (the scientific study of the measurements and proportions of the human body). So when N Annandale, the then director of the Zoological and Anthropological Survey of India, provided PCM with a dataset of about 300 Anglo-Indians, he developed a statistical tool which he used to measure what he called “caste distances”.

He wrote in his paper titled Analysis of Race Mixture in Bengal (1925), “How are… Anglo-Indians… related to the different caste groups of Bengal?... Are they more closely allied with the Hindus or with the Mahomedans?” He measured the facial features of the people, the length and breadth of their face, the size of their nose, etc and compared these individual physical traits before combining them to produce a relative value.

This study was instrumental in initiating his more than decade-long research on anthropometric data, resulting in the theorizing of the ‘Mahalanobis distance’, his most notable research contribution. This statistical measure is often used to compare two different data sets and applied in studies of population distribution.

Mahalanobis also analysed data regarding flood control in North Bengal and Odisha, which later formed the basis for the construction of the Hirakud Dam on the Mahanadi River.

Within no time, the work of the small, informal group Mahalanobis had got together led to the establishment of the Indian Statistical Institute (ISI) in 1931, which had an annual budget of less than Rs 250. Mahalanobis believed, “Statistics must have a clearly defined purpose, one aspect of which is scientific advancement and the other human welfare and national development.”

The ISI grew over time and conducted research into diverse subjects including biochemistry, crop science, human genetics, psychometry, pre-census and economics. The Mahalanobis-led ISI conducted some wonderful data analyses and large-scale surveys like the impact of the 1943 Bengal Famine, rural indebtedness, tea-drinking habits, crop yield estimation, family budgets and the circulation of rupee coins.

This attracted the attention of Jawaharlal Nehru, who asked Mahalanobis to be a part of Independent India’s Planning Commission and later outline the Second Five Year Plan (1956-1961). The Second Plan thus followed what came to be known as the ‘Mahalanobis Model’. It focused on the development of the public sector and rapid Industrialisation.

For his pioneering work, Mahalanobis was awarded the Padma Vibhushan in 1968 and in his honour, his birthday is observed as National Statistics Day every year.

– DID YOU KNOW?

The first English translation of Albert Einstein and H Minkowski's famous German paper The Principle of Relativity was undertaken by Indian scientists S N Bose and Meghnad Saha (with an introduction by P C Mahalanobis) and published in 1920.

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PC Mahalanobis: Know about the father of Indian statistics

Every year june 29 is observed as national statistics day in our country to create public awareness about the importance of statistics in socio-economic planning and policy formulation..

Prasanta Chandra Mahalanobis, considered the father of modern statistics in India, founded the Indian Statistical Institute (ISI), shaped the Planning Commission and pioneered methodologies for large-scale surveys. Every year June 29 is observed as National Statistics Day in our country to create public awareness about the importance of statistics in socio-economic planning and policy formulation.

During his initial working days, Mahalanobis joined the Cavendish Laboratory with physicist CTR Wilson.(@_shibendu/Twitter)

Born to Probodh Chandra Mahalanobis and Nirodbashini Devi on June 29, 1893, Prasanta Chandra Mahalanobis was the eldest of six children—two sons and four daughters. He died on June 28, 1972, a day before his 79th birthday.

Mahalanobis studied at the Brahmo Boys’ School, which was founded by his grandfather Guru Charan Mahalanobis in 1904 and joined the Presidency College to study physics. He also attended the King’s College in Cambridge, where he met mathematical genius--Srinivasa Ramanujan.

During his initial working days, Mahalanobis joined the Cavendish Laboratory with physicist CTR Wilson. Later, Mahalanobis returned to India and started teaching physics at the Presidency College in 1922. He remained a teacher there for over three decades and held the post of meteorologist at the Alipore Observatory in Calcutta, now Kolkata, from 1922 to 1926.

Mahalanobis formed a group that was interested in statistics, that later expanded and eventually, the Indian Statistical Institute (ISI) was founded in 1932. In the next year, he launched Sankhya: The Indian Journal Of Statistics.

He also established the National Sample Survey in 1950 and set up the Central Statistical Organisation to coordinate statistical activities. He became a member of the Planning Commission in 1955 and continued till 1967.

Contributions

Mahalanobis was instrumental in formulating India’s second five-year plan (1956-1961), which laid the blueprint for industrialisation and development in India.

One of his most remarkable achievements was when Mahalanobis devised a measure of comparison between two data sets, now popularly called "Mahalanobis distance". The study is widely used in the field of cluster analysis and classification.

He also introduced innovative techniques to devise a statistical method called fractile graphical analysis used to compare socio-economic conditions of varied groups. He analysed data regarding the floods in Odisha and published his findings in 1926. This analysis later formed the basis for the construction of the Hirakud dam on the Mahanadi River.

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Mahalanobis, who was a member of India’s first Planning Commission, set up the Indian Statistical Institute in Kolkata in 1932.

New Delhi: Today is the 125th birth anniversary of India’s legendary statistician and mathematician Prasanta Chandra Mahalanobis, who is also popularly known as the father of Indian statistics.

Former prime minister Manmohan Singh, in Mahalanobis’s honour declared 29 June as the National Statistics Day.

Mahalanobis, popularly called PCM by his colleagues and friends, founded the Indian Statistical Institute and was one of the main members of the first Planning Commission of India. In his capacity at the commission, Mahalanobis can easily be called a pioneer who brought the concept of planned governance to India.

Mahalanobis’s contribution to the field of statistics and mathematics was marked by a Google doodle, done by an acclaimed illustrator named Nishant Choksi. Choksi’s art projected the Bengali scientist in terms of “Mahalanobis distance”, a statistical measure frequently used in the studies of population distribution.

Mahalanobis was born on 29 June, 1893, to a family of intellectuals. His grandfather Gurucharan was involved in the Brahmo Samaj and was a follower of Debendranath Tagore, father of Rabindranath Tagore. He studied in the Brahmo Boys School in Calcutta (as the city was known then) and then went to Presidency College to study Physics.

The mathematician was taught by Jagadish Chandra Bose and Prafulla Chandra Ray in Presidency college. As his juniors, he had famous astrophysicist Meghnad Saha and the iconic Subhas Chandra Bose. He graduated in 1912.

A group consisting of people with interest in statistics was formed in Presidency College. Along with Pramatha Nath Banerji (Minto Professor of Economics), Nikhil Ranjan Sen (Khaira Professor of Applied Mathematics) and Sir R.N. Mukherji, Mahalanobis established the Indian Statistical Institute in 1932. The institute was declared as an institute of national importance in 1959. In 1933, they started the journal Sankhya .

Studies abroad

Mahalanobis left for London in 1913 and joined King’s College, Cambridge. He met mathematician Srinivasa Ramanujan at the university. He took a short break and returned to India where he was invited to teach Physics in Presidency College.

The scientist served as a secretary to Rabindranath Tagore and was also associated with Visva-Bharati University. Mahalanobis was awarded the Padma Vibhushan (1968), Weldon Memorial Prize from the University of Oxford (1944); Fellow of the Royal Society, London (1945).

The scientist is not only remembered for devising the Mahalanobis distance. His other contributions to statistics include the introduction of the concept of pilot surveys and for designing large-scale sample surveys.

The Indian Statistical Institute, under his leadership, grew out of the statistical laboratory in Presidency College, Calcutta (now Presidency University).

He died on 28th June 1972, just a day before his seventy-ninth birthday.

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P.C. Mahalanobis: Remembering the ‘Plan Man’ of India

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June 29, is national ‘Statistics Day’, in ‘recognition of the contributions made by Prof. Prasanta Chandra Mahalanobis’, the ‘Plan Man’ of India; it is also his birthday.

What are the contributions of P.C. Mahalanobis?

P.C. Mahalanobis is referred to as the chief architect of the Indian statistical system as well as the father of statistical science in India .

Believed in Data : Mahalanobis clearly believed data to be instrumental in efficient planning for national and human development. Planning in the newly independent nation in the 1950s was largely based on the data obtained from various surveys.

Contribution to Statistics :

-Mahalanobis established the Statistical Laboratory within the Baker Laboratory at Presidency College.

-In 1931, he established the Indian Statistical Institute (ISI) in Kolkata.

-In 1933, Mahalanobis founded Sankhyā , the Indian Journal of Statistics .

Other contributions :

-Mahalanobis helped in the establishment of the Central Statistical Organisation (CSO), the National Sample Survey (NSS) and the Annual Survey of Industries (ASI).

-Mahalanobis also served as the Chairman of the United Nations Sub-Commission on Statistical Sampling.

-In 1936, he introduced a statistical measure named the Mahalanobis distance . It is widely used in cluster analysis and classification techniques.

-He also devised a statistical method called ‘ Fractile Graphical Analysis ’. This method is used to compare the socio-economic conditions of varied groups.

-The Mahalanobis model was employed in the Second Five Year Plan. The model laid the blueprint for industrialisation and development in India.

Honours : In 1968, he was honoured with the Padma Vibhushan.

P.C. Mahalanobis’s Friendship with Rabindranath Tagore

Tagore treated Mahalanobis as a close confidant, despite an age gap of 32 years. Mahalanobis first met Tagore at Santiniketan in 1910.

Accompanied Tagore on multiple occasions : Mahalanobis accompanied Tagore on many of his international visits, mostly in the 1920s.

When Tagore met Einstein in 1930, Mahalanobis was also with him. In fact, Einstein asked Tagore about a young scientist named Bose. Mahalanobis then informed Tagore about Satyendra Nath Bose , who would be ever-remembered for Boson.

Mahalanobis’s literary works about Tagore : He wrote a series of essays titled ‘Rabindra Parichay’ (‘Introduction to Rabindra’) for the prestigious Bengali magazine, Probashi . He also wrote a book, Rabindranath Tagore’s Visit to Canada in 1929.

Helped in Tagore’s dream project : Mahalanobis helped Tagore immensely in his dream project — the founding of Visva Bharati. He also served as a joint secretary of Visva Bharati for 10 years from the beginning.

Tagore’s dance drama, ‘ Basanta ’ (meaning ‘Spring’), had a premier at the Calcutta University institute auditorium on Mahalanobis’ marriage day. Tagore attended the marriage ceremony and presented them with the manuscript of ‘Basanta’.

Source : The post is based on the article “Remembering the ‘Plan Man’ of India” published in “The Hindu” on 29 th June 2022 .

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P.C. Mahalanobis and the Theory of Development Planning

Référence bibliographique

Patnaïk Prabhat. P.C. Mahalanobis and the Theory of Development Planning. In: Économie appliquée , tome 47 n°2,1994. A. Lowe, P.C. Mahalanobis : un double centenaire. pp. 153-165.

DOI : https://doi.org/10.3406/ecoap.1994.1515

www.persee.fr/doc/ecoap_0013-0494_1994_num_47_2_1515

RIS (ProCite, Endnote, ...)

Résumé (eng)

Starting from the Mahalanobis two-sector model the paper shows how it can be restated either in the terminology of steady state growth theory, or in terms of the “turnpike theorem”. Then basic objections against Mahalanobis ’s assumptions are revisited e.g. trade, financial side of planning and the need for a rapid increase in the supply of wage goods. Finally emphasis is put on the vision behind the model and the idea that it would be useful only for a fully planned socialist economy is rejected.

Résumé (fre)

L’article présente le modèle de Mahalanobis et montre que son argument principal sur l’allocation sectorielle de l’investissement peut également être présenté dans la terminologie de la croissance équilibrée ou du théorème du «turnpike». Il réexamine les critiques adressées au modèle (en particulier celles qui visent les hypothèses retenues par Mahalanobis concernant le commerce extérieur, le financement du plan ainsi que la croissance de la production des biens de consommation ) et finalement récuse l’idée que le modèle de Mahalanobis correspond simplement à une vue «naïve» de l’Etat et de la société qui le rend inutile pour une économie qui n ’est pas entièrement planifiée.

Bibliography [link]

Texte intégral

In Economie Appliquée, 1994, n° 2, p. 153-165

Prabhat Patnaik

Centre for Economie Studies and Planning Jawaharlal Nehru University,

Like many other outstanding economists P.C. Mahalanobis followed a rather circuitous route to arrive at economics. He was a Physicist by

training and taught Physics for many years at the Presidency College, Calcutta. Convinced of the dictum that “measurement is science” he became increasingly interested in statistics and started applying statistical techniques in a number of disparate areas (1). He set up the Indian Statistical Institute in 1931-1932 and was appointed Honorary Statistical Adviser to the Indian cabinet in 1949. It is in the latter capacity that he became associated with the Planning Commission which was set up under the Chairmanship of Prime Minister Jawaharlal Nehru in 1950. This was the beginning of his interest in problems of development and development planning. He developed a series of models in the early fifties which were to act as precursors to the celebrated two-sector model of 1953 that provided the theoretical basis for India’s Second Plan strategy <2). This model which is similar to the one developed by the Soviet economist Feldman in the 1920s (of whose work however Mahalanobis was unaware) remains a major landmark in the theory of development planning.

The basic idea underlying the model is simple: if in an economy the magnitude of investment is constrained by the capacity of the investment goods producing sector, because transformation possibilities through trade are limited and capacity is non-shiftable across sectors, then a higher rate of growth can be achieved only by stepping up the allocation of investment in favour of the investment goods sector itself. If investment is denoted by I (we ignore for simplicity the distinction between gross and net by assuming infinite life for capital goods), consumption by C, the (constant) output-capital ratios of the two sectors by (3k and pc respectively, and the allocation of investment between the two sectors by Xk and Ac respectively (A* + Ac = 1), then it follows that

C(t + 1) = C{t ) 4-I(t).Xc • Pc (i )

and I(t + 1) = I(t) + I(t).Xk • Pk (H)

Economie Appliquée, 2/1994

P.C. MAHALANOBIS AND THE THEORY

Now, while the (3 s are technologically-determined (on this more later), Xk can be altered by the planners. If a0 denotes the initial ratio of investment to ouptput, then for any particular Xk fixed by policy, the time-path of output (which is C+I) would be given by

Y(t) = Y(<f>)[ 1 + ar0.{(l + Xk-Pk)* ~ 1 HA*./?* + Xc.pc)/Xk.pk] • • • (in)

It can be seen that if (3C > (3k, then the higher is Xk, the lower is the immediate growth of output, but the higher is the growth of output over a period of time. As long as one does not take an extremely myopic view but is willing to look into the future (as the planners must do), a rise in investment allocation in favour of the investment goods sector appears to be essential for growth.

While Mahalanobis expressed his argument in the context of a plan model, the argument can be restated in two alternative forms both of which bring out its theoretical significance extending beyond the Indian plan discussion. For doing so however it is more convenient to treat output not as an aggregate at some (constant) base prices, but as a vector (or as an aggregate at some “equilibrium” prices) and to define units in such a way that [3C = (3k. With this change the Mahalanobis argument can be restated in the terminology of steady-state growth theory

Let us start with some arbitrary initial configuration of capital stock. If the ratio of the capital stock in the investment goods sector to the total capital stock (since capital goods everywhere are identical no problem of valuation of capital arises) is exactly the same as the ratio of investment allocation for the investment goods sector to total investment, then the economy would be in steady-state growth. If we denote this ratio by Xk, and the output-capital ratio (identical between the two sectors) by /?, then the rate of steady growth would be A k(3. Along this steady-growth path there would be a certain level of consumption good output per employed worker which would be determined by Afc and the labour requirement per unit of capital good in each sector. If we assume identical labour requirement per unit of capital good in the two sectors and denote it by l, then consumption good per employed worker is simply (3(1 -X k)/l. This in fact would be identical with the real wage rate if, as we assume for the present, all wages, and only wages, are consumed. Now it is clear that a higher Xk is associated with a higher rate of steady growth but a lower real wage-rate. And, starting from any steady-state path, if the

allocation ratio in favour of the investment goods sector is raised (and kept at a higher level), then the economy would asymptotically approach a new steady-state path with a higher growth rate and lower real wages. During the transition, the employment and output growth-rates would be increasing (4) but the real wage-rate would be falling; the latter, however, does not entail a fall in the absolute level of per capita consumption (i.e. in consumption good output divided by total population including both the employed and the unemployed). The Mahalanobis strategy then can be interpreted as a means of taking the economy from a lower rate of steady-state growth to a higher rate through a step-up in investment allocation in favour of the investment goods sector. Though it entails a lowering of the real wage rate, the redistribution is really from the employed to the unemployed (5).

The second way in which the Mahalanobis strategy can be interpreted is in terms of the “Turnpike Theorem” in the theory of optimal growth. If we assume that real wages can be lowered without limit then the Von-Neumann growth-rate of the economy is simply (3 (If there is a positive lower limit to the real wage-rate, then the Von-Neumann growth-rate would be correspondingly lower). Now the Turnpike Theorem states that starting from any initial configuration of outputs if we wish to achieve some target configuration in the minimum time, or starting from this initial configuration wish to maximise the scale of some final configuration within a given time period, then the optimal strategy would be to approach the Von-Neumann path and then move away from it. Since the Von-Neumann path in the present context has a Xk equal to 1, the Turnpike strategy would entail a rise in Xk from its initial level. Even if in other words our objective is to achieve a certain level of per capita consumption on a sustainable basis (the rate of growth of population is exogenously given), the strategy that would enable us to do so in the minimum time would entail a rise in Afc from its initial level, followed possibly by a subsequent lowering of it. The Mahalanobis strategy in short has a validity quite independent of whether we are interested in raising the economy’s growth-rate per se. Even if we wish to move from one growth-path, along which the growth-rate is the same as the population growth rate but which entails high unemployment, to another path, along which the growth-rate is once again the same as

initially but where unemployment is lower, the quickest way of doing so is by first raising the allocation in favour of the investment goods sector, and then lowering it at a later stage. The Mahalanobis strategy is thus a particular case of a more general “Turnpike Strategy” according to which overcoming immediate bottlenecks through an appropriate concentration of effort is the optimal way of moving forward (6).

The optimality defined by the Turnpike Theorem however is of a special kind. For a given time-horizon the concern here is only with the terminal state, or for a given terminal specification the concern is with getting there in the quickest time. This is quite different from the Ramsey-type optimisation exercise (for finite horizons) where for given initial and terminal specifications and for a given time-horizon, the objective is to select the “best path” which maximises an integral of utilities derived from a “social utility” function. Interestingly, it turns out that even in these kinds of optimisation exercises carried out for a Mahalanobis-type closed economy with non-shiftable capital and fixed coefficients, increasing the allocation for the investment goods sector in the initial phase (not necessarily of course in the one-shot fashion envisaged by Mahalanobis) is the optimal strategy for a whole class of utility functions (7>.

Given its stylisation of the state of an underdeveloped economy the Mahalanobis strategy is thus intellectually highly robust. The crucial issue therefore relates to the plausibility of its assumptions, an issue that has been much debated. At least three basic objections have been raised from differing perspectives against Mahalanobis’ assumptions. The first which has gained currency of late objects to Mahalanobis’ assumption of a closed economy which was but a reflection of his recognition of limited transformation possibilities through trade. If by contrast we assume unlimited transformation possibilities through trade at given prices (the usual small country assumption), then comparative advantage would dictate the investment pattern and there would be no need for any priority for the investment goods sector per se.

Mahalanobis of course was acutely aware of the possibilities offered by trade <8>. His argument against the exclusive reliance on comparative advantage stemmed not only from a recognition of the limited transformation opportunities through trade faced by an essentially primary producing economy (9) ; it had an additional dimension as well. And this incorporated the fact that excessive trade dependence was a potential threat to economic independence, and hence was strategically unwise for a country that in any case had the natural resources to diversify its production structure (10). Besides in the Indian context because of the rich iron ore resource base even long-run comparative advantage would have dictated concentrating on capital goods industries (he visualised for instance India exporting capital goods), so that the conflict between the two criteria would not have appeared to him to be a particularly strong one.

The second criticism relates to his underplaying the financial side of development planning. In the context of the original Mahalanobis model, the term XkPk/(�kPk + A C(3C), whose reciprocal appears in (iii) above, represents the marginal savings ratio warranted from the production side. A rise in Afc raises this marginal savings ratio. If this is not matched by the marginal savings ratio enforced upon the economy by the government through fiscal means, but instead exceeds the latter, then there would be excess demand for consumption goods resulting in a rise in their prices. Of course such a rise in their prices could itself be a means of ex post equilibrating demand and supply in the consumption goods market with no adverse consequences for the plan, provided the investment allocation policy of the plan is not subverted by such a rise in prices. This for instance is what happened in the Soviet Union where the profit inflation in consumption goods was taxed away through a

system of “turnover taxes” to finance the larger investment allocation for investment goods. But in a mixed economy where such taxes cannot be effectively imposed to wipe out the effects of profit-inflation, and where production decisions are bound to respond to profitability, the actual pattern of production would inevitably turn out to be different from that envisaged by the plan unless fiscal policy can equate the ex ante marginal savings ratio with that implicit in the production plan. And in such a case in practice the functioning of the economy would fall below potential with unutilised capacities emerging, possibly in both sectors and certainly in the investment goods sector, as current inputs earmarked for the latter are pulled away for consumption goods production (especially for luxûry consumption goods production the demand for which would be stimulated by the profit-inflation itself). This would make the plan projections completely meaningless.

It is altogether unfair to say, as some have done, that Mahalanobis was unaware of this problem and thought that since “one cannot eat steel” the financial problem was secondary. What is true however is that he believed that the State even in a mixed economy could use the instruments at its command, e.g. fiscal and licensing policies, to ensure that the production pattern envisaged in the plan could be actually realised. This entailed a certain perception of the State which was simpliste, a point discussed later.

The third, and perhaps the most potent, criticism of the Mahalanobis strategy is its underplaying the need for a rapid increase in the supply of wage goods. There are two distinct questions involved here; the first is the extent to which the wage goods constraint is binding, and the second is, even if the wage goods constraint is not binding, the extent to which it is desirable in practice to restrict supplies of wage goods. Larger investment allocation in favour of the investment goods sector, we have seen, would result in practice in a rise in the prices of essentials relative to the money wage rate. If the workers succeed without much lag in obtaining money wage increases in keeping with price increases, then the economy would move rapidly into accelerating inflation. On the other hand, even if they do not, and real wages are kept down without the inflation rate accelerating because money-wages are allowed to adjust only with a lag, it would nonetheless give rise to industrial strife and social instability which would undermine the social legitimacy of the planning process.

There is a further point to consider. Wage-goods are not a single commodity or a basket in which there are fixed bundles of particular commodities. On the contrary there is from the workers’ point of view an

ordering in terms of priority of consumption among wage-goods. If the most essential wage-good, food, experiences a price-rise, then they do not cut down per capita consumption of other less essential wage goods. So, a rise in some wage-goods’ prices has an adverse employment effect as well, in which case (even ignoring luxury consumption) to see a lowering of real wage owing to a rise in Xk as involving a redistribution from the employed to the unemployed is a misnomer. In other words, there are more complex employment effects than captured in the simple Mahalanobis model.

There were at least three obvious contextual factors that might have contributed to Mahalanobis’ underplaying the wage-goods constraint. First, after the end of the Korean war boom agricultural prices had declined sharply and the terms of trade had moved against agriculture. It was scarcely the appropriate time to worry about the consequences of an inflation in agricultural prices. Secondly, the later part of the First plan was marked by a couple of bumper harvests which must also have contributed to a sense of complacency about food prices. Thirdly, and more importantly, there was a prevalent view at the time that agriculture was a “bargain” sector, in the sense that an increase in its growth-rate could come about, even without any significant step-up in investment devoted to it, by undertaking institutional changes such as land reforms <nh While Mahalanobis himself did not argue this anywhere, he could not but have been influenced by such thinking which was quite pervasive even within the Planning Commission he was leading. In terms of his model this amounted to saying that as Xk was stepped up, (3C could also be raised through institutional reforms so that inflationary pressures on wage goods could be contained. That this hope remained unfulfilled, and that serious inflationary pressures developed in the foodgrain market in the Second plan may point to a misreading of the nature of the Indian State, but does not nullify the intellectual germaneness of this more comprehensive development strategy.

While Mahalanobis did not explicitly theorise about an increase in pc through agrarian reforms, he did explicitly recognise the possibility of such an increase in pc in the role he assigned to the cottage industries

sector. His two sector model was followed by a four-sector model, in which he split the consumption goods sector into three separate sectors: the factory sector, the household sector, and services such as health, education etc. We now have four (3S, four As, and four 6S, the last denoting the amount of investment required in each sector to employ one person. Taking a particular plan-period of five years, there is a total investment over this period, say A, there is an increase in income over this whole period, say E, and there is an increase in employment over this period, say N. If A k is given by long-term growth considerations, the ps and the 6S being parameters, we have two independent instruments in the form of the As (since the sum of all four As must equal unity only two out of the three A.s can be fixed). For any given A we then have a certain N and E determined by the system and corresponding to the two As fixed; and by varying the two As we could get alternative values of E and N. Or, if we fix our target E, then by varying the two As we can get alternative estimates of A and N. From these alternative estimates we can select the best and fix our investment allocation accordingly (12).

This however was clearly not a very meaningful exercise. If, as is likely, among the consumption good sub-sectors the ps and the 6S are inversely correlated, then there is no reason whatsoever why the economy should invest in any subsector other than the one with the highest p. Unless in other words some minimum complementarity between the sizes of the consumption good sub-sectors is postulated, there is no reason why some of them should continue to exist at all; and this absence of any raison d’être for their existence should manifest itself in terms of a zero investment allocation for them.

While the theoretical basis for the four-sector planning exercise was thus shaky, the role assigned by Mahalanobis to the household sector was of significance. This role had two aspects: first, while he had no doubts taht the “long-term aim would be to use as quickly as possible the most technologically advanced machinery for the production of both investment and consumer goods”, since this was not immediately possible “because of the lack of a sufficiently broad base of heavy industries”, a transition phase was required during which “preference would be given to capital-light and labour-intensive small-scale and household industries to create as much employment as possible in the immediate future and, at the same time, to release capital resources for the heavy industries” (1963, p. 71).

Eoonomie Appliquée, 2/1894

Secondly, even in the long-run in a number of spheres Mahalanobis had doubts about the superiority of large-scale over small-scale production, provided the latter was technologically upgraded. And in these he saw the specific need to nurture small-scale production, even in the long-run. This according to him would have two important advantages. In the first place it would bring about industrial dispersal and hence a dispersal of employment without necessitating labour mobility (which he thought was limited in India in any case) and labour concentration in particular production centres. Besides it would break the concentration of economic power, stimulate the tendency towards co-operative association among small producers, and hence provide a firm basis to Indian democracy, as well as achieving the professed aim of a “socialistic pattern of society”.

While the latter has been a recurring theme in Indian debates, and deserves serious consideration in any development discussion, the transitional role he assigned to cottage and household production has come in for a certain amount of criticism. Having distinguished between the nature of unemployment in the advanced and the backward economies, namely that in the former it is because of inadequate aggregate demand, while in the latter it is because of capital shortage, he then proceeded to argue as if the increase in demand would automatically stimulate production in household industries provided the factory sector was not allowed to encroach upon it, which contradicts his own earlier statement (13). But the alleged contradiction is more a matter of language than of substance. The fact that a certain amount of investment had to be undertaken in order to make the household sector fulfill its assigned role during the transition period was certainly also mentioned by him. The crucial point emphasised by him is that in the early stage of planning while A k is raised, /3C could also be raised provided an appropriate effort was made both through controls over the factory sector and through encouragement of household production. This of course did not happen, but as a perception it was as bold as it was imaginative.

The Mahalanobis strategy then which is usually interpreted simply as giving priority to the heavy and capital goods industries, was a more

complex one; it entailed in addition giving encouragement to household production, so that there was a simultaneous increase in Xk and in (3C. It had a two-pronged rather than a single emphasis. And even though Mahalanobis himself was curiously reticent about the role of agrarian reforms in raising agricultural growth, if this is assimilated into the two-pronged approach of which Mahalanobis would be considered a leading advocate, we have a powerful vision of a development strategy.

The real problem with the Mahalanobis-type vision therefore lies not in the vision itself, but elsewhere, namely in the theory of society and the theory of the State which is implicit in, the belief that this vision would be realised through planning. On the one hand the State is seen as a dispassionate disinterested entity standing above society, an embodiment of reason, that carries through with diligence and vigour an optimal plan for social engineering. On the other hand social structures are seen as malleable before the actions of this all-powerful and “rational” State, dissolvable in the face of its attempts to introduce this optimal plan. The fact that in the “messy” world of classes and class-domination which influences in turn the nature of the State itself, both the attempt by the latter to implement the plan would itself be selective, and what is sought to be implemented would itself have consequences quite different from what was envisaged, is not reckoned with.

To be sure, Mahalanobis was not the only one guilty of such a “naive” view of society and the State. This view is implicit in the theory of development planning itself. If anything, he was more sensitive than others to this problem of development planning when he wrote: “The logical consistency of the Plan-frame is not a sufficient guarantee of its feasibility in practice... However, so far as plan-making is concerned (as distinguished from plan-implementation) all that can be demanded is internal consistency, valid technical reasoning, and a correct appreciation of social needs. If the present plan has these merits, then there is only one single issue, namely whether there is any alternative plan which would eliminate unemployment and poverty more quickly and more effectively; and at the same time, lay the foundation for a continuing increase in the level of living in the future. If there is no alternative plan which is more satisfactory, then the proper policy would be to try to implement the present plan” (1963, p. 33). This of course was a wholly unsatisfactory position informed by a narrow view of planning, and an untenable distinction between plan-making and plan-implementation. Nonetheless it does show, in however limited a fashion, the “realism” in Mahalanobis’ thinking.

Economie Appliquée. 2/1994

But Mahalanobis’ perceptions too, like those of many other third world, and even first world, intellectuals, were shaped by his times. There was an admixture of Fabian socialism, Keynesian belief in the efficacy of State intervention, and admiration for Soviet planning which it was thought could be replicated elsewhere by an all-powerful State. Such perceptions underlay the entire literature on development planning which grew up in the fifties. The subsequent developments in the third world, which have seen the growth of a predatory capitalism instead of the elimination of poverty and unemployment, which have seen the bourgeoisie and the proto-bourgeoisie exhibiting a preference for “Western” life-styles and hence going in either for imports in preference to domestically-produced goods under their own aegis, or for continuously renovating the production-structure with ever-newer “assembly” industries that entail heavy demands for imported inputs and foreign technology, have belied the expectations of the early development planners. But this should come as no surprise as these expectations themselves were based on a misreading of societal dynamics.

To say this is not to make the naive point that is often made to the effect that the Mahalanobis strategy is appropriate for a fully-planned socialist economy but not for a mixed economy. Such a view is based on the presumption, shared by many for a long time, that while capitalist or mixed economies have an autonomous societal dynamics, a socialist economy represents a clean slate on which the planners can write what they like. The untenability of this view is obvious when we look at the fate of the erstwhile socialist economies. The journey of a backward economy towards freedom from unemployment and poverty is going to be a complex one and this complexity does not by any means disappear if the means of production are taken over by the State. The precise contours of this journey, and the role that the vision presented by the Mahalanobis strategy would play in it, are for the future to decide; but the vision nonetheless would play a role.

The most vociferous critics of Mahalanobis today are those who are against all development planning, not because they consider its societal assumptions simpliste, but because they uphold the virtues of the free market and of free trade. Mahalanobis’ argument was directed precisely against this position. And even though his social vision of the elimination of poverty and unemployment was not realised, the intellectual force of his argument was no mean factor contributing to the development of the productive base of an Indian economy emerging from a century and a half of colonial rule. When much of the third world, currently

under thraldom to the IMF and pursuing free market and free trade policies reminiscent of the colonial times, is experiencing economic stagnation or retrogression, one cannot but celebrate the intellectual force of Mahalanobis’ argument.

Bibliography

Bagchi A.K., Closed Economy Structuralist Models for a Less-developed Economy (mimeo.), 1993.

Bhagwati J.N. and Desai R, India: Planning for Industrialisation, Oxford University Press, London, 1970.

Chakravarty S., Development Planning: The Indian Experience, Clarendon Press, Oxford, 1987.

Chakravarty S., Selected Economic Writings, Oxford University Press, Delhi, 1993.

Dobb M.H., An Essay on Economic Growth and Planning, Routledge and Keegan Paul, London, 1960.

Dobb M. H., Papers on Capitalism, Development and Planning, RKP London, 1967.

Mahalanobis P.C., Some Observations on the Process of Growth of National Income, Sankhya 12 (4), 1953.

Mahalanobis P.C., The Approach of Operational Research to Planning in India, Asia and Statistical Publishing Society, Calcutta, 1963.

For the influence of physicists like Lord Kelvin who had emphasised the need for quantitative reasoning on Mahalanobis’thinking, see “P.C. Mahalanobis : A Personal Tribute” by S. Chakravarty, reprinted in Chakravarty (1993).

(2) See Mahalanobis (1963) for a brief discussion of the earlier models as well as of Mahalanobis (1953).

(3) For a discussion of the Mahalanobis argument along these lines see Maurice Dobb (1960).

� Since they are using the investment good and labour in an identical manner, a unit of investment good and a unit of consumption good as defined here have the same value, so that aggregating the two into overall output poses no problems.

For an elaboration of this argument see Dobb “On the Question of Investment Priority for Heavy Industry” in Dobb (1967).

® Leif Johansen is mentioned in Dobb (1967) as having originally made the point that the Mahalanobis strategy is a special case of the “turnpike strategy”.

(7-* S. Chakravarty, “Some Aspects of Optimal Investment Policy in an Underdevel¬ oped Economy” in Chakravarty (1993).

(8) It is surprising to find Bhagwati and Desai (1970), p. 236, suggesting that Mahalanobis’training in Physics and subsequently Statistics may have been responsible for his overlooking trade possibilities. The fact that the Second Plan document did not give any justification for ignoring trade possibilities is used by them as evidence for this “overlooking” argument. As a matter of fact Mahalanobis (1963) which was originally published in Sankhya in 1955 discusses the question of why India should develop heavy industries despite the existing trade possibilities at great length.

(9) Mahalanobis’ implicit rejection of the “small country” assumption is clear from his fear expressed on p. 26 of (1963) that if all investment is made in industries producing consumer goods by importing machinery from abroad, then there may be a glut of consumer goods.

(,0) “... if for any reason (such as lack of foreign currency, shortage of supply or high prices in the world market, state of blockade or war etc.) there is difficulty in securing essential investment goods from abroad, India should be able to manufacture such goods within the country”, p. 35 in Mahalanobis (1963).

(1 There were no doubt different versions of the “bargain sector” hypothesis, but that such a hypothesis was prevalent is discussed in Chakravarty (1987).

(12) See Mahalanobis (1963), p. 36-38.

(13) This criticism is made in A.K. Bagchi (1993).

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In Context

National Statistics Day is celebrated every year on 29 June to mark the birth anniversary of Professor Prasanta Chandra Mahalanobis.

About National Statistics Day

Government of India in 2007 designated June 29 as the “Statistics Day ” in the category of Special Days to be celebrated every year at the National level in recognition of Professor Prasanta Chandra Mahalanobis’s notable contributions in the fields of statistics, statistical systems, and economic planning.
Theme : ‘Data for Sustainable Development’.
To spread awareness among the youth of the country about the importance of Statistics in policy formulation and socio-economic planning.

About Prasanta Chandra Mahalanobis

He was born on 29 June 1893 in Calcutta and is known as the father of Indian statistics
A physicist by training, he g ot interested in statistics when he came across Biometrika, a r eputed peer reviewed journal of statistics during his time.
He certainly believed data to be instrumental in efficient planning for national and human development.
He made several contributions to the field of statistics, including the ‘Mahalanobis distance’ , a statistical measure.
He was also a pioneer in the field of anthropometry , the study of human measurements , in India and helped design large scale sample surveys and sampling methods.
He also developed the Feldman-Mahalanobis model, a Neo-Marxian model of economic development , which was employed in the Second Five Year Plan of India, which promoted rapid industrialization of the country.
He was also one of the members of the first Planning Commission of India.
He introduced the concept of pilot surveys and advocated the importance of sampling methods.
He also introduced a method for the estimation of crop yields using statistical sampling.
The Indian Statistical Institute (ISI) at Kolkata, set up him

Importance

Revisiting the life of India’s statistical inheritance from P.C. Mahalanobis is of utmost importance as various kinds of concerns regarding data collection, its publication, and data quality have emerged in recent years.
Professor Mahalanobis has made an immense contribution to the fields of economic planning and statistical development in the post-independent era.

Awards to honour him

He was also conferred with several awards including the Padma Vibhushan.

Mains Practice Question

[Q] Prasanta Chandra Mahalanobis was known as the ‘Plan Man’ of India. Elaborate

Questions related to PC Mahalanobis for UPSC

What was pc mahalanobis famous for, what is mahalanobis strategy, what is the feldman-mahalanobis model.

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CBSE Class 12 Indian Economic Development Notes

Chapter 1: Indian Economy on the Eve of Independence

Indian Economy on the eve of Independence
Agriculture Sector on the Eve of Independence
Industrial Sector on the Eve of Independence
Foreign Trade and Demographic Condition on the Eve of Independence
Occupational Structure and Infrastructure on the Eve of Independence
Policies of British Rulers that led to Exploitation of Indian Economy
Impact of Partition on the Indian Economy

Chapter 2: Indian Economy (1950-1990)

Indian Economy (1950-1990): Economic System adopted by Independent India
Economic Planning during 1950-1990
India’s Five Year Plan
Evaluation (Achievements and Failures) of Economic Planning till 1991
Agriculture during 1950-1990
Policies or Measures to Solve Agricultural Problems during 1950-1990
Green Revolution: Impacts, Achievements and Shortcomings
Debate Over Subsidies to Agriculture
Industries during 1950-1990
Industrial Policy Revolution, 1956
Foreign Trade during 1950-1990|Trade Policy: Import Substitution

P.C. Mahalanobis and His Contribution

Chapter 3: liberalisation, privatisation, and globalisation: an appraisal.

Economic Reforms: Need and Criticism of Economic Reforms
New Economic Policy 1991: Objectives and Components
Liberalisation: Meaning, Economic Reforms Adopted by Indian Government and Objectives
Privatisation: Meaning, Disinvestment, Rationale and Obstacles to Privatisation in India
Globalisation: Meaning, Advantages, Disadvantages and Types
World Trade Organisation (WTO): Features, Functions and Objectives
Impact of Liberalisation, Privatisation, and Globalisation
Concept and Features of Demonetization
What is GST? Types, Features, Benefits, Input Tax Credit, GST Council

Chapter 4: Poverty

Poverty : Meaning, Characteristics, and Measures
Difference between Relative Poverty and Absolute Poverty
Poverty Line: Meaning, Determination, Types and Criticism
Trends and Dimensions of Poverty in India
Impact and Causes of Poverty
What are the Government Approach to remove Poverty?
Poverty Alleviation Programmes in India
Measures to Remove Poverty
Anti-Poverty Measures

Chapter 5: Human Capital Formation in India

Human Capital Formation: Meaning, Sources, Role and Importance
Difference between Physical Capital and Human Capital
Sources of Human Capital Formation
Problems of Human Capital Formation
Role of Human Capital on Economic Growth
Difference between Human Capital and Human Development
Human Capital Formation in India: Growth of the Education Sector in India

Chapter 6: Rural Development

Rural Development: Meaning, Significance, Process and Evaluation
Rural Credit: Meaning, Purpose, Need, Sources and Critical Appraisal
Sources of Rural Credit
Agricultural Marketing: Meaning, Measures, Defects and Alternate Marketing Channels
Agricultural Diversification: Needs, Benefits and Types
Organic Farming: Meaning, Benefits, Challenges and Future Prospects of Organic Farming

Chapter 7: Employment: Growth, Informalisation and Other Issues

Employment: Meaning, Importance, Basic Terms of Employment and Participation of people in Employment
Forms of Employment: Self and Wage Employment
Distribution of Employment
Growth and Changing Structure of Employment
Informalisation of Indian Workforce
Difference between Formal Sector and Informal Sector
Unemployment: Meaning, Types, Causes, Effects and Remedial Measures
Unemployment and its Types

Chapter 8: Infrastructure

Infrastructure: Meaning, Characteristics, Importance and Types
Energy Infrastructure
Difference between Commercial and Non-commercial Sources of Energy
Conventional vs Non-Conventional Sources of Energy
Health Infrastructure in India
Power Infrastructure: Sources, Challenges and Measures to meet Power Crisis
Difference between Economic Infrastructure and Social Infrastructure

Chapter 9: Environment and Sustainable Development

Environment: Meaning, Functions, and Reasons for Environmental Crisis
Environmental Degradation in India
Causes and Impact of Environmental Degradation
What are the measures to control Environmental Degradation ?
Sustainable Development: Meaning, Objectives and Strategies

The architect of Indian economic planning, P.C Mahalanobis, is well-known. As a member of an independent India’s planning committee, he was instrumental in the drafting of a plan that would see India experience fast economic growth while also assisting in the eradication of the colonialists’ poverty.

An Indian scientist and applied statistician named Prasanta Chandra Mahalanobis (1893-1972) built the groundwork for India’s institutional economic planning. He was the first to apply statistical methods to anticipate, plan, analyze, and evaluate social and economic welfare operations in the country, as a member of the first Planning Commission of independent India. The Mahalanobis Model prioritized India’s fast industrialization in the Second Five Year Plan (1961–66). He was the founder of the Indian Statistical Institute (ISI) in Kolkata and the founder of the prestigious Sankhya Journal.

Architect of Indian Economic Planning

1. role in second five year plan.

P.C. Mahalanobis was also a key figure in the development of India’s second five-year plan (1956-1961), which laid the groundwork for the country’s industrialization and development. The heavy industries were emphasized in the Second FYP. It was written by a group of economists and planners led by P. C. Mahalanobis. If the first plan emphasized patience, the second aimed to achieve rapid structural transformation by making adjustments in all feasible directions at the same time. Before this strategy was finalized, the Congress party passed an important resolution at a meeting held in Avadi, near Madras at the time. According to the text, the goal was to create a “socialist design of society.”

To protect indigenous industry, the government levied hefty levies on imports. The growth of both public and private sector industries was aided by such a protected environment. Because savings and investment increased during this time, the public sector could build a large portion of these industries, such as electricity, railways, steel, machines, and communication. Such a push for industrialization was, in fact, a watershed moment in India’s history. The second five-year plan, based on a socialist model, aimed for a 25 percent rise in national income through rapid industrialization.

Critical Evaluation of the Second Five-Year plan

The second five-year plan was a significant step forward, with a strong focus on heavy industry. During this plan period, the Industry Policy Resolution was revised, and the Public Sector was given major responsibility for development. The private sector was largely limited to the consumer goods industry. During this plan, the small and cottage industries remained sluggish. Imports grew dramatically, exposing India’s sterling balances. India was compelled to devalue its currency twice during the third plan, as an outcome of this FYP .

2. Contributions to Statistics

Mahalanobis was a pioneering researcher in statistics and related fields, but he was also a polymath, planner, educator, and visionary, and one of the architects of India’s post-independence nation. In addition to his fundamental contributions in statistics, he made significant research contributions, thinking, and societal value in planning and economics, particularly in econometrics; our focus here is solely on his econometrics contributions. He was a founder of The Indian Econometric Society and the first Indian elected member of the Econometric Society, as well as the first fellow elected from India (1951).

Statistics and Mathematics

The main goal of the Econometric Society is “ the advancement of economic theory in its relation to statistics and mathematics, ” but we’ve narrowed the definition of econometrics to “ the study of economic data aligned with economic reasoning and the advancement of the discipline of economics ” for this special issue. As a result, we place a stronger focus on economic data measurement and statistical inference. This concentration is in line with Mahalanobis’ philosophy and Sankhya’s objectives. P.C. Mahalanobis created the Mahalanobis distance as a statistical theory for comparing data sets. He devised a technique of calculating agricultural production using random sample methods, and he used statistics to flood-control economic planning.

Mahalanobis Distance

The anthropometric research led to the development of the D2- Statistic, also known as Mahalanobis Distance in the statistical literature, which has shown to be a useful tool not only in taxonomy but also in other domains such as economics and geology. Sir Ronald Aylmer Fisher (R.A.Fisher) recognized this concept by naming it the ‘Mahalanobis D-square’ or ‘Mahalanobis distance,’ and so a rich field of research in multivariate analysis arose.

The Mahalanobis distance is a measure of comparison between two data sets created by Mahalanobis. He developed new methods for performing large-scale sample surveys and using the random sampling approach, he determined acreage and agricultural yields. He developed fractile graphical analysis, a statistical tool for comparing the socioeconomic circumstances of different groups of individuals. He also used statistics in flood control economic planning.

3. Role in the National Sample Survey

Mahalanobis organized India’s statistical efforts by establishing the National Sample Survey and the Central Statistical Organization in 1950. From 1955 until 1967, he was a member of India’s Planning Commission. The Second Five-Year Plan of the Planning Commission promoted heavy industrial growth in India and depended on Mahalanobis’ mathematical description of the Indian economy, which became known as the Mahalanobis model.

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The Mahalanobis Growth Model pp 151–176 Cite as

The Mahalanobis Four-Sector Model

Chetan Ghate 4 , 5 ,
Pawan Gopalakrishnan 6 &
Srishti Grover 7
First Online: 14 July 2022

140 Accesses

Mahalanobis (1955) extended the two-sector framework to a four-sector framework, which formed the analytical foundation for India’s Second Five Year Plan (1956–1961). The four-sector model included the original capital goods sector of the two-sector model, and then disaggregated the consumption goods sector into three other consumption goods sectors. The model was calibrated to India to determine investment allocations—especially in the consumption goods sectors—during the Second Five Year Plan and derive the growth and employment implications of various planned investment targets. In this chapter, we solve and calibrate the four sector Mahalanobis model. We also examine it’s long run growth properties. Following Rangaswami and Somasekhara (1974), we also discuss the open economy version of the four sector Mahalanobis model. We then discuss two major critiques of the four-sector Mahalanobis framework: Shenoy (1955) and Komiya (1959). Shenoy points to a variety of unrealistic investment and savings targets in the Second Five Year Plan, which is useful from the standpoint of conducting counter-factual experiments on the patterns of investment. Komiya suggests that the Mahalanobis pattern of investment is not “optimal”, or inefficient, and suggest ways through which additional national income can be obtained by re-allocating resources across sectors.

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To the best of our ability, we know of no other source which has calibrated Mahalanobis’ four-sector model using Octave/MATLAB. With the code, students can play around with various simulations and conduct policy experiments.

We leave it to the reader to look up the references in this book for other criticisms made of the framework, of which there were multiple, and would require a separate book in itself.

Since the model was primarily based on the Second Five Year Plan, we consider a period of 5 years for calculations in this chapter.

Note that INR stands for Indian Rupee; \(Lakh=1\times 10^{5};\) \(Crore=1\times 10^{7}.\)

The above system of equations can be written as follows:

The solution to X is such that

as long as A is a non-singular matrix, i.e., \(\left| A\right| \ne 0.\) See Blume and Simon ( 1994 ), Chap. 9.

We can alternatively minimize the sum of the squared error terms between the LHS and the RHS.

The reader is also encouraged to check these results algebraically.

Note, we have assumed in Fig. 6.2 that \(\alpha _{i0}=0.04,\) \(\alpha _{10}=\alpha _{20}=\alpha _{30}=0.32.\)

See also Raj and Sen ( 1961 ). Unlike Mahalanobis, these authors distinguish between investment goods which produce consumer goods, and investment goods which produce investment goods. They also allow for a more realistic depiction of intermediate goods in the sectoral structure of the model. These changes have a number of implications connected with the pattern of investment.

Rangaswami and Somasekhara ( 1974 ) do detailed calculations of revising all the \(\theta s\) of the open-economy model based on actual data. Their estimates show that the 5-year growth would have been \(6\%.\)

B.R Shenoy (1905–1978) was an Indian economist. As a student he participated in the Indian independence movement, and was jailed in Nagpur. In 1955, Shenoy was appointed to the Panel of Economists to appraise the Second Five Year Plan. He was the only one to submit a note of dissent. See https://en.wikipedia.org/wiki/Bellikoth_Raghunath_Shenoy

In Solow-Swan parlance, this would mean that at India’s level of development in the 1950s, the amount of capital deepening was much less than the amount of capital widening.

Ryutaro Komiya (1928– ) was one of Japan’s leading academic economists who wrote extensively on the Japanese economy.

Note that INR. 37, 520 million is the total investment target net of the investment allocated to the investment goods sector and is equal to \((1-\lambda _{i}^{*})\times A.\)

Note that 10.1 million is the difference between new employment targeted and employment generated in the investment goods sector, i.e., \(N-\frac{\lambda _{i}^{*}}{\theta _{i}}\times A=N-\lambda _{i}^{*}\times \frac{b_{i}}{a_{i}}\times A.\)

From Table 6.5 , it can be checked that \(C_{2}\) sector has the lowest capital and labor requirements per INR 1 million of output produced among the \(C_{1}\) , \(C_{2}\) , and \(C_{3}\) sectors.

Note that INR 25,250 million is equal to \(a_{2}\times Y_{2}^{*}.\)

Note that 10.1 million is equal to \(b_{2}\times Y_{2}^{*}.\)

Note that INR 27,850 million is the total increase in national income targeted net of the increase in national income due to the investment goods sector. That is, \(Y_{0}\times ((1+\eta )^{5}-1)-\frac{\lambda _{i}^{*}}{a_{i}}\times A.\)

Komiya argued that any other choice of excise duty and subsidy will also produce similar results.

Note that \(C_{1}\) now is equal to \(a_{1}^{\prime }\times \left( Y_{1}^{^{\prime }}\right) ^{*}\) , whereas \(C_{2}\) is equal to \(a_{2}^{\prime }\times \left( Y_{2}^{^{\prime }}\right) ^{*}.\)

Total employment of 1.96 million in the \(C_{1}\) sector is obtained from \(b_{1}^{\prime }\times \left( Y_{1}^{^{\prime }}\right) ^{*}.\)

Total employment of 8.14 million in the \(C_{2}\) sector is obtained from \(b_{2}^{\prime }\times \left( Y_{2}^{^{\prime }}\right) ^{*}.\)

Blume, L.E., and C.P. Simon. 1994. Mathematics for Economists . W.W: Norton & Company.

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Economics and Planning Unit, Indian Statistical Institute, New Delhi, India

Chetan Ghate

Institute of Economic Growth, New Delhi, India

Department of Economic and Policy Research, Reserve Bank of India, Mumbai, Maharashtra, India

Pawan Gopalakrishnan

Former MSQE Student (Batch of 2021), Indian Statistical Institute, New Delhi, India

Srishti Grover

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Correspondence to Chetan Ghate .

6.1 Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (zip 535 KB)

6.7 technical appendix.

To solve Komiya’s optimization problem, consider the following three cases:

Case 1 : Let \(Y_{1}=0\)

Source : Authors’ calculations

Solving Komiya’s optimization problem.

The optimization problem is reduced to the following:

From Fig. 6.5 Panel A, we see that the both the constraints are satisfied within the yellow-shaded region. Subjected to the yellow-shaded region, \(Y_{2}+Y_{3}\) is maximized at the corner solution \(Y_{2}=31,562.5,\) \(Y_{3}=0.\) Hence, the maximum increase in national income possible in this case is INR. 31, 562.5 million.

Case 2 : Let \(Y_{2}=0\)

The optimization problem is reduced to the following:

From Fig. 6.5 Panel B, we see that both the constraints are satisfied within the yellow-shaded region. Subjected to the yellow-shaded region, \(Y_{1}+Y_{3}\) is maximized at the corner solution \(Y_{1}=0,\) \(Y_{3}=16,891.\) Hence, the maximum increase in national income possible in this case is INR. 16, 891 million.

Case 3 : Let \(Y_{3}=0\)

From Fig. 6.5 Panel C, we see that the both the constraints are satisfied within the yellow-shaded region. Subjected to the yellow-shaded region, \(Y_{1}+Y_{2}\) is maximized at the corner solution \(Y_{1}=0,\) \(Y_{2}=31,562.5.\) Hence, the maximum increase in national income possible in this case is INR. 31, 562.5 million.

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Ghate, C., Gopalakrishnan, P., Grover, S. (2022). The Mahalanobis Four-Sector Model. In: The Mahalanobis Growth Model. Springer, Singapore. https://doi.org/10.1007/978-981-16-8980-2_6

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