Biographical Memoirs Volume 67 (1995) / Chapter Skim
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Tjalling Charles Koopmans
Tjalling Charles Koopmans
Pages 262-291
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From page 263... ...
In both of these areas Koopmans creatively mobilized and developed the methods of other quantitative disciplines for the purposes of economics: mathematical statistics became econometrics, and linear programming became the activity analysis mode! of production.
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From page 264... ...
Wijtske was also trained as a schoolteacher and, after their marriage, the couple left Frisia and eventually settled in 's Gravelanc3, where Koopmans's father became the principal of a much larger "school with the bible." The family house, as Koopmans described it in an autobiographical sketch written when he received the Nobel Prize in economic sciences in 1975, .
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From page 265... ...
T) AL L I N G C H A R L E S K O O P M A N S 265 Latin, Greek, mathematics, physics, chemistry, and three modern languages.
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From page 266... ...
" in ~ 933 Koopmans wrote an important paper on quantum mechanics, which is still frequently cited by physicists many years after its publication. But, of course, these were the years of the Great Depression, and theoretical physics must have seemed remote from the distress of daily economic life.
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From page 267... ...
Tinbergen, who was to share the first Nobel Prize in economic science with Ragnar Frisch in 1969, tract been trained in mathematical physics as a student of Ehrenfest. He had been a conscientious objector to military service at the age of eighteen and, as an alternative obligation, was required to spend some time at the Statistical Office in the Hague, where he became acquainted with en c!
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From page 268... ...
Tinbergen had a profound influence on Koopmans's professional career, and it may be useful to make a brief digression about Tinbergen's work on business cycles and macroeconomic moclels. In order to place this work in perspective, let me describe a fundamental distinction between two attitudes toward dynamic models in economic theory.
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From page 269... ...
Tinbergen was drawn to the alternative formulation, which had played an important role in the analysis of business cycles and which was ultimately to lead to the Keynesian model. For example, Tinbergen published a paper in 1931 in which cycles in shipbuilding are analyzed by means of a simple differencedifferential equation stating that the increase in available shipping tonnage at a particular time is related linearly to the stock of tonnage with a fixed time delay.
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From page 270... ...
By the 1930s economists had already been exposed to the use of regression analysis and other statistical techniques in analyzing the relationship between the demand for a particular good and its price and in the study of business cycles. The parameters in Tinbergen's model of the Dutch economy had been estimated using multiple correlation analysis with a degree of care and detail not seen in previous economic reports, and Frisch had developed his own ingenious statistical methods.
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From page 271... ...
In order to justify the use of one particular method, Fisher introducer! an underlying probabilistic model that is assumed to generate the observed data.
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From page 272... ...
The study was not based on a formal mathematical moclel, but it ctid display a sure grasp of economic theory and a detailed knowIedge of the tanker industry that was remarkable for a young scholar recently preoccupied with mathematical physics. The work was published as a monograph titled Tanker Freight Rates and Tankship Building by the Netherlands Economic Institute in 1939.
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From page 273... ...
At the conference Koopmans met a number of economists, including Jacob Marschak, with whom he was to have a long and significant relationship. Later in the year the Koopmans went on a leisurely vacation, traveling through the French Alps by bus.
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From page 274... ...
Koopmans derived a representation for this distribution by means of a contour integral and illustratecI the use of an ingenious smoothing approximation that facilitated numerical computations. His paper, titlecl "Serial Correlation and Quadratic Forms in Normal Variables," was published in the Annals of Mathematical Statistics.
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From page 275... ...
The problem of determining the shipping plan that minimizes total cost, given a preassigned pattern of availabilities of supplies en cl clemands, is known as the transportation problem. It is one of the most elementary examples of a linear programming problem, that is, the maximization of a linear function of several variables, subject to a series of linear inequality constraints.
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From page 276... ...
thus began a long association both with Marschak anct the commission that was to prove extraordinarily productive. The Cowles Commission for Research in Economics was founded in 1932 by Alfred Cowles, the president of Cowles and Company, an investment counseling firm with offices in Colorado Springs, Colorado.
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From page 277... ...
The early research agenda, set by Marschak, was primarily concerned with the particular statistical problems arising in the estimation of parameters in a set of simultaneous equations. The idea that the relationships among economic variables are best described by a set of simultaneous equations
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From page 278... ...
series of economic variables satisfied a system of, say, linear equations with stochastic errors governed by specific probability distributions with unknown parameters. Given the parameters of the error terms and of the equations themselves, any particular set of possible values will have a well-def~ned probability.
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From page 279... ...
A first paper concerned the bias arising from an ordinary least squares regression of the parameters of a single equation, if the equation is, in reality, part of a larger system. A second paper, written with the assistance of Herman Rubin and Roy Leipnik, provided a complete solution to the problem of "identification," that is, a description of the necessary and sufficient conditions that permit the structural parameters of a linear system to be determined uniquely from the probability distributions of the data and hence amenable to statistical estimation.
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From page 280... ...
Second, the statistical approach was eclectic, with no formal probabilistic model to account for the data and to justify the use of the author's statistical techniques. The methodology used by Burns and Mitchell was descriptive, Koopmans maintained, rather than flowing from the logical and analytical stance toward economic data that was at the heart of the Cowles program.
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From page 281... ...
Several months earlier he had a consequential meeting with George B Dantzig, who was the first Western scholar to study the general linear programming problem.
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From page 282... ...
in an activity analysis model the possible techniques of production available to a firm, or to the economy as a whole, are given by a finite list of elementary activities that can be used simultaneously and at arbitrary non-negative levels. The resulting production possibility set is a polyheciral cone, approximating the smooth transformation sets of neoclassical economics to an arbitrary degree of accuracy.
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From page 283... ...
In this paper and in a nontechnical essay published in Econometr~ca, Koopmans demonstrated a sharp awareness of the relationship of these ideas to the fascinating discussion of socialist economic planning in the 1930s. His strong convictions regarding the importance of the activity analysis model for economic planning in Eastern Europe led Koopmans to make extended trips to the Soviet Union in 1965 and 1970.
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From page 284... ...
The relationship between prices and economic efficiency in both static and dynamic models of production and the role played by the assumption of convexity in welfare economics are discussed by means of simple geometric diagrams and with a lucidity rarely attained by an active research scientist.
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the Nobel Prize, Koopmans says, "In most of my Yale period my research, chiefly on optimal allocation over time, had more of a solitary character." But this is only in contrast to the Chicago days, when the energies of the entire Cowles team were focused on specific projects. In Chicago the commission was engaged in a methodological revolution involving the use of formal mathematics in economic theory and econometrics.
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From page 286... ...
He began to apply the techniques of growth theory to the study of exhaustible resources and, in particular, those resources used in the provision of energy. A lengthy study of copper supplies was initiated, in colIaboration with William Morpheus, his colleague in the Department of Economics, and Robert Gordon and Brian Skinner, both geologists at Yale.
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From page 287... ...
The paper, written with Tjalling's characteristic conceptual clarity en c! mastery of the facts, was illustrated by his work on energy modeling and other topics adctressed in recent reports of the National Research Council.
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288 BIOGRAPHICAL MEMOIRS ~ AM WRY G^TEFU~ for many conversations with Truus Koopmans and for the advice and assistance given to me by Kenneth I Arrow, Gerard Debreu, George Dantzig, Leo Hurwicz, Alvin Klevorick, Peter Phillips, Martin Shubik, Herbert Simon, T
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From page 289... ...
1937 Linear Regression Analysis of Economic Time Series. Publication No.
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From page 290... ...
Selected topics in economics involving mathematical reasoning. SIAM Review 1: 79-148.
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From page 291... ...
1978 Energy Modeling for an Uncertain Future. Supporting Paper 2, Report of the Modeling Resource Group, Synthesis Panel of the Committee on Nuclear and Alternative Energy System, National Research Council, National Academy of Sciences, Washington, D.C.
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