Tjalling Koopmans was born in Graveland, The Netherlands in 1910. He studied mathematics and physics at the University of Utrecht and obtained his MA in 1933, before being awarded a PhD in mathematical statistics from the University of Leiden in 1936. After a period teaching at the Netherlands School of Economics in Rotterdam, and then employed as an economist at the League of Nations in Geneva, Koopmans emigrated in 1940 to the United States (later becoming a US citizen). Following employment in a research post at Princeton University he worked as a statistician at the Combined Shipping Adjustment Board in Washington from 1942 to 1944. In 1944 he moved to the University of Chicago where he was research associate (1944–48); Director of Research of the Cowles Commission (1948–54); associate professor (1944–48); and Professor of Economics (1948–55). In 1955 he moved, as did the Cowles Commission, from the University of Chicago to Yale University in New Haven, Connecticut. Here he served as director of the Cowles Foundation for Research in Economics from 1961 to 1967, and as Professor of Economics from 1955 until he retired from the university in 1981.

Koopmans’s many offices and honours included the presidencies of the Econometric Society in 1950, and the American Economic Association in 1978. In 1975 Koopmans was awarded, jointly with the Russian mathematician–economist Leonid Kantorovich, the Nobel Memorial Prize in Economics ‘for their contributions to the theory of optimum allocation of resources’ (Nobel Foundation, 2004).

Koopmans will be remembered first and foremost for his path-breaking work on activity analysis. The development of the technique arose out of his early research on transportation economics (Koopmans, 1939) and his work as a statistician at the Combined Shipping Adjustment Board during the Second World War. In a 1942 memorandum for the Board, ‘Exchange Ratios between Cargoes on Various Routes’ (first published in Koopmans, 1970), he put forward a scheme for deciding the optimal allocation of cargo ships among routes. He also showed how ‘potentials’ or shadow prices could aid decisions on the allocation of ships. However, his seminal article on the technique, entitled ‘Analysis of Production as an Efficient Combination of Activities’, appears in the proceedings of a conference he organised in 1949, published in 1951 (Koopmans, 1951). Rather than study the relationship between inputs and outputs from the standpoint of the existence of a conventional ‘production function’, he analysed the production choices of a firm operating under constraints. In reality, a firm is unable to adopt all possible combinations of inputs because it has limited amounts of inputs at its disposal. Furthermore, these limited inputs can only be combined in a finite number of ways as they are constrained by existing production techniques. In other words, activity levels or levels of output produced are constrained by the availability of inputs and how such inputs can be combined. Koopmans explored the implications of activity analysis, including optimality and efficiency in production and their relation to the price system. In subsequent work he extended activity analysis and examined its applications (for example, Koopmans,1953a). He applied the technique not only to problems in transportation economics but also to problems of allocating resources over time. His work in the field of activity analysis is intrinsically linked to the development of linear programming (see entry on Leonid Kantorovich).

In addition to his pioneering work on activity analysis, Koopmans also made important contributions to a number of other areas including econometric theory, methodology and the theory of optimal economic growth. His work in the field of econometrics can be traced back to the publication of his doctoral thesis: ‘Linear Regression Analysis of Economic Time Series’ (Koopmans, 1937). In the 1940s and early 1950s he focused his econometric research efforts on the problem of estimation and identification of structural parameters in economic models (Koopmans, 1945; 1949a). At the Cowles Commission he led a team of econometricians which tackled this problem, resulting in the publication of two important monographs which helped to popularise the use of simultaneous equation models (Koopmans, 1950; Hood and Koopmans, 1953b).

In the field of methodological debate, Koopmans’s most influential contribution was his review (Koopmans, 1947) of Arthur Burns and Wesley Mitchell’s book Measuring Business Cycles, which was published by the National Bureau of Economic Research (NBER) in 1946. He attacked Burns and Mitchell’s (NBER) ‘inductive–empirical’ methodology, where observation and measurement informs or suggests theory, describing it as ‘measurement without theory’. In its place he advocated the Cowles Commission’s ‘theoretical–deductive’ approach where theory is used to develop models whose parameters can be estimated and tested using econometric techniques. After Mitchell’s death in 1948, one of his colleagues at the NBER, Rudledge Vining, defended the NBER methodology and continued the debate with Koopmans (see Koopmans, 1949b). Finally, brief mention should be made of Koopmans’s research in the 1960s which contributed to the field of economic growth theory. In particular he made important contributions to the theory of optimal economic growth, efficiency in growth and preference orderings (see, for example, Koopmans, 1964; 1967).

For the interested reader, many of Koopmans’s most important scientific papers have been gathered together in two volumes (Koopmans, 1970; 1985). His views on the state of economic science can be found in his three essays on: allocation of resources and the price system; the construction of economic knowledge; and the interaction of tools and problems in economics (Koopmans, 1957).

(1937), Linear Regression Analysis of Economic Time Series, Haarlem: De Erven Bohn.

(1939), Tanker Freight Rates and Tankship Building, Haarlem: De Erven Bohn.

(1945), ‘Statistical Estimation of Simultaneous Economic Relations’, Journal of the American

Statistical Association, 40, December, pp. 448–66.

(1947), ‘Measurement without Theory’, Review of Economic Statistics, 29, August, pp. 161–72. (1949a), ‘Identification Problems in Economic Model Construction’, Econometrica, 17, April, pp. 125–44.

(1949b), ‘Koopmans on the Choice of Variables to be Studied and the Methods of Measurement: A Reply’, Review of Economic Statistics, 31, May, pp. 86–91.

(1950), Statistical Inference in Dynamic Economic Models (ed.), New York: John Wiley.

(1951), Activity Analysis of Production and Allocation (ed.), New York: John Wiley.

(1953a), ‘Activity Analysis and Its Applications’, American Economic Review, 43, May, pp. 406–14.

(1953b), Studies in Econometric Method (ed. with W.C. Hood), New York: John Wiley.

Koopmans’s many offices and honours included the presidencies of the Econometric Society in 1950, and the American Economic Association in 1978. In 1975 Koopmans was awarded, jointly with the Russian mathematician–economist Leonid Kantorovich, the Nobel Memorial Prize in Economics ‘for their contributions to the theory of optimum allocation of resources’ (Nobel Foundation, 2004).

Koopmans will be remembered first and foremost for his path-breaking work on activity analysis. The development of the technique arose out of his early research on transportation economics (Koopmans, 1939) and his work as a statistician at the Combined Shipping Adjustment Board during the Second World War. In a 1942 memorandum for the Board, ‘Exchange Ratios between Cargoes on Various Routes’ (first published in Koopmans, 1970), he put forward a scheme for deciding the optimal allocation of cargo ships among routes. He also showed how ‘potentials’ or shadow prices could aid decisions on the allocation of ships. However, his seminal article on the technique, entitled ‘Analysis of Production as an Efficient Combination of Activities’, appears in the proceedings of a conference he organised in 1949, published in 1951 (Koopmans, 1951). Rather than study the relationship between inputs and outputs from the standpoint of the existence of a conventional ‘production function’, he analysed the production choices of a firm operating under constraints. In reality, a firm is unable to adopt all possible combinations of inputs because it has limited amounts of inputs at its disposal. Furthermore, these limited inputs can only be combined in a finite number of ways as they are constrained by existing production techniques. In other words, activity levels or levels of output produced are constrained by the availability of inputs and how such inputs can be combined. Koopmans explored the implications of activity analysis, including optimality and efficiency in production and their relation to the price system. In subsequent work he extended activity analysis and examined its applications (for example, Koopmans,1953a). He applied the technique not only to problems in transportation economics but also to problems of allocating resources over time. His work in the field of activity analysis is intrinsically linked to the development of linear programming (see entry on Leonid Kantorovich).

In addition to his pioneering work on activity analysis, Koopmans also made important contributions to a number of other areas including econometric theory, methodology and the theory of optimal economic growth. His work in the field of econometrics can be traced back to the publication of his doctoral thesis: ‘Linear Regression Analysis of Economic Time Series’ (Koopmans, 1937). In the 1940s and early 1950s he focused his econometric research efforts on the problem of estimation and identification of structural parameters in economic models (Koopmans, 1945; 1949a). At the Cowles Commission he led a team of econometricians which tackled this problem, resulting in the publication of two important monographs which helped to popularise the use of simultaneous equation models (Koopmans, 1950; Hood and Koopmans, 1953b).

In the field of methodological debate, Koopmans’s most influential contribution was his review (Koopmans, 1947) of Arthur Burns and Wesley Mitchell’s book Measuring Business Cycles, which was published by the National Bureau of Economic Research (NBER) in 1946. He attacked Burns and Mitchell’s (NBER) ‘inductive–empirical’ methodology, where observation and measurement informs or suggests theory, describing it as ‘measurement without theory’. In its place he advocated the Cowles Commission’s ‘theoretical–deductive’ approach where theory is used to develop models whose parameters can be estimated and tested using econometric techniques. After Mitchell’s death in 1948, one of his colleagues at the NBER, Rudledge Vining, defended the NBER methodology and continued the debate with Koopmans (see Koopmans, 1949b). Finally, brief mention should be made of Koopmans’s research in the 1960s which contributed to the field of economic growth theory. In particular he made important contributions to the theory of optimal economic growth, efficiency in growth and preference orderings (see, for example, Koopmans, 1964; 1967).

For the interested reader, many of Koopmans’s most important scientific papers have been gathered together in two volumes (Koopmans, 1970; 1985). His views on the state of economic science can be found in his three essays on: allocation of resources and the price system; the construction of economic knowledge; and the interaction of tools and problems in economics (Koopmans, 1957).

**Main Published Works**(1937), Linear Regression Analysis of Economic Time Series, Haarlem: De Erven Bohn.

(1939), Tanker Freight Rates and Tankship Building, Haarlem: De Erven Bohn.

(1945), ‘Statistical Estimation of Simultaneous Economic Relations’, Journal of the American

Statistical Association, 40, December, pp. 448–66.

(1947), ‘Measurement without Theory’, Review of Economic Statistics, 29, August, pp. 161–72. (1949a), ‘Identification Problems in Economic Model Construction’, Econometrica, 17, April, pp. 125–44.

(1949b), ‘Koopmans on the Choice of Variables to be Studied and the Methods of Measurement: A Reply’, Review of Economic Statistics, 31, May, pp. 86–91.

(1950), Statistical Inference in Dynamic Economic Models (ed.), New York: John Wiley.

(1951), Activity Analysis of Production and Allocation (ed.), New York: John Wiley.

(1953a), ‘Activity Analysis and Its Applications’, American Economic Review, 43, May, pp. 406–14.

(1953b), Studies in Econometric Method (ed. with W.C. Hood), New York: John Wiley.

(1957), Three Essays on the State of Economic Science, New York: McGraw-Hill.

(1964), ‘Economic Growth at a Maximal Rate’, Quarterly Journal of Economics, 78, August, pp. 355–94.

(1967), ‘Objectives, Constraints and Outcomes in Optimal Growth Models’, Econometrica, 35,

January, pp. 1–15.

(1964), ‘Economic Growth at a Maximal Rate’, Quarterly Journal of Economics, 78, August, pp. 355–94.

(1967), ‘Objectives, Constraints and Outcomes in Optimal Growth Models’, Econometrica, 35,

January, pp. 1–15.

(1970), The Scientific Papers of Tjalling C. Koopmans, Berlin: Springer-Verlag.

(1985), The Scientific Papers of Tjalling C. Koopmans, vol. 2, Cambridge, MA: MIT Press.

(1985), The Scientific Papers of Tjalling C. Koopmans, vol. 2, Cambridge, MA: MIT Press.