# Leo Törnqvist

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**Leo Waldemar Törnqvist** (14 February 1911 – 18 April 1983) was one of the first professors of statistics in Finland, and the first to achieve international recognition. He taught at the University of Helsinki from 1943 to 1974, and developed techniques that are used in official price and productivity statistics.^{[1]}^{[2]}

## Contents

## Life, education, and career

Törnqvist was born on 14 February 1911 in Jeppo, a Swedish-speaking village in Finland, near the Swedish border. He studied mathematics, physics, and chemistry at Åbo Akademi University in Turku, where his interests shifted to economics and statistics under the influence of Swedish economist Arthur Montgomery. He finished his studies in Turku in 1933 and continued with graduate work in mathematics at Stockholm University, earning a doctorate in 1937 under the supervision of Harald Cramér and Gunnar Myrdal.^{[2]}

After a short-term teaching position at Åbo Akademi University from 1937 to 1938,
he began his career working for the Finnish railway service from 1938 until 1943. He was appointed as an associate professor of statistics at the University of Helsinki in 1943 and promoted to full professor in 1950.
In the early 1950s he visited researchers in the US and, in the early 1960s, worked as a consultant for the United Nations in Indonesia.^{[2]}

He died on 18 April 1983.^{[2]}

## Contributions

Törnqvist developed an approach to creating weighted price indexes across discrete time periods using weighted averages of growth rates in prices where the weights were quantity averages across the two periods, in work he did with the Bank of Finland published in 1936.^{[3]}^{[4]} These Törnqvist indexes are used in official price and productivity statistics in many countries.^{[5]}^{[6]}^{[7]}^{[8]}
In a 1949 work,^{[9]} he also made "the first serious attempt to describe population forecasting from a stochastic point of view",^{[10]} providing "seminal works" in Bayesian inference in demography.^{[11]}

As a professor at the University of Helsinki, his students included economist Timo Teräsvirta.^{[12]} His student Vieno Rajaoja was the first Finnish woman to earn a doctorate in statistics, in 1958.^{[2]}

## Recognition

Törnqvist became a Fellow of the Econometric Society in 1951, and an Elected Member of the International Statistical Institute in 1956. He was made a member of the Order of the Lion of Finland in 1961, and given honorary doctorates by the University of Helsinki in 1971 and by Åbo Akademi University in 1978.^{[2]}

## Family

Törnqvist bought a Commodore VIC-20 about 1981 and asked his daughter Anna's son, Linus Torvalds, to help him program it. Törnqvist wrote out BASIC language programs, and grandson Linus, aged about eleven, typed them in. "He wanted me to share in the experience [and] get me interested in math," wrote Torvalds later.^{[13]} These were Linus's first programming experiences. Ten years later, Torvalds began to write the Linux kernel.

Leo Törnqvist’s brother was diplomat Erik Törnqvist.^{[1]} His son was the nuclear physicist Template:Ill (1938–2018).^{[14]}

## References

- ↑
^{1.0}^{1.1}Törnqvist, Leo in*Uppslagsverket Finland*Template:Sv icon. - ↑
^{2.0}^{2.1}^{2.2}^{2.3}^{2.4}^{2.5}Törnqvist, Leo (1911 – 1983),*Suomen kansallisbiografia*(in Finnish) - ↑ Törnqvist, Leo. 1936. The Bank of Finland's Consumption Price Index.
*Bank of Finland Monthly Bulletin*10, 1-8. - ↑ Törnqvist, Leo. 1981.
*Collected scientific papers of Leo Tornqvist.*Research Institute of the Finnish Economy. Series A. ISBN 951-9205-74-8 - ↑
*"BLS aggregates inputs for its multifactor productivity measures using a Tornqvist chain index."*U.S. Bureau of Labor Statistics. Chapter 10. Productivity Measures: Business Sector and Major Subsectors*BLS Handbook of Methods.*1997. - ↑
*"The Tornqvist index is used in the calculation of multifactor productivity."*Methodology Australian Government Productivity Commission, 2009. Viewed 11 Aug 2011. - ↑ The Tornqvist Index as a True-Cost Index, in Food Cost Indexes for Low-Income Households and the General Population, published by the Economic Research Service, US Dept of Agriculture, TB-1872, p.7
- ↑ Robert Cage; John Greenlees; Patrick Jackman. Introducing the Chained Consumer Price Index. For presentation at the Seventh Meeting of the International Working Group on Price Indices, May 2003
- ↑ Hyppölä, J.; Tunkelo, A.; Törnqvist, L. (1949) (in Finnish).
*Suomen väestöä, sen uusiutumista ja tulevaa kehitystä koskevia laskelmia*. Tilastollisia tiedonantoja.**38**. Helsinki: Statistics Finland. As cited by Template:Harvtxt - ↑ Alho, Juha M.; Spencer, Bruce D.. "Statistical Propagation of Error in Forecasting".
*Statistical Demography and Forecasting*. Springer Series in Statistics. Springer-Verlag. pp. 269–295. Template:Citation error. - ↑ Wiśniowski, Arkadiusz; Smith, Peter W. F.; Bijak, Jakub; Bijak, James; Forster, Jonathan J. (May 2015). "Bayesian Population Forecasting: Extending the Lee-Carter Method".
*Demography***52**(3): 1035–1059. Template:Citation error. - ↑ Jawadi, Fredj (June 2018). "An Interview with Timo Teräsvirta".
*Studies in Nonlinear Dynamics & Econometrics***22**(5). Template:Citation error. - ↑ Torvalds, Linus; David Diamond (2001).
*Just For Fun: The Story of an Accidental Revolutionary*. New York City, US: HarperCollins. ISBN 0-06-662072-4., pp. 6-7. - ↑ Hoyer, Paul & Montonen, Claus & Roos, Matts (5 September 2018). "Kansainvälinen fyysikko" (in Finnish).
*Helsingin Sanomat*: p. B 17. http://www.hs.fi/muistot/art-2000005815327.html.

## Further reading

- Nordberg, Leif (1999). "Leo Törnqvist – the "grandfather" of Finnish statistics". In Alho, Juha M..
*Statistics, registries, and science: Experiences from Finland*. Helsinki: Statistics Finland. pp. 163–176.

- Deleted December 2019
- Articles which use infobox templates with no data rows
- Finnish statisticians
- Academics of the University of Helsinki
- 1911 births
- 1983 deaths
- 20th-century mathematicians
- Elected Members of the International Statistical Institute
- Fellows of the Econometric Society
- Recipients of the Order of the Lion of Finland
- Swedish-speaking Finns
- Torvalds family