IDEAS home Printed from https://ideas.repec.org/a/sae/jinter/v35y2023i1p29-60.html
   My bibliography  Save this article

Separation Theorems in Econometrics and Psychometrics: Rasch, Frisch, Two Fishers and Implications for Measurement

Author

Listed:
  • William P. Fisher Jr.

Abstract

In 1959, Ragnar Frisch prompted Georg Rasch to formalise a separability theorem that continues today to serve as the basis of a wide range of theoretical and applied developments in psychological and social measurement. Previously unnoted are the influences on Rasch exerted by Frisch’s concerns for data autonomy, model identification and necessary and sufficient conditions. Although Rasch acknowledged Frisch’s prompting towards a separability theorem, he did not acknowledge any substantive, intellectual debt to him, nor to Irving Fisher, but only to Ronald Fisher. Rasch appears to have developed a special interest in sufficiency and identified models when studying with Frisch in 1935, and in 1947, when Rasch accompanied Tjalling Koopmans to the University of Chicago and the Cowles Commission for Research in Economics. I. Fisher’s separation theorem continues to be relevant in econometrics, and interest in Rasch’s separability theorem is growing as the measurement models based on it are adopted in metrological theory and practice. The extensive interrelations between measurement science, metrological standards and economics suggest paths towards lower transaction costs and more efficient markets for individualised exchanges of human, social and natural capital. Equally, if not more, surprising are the implications for a poetic art of complex, harmonised relationships played out via creative improvisations expressed using instruments tuned to shared scales. JEL: B41, C10, C13, C20, C42, D70, E60, H54, I11, I21, I31, P11

Suggested Citation

  • William P. Fisher Jr., 2023. "Separation Theorems in Econometrics and Psychometrics: Rasch, Frisch, Two Fishers and Implications for Measurement," Journal of Interdisciplinary Economics, , vol. 35(1), pages 29-60, January.
    • Handle: RePEc:sae:jinter:v:35:y:2023:i:1:p:29-60
    DOI: 10.1177/02601079211033475
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/02601079211033475
    Download Restriction: no
    File URL: https://libkey.io/10.1177/02601079211033475?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. San Martin, Ernesto & Rolin, Jean-Marie, 2013. "Identification of parametric Rasch-type models," LIDAM Reprints ISBA 2013002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. David Andrich, 2010. "Sufficiency and Conditional Estimation of Person Parameters in the Polytomous Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 75(2), pages 292-308, June.
    3. Ellison, Brenna & Bruening, Meg & Hruschka, Daniel J. & Nikolaus, Cassandra J. & van Woerden, Irene & Rabbitt, Matthew P. & Nickols-Richardson, Sharon M., 2021. "Viewpoint: Food insecurity among college students: A case for consistent and comparable measurement," Food Policy, Elsevier, vol. 101(C).
    4. Rice K.M., 2004. "Equivalence Between Conditional and Mixture Approaches to the Rasch Model and Matched Case-Control Studies, With Applications," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 510-522, January.
    5. Erling Andersen, 1977. "Sufficient statistics and latent trait models," Psychometrika, Springer;The Psychometric Society, vol. 42(1), pages 69-81, March.
    6. Koustas, Zisimos & Serletis, Apostolos, 1999. "On the Fisher effect," Journal of Monetary Economics, Elsevier, vol. 44(1), pages 105-130, August.
    7. Marcel Boumans, 2001. "Fisher's Instrumental Approach to Index Numbers," History of Political Economy, Duke University Press, vol. 33(5), pages 313-344, Supplemen.
    8. Bjerkholt, Olav, 2005. "Frisch'S Econometric Laboratory And The Rise Of Trygve Haavelmo'S Probability Approach," Econometric Theory, Cambridge University Press, vol. 21(3), pages 491-533, June.
    9. Alexandra Benham & Lee Benham, 2000. "Measuring the costs of exchange," Chapters, in: Claude Ménard (ed.), Institutions, Contracts and Organizations, chapter 24, Edward Elgar Publishing.
    10. Bjerkholt,O., 2001. "Tracing Haavelmo's steps from confluence analysis to the probability approach," Memorandum 25/2001, Oslo University, Department of Economics.
    11. Kiefer, Nicholas M, 1988. "Economic Duration Data and Hazard Functions," Journal of Economic Literature, American Economic Association, vol. 26(2), pages 646-679, June.
    12. Dimand, Robert W, 1997. "Irving Fisher and Modern Macroeconomics," American Economic Review, American Economic Association, vol. 87(2), pages 442-444, May.
    13. James E. Smith & Robert F. Nau, 1995. "Valuing Risky Projects: Option Pricing Theory and Decision Analysis," Management Science, INFORMS, vol. 41(5), pages 795-816, May.
    14. Olatunji Abdul Shobande & Oladimeji Tomiwa Shodipe, 2021. "Monetary Policy Interdependency in Fisher Effect: A Comparative Evidence," Journal of Central Banking Theory and Practice, Central bank of Montenegro, vol. 10(1), pages 203-226.
    15. Christ, Carl F, 1994. "The Cowles Commission's Contributions to Econometrics at Chicago, 1939-1955," Journal of Economic Literature, American Economic Association, vol. 32(1), pages 30-59, March.
    16. William P. Fisher, 2012. "Measure and Manage: Intangible Assets Metric Standards for Sustainability," Palgrave Macmillan Books, in: Joan Marques & Satinder Dhiman & Svetlana Holt (ed.), Business Administration Education, chapter 3, pages 43-63, Palgrave Macmillan.
    17. Gerhard Fischer, 1981. "On the existence and uniqueness of maximum-likelihood estimates in the Rasch model," Psychometrika, Springer;The Psychometric Society, vol. 46(1), pages 59-77, March.
    18. Hakan Berument & Richard T. Froyen, 2021. "The Fisher effect on long-term U.K. interest rates in alternative monetary regimes: 1844-2018," Applied Economics, Taylor & Francis Journals, vol. 53(33), pages 3795-3809, July.
    19. Susan Leigh Star & Karen Ruhleder, 1996. "Steps Toward an Ecology of Infrastructure: Design and Access for Large Information Spaces," Information Systems Research, INFORMS, vol. 7(1), pages 111-134, March.
    20. William P. Fisher, 2020. "Contextualizing Sustainable Development Metric Standards: Imagining New Entrepreneurial Possibilities," Sustainability, MDPI, vol. 12(22), pages 1-22, November.
    21. David Andrich, 1978. "A rating formulation for ordered response categories," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 561-573, December.
    22. Robert W. Dimand & John Geanakoplos, 2005. "Celebrating Irving Fisher: The Legacy of a Great Economist," American Journal of Economics and Sociology, Wiley Blackwell, vol. 64(1), pages 3-18, January.
    23. Monya Baker, 2016. "1,500 scientists lift the lid on reproducibility," Nature, Nature, vol. 533(7604), pages 452-454, May.
    24. Arnold, Steven F., 1985. "Sufficiency and invariance," Statistics & Probability Letters, Elsevier, vol. 3(5), pages 275-279, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Clemens Draxler & Rainer Alexandrowicz, 2015. "Sample Size Determination Within the Scope of Conditional Maximum Likelihood Estimation with Special Focus on Testing the Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 897-919, December.
    2. Christopher L. Gilbert & Duo Qin, 2005. "The First Fifty Years of Modern Econometrics," Working Papers 544, Queen Mary University of London, School of Economics and Finance.
    3. Henrik Egbert & Teodor Sedlarski, 2017. "Fundamentals of modern economy: Irving Fisher and intertemporal choice theory," Economic Thought journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 1, pages 132-143.
    4. David Andrich, 2010. "Sufficiency and Conditional Estimation of Person Parameters in the Polytomous Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 75(2), pages 292-308, June.
    5. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    6. Clio Kenterelidou & Fani Galatsopoulou & Antonis Skamnakis, 2017. "Agrotourism and well-being sustainability: A communication and journalistic approach to ?what matters and better life?," RIVISTA DI STUDI SULLA SOSTENIBILITA', FrancoAngeli Editore, vol. 0(1), pages 129-147.
    7. Robert W. Dimand, 2020. "Macroeconomic dynamics at the Cowles Commission from the 1930s to the 1950s," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 27(4), pages 564-581, July.
    8. Enrico Gori & Ting Fa Margherita Chang & Luca Iseppi & Beniamino Cenci Goga & Maria Francesca Iulietto & Paola Sechi & Maria Antonietta Lepellere, 2017. "The assessment of consumer sensitivity to animal welfare: An application of Rasch Model," RIVISTA DI STUDI SULLA SOSTENIBILITA', FrancoAngeli Editore, vol. 0(1), pages 107-127.
    9. Clemens Draxler, 2010. "Sample Size Determination for Rasch Model Tests," Psychometrika, Springer;The Psychometric Society, vol. 75(4), pages 708-724, December.
    10. Erling Andersen, 1995. "Residualanalysis in the polytomous rasch model," Psychometrika, Springer;The Psychometric Society, vol. 60(3), pages 375-393, September.
    11. Bas Hemker & L. Andries van der Ark & Klaas Sijtsma, 2001. "On measurement properties of continuation ratio models," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 487-506, December.
    12. C. Glas & N. Verhelst, 1989. "Extensions of the partial credit model," Psychometrika, Springer;The Psychometric Society, vol. 54(4), pages 635-659, September.
    13. Bordo, Michael D. & Rockoff, Hugh, 2013. "The Influence Of Irving Fisher On Milton Friedman’S Monetary Economics," Journal of the History of Economic Thought, Cambridge University Press, vol. 35(2), pages 153-177, June.
    14. Bjerkholt, Olav, 2015. "Trygve Haavelmo At The Cowles Commission," Econometric Theory, Cambridge University Press, vol. 31(1), pages 1-84, February.
    15. Basse, Tobias & Wegener, Christoph, 2022. "Inflation expectations: Australian consumer survey data versus the bond market," Journal of Economic Behavior & Organization, Elsevier, vol. 203(C), pages 416-430.
    16. Vladimir Turetsky & Emil Bashkansky, 2022. "Ordinal response variation of the polytomous Rasch model," METRON, Springer;Sapienza Università di Roma, vol. 80(3), pages 305-330, December.
    17. William P. Fisher, 2020. "Contextualizing Sustainable Development Metric Standards: Imagining New Entrepreneurial Possibilities," Sustainability, MDPI, vol. 12(22), pages 1-22, November.
    18. André K. Anundsen & Tord S. Krogh & Ragnar Nymoen & Jon Vislie, 2014. "Overdeterminacy and Endogenous Cycles: Trygve Haavelmo's Business Cycle Model," Metroeconomica, Wiley Blackwell, vol. 65(3), pages 460-486, July.
    19. Brzezińska Justyna, 2016. "Latent Variable Modelling and Item Response Theory Analyses in Marketing Research," Folia Oeconomica Stetinensia, Sciendo, vol. 16(2), pages 163-174, December.
    20. Jiao Wang & Lima Zhao & Arnd Huchzermeier, 2021. "Operations‐Finance Interface in Risk Management: Research Evolution and Opportunities," Production and Operations Management, Production and Operations Management Society, vol. 30(2), pages 355-389, February.

    More about this item

    Keywords

    Econometric models; parameter separation; identified models; minimally sufficient statistics; psychometrics;
    All these keywords.

    JEL classification:

    • B41 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Economic Methodology
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C42 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Survey Methods
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • E60 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - General
    • H54 - Public Economics - - National Government Expenditures and Related Policies - - - Infrastructures
    • I11 - Health, Education, and Welfare - - Health - - - Analysis of Health Care Markets
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education
    • I31 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General Welfare, Well-Being
    • P11 - Political Economy and Comparative Economic Systems - - Capitalist Economies - - - Planning, Coordination, and Reform

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:jinter:v:35:y:2023:i:1:p:29-60. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.