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

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