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The Regrettable Loss of Mathematical Molding in Econometrics

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Book cover Mechanism and Causality in Biology and Economics

Part of the book series: History, Philosophy and Theory of the Life Sciences ((HPTL,volume 3))

Abstract

Although most accounts on causality discuss the specific role statistics and theory should have, it is taken for granted that they at least have a role in finding causal structures. The role for mathematics is not so obvious. However, before what is called the Probabilistic Revolution in econometrics, identification of causal relations was not a matter of economic-theoretical and statistical significance alone. Mathematical molding was considered as an essential tool in finding significant causal factors. In the 1940s, mathematical molding disappeared in the changeover from methods to specify causal mechanisms of business cycles to methods to identify economic structures, that is, invariant relationships underlying the workings of an economy. Mathematical molding could fulfill its role in modeling business cycle mechanisms because of the assumed close connection between mathematical representations of the business-cycle phenomenon and those of the explanatory mechanism. When the econometric program shifted its focus from mechanisms explaining phenomena to uncovering structural relationships, direct feedback from the phenomenon to the mechanism was lost and the role of mathematical molding ceased to exist.

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Notes

  1. 1.

    See, for example, the opening sentence of Aldrich’s (1989) paper on Autonomy: “Knowledge of structure is valuable and available – but only to those prepared to use both economic theory and statistical analysis.”

  2. 2.

    This explains the name “quadrature theory.” Quadrature stands for the process of determining the area of a plane geometric figure by dividing it into a collection of shapes of known area (usually rectangles) and then finding the sum of these areas. The integral denotes this process for infinitesimal rectangles.

  3. 3.

    Translated by the author.

  4. 4.

    This was not Frisch’s terminology, but Koopmans’. Aldrich (1994) gives an account of the development of the identification theory from Frisch to Koopmans by focusing on Haavelmo (1944), including a discussion of the change in terminology.

  5. 5.

    Boumans (1995), which discusses the more technical details of Frisch’s memorandum, also provides the derivation of this rule.

  6. 6.

    In Boumans (2005), it is shown that Haavelmo’s definitions of potential and factual influences can be represented in this way.

  7. 7.

    Both monographs are considered as containing the main body of the Cowles Commission’s theoretical results (see Christ 1994, p. 32).

  8. 8.

    For a more sophisticated account of this convergence, see Chao (2009), where he distinguishes between the invariance view and the theory view. Autonomy is equivalent to invariance but “does not say anything about the constitution of a system” (p. 71). So, the convergence is best described as the “invariance view of structure.”

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Authors and Affiliations

  1. Amsterdam School of Economics, University of Amsterdam, Valckenierstraat 65, 1018 XE, Amsterdam, The Netherlands

    Marcel Boumans

  2. Erasmus Institute for Philosophy and Economics, Erasmus University Rotterdam, Rotterdam, The Netherlands

    Marcel Boumans

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  1. Marcel Boumans
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Correspondence to Marcel Boumans .

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Editors and Affiliations

  1. Economics, National Tsing Hua University, Hsinchu, Taiwan

    Hsiang-Ke Chao

  2. Philosophy, National Tsing Hua University, Hsinchu, Taiwan

    Szu-Ting Chen

  3. Department of Philosophy, University of California, Davis, Davis, California, USA

    Roberta L. Millstein

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Boumans, M. (2013). The Regrettable Loss of Mathematical Molding in Econometrics. In: Chao, HK., Chen, ST., Millstein, R. (eds) Mechanism and Causality in Biology and Economics. History, Philosophy and Theory of the Life Sciences, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2454-9_4

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