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Qualitative Matrices and Information


  • Andrew J. Buck

    () (Department of Economics, Temple University)

  • George M. Lady

    () (Department of Economics, Temple University)


This paper proposes a method for assessing the information content and validity of a mathematical structural model for which only the directions of influence among its endogenous and exogenous variables are known, as expressed by the sign patterns of associated arrays. The traditional literature on this issue presents extremely restrictive conditions under which such a “qualitative analysis” can be conducted. As a result, there have been very few successful applications of the traditional method. We propose a means of vastly expanding the scope of such an analysis to virtually any applied model. Our method works with the restrictions found for the sign patterns of complete rows and columns, or even the entire sign pattern, of the reduced form, rather than only individual entries. The information provided by the model is measured by the Shannon entropy of the possible sign patterns of the reduced form and the frequency of occurrence of each possibility. An example of the method is provided for Klein’s Model I. Although this model has been used for over fifty years for a variety of purposes, we found that the sign pattern of the estimated, unrestricted reduced form from the original data set was not consistent with the proposed, structural directions of influence among the model’s variables.

Suggested Citation

  • Andrew J. Buck & George M. Lady, 2010. "Qualitative Matrices and Information," DETU Working Papers 1003, Department of Economics, Temple University.
  • Handle: RePEc:tem:wpaper:1003

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    References listed on IDEAS

    1. Buck, Andrew J. & Lady, George M., 2005. "Falsifying economic models," Economic Modelling, Elsevier, vol. 22(5), pages 777-810, September.
    2. Kelvin Lancaster, 1962. "The Scope of Qualitative Economics," Review of Economic Studies, Oxford University Press, vol. 29(2), pages 99-123.
    3. Lady, George M, 1983. "The Structure of Qualitatively Determinate Relationships," Econometrica, Econometric Society, vol. 51(1), pages 197-218, January.
    4. Ritschard, Gilbert, 1983. "Computable Qualitative Comparative Static Techniques," Econometrica, Econometric Society, vol. 51(4), pages 1145-1168, July.
    5. Lady, George M. & Maybee, John S., 1983. "Qualitatively invertible matrices," Mathematical Social Sciences, Elsevier, vol. 6(3), pages 397-407, December.
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    More about this item


    Qualitative Analysis; Entropy; Falsification; Comparative Statics;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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