Qualitative Matrices and Information
AbstractThis 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.
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Bibliographic InfoPaper provided by Department of Economics, Temple University in its series DETU Working Papers with number 1003.
Date of creation: Mar 2010
Date of revision:
Qualitative Analysis; Entropy; Falsification; Comparative Statics;
Find related papers by 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-03-20 (All new papers)
- NEP-CBA-2010-03-20 (Central Banking)
- NEP-ECM-2010-03-20 (Econometrics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Lady, George M, 1983. "The Structure of Qualitatively Determinate Relationships," Econometrica, Econometric Society, vol. 51(1), pages 197-218, January.
- Ritschard, Gilbert, 1983. "Computable Qualitative Comparative Static Techniques," Econometrica, Econometric Society, vol. 51(4), pages 1145-68, July.
- Lady, George M. & Maybee, John S., 1983. "Qualitatively invertible matrices," Mathematical Social Sciences, Elsevier, vol. 6(3), pages 397-407, December.
- Buck, Andrew J. & Lady, George M., 2005. "Falsifying economic models," Economic Modelling, Elsevier, vol. 22(5), pages 777-810, September.
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