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A Property of the Leontief Inverse and its Applications to Comparative Static Analysis

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  • Lisheng Zeng

Abstract

We arbitrarily choose a submatrix of order 2 in the Leontief inverse matrix B . If a main diagonal element in the submatrix is a main diagonal element in B , then the determinant of the submatrix is non-negative; in particular, if the two main diagonal elements in the submatrix are all the main diagonal elements in B , then the determinant of the submatrix is greater than or equal to 1. This property can be used in the comparative static analysis for the input-output model. For example, when the change only occurs in one sectoral final demand or one corresponding row of the input coefficient matrix, which leads to a change of this sectoral gross output, the equivalent conditions that the absolute value of the rate of change of this sectoral gross output is larger than or equal to all other sectoral change rates and larger than at least one sectoral rate of change are shown. It is impossible to derive the exact results for the comparative static analysis if the property is not applied. A previous fault confirms this point.

Suggested Citation

  • Lisheng Zeng, 2001. "A Property of the Leontief Inverse and its Applications to Comparative Static Analysis," Economic Systems Research, Taylor & Francis Journals, vol. 13(3), pages 299-315.
    • Handle: RePEc:taf:ecsysr:v:13:y:2001:i:3:p:299-315
    DOI: 10.1080/09537320120070185
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    References listed on IDEAS

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    1. Sonis, Michael & Hewings, Geoffrey J.D., 1998. "Temporal Leontief Inverse," Macroeconomic Dynamics, Cambridge University Press, vol. 2(1), pages 89-114, March.
    2. Michael Sonis & J. D. Hewings & Jiemin Guo, 2000. "A New Image of Classical Key Sector Analysis: Minimum Information Decomposition of the Leontief Inverse," Economic Systems Research, Taylor & Francis Journals, vol. 12(3), pages 401-423.
    3. repec:cup:macdyn:v:2:y:1998:i:1:p:89-114 is not listed on IDEAS
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    Cited by:

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    2. Umed Temurshoev, 2010. "Identifying Optimal Sector Groupings With The Hypothetical Extraction Method," Journal of Regional Science, Wiley Blackwell, vol. 50(4), pages 872-890, October.
    3. Zeng, Lisheng, 2014. "Two kinds of Pareto improvements of the economic system: An input–output analysis using the nonnegative matrices theory," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 12-19.

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