Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/267004 
Year of Publication: 
2022
Series/Report no.: 
Working Paper No. 2022-14
Publisher: 
University of Massachusetts, Department of Economics, Amherst, MA
Abstract: 
Recent developments in the theory of production networks offer interesting applications and revival of input-output analysis. Some recent papers have studied the propagation of a temporary, negative shock through an input-output network. Such analyses of shock propa- gation relies on eigendecomposition of relevant input-output matrices. It is well known that only diagonalizable matrices can be eigende- composed; those that are not diagonalizable, are known as defective matrices. In this paper, we provide necessary and sufficient conditions for diagonalizability of any square matrix using its rank and eigenval- ues. To apply our results, we offer examples of input-output tables from India in the 1950s that were not diagonalizable and were hence, defective.
Subjects: 
input-output tables
diagonalizability
JEL: 
C60
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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