Input-Output Tables and Some Theory of Defective Matrices

Authors

Mohit Arora, University of Massachusetts AmherstFollow
Deepankar Basu, University of Massachusetts AmherstFollow

Working Paper Number

2022-14

Publication Date

2022

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 propagation relies on eigendecomposition of relevant input-output matrices. It is well known that only diagonizable matrices can be eigendecomposed; 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 eigenvalues. To apply our results, we offer examples of input-output tables from India in the 1950s that were not diagonalizable and were hence, defective.

DOI

https://doi.org/10.7275/pkv2-jm10

License

UMass Amherst Open Access Policy

Recommended Citation

Arora, Mohit and Basu, Deepankar, "Input-Output Tables and Some Theory of Defective Matrices" (2022). Economics Department Working Paper Series. 331.
https://doi.org/10.7275/pkv2-jm10