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Contents
1. Introduction
2. Why are matrix methods useful in econometrics?
2.1. Linear systems and quadratic forms
2.2. Vectors and matrices in statistical theory
2.3. Least squares in the standard linear model
2.4. Vectors and matrices in consumption theory
3. Partitioned matrices
3. I, The algebra of partitioned matrices
3.2. Block-recursive systems
3.3. Income and price derivatives revisited
4. Kronecker products and the vectorization of matrices
4. I. The algebra of Kronecker products
4.2. Joint generalized least-squares estimation of several equations
4.3. Vectorization of matrices
5. Differential demand and supply systems
5.1. A differential consumer demand system
5.2. A comparison with simultaneous equation systems
5.3. An extension to the inputs of a firm: A singularity problem
5.4. A differential input demand system
5.5. Allocation systems
5.6. Extensions
6. Definite and semidefinite square matrices
6. I. Covariance matrices and Gauss-Markov further considered
6.2. Maxima and minima
6.3. Block-diagonal definite matrices
7. Diagonalizations
7.1. ne standard diagonalization of a square matrix
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*Research supported in part by NSF Grant SOC76-82718. The author is indebted to Kenneth
Clements (Reserve Bank of Australia, Sydney) and Michael Intriligator (University of California, Los
Angeles) for comments on an earlier draft of this chapter.
Hundhook of Econometrics, Volume I, Edited by Z. Griliches and M.D. Intriligator
0 North- Holland Publishing Company, I983
H. Theil
1.2. Special cases
7.3. Aitken’s theorem
7.4. The Cholesky decomposition
7.5. Vectors written as diagonal matrices
7.6. A simultaneous diagonalization of two square matrices
7.7. Latent roots of an asymmetric matrix
8. Principal components and extensions
8.1. Principal components
8.2. Derivations
8.3. Further discussion of principal components
8.4. The independence transformation in microeconomic theory
8.5. An example
8.6. A principal component interpretation
9. The modeling of a disturbance covariance matrix
9.1. Rational random behavior
9.2. The asymptotics of rational random behavior
9.3. Applications to demand and supply
10. The Moore-Penrose inverse
10.1. Proof of the existence and uniqueness
10.2. Special cases
10.3. A generalization of Aitken’s theorem
10.4. Deleting an equation from an allocation model
Appendix A: Linear independence and related topics
Appendix B: The independence transformation
Appendix C: Rational random behavior
References
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