A test for kronecker product structure covariance matrix
We propose a test for a covariance matrix to have Kronecker Product Structure (KPS). KPS implies a reduced rank restriction on a certain transformation of the covariance matrix and the new procedure is an adaptation of the Kleibergen and Paap (2006) reduced rank test. To derive the limiting distribu...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Elsevier
2022
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| Summary: | We propose a test for a covariance matrix to have Kronecker Product Structure
(KPS). KPS implies a reduced rank restriction on a certain transformation of
the covariance matrix and the new procedure is an adaptation of the Kleibergen
and Paap (2006) reduced rank test. To derive the limiting distribution of the
Wald type test statistic proves challenging partly because of the singularity
of the covariance matrix estimator that appears in the weighting matrix. We
show that the test statistic has a chi square limiting null distribution with
degrees of freedom equal to the number of restrictions tested. Local asymptotic
power results are derived. Monte Carlo simulations reveal good size and power
properties of the test. Re-examining fifteen highly cited papers conducting
instrumental variable regressions, we find that KPS is not rejected in 56 out
of 118 specifications at the 5% nominal size. |
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