A test for Kronecker Product Structure covariance matrix

We propose a test for covariance matrix to have Kronecker Product Structure (KPS). KPS implies reduced rank restriction on certain transformation of the and new procedure is an adaptation Kleibergen Paap (2006) test. To derive limiting distribution Wald type statistic proves challenging partly because singularity estimator that appears in weighting matrix. show has ? 2 null with degrees freedom equal number restrictions tested. Local asymptotic power results are derived. Monte Carlo simulations reveal good size properties Re-examining fifteen highly cited papers conducting instrumental variable regressions, we find not rejected 56 out 118 specifications at 5% nominal size.