linear-algebra


Linear Algebra Derivation in Gertler-Karadi (2015) AEJ


I'm having trouble following a derivation that Gertler-Karadi (2015) AEJ http://pubs.aeaweb.org/doi/pdfplus/10.1257/mac.20130329
do in their paper on Footnote 4 on the bottom of page 52. I've tried many attempts in deriving their equation 17 and 18 but to no avail. In particular, I can easily match elements of the matrix in (15) with that of (14) in order to get (16) but cannot move any further. I've concluded that this case is only true if s12 and s21 are scalars. I've attached a copy of the derivation thus far. Any advice would be greatly appreciated.

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