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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.

Derivation Attempt

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    $\begingroup$ Apart from the fact that photos to avoid mathjax are rather frowned upon here, the real issue is that we should have to look at the cards (shown at the bottom) to understand your attempt at the derivation. It is my impression that you should present clearly in your question the subset of the derivation problem that causes you trouble (requiring from us to go through the whole paper in order to understand all symbols and how we can help you, is a bit too much, don't you think?) $\endgroup$ – Alecos Papadopoulos May 19 '16 at 15:12
  • $\begingroup$ Alecos, that's a fair point. I apologize. My main confusion is in tackling the derivation on the bottom of page 52 in trying to derive equation 17 and 18 from 16. I attempted this by matching items from the matrix of equation 15 and 14. It is not needed to go through the entire paper. I believe this is a Linear Algebra exercise but I am unable to proceed forward. $\endgroup$ – jussplayin16 May 22 '16 at 16:37

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