I was wondering if anyone has managed to simulate the Iacoviello 2005 (House prices, borrowing constraints, and monetary policy in the business cycle). If so could you please help me with the code and uploade it on this forum? I am trying to simulate the 2013 paper (financial business cycle) but first l want to undersatnd how he goes about it in the 205 paper.

This model is in the database. You have to log in or register to download it. The model is under the short name of US_IAC05.
US_IAC05: Iacoviello (2005)

Regarding the Iacoviello model (2005), I don’t understand the first-order condition with respect to capital in the extended model (the first equation p.760 of the AER version).
I use the specification of capital adjustment cost provided p.747 but I can’t find the same result as Iacoviello.
It seems to me that the first-order equation provided p.760 is partly derived with respect to K_(t-1) which I don’t understand because K_t is the control variable in period t.
I am probably missing something but I can’t see what.

That equation in the Appendix is clearly wrong. The correct equation is equation (11) in www2.bc.edu/matteo-iacoviello/research_files/AER_TA_2005.pdf. You can see on page 7 of that document that there are various timing errors when translating equations (6) and (7) into (xx). Therefore the equation in the Appendix of the AER paper on page 760 is wrong, while the linearized FOC is correct again.