Hi Sébastien,
thank you for your help. The first part of your answer mostly clarifies the issue. Unfortunately, the second issue still puzzles me.
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The steady state is numerically stable. Although I use fsolve in the steady state-file, I always get the same steady state values for all variables. In contrast to csminwel, fsolve works deterministically, so there is no random element, if I keep parameters constant. I explicitely checked for the stability of the steady state estimates by saving oo_.steady_state from order=1 and order=2 and comparing it in Matlab with the isequal command. They are identical. I did the same with Matlab 2009a 64bit and 2009b 64 bit and the steady states are also identical. The same applies to the eigenvalues saved in oo_.dr1.eigval. Hence, the steady state should not be the issue.
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The problem with the different IRs is not due to 32-bit vs. 64-bit systems. Rather, there is a difference in the IRs between Matlab 2009a and 2009b, but I do not know why this is the case.
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I could trace back the third issue in my initial post (second order IRs do not work while first order IRs do) to the NaNi in the eigenvalues as described in a related post [NaN in the list of eigenvalues) .