Steady state of a Ramsey model is wrong in some cases

If a Lagrange multiplier appears in the Ramsey model with a lead or a lag of more than one period, the steady state may be wrong.

@MichelJuillard Could you please elaborate on why this is the case and what needs to be done to fix this

When there are lead or lag on more than one period, we add auxiliary variables to transform the model so as to have leads and lags on only one period. In order to get the first order condition of Ramsey problem right, one needs to compute FOC first THEN reduce the model to leads and lags on one period. Currently Dynare preprocessor does it in the wrong order. There a branch where this has been corrected, but it still needs testing. @sebastien-villemot was afraid of possible side effects.

Currently, the problem seems to be limited to expectation operator. We need to come up with a test case for this issue.

@MichelJuillard Could it be we have a test case in optimal_policy/Ramsey/ramsey_ex_aux.mod? See #1119 (closed)

YES! It is exactly it. I have started working of it but the solution is difficult.

mentioned in commit preprocessor@0169240f

mentioned in commit preprocessor@fe3f1894

mentioned in commit 69d0aa67