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Sébastien Villemot's avatar
Sébastien Villemot authored
The computing of the Ramsey steady state relies on the fact that Lagrange
multipliers appear linearly in the system to be solved. Instead of directly
solving for the Lagrange multipliers along with the other variables,
dyn_ramsey_static.m reduces the size of the problem by always computing the
value of the multipliers that minimizes the residuals, given the other
variables (using a minimum norm solution, easy to compute because of the
linearity property). That function thus needs the derivatives of the optimality
FOCs with respect to the multipliers. The problem is that, when multipliers
appear in an auxiliary variable related to a lead/lag, then those derivatives
need to be retrieved by a chain rule derivation, which cannot be easily done
with the regular static file.

This commit implements the creation of a new file,
ramsey_multipliers_static_g1.{m,mex}, that provides exactly the needed
derivatives w.r.t. Lagrange multipliers through chain rule derivation.

Ref. dynare#633, dynare#1119, dynare#1133
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