Update Auxiliary variables authored by Normann Rion's avatar Normann Rion
...@@ -120,7 +120,7 @@ The auxiliary variable captures the result of this operation and ensures that: ...@@ -120,7 +120,7 @@ The auxiliary variable captures the result of this operation and ensures that:
* the aggregation is handled symbolically, * the aggregation is handled symbolically,
* and the associated value is available for inclusion in residual and Jacobian evaluation. * and the associated value is available for inclusion in residual and Jacobian evaluation.
## Type 15: heterogeneous model multipliers (since Dynare 7) ## Type 15: heterogeneous model multipliers (since Dynare 6.2)
Considerins heterogeneity dimension `j`, This kind of auxiliary variable has `M_.heterogeneity(j).aux_vars(i).type = 15` and is introduced to represent Lagrange multipliers associated with complementarity constraints in heterogeneous-agent models. These arise when an agent's decision is constrained by inequality bounds, such as borrowing constraints, portfolio limits, or non-negativity requirements. Considerins heterogeneity dimension `j`, This kind of auxiliary variable has `M_.heterogeneity(j).aux_vars(i).type = 15` and is introduced to represent Lagrange multipliers associated with complementarity constraints in heterogeneous-agent models. These arise when an agent's decision is constrained by inequality bounds, such as borrowing constraints, portfolio limits, or non-negativity requirements.
...@@ -139,7 +139,7 @@ ensuring that at most one of the two is active in equilibrium, and that compleme ...@@ -139,7 +139,7 @@ ensuring that at most one of the two is active in equilibrium, and that compleme
* if the bound is not binding, the multiplier is zero; * if the bound is not binding, the multiplier is zero;
* if the multiplier is strictly positive, the bound is tight. * if the multiplier is strictly positive, the bound is tight.
These multipliers are automatically inserted into the first-order conditions of the agent's problem. For instance, an Euler equation might become: These multipliers are automatically inserted into the first-order conditions of the agent's problem. For instance, an Euler equation might become:1e68b2fc
``` ```
u′(cₜ) = β · (1 + rₜ₊₁) · u′(cₜ₊₁) − MULT_L_a + MULT_U_a u′(cₜ) = β · (1 + rₜ₊₁) · u′(cₜ₊₁) − MULT_L_a + MULT_U_a
... ...
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