61 lines
3.0 KiB
Matlab
61 lines
3.0 KiB
Matlab
% [unc_welfare, U_dynpp_derivs, W_dynpp_derivs, U_dyn_derivs, W_dyn_derivs] = k_order_welfare(dr, DynareModel, DynareOptions)
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% computes a k-th order approximation of welfare
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%
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% INPUTS
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% dr: struct describing the reduced form solution of the model.
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% DynareModel: struct jobs's parameters
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% DynareOptions: struct job's options
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%
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% OUTPUTS
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%
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% unc_welfare double approximation of conditional welfare from the non-stochastic steady state and allowing stochastic shocks
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%
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% U_dynpp_derivs struct Derivatives of the felicity function in Dynare++ format.
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% The tensors are folded and the Taylor coefficients (1/n!) are
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% included.
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% Fieldnames are U_0, U_1, U_2, …
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% W_dynpp_derivs struct Derivatives of the welfare function in Dynare++ format.
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% The tensors are folded and the Taylor coefficients (1/n!) are
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% included.
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% Fieldnames are W_0, W_1, W_2, …
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% U_dyn_derivs struct Derivatives of the felicity function in Dynare format, up to third order.
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% Matrices are dense and unfolded. The Taylor coefficients (1/2
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% and 1/6) aren't included.
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% The derivatives w.r.t. different categories of variables
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% are separated.
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% Fieldnames are:
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% + Uy, Uu
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% + if order ≥ 2: Uyy, Uyu, Uuu, Uss
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% + if order ≥ 3: Uyyy, Uyyu, Uyuu, Uuuu, Uyss, Uuss
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%
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% W_dyn_derivs struct Derivatives of the welfare function in Dynare format, up to third order.
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% Matrices are dense and unfolded. The Taylor coefficients (1/2
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% and 1/6) aren't included.
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% The derivatives w.r.t. different categories of variables
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% are separated.
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% Fieldnames are:
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% + Wy, Wu
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% + if order ≥ 2: Wyy, Wyu, Wuu, Wss
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% + if order ≥ 3: Wyyy, Wyyu, Wyuu, Wuuu, Wyss, Wuss
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%
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% k_order_welfare is a compiled MEX function. Its source code is in
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% dynare/mex/sources/k_order_welfare/k_order_welfare.cc and it uses code provided by
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% dynare++
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% Copyright © 2021 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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