How should matlab solve two nonlinear equations with two variables?

wangshiye · September 5, 2021, 1:13am

When dealing with the steady state of the model, I encountered two endogenous variables in two nonlinear equations, and I couldn’t solve them manually. Can matlab solve it? If so, is there any way? Thanks everyone for your help.

wangshiye · September 5, 2021, 3:17am

I noticed that the “vpasolve” function can be used to find a system of nonlinear equations. Can I solve the steady-state value directly, and assign the steady-state value to the solved value directly in dynare?

jpfeifer · September 6, 2021, 7:02am

You can use fsolve in a steady state file to deal with this issue. See for example

github.com

JohannesPfeifer/DSGE_mod/blob/master/Jermann_Quadrini_2012/Jermann_Quadrini_2012_RBC/Jermann_Quadrini_2012_RBC_steadystate.m

function [ys,params,check] = Jermann_Quadrini_2012_RBC_steadystate(ys,exo,M_,options_)
% [ys,params,check] = Jermann_Quadrini_2012_RBC_steadystate(ys,exo,M_,options_)
% computes the steady state for the Jermann_Quadrini_2012_RBC.mod and uses a numerical
% solver to do so
% Inputs: 
%   - ys        [vector] vector of initial values for the steady state of
%                   the endogenous variables
%   - exo       [vector] vector of values for the exogenous variables
%   - M_        [structure] Dynare model structure
%   - options   [structure] Dynare options structure
%
% Output: 
%   - ys        [vector] vector of steady state values for the the endogenous variables
%   - params    [vector] vector of parameter values
%   - check     [scalar] set to 0 if steady state computation worked and to
%                    1 of not (allows to impose restrictions on parameters)
%
% Copyright (C) 2014-2020 Johannes Pfeifer
% 
%  This is free software: you can redistribute it and/or modify

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wangshiye · September 7, 2021, 12:07pm

Thank you