fsolve - Endogenous, Exogenous variables and Constants

Question

Konstantin 2014-2-15

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/116273-fsolve-endogenous-exogenous-variables-and-constants

Hello,

I have a system of nonlinear equations which I need to solve multiple times with different arguments.

This is the function that will be given to fsolve (7 equations 7 unknowns):

function F = myfun(x)
F=[ - x(1) + Cs + gama*( Km - Ks);
      x(2)*(gy - 1) + x(1) + x(3);
    - x(2) + ((A*x(7))^alpha)*(Km^(1-alpha)) ; 
    - alpha*x(2)/x(7) + x(6) ;
    ( ( varrho*x(1)^((1-varrho)*(1 - sigmac)) ) * ( (1 - x(7))^(varrho*(1-sigmac)-1) ) ) 
/ ( (1-varrho)*x(1)^((1-varrho)*(1 - sigmac) - 1) * ( (1-x(7))^(varrho*(1-sigmac)) ) ) - x(6);
    - x(5) - 1 + delta + ((1-alpha)*x(2)) / Km;
    - x(3) + x(4) - (1-delta)*Km;
    ]; 
end

1. The first problem that I had was that I cannot leave the Endog. variables (those for which we find solution) with their names such as: I, Y, C. Instead I had to rename them as x(1) ... x(n) and remember which field of the vector x is which variable. This makes the system less readable and more difficult to manipulate. Any advice how to avoid this?

2. It appears that any function in F can have only the Endog. arguments x(n) and even though all the: alpha, beta... are defined and have value in the memory when executed the function needs to take everything as an argument. Perhaps for the greeks which are constants I can just replace their value (which will also decrease the flexibility of the code), but for the other Exogenous variables: Cs, Km, Ks. That is impossible as their values will be updated before every fsolve. If I include them in x(n) that is wrong as they are not arguments and don't need to be solved for.

Is there any way to make fsolve take a system of equations which has its vector of arguments but also constants and exogenous variables for which it takes the current values from the memory?

I know that this can all be done with dynare. But I need to do it in Matlab alone.

Thanks