i cannot solve the Dynare functions in matlab, is there any thing wrong with my code

i want to solve the three variables as below:

i use two different codes:

syms X Y Z
[solX,solY,solZ]=solve('.9945*X^(-1/1.8)*( 0.35*(1-.5)*(.5*1.65)^(.5/(1-.5))*Y^(0.35-1) + 1 - .02 )=1','X - .343*Z^0.83=(1- .9625)','Z = .9945*X^(-1/1.8)*( ( (1/1.65-1)*(.5*1.65)^(1/(1-.5))*Y^0.35 )/( 1-(1-.9625)*.9945*X^(-1/1.8) ) )*(X-(1-.9625))','X','Y','Z')

and

function F = NKS(Z,alpha,xi,nu,delta,phi,chi,bbeta,psi,eta)

% Z(1) = Ngbar
% Z(2) = Kbar
% Z(3) = Sbar

F(1) = bbeta*Z(1)^(-1/psi)*( alpha*(1-xi)*(xi*nu)^(xi/(1-xi))*Z(2)^(alpha-1) + 1 - delta ) - 1;
F(2) = Z(1) - chi*Z(3)^eta -(1- phi);
F(3) = Z(3) - bbeta*Z(1)^(-1/psi)*( ( (1/nu-1)*(xi*nu)^(1/(1-xi))*Z(2)^alpha )/( 1-(1-phi)*bbeta*Z(1)^(-1/psi) ) )*(Z(1)-(1-phi));

end

Z0 = [1.05 ,1.7,0.09];
Z = fsolve(@(Z) NKS(Z,alpha,xi,nu,delta,phi,chi,bbeta,psi,eta),Z0);

Ngbar = Z(1);
Kbar = Z(2);
Sbar = Z(3);

and

bbeta = .9945;
psi = 0.8;
xi = 0.5;
nu = 1.65;
alpha = 1 -((xi/nu)-xi)/(1-xi);  
chi = .343;
phi = .98;
eta = .83;
delta = .02;

i know the initial value for Z0 is important, because i could get it solved, however, the value are complex.

In dynare, i cannot use complex value, so is any advice for this?

[Fabio Franceschini]

Did you find a solution at the end?

[Walter Roberson]

syms X Y Z
Q = @(v) sym(v);
Z = Q(.9945)*X^(-1/Q(1.8))*( ( (1/Q(1.65)-1)*(Q(.5)*Q(1.65))^(1/(1-Q(.5)))*Y^Q(0.35) )/( 1-(1-Q(.9625))*Q(.9945)*X^(-1/Q(1.8)) ) )*(X-(1-Q(.9625)));
Z = simplify(Z)

Z = 

expr(1,1) = Q(.9945)*X^(-1/Q(1.8))*( Q(0.35)*(1-Q(.5))*(Q(.5)*Q(1.65))^(Q(.5)/(1-Q(.5)))*Y^(Q(0.35)-1) + 1 - Q(.02) )==1;
expr(2,1) = X - Q(.343)*Z^Q(0.83) == 1-Q(.9625);
expr = simplify(expr)

expr = 

string(Z)

ans = "-(853281*Y^(7/20)*(X - 3/80))/(20*(160000*X^(5/9) - 5967))"

string(expr)

ans = 2×1 string array
    "(231/(1600*Y^(13/20)) + 49/50)/X^(5/9) == 2000/1989"
    "686*(-(853281*Y^(7/20)*(X - 3/80))/(20*(160000*X^(5/9) - 5967)))^(83/100) + 75 == 2000*X"

sol = vpasolve(expr)

sol = struct with fields:
    X: [0×1 sym]
    Y: [0×1 sym]

X = sol.X

 
X =
 
Empty sym: 0-by-1
 

Y = sol.Y

 
Y =
 
Empty sym: 0-by-1
 

Z = subs(Z,sol)

 
Z =
 
Empty sym: 0-by-1
 

[Walter Roberson]

My tests suggest that there are no real-valued solutions.

[Fabio Franceschini]

Interesting! Then I guess the problem lies in the derivation of the equations stated at the beginning