How can I estimate nonlinear parameter simultaneous equation with endogeneity

Hi all,

I would like to estimate the nonlinear parameterised demand system with endogeneity problem using MATLAB. Basically, my model is

 e1(i)=a1*g+b1*p1(i) +a1*(d*m(i)-b1*p1(i)-b2*p2(i)-b3*p3(i))
 e2(i)=a2*g+b2*p2(i) +a2*(d*m(i)-b1*p1(i)-b2*p2(i)-b3*p3(i))
 e3(i)=a3*g+b3*p3(i) +a3*(d*m(i)-b1*p1(i)-b2*p2(i)-b3*p3(i))

In which, e1, e2, e3 are expenditure of foods, p1, p2,p3 are food prices and z1,…,z12 are instruments such as unemployment rate, wage rate and so forth. Conditions are a1+a2+a3=1

I know that there are simultaneous endogeneity between prices and quantity so that I need to use instruments.

This is a non-linear parameter model so first, I need to estimate reduce forms of prices and use predicted prices as exogenous variable. Then I need to calculate and replace the weighting matrix use in nonlinear seemingly unrelated regression, probably using nlinfit. However, I do not know how to code it in MATLAB. I really appreciate if you can give me some hints for this problem.

Thank you so much.

With best regards,

Son