Eviews 3 stage least squares near singular matrix

[Econrocks]

I'm doing a replication paper and having a bit of issues. The author uses 2 instruments and has 4 endogenous variables. Since he is under-identified, he runs 4 separate regressions, so that each equation has 1 overidentifying restrictions. I want to extend this and run the four equations as a system, because I'm sure that the error terms for each equation is correlated. however, every time I run this, I get a "near singular matrix" error. I have written my system below.

essentially, I control for the fixed effects for the 8 countries in my data set, schooling, and urbanization in 1850. Each equation has a different variable that measure culture (control, obedience, tolerance, and trust). I am using the same instruments of institutions and literacy for each equation. so the only difference with each equation is which culture variable is being used.

System:

gdp_pc_ca9500= C(1)*country1 + C(2)*country15 + C(3)*country2 + C(4)*country3 + C(5)*country4 + C(6)*country5 + C(7)*country7 + C(8)*country8 + C(9)*school + C(10)*urb_1860_1850_30 + C(100)*control

gdp_pc_ca9500= C(12)*country1 + C(12)*country15 + C(14)*country2 + C(15)*country3 + C(16)*country4 + C(17)*country5 + C(18)*country7 + C(19)*country8 + C(20)*school + C(21)*urb_1860_1850_30 + C(101)*obedience

gdp_pc_ca9500= C(23)*country1 + C(24)*country15 + C(25)*country2 + C(26)*country3 + C(27)*country4 + C(28)*country5 + C(29)*country7 + C(30)*country8 + C(31)*school + C(32)*urb_1860_1850_30 + C(102)*tolerance

gdp_pc_ca9500= C(34)*country1 + C(35)*country15 + C(36)*country2 + C(37)*country3 + C(38)*country4 + C(39)*country5 + C(40)*country7 + C(41)*country8 + C(42)*school + C(43)*urb_1860_1850_30 + C(104)*trust

@inst pc_institutions literacy1880

My question is whether or not my problem lies in bad programming (if you can call eviews programming), or in something I'm missing in the theory. If I do it in 3SLS or Multiple equation Generalized method of moments, I get the near singular matrix error (which makes sense, since 3SLS is a special case of GMM).

I would appreciate any help

 

[Econrocks]

Nevermind: I figured out the problem. Putting it in a system doesn't solve the under-identification problem, and the near singular matrix issue goes away when I only included 2 of the equations/