Consider the following 2 systems of equations:
System1:
y1=a1+b1y2+b2y3+b3z1+e1
y2=a2+b4y2+b5y3+b6z2+e2
y3=a3+b7y1+b8y2+b9z3+e3
System2:
y1=a1+b1y2+b2y3+b3z1+e1
y2=a2+b4y3+b5z2+e2
y3=a3+b6y1+b7y2+b8z3+e3
Estimating these 2 systems using 3SLS (reg3) works just fine.
However, while I'm able to reproduce the parameters of System1 using matrix language*, I'm not able to reproduce the parameters of System2. The first-stage regressions are correct (tested using reg3, first) and so are the second-stage regressions (tested using reg3, 2sls), but the final estimates are not. My gut feeling is that 'sigma' cannot be computed using the regular expressions for such asymmetric systems like System2. Can anybody refer to a paper or notes that do something similar?
*1. estimating the reduced form equations and saving the predicted y's, 2. estimating the structural equations using the predicted y's and saving the residuals, 3. computing 'sigma' using the residuals ((residuals' * residuals)/n) and using matrix language to compute the FGLS estimates
System1:
y1=a1+b1y2+b2y3+b3z1+e1
y2=a2+b4y2+b5y3+b6z2+e2
y3=a3+b7y1+b8y2+b9z3+e3
System2:
y1=a1+b1y2+b2y3+b3z1+e1
y2=a2+b4y3+b5z2+e2
y3=a3+b6y1+b7y2+b8z3+e3
Estimating these 2 systems using 3SLS (reg3) works just fine.
However, while I'm able to reproduce the parameters of System1 using matrix language*, I'm not able to reproduce the parameters of System2. The first-stage regressions are correct (tested using reg3, first) and so are the second-stage regressions (tested using reg3, 2sls), but the final estimates are not. My gut feeling is that 'sigma' cannot be computed using the regular expressions for such asymmetric systems like System2. Can anybody refer to a paper or notes that do something similar?
*1. estimating the reduced form equations and saving the predicted y's, 2. estimating the structural equations using the predicted y's and saving the residuals, 3. computing 'sigma' using the residuals ((residuals' * residuals)/n) and using matrix language to compute the FGLS estimates
