panel system using GMM

[Philippe Rous]

Hi Gareth !

I want to estimate a two equations model with panel data (N = 10, T = 5)

Y1 and Y2 are the endogenous ; X1 and X2 are the exogenous ; D_1, D_2,... , D_10 are individual dummies

The equations are :

Equation: Y1 = DUM1(1) * D_1 + DUM1(2) * D_2 + DUM1(3) * D_3 +
DUM1(4) * D_4 + DUM1(5) * D_5 + DUM1(6) * D_6 + DUM1(7)
* D_7 + DUM1(8) * D_8 + DUM1(9) * D_9 + DUM1(10) * D_10 +
C(3) * Y2 + C(4) * X1

Equation: Y2 = DUM2(1) * D_1 + DUM2(2) * D_2 + DUM2(3) * D_3 +
DUM2(4) * D_4 + DUM2(5) * D_5 + DUM2(6) * D_6 + DUM2(7)
* D_7 + DUM2(8) * D_8 + DUM2(9) * D_9 + DUM2(10) * D_10 +
C(8) * Y1 + C(10) * X2

At first, I have estimated the two equations
* separately
* using GMM
* a fixed individual effects option
* the same set of instruments for the two equations (Instruments: D_1 D_2 D_3 D_4 D_5 D_6 D_7 D_8 D_9 D_10 X1 X2)
* White cross section covaraiance matrix (allowing for individual heteroscedasticity)

Then, I estimated the two equations
* simultaneously
* using GMM
* the same set of instruments for the two equations (Instruments: D_1 D_2 D_3 D_4 D_5 D_6 D_7 D_8 D_9 D_10 X1 X2)
* White cross section covariance matrix

The estimated coefficients induced by these two methods are the same ; the estimated std deviations are not.

Unless I'm mistaken, White cross section option, in this last method, only allows for heteroscedasticity betwwen the errors of the two equations and not for heteroscedasticity between the N individual errors. Is it true ??? And, if so, is there any way to take into account these two heteroscedasticity sources ?

Thanks a lot !

Phil

[EViews Gareth]

You are correct, an there is no way I can think of to account for the heteroskedasticity.