Programming the statistical procedures from SAS

Simultaneous Eqns. & GMM Est.

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Simultaneous Eqns. & GMM Est.

Hello,

I want to estimate a simultaneous equations model using GMM (2-step GMM/iterated GMM or continuously updated GMM) estimation technique.

I want to jointly estimate the equations using system estimation technique (both equations together).

I have the following two equations:

(1) Y1=a0+a1*Y2+a2*X1+a3*L1+e1.
(2) Y2=b0+b1*Y1+b2*X2+b3*L2+e2.

Where Y2 is the endogenous regressor in eqn. (1) and Y1 is endogenous regressor in eqn. (2). X1 and X2 are sets of included exogenous regressors in each equation respectively (X1 & X2 may also have some common variables). L1 is the set of excluded exogenous variables or instrumental variables for Y2 in eqn. (1) and L2 is the set of excluded exogenous variables or instrumental variables for Y1 in eqn. (2). e1 & e2 are independent but heteroskedastic errors.

(1) Can anyone tell me how to do SIMULTANEOUS EQUATIONS GMM estimation in SAS?

I have seen examples using the Klein model in SAS-ETS website but I could not understand what variables to supply under the option 'INSTRUMENTS'. Do I have to feed in all the included & excluded exogenous variables in there?

Here is the example:

proc syslin data=klein outest=b liml;
endogenous c p w i x wsum k y;
instruments klag plag xlag wp g t yr;
consume: model c = p plag wsum;
invest: model i = p plag klag;
labor: model w = x xlag yr;
run;

Using the above commands for my equations:

proc syslin data=A outest=B GMM;
endogenous Y1 Y2;
instruments X1 X2 L1 L2;
model Y1= Y2 X1;
model Y2= Y2 X2;
run;

(2) Is the above command correct? Instead of 'liml' can I use 'gmm' option? Is there separate commands for 2-step GMM or iterated GMM or continuously updated GMM?

(3) How then SAS understands that L1 instruments are for Y2 regressor and L2 instruments are for Y1 regressor (since I have supplied both under 'instruments')?

(4) Is there any other commands or options in SAS to do simultaneous equation GMM estimation?

(5) Also how to test instruments in SAS (overidentifying restriction tests, first-stage F-stat, weak identification test etc..)?

Please, please help.

Thank you in advance.

Regards,

Nil
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