GMM moment conditions for time series?

[LzEr23]

Dear all,

I'm trying to run an estimation of a model using GMM.

And I would be very grateful if someone can help me on this.

Problem is, the data are in time series, and I am having trouble in setting the moment equations.

response var: resv

independent vars: x1, x2, x3, x4, x5 c1

time series length = 20

observations = 20

proc model data=work.gmmtest;
parms a1 a2 a3 a4 a5 p r;
endogenous resv;
instruments x1 x2 x3 x4 x5 c1;
eq.m1= resv-p*lag(resv);
eq.m2=           .......       ;
fit m1 m2  .... / gmm;
run; quit;

This is the code I used.

I put the first equation m1 that way since I was expecting an autocorrelation.

But, from there, I am not sure what to put as a moment condition here.

How should I set up the moment equation there?

[kessler · Accepted solution]

The moment conditions depend on the formulation of your model.  A simple model with a single moment condition which includes your 6 independent variables, 1 response variable, and an autocorrelated error term could be specified as:

proc model data=work.gmmtest;
   parms a1 a2 a3 a4 a5 p r;
   endogenous resv;
   instruments x1 x2 x3 x4 x5 c1;

   resvstruct = resv - (a1*x1 + a2*x2 + a3*x3 + a4*x4 + a5*x5 + r*c1);
   eq.m1= resvstruct -p*lag(resvstruct);
  
   fit m1  / gmm;
quit;

-Marc

[LzEr23]

Thank you. I did help.