The MODEL Procedure

(View the complete code for this example.)

This example illustrates how to use SMM to estimate a simple linear regression model for the following process:

In the following SAS statements, is simulated, and the first moment and second moment of are compared with those of the observed endogenous variable y:

title "Simple regression model";

data regdata;
   do i=1 to 500;
      x = rannor( 1013 );
      Y = 2 + 1.5 * x + 1.5 * rannor( 1013 );
      output;
   end;
run;

proc model data=regdata;
   parms a b s;
   instrument x;

   ysim = (a+b*x) + s * rannor( 8003 );
   y = ysim;
   eq.ysq = y*y - ysim*ysim;

   fit y ysq / gmm ndraw;
   bound s > 0;
run;

Alternatively, the MOMENT statement can be used to specify the moments using the following syntax:

proc model data=regdata;
   parms a b s;
   instrument x;

   ysim = (a+b*x) + s * rannor( 8003 );
   y = ysim;
   moment y = (2);

   fit y / gmm ndraw;
   bound s > 0;
run;

The output of the MODEL procedure is shown in Output 25.15.1.