Example 18.18 Duration Data Model with Unobserved Heterogeneity

All of the previous three models actually have closed-form moment conditions, so the simulation approach is not necessarily required for the estimation. This example illustrates how to use SMM to estimate a model for which there is no closed-form solution for the moments and thus the traditional GMM method does not apply. The model is the duration data model with unobserved heterogeneity in Gourieroux and Monfort (1993):

The SAS statements are:

title1 'SMM for Duration Model with Unobserved Heterogeneity';

%let nobs=1000;
data durationdata;
   b=0.9; s=0.5;
   do i=1 to &nobs;
      u = rannor( 1011 );
      v = ranuni( 1011 );
      x = 2 * ranuni( 1011 );
      y = -exp(-b * x + s * u) * log(v);
      output;
   end;
run;

proc model data=durationdata;
   parms b .5 s 1;
   instrument x;

   u = rannor( 1011 );
   v = ranuni( 1011 );
   y = -exp(-b * x + s * u) * log(v);

   moment y = (2 3 4);
   fit y / gmm ndraw=10 ;* maxiter=500;
   bound s > 0, b > 0;
run;

The output of the MODEL procedure is shown in Output 18.18.1.