Example 21.3 Bivariate Probit Analysis
This example shows how to estimate a bivariate probit model. Note the INIT statement in the following program, which sets the initial values for some parameters in the optimization:
data a;
keep y1 y2 x1 x2;
do i = 1 to 500;
x1 = rannor( 19283 );
x2 = rannor( 19283 );
u1 = rannor( 19283 );
u2 = rannor( 19283 );
y1l = 1 + 2 * x1 + 3 * x2 + u1;
y2l = 3 + 4 * x1 - 2 * x2 + u1*.2 + u2;
if ( y1l > 0 ) then y1 = 1;
else y1 = 0;
if ( y2l > 0 ) then y2 = 1;
else y2 = 0;
output;
end;
run;
/*-- Bivariate Probit --*/
proc qlim data=a method=qn;
init y1.x1 2.8, y1.x2 2.1, _rho .1;
model y1 = x1 x2;
model y2 = x1 x2;
endogenous y1 y2 ~ discrete;
run;
The output of the QLIM procedure is shown in Output 21.3.1.
Output 21.3.1
Bivariate Probit Analysis Results
2 |
y1 y2 |
500 |
-134.90796 |
3.23363E-7 |
17 |
Quasi-Newton |
283.81592 |
313.31817 |
1 |
1.003639 |
0.153678 |
6.53 |
<.0001 |
1 |
2.244374 |
0.256062 |
8.76 |
<.0001 |
1 |
3.273441 |
0.341581 |
9.58 |
<.0001 |
1 |
3.621164 |
0.457173 |
7.92 |
<.0001 |
1 |
4.551525 |
0.576547 |
7.89 |
<.0001 |
1 |
-2.442769 |
0.332295 |
-7.35 |
<.0001 |
1 |
0.144097 |
0.336459 |
0.43 |
0.6685 |