The QLIM Procedure

## 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( 98721 );
u1 = rannor( 76527 );
u2 = rannor( 65721 );
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
 Estimating a Tobit model

The QLIM Procedure

Model Fit Summary
Number of Endogenous Variables 2
Endogenous Variable y1 y2
Number of Observations 500
Log Likelihood -134.90796
Number of Iterations 17
Optimization Method Quasi-Newton
AIC 283.81592
Schwarz Criterion 313.31817

Parameter Estimates
Parameter DF Estimate Standard Error t Value Approx
Pr > |t|
y1.Intercept 1 1.003639 0.153678 6.53 <.0001
y1.x1 1 2.244374 0.256062 8.76 <.0001
y1.x2 1 3.273441 0.341581 9.58 <.0001
y2.Intercept 1 3.621164 0.457173 7.92 <.0001
y2.x1 1 4.551525 0.576547 7.89 <.0001
y2.x2 1 -2.442769 0.332295 -7.35 <.0001
_Rho 1 0.144097 0.336459 0.43 0.6685

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