The QLIM Procedure

## Example 21.4 Sample Selection Model

This example illustrates the use of PROC QLIM for sample selection models. The data set is the same one from Mroz (1987). The goal is to estimate a wage offer function for married women, accounting for potential selection bias. Of the 753 women, the wage is observed for 428 working women. The labor force participation equation estimated in the introductory example is used for selection. The wage equation uses log wage (lwage ) as the dependent variable. The explanatory variables in the wage equation are the woman’s years of schooling (educ ), wife’s labor experience (exper), and square of experience (expersq ). The program is as follows:

```   /*-- Sample Selection --*/
proc qlim data=mroz;
model inlf = nwifeinc educ exper expersq
age kidslt6 kidsge6 /discrete;
model lwage = educ exper expersq / select(inlf=1);
run;
```

The output of the QLIM procedure is shown in Output 21.4.1.

Output 21.4.1 Sample Selection
 Binary Data

The QLIM Procedure

Model Fit Summary
Number of Endogenous Variables 2
Endogenous Variable inlf lwage
Number of Observations 753
Log Likelihood -832.88509
Number of Iterations 78
Optimization Method Quasi-Newton
AIC 1694
Schwarz Criterion 1759

Parameter Estimates
Parameter DF Estimate Standard Error t Value Approx
Pr > |t|
lwage.Intercept 1 -0.552716 0.260371 -2.12 0.0338
lwage.educ 1 0.108351 0.014861 7.29 <.0001
lwage.exper 1 0.042837 0.014878 2.88 0.0040
lwage.expersq 1 -0.000837 0.000417 -2.01 0.0449
_Sigma.lwage 1 0.663397 0.022706 29.22 <.0001
inlf.Intercept 1 0.266459 0.508954 0.52 0.6006
inlf.nwifeinc 1 -0.012132 0.004877 -2.49 0.0129
inlf.educ 1 0.131341 0.025383 5.17 <.0001
inlf.exper 1 0.123282 0.018728 6.58 <.0001
inlf.expersq 1 -0.001886 0.000601 -3.14 0.0017
inlf.age 1 -0.052829 0.008479 -6.23 <.0001
inlf.kidslt6 1 -0.867398 0.118647 -7.31 <.0001
inlf.kidsge6 1 0.035872 0.043476 0.83 0.4093
_Rho 1 0.026617 0.147073 0.18 0.8564

Note the correlation estimate is insignificant. This indicates that selection bias is not a big problem in the estimation of wage equation.

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