The QLIM Procedure

Example 28.4 Sample Selection Model

(View the complete code for this example.)

This example illustrates the use of PROC QLIM for sample selection models. The data set is the 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 28.4.1.

Output 28.4.1: Sample Selection

Binary Data

The QLIM Procedure

Model Fit Summary
Number of Endogenous Variables2
Endogenous Variableinlf lwage
Number of Observations753
Log Likelihood-832.88509
Maximum Absolute Gradient0.00502
Number of Iterations78
Optimization MethodQuasi-Newton
AIC1694
Schwarz Criterion1759

Parameter Estimates
ParameterDFEstimateStandard
Error
t ValueApprox
Pr > |t|
lwage.Intercept1-0.5527160.260371-2.120.0338
lwage.educ10.1083510.0148617.29<.0001
lwage.exper10.0428370.0148782.880.0040
lwage.expersq1-0.0008370.000417-2.010.0449
_Sigma.lwage10.6633970.02270629.22<.0001
inlf.Intercept10.2664590.5089540.520.6006
inlf.nwifeinc1-0.0121320.004877-2.490.0129
inlf.educ10.1313410.0253835.17<.0001
inlf.exper10.1232820.0187286.58<.0001
inlf.expersq1-0.0018860.000601-3.140.0017
inlf.age1-0.0528290.008479-6.23<.0001
inlf.kidslt61-0.8673980.118647-7.31<.0001
inlf.kidsge610.0358720.0434760.830.4093
_Rho10.0266170.1470730.180.8564


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