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 22.4.1.
Output 22.4.1: Sample Selection
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.