Predicting outcome in Sample Selection Model using PROC QLIM

[ZMX]

I was looking at the example below on the SAS website and I was wondering how to use the results of this model to predict unconditional wages (ie. E(w) versus E(w|inlf=1).

Are the wages predicted using the second regression conditional wage (ie. E(wage|inlf=1) )?

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

 Thanks for the help.

[SASCom1 · Accepted solution]

Hello @ZMX ,

You can obtain unconditional expected value and conditional expected values using the EXPECTED and CONDITOINAL options in the OUTPUT statement directly in PROC QLIM.

For the sample selection model, the PREDICTED value is equal to the EXPECTED value, which is also equal to the XBETA value for the continuous dependent variable in the main equation(lwage in the example). You can verify this by specifying the OUTPUT statement like below:

 output out = outdata expected xbeta predicted conditional mills ;

and look at the outdata data set.

The conditional expected value differs from the  expected/predicted/xbeta values by adding to it another term,  rho*sigma_lwage*Mills_inlf, in other words,

Predicted_lwage = Expected_lwage = xbeta_lwage  ;

Conditional_lwage = xbeta_lwage + rho*sigma_lwage*Mills_inlf ;

I hope this helps.

[SASCom1]

@ZMX ,

Sorry, in my previous post, 'CONDITOINAL' is a typo, it should be CONDITIONAL 🙂 

[ZMX]

It did help. Thank you for the response. 🙂