I use a conditional logit model with income, leisure time and interaction terms of the two variables with other variables (describing individual's characteristics) as independent variables.
After running the regression, I use the predict command to obtain probabilities for each individual and category. These probabilities are then multiplied with the median working hours of the respective categories to compute expected working hours.
The next step is to increase wage by 1%, which increases the variable income by 1% and thus also affects all interaction terms which include the variable income.
After running the modified regression, again I use the predict command and should obtain slightly different probabilities. My problem is now that the probabilities are exactly the same, so that there would be no change in expected working hours, which indicates that something went wrong.
On the attached images with extracts of the two regression outputs one can see that indeed the regression coefficients of the affected variables are very, very similar and that both the value of the R² and the values of the log likelihood iterations are exactly the same. To my mind these observations should explain why probabilities are indeed very similar, but I am wondering why they are exactly the same and what I did possibly wrong. I am replicating a paper where they did the same and where they were able to compute different expected working hours for the different scenarios.
Hello Max,
Maybe I'm missing something in your explanation, but if the only distinction between model 1 and model 2 is a linear trasnform of the variable, income (e.g., income for model 2 = income * 1.01), why should any of the coefficients or associated predicted log-odds, odds, or probabilities change?
You're still modeling functionally the same IVs to account for status/level on the same DV, using the same cases.
Good luck with your work.
If you want to predict out of the sample (e.g., increasing wage in 1%), you could try to modify the wages and use the command predict.
See, for instance,
https://www.statalist.org/forums/forum/general-stata-discussion/general/1544410-hold-out-sample-or-out-of-sample-estimation-of-logit-model
Either something went wrong or performed the same test. Did you use the same version of the software as the original study?
Thank you for all your answers. Due to some other projects this project was on hold so that I am coming back to you now.
David Morse Yes, indeed the only difference is a linear transformation of the varibale income. But as the authors describe it, this is what they do, too. According to one of the authors they also used the predict command. The discription of their method as explained in the paper is attached.
José-Ignacio Antón How exactly would you intend to modify the wages? Probably I have to do some out-of-sample prediction, but I do not know how to proceed here.
Valentine Joseph Owan I used Stata and so did the authors of the original study. They also told me they used the predict command:
"We used the estimates to get the probability for each category of hours using the "predict" command. And with the probability for each category, we could then calculate the expected value (i.e., how many hours were chosen). [Note: This worked for me as well] Using the estimation parameters from the baseline scenario, we ran the whole thing for a 1% higher hourly wage, and the difference between the two hourly expected values then gives the elasticity." If I run it with the 1% higher hourly wage (which affects the variable income), I obtain the same probabilities so that I cannot compute the difference.
I would be very grateful if someone could help me out. Thank you!
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