Probit Model: Coefficients Interpretation

[Mohsin Javed]

I have estimated the following equation using the probit model:

labour_force_participation = 0.270 + 0.131education + 0.123experience - 0.0019exper^2

Suppose now I want to find the relationship between the probability of labour force participation and experience, then as it is a Probit model the coefficient on experience and experience squared cannot be interpreted as we do in OLS regression. How to proceed ahead?

[Clyde Schechter]

If you didn't use factor variable notation when you ran the -probit-, go back and do so now, and then use -margins- and -marginsplot-

probit labour_force_participation education c.experience##c.experience
margins, at(experience = (list of values of experience))
marginsplot

In the -margins- command replace list of values of experience by a list of numbers corresponding to the range of values of experience that are of interest to you, and closely spaced enough that the resulting sort-of parabolic curve will come out reasonably smooth.

[Mohsin Javed]

Clyde Schechter:

1. Do we ignore the other explanatory variables? In this case, education?
2. Why have you used c.experience##c.experience? Can you explain it?
3. For list of values of experience, can I use the average experience?
4. Lastly, will -marginsplot- give the particular point at which the experience will start having a negative effect on the probability of Labour force participation?

[Clyde Schechter]

1. No, the -margins- command adjusts for education ( or any other variablesin the regression).

2. See -help fvvarlist-. It's the way you write a quadratic relationship in factor-variable notation.

3. Yes, but then you only get the predicted probability of labor force participation at that one value. You asked about the relationship between experience and participation--that can't be adequatlely described by a single point. If all you want to know is the extent of participation at average experience, that's fine, but that's not the relationship between those variables.

4. You can use -marginsplot- for that, but the syntax for that purpose would be different. And -marginsplot- is not the best way to do that. The probit function is monotone increasing. So the marginal effect of experience on participation will be negative precisely when the effect of experience on the Xb portion of your probit model is negative. Now dXb/d(experience) = coefficient of experience + 2*coefficient of experience^2 * experience, which in your case is

0.123 -2* 0.0019experience. So this will be negative when experience > 0.123/(2*0.0019), i.e. when experience > 32.37 (to two decimal places). So 32.37 (whatever the unit of time is) is your turning point in the relationship.

[Mohsin Javed]

Clyde Schechter : thanks a lot! I will check -fvvarlist-