Chamberlain-Mundlak CRE Model - computing the Average Marginal Effects

[Sasha Gulabivala]

I have a panel datatset and I am using the Chamberlain-Mundlak Correlated Random Effects probit model, as follows:

xtprobit saving1 $xlist $controllist $xbarlist $controlbarlist i.year, re vce(cluster hhid) nolog

I have only included screenshots of the key x variables below (not the control variables):




I would then like to calculate the average partial effects, APEs (which, according to http://stats.stackexchange.com/quest...artial-effects, is equivalent to average marginal effects, AMEs).

(1) In my first attempt, with margins, dydx($xlist), I am puzzled that the outcome is exactly identical to the regression coefficients . I do not understand why this has happened?


(2) I then used margins, dydx($xlist) predict(pu0), which returned a different outcome. I wonder whether this outcome is any better - it assumes u_i=0, and I am unsure whether it is valid for me to assume this, and whether I can justify this?



(3) I looked back at Prof Wooldridge's textbook (econometric analysis of cross section & panel data) on page 485 (chapter 15), where he talks about the Model I am using, and says the APEs can be calculated as such:

So I run the commands after my regression:

di 1/sqrt(1 + e(sigma_u)^2)

di (1/sqrt(1 + e(sigma_u)^2))*_b[prec]

Now I get a different result! Although I think this is the correct one as I followed Wooldridge, unless I misinterpreted it along the way.

So with three different methods, I have three different APEs.
E.g. for the APE of "prec", in (2) I got -0.0076146. In (3) I got -0.0015041. In (4) I got -0.0068522.

I wondered if anyone could please explain why my methods in (1), (2) or (3) might be correct or incorrect for the application of the CRE Probit model?

Many thanks

[Rose Simmons]

I also have a panel dataset and am using nonlinear methods. Like in your step (1), I too found that running margins dydx(*) returned the same outcome as the coefficients in the original regression. Could someone please suggest why this is the case?

[Sasha Gulabivala]

In https://www3.nd.edu/~rwilliam/stats3/Margins02.pdf Richard Williams obtains marginal effects that are the same as the slope coefficients. He says

This is because relationships are linear in OLS regression and do not vary depending on the values of the other variables

However, that is related to OLS regression (linear methods). I don't know what the explanation would be for nonlinear methods. Hopefully someone can advise please