recovering the estimate of an interaction term using margins

[Ariel Linden]

Hi All,

I am trying to recover the estimates of an interaction term produced by -regress- using -margins- (followed by -lincom-).

In the example below, the estimates for foreign and bin_wt derived by -margins- / -lincom- are the same as those as the coefficients in the regress output.

However, I can't figure out how to replicate the interaction term estimate of -2.742342 for 1.foreign#1.bin_wt in the regression output.

Thanks in advance!

Ariel

sysuse auto
gen bin_wt = weight > 3020
regress mpg i.foreign##i.bin_wt
margins foreign#bin_wt, coefl post
lincom _b[1.foreign#0bn.bin_wt]-_b[0bn.foreign#0bn.bin_wt] // reproduces coefficient for foreign
lincom _b[0bn.foreign#1.bin_wt]- _b[0bn.foreign#0bn.bin_wt] // reproduces coefficient for bin_wt

[Clyde Schechter]

lincom (_b[1.foreign#1.bin_wt]-_b[0.foreign#1.bin_wt]) - (_b[1.foreign#0.bin_wt] - _b[0.foreign#0.bin_wt])

That is why interaction terms like this are the basis of "difference in differences" analysis.

[daniel klein]

Well, in this saturated model, the coefficient of the interaction term is recovered as

lincom  ///
    (_b[1.foreign#1.bin_wt]-_b[0bn.foreign#1.bin_wt]) ///
    - (_b[1.foreign#0bn.bin_wt]-_b[0bn.foreign#0bn.bin_wt])

[Enrique Pinzon (StataCorp)]

To add to the suggestions, you could also use -margins- directly.

margins foreign, dydx(bin_wt) pwcompare
margins r.foreign, dydx(bin_wt)

This approach would also work to get interaction effects if -bin_wt- were a continuous variable. Think about it as -margins- computing double derivatives.

[Ariel Linden]

Thank you all!