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Posted 06-26-2018 12:49 PM
(1804 views)

I have a multiple regression equation with year and industry fixed effect as below.

y = x1 + D + x1*D + FE + error (x1 is continuous and D is binary)

and I have another dummy variable (let's say, Z = 0 or 1).

What I want to see is if the coefficients on x1*D are statistically significantly different for the subsample Z =1 and Z=0.

What I have tried is 3-way interaction (x1*D*Z). However, because of fixed effects, the difference in the coefficient on x1*D from separate regression for Z=0 and Z=1 is not the same as the coefficient on 3-way interaction. (Separate regression allows the error term to vary separately whereas 3-way interaction multiple regression does not)

In the end, what I want is 3 columns with the coefficients for Z=0, Z=1, and the difference. Is there some type of test in SAS where I can achieve this?

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I apologize that my explanation was inadequate. FE is for fixed effect. So original model looks like below.

y = α1 x1 + α2 D + α3 x1*D + α4 d_1990 + α5 d_1991 + ... + d_2017 + d_sic1 + d_sic2 + ... + d_sic48 + error

where d_1990 to d_2017 are year dummies and d_sic1 to d_sic48 are industry dummies.

What I want is to look at the difference in α3 for the sample with Z=0 and the sample with Z=1.

But because of FE (fixed effects) that are laid out as d_1990 to d_2017 and d_sic1 to d_sic48, if I run the regression separately for Z=0 group and Z=1 group, the the difference in α3 from the two regressions is not the same as the coefficient on 3-way interaction (x1*D*Z) from 1 multiple regression with bunch of interactions.

I know the intuition and interpretation won't be different, but I need the numbers (the difference and the 3-way interaction) to be the same to put in my result table.

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why do you create indicator variables instead of using a class statement? Running the models separately versus using an interaction won't necessarily give exactly the same result; i would use the interaction, others have discussed it in detail eg: https://www.lexjansen.com/pharmasug/2009/po/PO08.pdf

https://communities.sas.com/t5/SAS-Statistical-Procedures/How-to-do-subgroup-analysis/td-p/82638

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