Interpretation of the triple difference-in-differences coefficient.

[Nicolas Orgeira]

Hi,

I am using a triple difference-in-differences to analyze the effect of an intervention where I suspect the impact will differ between the small and large firms:



where G is a dummy variable for the intervention group (treatment=1, control=0), T is the time period variable (also a dummy variable) and S is a dummy variable indicating the size of the firm (large firm=1).
From my understanding, beta 3 is the difference-in-differences coefficient and therefore the effect of the intervention on small firms while the effect of the intervention on large firms is equal to beta 3+ beta 7. I run the following regression on Stata:

xi: regress outcome_variable intervention##time_period##firm_size $covariates, vce(cluster region)

In the attached example (at the end of the log file), the difference-in-differences and triple differences coefficient for taxmorale2 are respectively -0.153* and -0.048.. If I understood well, that would mean that the effect of the intervention on large firms would be -0.153+(-0.048)=-0.201.

I was wondering if there is a way to determine the significance level of the coefficient -0.201? And to determine if there is a statistical difference in coefficient between the two coefficients?

Thank you for your help

[Clyde Schechter]

The .smcl file you attached appears to be some other product: the key variables in the model you show in #1 are mostly absent from the models in the .smcl file. Nor do I find any coefficients that look like -0.153 and -0.048. So I'll just ignore that attachment. Presumably your output does contain coefficients for 1.intervention#1.time_period and 1.intervention#1.time_period#1.firm_size. You can get confidence intervals and a test statistic for the sum of those coefficients by running

lincom 1.intervention#1.timer_period + 1.intervention#1.time_period#1.firm_size

[Nicolas Orgeira]

Dear Clyde,

Thank you very much, this is very helpful.

Apologies for attaching the wrong format for my log file. I have updated it. Near the very end, you should see a table with two columns (did and didid). For taxmorale2, the coefficient for did is -0.154* while the coefficient for didid is -0.048.

Using the lincom code you have suggested, I get the coefficient and standard error for the sum of the did and didid coefficients (equal to -0.202). I was wondering if there would be an way to replace the didid coefficient by -0.202 with its associated new standard error?

Thank you again for your help

[Clyde Schechter]

I don't myself use -esttab- and I have only a primitive acquaintance with what it can do. I don't know if what you ask can be done or not. If it can, I don't know how to do it.