4-way interactions

[Nicolas Orgeira]

Hi,

I am looking for suggestions on how to analyse heterogenous effects of an intervention. I am working with a panel data, with respondents of two different types (type A and type B), allocated in two different treatment groups (Control and Treatment). I have generated three dummy variables: type (for respondent type), treatment (for treatment group allocation) and time (for data collection periods).

To evaluate the effect of the intervention by treatment group, I first ran a simple difference-in-differences regression:

regress outcomevar time#treatment

And then a 3-way interactions, to evaluate the effect by respondent type:

regress outcomevar time##treatment##type

Finally, I would also like to measure the effect depending on whether respondents are more or less satisfied with a given service between periods. I have generated another dummy variable services (1 if increase in service satisfaction, 0 if decrease). As such, the code I am using is:

regress outcomevar time##treatment##services

I was wondering if it is econometrically accurate to add a fourth interaction to evaluate the effect by respondent type? i.e.:

regress outcomevar time##treatment##services##type

Or if I should use another method?

Thank you very much

[Carlo Lazzaro]

Nicolas:
two comments on your codes:
- assuming you want to go diff-indiff, I would however rewrite your first code using -fvvarlist- notation:

regress outcomevar i.time#i.treatment

- in my experience, interactions that includes more than two predictors are really difficult to understand and very unlike to be disseminated successfully in papers/research reports/conference speechs.

[Nicolas Orgeira]

Hi Carlo,

Thank you for your reply and for your constructive feedback, which I will reflect in my do-files.

- in my experience, interactions that includes more than two predictors are really difficult to understand and very unlike to be disseminated successfully in papers/research reports/conference speechs.

Regarding the interactions - I agree with you that using 4-way interactions is not ideal. I was wondering if you had any suggestions to analyse the effect of the intervention by respondent type and by service dummy using a diff-in-diff approach? Measuring the heterogenous treatment effects by respondent type and service dummy is a key hypothesis of the research and I would like to ensure that the method I am employing is econometrically accurate and supported by the literature.

Many thanks again