Interpreting main effects with interaction term of continuous variables

[Mihir Sharma]

Dear Statalisters,

I am working with an unbalanced panel data (385 observations, T=21, N=21). I am trying to estimate a fixed effects IV regression:

 xi: xtivreg2 y var1 var2 var4 var5 i.year (var3 var2_var3 = z var2_z), fe gmm cluster(id) partial(i.year)

var1, var2, var4, var5 are exogenous independent variables, var3 is endogenous and I instrument it using z. var2_var3 = var2*var3 and is instrumented using var3_z = var2*z. (-xtivreg2 is not allowing me to use -fvarlist- so I am constructing interactions manually).

Given that I have interaction terms in my specification, the coefficient for main effects, e.g. for var2 alone, is interpreted as the marginal impact of var1 conditional on var3=0. However, var3=0 is not a sensible value in my context. Is there a way for me to calculate the marginal impact of var1 if, say var3 is equal to its median or mean value instead? I was exploring the possibility of estimating the above xtivreg2 command on data that is centred on means (according to https://www3.nd.edu/~rwilliam/stats2/l53.pdf).

foreach v of var var1 var2 var3 var3 var5 z {
    sum `v', meanonly
    gen c`v' = `v' - r(mean)
}

xi: xtivreg2 y cvar1 cvar2 cvar4 cvar5 i.year (cvar3 cvar2_cvar3 = cz cvar2_cz), fe gmm cluster(id) partial(i.year)

But I am not sure if this is correct. (1) should I demean ALL the variables or only those which are interacted (var2 and var3)? (2) Is there a more straightforward way to interpret standalone main effects in such a model?

Many thanks,
Mihir

[Phil Bromiley]

You didn't get a quick reply. You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex. Also, simplify your question to the minimum needed to generate the problem you want us to address.

There is no good way to interpret standalone main effects in a model with interactions. The main effect is the influence if all the interacting variables equal zero, which is often not a meaningful set of values in the dataset. Demeaning changes where that zero lies, but that is all. You can get identical substantive results by correct choice of at() values in margins. So, you can easily run the estimate on the original variables and then do margins at whatever values you like.

[Mihir Sharma]

Got it, thanks Phil.