Is a Logarithmic interaction term possible?

[Asma Zahel Kh]

Hello,
I'm currently working on an econometric conflict model, where I've taken the natural logarithms of my independent and dependent variables mainly to reduce data skewness. Now I want to add a variable interaction, but I'm not sure if it's interfering and if it's ok too.

My equation has this form:

LogConflict = a * log (Quantities) + b * log (Value) + c * (log (Quantities) * log (Value)) + epsilon

Does it make sense? I hope someone here can help me. I will appreciate it a lot.

[John Mullahy]

From a statistical perspective what you have specified is a restricted version of a translog function. In unrestricted form one would have:

log(y) = constant + a1*log(x1) + b1*log(x2) + a11*log(x1)^2 + b11*log(x2)^2 + c12*log(x1)*log(x2) + epsilon

Your specification effectively sets a11=b11=0. So I suggest that you take a look at the literature on translog functions (often translog cost functions or translog production functions) to learn more about the properties of such functions and what such restricted versions might imply

Whether the economic content of the model is sensible others will have to decide.

[Phil Bromiley]

A couple of small comments.

1. If you log everything this way, you are making assumptions about the non-logged functional form that may not be what you want. For example, in the Cobb-Douglas production function, folks commonly create the log version to estimate it, but inherent in the production function is the assumption that zero on capital or labor (the rhs variables) results in zero on the output.

2. It is not clear that reducing skewness is necessary in many cases. The assumptions you make in a regression largely deal with the distribution of the errors, not the structural variables (except that they're uncorrelated with the errors). There are other ways to handle outliers - robust estimators, winsorizing, cook's d, etc.

3. I don't see an obvious reason that you can't do the interactions that way.

4. translog production functions have been extensively studied in economics, but that doesn't mean they're right for a model of conflict.