Centering variables in panel data

[Stefan Bradeanu]

Hello everyone,


I have an unbalanced panel data at subnational level based on survey years which differ from one country to another. In my analysis I have interactions terms between some variables which I need to center. Therefore, when centering these variables, it is correct to take out the mean of all values for all years from each value? Or it is necessary to compute the mean for all values, but for each different year.
Thanking you in advance.

Best wishes,
Stefan Bradeanu

[Joro Kolev]

You do not need to center in such situation, nothing stops you from forming nonlinear terms and interactions between non-centered variables.

I do center in such situations because it helps me with the interpretation of the coefficients. E.g., in

wage = b*experience + c*experience^2 + e

the marginal effect d(wage)/d(experience) = b +2*c*experience.

If I center the experience by the grand mean of experience, then the meaning of the estimated b is the marginal effect evaluated at the grand mean of experience.

In short, you do not need to center, if you want to center, by what you center depends on what you are trying to achieve by centring. In your case I would have centered by the grand mean.

[Stefan Bradeanu]

Dear Joro Kolev,

Thank you for your clear explanation. However, I need to center for interpretation purposes and I would do it as you suggested by using the grand mean of the values over the all years.

[Joro Kolev]

Yes Stefan, this is a good plan. Then, if you lets say have

y = b*x + c*w + d*(x*w) + e,

and you center your variables x and w by their grand means, then

dy/dx = b + d*w, so the interpretation of the estimate of b would be the marginal effect of x on y evaluated at the grand mean of w.

Similarly dy/dw = c + d*x, so the interpretation of the estimate of c would be the marginal effect of w on y evaluated at the grand mean of x.

[Stefan Bradeanu]

Dear Joro Kolev,

Thank you again for your helpful response. Now it is more clear for me how should I estimate and interpret the interaction terms. However, I still have one more question related to this topic. Can I center just one variable of the interaction term? How this will affect the interpretation?

Best regards,

[Minhaj uddin]

Hello Prof. Joro, it is an interesting explanation. My doubt is whether, if the data comprises several subgroups, such as domestic and foreign firms, and the analysis is performed on consolidated data and then on subgroups, the grand mean will still be appropriate in that case.