interpretation of interaction terms

[Farida Hassan]

Hello,

I am doing pooled OLS and I needed help regarding the interpretation of my regression equation that includes an interaction term:

Ln(VAperworker _i,j,r,k,t) = α₀ + 1.422 GVC_i,j,r,k,t + -0.0362 Ln(serv.rest._j,k,t) - 0.364GVC_i,j,r,k,t x Ln(serv.rest._j,k,t) + α₄ X_i,j,r,k,t + γ_t + γ_j +γ_r+ γ_k+ ε_i,j,r,k,t
GVC is a dummy variable = 1 if the firm is in a GVC, and serv.rest is continuous with LN. the dependent variable is also continuous with LN. My questions are:

1. how can i calculate the magnitude of the average effect of GVC on Y ( VA per worker) ?
2. how can i calculate the magnitude of the average effect of ln (serv.rest) on Y ?
3. how can i interpret the coefficient of the interaction ? ( -0.0362)

[Rhys Williams]

Hi Farida,

It would probably help if you provided a brief explanation of your variables and shared the code you are using for the regression. It might also help to show a subset of the data (see FAQ on how to do this).

Best,
Rhys

[Farida Hassan]

Thank you for your answer.

My dependent variable is the value added per worker, GVC is a dummy equal to 1 if the firm is in a global value chain and serv rest is continous variable of a measure of service trade protection, X is a control vector such as age and size of the firm. the rest of the gammas are city, country, industry and year fixed effects. I am using pooled OLS.

My code is :

areg ln_valueaddedperworkerdef i.yearnew i.countrynew i.newsector i.size ln_age logmeanSTRI i.gvc5 gvc5##c.logmeanSTRI ,absorb (regioninside) robust

Here is a subset of the data i am using it is the world bank enterprise survey firm level data all economies:

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(ln_valueaddedperworkerdef gvc5 logmeanSTRI ln_age) double size float(countrynew yearnew newsector regioninside)
 10.42229 0 1.875691  .6931472 1 1 2 0 169
        . 0 1.875691  .6931472 1 1 2 0 557
 9.976004 0 1.875691  .6931472 1 1 2 0 179
 9.793682 0 1.875691 1.0986123 1 1 2 0 156
        . 0 1.875691  2.484907 3 1 2 0 588
        . 0 1.875691  2.564949 2 1 2 0 557
 9.416388 0 1.875691   1.94591 2 1 2 0 156
  8.52479 0 1.875691  2.397895 1 1 2 0 557
10.484827 0 1.875691   2.70805 1 1 2 0 557
        . 0 1.875691  2.397895 2 1 2 0 268
        . 0 1.875691 1.0986123 1 1 2 0 557
10.033738 0 1.875691 2.1972246 3 1 2 0 557
        . 0 1.875691  1.609438 2 1 2 0 557
 9.805676 0 1.875691  .6931472 1 1 2 0 557
        . 0 1.875691 2.6390574 2 1 2 0 557
 10.66915 1 1.875691 2.1972246 2 1 2 0 169
10.499403 1 1.875691 2.6390574 2 1 2 0 557
        . 0 1.875691 1.3862944 2 1 2 0 190
        . 0 1.875691  1.609438 1 1 2 0 156
 9.199474 0 1.875691  2.484907 2 1 2 0 156
        . 0 1.875691  2.484907 1 1 2 0 557
        . 0 1.875691 2.6390574 2 1 2 0 557
12.965766 0 1.875691  2.564949 2 1 2 0 557
 9.727542 0 1.875691  2.397895 2 1 2 0 557
 8.946384 0 1.875691 2.6390574 1 1 2 0 557
 10.68568 0 1.875691 3.8501475 3 1 2 0 557
        . 0 1.875691  .6931472 2 1 2 0 557
        . 0 1.875691 2.1972246 2 1 2 0 268
        . 0 1.875691   2.70805 2 1 2 0 557
        . 0 1.875691  2.397895 2 1 2 0 156
 9.165073 0 1.875691 2.0794415 1 1 2 0 557
        . 0 1.875691 1.7917595 1 1 2 0 557
        . 0 1.875691 1.7917595 2 1 2 0 557
11.017457 0 1.875691  1.609438 1 1 2 0 557
 9.846545 0 1.875691  2.397895 1 1 2 0 588
 9.704195 0 1.875691  2.484907 2 1 2 0 557
        . 0 1.875691 2.0794415 2 1 2 0 588
        . 0 1.875691   2.70805 3 1 2 0 557
        . 0 1.875691 1.7917595 1 1 2 0 557
        . 0 1.875691 2.3025851 1 1 2 0 557
 7.673419 0 1.875691 2.6390574 3 1 2 0 557
        . 0 1.875691  2.484907 2 1 2 0 557
        . 0 1.875691  2.564949 3 1 2 0 557
        . 0 1.875691 2.6390574 2 1 2 0 268
 10.08848 1 1.875691 2.0794415 2 1 2 0 169
        . 1 1.875691 2.1972246 3 1 2 0 156
 8.250406 0 1.875691 1.0986123 1 1 2 0 557
        . 0 1.875691 1.7917595 2 1 2 0 156
        . 0 1.875691 1.7917595 1 1 2 0 557
 9.817795 0 1.875691  2.484907 1 1 2 0 557
 9.311028 0 1.875691 1.7917595 2 1 2 0 557
        . 0 1.875691 2.0794415 1 1 2 0 557
 9.626628 1 1.875691  2.564949 2 1 2 0 557
        . 0 1.875691  .6931472 2 1 2 0 557
        . 1 1.875691 2.1972246 3 1 2 0 557
        . 0 1.875691 2.3025851 1 1 2 0 557
        . 0 1.875691  2.484907 2 1 2 0 557
        . 0 1.875691  .6931472 2 1 2 0 156
        . 0 1.875691   2.70805 1 1 2 0 557
        . 0 1.875691   1.94591 2 1 2 0 557
 9.231563 0 1.875691 2.0794415 2 1 2 0 156
11.626684 0 1.875691  1.609438 2 1 2 0 557
        . 0 1.875691  2.564949 2 1 2 0 588
 8.461876 0 1.875691 2.3025851 1 1 2 0 557
        . 0 1.875691  .6931472 1 1 2 0 557
        . 0 1.875691 2.6390574 1 1 2 0 557
 7.811561 0 1.875691 2.6390574 2 1 2 0 557
        . 0 1.875691  2.772589 2 1 2 0 557
        . 0 1.875691 1.3862944 2 1 2 0 557
 9.056045 0 1.875691  1.609438 2 1 2 0 557
        . 0 1.875691 2.6390574 1 1 2 0 169
        . 0 1.875691 1.3862944 1 1 2 0 557
        . 0 1.875691 2.3025851 2 1 2 0 557
 8.366566 0 1.875691 1.7917595 1 1 2 0 557
        . 0 1.875691  2.772589 1 1 2 0 557
 9.724689 0 1.875691 2.1972246 1 1 2 0 557
 10.50625 0 1.875691  1.609438 1 1 2 0 557
 9.362899 0 1.875691 1.3862944 1 1 2 0 557
        . 0 1.875691   2.70805 1 1 2 0 557
        . 0 1.875691 2.6390574 3 1 2 0 557
        . 0 1.875691 2.3025851 1 1 2 0 557
        . 0 1.875691  2.397895 2 1 2 0 557
        . 0 1.875691 1.7917595 3 1 2 0 557
        . 0 1.875691  2.484907 3 1 2 0 588
 8.991464 0 1.875691 2.6390574 1 1 2 0 557
11.816553 0 1.875691 1.3862944 2 1 2 0 156
        . 0 1.875691 2.1972246 1 1 2 0 557
        . 0 1.875691   1.94591 1 1 2 0 557
        . 0 1.875691 1.7917595 2 1 2 0 588
        . 0 1.875691 2.1972246 1 1 2 0 557
10.506632 0 1.875691  2.397895 2 1 2 0 169
        . 0 1.875691  2.484907 3 1 2 0 557
        . 0 1.875691  .6931472 1 1 2 0 588
        . 0 1.875691 2.0794415 3 1 2 0 156
        . 0 1.875691  2.397895 2 1 2 0 557
        . 0 1.875691  2.564949 2 1 2 0 557
 8.743859 0 1.875691  .6931472 1 1 2 0 179
        . 0 1.875691 2.3025851 2 1 2 0 169
 8.366566 0 1.875691  2.564949 1 1 2 0 557
        . 0 1.875691  1.609438 1 1 2 0 557
end
label values size size
label def size 1 "Small(<20)", modify
label def size 2 "Medium(20-99)", modify
label def size 3 "Large(100 And Over)", modify