Interpreting polynomial regression results

Hello everyone,

This is the first time I've seen the polynomial regression results presented in this way, and I don't understand how to interpret the coefficients.
Specifically, what coefficient does the table in this paper refer to? It specifies that it uses third, fourth, and fifth-order polynomial regressions, but only one parameter is shown in the table. To which degree of the explanatory variable does it refer?



Active Member
my guess = that the 'time-invariant' label means that the polynomial is in time, those coefficients are not shown, and the 'obj1' 'HC' and 'obj1 x HC' are the main effects and interaction, thus 'time-invariant'. That is, they are the intercepts. FE you guess is as good as mine.

Could always actually read the methods, as a last resort.
Hi fed,

Thanks for your reply. I assumed as well it was the interceptions, but I don't understand the point.
Regarding the time-invariant, it refers to the fact that they use for the variable HC (human capital) du specification one that changes over time and another index that is kept constant throughout the analysis.
Attached you will find the results for both the time-variant and invariant versions.


In the end, I found the answer in a note in the paper. It is my fault for not reading it carefully. It would have been quite strange if they had not indicated the method of presenting the results.
In the end, they decided to report only the results of the interactions the treatment (Objective 1) with the linear terms of the covariates (HC and QoG), arguing that more flexible polynomial specifications indicate that one can safely model the interaction linearly without introducing much bias.