[Richard Williams]

Thanks. Footnote 20 says

Specifically, for each of the two variables, we deduct the sample mean and then divide the difference by the sample standard deviation of the variable

So, if you want to clone them, it sounds like you want to do a Z-score transformation.

But, it also says

Exec_Horizon Subordinate executives’ decision horizon, defined as retirement age of 65 minus the average age of other executives.

Do you really have companies where the average age of other executives is 105??? Especially since, as the next quote points out, there have to be at least 5 executives in the company?

Other tidbits:

We obtain our initial sample of firms from Compustat ExecuComp in the period from 1993 to 2011. We limit our examination to firms with compensation details of the top five executives and require at least five executives (including the CEO) to be reported in the annual proxy statement... Our final sample consists of 11,994 firm-years.

Is your sample and your sample selection procedures comparable?

I'm not convinced that the authors are doing things right, but I probably shouldn't make a definitive statement based on 10 minutes skimming of a 72 page paper published in a good journal. But I'd encourage you to compare your data set to theirs to see how comparable they are, and to also pay attention to the other methodological things they do.

And, while I won't say the paper is wrong, I don't think you should assume that just because it got published means it must be right. It might be interesting to hear what the authors have to say about all the concerns raised here.

[Raja Hasan]

Dr. Richard

Please ignore 105 as I mentioned the range is between -10 and 28. I adjusted everything. I have all the things you are asking for. Also, my sample period is from 1993 to 2018. The published paper is short, not 72 pages. I am not willing to use the same measure as they did simply because others might have questions about their measure considering the issues we have so far discussed. I am in favor of interacting the two variables to create a composite score. But again interaction terms from the two raw variables will create more questions as the larger values will affect the regression result. So, to avoid the effect of large values from the interaction, I have to find some sort of transformation.
Also, in the accounting field, sometimes interacting the two variables which are of different scales may create more questions. So, I got stuck here because I do not completely agree with what the authors did but at the same time, I do not find any remedy that will give answers to so many questions a reviewer might ask. So, whatever measure I use I have to give sound logic to my measure. Otherwise, the paper will be rejected straightforward.

[Richard Williams]

Well, they got published, so it is possible! (I found the final publication -- it is 36 single-spaced pages whereas the working paper version you linked to was 72 double-spaced pages. )

Your paper might mention what they did, explain what is wrong with that approach, and then explain why yours is better.

I would just do whatever you think is best. To me, it seems like interaction effects are the way to go. Sure, whatever you do, there will be something to complain about. But do what you think is best, and do your best to justify it.

The authors of the paper you cite just say what they are doing. They seem to just assert that this is a good way to go. Maybe the reviewers let them off easy. Or maybe I am underestimating how good their approach is -- but it seems weird to me.

Good luck whatever you do!