Can I add an "author contributions" section to make clear that I did all the work on a paper?
I think you need to consider for a moment if this is in your own benefit.
Depending on how you go about it, adding such a section without your contributors knowing can come off as a backstab, and hurt your relationship with your contributors. Especially since the paper is already under review, and you seem quite adamant to have it included. If you do let them know (and review) beforehand, it might still come off to them as off-putting that you are adamant about discrediting their contribution (in your own words "I did all the work"). Sure they might not have written the paper, but is it really true that they contributed nothing of note? It is very common for supervisors who do reviewing or who only give advice to be listed, even if they have not written any original text. Other academics are aware of this, so what do you really gain by asserting yourself as the sole author?
If you do chose to include a contribution section, make sure that you go about it in a way that does not hurt your relationship with your colleagues, something which is far more important than the exact credits of one publication.
I'll take an even firmer stance than @ElectricToothpick: Don't
To put this another way, what's the cost-benefit analysis? The cost is that you could make a reputation for yourself as someone who looks to gain too much of the credit. This is a reputation that will hinder your ability to get on future papers. The benefit is that you get more credit for this paper.
In the papers that I have read, there is the tendency to assume that the order of authors is in decreasing contributions. I have seen one author contribution section; it was in a paper where the two authors wanted to make it clear that they were equal contributors. In that case, the response of the the folks with whom I was talking about was along the lines of "Oh, that's nice." Had the contribution section been more along the lines of "The first author contributed 90% of the data", it would have been very jarring to us. The only time that this sort of a thing wouldn't look bad would be if an advisor wants to make sure a student gets credit. But there are other ways to do this.
You can get more credit as the primary author in other ways. Principally, if you are the face that champions this paper; e.g. in conference presentations or future papers, the ideas from this paper will become tied to you without needing to intentionally draw attention to yourself.
Now, granted, my papers have been in a different realm than yours, so maybe there's a practice of this in Econ. I think the easiest way to answer this question is to ask you how many of the papers you have read include a section like this? If you can't point to a sizeable percent of papers that include contribution sections to denote primary contribution, the inclusion of the section is liable to draw more negative attention than positive.
I'm usually all in favor of contribution sections (I've been at the border between medical and natural sciences for a long time, and I've met this custom in medical papers). However, for the present situation I agree with @ElectronicToothpick that for a paper already submitted and under review it is too late to take any such step. IMHO the starting of this paragraph should already be in the first draft of the paper that is sent around.
- I've found contribution sections a nice instrument in situations similar to yours: having coauthors where a substantial contribution to the paper is not clear or did not happen.
PhD students are often not in a position to question higher up faculty on whether they should not be coauthor without significant risk to their standing. The contribution section can hand over part of this to the editor who is not in any dependency situation with possibly gift coauthors.
While I've not yet seen any coauthors being thrown out of the author list by an editor, I've seen author order (1st authors) being changed on the basis of the contributions section. Even as the main author of a paper (in the sense of doing the major part of writing up and integrating the various coauthors' text contributions) I would not write up any but my own contribution to the paper. I usually start a "Contributions" paragraph and then
"CB did this, that and that."plus a comment that everyone please fill in your contributions. That way, the "small" coauthors have to spell out that they did not do anything substantial - or they may spell out valid intellectual contributions that you didn't even suspect like being the source of the idea for solution your supervisor told you as a starting point.I also think (hope?) that everyone who truly did not contribute substantially will find it very embarrassing to spell this out - and may retract their wish to be a coauthor and say they'd rather be acknowledged.
But even if that doesn't happen, again the editor or worst case the reader will know that they didn't contribute.
I'd like to point out that I think contributions sections genuinely useful for readers as well - in case you have to argue for including one in the future:
Particularly in interdisciplinary papers, readers may want to get into contact about a variety of things. Saying who did what allows them to directly contact the person they look for.
And, of course, in any situation where it is important to judge the actual contribution (e.g. if someone wants to check expertise in an application).