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The following writeup is an excellent guide from:
Professor Michelle Alexopoulos, Department of Economics, University of Toronto

Tips for Discussants

As a discussant, you must serve two different needs. Your first and most important responsibility is to help those in the audience understand the paper better. You have read the paper very carefully and have taken the time to understand the paper's contributions, its strengths and weaknesses, and what the audience needs to know about the paper. Your second responsibility is to the author. What's your reaction to the paper and why? What can the author do to improve the paper? Developing the skills of a good discussant pays off in various ways. It's something that economists are often asked to do, and gives you an opportunity to look good in front of your peers. The same skills that you develop in order to be a good discussant will also be used in your future responsibility as a journal referee. And learning how to read other papers with the critical eye of a good discussant will help you to learn how to write papers that will appeal to the profession.

There are various strategies to follow in forming your discussion. Here are some tips.

  1. Briefly summarize the paper's main message and its contribution.
    The presenter must spend a good deal of time developing the ideas in her paper, carefully presenting the steps in the argument, and reporting the main findings. Sometimes, the audience gets lost in the detail. On one slide, you can summarize the paper's main contribution in a very stylized way that reminds the audience what the paper is about. With a very good presentation, this step of the discussion can be very abbreviated, but is almost always welcomed. If the presenter got lost in details, then your summary is often the best way for the audience to follow the paper's contribution and you can spend a bit more time on reviewing the paper.

  2. How does the paper fit into the literature?
    Usually, this is clear from your summary of the paper's main message and its contribution and does not require any further elaboration. However, sometimes there are important references that the paper does not mention or entire literatures are ignored. Or you may wish to point out that the paper's message is applicable beyond the narrow focus described in the paper.

  3. Does the paper make its case?
    Almost every paper sets out in the introduction the contribution that it claims to make. Are the claims convincing? Are there problems with specific parts of the argument (it succeeds in making points 1-5 but not 6-8)? If there are problems, then just what are they? Is it a mistake in economics, mathematics, data analysis, or interpretation?

  4. Is there a particularly useful and interesting trick in the paper?
    If the paper introduces you to a new technique or interesting data set and you think that it will be useful in other applications, then you may want to share it with the audience.

  5. Is there a simple way of understanding the paper's technical contribution?
    Sometimes a paper's results are hard to understand. There's a lot of technical detail that obscures the intuition behind a result. Or something may seem counterintuitive at first, but not if you look at in the right way. You may be able to make the main points in a very simple setting that highlights what's going on in the paper. This is very hard to pull off, but can be a great help to the audience. And it's good training for you to think about just what you need (and don't need) to get to your important results.

  6. Do you have any interesting suggestions to improve the paper?
    Do you think the paper could be strengthened by changing it in some direction, or there are obvious directions for future research? Try to be specific. It's not helpful to make very general and vague recommendations, so don't.

  7. Focus on the big picture.
    Try not to get bogged down in details. A typical discussion lasts 10 minutes and you have time for 4-5 overheads. Decide what needs to be said and focus on making your points to the audience and author on those slides. Try to distill your discussion to one or two important points and use most of your time in discussing them. After the seminar is usually the best time to go over the many small but useful comments and corrections (including spelling errors or incorrect citations) that you found while working through the paper. Don't waste your discussion time going over such minutiae, unless you think the author has been so sloppy and inconsiderate of your time by handing you such a poorly written paper that you no longer feel obligated to discuss matters of substance.

  8. Try to be constructive.
    Authors need feedback on their work. Did she miss something that's obviously wrong? Is her work interesting? And, most importantly, how can the paper be improved? Again, many small suggestions are best handled in a private conversation between you and the author after the seminar, but if one or two are particularly clever then you can share them with the audience. Above all, try to avoid sounding like an old fart (A. Most of what's in this paper is not new. It was already well known. B. Most of what is new in this paper is wrong. C. The rest is uninteresting).

  9. Don't apologize for being a poor choice to discuss the paper.
    Over time, we all get asked to discuss papers that are not in our immediate area of expertise. Just do the best you can without whining. If the paper was delivered to you very late, or if the paper presented has undergone major changes from the draft the author sent you, then the presenter should apologize to you and the audience and should let everyone know that you were not given the tools to do your job as a discussant properly. If she does not, then you have a right to complain ("I got this paper ten minutes before the seminar, so my comments will be brief" or, "I haven't seen this draft of the paper so some of my comments may no longer be relevant. I'll do my best.").

To read a paper carefully, I usually start by making a list of all of the paper's sections, tables, figures, etc., and the approximate number of pages devoted to each. I then read the paper once just to form an initial impression of what each section does and how they fit together. As I'm reading, I make a list of things that I notice or questions that are raised in my own mind while reading the paper. The second time through the paper, I make a new list checking to see which of my previous items turned out to be silly upon more careful reading. I also work through each equation and table, making sure that I can either reproduce the algebra, verify how the entry was calculated, and, most importantly, that I understand the result. I jot down anything else that seems unusual, interesting, or any ideas that I have for a potential extension. After reading the paper twice, I then quickly read a few of the background papers from the references to get a better idea of how the paper fits into the literature. I look at all my notes and then sketch out a discussion outline. I then usually put the paper aside for a day or so before reading the paper one more time. On this potentially last reading, I keep my discussion outline in mind and try to assess if my summary of the paper, criticisms, extensions, etc. are relevant and make sense when looked at in isolation from how I constructed the outline. If I'm happy, I stop thinking about the paper and make overheads with a very stylized list of points and only the most important details/equations/results/etc. that I need to show the audience. If I don't think my discussion is useful, I'll read the paper and citations again until I'm confident that I understand what's going on and what needs to be done.

During the presentation, I pay careful attention and try to adjust the emphasis in my presentation slightly based on the presentation rather than the paper. If a point is particularly well made by the presenter, then I will gloss over it in my discussion. If I think that an important idea was not well presented, needs to be, and I feel up to it, then I'll use some of my time to make the point again for the audience's benefit. I also look to see if something comes up during the seminar that either clarifies a question I have in my own mind or contradicts what I thought was in the paper and then try to modify my comments as quickly and cleanly as I can manage.

The above writeup is an excellent guide from:
Professor Michelle Alexopoulos, Department of Economics, University of Toronto