# On Signalling Research Quality

Posted on Sat 06 April 2013 in Random Thoughts

Consider a researcher who has submitted a paper to a good journal, and receives a revise & resubmit decision. Should the researcher revise the paper and resubmit it as soon as possible, or should she wait a fashionable amount of time before resubmitting the paper? Below is a simple model I made to help me think through the question.

Suppose there are two types of papers - marginal papers and truly awesome papers. Reviewers are after all human, and so I expect that the reviewer’s prior about the quality of the paper does affect their decision. Specifically, upon resubmission, if the reviewers have a prior that it is an awesome paper, then the paper has a probability 1 of getting accepted if it is indeed truly awesome; and a probability \(\lambda\) of getting accepted if it is actually a marginal paper.

Similarly, upon resubmission, if the reviewers have a prior that it is a marginal paper, then the paper has a probability \(p\) of getting accepted if it is truly awesome; and a probability \(p\theta\) of getting accepted if it is actually a marginal paper. Let the discount rate the authors have be \(\delta\), and suppose that the authors are trying to maximize the probability of acceptance.

Suppose there is an equilibrium where the reviewers have the prior is that (fashionably) late submissions are awesome, and early are marginal papers. Then, for a person with marginal paper submits early iff \(p\theta > \lambda\delta\). And, a person with an awesome paper submits fashionably late iff \(p < \delta\)

Jointly, this means that the above equilibrium is feasible iff \(p < \delta < \frac{p\theta}{\lambda}\). Note that while the high and low type agents have the same discount rates, in this model, the higher marginal value from waiting for the awesome paper is because of the reviewers beliefs, which end up being self-fulfilling.

At equilibria, the people with truly awesome papers, even when they are impatient (and have a discount factor) will wait to submit their papers (a kind of strategic procrastination?). Moreover, note that the equilibria exists only when \(\delta\) is in an interval. That is, for this type of signalling equilibrium to hold, the time that the author waits cannot be too short or too long!\ While it appears relatively simple to build a more “micro-model” of evaluation (to thus derive the probabilities as coming from reviewers optimal choices), besides being a tedious exercise, it does not appear to have much theoretical value. In any case, the above model does answer the question I was interested in: should the researcher wait a fashionable amount of time before resubmitting the paper. The answer seems to be yes.