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From Wikipedia:

Simpson’s paradox, or the Yule-Simpson effect, is a paradox in probability and statistics, in which a trend appears in different groups of data but disappears or reverses when these groups are combined. … This result is often encountered in social-science and medical-science statistics, and is particularly confounding when frequency data is unduly given causal interpretations. The paradoxical elements disappear when causal relations are brought into consideration.

What does this mean, specifically? Suppose you are estimating the equation

(1) [math]y = {\alpha} + {\gamma}{D} + {\epsilon}[/math]

with observational (i.e., nonexperimental) data, and you are interested in the causal effect of [math]D[/math] on [math]y[/math]. Suppose further that after estimating equation (1), you find that [math]\hat{\gamma} < 0[/math].

Yesterday, the Royal Swedish Academy of Sciences announced that the 2016 Nobel Memorial Prize in Economic Sciences was given to Oliver Hart and Bengt Holmström, respectively of Harvard and MIT, for their work on contract theory.

As far as I am concerned, it was about time those two got the Nobel. But then again, I have been a big fan of Holmström and Hart for a long time–I went into graduate school wanting to work on applications of contract theory, and I did just that by writing a dissertation titled, rather un-enticingly, Three Essays on Agrarian Contracts.

In 2004, I spent eight months in Madagascar to collect primary survey data for my dissertation. Because I arrived during cyclone season, my field site was not accessible for some time, and so I decided to go through the entire syllabus for a course in applied contract theory that was then taught at the European University Institute by Pascal Courty. In the process, I read a number of things by Hart and Holmström, all of which were very enlightening.

Since I joined Minnesota in 2013, I have had the privilege of teaching the second-year paper seminar, which all of our PhD students are required to take, and in which they get to write an entire research paper from start to finish.

Every fall, I go over Keith Head’s tremendously useful Introduction Formula, which has the double benefit of (i) minimizing the amount of uncertainty you face when writing the introduction for your research papers, and (ii) ensuring that you follow the social norm(s) surrounding how an introduction should be written for an economics paper. Then, because there isn’t much more to the introduction formula than Hook-Research Question-Antecedents-Value Added-Roadmap, I show students examples of introductions written using that formula, to show them that the formula does indeed work.

When I taught the introduction formula last week, someone asked: “But how should we write the conclusion?” Beyond what I had learned in high school, I didn’t really have a good answer, so I figured I should look around and see if there are any obvious social norms surrounding how conclusions are written for economics papers; I found nothing. Even William Thomson’s otherwise wonderful Guide for the Young Economist has nothing about how to write conclusions.