Difference-in-Differences (DiD). Suppose you are an instructor of ECON 4211 interested
in the causal effect of holding review sessions on final exam performance. You devise the
following strategy: across a series of semesters t = 1, . . . , T , you randomize review sessions to
some semesters while in other semesters you do not hold a review session. You then record
the final exam score Yit of student i = 1, . . . , N in semester t (for simplicity assume the same
number of students N enroll in each semester). Let Rit = 1 if semester t had a review session,
with Rit = 0 otherwise.
(a) Consider a difference-in-differences approach which compares trends in average test scores
across semesters (t − 1, t) where Ri,t−1 = 0 and Rit = 1 (i.e., no review session was held,
and then a review session was held) to trends in test scores across semesters (t−1, t) where
Ri,t−1 = 0 and Rit = 0 (i.e., no review session was held in either consecutive semester).
Using potential outcomes notation, state the estimand and formalize the two key assump-
tions for it to identify a causal parameter (you do not need to prove identification).
(c) Show that randomization of Rit satisfies both sets of identifying assumptions in (a) and
(b).
(d) How would you tell Stata (or any other language) to compute standard errors in either
estimation strategy? How concerned would you be if you only randomized review sessions
across T = 2 semesters?
(e) Do the two approaches in (a) and (b) identify the same causal parameter or different
causal parameters? Explain