Staggered diff-in-diff - interpretation

Question

Reading a great study by D’Andrea and Limodio (2020), on the effects of expansion of broadband in Africa on fintech adoption and credit markets. They use a staggered diff-in-diff, taking advantage of staggered arrival of broadband in African countries (see, e.g., figure 4).

Specifically, their specification is the following : In the main specification, their specification is the following :

$$ y_{ict} = a_{i} + b_{t} + k_{ct} $$

Where:

$y_{ict}$ is the outcome of interest (e.g., number of loans given)

$a_{i}$ = bank fixed effects

$b_{t}$ = time fixed effects

$k_{ct}$ = dummy which equals 1 if country $c$ has broadband at time $t$

My questions are the following:

• My understanding of staggered diff-in-diff is that we need a "never treated" group to serve as a comparison. My understanding of the paper is that all groups are in fine treated (see, e.g., figure 4 again). What am I missing?

• My understanding (again) is that having a fixed effect at a lower unit than treatment (here, banks as a FE vs countries which are treated) would lead to smaller SE as more variation would be absorbed. However, the authors find that using country rather than bank fixed effects (in a robustness check) significantly increases standard errors. How should I interpret this?

Answer 1

We appreciate papers that aren't gated so we can review the relevant tables/figures.

My understanding of staggered diff-in-diff is that we need a "never-treated" group to serve as a comparison.

In settings where the exposure is rolled out over time (i.e., staggered), a "never treated" group is not a requirement, though it's always ideal. A slew of econometric research has shown how the two-way fixed effects estimator can misbehave when the "timing" of a treatment or intervention is not uniform. Having those true controls allows you to compare the different timing cohorts against a clean group of "never treated" units. So you don't necessarily need those non-receivers of treatment, but having them can help you overcome the "negative weighting" problem we often read about. The authors specifically address this concern on pages 32–33.

Just note that in the absence of a true control group, the treatment effect is identified strictly in terms of variation in treatment timing.

My understanding of the paper is that all groups are in fine treated (see figure 4 again). What am I missing?

You're not missing much.

As noted earlier, it's okay to limit your sample to only those units that experience of treatment change. Their analysis primarily focuses on the restricted sample of African coastal countries, in which it appears all countries eventually become treated. Later, they include the landlocked countries, which they assume (tenuously so) are never treated. Again, since the arrival of the fibre-optic submarine cables is staggered, the authors do not need the landlocked countries, though including them is ideal, or at least worthy of a robustness check.

My understanding (again) is that having a fixed effect at a lower unit than treatment (here, banks as a FE vs countries which are treated) would lead to smaller SE as more variation would be absorbed.

In general, this seems correct.

I suspect estimating effects at the bank level might soak up some of the residual variance, which in turn, might result in smaller standard errors. But some of the variability in the uncertainty estimates seems related to the different datasets the authors use. The models employing country fixed effects were estimated using the firm level data, of which there were many, many more observations.