Methods
The paper uses two complementary econometric strategies: a difference-in-differences (DiD) model that estimates the average effect of the pandemic on each outcome, and a difference-in-differences-in-differences (DDD) model that estimates whether the effect differed across institutional and student subgroups.
Strategy 1: Difference-in-Differences
Intuition
The DiD approach exploits the fact that the COVID-19 pandemic hit Mexico in the 2019-2020 academic year (March 2020) and continued through 2020-2021. The identifying idea is to compare how outcomes changed from the first to the second year within the pandemic window (2019-2020 to 2020-2021), relative to how the same outcomes changed from the first to the second year within the pre-pandemic window (2017-2018 to 2018-2019).
Treatment group: higher education institutions observed during academic years 2019-2020 and 2020-2021 (the pandemic cohort).
Control group: the same higher education institutions observed during academic years 2017-2018 and 2018-2019 (the pre-pandemic cohort).
Post indicator: equals 1 for the second year in each two-year window — academic years 2018-2019 and 2020-2021 — and 0 for the first year in each window — 2017-2018 and 2019-2020.
The interaction Post × Treatment is the DiD estimator: it captures the pandemic’s effect by comparing the year-over-year change in the pandemic cohort to the year-over-year change in the pre-pandemic cohort.
Specification
Difference-in-Differences Equation (1)
\[Y_{icmy} = \alpha + \gamma\,\text{Treatment}_{imy} + \delta\,\text{Post}_{imy} + \beta\,(\text{Post} \times \text{Treatment})_{imy} + \delta X_{imy} + e_{icmy}\]
where:
| Term | Definition |
|---|---|
| \(Y_{icmy}\) | Outcome (new entry, enrollment, or graduation) for institution \(i\), campus \(c\), area of study \(m\), year \(y\) |
| \(\text{Treatment}_{imy}\) | = 1 for the pandemic cohort (2019-2020 and 2020-2021), = 0 for pre-pandemic (2017-2018 and 2018-2019) |
| \(\text{Post}_{imy}\) | = 1 for the second year in each cohort (2018-2019 and 2020-2021), = 0 for the first year (2017-2018 and 2019-2020) |
| \(\beta\) | The average treatment effect on the treated (ATT): the pandemic’s causal effect on the outcome |
| \(X_{imy}\) | Controls: delivery format dummy, public/private dummy, top-20 dummy |
| \(e_{icmy}\) | Residual; standard errors clustered at the municipality level |
What \(\beta\) estimates. The DiD estimator \(\beta\) compares the year-over-year change during the pandemic window (2019-20 to 2020-21) with the year-over-year change during the pre-pandemic window (2017-18 to 2018-19). If both cohorts would have followed the same trend absent the pandemic, then any additional change in the pandemic cohort is attributable to COVID-19.
Key Assumption: Parallel Trends
The identifying assumption is that, absent the pandemic, the pandemic-cohort and pre-pandemic-cohort institutions would have experienced the same year-over-year change in outcomes. This cannot be directly tested, but the paper supports it with a placebo test: shifting the treatment window back by two years (using 2018-2019 and 2019-2020 as the “treatment cohort” and 2016-2017 and 2017-2018 as the control cohort) should produce null effects. Panel A of Table 3 confirms this: the placebo estimates are statistically insignificant, consistent with pre-parallel trends.
Strategy 2: Difference-in-Differences-in-Differences
Intuition
The DDD approach extends the DiD to test whether the pandemic’s effect differed across subgroups. For each heterogeneity dimension (public vs. private funding, top-20 vs. non-top-20 status, synchronous vs. asynchronous delivery), a third interaction term is added: Post × Treatment × Subgroup indicator.
Specification
DDD Equation (2)
\[Y_{icmy} = \alpha + \beta_1\,\text{Treatment}_{imy} + \beta_2\,\text{Het}_{icy} + \beta_3\,\text{Post}_{my} + \beta_4\,(\text{Post} \times \text{Treatment})_{imy}\] \[+ \beta_5\,(\text{Treatment} \times \text{Het})_{icmy} + \beta_6\,(\text{Het} \times \text{Post})_{icmy} + \beta_7\,(\text{Post} \times \text{Treatment} \times \text{Het})_{icmy} + e_{icmy}\]
where \(\text{Het}_{icy}\) is a dummy equal to 1 if the institution belongs to the heterogeneous subgroup of interest (e.g., public, top-20, synchronous), and 0 otherwise.
The parameter \(\beta_7\) captures the differential pandemic effect for the subgroup relative to the complement. A positive \(\beta_7\) means the subgroup fared better than the non-subgroup; a negative \(\beta_7\) means it fared worse.
Robustness Suite
The paper validates the main DiD estimates with four robustness checks:
1. Placebo test (pre-parallel trends). Shifts the treatment window one year earlier. Finding null effects supports the parallel trends assumption.
2. False Discovery Rate correction. Because three outcomes are tested simultaneously, the paper applies the FDR q-value correction of Anderson (2008). No significant result becomes insignificant after this correction.
3. Oster (2019) bounds for omitted variable bias. Simulates bounds around \(\beta\) based on an expected R². When bounds exclude zero, the estimate is robust to omitted variable bias. All main bounds exclude zero.
4. Leave-one-major-out sensitivity. Re-estimates the DiD specification ten times, each time excluding one area of study. Estimates remain stable across all exclusions, confirming the results are not driven by any single field.