Methods

The paper uses two complementary econometric strategies: a difference-in-differences (DiD) model that estimates the average effect of the pandemic, and an event study that traces the dynamic path of that effect month by month.

Strategy 1: Difference-in-Differences

Intuition

The DiD approach compares how much the DCVB ratio changed after the pandemic began for institutions affected by the treatment (2020) relative to a counterfactual trend estimated from pre-pandemic data (2018 and 2019). The key assumption is that, absent the pandemic, all institutions would have followed the same trend.

The treatment variable is not a subset of institutions: all institutions are treated by the pandemic. Instead, the variation comes from the time dimension: months after March 2020 are “treated” months, while all months in 2018 and 2019 (and January to February 2020) are “control” months.

In this study, the treatment indicator takes the value of 1 for year 2020 and 0 for years 2018 and 2019. The time indicator takes the value of 1 for the months of March through December and 0 for January and February. The COVID-19 variable is their interaction: it equals 1 from March to December 2020, and 0 otherwise. It is this interaction that \(\beta^{DD}\) captures.

Specification

Difference-in-Differences Equation

\[\text{Corruption}_{imy} = \alpha + \beta^{DD}\,\text{COVID19}_{imy} + a_i + \gamma_m + \nu_y + e_{imy}\]

where:

Term Definition
\(\text{Corruption}_{imy}\) DCVB ratio for institution \(i\), month \(m\), year \(y\)
\(\text{COVID19}_{imy}\) Dummy = 1 for March through December 2020, 0 otherwise
\(a_i\) Institution fixed effects (absorb time-invariant differences across institutions)
\(\gamma_m\) Month fixed effects (absorb seasonality common to all institutions)
\(\nu_y\) Year fixed effects
\(\beta^{DD}\) The DiD estimator: average effect of the pandemic months on DCVB

Standard errors are clustered at the institution level to account for within-institution serial correlation.

What \(\beta^{DD}\) estimates: The average change in DCVB attributable to the pandemic, pooled across all ten treatment months (March to December 2020). It does not distinguish whether the effect was immediate, delayed, or fading.

Strategy 2: Event Study

Intuition

The DiD gives one number: the average effect. The event study gives a picture: how did the effect evolve, month by month, before and after the pandemic began? This serves two purposes:

  1. Parallel trends validation: if the pre-pandemic coefficients are close to zero and statistically insignificant, this supports the assumption that treatment and control periods were on the same trend before the shock.
  2. Dynamic effects: the post-pandemic coefficients reveal whether the effect was immediate or delayed, temporary or persistent.

Specification

Event Study Equation

\[\text{Corruption}_{imy} = \alpha + \sum_{\substack{q=-9 \\ q \neq -1}}^{9} \beta_q\,\text{COVID19}_{iqy} + a_i + \gamma_m + \nu_y + e_{imy}\]

where \(\text{COVID19}_{iqy}\) is a dummy equal to 1 for the period \(q\) months relative to the lockdown (March 2020 = \(q=0\)). The period \(q = -1\) (February 2020) is excluded as the reference category to avoid multicollinearity.

  • \(q = -9\) corresponds to June 2019 (nine months before the lockdown)
  • \(q = 9\) corresponds to December 2020 (nine months after the lockdown)
  • Each \(\beta_q\) traces the effect of being \(q\) months away from the lockdown start

Why \(q = -1\) as the reference? This is standard in the event-study literature (Balmori de la Miyar et al., 2021; Brodeur et al., 2021; Leslie & Wilson, 2020). It ensures the pre-pandemic coefficients are interpretable as deviations from February 2020, the last pre-treatment month.