Empirical Specification: Event Study Analysis

The formal approach adopted in the analysis to assess the differential impact of the COVID-19 crisis across groups of workers is a difference in differences event study panel regression. A multiperiod specification is used for the employment regression, as follows:

Employedit = α WorkerCategoryi + Σtβt WAVEt + Σt,cγt,cWorkerCategoryi × WAVEt + Σt,jλjt(Xj × WAVEt) + εit, (7.1)

where the dependent variable is a dummy variable equal to 1 if the worker is employed and zero otherwise; WorkerCategoryi is a variable representing whether a worker is informal or self-employed (formal workers are the omitted category); WAVEt is a dummy variable indicating each survey wave; Σt,j Xj × WAVEt are time interacted fixed effects, specifically, State × Wavet, Industry × Wavet, Occupation × WAVEt. 9 These control for district-wave–specific shocks, such as the incidence of COVID-19 and the intensity of lockdown measures in a district over time, and time varying shocks at the industry and occupation levels.

WorkerCategoryi does not have a time subscript. An individual’s worker category in December 2019 defines this time-invariant attribute. The main coefficients of interest, the γ ’s, thus capture the differential impact of the crisis on workers who were initially informal or self-employed relative to initially formal workers.

This specification is also used for the income and consumption regressions. However, because income and consumption are observed for each month, monthly time dummies are used instead of wave dummies, as in equation 7.1.

The event study approach estimates the heterogeneous impact of COVID on different worker categories during each time period. Thus, not only can the differential impact be estimated during the lockdowns, but whether the recovery in later month differs across worker types may also be observed. For all regressions, the last observed pre-COVID time period is the omitted time dummy so that all regression coefficients are scaled with reference to this base period. For employment regressions that are at a four-month wave frequency, the base period is wave 18 of the survey (ending in December 2019); for monthly frequency regressions for income and consumption, the base period is February 2020.

Event study visuals also allow us to examine whether the assumption of parallel trends holds for the dependent variable or variables before the shock. This flexible approach exploits the time dimension of the panel data. The cost of restricting the sample to individuals who are repeatedly observed is a slightly reduced household sample size. The main results on the differential impact of COVID-19 are robust to the use of a two-period panel with a larger sample size.