the beginning of the crisis.<sup>10</sup> These controls net out any effects that may arise from the unequal distribution of men- and women-led firms across regions and income-groups, or from differences across countries in the timing of the survey and severity of the COVID-19 shock. We still denote these estimates unconditional because–unlike the conditional estimates further below–they do not control for any firm-level traits that may drive gender gaps.

We estimate (1) using ordinary least squares (OLS) when the dependent variable is continuous, and using a Probit model when the dependent variable is binary. All our computations use the inverse of the number of observations in each country as weights (to give each country the same weight regardless of the sample size).

We use Google mobility trends around transit stations to proxy for both the peak and the severity of the first wave of the COVID-19 shock (Google, 2020; Apedo-Amah et al., 2020). The peak of the crisis corresponds to the peak in the mobility drop in each country during the first phase of the pandemic, which occurred at varying dates in the spring of 2020. The fixed effects for the timing of the interview measure the number of months before or after this peak.<sup>11</sup> To proxy for the severity of the shock we use the magnitude of the drop in mobility at the peak. More precisely, we sort countries into quartiles of the cross-country distribution of mobility drops at the peak. In our sample countries in the top 25% (for example Greece, Italy, South Africa) faced more severe shocks with drops of 73 to 88% relative to the February baseline than countries in the first quartile (such as Kenya, Mongolia, and Tanzania), which exhibited drops at the peak of 24 to 45%.

Our conditional estimates test whether the gender gap is larger among specific groups of businesses, for example, in particular sectors (e.g. hospitality) or among businesses of a particular size (e.g. micro or small). We also test whether gender differences vary with the severity of the shock (because countries more severely affected could exhibit, for example, larger increases in demand for caregivers which in turn could disproportionately affect women). The conditional specification introduces into (1) controls for the size and the sector of the business and in addition, interacts size, sector, income, and the severity of the shock with the indicator for whether the business is led by a woman: where _δn_ and _δg_ denote size and sector fixed effects.

The estimated _unconditional_ gender gaps _β_ in (1) combine composition effects–which arise from the composition of the sample collected or from men- and women-led businesses operating in different sectors or having different sizes–and gender gaps that exist after controlling for these compositional characteristics (for example, due to some forms of discrimination or because women entrepreneurs were disproportionately affected by the increase in care demands due to school closures). In contrast, the _conditional_ model in (2) estimates gender differences controlling for firm characteristics, hence net of the above composition effect. In addition, (2) allows us to test whether gender gaps are larger in some sectors relative to others and for some firm sizes. To estimate the gender gap in businesses of a specific size, for example, we use the fitted model to

> 10The control for the timing of the survey is the number of weeks between the date of the interview and March 11, 2020 (the date when the World Health Organization declared COVID-19 a pandemic).

> 11For countries without coverage in the Google mobility data, mobility is predicted using data on the stringency of the lockdown restrictions in Hale et al. (2020). See Apedo-Amah et al. (2020) for details.

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