control for variations in the sample size by countries, estimations are weighted by using the inverse of the number of observations in each country, that is, the sum of weights of each country has the same weight in our summary statistics.<sup>8</sup> For the second approach, the paper compares measures of inequality based on the distribution of total online sales across firms. First, the average monthly sales pre-pandemic is multiplied by the change in sales observed in each wave of the BPS as a reference to estimate the monthly sales during COVID-19.<sup>9</sup> Then, a multiplication of the estimated sales for each firm by the share of online sales is calculated, which allows to compute the value of online and off-line sales. The paper then uses these variables to estimate the relative mean deviation (RMD) for the share of online sales. This mean deviation measure is calculated as follows: This analysis is complemented by computing the Gini coefficient for online and offline sales and compare them across time.

A third approach used in the paper is a Shapley decomposition. To calculate the Shapley values for each group of variables in a regression (i.e. size, sector, management quality), n! regressions are estimated by eliminating each component at once and then taking the average of the contributions of the component. Shapley values represent the proportion of the R-squared explained by each component. It is important to note that these values do not point out the direction of the effect, but rather identify which grouping of variables contributes the most at explaining differences in each of the outcomes of interest.

# **3. An unprecedented wave of digitalization**

The stringency of the measures adopted to reduce the spread of the pandemic created a large disruption to the way firms had to operate. Restrictions restrained workers’ mobility, introduced bottlenecks in supply chains and made it difficult for firms to reach consumers in person. These constraints, in turn, induced changes in production and demand patterns to which firms had to rapidly respond if they wanted to continue to operate. Indeed, Apedo-Amah et al. (2020) found evidence of accelerated digitalization among firms as an immediate response to the pandemic with BPS data collected between April and August 2020. Using a subsequent wave of these data, Cirera et al. (2021) document that this pattern of digitization persisted between September 2020 and February 2021 in medium-term patterns (for more details on digital adoption see Comin et al.

> 8In some countries, sampling weights are available in order to produce nationally representative results at the country level, but for cross-country comparison purposes, these weights are not included.

> 9This exercise is based on strong assumptions of no seasonality, which means that sales per month in 2019 were constant so total sales can be recovered using the percentage change in sales in each wave. Because there is no information on differences in sales across firms in levels, one way to think about this exercise is that we weight the changes in sales observed in the BPS by the participation in the total sales of the economy pre-COVID 19.

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