occurred between May and October 2020, and two rounds of follow-up surveys were implemented. Wave 2 was implemented between November 2020 and April 2021; and wave 3 was implemented . between May 2021 and November 2021<sup>6</sup> The analysis is restricted to small, medium and large firms, unless otherwise specified, and excludes firms that were closed at the time of the survey, or those in the health or education sector.

Throughout the paper, three main approaches are used to analyze the digital divide in response to COVID-19 across firms. First, the paper compare the digital response across groups of firms based on basic observable characteristics (e.g., country, sector, size). This exercise mostly relies on estimating and comparing the likelihood that firms in these respective groups have increased the use of or invested in digital technology in response to COVID-19. The second approach analyzes measures of inequality with focus on online sales, to assess if there was an increase in the concentration towards firms with the highest digital market share at the start of the pandemic. A third approach is decomposing the explanatory power of different set of variables (size, sector, management quality, among others) to explain changes in digitalization. These approaches are complementary and allows to investigate if the digital divide across businesses has changed across different dimensions.

To implement the first approach a probit model is used to compare the likelihood of the digital response across groups of firms. Estimations control for pre-pandemic firm size, sub-sector, country fixed effects, and the constructed measure of the severity of the crisis faced by firms at the time of the survey. More specifically, the estimations follow this equation: where _Yit_ refers to the outcome of interest of firm i in time t. The main two outcomes are dummy variables indicating whether the firm increased the use of digital platforms, and whether the firm invested in digital solutions. Time _t_ is split into two periods, broadly defined as the first and last rounds in which the survey was conducted. For all specifications the vector of firm characteristics _X_ includes dummies for the size of the firm based on number of workers (small; medium; and large). Estimations also control for 12 sectors and country fixed effects. To control for variation in the severity of the shock within the period the survey is implemented, _Shockict_ includes the severity of the crisis measure using Google mobility trends around transit stations.<sup>7</sup> All variables are interacted with a time measure _t_ to allow for changes in the coefficients between the first and the latest rounds. Analysis estimate the margins at the means for the variable of interest (e.g., size, sector, or country), for which results are compared across time, keeping the distribution of size, sector, and country constant across waves to ensure that the results are not driven by differences in composition. To

> the first round but did not respond to the follow-up survey, and some of them are replacement firms collected in follow-up surveys. The methodology section in Cirera et al. (2021) describes the robustness checks implemented and the handling of the different sample of firms.

> 6For more details on the surveys and aggregate results see Cirera et al. (2021)

> 7Authors construct an indicator of the severity of the crisis that is a weighted average of 30-day periods since the start of the pandemic until the date of the survey. Specifically, the 30-day period average just before the survey has a weight of 1, the average from day 31-60 has a weight of 1/2, the average from day 61 to 90 has a weight of 1/3, and so on until the start of the pandemic. This approach is aligned with Apedo-Amah et al. (2020) and Cirera et al. (2021), which analyze the overall results from the 1st and 2nd waves of BPS and the WBES follow up.

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