challenges associated with attrition, typical of longitudinal studies, are exacerbated in the context of the COVID-19 crisis due to mobility restrictions, in times of higher likelihood of business closures, and potentially larger opportunity costs of responding to a survey rather than working when restrictions are lifted. Such idiosyncrasies may systematically influence the availability of certain types of firms to respond to the follow up surveys.

Although attrition of firms in our sample is not large, it is not trivial. On average, the attrition rate is 28% (see Appendix Figure B3 for attrition rates by country). Moreover, attrition is not random. For instance, firm characteristics such as size and sector determine the follow-up responses. In particular, micro firms, those in the retail sector, the ones that had larger declines in sales (more than 50% or 90%) in wave 1, and those that were already in arrears or expecting to fall into arrears at the time of wave 1 surveys were less likely to respond to the wave 2 survey (see Figure B4 of Appendix B.4). To avoid a reduction in sample size, attriting firms were replaced with other firms with similar characteristics, as per the original sample design, such as stratification by size and sector. Thus, we observe a balance between waves in terms of general characteristics of the firms, such as size and sector (Figure B5 of Appendix B.4). However, we cannot rule out differences in unobserved performance of the firm during the first months of the pandemic.

# _Estimation Methodology_

To address the heterogeneity in the sample across countries, we conduct our analysis through regressions that controls for such differences in survey implementation. Following a similar approach used to analyze the BPS data from the first wave (Apedo-Amah et al., 2020), our basic specification controls 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, we estimate the following equation.

Where _Yit_ refers to the outcome of interest of firm i in time t. Outcomes explored in this paper include indicators of firm performance, such as sales, operating status, probability of falling arrears. Other outcomes are related to adjustments in business operational dimensions, including changes in employment, digital response, innovation, and the likelihood to access public support. We split time _t_ into two periods, broadly defined as the period in which each wave was conducted. For all specifications the vector of firm characteristics _X_ includes dummies for the size of the firm based on the number of full-time workers (micro; small; medium; and large). Depending on the outcome of interest, additional firm characteristics were included to investigate the association between these variables (e.g. a dummy identifying if the firm is above or below the average level of uncertainty to estimate the association between employment elasticity and uncertainty). Estimations also control for 12 sectors and country fixed effects. To control for variation in the severity of the shock within the period we implement the survey, _Shockict_ includes the severity of the crisis measure explained in the data subsection (for more details see Apedo-Amah et al., 2020). All variables are interacted with time measure _t_ to allow for changes in the coefficients between the first and the second waves.

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