risk and realized _ex post_ default (for the period after 2020).<sup>31</sup> There is a strong positive correlation, with _ex ante_ default risk explaining 75% of the variance of _ex post_ defaults. Figure 3, Panel B shows the correlation between the same variables but using a non-parametric fit with a local polynomial smoothing to address the uncertainty of the correlation. For the majority of the mass of the distribution (up until .25 of the horizontal axis), the fit is tight. The model performs even better if one considers only the center of the distribution, where the mass of the correlation lies on top of the 45-degree line. For values in the lower tail of the distribution of _ex ante_ risk, _ex post_ default is higher, whereas for values in the upper tail of the distribution, _ex post_ default is lower.<sup>32,33</sup> Our risk model appears to be a mean-preserving spread of _ex post_ default, implying that _ex post_ risk is less heterogeneous across firms than the prediction of our risk model.<sup>34</sup> That said, banks face significant uncertainty at the beginning of 2020 about the intensity and duration of the pandemic. Our risk measure does not capture this increased uncertainty because it is calculated using data from 2019. Nevertheless, we believe our measure of default probability can be useful because it is based on the information set that banks have about each firm before the start of the pandemic (including firm age, measures of size, productivity, and indebtedness).

# **4.2 Selection into the Government Programs**

We next focus on the selection into the credit and employment programs by firms with different characteristics. Based on the findings in the literature (Jim ́enez et al., 2018; Cascarino et al., 2022; Core and De Marco, 2023), we expect that riskier firms are more likely to apply to and receive program credit. The reason is that, as the government guarantees loans and sets a ceiling on interest rates, banks are more willing to lend (since they bear only part of the risk), while riskier firms (which typically face high borrowing costs) find it cheaper to borrow. On

> 31The _ex post_ default rate is only one of the alternative measures available to assess _ex post_ outcomes. 32 We assess whether the relation between predicted and realized default holds for the sample of 96,411 firms used in Table 1 and before the pandemic. When using 96,411 firms, the R-squared rises to 0.891. This suggests that the additional observations allow the model to have more predictive power and, thus, provide a better goodness of fit, as shown in Appendix Figure 2, with the points aligning above the 45-degree line. To study how the model performs before the pandemic, we regress 2018 loan defaults on 2017 firm-level characteristics. We use that model to compare the predicted versus the actual defaults in 2019. The results, shown in Appendix Figure 3, mirror the original model: the fit is tighter at the center, suggesting this effect is not pandemic-specific.

> 33To test the robustness of our results across the _ex ante_ risk distribution, we divide firms into terciles: low, medium, and high risk. For each group, we interact the original risk measure with a dummy indicating tercile membership (“low risk,” “medium risk,” and “high risk”). We then re-estimate the main regressions with these tercile-specific variables. The results show that the main conclusions hold for applications and credit use, while for approvals, the coefficient for the low-risk group is not statistically significant, indicating weaker sensitivity among the safest firms (see Appendix Table 6).

> 34This is not explained by differences of risk between sector-location bins. In fact, Figure 3 shows that the shape of the correlation between the two types of risk is robust after residualizing the sector-location variation.

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