it is distributed, we first estimate the probability of default in 2020 for firms in each risk bin. To do so, we use the coefficients of the default risk model in Section 4 and plug in the 2019 information for the different regressors. This yields predicted _ex ante_ default values for 2020 for firms that use the credit program across different risk groups. As expected, the predicted default probability declines monotonically with risk, going from 18.2% for high-risk firms to 2.1% for low-risk firms (Table 7, Panel A, Column 4).<sup>61</sup> We then calculate a measure of total credit risk (i.e., expected loss) for each risk group by multiplying the dollar value of program loans (Column 2) by the default probability (Column 4).<sup>62</sup> As a proportion of GDP, the total credit risk related to formal firms corresponds to an expected credit loss of 0.27% (Panel A, Column 5). When using all guaranteed loans to formal firms and natural persons, the expected credit loss is 0.45% of GDP (Panel B, Column 5), which corresponds to a 9.8% default probability of the guaranteed credit (=0.45%/4.6%).

These estimates of the expected loss do not capture the increased uncertainty at the onset of the pandemic. They are calculated using the 2019 data available to banks and the government at the start of the pandemic. Thus, the estimated expected loss can represent a lower bound of the actual expected loss. To provide an alternative measure of the program’s cost and with the benefit of hindsight, we use data on the actual _ex post_ default rates after 2020 (Column 6).

The _ex post_ default rate is monotonically increasing in the risk categories, just like the _ex ante_ default rate, as shown in Section 4.1. Moreover, the _ex post_ default rates of firms with low and medium-low risks are significantly higher than the ones obtained from the _ex ante_ default rates. Still, even after accounting for those firms’ larger _ex post_ default rates and their significant share of the credit program, aggregate loss using _ex post_ defaults does not increase significantly. It remains at 0.38% of GDP for formal firms (Panel A, Column 7) and 0.55% of GDP for formal firms plus natural persons (Panel B, Column 7).

Two points are worth noting about the credit allocation and aggregate loss. First, the expected default rate of 9.8% is higher than the maximum interest rate of 3.5%. Assuming a zero recovery rate and ignoring the opportunity cost of these funds, the 6.3% differential provides a benchmark of the expected loss from the credit program. To compensate, the total economic benefits of the program in terms of firms saved and impact on economic activity

> 61A small fraction of firms do not have data to be classified in a risk category. To be conservative, we assume that those firms (and natural persons) have the default probability of the riskiest group of firms.

> 62Expected loss technically ought to be equal to the probability of default times the loss given default. Given data restrictions on loan recovery rates, in the analysis, we assume that the loss given default equals one, i.e., we assume that banks do not recover anything after a borrower defaults (no partial recovery). The expected loss would be lower if we considered a recovery value.

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