_e_ , existing labor, _l_ , and expected productivity, _z_ .<sup>67</sup> The firm makes two contemporaneous decisions. It decides how much to adjust labor ∆ _l_ given the wage, _w_ , and an adjustment cost, _η < w_ , that must be paid for any operating firm not in default. It also decides how much to borrow, _b_ , given an interest rate schedule for borrowing, _rb_ ( _b_ ; _e, z, l_ ) _._<sup>68</sup> Operating profits, _π_ (revenues minus expenses before debt servicing), are determined by a Leontieff-type production technology that depends on aggregate productivity, firm-specific expected productivity _z_ , capital _e_ + _b_ , labor _l_ + ∆ _l_ , and a stochastic revenue shock _ε_ , which can lead to default when sufficiently low. That is, _α π_ = _εzA_ �min _{e_ + _b, ψ_<sup>1(</sup><sup>_l_+ ∆</sup><sup>_l_)</sup><sup>_}_</sup> � _− w_ ( _l_ + ∆ _l_ ) _− η|_ ∆ _l|,_ (5) where _ε_ is a random variable with _E_ ( _ε_ ) = 1, continuously distributed over R<sup>+</sup> according to a cumulative distribution function, Φ( _·_ ). The parameter _ψ_ captures the fixed ratio of workers to capital.<sup>69</sup> Capital depreciates at rate _δ_ . In this static model, the labor adjustment cost _η_ is symmetric and designed to capture both the current cost of hiring additional labor and the future costs associated with (potentially temporary) reductions in labor. This cost makes the employment protection program valuable to firms.

Competitive banks price loans at zero profit based on a common cost of capital, an intermediation cost also capturing banks’ willingness to lend, and default risk. Default is costly, which entails the loss of a fraction _μ_ of firm revenues. Thus, priced competitively, interest rates reflect _ex ante_ default risks and therefore vary by debt, equity, expected revenue productivity, the labor endowment of the firm, and revenue productivity risk, _σε_<sup>2.Inthe</sup> baseline, banks are constrained by a regulatory cap of 20% on annual interest rates.<sup>70</sup> To quantify aggregate outcomes, we assume that firm-level heterogeneity in equity, labor, productivity, and risk follows a joint log normal distribution, with productivity, equity, and labor positively correlated. We calibrate the key technological and distributional parameters to match pre-COVID data, disciplining 11 parameters to fit 12 empirical moments related to interest rates, default rates, the distributions of sales, debt over sales, debt over equity, labor growth, and labor over equity, as detailed in Appendix D.

> 67We abstract from informational frictions and follow the literature on firm finance with endogenous default (e.g., Cooley and Quadrini, 2001; Covas and Den Haan, 2012; Gilchrist et al., 2014). Given the suddenness of the pandemic, we model a static problem with firm equity and labor stocks taken as given.

> 68We use the term equity in the model to be consistent with the existing literature of firm finance with endogenous default. But equity is equivalent to net worth (i.e., assets minus debt), as used in the empirical part of the paper.

> 69The fixed proportions assumption is natural given the short-term, unexpected nature of our analysis and is also simplifying, yielding ∆ _l_ = _ψ_ ( _e_ + _b_ ) _− l_ . We abstract from explicit material costs, but if these are also a fixed proportion of capital, they can be incorporated into the _ψw_ term, as in our calibration below.

> 70Law 18,010 sets a maximum conventional interest rate by loan size, currency, and term. For commercial loans in local currency over 90 days, the cap during our sample period is 20% per year.

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