entiated intermediate inputs. Third, in line with the previous literature, we find that the estimation of this elasticity is necessarily tied to the time horizon (Ruhl et al., 2008; Peter and Ruane, 2022). Allowing buyers a longer time to substitute—e.g., a quarter rather than a month—increases the value of the elasticity of substitution. Given the expectations that many large shocks may be shortlived, our estimates are relevant for short-run shocks rather than longer-term structural changes. Finally, we find that the level of inventory in the buyer’s industry helps to substitute inputs to some degree. When buyers are in industries with high levels of inventory, inputs across suppliers of the same product are less complementary. This is because the buyer can temporarily substitute a costly input from a seller with its input inventory holdings.

As our model framework is intentionally parsimonious, we recognize that our elasticity estimates should be thought of as an empirical average over industries, locations, and types of firms. That is, we do not think that the elasticity is a fixed exogenous parameter that applies to every buyer. Rather, it likely depends on various factors, such as the contracting structure and the enforcement of contracts, the level of inventories by industry, and the types of products produced. This is why our heterogeneity analysis adds much nuance to our understanding of why (on average) we find low substitutability.

In the final part of our paper, we embed the estimated elasticities in our model and quantify how input complementarities at the firm level affect aggregate economic outcomes. Considering a firm’s full network is a highly computationally demanding task. In our case, it involves inverting a 94,555 by 94,555 input-output matrix.<sup>6</sup> We apply state-of-the-art techniques from computer science to our input-output matrix to derive the full connectivity of each firm. Compared to our baseline case ( _ε_ = 0 _._ 55), we find that the quarterly fall in GDP induced by a negative 25% shock to firms in _Red_ zones would be 2 _._ 68 _pp_ less in a model where firms in the same HS-4 product category are substitutes ( _ε_ = 2) and 0 _._ 99 _pp_ more when they are almost Leontief ( _ε_ = 0 _._ 001).<sup>7</sup> The additional losses due to firm-level complementarities translate into a GDP loss of 870 million USD, which is about 25 USD per capita per quarter. Additionally, under our estimated elasticity, the shock to _Red_ zone firms spreads widely through the network to other parts of the economy.

In our policy counterfactuals, we quantify the importance of firm connectivity separately from firm size and the effects of allowing the most connected firms (measured by all direct and indirect connections) to operate during lockdowns as opposed to allowing the most directly connected firms to operate. In policy and academic circles, much importance has been paid to large firms, as Hulten (1978) emphasized the importance of firm sizes in the propagation of shocks through production networks. We show that controlling for size, the fall in GDP is much larger if

> 6As a reference, the typical sector-level input-output matrix from the BEA 2012 is 405 by 405.

> 7 We find that a 25% productivity shock to firms in _Red_ zones reduces GDP by 10 _._ 95%. As an empirical benchmark, the state’s annual GDP fell by 11 _._ 3% in 2020/21.

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