key: cord-0586096-uzdbibf5 authors: Pichler, Anton; Pangallo, Marco; Rio-Chanona, R. Maria del; Lafond, Franccois; Farmer, J. Doyne title: Production networks and epidemic spreading: How to restart the UK economy? date: 2020-05-21 journal: nan DOI: nan sha: 7382741e29807a73e71a2431c2e1ed4ab36ade37 doc_id: 586096 cord_uid: uzdbibf5 We analyse the economics and epidemiology of different scenarios for a phased restart of the UK economy. Our economic model is designed to address the unique features of the COVID-19 pandemic. Social distancing measures affect both supply and demand, and input-output constraints play a key role in restricting economic output. Standard models for production functions are not adequate to model the short-term effects of lockdown. A survey of industry analysts conducted by IHS Markit allows us to evaluate which inputs for each industry are absolutely necessary for production over a two month period. Our model also includes inventory dynamics and feedback between unemployment and consumption. We demonstrate that economic outcomes are very sensitive to the choice of production function, show how supply constraints cause strong network effects, and find some counter-intuitive effects, such as that reopening only a few industries can actually lower aggregate output. Occupation-specific data and contact surveys allow us to estimate how different industries affect the transmission rate of the disease. We investigate six different re-opening scenarios, presenting our best estimates for the increase in R0 and the increase in GDP. Our results suggest that there is a reasonable compromise that yields a relatively small increase in R0 and delivers a substantial boost in economic output. This corresponds to a situation in which all non-consumer facing industries reopen, schools are open only for workers who need childcare, and everyone who can work from home continues to work from home. The social distancing measures imposed to combat the COVID-19 pandemic have created severe disruptions to economic output. Governments throughout the world are contemplating or implementing measures to ease social distancing and reopen the economy, which may involve a tradeoff between increasing economic output vs. increasing the expected number of deaths due to the pandemic. Here we investigate several scenarios for the phased reopening of the economy. At one extreme, we find that reopening only a very limited number of industries can create supply chain mis-coordination problems that in some cases might actually decrease aggregate output. In contrast, reopening all industries would most likely increase R 0 above 1. We find a good scenario in-between these extremes: reopening a large part of the upstream industries, while consumer-facing industries stay closed, limits supply chain mis-coordination while providing a large boost to output and a relatively small increase in infection rates. The shocks to the economy caused by social distancing are highly industry specific. Some industries are nearly entirely shut down by lack of demand, others are restricted by lack of labor, and many are largely unaffected. Feedback effects amplify the initial shocks. The lack of demand for final goods such as restaurants or transportation propagates upstream, reducing demand for the intermediate goods that supply these industries. Supply constraints due to lack of labor under social distancing propagate downstream, by creating input scarcity that can limit production even in cases where the availability of labor and demand would not have been an issue. The resulting supply and demand constraints interact to create bottlenecks in production. The resulting decreases in production may lead to unemployment, decreasing consumption and causing additional amplification of shocks that further decrease final demand. Understanding these effects requires a model at the level of individual industries. Most of the economic analysis of the COVID-19 pandemic uses relatively aggregate macro models (Eichenbaum et al. 2020 , Bodenstein et al. 2020 , with only a few studies predicting the economic effects using input-output (IO) models. IO models are particularly relevant to evaluate the consequences of crises such as COVID-19, where different sectors are affected differently, and the propagation of shocks through supply chains is likely to amplify the initial effects. Table 1 summarizes the main features of several IO models that have been put forward recently to evaluate the macroeconomic effects of the COVID-19 crisis. Our paper differs in a number of important ways from the literature. On one hand, we provide comprehensive scenarios, an estimation of the epidemic spreading, non-equilibrium dynamics, and explicit demand shocks together with a sophisticated consumption response. On the other hand, we do not model prices, as we argue that price changes during the lockdown are relatively small. The most important conceptual difference that distinguishes our model is our treatment of the production function, which dictates most of the behavior of the models listed in Table 1 . Essentially, the literature can be ordered by the degree to which the production function allows substitutions between inputs. At one extreme, the Leontief production function assumes a fixed recipe for production, allowing no substitutions and restricting production based on the limiting input (Inoue & Todo 2020) . Under the Leontief production function, if a single input is severely reduced, overall production will be reduced proportionately, even if that input is ordinarily relatively small. This can lead to unrealistic behaviours. For example, the steel industry has restaurants as an input, presumably because steel companies have a workplace canteen and sometimes entertain their clients and employees. A literal application of the Leontief production function would predict that a sharp drop in the output of the restaurant industry will dramatically reduce steel output. This is unrealistic, particularly in the short run. Inoue & Todo (2020) Barrot The alternatives used in the literature are the Cobb-Douglas production function (Fadinger & Schymik 2020) , which has an elasticity of substitution of 1, and the CES production function, where typically calibration for short term analysis uses an elasticity of substitution less than 1 (Barrot et al. 2020 , Mandel & Veetil 2020 , Bonadio et al. 2020 . Some papers (Baqaee & Farhi 2020 ) consider a nested CES production function, which can accommodate a wide range of technologies. In principle, nests could allow for substitution between some inputs and forbid it between others, in different ways for different industries. However, it is hard to calibrate all these elasticities, so that in practice many models end up using very limited nesting structure or assuming uniform substitutability. Consider again our example of the steel industry. With common calibrations of the (nested) CES production function, firms could substitute iron for energy, while still producing the same output. To the extent that certain production processes are encoded in fixed technological "recipes", this is clearly unrealistic 1 . We argue that modeling production during the COVID-19 crisis requires a new approach to production functions, that is different from both standard Leontief and CES production functions. In this paper, we mostly keep the basic Leontief assumption that firms cannot substitute one input for another. However, we depart from the Leontief assumption in that we allow firms to keep producing as long as they have the inputs that are absolutely necessary, which we call "critical inputs". The steel industry cannot produce steel without iron and energy, but it can operate for a considerable period of time without restaurants or logistics consultants. Specifically, we make the assumption that if restaurants cannot supply the steel industry, the steel industry simply keeps producing at the same rate. This is of course only an approximation. To keep the same example, by not using restaurants, the costs of the steel industry are reduced and, ceteris paribus, its profits increase. In reality, non-critical inputs may have an impact on steel output that could be modeled as a shock to productivity. However, we think that during the short time-scales of the pandemic, these problems are second-order effects, and our production function provides a better assumption than Leontief or CES production functions. In order to determine which inputs are critical and which are not, we use a survey that IHS Markit performed at our request. In this survey they asked "Can production continue in industry X if input Y is not available for two months?". The list of possible industries X and Y was drawn from the 55 industries in the World Input-Output Database. This question was presented to 30 different industry analysts who were experts in industry X. Each of them was asked to rate the importance of each of its inputs Y. They assigned a score of 1 if they believed input Y is critical, 0 if it is not critical, and 0.5 if it is in-between, with the possibility of a rating of NA if they could not make a judgement. We then apply the Leontief function to the list of critical inputs, ignoring non-critical inputs. We experimented with several possible treatments for industries with ratings of 0.5 and found that we get somewhat better empirical results by treating them as non-critical (though at present we do not have sufficient evidence to resolve this question unambiguously). Besides the bespoke production function discussed above, we also introduce a COVID-19-specific treatment of consumption. Most models do not incorporate the demand shocks that are caused by changes in consumer preferences in order to minimize risk of infection. The vast majority of the literature has focused on the ability to work from home, and some studies incorporate lists of essential vs. inessential industries, but almost no papers have also explicitly added shocks to consumer preferences. (Baqaee & Farhi (2020) is an exception, but the treatment is only theoretical). Here we use the estimates from del Rio-Chanona et al. (2020) , which are taken from a prospective study by the Congressional Budget Office (2006) . These estimates are crude, but we are not aware of estimates that are any better. As we write, data on actual consumption starts to become available; what we have seen so far is qualitatively consistent with the shocks predicted by the CBO, with massive shocks to the hospitality industry, travel and recreation, milder (but large) shocks elsewhere, and increased expenses in groceries/food retail (Andersen et al. 2020 , Carvalho et al. 2020 , Chen et al. 2020 . Besides the initial shock, we also attempt to introduce realistic dynamics for recovery and for savings. The shocks to on-site consumption industries are more long lasting, and savings from the lack of consumption of specific goods and services during lockdown are only partially reallocated to other expenses. The first step in the analysis of our model is empirical validation: We compare model predictions to the economic data that statistical agencies have started to disseminate. To compare to UK data, we start the lockdown in our model on March 23 rd , and keep it for two months. For 2020Q1, we find a 1.7% reduction in GDP compared to 2019Q4, which is close to the 2% early estimate recently released by the Office for National Statistics. For 2020Q2, we forecast that GDP would be 21.5% lower than in 2019Q4, which is in the range of forecasts provided by economic institutions and consulting firms. We also compare model predictions to sectoral unemployment data, finding good agreement. As a second step, we investigate some theoretical properties of the model. Our analysis makes it clear that bottlenecks in supply chains can strongly suppress aggregate economic output. The extent to which this is true depends on the production function. These effects are extremely strong with the Leontief production function, are much weaker with a linear production function (which allows unrealistically strong substitutions) and have an intermediate effect with our modified Leontief function. Network effects can strongly inhibit recovery, and can cause counter-intuitive results, such as situations in which reopening a few industries can actually depress economic output. Our third step, which is the key aim of this paper, is to find a good compromise between the economic benefit of reopening industries and negative health consequences of doing so. It is worth keeping in mind that many health outcomes depend on the state of the economy, so that keeping the economy closed also has negative health consequences. The fundamental principles of epidemic spreading are relatively well understood, and it is clear that social distancing measures reduce the spreading of COVID-19 (Jarvis et al. 2020 , Maier & Brockmann 2020 , Arenas et al. 2020 . The difficulty comes with obtaining good estimates of the key parameters that govern the fate of an epidemic, and in particular, the reproduction number R 0 , which gives the number of secondary cases for each primary case in a largely unaffected population. If R 0 is above one, the disease spreads to a given percentage of the population, otherwise the epidemic dies out. In this paper, we side-track the problem of developing a full-fledged epidemic spreading model, and focus on estimating R 0 . We decompose the reproduction number into the infections caused by contacts during work, during consumption, during public transport, and in other contexts, i.e. home and other social interactions. We use recent contact survey data from Sweden to estimate the share of infection due to each type of contact. For each industry we estimate its relative contribution to overall work and consumption infections. For instance, the Health sector is responsible for more work-related infections than the Forestry sector. This is because workers have more contacts, contacts are more risky, and there are more Health workers than Forestry workers. As another example, the Retail and Restaurant sectors contribute much more to consumption infections than the Mining sector, because there are virtually no direct consumption activities in the Mining industry. We estimate the epidemiological consequences of scenarios for coming out of lockdown. Lifting the lockdown for a specific industry has several effects: workers of this industry contribute to increased work-related infection; consumers of this industry (if any) contribute to increased consumption-related infections; workers of this industry contribute to increased public transport infections; and finally, children of these workers go back to school if the workers cannot work from home, contributing to increased school-related infections. We assume in all the scenarios that workers who can work from home continue working remotely. We present a summary of our re-opening scenarios results in the next section. We then present in detail our economic model and its calibration in Section 3. We show our model predictions for the UK economy in Section 4 and discuss production network effects and reopening single industries in Section 5. We introduce the epidemic model and present effects of re-starting the economy on infectious contagion in Section 6. We conclude in Section 7. 2 A sweet spot for partially reopening the economy with only a minimal boost to the epidemic Agriculture, Mining, Manufacturing, Utilities and Construction); opening all industries except consumer-facing industries; same, but additionally opening schools; and opening all industries. We find that a two-month lockdown has a strong impact on the economy, with gross output, value added, and consumption decreased by 26%, 25%, and 18%, respectively, compared to the UK pre-lockdown levels. Compared to the economy's performance before the lockdown, an additional month of lockdown would decrease GDP from 75% to 74%, while re-opening only the Manufacturing and Construction sectors would increase GDP from 75% to 76% in a month. Re-opening all sectors except those that are consumer-facing would increase GDP to 82% of its pre-lockdown value, i.e. in a month it would increase GDP by 8 percentage points with respect to the lockdown scenario. Opening all industries only adds an additional 2% boost to GDP. Note that the scenario with all industries open has only 84% of pre-lockdown GDP. This is due to a combination of a persistent depression in demand for industries like restaurants (even if they are open) and the fact that consumer expectations take time to recover. Figure 1 : How different policy scenarios affect R0 and economic output. The coloured bars show the expected reproduction number of the epidemic for each policy scenario. Different colours designate the activities that cause the epidemic to spread. The purple bars denote the percentage increase in value added relative to lockdown a month after the economy is opened under each scenario. Black lines are two standard deviation error bars. Note that we have normalized the infection rates for all scenarios so that they correspond to the Jarvis et al. (2020) study during lockdown. (Our estimate during lockdown is roughly R0 ≈ 0.90; their estimate is 0.62; these agree with the error bars). Note that Manufacturing and Construction also includes mining, agriculture, and a few others. A comparison to our predictions for the increase in R 0 under each scenario shows that for the scenario where all industries except consumer facing industries are opened, the increase in R 0 relative to lockdown is small. In contrast, as soon as schools are open R 0 rises dramatically, and is very likely greater than one. If the economy is fully reopened, the predicted rise in R 0 is very likely substantially greater than one. Note that when the economy is fully reopened we find an R 0 still disturbingly greater than one, although much lower than the pre-lockdown value, as we assume that work from home continues and non-work related social distancing measures continue. Another reason for this is that we renormalize all our epidemiological results by the factor of 0.62/0.90, corresponding to the ratio of our original estimate to that of Jarvis et al. (2020) for the lockdown situation, thus ensuring that our estimate for the lockdown scenario corresponds to theirs. We did this because we feel that the relative values of our estimated R 0 across different scenarios are more reliable than the absolute values, and we defer to professional epidemiologists for estimating the absolute values. It is important to bear in mind that all these values are uncertain, and the uncertainties potentially make the difference in determining whether there will be a second wave of the epidemic in the UK. We should also stress the uncertainties in the economic results -as we will show here, they depend rather sensitively on assumptions about the production function. Thus, our results suggest that there is a "sweet spot", corresponding to the scenario in which all except consumer facing industries reopen, with schools remaining closed for the children of parents who do not work or can work from home. 2 This scenario provides a good combination of a minimal predicted increase in R 0 and a substantial economic boost over remaining in lockdown. The official UK government guidelines for COVID-19 recovery " Step one" (until June 1st) 3 recommend that, in addition to sectors that were previously considered essential, manufacturing and construction should reopen, but that consumer-facing industries such as hospitality and non-essential retail should remain closed. Overall, this scenario corresponds to something in between our second and third scenario, depending on whether sectors such as business services fully reopen. By contrast, other countries (e.g. France) reopened personal services and nonessential retail soon after lockdown was lifted, which would correspond to something between our fourth and fifth scenario (depending on whether schools are open). To analyse the economic benefits of staged re-opening we introduce a sectoral macroeconomic model that was inspired by the work of Battiston et al. (2007) , Hallegatte (2008) , Henriet et al. (2012) and Inoue & Todo (2019) . We combine elements of these models and extend them to include new features. Our model incorporates production network effects that can amplify economic shocks both upstream and downstream. In our model producers experience supply shocks caused by a nationwide lockdown. In the lockdown workers in non-essential industries who are unable to work from home become unproductive, resulting in lowered productive capacities of industries. At the same time demand-side shocks hit as consumers adjust their consumption preferences to avoid getting infected. We use the first-order supply and demand shocks predicted by del Rio-Chanona et al. (2020) to initialise our macro model. Our model is open-source and can be downloaded together with all relevant data 4 . We also provide an interactive online interface for our model, allowing the user to explore alternative scenarios and parameter ranges 5 . A time step t in our economy corresponds to one day. There are N industries 6 , one representative firm for each industry, and one representative household that owns the industries. Every day: 1. Firms hire or fire workers depending on whether their workforce was insufficient or redundant to carry out production in the previous day. 2. The representative household decides its consumption demand and industries place orders for intermediate goods. https://www.gov.uk/government/publications/our-plan-to-rebuild-the-uk-governments-covid-19-recovery-strategy (accessed: 2020/05/21). 4 https://doi.org/10.5281/zenodo.3834116. 5 https://anton-pichler.shinyapps.io/UK_COVID-19_economic_simulator/ 6 See Appendix G, Tables 12-13 for a comprehensive summary of notations used. 3. Industries produce as much as they can to satisfy demand, given that they could be limited by lack of critical inputs or lack of workers. 4. If industries do not produce enough, they distribute their production to final consumers and other industries on a pro rata basis, that is, proportionally to demand. 5. Industries update their inventory levels, and profits and labor compensation are distributed to households. The model is initialized at time t = 0 in the steady state corresponding to input data. We apply the pandemic shocks on day t start lockdown and keep the economy in lockdown until day t end lockdown . At that point we remove the supply-side restrictions corresponding to the scenario. Some consumption demand-side shocks remain in place until the pandemic is suppressed on day t end pandemic . In our scenarios we do not lift shocks of other final demand shocks (investment, international trade). Fig. 2 schematically displays the overall chronology of the model. Let x i,t denote total output of industry i at time t and Z ji,t the intermediate consumption by industry i of good j. Industry i is demand and j is supply. We adopt the standard convention that in the input-output matrix columns represent demand and rows represent supply. In an economy with no "excess" output, i.e. in which all produced output is used up, the output of i is equal to where c i,t is household consumption of good i at time step t and f i,t is all other (exogenous) final demand, including government consumption and exports. We let l i,t denote labor compensation to workers in industry i. This also indicates the number of workers employed in industry i, under the assumption that all workers employed in the same industry earn the same wage. Profits of industry i can then be written as where e i,t represents all other expenses (taxes, imports, etc.) . Note that we do not model physical capital explicitly, and we take prices as time-invariant. For total output, total labor income, total profits and total household consumption we writẽ respectively. We focus on these four variables when discussing aggregate economic impacts of the pandemic in subsequent sections. Our analysis is based on the UK economy. We use the latest release of the World Input-Output Database (WIOD) (Timmer et al. 2015) to determine the relevant values for gross output x i,0 , intermediate consumption Z ij,0 , household consumption c i,0 , other final demand f i,0 , labor compensation l i,0 , and all other expenses e i,0 (2014 values). Overall, we can distinguish 55 separate industries. It will become important to distinguish between demand, that is orders placed by customers to suppliers, and actual realized transactions. All the steps outlined above are realized transactions, which might or might not be equal to demand. Industry demand. The total demand faced by industry i at time t, d i,t , is the sum of the demand from all its customers, where O ij,t (for orders) denotes the demand from industry j, c d i,t the demand from households and f d i,t all other final demand. Recipes. Industries produce output according to a production recipe encoded in the technical coefficient matrix A, where the element A ij = Z ij,0 /x j,0 is the expense in input i per unit of output j. We will relax the assumption of fixed production recipes, since not every input is critical for production in the short-run (see Appendix C). Industries always demand and aim to consume inputs according to their recipe, even if lacking non-critical inputs does not cause immediate effects on its output in the short time horizon considered here. Inventories. Due to the dynamic nature of the model, production and demand are not immediate. Instead industries use an inventory of inputs in production. We let S ij,t denote the stock of material i held in j's inventory. Each industry j aims to keep a target inventory n j Z ij,0 of every required input i to ensure production for n j further days 7 . We explain how we calibrate the parameters n j in Appendix B. Intermediate demand. Intermediate demand follows the dynamics originally introduced by Henriet et al. (2012) and adopted by Inoue & Todo (2019) in the context of firm-level production network models. To satisfy incoming demand (from t − 1) and to reduce the gap to its target inventory, an industry j makes orders to its suppliers at every time step t. More specifically, industry j demands from industry i where τ indicates how quickly an industry adjusts its demand due to an inventory gap. Small τ corresponds to responsive industries that aim to close inventory gaps quickly. In contrast, if τ is large, intermediate demand adjusts slowly in response to inventory gaps. In the literature we find different choices for τ , ranging from 1 (Henriet et al. 2012) to 30 (Hallegatte 2012) time steps. In our simulations, we choose an intermediate value τ = 10. We present sensitivity tests with respect to τ in Appendix D.4. Consumption demand. We let consumption demand for good i be where θ i,t is a preference coefficient, giving the share of goods from industry i out of total consumption demandc d t . The coefficients θ i,t evolve exogenously, following assumptions on how consumer preferences change during the various phases of the pandemic; see Section 3.5, Eq. (25). Total consumption demand evolves following an adapted and simplified version of the consumption function in Muellbauer (2020) . In particular,c d t evolves according to wherel t is current labor income,l p t is an estimation of permanent income and m is the share of labor income that is used to consume final domestic goods, i.e. that is neither saved nor used for consumption of imported goods. From our data we find m = 0.82. Consumption demand during the pandemic is affected by a change of permanent income expectations and the exogenous shock term˜ t ; see Section 3.5, Eqs. (22) and (24). The parameter ρ indicates sluggish adjustment to new consumption levels. Assuming that a time step corresponds to a quarter, Muellbauer (2020) takes ρ = 0.6, implying that more than 70% of adjustment to new consumption levels occurs within two and a half quarters. We modify ρ to account for our daily timescale: By lettingρ = 0.6, we take ρ = 1 − (1 −ρ)/90 to obtain the same time adjustment as in Muellbauer (2020) 8 . Note that, in the steady state, by definition permanent income corresponds to current income, i.e.l p t =l t , and thus total consumption demand corresponds to ml t . 9 7 Considering an input-specific target inventory would require generalizing nj to a matrix with elements nij, which is easy in our computational framework but difficult to calibrate empirically. 8 In an autoregressive process like the one in Eq. (10), about 70% of adjustment to new levels occurs in a time ι related inversely to the persistency parameter ρ. Letting Q denote the quarterly timescale considered by Muellbauer (2020) , time to adjustment ι Q is given by ι Q = 1/(1 −ρ). Since we want to keep approximately the same time to adjustment considering a daily time scale, we fix ι D = 90ι Q . We then obtain the parameter ρ in the daily timescale such that it yields ι D as time to adjustment, namely 1/(1 − ρ) = ι D = 90ι Q = 90/(1 −ρ). Rearranging gives the formula that relates ρ andρ. 9 To see this, note that in the steady statec d t =c d t−1 . Moving the consumption terms on the left hand side and dividing by 1 − ρ throughout yields logc d t = log mlt +˜ t. With no exogenous shock, we findc d t = mlt. To test robustness, we present model results for alternative consumption functions in Appendix D.4. We find that our simulations are highly robust against alternative consumption models. Other components of final demand. In addition, an industry i also faces demand f d i,t from sources that we do not model as endogenous variables in our framework, such as government or industries in foreign countries. f d i,t is not affected by the dynamics of the model. We discuss the composition and calibration of f d i,t in detail in Section 3.5. Every industry aims to satisfy incoming demand by producing the required amount of output. Production is subject to the following two economic constraints: Productive capacity. First, an industry has finite production capacity x cap i,t , depending on the amount of available labor input. Initially every industry employs l i,0 of labor and produces at full capacity x cap i,0 = x i,0 . We assume that productive capacity depends linearly on labor inputs, Input bottlenecks. Second, the production of an industry might be constrained due to an insufficient supply of critical inputs. This can be caused by production network disruptions. While the empirical intermediate consumption at the initial time step is embodied in the technical coefficient matrix A, not every input is necessarily critical for production. Modeling the severeness of intermediate input constraints realistically requires an understanding of how critical inputs are in the production of a given industry (Barrot & Sauvagnat 2016) . We use the ratings of IHS Markit analysts to differentiate three types of inputs: critical, important and non-critical inputs (Appendix C). If an industry runs out of critical inputs, economic production halts immediately. Conversely, if an industry runs out of non-critical inputs, we assume that economic production is not affected. We also have ratings on important but not critical inputs. As a baseline we treat important inputs as non-critical. In Section 5.1 we investigate in detail how alternative assumptions on the input-production relationship affect economic impacts. For a given set of inputs if there are no limits on production capacities, industry i can produce where V i is the set of critical suppliers to industry i. If every input is critical, every input is binding, and this reduces to a Leontief production function. Output level choice and input usage. Since an industry aims to satisfy incoming demand within its production constraints, realized production at time step t is Thus production level of an industry is constrained by the smallest of three values: laborconstrained production capacity x cap i,t , intermediate input-constrained production capacity x inp i,t , or total demand d i,t . The level of output then determines the actual use of inputs according to the production recipe. Industry i uses an amount A ji x i,t of input j, unless j is not critical and the amount of j in i's inventory is less than A ji x i,t . In this case, the quantity consumed of input j by industry i is equal to the remaining inventory stock of j-inputs S ji,t < A ji x i,t . Rationing. Without any adverse shocks, industries are always able to meet total demand, i.e. x t = d t . But in case of production capacity or/and input bottlenecks, industries may not be able to meet total demand, x i,t < d i,t , so they need to ration their output. We assume simple proportional rationing, although alternative rationing mechanisms could be considered (e.g. Inoue & Todo (2019) ). The final delivery from industry i to industry j then is the share of orders received Households receive a share of their demand and the realized final consumption of agents with exogenous final demand is Inventory updating. The inventory of j for every input i is updated according to In a Leontief production function, where every input is critical, the minimum operator would not be needed since production could never continue once inventories are run down. It is necessary here, since when inventories of non-critical inputs i are depleted, industry j produces output using less goods i than A ij x j,t . Hiring and firing. Firms adjust their labor force depending on which production constraints in Eq. (13) are binding. If the capacity constraint x cap i,t is binding, industry i decides to hire as many workers as necessary to make the capacity constraint no longer binding. Conversely, if either input constraints x inp i,t or demand constraints d i,t are binding, industry i lays off workers until capacity constraints become binding. More formally, at time t labor demand by industry i is given by l d i,t = l i,t−1 + ∆l i,t , with Note that the term l i,0 /x i,0 reflects the assumption that the labor share in production is constant over the considered period. We assume frictions in the labor market in a sense that it takes time for firms to adjust their labor inputs. Specifically, we assume that industries can increase their labor force only by a fraction γ H in direction of their target. Similarly, industries can decrease their labor force only by a fraction γ F in the direction of their target. In the absence of additional policies we usually have γ F > γ H , indicating that it is easier for firms to lay off employed than hire new workers. Industry-specific employment evolves then according to As we discuss further in Section 3.6, γ H and γ F can be interpreted as policy variables. For example, the implementation of a furloughing scheme makes re-hiring of employees easier, corresponding to an increase in γ H . In our baseline simulations we choose γ H = 1/30 and γ F = 2γ H . Given our daily time scale, this is a rather rapid adjustment of the labor force. We present sensitivity tests for these parameters in Appendix D.4. Timeline The simulation starts in the steady state. For simplicity we let the pandemic shock hit at the same time as the lockdown starts, i.e. we do not take into account reduced demand beforehand. We let the lockdown last for two months (60 time units), and then lift it according to the specifications below. Supply shocks At every time step during the lockdown an industry i experiences an (exogenous) first-order labor supply shock S i,t ∈ [0, 1] that quantifies labor reductions. These reductions are caused by the lack of labor that was previously provided by workers in nonessential industries (del Rio-Chanona et al. 2020 , Fana et al. 2020 , Galasso 2020 ) who cannot work remotely (del Rio-Chanona et al. 2020 , Dingel & Neiman 2020 , Gottlieb et al. 2020 , Koren & Pető 2020 . For instance, if an industry is non-essential, and none of its employees can work from home, it faces a labor supply reduction of 100% during lockdown i.e., S i,t = 1, ∀t ∈ [t start lockdown , t end lockdown ). Instead, if an industry is classified as fully essential, it faces no labor supply shock and S i,t = 0 ∀t. Letting l i,0 be the initial labor supply before the lockdown, the maximum amount of labor available to industry i at time t is given as If S i,t > 0, the productive capacity of industry i will be smaller than in the initial state of the economy. We assume that the reduction of total output is proportional to the loss of labor. In that case the productive capacity of industry i at time t is Recall from Section 3.4 that firms can hire and fire to adjust their productive capacity to demand and supply constraints. Thus, productive capacity can be lower than the initial supply shock. However, during lockdown they can never hire more than (1 − S i,t )l i,0 workers. If the lockdown is unwound for an industry i, first-order supply shocks are removed, i.e. we set S i,t = 0, for t ≥ t end lockdown . Supply shock calibration To initialise the economic model with first-order supply shocks from the pandemic we use the shock predictions of the recent study by del Rio-Chanona et al. (2020) . In del Rio-Chanona et al. (2020) supply shocks of the pandemic are derived by quantifying which work activities of different occupations can be performed from home (Remote-Labor-Index) and by using the occupational compositions of industries. Moreover, the predictions also take into account whether an industry is essential in the sense that it needs to continue operating during a lockdown. The predictions of first-order shocks are based on the US economy using a different industrial classification system. These predictions therefore need to be adopted for the UK economy and the WIOD industry classification as we outline in detail in Appendix A. For the UK we estimate that 67% of the work force has an essential job. However, much of this essential work can be done remotely (e.g. government and financial services). In total we estimate that 44% of workers can work remotely and that 37% of workers are currently going to work, assuming that people work from home whenever possible. Consumption demand shocks A first shock to consumption demand occurs through reductions in current income and expectations for permanent income. Expectations for permanent income depend on whether households expect a V-shaped vs. L-shaped recovery, that is, whether they expect that the economy will quickly bounce back to normal or there will be a prolonged recession. Let expectations for permanent incomel p t be specified bỹ In this equation, the parameter ξ t captures the fraction of pre-pandemic labor incomel 0 that households expect to retain in the long run. We first give a formula for ξ t and then explain the various cases. Before lockdown, we let ξ t ≡ 1. During lockdown, following Muellbauer (2020) we assume that ξ t is equal to one minus half the relative reduction in labor income that households experience due to the direct labor supply shock, and denote that value by ξ L . (For example, given a relative reduction in labor income of 16%, ξ L = 0.92.) 10 After lockdown, we assume that 50% of households believe in a V-shaped recovery, while 50% believe in an L-shaped recovery. We model these expectations by letting ξ t evolve according to an autoregressive process of order one, where the shock term ν t is a permanent shock that reflects beliefs in an L-shaped recovery. With 50% of households believing in such a recovery pattern, it is ν t ≡ −(1 − ρ)(1 − ξ L )/2. 11 In addition to the income effect, during a pandemic consumption/saving decisions and consumer preferences over the consumption basket are changing, leading to first-order demand shocks (Congressional Budget Office 2006 , del Rio-Chanona et al. 2020 . For example, consumers are likely to demand less services from the hospitality industry, even if it is able to supply these services. Transport is very likely to face substantial demand reductions, despite being classified as an essential industry in many countries. A key question is whether reductions in demand for "risky" goods and services is compensated by an increase in demand for other goods and services, or if lower demand for risky goods translates into higher savings. We consider a demand shock vector t , whose components i,t are the relative changes in demand for goods of industry i. These components evolve in the various phases of the pandemic, 10 During lockdown, labor income may be further reduced due to firing. For simplicity, we choose not to model the effect of these further firings on permanent income. 11 The specification in Eq. (23) reflects the following assumptions: (i) time to adjustment is the same as for consumption demand, Eq. (10); (ii) absent permanent shocks, νt = 0 after some t, ξt returns to one, i.e. permanent income matches current income; (iii) with 50% households believing in an L-shaped recovery, ξt reaches a steady state given by 1 − (1 − ξ L )/2: with ξ L = 0.92 as in the example above, ξt reaches a steady state at 0.96, so that permanent income remains stuck four percentage points below pre-lockdown current income. as defined in the following equations: We use the estimates by the Congressional Budget Office (2006), del Rio-Chanona et al. (2020) , which we denote by D i , to parameterize i,t during lockdown. Roughly speaking, these shocks are massive for restaurants and transport, mild for manufacturing, null for utilities, and positive for health (see Appendix A). When the lockdown is lifted, demand shocks for industries that do not involve on-site consumption are removed; in contrast, demand for industries that involve on-site consumption (restaurants, theatres, etc.) 12 goes back to normal more slowly, and in a non-linear way. The specification in Eq. (24) captures the idea that demand for on-site consumption industries is likely to resume very slowly after lockdown and to accelerate towards its pre-pandemic level as the pandemic approaches an end (or at least is perceived to come to a conclusion). 13 Recent evidence from transaction data in China (Chen et al. 2020 ) backs the assumption that demand for these industries resumes more slowly than for industries that do not face on-site consumption. An illustration for three industries that either do not experience any demand shock, experience a demand shock only during lockdown or experience a demand shock throughout the pandemic is given in Fig. 3 . We now explain how the demand shock vector affects consumption demand. Recall from Eq. (9), c d i,t = θ i,tc d t , that consumption demand is the product of the total consumption scalar c d t and the preference vector θ t , whose components θ i,t represent the share of total demand for good i. We initialize the preference vector by considering the initial consumption shares, that is θ i,0 = c i,0 / j c j,0 . By definition, the initial preference vector θ 0 sums to one, and we keep this normalization at all following time steps. To do so, we consider an auxiliary preference vector θ t , whose componentsθ i,t are obtained by applying the shock vector i,t . That is, we definē The difference 1 − iθ i,t is the aggregate reduction in consumption demand due to the demand shock, which would lead to an equivalent increase in the saving rate. However, households may not want to save all the money that they are not spending. For example, they most likely want to spend on food the money that they are saving on restaurants. Therefore, we define the 12 For deciding whether an industry faces on-site consumption we use the same list that we compiled for the epidemic model, supplementing it with industries that are not very infectious collectively, but that individually could be perceived as risky. For example, infections while buying a car are a negligible share of all infections, but visiting a car seller might be perceived as risky. Specifically, we classify as industries involving on-site consumption those with the following codes: G45, G47, H49, H50, H51, H52, H53, I, L68, M69 M70, O84, P85, R S, T. 13 Note that the specification in Eq. (24) also allows for a small bump in consumption demand at the time the lockdown is lifted. Figure 3 : Illustration of demand shocks. Electricity (blue line) does not experience any demand shock; paper manufacturing (green line) only experiences a moderate demand shock during lockdown; restaurants (red line) experience a strong demand shock during lockdown, and then the demand shock remains persistent in the initial phase of reopening, disappearing only as the end of the pandemic approaches. aggregate demand shock˜ t in Eq. (10) as where ∆s is the change in the savings rate. When ∆s = 1, households save all the money that they are not planning to spend on industries affected by demand shocks; when ∆s = 0, they spend all that money on goods and services from industries that are affected less. For our simulations, we take an intermediate value ∆s = 0.5. Finally, the term (1 − ρ) is needed to account for the autoregressive process in Eq. (10). 14 Demand shock calibration. Note that WIOD distinguishes five types of final demand: (I) Final consumption expenditure by households, (II) Final consumption expenditure by nonprofit organisations serving households, (III) Final consumption expenditure by government (IV) Gross fixed capital formation and (V) Changes in inventories and valuables. Additionally, all final demand variables are available for every country. The endogenous consumption variable c i,0 corresponds to (I), but only for domestic consumption. All other final demand categories, including all types of exports, are absorbed into f i,0 . We apply different initial shocks to the different demand categories presented above. For domestic final demand variables we assume the following initial shocks: We use the estimates from Congressional Budget Office (2006) and del Rio-Chanona et al. (2020) to calibrate the consumption demand shock variable D i which we apply to the final consumption variables (I) and (II). We assume that investment (IV) is reduced by 5.6%, in line with the US Bureau of Economic Analysis (BEA) estimates for the reduction in investment in the US from 2019Q4 to 2020Q1. We do not apply any exogenous shocks to categories (III) Final consumption expenditure by government and (V) Changes in inventories and valuables. To initialise the model with foreign demand shocks, we use the recent estimates on trade by the World Trade Organisation. In their recent forecast international trade is predicted to decline between 12-33% for European countries (Bekkers et al. 2020) . We follow the pessimistic scenario of the WTO and assume a drop of 33% in foreign intermediate and final demand. A summary of all shocks is provided in Appendix A, Table 5 . There is considerable uncertainty in our estimates of first-order demand shocks, which we aim to reduce in the future by collecting additional data. However, sensitivity tests shown in Appendix D.1 suggest that our model predictions are fairly robust against uncertainties in the shock estimates. An exogenous policymaker -the government -can influence economic outcomes in three possible ways. First, the key policy which we are considering is the implementation and withdrawal of a lockdown. While the implementation of a lockdown affects all industries simultaneously according to the exogenous first-order supply and demand shocks, the lockdown can be unwound for different sets of industries. We experiment with different re-opening scenarios which we also evaluate with respect to their impact on infectious contagion (Section 6). Second, the government can also pay out additional social benefits to workers to compensate income losses. During the pandemic only a fraction of the initial labor force is employed, due both to direct shocks and subsequent firing/furloughing, resulting in lower labor compensation, i.e.l t 90%). A detailed breakdown of the input-and industry-specific ratings are given in Table 9 . In this appendix we perform sensitivity analysis of the economic model with respect to both supply and demand shocks (Appendices D.1 and D.2) and model parameters and assumptions (Appendices D.3 and D.4) . For the latter, we follow a one-at-a-time sensitivity analysis approach (Borgonovo & Plischke 2016) , in the sense that we start from the baseline scenario described in the main text and vary some assumptions while holding all other assumptions fixed to the baseline scenario (see Table 10 ). Further, in Appendix D.5 we show how the various scenarios compare in terms of matching sectoral unemployment data from the U.S. states of Washington and Texas, see Section 4. Finally, in Appendix D.6, we compare our model results to those of traditional input-output models, namely the Leontief and Gosh models. Since there is substantial uncertainties in first-order shocks discussed in Section 3.5, we test how sensitive model results are with respect to the shock initialisation considered in the main text. To do this, we first randomly perturb the supply and demand shocks for every industry. More specifically, we create perturbed supply and demand shock vectors by lettinḡ where ψ S i , ψ D i ∼ N (0, σ). We use different values for standard deviation, σ ∈ {0.01, 0.1, 0.2}, representing a normal randomization of original values by 1-20% standard deviations. We then initialise the model with the perturbed first-order shocks and run the lockdown simulations. We repeat this procedure 1,000 times and report median values, interquartile range (IQR) and the 95% confidence bounds of aggregate output values. We did not investigate perturbing other final demand f d i,0 . The upper left panel of Fig. 17 presents the result of this analysis. Since results are qualitatively very similar for the explored standard deviation specifications, we only show the largest perturbation case with σ = 0.2. First note that the default model result (red line) follows very closely the median result (black line). Also, the IQR is only a narrow band around the reported default values. These results are reassuring as they indicate strong robustness of the model result against uncertainty in initial shock values for a large range of simulations. This picture changes when considering the 95% confidence bounds instead. Here, the ribbon expands dramatically towards small values after around 110 time steps. This finding suggests that for a certain range of initial shocks our model would predict a substantial collapse of the economy. Since we do not observe similar nonlinearities for the IQR, this initial shock arrangement is not particularly likely given our estimates represent reasonable expected values of the "true" shocks. Also, the economic collapse happens only after almost four months of lockdown, a much longer time horizon as considered in the simulations for the main results. Nevertheless, the results emphasizes the importance of nonlinearities in the economic system by demonstrating how related initial economic shocks can be amplified in very different ways. The upper right and lower panels of Fig. 17 show the same simulations but using exclusively perturbations on the supply and demand side, respectively. It is immediately evident that the large confidence bounds after four months of lockdown are driven by the supply side shock uncertainty. When perturbing only demand shocks and setting supply shocks to the default values (lower panel), there is very little variance in our model prediction. We repeat the analysis in Section 5.2 of running model simulations with only parts of the initial shocks being switched on for alternative production function specifications. In the left and right panels of Fig. 16 we show simulation results for Leontief and linear production functions, respectively. We find for all production functions that supply shocks are substantially more severe than demand shocks, in particular for Leontief production. For the Leontief production model, economic impacts on gross output are almost identical for the supply-shocks-only and baseline scenarios. There is a slightly less realized consumption when having only supply shocks present compared to both supply and demand shocks being switched on. In the case of linear production functions there is a clearer ordering of how severe demand, supply and both shocks together impact overall economic performance. Here, impacts on gross output are smaller if only supply shocks are considered compared to the baseline case where both demand and supply shocks are switched on. This makes sense since there are no input bottlenecks in this case, making higher competition for given production levels less problematic. Nevertheless, realized final consumption is also smaller for the linear production model if only supply shocks are considered. We re-run the same simulations as in Section 5.1, but now open all industries after two months of lockdown to also compare recovery paths between different production function specifications. Fig. 18 shows the results of these simulations where the lockdown ends at t = 62 (vertical dashed line). We find that after six months the five recovery paths converge for different production function specifications, although the transient looks very different for an extended period of time. Note that the economy does not fully recover after six months due to the slow rebouncing of pessimistic consumer expectations consumers and persistence of shocks in exports and investments (see Section 3.5). To better understand how results are affected by particular model parameter choices, we conduct a series of sensitivity tests. We make 'local' sensitivity tests, meaning that we take the default model setup and then vary a set of parameter to investigate how simulation results are affected. We first present sensitivity tests on inventory adjustment parameter τ which plays an important role in intermediate demand; Eq. (8). Note that a small τ represents quick adjustment behavior where firms aim to replenish run-down inventories essentially within a day. On the other hand, if τ is large, firms react slowly to changes in their input inventories, even when at risk of facing input bottlenecks. We see in Fig. 19 how aggregate economic outcomes depend on parameter τ . We find that small values of τ , representing highly responsive firms, dampen adverse economic impacts, while negative impacts are larger if we assume higher sluggishness. We also make sensitivity tests with respect to different consumption functions. We test following specifications. First, we use the default consumption function inspired by Muellbauer (2020) which is discussed in detail in Section 3.3. As alternative we also consider a simpler consumption function where consumers demand simply a fixed portion of their current income (i.e. have a fixed marginal propensity to consume) which for brevity we call "Keynesian" consumption function. As an even simpler specification we also consider a fixed consumption function where consumers demand a fixed portion of their initial income. For the two alternative consumption functions we choose marginal propensities to consume equal to one such that all of present or initial income is consumed. Model results for alternative consumption function specifications are shown in Fig. 20 . There are only negligible differences between different production functions on gross output and labor compensation. Realized consumption is slightly higher for a fixed consumption function which is not surprising and somewhat artificially achieved since here consumers demand based on comparatively large initial income values. We also investigate how model results depend on the speed of adjustment in labor inputs. In Section 3.3 we introduced a parameter γ H which represents how quickly firms can hire employees in case they want to ramp up their productive capacities. Values of γ H close to one represent the case where hiring can happen very quickly, whereas values close to zero indicate that it is very hard for firms to hire new workers. Similarly, we considered an equivalent parameter γ F for firing workers. In Fig. 21 we show how model results are affected if different γ H values are used as well as if hiring and firing are completely ruled out. All these simulations use γ F = 2γ H to reflect the situation where firing of employees takes less them than hiring if allowed. We find almost no differences on gross output and realized consumption for all these cases. In line with intuition the exact specification of hiring and firing affects labor compensation and firms' profits. In case of no hiring and firing, labor compensation remains constant throughout the simulation, once the initial labor supply shock is applied. Labor compensation is smaller the easier it is for firms to fire (and hire) employees. This makes sense since firms which face production constraints other than capacity constraints will lay off employees, reducing overall labor income. The picture is reversed for profits. If there is no flexibility for firms in adjusting labor input, there is a larger negative impact on profits. The easier firms can lay off workers, the more they reduce costs on labor which they do not need to satisfy aggregate demand. In Section 4, we compared model predictions to data coming from the U.S. states of Washington and Texas, when running the model in the baseline scenario. In this section, we consider the other scenarios outlined in Table 10 and described in the previous appendices. We do not find much difference in terms of the relative performance of each scenario when either comparing to Washington or Texas, or using the Pearson or weighted correlation coefficients. We thus report in Fig. 22 only results for Washington, using a weighted correlation coefficient to compare model predictions and empirical data. Table 10 for a definition of the various scenarios. It is immediately apparent that the performance of the various scenarios is similar, except for the cases of the basic Leontief production function and of the Leontief production function with important inputs considered as critical or half-critical. In these cases, and especially in the Leontief case, performance is substantially lower, suggesting that our modeling choice of distinguishing between critical and non-critical inputs adds realism to our model. Correlation between model predictions and empirical data is somewhat lower in case no hiring or firing takes place (in the sense that workers are only furloughed due to the epidemic shock and not due to second-order effects), but this is a clearly unrealistic assumption. Given the combined uncertainties of comparing the model to the data, and the intrinsic uncertainty in these preliminary data, it would not be wise to select an unrealistic assumption based on a small increase in empirical performance. Therefore, our choice of the baseline reflects a balance between ability to reproduce empirical patterns and prior belief in certain assumptions/parameter values. We use poor empirical performance to exclude the Leontief, "important inputs critical" and "important inputs halfcritical" scenarios. We use instead our best judgement to exclude too fast or slow adjustments of inventories and labor force, full substitution of inputs in the linear production function, and too simple consumption functions such as the fixed or "Keynesian" ones. As shown in Appendices D.3 and D.4, in any case, model results tend to depend weakly on these specific assumptions, consistently with the little ability of data to distinguish between the respective scenarios. We also compare our model results to traditional input-output (IO) models. In particular, we compare the steady state of our model with two models, the demand-driven Leontief (Leontief 1936 ) and the supply-driven Gosh model (Ghosh 1958) . Since these simpler IO models do not include inventory effects, we set input inventories artificially high such that they do not restrict economic production. In the Leontief model final demand is exogenous, and under the assumption of fixed production recipes, gross output per industry is endogenously determined by multiplying demand with the Leontief inverse (Miller & Blair 2009 ). When considering only demand shocks, we can write the Leontief prediction as (49) We also rerun our model with all supply shocks being switched off and only considering demand shocks. We then compare the steady state results of our model with the Leontief prediction. Fig. 23 (left panel) shows the reduction of sectoral gross output compared to the preshock state as barplots for our and the Leontief model. We find that our model very closely recovers the Leontief prediction in the steady state. Gross output per industry in the steady state of our model and the Leontief model have almost a correlation of one. The differences between predicted sectoral reductions in gross output are almost zero in all cases. Only for Health (Q) they differ by 2.3%, since the Leontief model would predict an increase as a result of positive demand shocks which cannot be satisfied in our model due to fixed maximum capacity constraints. These results are very robust against using empirical inventories. It should be noted that the Leontief model is static and we are comparing the steady state of our dynamic model. Thus, modeling the transient which is relevant for the short time-scales considered in the main text is not possible with the traditional Leontief model. We do a similar comparison with the supply-driven Gosh model. There are no fixed production recipes in the Gosh model, but fixed "allocation coefficients" B ij = Z ij,0 /x i,0 . Here, a change in gross output is due to a change in primary inputs, i.e. represented as value added. In the notation used here we can formulate the Gosh prediction as We plot the Gosh predictions and the steady state results of our model with only supply shocks turned on in the right panel of Fig. 23 . We find greater differences between the Gosh and our model for the supply shocks. This should not come as a surprise, since the Gosh model builds upon a very different production function. Rankings of sectoral declines are still very correlated (Spearman correlation of 0.91). This is higher than the correlations between our model's steady state rankings of industries and the initial shock rankings (correlation of 0.87). Unsurprisingly, the Gosh model rankings are most similar as the ones obtained from using initial supply shocks only (correlation of 0.94). These results are not very robust with respect to the specifications of the economic model considered here. Using empirical inventories in our model enlarges differences in model predictions tremendously. We compared our model also to slightly more complex mixed endogenous/exogenous IO models (Dietzenbacher & Miller 2015 , Arto et al. 2015 which simultaneously can take supply and demand shocks into account. Yet these models do not always guarantee positive solutions for variables such gross output and final consumption (Miller & Blair 2009, p.628) . In particular when applying the large first-order supply and demand shocks of the pandemic to the UK economy, the mixed IO model does not yield feasible allocations. In this appendix we present our epidemic model where we divide contagion channels by activities. As we focus on the early stage of the epidemic, we do not explicitly model the number of recovered individuals R, although that plays a role to determine the total population M . We start denoting the number of susceptible and infected people in the pupils and students and in the non-working adults category by S s , I s , S u , I u respectively. Similarly, S i and I i denote the number of susceptible and infected workers of industry i. It follows that the decrease in the overall susceptible population S is given by In what follows, we compute the rate of infection of each population category by focusing on the different channels of contagion each person is exposed to. In these computations we assume homogeneous mixing of the population, meaning that the probability that a person had contact with an individual that was infected is I M , regardless on the channel they had contact in. Normalizing contact-weighted shares by population As we discuss in Appendix F we have data on the share of intensity-weighted contacts in each activity of the overall population. For the derivation of the epidemiological model it is useful to renormalize these shares of weighted contacts (i.e. the β's) by the population they come from. This is not necessary for β c (0) or β h (0), since consumption and other household interaction related contacts are spread evenly across the whole population. On the contrary, we do need to renormalize β s (0) by the student and pupil population η s , so thatβ Another way to look at the equation above is to note thatβ s (0) is the share of intensity-weighted contacts in school per unit population, and to obtain the actual share of intensity-weighted contacts β s (0) one needs to multiplyβ s (0) by the population share of students, η s . Similarly, we renormalize the work intensity-contacts across the workers of different industries as followŝ where the normalization includes the b i,w factors i.e., the heterogenous distribution of intensityweighted contacts across industries. In the transport channel, we must distribute the contacts across the commuter population (i.e. workers and students). To account for a density effect (see below), we assume that the number of contacts scales with the square of the number of people in public transport, and use the normalization factorβ distancing. Notice that since transport is shared with both students and workers, the transport term includes both I s and I k . The fact that we are considering the fractions µ s and δ k,w of infected in the transport term reflects our assumption that density matters in particular in transports; note, for example, that we are not multiplying infected individuals by µ s in the school term. We simplify the above equation using the mean field approximation S i ≈ η i S, I i ≈ η i I, S s ≈ η s S, and I s ≈ η s I and obtain Working population Workers are exposed to infection due to work, transport, consumption, and other household interaction. For a worker in industry i, the infection rate is where we have assumed that workers that go to work make the same amount of contacts at work as before lockdown, while for transport we consider that the number of contacts decreases due to the reduced density of people in public transport. We have made explicit that the work and transport infection channels only apply to the fraction δ i,w of the working population in i going to work and to the µ s fraction of students going to school. As before, we use the mean field approximation S i ≈ η i S, I i ≈ η i I, S s ≈ η s S, and I s ≈ η s I to simplify the equation to We now sum across all N industries to obtain Non-working adults By definition non-working adults are not exposed to the work or school infection channel. Furthermore, since we only consider work-commuting transport use, the nonworking adults are not exposed to the transport infection channel either. It follows that the decrease in the susceptible population depends only on the consumption and other household interaction channel where we have again used the approximation S u ≈ η u S. Total population To get the infection rate of the overall population we substitute Eqs. (56)-(60) in equation Eq. (51). It follows that where we have used the fact that η s + η u + N i=1 η i = 1. The above terms correspond to the infection due to work, school, transport, consumption, and other household interaction respectively. We can write the above equation as where β(t) = β * β w (t) + β s (t) + β c (t) + β T (t) + β h (t) , which is Eq. (37) of the main text. The β's are given by β s (t) =β s (0)µ s η s = β s (0)µ s , and F Calibration of epidemic model F.1 Literature review In epidemiology, the main method to understand contact patterns is to use social contact surveys. A landmark study is the Polymod study (Mossong et al. 2008) . Several other studies in the last decade have confirmed that, roughly speaking, people have about 10-20 non casual contacts per day, mostly at home and at work. By "non-casual" contact, we mean contacts as defined by these studies, that is, either physical contact or non physical contact defined as "a two-way conversation with three or more words in the physical presence of another person". The Polymod study is very interesting for us because it reports where contacts take place. Averaging across countries and pooling physical and non-physical contacts, 23%, 21%, 14%, 3%, and 16% are made at home, at work, at school, while travelling, and during leisure activities, respectively. There are still significant uncertainties on the mode of transmission of SARS-CoV-2, and in particular whether it can diffuse through casual contact (whether simply 'sharing air' is risky, because aerosolized particles, rather than just droplets, are risky). Fortunately, there have also been a couple of studies quantifying "casual" contacts, that is, contacts between anonymous individuals but that nevertheless involve enough proximity to result in a transmission. Mikolajczyk & Kretzschmar (2008) report several studies where participants (students) were "asked about aggregate numbers of contacts on six levels of proximity: intimate contacts, close contacts (same household), direct conversation (> 2 min duration, max. 2 m distance), small group (with conversations, but less intensive than in direct conversations), larger group (seminary or lecture room) and occasional contacts (in the range of 2 m in local transportation, cinema, etc.)." The number of conversational contacts (i.e. including intimate, close and direct conversation ) was sensibly below but in line with the Polymod study (6-13 contacts vs 10-20). Their Fig. 2 suggests that the number of contacts in small groups, large groups, and random contacts was roughly speaking 8, 30 and 40, with variations depending on study design. Roughly speaking, people have on average 10 close contacts per day but 80 casual (non-close) contacts. A few studies have looked at social contact patterns to understand the diffusion of tuberculosis, which spreads very easily. Reading from their Fig. 3 , the estimates of mean casual contacts per day obtained by McCreesh et al. (2019) for South Africa are about 10 for transport (combining trains and large taxis), 6 for school and work, 5 for shops (spaza shop, shebeen and mall), 2 for home, and less than 2 for church and community hall. These estimates are for the mean number of contacts per day, but McCreesh et al. (2019) also asked participants for the number of casual contact present during the visit to a location (Fig. S2) , showing about 40 casual contacts in Malls and Trains. In many other categories relating to transport or shopping, the number of casual contacts is around 10-15. In this paper, we use a study from Sweden (Strömgren et al. 2017 ). The study reports, for a variety of places, the likelihood that it is visited during an average day, the duration of the visit 26 , the number of people present, and the likelihood of physical contact, see Table 11 . Table 11 : The columns Duration and Crowd for the rows School and Pre-school are inferred from the equivalent number in the row Work. "Large store" is short for "Large and specialist store". The source of raw data is Strömgren et al. (2017) . Intensity-weighted contacts are our own calculations, see text. The last column shows the values calculated for Table 3 , Eq.s (37)-(38) in the main text. We used the data from Table 11 to create an intensity-weighted number of contacts. We define for each of the 12 places 27 . To compute the values in Table 3 for Eqs. (37)-(38), we sum-up the relevant Intensity variables. Work. To calibrate b iw , we create an index based on the physical proximity and exposure to infection index of each industry, which, as explained in Appendix A, we map from O'NET data. At the occupation level, physical proximity and exposure to infection range from 0 to 100 and are described as follows. • Exposure to disease and infection. O*NET assigns a score to each occupation depending on the frequency with which workers in that occupation are exposed to disease and infection in normal times. The scale runs from 0, indicating that the worker is never exposed to 100, indicating that the worker is exposed every day. It is important to consider that this rating was done before the pandemic, and doesn't seem to properly take into account the properties of COVID-19 26 The duration of shop visits is highly consistent with the data reported by Goldfarb & Tucker (2020) , who use mobile phone data for the US and report an average visit of 22 to 42 minutes across 11 categories of retail shops. 27 Note that we could have used the variable showing the likelihood of physical contact as proxy for the closeness of contact, as an additional factor in Eq. (69). We have done so in a robustness check and most results are similar, except for Sports Venue which becomes an even larger share of all consumption risks. We decided against using this additional variable in the current draft as we match this activity with the industry that contains cinemas, theatres, religious gatherings, etc. It is true that, like sports, these activities have a significant duration, but they are not as likely to involve physical contact. • Physical proximity. O*NET also considers to what extent performing job tasks requires physical proximity. A score of 75 implies being moderately close (at arm's length) and 100 implies near touching. To obtain a score at the industry level, we aggregate occupation-level scores using employment data from the BLS, which indicates the occupational composition of each industry and then map into the WIOD classification (see Appendix A for details). Our industry-specific infection risk is the average of physical proximity and exposure to infection. That is b iw = 1 2 (exposure to infection i + physical proximity i ). Consumption. We consider that, from Table 11 , there are three types of consumption activities: Shopping (Convenience stores and Large stores), Restaurants, and Sports Venue. We then map these into the WIOD but looking at the list of industries (Table 5 ) and assuming that all Shopping activity comes from the WIOD industry G47: Retail ; that all Restaurant activity comes from the Industry I:Accomodation-Food ; and all Sports Venue activity comes from the Other Services activity. Transport. We consider the value from Table 11 . We note that Strömgren et al. (2017) observe an important divide between rural and urban places in terms of time spent in public transports. Home-related. In the main text, we need to consider the impact of social distancing measures on β h , the share of contacts that are unrelated to whether industries are open or not. We assume that during lockdown, the number of contacts at home stay the same, but the number of contacts with Friends and Relatives, within a family car, or in public urban spaces fall to zero. Since Home is responsible for 76% (16/21) of the home related contacts, we take beta h (lockdown) = β h (t = 0) * 0.7. Population data. To obtain the share of population in the special industries Schools and Outof-the-labor-force, we use the ONS Current Population Survey 28 According to these surveys 62% of the population is employed and 23% of the population is between 0-19 years old. Therefore, we assign 62% of the population to the i = 1, ..., M − 2 working industries, 23% to the school industry 29 and the rest to the retired industry (unemployed and all inactive are thus assigned into this industry). From the 62% of the working population we assign them to the i = 1, ..., M − 2 working industries according to the shares of employment calculated from the WIOD employment data. Finally, again using the ONS CPS, we compute that the share of 0-19 year old who are 14 or below is g = 17/23. https://www.ons.gov.uk/peoplepopulationandcommunity/populationandmigration/ populationestimates/datasets/populationestimatesforukenglandandwalesscotlandandnorthernireland 29 We assume that all people between 0-19 years old go to school. Symbol Name S s , S u , S i Number of Susceptible individuals in the student, adult non-working, and working population I s , I u , I i Number of Infected individuals in the student, adult non-working, and working population S = S s + S u + S i Number of Susceptible individuals I = I s + I u + I i Number of Infected individuals R Number of Recovered individuals M = (S + I + R) Number of individuals in the population β * Force of infection γ Recovery rate R 0 Reproduction number η s , η u , η i Share of people in the student category, the adult non-working category and in industry i µ s Share of the student population that attends school βw Share of intensity-weighted contacts at work βs Share of intensity-weighted contacts in schools βc Share of intensity-weighted contacts in consumption β T Share of intensity-weighted contacts in transports β h Share of intensity-weighted contacts at home Consumer reponses to the covid19 crisis: Evidence from bank account transaction data Essays on the structure of social science models A mathematical model for the spatiotemporal epidemic spreading of covid19 Global impacts of the automotive supply chain disruption following the japanese earthquake of Sectoral effects of social distancing Input specificity and the propagation of idiosyncratic shocks in production networks Credit chains and bankruptcy propagation in production networks Trade and covid-19: The wtos 2020 and 2021 trade forecast Social distancing and supply disruptions in a pandemic Sensitivity analysis: a review of recent advances Tracking the covid-19 crisis with high-resolution transaction data The impact of the covid-19 pandemic on consumption: Learning from high frequency transaction data Potential influenza pandemic: Possible macroeconomic effects and policy issues Supply and demand shocks in the covid-19 pandemic: An industry and occupation perspective Reflections on the inoperability input-output model How many jobs can be done at home? 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We thank Baillie Gifford, IARPA, the Oxford Martin School and JSMF for the funding that made this possible. We appreciate that IHS Markit provided us with A First-order economic shocks and work context industry variables A.1 NAICS-WIOD mapping of shocks Due to the COVID-19 pandemic industries experience supply-side reductions due to the closure of non-essential industries and workers not being able to perform their activities at home. Many industries also face substantial reductions in demand. del Rio-Chanona et al. (2020) provide quantitative predictions of these first-order supply and demand shocks for the US economy. To calculate supply-side predictions, del Rio-Chanona et al. (2020) classified industries as essential or non-essential and constructed a Remote Labor Index, which measures the ability of different occupations to work from home. Under the assumption that the distribution of occupations across industries and that the percentage of essential workers within an industry is the same for the US and the UK, we can map the supply-shocks estimated by del Rio-Chanona et al. (2020) into the UK economy as follows. First, we build a crosswalk from the NAICS 4-digit industry classification to the classification system used in WIOD, which is a mix of ISIC 2-digit and 1-digit codes. We build this crosswalk using the NAICS to ISIC 2-digit crosswalk from the European Commission and then aggregating the 2-digit codes that are presented as 1-digit in the WIOD classification system. We then do an employment-weighted aggregation of the supply shocks from del Rio-Chanona et al. (2020) for the 277 industries at the NAICS 4-digit classification level to the 55 industries in the WIOD classification. Some of the 4-digit NAICS industries map into more than one WIOD industry classification. When this happens we assume employment is split uniformly among the WIOD industries the NAICS industry maps into. Finally, we make one modification to deal with imputed rents for the Real Estate Sector. Imputed rents account for 69% of the monetary value of the sector 21 . We assume that the supply shock does not affect imputed rents for the Real State Sector and thus consider that the supply shock only affects 31% of the sector. With this modification the final supply shock to the Real Estate Sector is 15%.For calibrating consumption demand shocks, we use the same data as del Rio-Chanona et al. (2020) which are based on the Congressional Budget Office (2006) estimates. These estimates are available only on the more aggregate 2-digit NAICS level which are straightforward to map into WIOD ISIC categories. Table 5 gives an overview of all first-order shocks applied to WIOD industries.A.2 Essential score, remote labor index, and industries' work context Using the same methodology as before, i.e., doing a crosswalk from NAICS-4 digit to the classification system used in WIOD and using employment shares to aggregate, we map the essential score and remote labor index computed in del Rio-Chanona et al. (2020) into the WIOD list of industries. We use these industry remote labor index and essential score at the WIOD industry classification level to estimate the number of people working in each industry for each scenario i.e., to estimate δ iw (t).O*NET provides different Work Context 22 indices for occupations, including "Exposure to disease and infection" and "Physical proximity", for brevity we refer to these indexes as exposure show how often an industry has been rated as critical (score=1), half-critical (score=0.5) or non-critical (score=0) input for other industries, or how often the input was rates as NA. Columns under Industry-based rankings give how often an input has been rated as with 1, 0.5, 0 or NA for any given industry. Column n indicates the number of analysts who have rated the inputs of any given industry. Industry T uses no inputs and is therefore not rated. share of labor income used to consume final domestic goods ξt fraction of pre-pandemic labor income that households expect to retain in the long-run ξ L t fraction of pre-pandemic labor income that households expect to retain in the long-run during the lockdown x cap i,t industry production capacity based on available labor x inp i,t industry production capacity based on available inputs