In and out of lockdown: Propagation of supply and demand shocks in a dynamic input-output model
Anton Pichler, Marco Pangallo, R. Maria del Rio-Chanona, François Lafond, J. Doyne Farmer
IIn and out of lockdown: Propagation of supply and demandshocks in a dynamic input-output model
Anton Pichler , , , Marco Pangallo , R. Maria del Rio-Chanona , ,Fran¸cois Lafond , , J. Doyne Farmer , , Institute for New Economic Thinking at the Oxford Martin School, University of Oxford, UK Mathematical Institute, University of Oxford, UK Complexity Science Hub Vienna, Austria Institute of Economics and EMbeDS Department, Sant’Anna School of Advanced Studies, Pisa, Italy Santa Fe Institute, US
February 22, 2021
Abstract
Economic shocks due to Covid-19 were exceptional in their severity, suddenness and het-erogeneity across industries. To study the upstream and downstream propagation of theseindustry-specific demand and supply shocks, we build a dynamic input-output model in-spired by previous work on the economic response to natural disasters. We argue thatstandard production functions, at least in their most parsimonious parametrizations, arenot adequate to model input substitutability in the context of Covid-19 shocks. We use asurvey of industry analysts to evaluate, for each industry, which inputs were absolutely nec-essary for production over a short time period. We calibrate our model on the UK economyand study the economic effects of the lockdown that was imposed at the end of March andgradually released in May. Looking back at predictions that we released in May, we showthat the model predicted aggregate dynamics very well, and sectoral dynamics to a largeextent. We discuss the relative extent to which the model’s dynamics and performance wasdue to the choice of the production function or the choice of an exogenous shock scenario.To further explore the behavior of the model, we use simpler scenarios with only demand orsupply shocks, and find that popular metrics used to predict a priori the impact of shocks,such as output multipliers, are only mildly useful.Keywords: Covid-19; production networks; epidemic spreadingJEL codes: C61; C67; D57; E00; E23; I19; O49
This is a substantially revised version of Pichler et al. (2020), which was released early in the pandemic (May2020) and included a cost-benefit analysis of both the economic and epidemiological consequences of reopeningspecific industries. In this new version we focus solely on the economic model.
Acknowledgements:
We would like to thank Eric Beinhocker, David Van Dijcke, John Muellbauer and DavidVines for many useful comments and discussions. This work was supported by Baillie Gifford, Partners for a NewEconomy, the UK’s Economic and Social Research Council (ESRC) via the Rebuilding Macroeconomics Network(Grant Ref: ES/R00787X/1), the Oxford Martin Programme on the Post-Carbon Transition, James S. McDonnellFoundation, and the Institute for New Economic Thinking at the Oxford Martin School. This research is basedupon work supported in part by the Office of the Director of National Intelligence (ODNI), Intelligence AdvancedResearch Projects Activity (IARPA), via contract no. 2019-1902010003. The views and conclusions containedherein are those of the authors and should not be interpreted as necessarily representing the official policies,either expressed or implied, of ODNI, IARPA, or the US Government. The US Government is authorized to a r X i v : . [ ec on . GN ] F e b eproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein.We appreciate that IHS Markit provided us with a survey on critical vs. non-critical inputs. (Note that JDF ison their advisory board). We thank Diana Beltekian for excellent research assistance. Contacts: [email protected], [email protected], [email protected],[email protected], [email protected] Introduction
The social distancing measures imposed to combat the Covid-19 pandemic created severe dis-ruptions to economic output, causing shocks that were highly industry specific. Some industrieswere shut down almost entirely by lack of demand, labor shortages restricted others, and manywere largely unaffected. Meanwhile, feedback effects amplified the initial shocks. The lack ofdemand for final goods such as restaurants or transportation propagated upstream, reducingdemand for the intermediate goods that supply these industries. Supply constraints due toa lack of labor under social distancing propagated downstream, creating input scarcity thatsometimes limited production even in cases where the availability of labor and demand wouldnot have been an issue. The resulting supply and demand constraints interacted to create bot-tlenecks in production, which in turn led to unemployment, eventually decreasing consumptionand causing additional amplification of shocks that further decreased final demand.In this paper we develop a model that respects the three main features that made the Covid-19 episode exceptional: (1) The shocks were highly heterogeneous across industries, making itnecessary to model the economy at the sectoral level, taking sectoral inter-dependencies intoaccount; (2) the shocks affected both supply and demand simultaneously, making it necessaryto consider both upstream and downstream propagation; (3) the shocks were so strong and wereimposed and relaxed so quickly that the economy never had time to converge to a new steadystate, making dynamic models better suited than static models.In the first version of this work, results were released online on 21 May, not long aftersocial distancing measures first began to take effect in March (Pichler et al. 2020). Based ondata from 2019 and predictions of the shocks by del Rio-Chanona et al. (2020), we predicteda 21.5% contraction of GDP in the UK economy in the second quarter of 2020 with respect tothe last quarter of 2019. This forecast was remarkably close to the actual contraction of 22.1%estimated by the UK Office of National Statistics. (The median forecast by several institutionsand financial firms was 16.6% and the forecast by the Bank of England was 30%). In this substantially revised paper we present our model and describe its results, but wealso take advantage of the benefits of hindsight to perform a “post-mortem”. This allows usto better understand what worked well, what did not work well, and why. To what extent didwe succeed by getting things right vs. just getting lucky? We systematically investigate thesensitivity of the results under different specifications, including variations in the shock scenario,production function, and key parameters of the model. We examine the performance at boththe aggregate and sectoral levels. We also look at the ability of the model to reproduce the timeseries patterns of the fall and recovery of sectoral output. Surprisingly, we find that the originalspecification used for out-of-sample forecasting performs about as well at the aggregate level asany of those developed with hindsight; with a minor adjustment its results are also among thebest at the sectoral level. We show how getting good aggregate results depends on making theright trade-off between the severity of the shocks and the rigidity of the production function,as well as other key factors such as the right level of inventories. This provides valuable lessonsabout modeling the economic effects of disasters such as the Covid-19 pandemic.Our model is inspired by previous work on the economic response to natural disasters (Hal-legatte 2008, Henriet et al. 2012, Inoue & Todo 2019). As in these models, industry demand andproduction decisions are based on simple rules of thumb, rather than resulting from optimiza-tion in a dynamic general equilibrium setup. We think that the Covid-19 shock was so sudden Sources: ONS estimate: ; median forecast of institutions and financial firms (in May): ; forecast by theBank of England (in May): . critical inputs . The steel industry cannotproduce steel without the critical inputs iron and energy, but it can operate for a considerableperiod of time without non-critical inputs such as restaurants or management consultants. Weapply the Leontief function only to the critical inputs, ignoring the others. Thus we makethe assumption that during the pandemic the steel industry requires iron and energy in theusual fixed proportions, but the output of the restaurant or management consultancy industriesis irrelevant. Of course restaurants and logistics consultants are useful to the steel industryin normal times – otherwise they wouldn’t use them. But during the short time-scale of thepandemic, we believe that neglecting them provides a better approximation of economic behaviorthan either a Leontief or a CES production function with uniform elasticity of substitution. Inthe appendix, we show that our production function is very close to a limiting case of anappropriately constructed nested CES, which we could have used in principle, but is less well-suited to our calibration procedure.To determine which inputs are critical and which are not, we use a survey performed byIHS Markit at our request. This survey asked “Can production continue in industry X if inputY is not available for two months?”. The list of possible industries X and Y was drawn fromthe 55 industries in the World Input-Output Database. This question was presented to 304ifferent industry analysts who were experts of industry X. Each of them was asked to rate theimportance 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 theycould 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 industrieswith ratings of 0.5 and found that we get somewhat better empirical results by treating themas half-critical (though at present we do not have sufficient evidence to resolve this questionunambiguously).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 thatare caused by changes in consumer preferences in order to minimize risk of infection. The vastmajority of the literature has focused on the ability to work from home, and some studies in-corporate lists of essential vs. inessential industries, but almost no papers have also explicitlyadded shocks to consumer preferences. (Baqaee & Farhi (2020) is an exception, but the treat-ment is only theoretical). Here we use the estimates from del Rio-Chanona et al. (2020), whichare taken from a prospective study by the Congressional Budget Office (2006). These estimatesare crude, but we are not aware of estimates that are any better. The currently available dataon actual consumption is qualitatively consistent with the shocks predicted by the CBO, withmassive shocks to the hospitality industry, travel and recreation, milder (but large) shocks else-where (Andersen et al. 2020, Carvalho et al. 2020, Chen et al. 2020, Surico et al. 2020). Thelargest mismatch between the CBO estimates and consumption data is in the healthcare sector,whose consumption decreased during the pandemic, in contrast to the estimated increase bythe CBO. There was also an increase in some specific retail categories (groceries) which theCBO estimates did not consider. However, overall, as del Rio-Chanona et al. (2020) argue, theestimates remain qualitatively accurate. Besides the initial shock, we also attempt to introducerealistic dynamics for recovery and for savings. The shocks to on-site consumption industriesare more long lasting, and savings from the lack of consumption of specific goods and servicesduring lockdown are only partially reallocated to other expenses.Our key finding is that there is a trade-off between the severity of the shocks and the rigidityof the production function. At one extreme, severe shocks with a Leontief production functionlead to an almost complete collapse of the economy, and at the other, small shocks with a linearproduction function fail to reproduce the massive recession observed in the data. There is asweet spot in the middle, with empirically good results based on various mixes of productionfunction rigidity and shock severity. We also find that our models’ performance improved afterwe used better data for inventories.Our selected scenario predicts the aggregate UK recession in Q2 2020 about as well asour initial forecast. It also correctly predicts a stronger reduction in private consumption,investment and profits than in government consumption, inventories and wages. At the sectorallevel, the mean absolute error is around 12 percentage points, slightly lower than in our initialforecast (14 p.p.). The correlation between sectoral reductions in the model and in the data isgenerally high (the Pearson correlation coefficient weighted by industry size is 0.75). However,this masks substantial differences across industries: while our model makes a good job atpredicting sectoral outcomes in most industries, it fails at others such as vehicle manufacturingand air transport. We conjecture that this is due to idiosyncratic features of these industriesthat our model could not capture. Conversely, we provide examples where our model predictssectoral outcomes correctly when these depend on inter-industry relationships, both staticallyand dynamically.We conclude by investigating some theoretical properties of the model using a simpler set-ting. We ask whether popular metrics of centrality, such as upstreamness and output multipliers,5re useful to understand the diffusion of supply and demand shocks in our model. We find thatstatic measures are only partially able to explain modeling results. Nevertheless, an industry’supstreamness is a strong indicator of its potential to amplify shocks - this is true for supplyshocks, as expected, and for demand shocks, which is somewhat more surprising.The paper is organized as follows. The details of the model are presented in Section 2. Wediscuss the shocks induced by the pandemic which we use to initialize the model in Section 3.We show our model predictions for the UK economy in Section 4 and discuss production networkeffects and re-opening single industries in Section 5. We conclude in Section 6. Our model combines elements of the input-output models developed by Battiston et al. (2007),Hallegatte (2008), Henriet et al. (2012) and Inoue & Todo (2019), together with new featuresthat make the model more realistic in the context of a pandemic-induced lockdown.The main data input to our analysis is the UK input-output network obtained from thelatest year (2014) of the World Input-Output Database (WIOD) (Timmer et al. 2015), allowingus to distinguish 55 sectors.
A time step t in our economy corresponds to one day. There are N industries , one representativefirm for each industry, and one representative household. The economy initially rests in asteady-state until it experiences exogenous lockdown shocks. These shocks can affect the supplyside (labor compensation, productive capacity) and the demand side (preferences, aggregatespending/saving) of the economy. Every day:1. Firms hire or fire workers depending on whether their workforce was insufficient or redun-dant to carry out production in the previous day.2. The representative household decides its consumption demand and industries place ordersfor intermediate goods.3. Industries produce as much as they can to satisfy demand, given that they could be limitedby lack of critical inputs or lack of workers.4. If industries do not produce enough, they distribute their production to final consumersand to other industries on a pro rata basis, that is, proportionally to demand.5. Industries update their inventory levels, and labor compensation is distributed to workers. It will become important to distinguish between demand, that is, orders placed by customersto suppliers, and actual realized transactions, which might be lower.
The total demand faced by industry i at time t , d i,t , is the sum of the demandfrom all its customers, d i,t = N (cid:88) j =1 O ij,t + c di,t + f di,t , (1) See Appendix G for a comprehensive summary of notations used. O ij,t (for orders ) denotes the intermediate demand from industry j to industry i , c di,t rep-resents (final) demand from households and f di,t denotes all other final demand (e.g. governmentor non-domestic customers). Intermediate demand.
Intermediate demand follows a dynamics similar to the one studiedin Henriet et al. (2012), Hallegatte (2014), and Inoue & Todo (2019). Specifically, the demandfrom industry i to industry j is O ji,t = A ji d i,t − + 1 τ [ n i Z ji, − S ji,t ] . (2)Intermediate demand thus is the sum of two components. First, to satisfy incoming demand(from t − i demands an amount A ji d i,t − from j . Therefore, industries orderintermediate inputs in fixed proportions of total demand, with the proportions encoded inthe technical coefficient matrix A , i.e. A ji = Z ji, /x i, where Z ji, is realized intermediateconsumption and x i, is total output of industry i . Before the shocks, both of these variablesare considered to be in the pre-pandemic steady state. While we will consider several scenarioswhere industries do not strictly rely on fixed recipes in production, demand always depends onthe technical coefficient matrix.The second term in Eq. (2) describes intermediate demand induced by desired reductionof inventory gaps. Due to the dynamic nature of the model, demanded inputs cannot be usedimmediately for production. Instead industries use an inventory of inputs in production. S ji,t denotes the stock of input j held in i ’s inventory. Each industry i aims to keep a target inventory n i Z ji, of every required input j to ensure production for n i further days . The parameter 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. Consumption demand.
We let consumption demand for good i be c di,t = θ i,t ˜ c dt , (3)where θ i,t is a preference coefficient, giving the share of goods from industry i out of totalconsumption demand ˜ c dt . The coefficients θ i,t evolve exogenously, following assumptions on howconsumer preferences change due to exogenous shocks (in our case, differential risk of infectionacross industries, see Section 3).Total consumption demand evolves following an adapted and simplified version of the con-sumption function in Muellbauer (2020). In particular, ˜ c dt evolves according to˜ c dt = (cid:0) − ˜ (cid:15) Dt (cid:1) exp (cid:26) ρ log ˜ c dt − + 1 − ρ (cid:16) m ˜ l t (cid:17) + 1 − ρ (cid:16) m ˜ l pt (cid:17)(cid:27) . (4)In the equation above, the factor (cid:0) − ˜ (cid:15) Dt (cid:1) accounts for direct aggregate shocks and will beexplained in Section 3. The second factor accounts for the endogenous consumption responseto the state of the labor market and future income prospects. In particular, ˜ l t is current laborincome, ˜ l pt is an estimation of permanent income (see Section 3), and m is the share of laborincome that is used to consume final domestic goods, i.e. that is neither saved nor used forconsumption of imported goods. In the pre-pandemic steady state with no aggregate exogenous Considering an input-specific target inventory would require generalizing n i to a matrix with elements n ji ,which is easy in our computational framework but difficult to calibrate empirically. (cid:15) Dt = 0 and by definition permanent income corresponds to current income, i.e. ˜ l pt = ˜ l t .In this case, total consumption demand corresponds to m ˜ l t . Other components of final demand.
In addition, an industry i also faces demand f di,t fromsources that we do not model as endogenous variables in our framework, such as governmentor industries in foreign countries. We discuss the composition and calibration of f di,t in detail inSection 3. 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 , which dependson the amount of available labor input. Initially every industry employs l i, of labor andproduces at full capacity x cap i, = x i, . We assume that productive capacity depends linearly onlabor inputs, x cap i,t = l i,t l i, x cap i, . (5) Input bottlenecks.
Second, the production of an industry might be constrained due to aninsufficient supply of critical inputs. This can be caused by production network disruptions.Intermediate input-based production capacities depend on the availability of inputs in an in-dustry’s inventory and its production technology, i.e. x inp i,t = function i ( S ji,t , A ji ) . (6)We consider five different specifications for how input shortages impact production, rangingfrom a Leontief form, where inputs need to be used in fixed proportions, to a Linear form,where inputs can be substituted arbitrarily. As intermediate cases we consider specificationswith industry-specific dependencies of inputs. For this purpose, IHS Markit analysts rated atour request whether a given input is critical , important or non-critical for the production of agiven industry (see Appendix C for details). We then make different assumptions on how thecriticality ratings of inputs affect the production of an industry. We now introduce the fivespecifications in order of stringency with respect to inputs. (1) Leontief: As first case we consider the Leontief production function, in which every positiveentry in the technical coefficient matrix A is a binding input to an industry. This is the mostrigid case we are considering, leading to the functional form x inp i,t = min { j : A ji > } (cid:26) S ji,t A ji (cid:27) . (7)In this case, an industry would halt production immediately if inventories of any input are rundown, even for small and potentially negligible inputs. (2) IHS1: As most stringent case based on the IHS Markit ratings, we assume that productionis constrained by critical and important inputs, which need to use in fixed proportions. In To see this, note that in the steady state ˜ c dt = ˜ c dt − . Taking logs on both sides, moving the consumptionterms on the left hand side and dividing by 1 − ρ throughout yields log ˜ c dt = log (cid:16) m ˜ l t (cid:17) . x inp i,t = min j ∈{V i ∪ U i } (cid:26) S ji,t A ji (cid:27) , (8)where V i is the set of critical inputs and U i is the set of important inputs to industry i . (3) IHS2: As second case using the input ratings, we leave the assumptions regarding critical and non-critical inputs unchanged but assume that the lack of an important input reduces anindustry’s production by a half. We implement this production scenario as x inp i,t = min { j ∈V i , k ∈U i } (cid:26) S ji,t A ji , (cid:18) S ki,t A ki + x cap i, (cid:19)(cid:27) . (9)This means that if an important input goes down by 50% compared to initial levels, productionof the industry would decrease by 25%. When the stock of this input is fully depleted, productiondrops to 50% of initial levels. (4) IHS3: Next we treat all important inputs as non-critical , such that only critical supplierscan create input bottlenecks. This reduces the input bottleneck equation, Eq. (6), to x inp i,t = min j ∈V i (cid:26) S ji,t A ji (cid:27) . (10) (5) Linear: Finally, we also implement a linear production function for which all inputs areperfectly substitutable. Here, production in an industry can continue even when inputs cannotbe provided, as long as there is sufficient supply of alternative inputs. In this case we have x inp i,t = (cid:80) j S ji,t (cid:80) j A ji . (11)Note that while production is linear with respect to intermediate inputs, the lack of labor supplycannot be compensated by other inputs.We assume for any production function that imports never cause bottlenecks. Thus, importsare treated as non-critical inputs or, equivalently, there is no shortages in foreign intermediategoods.Input bottlenecks are most likely to arise under the Leontief assumption, and least likelyunder the linear production function. The IHS production functions assume intermediate levelsof input specificity. In Appendix D we show that the IHS production functions are almostequivalent to (suitably parameterised) CES production functions and that results are evenidentical using these CES specifications instead of the IHS production functions. Output level choice and input usage.
Since an industry aims to satisfy incoming demandwithin its production constraints, realized production at time step t is x i,t = min { x cap i,t , x inp i,t , d i,t } . (12)Thus, the output level of an industry is constrained by the smallest of three values: labor-constrained production capacity x cap i,t , intermediate input-constrained production capacity x inp i,t ,or total demand d i,t .The output level x i,t determines the quantity used of each input according to the productionrecipe. 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 .9 ationing. Without any adverse shocks, industries can always meet total demand, i.e. x i,t = d i,t . However, in the presence of production capacity and/or input bottlenecks, industries’output may be smaller than total demand (i.e., x i,t < d i,t ) in which case industries rationtheir output across customers. We assume simple proportional rationing, although alternativerationing mechanisms could be considered (Pichler & Farmer 2021). The final delivery fromindustry j to industry i is a share of orders received Z ji,t = O ji,t x j,t d j,t . (13)Households receive a share of their demand c i,t = c di,t x i,t d i,t , (14)and the realized final consumption of agents with exogenous final demand is f i,t = f di,t x i,t d i,t . (15) Inventory updating.
The inventory of i for every input j is updated according to S ji,t +1 = min { S ji,t + Z ji,t − A ji x i,t , } . (16)In a Leontief production function, where every input is critical, the minimum operator would notbe needed since production could never continue once inventories are run down. It is necessaryhere, since industries can produce even after inventories of non-critical input j are depleted andinventories cannot turn negative. Hiring and separations.
Firms adjust their labor force depending on which production con-straints in Eq. (12) are binding. If the capacity constraint x cap i,t is binding, industry i decidesto hire as many workers as necessary to make the capacity constraint no longer binding. Con-versely, if either input constraints x inp i,t or demand constraints d i,t are binding, industry i laysoff workers until capacity constraints become binding. More formally, at time t labor demandby industry i is given by l di,t = l i,t − + ∆ l i,t , with∆ l i,t = l i, x i, (cid:104) min { x inp i,t , d i,t } − x cap i,t (cid:105) . (17)The term l i, /x i, reflects the assumption that the labor share in production is constant overthe considered period. We assume 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 indirection 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 strong labor market regulations, we usuallyhave γ F > γ H , indicating that it is easier for firms to lay off employed workers than to hire newworkers. Industry-specific employment evolves then according to l i,t = (cid:40) l i,t − + γ H ∆ l i,t if ∆ l i,t ≥ ,l i,t − + γ F ∆ l i,t if ∆ l i,t < . (18)The parameters γ H and γ F can be interpreted as policy variables. For example, the implemen-tation of a furloughing scheme makes re-hiring of employees easier, corresponding to an increasein γ H . 10 Pandemic shock
Simulations of the model described in Section 2.2 start in the pre-pandemic steady state. Whilethere is evidence that consumption started to decline prior to the lockdown (Surico et al. 2020),for simplicity we apply the pandemic shock all at once, at the date of the start of the lockdown(March 23 rd in the UK).The pandemic shock is a combination of supply and demand shocks that propagate down-stream and upstream and get amplified through the supply chain. During the lockdown, workerswho cannot work on-site and are unable to work from home become unproductive, resultingin lowered productive capacities of industries. At the same time demand-side shocks hit asconsumers adjust their consumption preferences to avoid getting infected, and reduce overallconsumption out of precautionary motives due to the depressed state of the economy.For diagnostic purposes, in addition to the shocks that we used for our original predictions,we consider a few additional supply shock scenarios that are grounded on what happened in theUK specifically . We then compare the outcomes under each scenario based on its aggregate andsectoral forecasts (see Section 4.2). In the following, we describe all the scenarios for supply anddemand shocks that we consider. Further details and industry-level shock statistics are shownin Appendix A. At every time step during the lockdown an industry i experiences an (exogenous) first-orderlabor supply shock (cid:15) Si,t ∈ [0 ,
1] that quantifies reductions in labor availability. Letting l i, be theinitial labor supply before the lockdown, the maximum amount of labor available to industry i at time t is given as l max i,t = (1 − (cid:15) Si,t ) l i, . (19)If (cid:15) Si,t >
0, the productive capacity of industry i is smaller than in the initial state of theeconomy. We assume that the reduction of total output is proportional to the loss of labor. Inthat case the productive capacity of industry i at time t is x cap i,t = l i,t l i, x cap i, ≤ (1 − (cid:15) Si,t ) x i, . (20)Recall from Section 2.2.2 that firms can hire and fire to adjust their productive capacity todemand and supply constraints. Thus, productive capacity can be lower than the initial supplyshock, in case industry i has some idle workers that are not prevented to go to work by lockdownmeasures. In any case, during lockdown firms can never hire more than l max i,t workers. Whenthe lockdown is lifted for a specific industry i , first-order supply shocks are removed, i.e., weset (cid:15) Si,t = 0, for t ≥ t end lockdown .For diagnostic purposes we consider six different scenarios for the supply shocks (cid:15) Si,t , S toS , ordered from lowest to the highest severity of lockdown restrictions. Scenario S is theone that was used to produce out of sample forecasts in our original paper. We follow delRio-Chanona et al. (2020) and estimate the supply shocks in each scenario by calculating for As described below, here we use estimates of the shocks that we develop a priori, based on empiricallymotivated assumptions on labor supply constraints and changes in preferences. We could have, in principle, useda traditional macro approach (see Brinca et al. (2020) in the case of Covid-19) where one can infer the shocksbased on data. We did not pursue this here for several reasons. Our model does not feature price changes (whichare crucial to separately identify supply and demand shocks), and we would have had to develop a method toinfer the shocks based on model’s fit to the data, a problem that is unlikely to have a unique solution. Mostimportantly, inferring shocks this way is only useful in hindsight, whereas our goal was to make predictions. (cid:15)
Si,t = 1 , ∀ t ∈ [ t start lockdown , t end lockdown . Instead, if an industry isclassified as fully essential, it faces no labor supply shock and (cid:15) Si,t = 0 ∀ t . In some scenarios, wefurther refine the supply shocks estimates by taking into account the difficulty of adjusting tosocial distancing measures. To do this refinement we use the Physical Proximity work contextprovided by O*NET, as others have done (Mongey et al. 2020, Koren & Pet˝o 2020).To estimate the shocks we define a Remote Labor Index , an
Essential Score and a
PhysicalProximity Index at the WIOD industry level. We interpret these indices as follows. The RemoteLabor Index of industry i is the probability that a worker from industry i can work from home.The Essential Score is the probability that a worker from industry i has an essential job. ThePhysical Proximity Index is the probability that an essential worker that cannot work fromhome cannot go to work due to social distancing measures. In Appendix A we explain how,similarly to del Rio-Chanona et al. (2020), Dingel & Neiman (2020), Gottlieb et al. (2020),Koren & Pet˝o (2020), we use O*NET data to estimate our Remote Labor Index and PhysicalProximity Index. Below we explain each scenario in more detail and how we determine theessential score in each scenario. Figure 8 in Appendix A shows time series of supply shocks (cid:15) Si,t for all scenarios throughout our simulations, while Table 5 shows the cross section of shocks. S : UK policy. In contrast to some European countries such as Italy and Spain, in the UKshutdown orders were only issued for a few industries . Although social distancing guidelineswere imposed for all industries (see S − S below), strictly speaking only non-essential retail,personal and recreational services, and the restaurant and hospitality industries were mandatedto shut down. While some European countries shut down some manufacturing sectors andconstruction, the UK did not explicitly forbid these sectors from operating.Based on the UK regulations, we assume that all WIOD industries have an essential scoreof one with the exception of industries G45 and G47 (vehicle and general retail), I (hotels andrestaurants) and R S (recreational and personal services). We break down these industries intosmaller subcategories that we can directly match to shutdown orders in the UK, and computean essential score from a weighted average of these subcategories, where weights correspond tooutput shares (see Appendix A for more details). The resulting essential scores are 0.64 forG45, 0.71 for G47, 0.05 for I and 0.07 for R S.Similarly to del Rio-Chanona et al. (2020), we assume an industry’s supply shock is givenby the fraction of workers that cannot work. If we interpret the Remote Labor Index and theessential score as independent probabilities, the expected value of the fraction of workers ofindustry i that cannot work is (cid:15) Si,t = (1 − RLI i )(1 − ESS i ) ∀ t ∈ [ t start lockdown , t end lockdown ) , where RLI i and ESS i are the Remote Labor Index and Essential Score of industry i respec-tively. We lift labor supply shocks to trade industries on June 15 th and shocks to other sectorsin July, as per official guidance. That is, (cid:15) Si,t = 0 , ∀ t ∈ [ t end lockdown , ∞ ) . S , S , S : UK policy + difficulty to adapt to social distancing. In monthly com-munications on the impact of Covid-19 on the UK economy , the ONS reported that several See, e.g., , we also consider the practical constraints of operating under the newguidance. For all industries that were not explicitly forbidden to operate, we consider a supplyshock due to the difficulties of adapting to social distancing measures.We assume that industries with a higher index of physical proximity have more difficultyto adhere to social distancing, so that only a portion of workers that cannot work from homecan actually work at the workplace. In particular, in-person work can only be performed bya fraction of workers that is proportional to the Physical Proximity Index of industry i (seeAppendix A for details). We rescale this index so that it varies in an interval between zero and ι , and consider three values ι = 0 . , . , .
7. These three values distinguish between scenariosS , S and S , which are reported in order of severity. At the time when lockdown starts, thesupply shocks are given by (cid:15) Si,t start lockdown = (1 − RLI i ) (cid:18) − ESS i (cid:18) − ι PPI i max j (PPI j ) (cid:19)(cid:19) , where PPI i is the Physical Proximity Index.Differently from the scenarios above, we do not assume that shocks due to the difficulty toadapt to social distancing are constant during lockdown. In line with ONS reports, firms are ableto bring a larger fraction of their workforce back to work as they adapt to the new guidelines.For simplicity, we assume that these shocks vanish when lockdown is lifted (May 13 th ), andinterpolate linearly between their maximum value (which is when lockdown is imposed, March23 rd ) and the time when lockdown is lifted. This leads to the following supply shocks (cid:15) Si,t = (1 − RLI i ) (cid:18) − ESS i (cid:18) − ι PPI i,t max j (PPI j ) (cid:19)(cid:19) , where PPI i,t = PPI i (cid:18) − t − t start lockdown t end lockdown − t start lockdown (cid:19) . Note that lockdown did not have a clear end date in the UK. However, we conventionallytake May 13 th as t end lockdown . This is the day when the UK government asked all workers togo back to work, and we assume that at this time most firms had had sufficient time to complyto social distancing guidelines. S : Original shocks. This baseline scenario corresponds to the original shocks (cid:15)
Si,t we usedin our previous work (Pichler et al. 2020) and was based on the estimates by del Rio-Chanonaet al. (2020). The supply shocks were estimated by quantifying which work activities of differentoccupations can be performed from home based on the Remote Labor Index and using theoccupational compositions of industries. The predictions also considered whether an industrywas essential in the sense that on-site work was allowed during the lockdown. We then compileda list of essential industries within the NAICS classification system, based on the list of essentialindustries provided by the Italian government using the NACE classification system. Then, wecomputed an essential score ESS i for each industry i in their sample of NAICS industries andcalculated the supply shock using the following equation (cid:15) Si = (1 − RLI i )(1 − ESS i ) . (21)Following our original work (Pichler et al. 2020), we map these supply shocks from theNAICS 4-digit industry classification system to the WIOD classification using a NAICS-WIOD13rosswalk. To deal with one-to-many and many-to-one maps in these crosswalks, we split eachNAICS industry’s contributions using employment data (see Appendix A for details). We followthis approach to weigh each worker in the NAICS industries’ sample from del Rio-Chanona et al.(2020) equally. In Appendix A we discuss the implications of this crosswalk methodology inmore detail. Finally, for the Real Estate sector, we assume that the supply shock does not applyto imputed rents (which represent about 2/3 of gross output). S : European list of essential industries. For comparison, we also consider the list ofessential industries produced by Fana et al. (2020). This list was compiled independentlyfrom del Rio-Chanona et al. (2020), and listed which industries were considered essential bygovernments of Spain, Germany and Italy. Using this list, we compute the essential score foreach industry by taking the mean across essential scores for the three countries considered. Wekeep labor supply shocks constant during lockdown, and lift them all when lockdown ends. Thisscenario produces the largest supply shocks of all. For comparison, the average supply shockfor S is 3%, while the average shock for S is 28%. The Covid-19 pandemic caused strong shocks to all components of demand. We consider shocksto private consumption demand, which we further distinguish into shocks due to fear of infectionand due to fear of unemployment, and shocks to other components of final demand, such asinvestment, government consumption and exports. We outline the basic assumptions on demandshocks below and show in in Appendix A the detailed cross-sectional and temporal shock profiles.We further demonstrate in Appendix F that alternative plausible demand shock assumptionsonly mildly influence model results.
Demand shocks due to fear of infection.
During a pandemic, consumption/saving deci-sions and consumer preferences over the consumption basket are changing, leading to first-orderdemand shocks (Congressional Budget Office 2006, del Rio-Chanona et al. 2020). For exam-ple, consumers are likely to demand less services from the hospitality industry, even when thehospitality industry is open. Transport is very likely to face substantial demand reductions,despite being classified as an essential industry in many countries. A key question is whetherreductions in demand for “risky” goods and services is compensated by an increase in demandfor other goods and services, or if lower demand for risky goods translates into higher savings.We consider a demand shock vector (cid:15) Dt , whose components (cid:15) Di,t are the relative changes indemand for goods of industry i at time t . Recall from Eq. (3), c di,t = θ i,t ˜ c dt , that consumptiondemand is the product of the total consumption scalar ˜ c dt and the preference vector θ t , whosecomponents θ i,t represent the share of total demand for good i . We initialize the preferencevector by considering the initial consumption shares, that is θ i, = c i, / (cid:80) j c j, . By definition,the initial preference vector θ sums to one, and we keep this normalization at all followingtime steps. To do so, we consider an auxiliary preference vector ¯ θ t , whose components ¯ θ i,t areobtained by applying the shock vector (cid:15) Di,t . That is, we define ¯ θ i,t = θ i, (1 − (cid:15) Di,t ) and define θ i,t as θ i,t = ¯ θ i,t (cid:80) j ¯ θ j,t = (1 − (cid:15) Di,t ) θ i, (cid:80) j (1 − (cid:15) Dj,t ) θ j, . (22)The difference 1 − (cid:80) i ¯ θ i,t is the aggregate reduction in consumption demand due to the de-mand shock, which would lead to an equivalent increase in the saving rate. However, householdsmay not want to save all the money that they are not spending. For example, they most likely14ant to spend on food the money that they are saving on restaurants. Therefore, we define theaggregate demand shock ˜ (cid:15) Dt in Eq. (4) as˜ (cid:15) Dt = ∆ s (cid:32) − N (cid:88) i =1 ¯ θ i,t (cid:33) , (23)where ∆ s is the change in the savings rate. When ∆ s = 1, households save all the money thatthey are not planning to spend on industries affected by demand shocks; when ∆ s = 0, theyspend all that money on goods and services from industries that are affected less.To parameterize (cid:15) Di,t , we adapt consumption shock estimates by the Congressional BudgetOffice (2006) and del Rio-Chanona et al. (2020). Roughly speaking, these shocks are massivefor restaurants and transport, mild for manufacturing and null for utilities. We make twomodifications to these estimates. First, we remove the positive shock to the health care sector, asin the UK the cancellation of non-urgent treatment for other diseases than Covid-19 far exceededthe additional demand for health due to Covid-19. Second, we apportion to manufacturingsectors the reduced demand due to the closure of non-essential retail. For example, retail shopsselling garments and shoes were mandated to shut down, and so we apply a consumption demandshock to the manufacturing sector producing these goods. We keep the intensity of demand shocks constant during lockdown. We then reduce demandshocks when lockdown is lifted according to the situation of the Covid-19 pandemic in the UK.In particular, we assume that consumers look at the daily number of Covid-19 deaths to assesswhether the pandemic is coming to an end, and that they identify the end of the pandemic asthe day in which the death rate drops below 1% of the death rate at the peak. Given officialdata , this happens on August 11 th . Thus, we reduce (cid:15) Di,t from the time lockdown is lifted (May13 th ) by linearly interpolating between the value of (cid:15) Di,t during lockdown and (cid:15)
Di,t = 0 on August11 th . The choice of modeling behavioral change in response to a pandemic by the death ratehas a long history in epidemiology (Funk et al. 2010). Demand shocks due to fear of unemployment.
A second shock to consumption demandoccurs through reductions in current income and expectations for permanent income.Reductions in current income are due to firing/furloughing, due to both direct shocks andsubsequent upstream or downstream propagation, resulting in lower labor compensation, i.e.˜ l t < ˜ l , for t ≥ t start lockdown . To support the economy, the government pays out social benefitsto workers to compensate income losses. In this case, the total income ˜ l t that enters Eq. (4)is replaced by an effective income ˜ l (cid:63)t = b ˜ l + (1 − b )˜ l t , where b is the fraction of pre-pandemiclabor income that workers who are fired or furloughed are able to retain.A second channel for shocks to consumption demand due to labor market effects occursthrough expectations for permanent income. These expectations depend on whether householdsexpect a V-shaped vs. L-shaped recovery, that is, whether they expect that the economy willquickly bounce back to normal or there will be a prolonged recession. Let expectations forpermanent income ˜ l pt be specified by ˜ l pt = ξ t ˜ l (24) To be fully consistent with the definition of demand shock, we should model non-essential retail closures assupply shocks, and propagate the shocks to manufacturing through reduced intermediate good demand. However,there are two practical problems that prevent us to do so: (i) the sectoral aggregation in the WIOD is too coarse,comprising only one aggregate retail sector; (ii) input-output tables only report margins of trade, i.e. theydo not model explicitly the flow of goods from manufacturing to retail trade and then from retail trade to finalconsumption. Given these limitations, we conventionally interpret non-essential retail closures as demand shocks. https://coronavirus.data.gov.uk/
15n this equation, the parameter ξ t captures the fraction of pre-pandemic labor income ˜ l thathouseholds expect to retain in the long run. We first give a formula for ξ t and then explain thevarious cases. ξ t = , t < t start lockdown ,ξ L = 1 −
12 ˜ l − ˜ l t start lockdown ˜ l , t ∈ [ t start lockdown , t end lockdown ] , − ρ + ρξ t − + ν t − , t > t end lockdown . (25)Before lockdown, we let ξ t ≡
1, i.e. permanent income expectations are equal to current income.During lockdown, following Muellbauer (2020) we assume that ξ t is equal to one minus half therelative reduction in labor income that households experience due to the direct labor supplyshock, and denote that value by ξ L . (For example, given a relative reduction in labor incomeof 16%, ξ L = 0 . 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 byletting 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 householdsbelieving in such a recovery pattern, it is ν t ≡ − (1 − ρ )(1 − ξ L ) / Other final demand shock scenarios
Note that WIOD distinguishes five types of final de-mand: (I)
Final consumption expenditure by households , (II)
Final consumption expenditure bynon-profit 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, meaning that it is possible to calculateimports and exports for all categories of final demand. The endogenous consumption variable c i,t corresponds to (I), but only for domestic consumption. All other final demand categories,including all types of exports, are absorbed into the variable f i,t .We apply different shocks to f i,t . We do not apply any exogenous shocks to categories (III) Final consumption expenditure by government and (V)
Changes in inventories and valuables ,while we apply the same demand shocks to category (II) as we do for category (I). To determineshocks to investment (IV) and exports we start by noticing that, before the Covid-19 pandemic,the volatility of these variables has generally been three times the volatility of consumption. The overall consumption demand shock is around 5% so, as a baseline, we assume shocks toinvestment and exports to be 15%. In Appendix F we show that the model results are fairlyrobust with respect to alternative choices.
As already mentioned, in the first version of this work we released results in May predicting a21.5% contraction of GDP in the UK economy in the second quarter of 2020 with respect to During lockdown, labor income may be further reduced due to firing. For simplicity, we choose not to modelthe effect of these further firings on permanent income. The specification in Eq. (25) reflects the following assumptions: (i) time to adjustment is the same as forconsumption demand, Eq. (4); (ii) absent permanent shocks, ν t = 0 after some t , ξ t returns to one, i.e. permanentincome matches current income; (iii) with 50% households believing in an L-shaped recovery, ξ t reaches a steadystate given by 1 − (1 − ξ L ) /
2: with ξ L = 0 .
92 as in the example above, ξ t reaches a steady state at 0.96, so thatpermanent income remains stuck four percentage points below pre-lockdown income. This is computed by calculating the standard deviation of consumption, investment and export growthover all quarters from 1970Q1 to 2019Q4. These are 1.03%, 2.87% and 3.24% respectively. Source: . This is in comparison to the contraction of 22.1% that was actuallyobserved. In this section we do a post-mortem to understand the factors that influenced thequality of the forecasts. To do this, we compare results under different scenarios defined bydifferent shocks and production functions. Our analysis includes a sectoral breakdown of theforecasts and a comparison of the time series of observed vs. predicted behavior. The model and shock scenarios that we described in the previous sections has several degrees offreedom that can be tuned when exploring the model. These are either model assumptions suchas the production function, shock scenarios, or parameters (see Table 1). To understand thefactors that influenced the quality of the forecasts, we focus on the assumptions and parametersthat cannot easily be calibrated from data and that have a strong effect on the results.As the sensitivity analysis in Appendix F shows, the model is most sensitive to two assump-tions: the supply shock scenario and the production function. So, we consider all combinationsof the six scenarios for supply shocks, S to S (Section 3.1), and of the five production functionsmentioned in Section 2.2.2. These are: standard Leontief, three versions of the IHS-Markit-modified Leontief that treat important inputs as critical (IHS1), half-critical (IHS2), and non-critical (IHS3) and the linear production function. Combining these two assumptions, we get6 × Table 1: Assumptions and parameters of the model that: (top) are varied across scenarios; (middle) are fixeddue to little effect on results; (bottom) are fixed due to direct data calibration.
Name Symbol ValueSupply shocks S S , S , S , S , S , S Production function Leontief, IHS1, IHS2, IHS3, linearFinal demand shocks Appendix AInventory adjustment τ γ H γ F s ρ n i Appendix BPropensity to consume m b • The parameter τ , capturing responsiveness to inventory gaps. We fix τ = 10 days, whichindicates that firms aim at filling most of their inventory gaps within two weeks. This liesin the range of values used by related studies (e.g. τ = 6 in Inoue & Todo (2019), τ = 30in Hallegatte (2014)). • The hiring and firing parameters γ H and γ F . We choose γ H = 1 /
30 and γ F = 2 γ H .Given our daily time scale, this is a rather rapid adjustment of the labor force, with firinghappening faster than hiring. Due to an error in how we dealt with Real Estate shocks, our prediction was slightly worse than it wouldhave been without the error, see Appendix A The parameter ρ , indicating sluggish adjustment to new consumption levels. We selectthe value assumed by Muellbauer (2020), adjusted for our daily timescale . • The savings parameter ∆ s . We take ∆ s = 0 .
5, meaning that households save half themoney they are not spending in goods and services due to fear of infection, and directhalf of that money to spending for other “safer” goods and services.Finally, we are able to directly calibrate some parameters against the data. For example, wecalibrate the inventory target parameters n i using ONS data for the usual stock of inventoriesthat different industries typically have (see details in Appendix B). These parameters are highlyheterogeneous across industries; typically manufacturing and trade have much higher inventorytargets than services. Another parameter which we can directly calibrate from data is thepropensity to consume m (see Eq. 4). Directly reading the share of labor income that is used tobuy final domestic goods from the input-output tables, we find m = 0 .
82. Finally, we calibratebenefits b based on official UK policy, b = 0 . We have chosen not to search for a calibration of the model that best fits the data. We do thisbecause we only have one real world example and this would lead to overfitting. Instead we startfrom the out-of-sample forecast we made in May and try to understand how performance wouldhave changed if we had made different choices. This helps us understand what is importantin determining the accuracy and gives some insight into how the model works, and where careneeds to be taken in making forecasts of this type.Since our initial forecast, we have made small changes to the model (in particular theconsumption function), and obtained better data to calibrate inventories (using ONS ratherthan US BEA data). Our initial forecast featured a supply shock scenario identical to S5 exceptfor Real Estate (Section 3.1 and Appendix A), and an IHS3 production function. In this section,we compare our original forecast to the forecasts made using the 30 possible scenarios discussedabove. To do so, we evaluate the forecast errors for each scenario at both the sectoral andaggregate levels, allowing us to better understand the trade-off involved in selecting amongstvarious assumptions and calibrations.For all 30 scenarios, we simulate the model for six months, from January 1 st to June 30 th ,2020. We start lockdown on March 23 rd , at which point we apply the supply and demandshocks described in Section 3. We then compare the monthly sectoral output of each scenario against empirical data fromthe indexes of agriculture, production, construction and services, all provided by the ONS (seeAppendix E.1). Specifically, we compute the sector-level Absolute Forecast Errors (AFE) for Assuming that a time step corresponds to a quarter, Muellbauer (2020) takes ρ = 0 .
6, implying that morethan 70% of adjustment to new consumption levels occurs within two and a half quarters. We modify ρ toaccount for our daily timescale: By letting ¯ ρ = 0 .
6, we take ρ = 1 − (1 − ¯ ρ ) /
90 to obtain the same timeadjustment as in Muellbauer (2020). Indeed, in an autoregressive process like the one in Eq. (4), about 70% ofadjustment to new levels occurs in a time ι related inversely to the persistency parameter ρ . Letting Q denotethe quarterly timescale considered by Muellbauer (2020), time to adjustment ι Q is given by ι Q = 1 / (1 − ¯ ρ ). Sincewe want to keep approximately the same time to adjustment considering a daily time scale, we fix ι D = 90 ι Q .We then obtain the parameter ρ in the daily timescale such that it yields ι D as time to adjustment, namely1 / (1 − ρ ) = ι D = 90 ι Q = 90 / (1 − ¯ ρ ). Rearranging gives the formula that relates ρ and ¯ ρ . We do not run the model further in the future, both because we focus on the first UK lockdown and theimmediate aftermath, and because our assumptions on non-critical inputs are only valid for a limited time span. E zi,t = | y i,t − ˆ y zi,t | , where y i,t = x i,t /x i, is the output of sector i during month t expressed as a percentage of theoutput of sector i during February, x i, . Here, ˆ y zi,t is the equivalent quantity in simulationsof scenario z . We then obtain a scenario-specific average sectoral AFE by taking a weightedmean of E zi,t across all sectors i and months t , where weights correspond to output shares inthe steady state (forecast errors for important sectors are more relevant than forecast errors forsmall sectors). This quantity is defined asAFE z sec = 13 N (cid:88) t (cid:88) i x i, (cid:80) j x j, E zi,t . (26)We also compare aggregate output reductions in all different scenarios in April, May andJune against empirical data. We compute a scenario-specific average aggregate AFE by aver-aging aggregate forecast errors over the three months we are considering. This isAFE z agg = 13 (cid:88) t (cid:32)(cid:88) i x i,t − (cid:88) i ˆ x zi,t (cid:33) , (27)where ˆ x zi,t is output of sector i at time t for scenario z . Note that, unlike the measure of sectoralerror AFE z sec , the aggregate measure AFE z agg does not include an absolute value – it is positivewhen true production is greater than predicted, and negative when it is smaller than predicted. − − − Absolute mean sectoral error (%) M ean agg r ega t e e rr o r ( % ) − − − Absolute mean sectoral error (%) M ean agg r ega t e e rr o r ( % ) Supplyshocks
S1S2S3S4S5S6
Productionfunction
LinearIHS3IHS2IHS1Leontief
Figure 1:
Sectoral and aggregate errors across scenarios.
We plot aggregate Average Forecast ErrorAFE agg z vs. sectoral Average Forecast Error AFE sec z for 30 different scenarios z , corresponding to all of the sixpossible shock scenarios (indicated by color) and the five possible production functions (indicated by symbol),as well as the original model forecast, indicated by a black asterisk. The other parameter values are indicated inTable 1. Both sectoral and aggregate AFE are multiplied by 100 to be interpreted as percentages. The right panelzooms on the region with lowest sectoral and aggregate errors. The dashed lines refer to an average forecast byinstitutions and financial firms (above zero) and to a forecast by the Bank of England (below zero), see footnote1. Figure 1 plots sectoral and aggregate AFE for the 30 scenarios, plus the original out-of-sample forecast. The sectoral and aggregate errors vary considerably across scenarios. The left We exclude January, February and March from our comparison as we do not model the reaction of theeconomy before the lockdown, when e.g. international supply chains started to be disrupted. S and S . The right panel blows up the region containing the other 28 scenarios.The sectoral errors range between roughly 10% and 20%, while the aggregate forecast errorsrange from roughly -10% to 10%.A close examination of the figure makes it clear that, as expected, the predicted downturngenerally gets stronger as the severity of the shock and the rigidity of the production functionincreases. With one exception, the choice of scenario has a bigger effect on the error thanthe production function. This is evident from the fact that there are clusters of points withthe same color associated with each scenario. The clusters are particularly tight for the lesssevere scenarios. The exception is the Leontief production function: The two most severe shockscenarios produce outliers with downturns that are much too strong and the remainder allproduce results clustered together, with aggregate errors in the range of −
4% to − S ; by comparison, every other production functionpredicts a downturn that is too weak under scenario S , in the range of 8% − scenario in combination with the IHS3 production function. Thisforecast performs better at the sectoral level, but worse at the aggregate level (the error is2.5%). Using an IHS2 production function with the S shock scenario seems to provide the bestcombination of sectoral and aggregate errors.To put these results in perspective, it is worth comparing to the other out-of-sample forecaststhat were made around the same time. We do not know their sectoral errors but we can comparethe aggregate errors. The Bank of England forecast, for example, predicted a downturn of about30%, which corresponds to an aggregate error of about -8%, comparable to the scenarios with S supply shocks and with Leontief production function and supply shocks S to S . Conversely,the average forecast by institutions and financial firms for the UK economy in Q2 2020 was -16.6%, which is 5.5% less than what was observed in reality. This forecast is in line with supplyshock scenarios S to S , as well as with S combined with a linear production function.Therefore, it seems that the more accurate predictions of our model are obtained by combin-ing shock scenario S – as in our original prediction – with one of the IHS production functions.Why does this scenario, which was not designed to capture specific features of the UK econ-omy, work so well? The evidence suggests that this is because there were many voluntary firmshutdowns, such as for the car manufacturing industry in the UK. The S shock scenario does abetter job of identifying industries that we not mandated to shut down, but did so in practice,and seems to better capture the behavioral response to the pandemic than a literal reading ofUK regulations. Given that it minimizes a combination of aggregate and sectoral error, and given that it is closeto the original scenario used for our out-of-sample predictions, we focus on the scenario thatcombines S and the IHS2 production function to illustrate the outcomes of our model in moredetail. We start by showing the dynamics produced by the model, and then we evaluate howwell the selected scenario explains some aspects of the economic effects of Covid-19 on the UKeconomy that we did not consider so far.Figure 2 shows model results for the selected scenario for production (gross output); results20 ockdown starts Lockdown ends Accommodation−Food0.000.250.500.751.00 − −
01 2020 − −
16 2020 − −
31 2020 − −
15 2020 − −
30 2020 − −
15 2020 − −
30 2020 − −
14 2020 − − G r o ss ou t pu t ( no r m a li z ed ) Aggregate Agriculture and industry Trade, transport, restaurants Business and social services
Figure 2:
Economic production for the chosen scenario as a function of time.
We plot production (grossoutput) as a function of time for each of the 55 industries. Aggregate production is a thick black line and eachsector is colored. Agricultural and industrial sectors are colored red; trade, transport, and restaurants are coloredgreen; service sectors are colored blue. All sectoral productions are normalized to their pre-lockdown levels, andeach line size is proportional to the steady-state gross output of the corresponding sector. For comparison, wealso plot empirical gross output as normalized with respect to March 2020. for other important variables, such as profits, consumption and labor compensation (net ofgovernment benefits) are similar. When the lockdown starts, there is a sudden drop in economicactivity, shown by a sharp decrease in production. Some other industries further decreaseproduction over time as they run out of critical inputs. Throughout the simulation, servicesectors tend to perform better than manufacturing, trade, transport and accommodation sectors.The main reason for that is most service sectors face both lower supply and demand shocks, asa high share of workers can effectively work from home, and business and professional servicesdepend less on consumption demand.In the UK, there was not a clear-cut lifting of the lockdown but, under scenario S , wetake May 13th as a conventional date in which lockdown measures are lifted (see Figure 8 inAppendix A for shock dynamics). By the end of June, the economy is still far from recovering.In part, this is due to the fact that the aggregate level of consumption does not return to pre-lockdown levels, due to a reduction in expectations of permanent income associated with beliefsin an L-shaped recovery (Section 2.2.1), and due to the fact that we do not remove shocks toinvestment and exports (see Section 3).We now turn to evaluating how well the selected scenario describes the economic effectsof Covid-19 on the UK economy. In terms of gross output, one can see in Table 2 that the The reduction in production due to input bottlenecks is somewhat limited in this scenario as compared tothe outliers in Figure 3. With supply shocks S or S and a Leontief production function, the economy collapsesby 50% due to the strong input bottlenecks created in a substantially labor-constrained economy in which allinputs are critical for production. Table 2: Comparison between data and predictions of the selected scenario for the main aggregate variables.All percentage changes refer to the last quarter of 2019, which we take to represent the pre-pandemic economicsituation. model slightly underestimates the recession in April and slightly overestimates it in May, whileit correctly estimates a strong recovery in June. Additionally, aggregate value added in thesecond quarter of 2020 is very close to the data.Our model, however, considers other macroeconomic variables than gross output and valueadded, so we also compare these other variables to data (Table 2). From national accounts, wecollect data on private and government consumption, investment, change in inventories, exportsand imports (expenditure approach to GDP); wages and salaries and profits (income approachto GDP). Looking at the expenditure approach to GDP, some variables have a worse reductionin the model, such as investment and exports, while other variables have a worse reduction inthe data, such as private and government consumption, inventories and imports. However,the model predicts the relative reductions fairly well, as we find a stronger collapse in privateconsumption and investment than in government consumption or inventories, as in the data.Finally, considering the income approach to GDP, we overestimate the reduction in wages andsalaries and underestimate the reduction in profits. Nonetheless, we correctly predict thatthe absolute reduction in wages and salaries is much smaller than in profits (due to governmentsubsidies).Turning to the performance of our model at the disaggregate level of industries, Figure 3shows gross output as predicted by the model and in the data. Here, gross output is averagedover the values it takes in March, April and June, both in the model and in the data, andcompared to the value it had in Q4 2019. To interpret this figure, note that for all pointson the left of the identity line, model predictions are lower than in the data, i.e. the modelis pessimistic. Conversely, on the right of the identity line model predictions are higher thanin the data, i.e. the model is optimistic. Note that model predictions and empirical data arecorrelated, although not perfectly: the Pearson correlation coefficient weighted by industry sizeis 0.75. The majority of sectors decreased production up to 60% of initial levels, both in themodel and in the data, but a few sectors were forced to decrease production much more. We aggregate empirical output from sectoral indexes using our steady-state output shares as weights. If one considers Exports-Imports as a component, the model predicts a current account deficit, while inreality there was a current account surplus. We should however note that we do not model international trade,we treat exports as exogenous and imports like locally produced goods and services. Note that these categories are not jointly exhaustive, as the ONS also considers mixed income and taxes lesssubsidies, which are difficult to compare to variables in our model. anuf. Metals−basicManuf. MachineryManuf. Vehicles Manuf. Transport−other WaterVehicle tradeLand transportWater transportAir transportAccommodation−Food InsurancePublic AdministrationEducationHousehold activities Model optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimistic Model pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimistic
Other scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther scienceOther science020406080100 0 20 40 60 80 100 data m ode l Industry group
Agriculture and industryTrade, transport, restaurantsBusiness and social services
Weight
Figure 3:
Comparison between model predictions and empirical data.
We plot predicted production(gross output) for each of 53 industries against the actual values from the ONS data, averaged across April, Mayand June. Values are relative to pre-lockdown levels and dot size is proportional to the steady-state gross outputof the corresponding sector. Agricultural and industrial sectors are colored red; trade, transport, and restaurantsare colored green; service sectors are colored blue. Dots above the identity line means that the predicted recessionis less severe than in the data, while the reverse is true for dots below the identity line.
While the predictions are generally very good, there are also some dramatic failures. Weconjecture that this is due to idiosyncratic features of these industries that we could not takeinto account without overly complicating our model. For example, one sector for which thepredictions of our model are completely off is C29 - Manufacturing of vehicles. Almost all carmanufacturing plants were completely closed in the UK in April and May, and so production wasessentially zero (7% of the pre-pandemic level in April and 14% in May). While they reopenedin June, production in Q2 is slightly above 20% of the pre-pandemic level. However, our modelpredicts a level of production around 63% of the pre-pandemic level. It is difficult to accountfor the complete shutdown of car manufacturing plants in our model, as our selected scenariofor supply shocks does not require manufacturing plants to completely close during lockdown.We think that this discrepancy between model predictions and data can be explained by twofactors. First, car manufacturing is highly integrated internationally, and, in a period wheremost developed countries were implementing lockdown measures, international supply chainswere highly disrupted. For simplicity, however, in our model we did not model input bottlenecksdue to lack of imported goods. Second, it is possible that firms producing non-essential goodsvoluntarily decided to stop production to protect the health of their workers, even if they werenot forced to do so. Another example for which the predictions of our model are off is H51 -Air transport. Production in the data is 3% of pre-lockdown levels, while our model predictsaround 50%. In the model, most activity of the air transport industry during lockdown is dueto business travel, which is a non-critical input to many industries that we do not exogenouslyshut down (recall that industries aim at using non-critical inputs if they are available).23
Model pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimistic Model optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimistic
Model prediction E m p i r i c a l da t a Industry share
Month
AprilJune
Figure 4:
Comparison between model predictions and empirical data.
We plot predicted production(gross output) vs. observed values from ONS data. Production is relative to pre-lockdown levels and dot size isproportional to the steady-state gross output of the corresponding sector. Yellow is April and red is June. Blacklines connect the same industry from April to June. Only a few industries are highlighted (see main text).
In some other cases, however, our model gave accurate predictions, even when the answer wasfar from obvious. Compare, for instance, industries M74 M75 (Other Science) and O84 (PublicAdministration). Both received a very weak supply shock (3% for Other Science and 1.1% forPublic Administration, see Table 5 in Appendix A), and no private consumption demand shocks.Yet, Public Administration had almost no reduction in production, while Other Science reducedits production to about 75% of its pre-pandemic level. The ONS report in May (see footnote7) quotes reduced intermediate demand as the reason why Other Science reduced its activity.Conversely, Public Administration’s output is almost exclusively sold to the government, whichdid not reduce its consumption. Because of its ability to take into account supply chain effectsand the resulting reductions in intermediate demand, our model is able to endogenously capturethe difference between these two sectors, even though their shocks are small in both cases.Figure 4 shows the ability of the model to predict sectoral dynamics. It is similar to Figure3 but shows output in both April and June. The dots that represent the same industry inApril and June are connected by a black line. We focus on a few industries that we discussin this section, making all other points light grey (Figure 14 in Appendix E.2 shows labelsfor all industries). To interpret changes from April to June, note that a line close to verticalimplies that a given industry had a much stronger recovery in the data than in the model, whilea horizontal line implies the opposite. A line parallel to the identity line indicates that therecovery was as strong in the data as in the model. Almost all sectors experience a substantialrecovery from April to June, both in the model and in the data.24n example in which our model correctly predicts dynamic supply chain effects is the recov-ery experienced by C23 (Manufacture of other non-metallic mineral products) as a consequenceof the recovery by F (Construction). According to ONS reports, increased activity in construc-tion in June is explained by the lifting of the lockdown and by adaptation to social distancingguidelines by construction firms. At the same, industry C23 recovers due to the productionof cement, lime, plaster, etc to satisfy intermediate demand by construction (construction isby far the main customer of C23, buying almost 50% of its output). This pattern is faithfullyreproduced by the endogenous dynamics in our model.
In the standard Cobb-Douglas Equilibrium IO model, productivity shocks propagate down-stream and demand shocks propagate upstream (Carvalho & Tahbaz-Salehi 2019). Thus, theelasticity of aggregate output to a shock to one sector depends on the type of shock, and on theposition of an industry in the input-output network. What can we say about these questions inour model? Are there properties of an industry that could be computed ex-ante to know howsystemic it is? Is this different for supply and demand shocks?To answer these questions, we run the model with a single shock – either supply or demand– to a single industry. All the other industries do not experience any shocks but have initialproductive capacities and face initial levels of final demand. We then let the economy evolveunder this specific setting for one month . We repeat this procedure for every industry, everyproduction function specification and different shock magnitudes. We then investigate if thedecline in total output can be explained by simple measures such as shock magnitude, outputmultipliers or upstreamness levels which we formally define below. We first explain the supplyand demand shock based scenarios in somewhat more detail. Supply shock scenarios.
When considering supply shocks only, we completely switch offany adverse demand effects, i.e. (cid:15)
Di,t = 0 (which implies θ i,t = θ i, and ˜ (cid:15) Dt = 0), ξ t = 1 and f di,t = f di, for all i and t . We also set all supply shocks equal to zero (cid:15) Si,t = 0, except for a singleindustry j which experiences a supply shock from the set (cid:15) Sj,t ∈ { . , . , ..., } . We then loopover every possible j . We do this for each of the different production function assumptions. Demand shock scenarios.
In our demand shock scenarios there are no supply shocks( (cid:15)
Si,t = 0 ∀ i, t ) and similarly there is no demand shocks for all but one industry j ( (cid:15) Di,t = 0, f di,t = f di, ∀ i (cid:54) = j, ∀ t ). For the single industry j we again let shocks vary between 10 and 100%; (cid:15) Dj,t ∈ { . , . , ..., } . For simplicity we assume uniform shocks across all final demand categoriesof the given industry, resulting in f dj,t = (1 − (cid:15) Dj,t ) f dj, . To keep things as simple as possible, wefurther assume that there is no fear of unemployment ξ t = 1 and that final consumers do notswitch to alternative products at all (∆ s = 1). Under these assumptions the values for θ i,t = θ i,t and ˜ (cid:15) Dt are then computed as outlined in Section 3.2.Figure 5 shows the simulation results broken down into the various shock magnitudes (ver-tical axis) and production function categories (horizontal axis). The coloring and the value of atile represent the average aggregate output (as a fraction of initial output), where the average istaken over all N runs. Results obtained from the demand shock scenarios, Figure 5(b), do not We also did the analysis with model simulations up to two months after the initial shock is applied. Sinceresults are similar for the two cases, we only report results for the one month simulations. which industries are affected by these shocks. For example, applying an 80%supply shock shock to industry Repair-Installation (C33) under the IHS2 assumption, collapsesthe economy by about 50%, although the industry accounts for less than half a percent ofthe overall economy. On the other hand, applying the same shock to the comparatively largeindustry Other Services (R S, 3% of the economy) leads to a mere 6% reduction of aggregateoutput.
100 100 10099 10099 99 9997 9997 97 9893 9995 96 9789 9992 93 9682 9988 90 9374 9882 86 9165 9874 81 8755 9862 75 8144 9843 68 7332 97
Production function S ho ck m agn i t ude ( % ) (a) Supply shocks Production function S ho ck m agn i t ude ( % ) (b) Demand shocks Figure 5:
Aggregate gross output as percentage of pre-shock levels after shocking single industries.
A column depicts different production functions and rows distinguish the supply (a) and demand (b) shockmagnitude which an industry is exposed to. Results in (b) are only shown for one production function, sincethey are identical across alternative specifications. The values in the tiles and their coloring denote aggregateoutput levels as percentage of pre-shock levels one month after the shock hits a given industry. This values arecomputed as averages from N runs, always shocking only a single industry. For a policymaker it is important to know what properties of an industry drive the am-plification of shocks, as this could inform both the design of lockdown measures as well asreopening policies. To explore this more systematically, we regress output levels against po-tential explanatory factors such as upstreamness, output multipliers and industry sizes. Anindustry’s upstreamness in a production network is its average distance to the final consumer26Antr`as et al. 2012) and also known as Total Forward Linkages (Miller & Temurshoev 2017).High upstreamness implies that the output of this industry requires several subsequent produc-tion steps before it is purchased by final consumers. Thus, relaxing shocks on industries withhigh upstreamness could potentially stimulate further economic activity. Since upstreamnessboils down to the row sums of the Gosh inverse (Miller & Temurshoev 2017), we obtain the N -dimensional upstreamness vector as u = ( I − B ) − , where a matrix element B ij = Z ij, /x i, represents “allocation coefficients”. Upstreamness ranges from 1.004 (Household activities) to2.742 (Warehousing) in our sample of UK industries.Output multipliers, or alternatively Total Backward Linkages, are a core metric in manyeconomic studies. In input-output analysis multipliers quantify the impact of a change in finaldemand in a given sector on the entire economy. Multipliers are related to various networkcentrality concepts and have been shown to be strongly predictive of long-term growth (Mc-Nerney et al. 2018). Since shocking an industry with a high multiplier should lead to largerdecreases in intermediate demand, it is plausible that high-multiplier industries tend to amplifyshocks more. The output multiplier is computed as the column sum of the Leontief inverse,i.e. m = ( I − A (cid:62) ) − . Multipliers range from 1 (Household activities) to 2.379 (Forestry) inour sample. Upstreamness and multipliers are different, but are fairly highly correlated, with aPearson correlation of 0.45.We then regress log aggregate output one month after the initial shock hits the economy,log( (cid:80) k x k, ), against the shocked industry’s log upstreamness and multiplier levels. Naturally,we would expect a larger decline if supply shocks hit an overall large industry and similarly fordemand shocks and the size of final consumption. Thus we also control for total industry sizemeasured in log gross output, log( x i, ), and industry-specific total demand, log( c di, + f di, ), inour regressions . We then run the regression for every given shock magnitude and productionfunction separately.Tables 3 summarizes the regression results for the supply shock scenarios. For supply shockswe find that upstreamness is a very good predictor of adverse economic impacts if the economybuilds upon Leontief production mechanisms. If industries use linear production technologies,on the other hand, it is rather the size of the industry than its upstreamness level that explainsreductions in aggregate output. When using the intermediate assumption of an IHS2 productionfunction, both upstreamness levels and industry size significantly affect aggregate impacts,although the overall model fit ( R ) drops substantially.Note that supply shocks are to a large extent a policy variable as they are directly coupled tonon-pharmaceutical interventions such as industry-specific shutdowns. Our results indicate thatupstreamness levels of industries are an important aspect for designing lockdown scenarios. Incase of limited production flexibilities, upstreamness might be even a better indicator of industryclosure related aggregate impacts than the actual size of the industry.Regression results for the demand shock experiments are shown in Table 4. The first fourcolumns show the results from univariate regressions where we include only one of the potentialcovariates: upstreamness, multipliers, final consumption and gross output. Somewhat surpris-ingly, output multipliers, a key metric for quantifying aggregate impacts resulting from demandside perturbations in simpler input-output models, do not exhibit any predictive power in ourcase. Upstreamness, on the other hand, is positively associated with aggregate output values,indicating that demand shocks to upstream industries have less adverse impacts on the economythan downstream industries. Better model fits, however, are obtained when regressing aggregateoutput against indicators of industry size gross output or final consumption. We do not include gross output and final demand values together as regressors to avoid multicolinearity.Industry gross output and final consumption are highly correlated; cor { log( x i, ) , log( c i, + f i, ) } = 0 .
89 (p-value < − ). ependent variable: log( (cid:80) i x i, )Shock size: 40% 40% 40% 80% 80% 80%Production: Leontief IHS2 Linear Leontief IHS2 Linearlog( u i, ) − ∗∗∗ − ∗∗∗ − ∗∗∗ − ∗∗∗ m i, ) 0.067 0.065 − − x i, ) − − ∗∗∗ − ∗∗∗ − − ∗∗∗ − ∗∗∗ (0.004) (0.004) (0.001) (0.005) (0.016) (0.001)Constant 15.512 ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ (0.050) (0.053) (0.009) (0.065) (0.197) (0.018)Observations 55 55 55 55 55 55Adjusted R Note: ∗ p < ∗∗ p < ∗∗∗ p < Regression results for supply shock experiments.
Dependent variable: log( (cid:80) i x i, )(1) (2) (3) (4) (5) (6)log( u i, ) 0.040 ∗∗ ∗∗∗ (0.010) (0.010) (0.008)log( m i, ) 0.021 − − c i, + f i, ) − ∗∗∗ − ∗∗∗ (0.002) (0.002)log( x i, ) − ∗∗∗ − ∗∗∗ (0.002) (0.002)Constant 15.443 ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ (0.006) (0.013) (0.016) (0.023) (0.025) (0.023)Observations 55 55 55 55 55 55Adjusted R − Note: ∗ p < ∗∗ p < ∗∗∗ p < Regression results for demand shock experiments.
As representative case we show regressionresults for the scenario of 60% shocks to final consumption, because results are similar for alternative shock sizes.Note that economic impacts are identical across alternative production functions. Discussion
In this paper we have investigated how locking down and re-opening the UK economy as apolicy response to the Covid-19 pandemic affects economic performance. We introduced a noveleconomic model specifically designed to address the unique features of the current pandemic.The model is industry-specific, incorporating the production network and inventory dynamics.We use survey results by industry experts to model how critical different inputs are in theproduction of a specific industry.We found in simulation experiments where we studied simpler shock scenarios and a simpli-fied model setup that an industry’s upstreamness is predictive of shock amplification. However,the relationship is noisy and strongly depends on the underlying production mechanism in caseof downstream propagation of supply shocks. These results underline the necessity of more so-phisticated macroeconomic models for quantifying the economic impacts resulting from nationallockdowns and subsequent re-opening.Real time GDP predictions for the UK economy made in an early version of this paperturned out to be very accurate (Pichler et al. 2020). But was this because we did things right,or because we just got lucky? Our analysis here shows that it was a mixture of the two. Byinvestigating both alternative shocks scenarios, alternative production functions and studyingthe sensitivity to parameters and initial conditions we are able to see how the quality of thepredictions depends on these factors. We find that the shock scenarios are the most importantdeterminant, but the production function can also be very important, and some of the otherparameters can affect the results as well.To make a real time forecast we had to act quickly. There were no data available aboutwhich industry classifications were considered essential in the UK and the few data availableon UK jobs that could be performed form home was based on US O*NET data . In theinterest of time, we estimated the UK supply shocks using predicted US supply shocks del Rio-Chanona et al. (2020). These supply shocks were based on a list of essential industries thatwas considerably less permissive (i.e., less industries were considered essential) than the UKguidelines. This turned out to be lucky: respecting social distancing guidelines caused manyindustries in the UK to close even though they were not formally and explicitly required todo so. With hindsight, this was fortuitous – if we had had a list of essential British industriesour supply shocks would have been too weak, or we would have had to model social distancingconstraints by industry, which is difficult. Even if it missed some of the details, the supplyshocks estimated by del Rio-Chanona et al. (2020) provided a reasonable approximation to thetruth.The choice of production function also matters a great deal. Our results suggest that theLeontief production function, which is widely used for understanding the response to disasters,is a poor choice. This is for an intuitive reason: Some inputs are not critical, and an industrycan operate reasonably well without them, at least for a few months. Our results here showthat production functions that incorporate this fact can do well. This could be further devel-oped by calibrating CES production functions to correctly incorporate when substitutions areappropriate. The IHS Markit survey that was performed should eventually be performed withlarger samples and tested in detail (but that is beyond the scope of this paper). At the otherextreme, our results also suggest that the linear production function is a poor choice. It comesclose to the correct aggregate error only with the strongest shock scenario and never performswell at the sectoral level.Our results indicate that dynamic models of the type that we developed here can do a good Andersen, A. L., Hansen, E. T., Johannesen, N. & Sheridan, A. (2020), ‘Consumer reponses to thecovid19 crisis: Evidence from bank account transaction data’,
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Plos one (9), e0239113.Mandel, A. & Veetil, V. (2020), ‘The economic cost of COVID lockdowns: An out-of-equilibrium analy-sis’, Economics of Disasters and Climate Change (3), 431–451.McNerney, J., Savoie, C., Caravelli, F. & Farmer, J. D. (2018), ‘How production networks amplifyeconomic growth’, arXiv preprint arXiv:1810.07774 .Miller, R. E. & Temurshoev, U. (2017), ‘Output upstreamness and input downstreamness of indus-tries/countries in world production’, International Regional Science Review (5), 443–475.Mongey, S., Pilossoph, L. & Weinberg, A. (2020), Which workers bear the burden of social distancingpolicies?, Technical report, National Bureau of Economic Research.Muellbauer, J. (2020), ‘The coronavirus pandemic and U.S. consumption’, VoxEU.org, 11 April . https://voxeu.org/article/coronavirus-pandemic-and-us-consumption .Pichler, A. & Farmer, J. D. (2021), ‘Modeling simultaneous supply and demand shocks in input-outputnetworks’, arXiv preprint arXiv:2101.07818 .Pichler, A., Pangallo, M., del Rio-Chanona, R. M., Lafond, F. & Farmer, J. D. (2020), ‘Productionnetworks and epidemic spreading: How to restart the uk economy?’, Covid Economics 23, 28 May2020: 79-151 . urico, P., K¨anzig, D. & Hacioglu, S. (2020), ‘Consumption in the time of covid-19: Evidence from uktransaction data’, CEPR DP14733 .Timmer, M. P., Dietzenbacher, E., Los, B., Stehrer, R. & De Vries, G. J. (2015), ‘An illustrated userguide to the world input–output database: the case of global automotive production’,
Review ofInternational Economics (3), 575–605. ppendixA First-order supply and demand shocks A.1 Supply shocks
Due to the Covid-19 pandemic, industries experience supply-side reductions due to the closureof non-essential industries, workers not being able to perform their activities at home, and diffi-culties adapting to social distancing measures. Many industries also face substantial reductionsin demand. del Rio-Chanona et al. (2020) provide quantitative predictions of these first-ordersupply and demand shocks for the U.S. economy. To calculate supply-side predictions, delRio-Chanona et al. (2020) constructed a Remote Labor Index, which measures the ability ofdifferent occupations to work from home, and scored industries according to their essentialnessbased on the Italian government regulations.We follow a similar approach. We score industries essentialness based on the UK governmentregulations and use occupational data to estimate the fraction of workers that could workremotely and the difficulties sectors faced in adapting to social distancing measures for on-sitework. Several of our estimates are based on indexes and scores available for industries in theNAICS 4-digit classification system. An essential step in our methodology is to map theseestimates into the WIOD industry classification system. We explain our mapping methodologybelow.
NAICS to WIOD mapping
We build a crosswalk from the NAICS 4-digit industry classi-fication to the classification system used in WIOD, which is a mix of ISIC 2-digit and 1-digitcodes. We make this crosswalk using the NAICS to ISIC 2-digit crosswalk from the EuropeanCommission and then aggregating the 2-digit codes presented as 1-digit in the WIOD clas-sification system. We then do an employment-weighted aggregation of the index or score inconsideration from the 277 industries at the NAICS 4-digit classification level to the 55 indus-tries in the WIOD classification. Some of the 4-digit NAICS industries map into more than oneWIOD industry classification. When this happens, we assume employment is split uniformlyamong the WIOD industries the NAICS industry maps into.
Remote Labor Index and Physical Proximity Index
To estimate the fraction of workersthat could work remotely, we use the Remote Labor Index from del Rio-Chanona et al. (2020).To understand the difficulties different sectors face in adapting to the social distancing measures,we compute an industry-specific Physical Proximity Index. Other works have also used thePhysical Proximity of occupations to understand the economic consequences of the lockdown(Mongey et al. 2020, Koren & Pet˝o 2020). We map the Physical Proximity Work Context of occupations provided by O*NET into industries, using the same methodology that del Rio-Chanona et al. (2020) used to map the Remote Labor Index into industries. That is, we use BLSdata that indicate the occupational composition of each industry and take the employment-weighted average of the occupation’s work context employed in each industry at the NAICS4-digit classification system. Under the assumption that the distribution of occupations acrossindustries and that the percentage of essential workers within an industry is the same for theUS and the UK, we can map the Remote Labor Index by del Rio-Chanona et al. (2020) and thePhysical Proximity Index into the UK economy following the mapping methodology explained inthe previous paragraph. The WIOD industry sector ’T’ (”Activities of households as employers;undifferentiated goods- and services-producing activities of households for own use”) does only igure 6: Remote Labor Index of industries.
Remote labor index of the WIOD industry classification. SeeTable 5 for code-industry name. maps into one NAICS code for which we do not have RLI or PPI. Since We consider sector ’T’to be similar to the ’R S’ sector (”Other service activities”) we use the RLI and PPI from ’R S’sector in the ’T’ sector. In Figures 6 and 7 we show the Remote Labor Index and the PhysicalProximity Index of the WIOD sectors.
Essential score
To determine the essential score of industries in scenarios S to S we followthe UK government guidelines. We break down WIOD sectors, which are aggregates of 2-digitNACE codes, into finer 3- and 4-digit industries. The advantage of having smaller subsectors isthat we can associate shutdown orders to the subsectors and then compute an average essentialscore for the aggregate WIOD sector. In the following, we provide some details on how wecalculate essential scores while referring the reader to the online repository to check all ourassumptions. • Essential score of G45 (Wholesale and retail trade and repair of motor vehicles and mo-torcycles). The only shops in this sector that were mandated to close were car showrooms(see footnote 6 for a link to official legislation). Lacking a disambiguation between retailand wholesale trade of motor vehicles, we assign a 0.5 essential score to subsector 4511,which comprises 72% of the turnover of G45, and an essential score of 1 to all othersubsectors. The average essential score for G45 turns out to be 64%. • Essential score of G47 (Retail trade, except of motor vehicles and motorcycles). All “non-essential” shops were mandated to close, except food and alcohol retailers, pharmacies andchemists, newsagents, homeware stores, petrol stations, bicycle shops and a few others.We assigned an essential score that could be either 0 or 1 to all 37 4-digit NACE subsectors35 igure 7:
Physical Proximity Index of industries.
Physical Proximity Index of the WIOD industry classi-fication. See Table 5 for code-industry name. that compose G47. Weighing essential scores by turnover results in an average essentialscore of 71%. • Essential score of I (Accommodation and food service activities). Almost all economicactivities in this sector were mandated to close, except hotels for essential workers (e.g.those working in transportation) and workplace canteens where there is no practical al-ternative for staff at that workplace to obtain food. Assigning a 10% essential score tothe main hotels subsector (551) and a 50% essential score to subsector 5629, includingworkplace canteens, results in an overall 5% essential score for sector I. • Essential score of R S (Recreational and other services). Almost all activities in this sectorwere mandated to close, except those related to repair, washing and funerals. Consideringall 34 subsectors yields an essential score of 7%.
Real Estate.
This sector includes imputed rents, which account for 69% of the monetaryvalue of the sector, . Because we think applying a supply shock to imputed rent does not makesense, we compute that the supply shock derived from the RLI and Essential Score (which isaround 50%) only affects 31% of the sector, leading to a 15% final supply shock to Real Estate(due to an error, our original work used a value of 4 . , Table 1B. In scenario S , we mapped the supply shocks estimated by del Rio-Chanona et al. (2020)at the NAICS level into the WIOD classification system as explained previously. The WIODindustry sector ’T’ (”Activities of households as employers; undifferentiated goods- and services-producing activities of households for own use”) does only maps into one NAICS code for whichwe do not have a supply shock. Since this sector is likely to be essential, we assume a zerosupply shock.The supply shocks at the NAICS level depend on the list of industries’ essential score at theNAICS 4-digit level provided by del Rio-Chanona et al. (2020). It is important to note that,although the list of industries’ essential score provided by del Rio-Chanona et al. (2020) is basedon the Italian list of essential industries, these lists are based on different industry classificationsystems (NAICS and NACE, respectively) and do not have a one-to-one correspondence. Toderive the essential score of industries at the NAICS level del Rio-Chanona et al. (2020) followedthree steps. (i) the authors considered a 6-digit NAICS industry essential if the industry hadcorrespondence with at least one essential NACE industry. (ii) del Rio-Chanona et al. (2020)aggregated the 6-digit NAICS essential lists into the 4-digit level taking into account the fractionof NAICS 6-digit subcategories that were considered essential. (iii) the authors revised each4-digit NAICS industry’s essential score to check for implausible classifications and reclassifiedten industries whose original essential score seemed implausible. Step (i) likely resulted in alarger fraction of industries at the NAICS level to be classified as essential than in the NACElevel. This, in turn, results in supply shocks S that are milder than they would have been ifthe essential score was mapped directly from NACE to WIOD and the supply shocks calculatedat the WIOD level.For scenario S we used the list of essential industries compiled by Fana et al. (2020) forItaly, Germany, and Spain. We make one list by taking the mean over the three countries ofthe essential score of each industry. This list is at the ISIC 2-digit level, which we aggregate toWIOD classification weighting each sector by its gross output in the UK.Table 5 gives an overview of first-order supply shocks and Figure 8 show the supply scenariosover time. A.2 Demand shocks
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 estimatesare available only at the more aggregate 2-digit NAICS level and map into WIOD ISIC categorieswithout complications. To give a more detailed estimate of consumption demand shocks, wealso link manufacturing sectors to the closure of certain non-essential shops as follows. • Consumption demand shock to C13-C15 (Manufacture of textiles, wearing apparel, leatherand other related products). Four subsectors (4751, 4771, 4772, 4782) selling goods pro-duced by this manufacturing sector were mandated to close, while one subsector waspermitted to remain open as it sells homeware goods (4753). Lacking more detailed in-formation about the share of C13-C15 products that these subsectors sell, we simply giveequal shares to all subsectors, leading to an 80% consumption demand shock to C13-C15. • Consumption demand shock to C20 (Manufacture of chemicals and chemical products).Three subsectors (4752, 4773, 4774) selling homeware and medical goods were consideredessential, while subsector 4775, selling cosmetic and toilet articles, was mandated to close. see for instance for ONS GDP quarterly national accounts revisions, which are of the order of 1 pp.) .00.20.40.6 −
16 03 −
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14 06 − S Figure 8:
Comparison of supply shock scenarios over time.
Each panel shows industry specific supplyshocks (cid:15)
Si,t for a given scenario. The coloring of the lines is based on the same code as in Figure 2.
Using the same assumptions as above, we get a 25% consumption demand shock for thissector.The same procedure leads to consumption demand shocks for all other manufacturing subsectors.Table 6 shows the demand shock for each sector and 9 illustrates the demand shock scenariosover time. 38 .00.10.20.3 −
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14 06 − e Figure 9:
Industry-specific demand shocks over time.
The upper left panel shows the change in preferences θ i,t . The bottom left panel shows shock magnitudes to investment and export. The upper right panel showsdemand shocks due to fear of unemployment ξ t . The bottom right panel is the aggregate demand shock ˜ (cid:15) t takingthe savings rate of 50% into account. The coloring of the lines for industry-specific results follows the same codeas in Figure 2. SIC Sector x S S S S S S A01 Agriculture 0.8 0.0 4.1 16.3 28.6 0.0 0.0A02 Forestry 0.0 0.0 3.2 12.7 22.2 85.0 85.0A03 Fishing 0.1 0.0 5.3 21.4 37.4 0.0 0.0B Mining 1.3 0.0 5.2 20.9 36.6 35.3 18.4C10.C12 Manuf. Food-Beverages 2.8 0.0 6.2 25.0 43.7 0.6 0.0C13.C15 Manuf. Textiles 0.4 0.0 5.1 20.4 35.7 37.1 64.5C16 Manuf. Wood 0.2 0.0 5.2 20.8 36.4 61.1 68.9C17 Manuf. Paper 0.4 0.0 4.9 19.7 34.5 7.5 27.6C18 Media print 0.3 0.0 4.2 16.7 29.2 6.0 0.0C19 Manuf. Coke-Petroleum 0.9 0.0 4.7 18.8 32.9 18.3 2.1C20 Manuf. Chemical 1.1 0.0 4.5 18.1 31.6 2.6 26.6C21 Manuf. Pharmaceutical 0.7 0.0 4.2 16.8 29.4 1.1 0.0C22 Manuf. Rubber-Plastics 0.7 0.0 5.3 21.1 36.9 28.3 51.0C23 Manuf. Minerals 0.5 0.0 4.8 19.2 33.6 50.3 63.1C24 Manuf. Metals-basic 0.6 0.0 5.4 21.6 37.8 57.7 72.6C25 Manuf. Metals-fabricated 1.1 0.0 4.8 19.1 33.4 54.8 66.3C26 Manuf. Electronic 0.8 0.0 2.8 11.4 19.9 38.5 41.6C27 Manuf. Electric 0.4 0.0 4.6 18.3 32.1 33.3 58.9C28 Manuf. Machinery 1.1 0.0 4.4 17.6 30.8 49.7 56.9C29 Manuf. Vehicles 1.6 0.0 5.1 20.5 35.8 22.6 69.7C30 Manuf. Transport-other 1.0 0.0 4.2 17.0 29.7 48.8 59.7C31 C32 Manuf. Furniture 0.6 0.0 4.8 19.2 33.5 36.6 60.5C33 Repair-Installation 0.4 0.0 4.9 19.7 34.5 3.3 51.8D35 Electricity-Gas 3.2 0.0 4.5 17.9 31.3 0.0 1.9E36 Water 0.2 0.0 4.8 19.4 33.9 0.0 0.0E37.E39 Sewage 0.8 0.0 4.8 19.3 33.8 0.0 0.0F Construction 7.9 0.0 6.1 24.2 42.4 35.6 66.3G45 Vehicle trade 1.7 19.7 22.4 30.8 39.1 31.6 19.7G46 Wholesale 3.5 0.0 3.6 14.4 25.3 23.6 21.1G47 Retail 4.7 14.6 17.8 27.3 36.8 30.5 25.2H49 Land transport 2.0 0.0 5.3 21.2 37.1 11.1 0.0H50 Water transport 0.6 0.0 5.7 22.8 39.9 12.4 0.0H51 Air transport 0.6 0.0 7.1 28.5 49.9 0.1 8.1H52 Warehousing 1.4 0.0 5.3 21.0 36.8 0.5 0.0H53 Postal 0.7 0.0 5.1 20.5 35.9 0.0 0.0I Accommodation-Food 2.9 61.4 61.7 62.7 63.6 60.8 63.2J58 Publishing 0.6 0.0 2.0 7.9 13.8 14.4 2.5J59 J60 Video-Sound-Broadcasting 0.9 0.0 3.4 13.5 23.7 32.8 5.0J61 Telecommunications 1.6 0.0 3.3 13.1 22.9 0.9 0.0J62 J63 IT 2.3 0.0 1.8 7.4 12.9 0.2 12.6K64 Finance 4.3 0.0 1.9 7.6 13.3 0.0 0.0K65 Insurance 3.2 0.0 1.9 7.5 13.2 0.0 0.0K66 Auxil. Finance-Insurance 1.1 0.0 1.9 7.6 13.2 0.0 0.0L68 Real estate 7.8 0.0 3.9 15.6 27.3 4.8 51.3M69 M70 Legal 2.8 0.0 2.2 8.9 15.5 2.0 18.9M71 Architecture-Engineering 1.7 0.0 3.0 12.2 21.3 0.0 30.6M72 R&D 0.5 0.0 2.6 10.3 17.9 0.0 27.4M73 Advertising 0.6 0.0 2.9 11.8 20.6 22.5 39.7M74 M75 Other Science 0.7 0.0 2.8 11.1 19.4 3.0 22.0N Private Administration 4.4 0.0 5.1 20.5 36.0 34.9 51.3O84 Public Administration 4.8 0.0 4.4 17.4 30.5 1.1 0.0P85 Education 4.2 0.0 4.0 16.2 28.3 0.0 15.3Q Health 7.0 0.0 6.3 25.3 44.2 0.1 0.0R S Other Service 3.2 56.9 57.3 58.4 59.5 34.5 57.7T Household activities 0.2 0.0 5.0 20.0 35.0 0.0 51.0
Table 5:
Industry-specific supply shock details.
Column x denotes relative shares of gross output. Supplyshocks (cid:15) Si for different scenarios are shown in the columns S to S . All values are in %. SIC Sector c (cid:15) Di f f shockA01 Agriculture 0.9 10.0 0.3 13.8A02 Forestry 0.0 10.0 0.0 11.9A03 Fishing 0.0 10.0 0.1 14.8B Mining 0.1 10.0 1.5 15.3C10.C12 Manuf. Food-Beverages 2.4 10.0 1.4 15.0C13.C15 Manuf. Textiles 0.1 80.0 0.5 13.4C16 Manuf. Wood 0.1 10.0 0.1 11.2C17 Manuf. Paper 0.1 10.0 0.2 14.1C18 Media print 0.1 66.0 0.1 9.4C19 Manuf. Coke-Petroleum 1.4 10.0 0.7 14.8C20 Manuf. Chemical 0.3 25.0 1.7 14.7C21 Manuf. Pharmaceutical 0.3 10.0 1.2 14.9C22 Manuf. Rubber-Plastics 0.1 10.0 0.6 14.0C23 Manuf. Minerals 0.1 10.0 0.2 13.0C24 Manuf. Metals-basic 0.0 10.0 1.7 15.0C25 Manuf. Metals-fabricated 0.1 10.0 0.8 14.4C26 Manuf. Electronic 0.2 100.0 1.5 14.9C27 Manuf. Electric 0.1 10.0 0.8 14.9C28 Manuf. Machinery 0.2 10.0 2.2 15.0C29 Manuf. Vehicles 1.2 100.0 2.8 14.8C30 Manuf. Transport-other 0.1 10.0 2.6 15.1C31 C32 Manuf. Furniture 0.2 40.0 0.8 14.7C33 Repair-Installation 0.0 10.0 0.0 11.8D35 Electricity-Gas 3.4 0.0 0.1 14.8E36 Water 0.5 0.0 0.0 14.8E37.E39 Sewage 0.5 0.0 1.1 7.6F Construction 0.3 10.0 12.1 15.2G45 Vehicle trade 1.9 10.0 0.6 15.0G46 Wholesale 3.1 10.0 4.5 15.0G47 Retail 15.5 10.0 0.6 14.1H49 Land transport 2.5 67.0 0.2 14.9H50 Water transport 0.6 67.0 0.7 15.0H51 Air transport 1.2 67.0 0.5 15.0H52 Warehousing 0.1 67.0 0.4 15.0H53 Postal 0.1 0.0 0.1 14.8I Accommodation-Food 7.9 80.0 0.8 15.0J58 Publishing 0.5 0.0 0.6 14.7J59 J60 Video-Sound-Broadcasting 1.0 0.0 1.2 9.9J61 Telecommunications 1.8 0.0 0.8 15.0J62 J63 IT 0.2 0.0 2.7 13.6K64 Finance 3.0 0.0 3.1 14.9K65 Insurance 6.0 0.0 1.6 14.9K66 Auxil. Finance-Insurance 0.1 0.0 2.1 15.0L68 Real estate 23.8 0.0 1.0 15.0M69 M70 Legal 0.1 0.0 1.4 14.4M71 Architecture-Engineering 0.1 0.0 1.4 15.1M72 R&D 0.0 0.0 1.1 14.9M73 Advertising 0.0 0.0 0.3 14.0M74 M75 Other Science 0.4 0.0 1.0 14.6N Private Administration 1.0 0.0 2.8 14.1O84 Public Administration 0.5 0.0 12.5 0.7P85 Education 4.7 0.0 6.4 1.8Q Health 3.7 0.0 14.8 0.2R S Other Service 6.7 5.0 1.3 8.5T Household activities 0.7 0.0 0.0 14.8 Table 6:
Industry-specific demand shock details.
Column c denotes relative shares of final consumerconsumption (which here aggregates column C1 and C2 in the WIOD) and (cid:15) Di represents final consumptionshocks. Columns f and f shock are relative shares of other final demand and the shocks applied to other finaldemand, respectively. All values are in %. Inventory data and calibration
In the previous version of our work (Pichler et al. 2020), we used U.S. data from the BEAto calibrate the inventory target parameters n j in Eq. (2). Here, we use more detailed UKdata from the Annual Business Survey (ABS) . The ABS is the main structural business surveyconducted by the ONS . It is sampled from all non-farm, non-financial private businesses inthe UK (about two-thirds of the UK economy); data are available up to the 4-digit NACE level,but for our purposes 2-digit NACE industries are sufficient. The survey asks for informationon a number of variables, including turnover and inventory stocks (at the beginning and endof each year). Data are available from 2008 to 2018. They show a general increase in turnoverand inventory stocks (consistent with growth of the UK economy in the same period), withmoderate year-on-year fluctuations.To proxy inventory levels available in February 2020, we proceed as follows, for each industry:(i) we take the simple average between beginning- and end-of year inventory stock levels; (ii)we calculate the ratio between this average and yearly turnover, and multiply this number by365, because we consider a daily timescale: this inventory-to-turnover ratio is our proxy of n j (as can be seen in Figure 10, the inventory/sales ratios are remarkably constant over time,suggesting that inventory stocks at the beginning of the Covid-19 pandemic could reliably beestimated from past data); (iii) we consider a weighted average between inventory-to-turnoverratios across all years between 2008 and 2018, giving higher weight to more recent years; (iv)we aggregate 2-digit NACE industries to WIOD sectors (for example, we aggregate C10, C11and C12 to C10 C12); (v) we fill in the missing sectors (K64, K65, K66, O84, T) by imputingthe average inventory-to-turnover ratio across all service sectors.The final inventory to sales ratios n j are shown in Figure 11. As can be seen, inventoriesare much larger relative to sales in production, construction and trade, while they are generallylower in services, although there is considerable heterogeneity across sectors. More specifically, we consider exponential weights, such that weights from a given year X are proportionalto 0 . (2018 − X ) . Some years are missing due to confidentiality problems, and data for some sectors have clearproblems in some years. We deal with missing values by giving zero weights to years with missing values andrenormalizing weights over the available years.
01 A02A03C10 C13C14 C15C16 C17C18C19 C20C21 C33D35E36E37E38E39 FJ58J59 J60J61J62J63L68 BC22C23C24 C25 C26C27C28C29C30 C31C32G45G46G47H49H50 H51H52H53 IM69M70M71M72M73M74 M75NP85 QRSBusiness and financial services Professional, social and other servicesRepair, utilities, construction Trade, transports, restaurants, hotelsNon−durable production Durable production2008 2010 2012 2014 2016 2018 2008 2010 2012 2014 2016 2018110100110100110100
Year I n v en t o r y / s a l e s r a t i o Figure 10:
Inventory/sales ratios over time. A A A B C − C C − C C C C C C C C C C C C C C C C C C C D E E − E F G G G H H H H H I J J J J J J K K K
66 L68 M M M M M M M N O P Q R _ S T U WIOD code I n v en t o r y / s a l e s r a t i o Figure 11:
Inventory/sales ratios for all WIOD industries. Critical vs. non-critical inputs
A survey was designed to address the question when production can continue during a lockdown.For each industry, IHS Markit analysts were asked to rate every input of a given industry. Theexact formulation of the question was as follows: “For each industry in WIOD, please ratewhether each of its inputs are essential. We will present you with an industry X and ask you torate each input Y. The key question is: Can production continue in industry X if input Y is notavailable for two months?” Analysts could rate each input according to the following allowedanswers: • – This input is not essential • – This input is essential • – This input is important but not essential • NA – I have no ideaTo avoid confusion with the unrelated definition of essential industries which we used to calibratefirst-order supply shocks, we refer to inputs as critical and non-critical instead of essential and non-essential. Analysts were provided with the share of each input in the expenses of the industry. It wasalso made explicit that the ratings assume no inventories such that a rating captures the effecton production if the input is not available.Every industry was rated by one analyst, except for industries Mining and Quarrying (B)and Manufacture of Basic Metals (C24) which were rated by three analysts. In case there areseveral ratings we took the average of the ratings and rounded it to 1 if the average was at least2 / /
3. Average input ratings lying between these boundariesare assigned the value 0.5.The ratings for each industry and input are depicted in Figure 12. A column denotes anindustry and the corresponding rows its inputs. Blue colors indicate critical , red important,but not critical and white non-critical inputs. Note that under the assumption of a Leontiefproduction function every element would be considered to be critical, yielding a completelyblue-colored matrix. The results shown here indicate that the majority of elements are non-critical inputs (2,338 ratings with score = 0), whereas only 477 industry-inputs are rates ascritical. 365 inputs are rated as important, although not critical (score = 0.5) and NA wasassigned eleven times.The left panel of Figure 13 shows for each industry how often it was rated as critical inputto other industries (x-axis) and how many critical inputs this industry relies on in its ownproduction (y-axis). Electricity and Gas (D35) are rated most frequently as critical inputs inthe production of other industries (score=1 for almost 60% of industries). Also frequently ratedas critical are Land Transport (H49) and Telecommunications (J61). On the other hand, manymanufacturing industries (ISIC codes starting with C) stand out as relying on a large numberof critical inputs. For example, around 27% of inputs to Manufacture of Coke and RefinedPetroleum Products (C19) as well as to Manufacture of Chemicals (C20) are rated as critical.The center panel of Figure 13 shows the equivalent plot for 0.5 ratings (important, but notcritical inputs). Financial Services (K64) are most frequently rated as important inputs whichdo not necessarily stop the production of an industry if not available. Conversely, the industryrelying on many important, but not binding inputs is Wholesale and Retail Trade (G46) of whichalmost half of its inputs got rated with a score = 0.5. This makes sense given that this industryheavily relies on all these inputs, but lacking one of these does not halt economic production.44 R_SQP85O84NM74_M75M73M72M71M69_M70L68K66K65K64J62_J63J61J59_J60J58IH53H52H51H50H49G47G46G45FE37−E39E36D35C33C31_C32C30C29C28C27C26C25C24C23C22C21C20C19C18C17C16C13−C15C10−C12BA03A02A01 A A A B C − C C − C C C C C C C C C C C C C C C C C C C D E E − E F G G G H H H H H I J J J J J J K K K
66 L68 M M M M M M M N O P Q R _ S Industry I npu t Non−criticalImportantCriticalNA
Figure 12: Criticality scores from IHS Markit analysts. Rows are inputs (supply) and columns industries usingthese inputs (demand). The blue color indicates critical (score=1), red important (score=0.5) and white non-critical (score=0) inputs. Black denotes inputs which have been rated with NA. The diagonal elements areconsidered to be critical by definition. For industries with multiple input-ratings we took the average of allratings and assigned a score=1 if the averaged score was at least 2 / / A01A03 BC10−C12C13−C15 C16C17 C19 C20C24 C25C26C27 C28C29C30C31_C32 C33 D35E36E37−E39G45 G46G47H51IJ58 J62_J63K65K66L68 M69_M70M71 NO84QT F r eq . o f i npu t s be i ng c r i t i c a l ( sc o r e = ) A01A03B C10−C12C13−C15C16 C17C19 C20C24 C25 C26C27 C28C29 C30C31_C32 C33D35E36E37−E39 G45G46G47 H51I J58 J62_J63K65K66L68 M69_M70M71 NO84 QT F r eq . o f i npu t s be i ng i m po r t an t ( sc o r e = . ) A01A03BC10−C12 C13−C15C16C17C19C20 C24C25C26 C27C28 C29C30 C31_C32C33D35 E36E37−E39 G45G46 G47H51 I J58J62_J63 K65 K66 L68M69_M70 M71N O84 Q T F r eq . o f i npu t s be i ng non − c r i t i c a l ( sc o r e = ) Figure 13: (Left panel) The figure shows how often an industry is rated as a critical input to other industries(x-axis) against the share of critical inputs this industry is using. The center and right panel are the same asthe left panel, except for using half-critical and non-critical scores, respectively. In each plot the identity line isshown. Point sizes are proportional to gross output. > nput-based rankings Industry-based rankingsISIC Sector (abbreviated) 1 0 . . Table 7: Summary table of critical input ratings by IHS Markit analysts. Columns below
Input-based rankings 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 givehow often an input has been rated as with 1, 0.5, 0 or NA for any given industry. Column n indicates the numberof analysts who have rated the inputs of any given industry. Industry T uses no inputs and is therefore not rated. Model production function and CES
Here we show that the production functions used in the main text are highly related to nestedCES production functions. Specifically, we consider a CES production function with three nestsof the form (we suppress time indices for convenience) x inp i = (cid:16) a C i ( z C i ) β + a IMP i ( z IMP i ) β + ( a NC i ) − β ( z NC i ) β (cid:17) β , (28)where β is the substitution parameter. Variables a C i = (cid:80) j ∈ C A ji , a IMP i = (cid:80) j ∈ IMP A ji and a NC i = (cid:80) j ∈ NC A ji are the input shares (technical coefficients) for critical, important and non-critical inputs, respectively. To be consistent with the specifications of the main text, we do notconsider labor inputs here and only focus on x inp i . Alternatively, we could include labor inputsin the set of critical inputs and derive the full production function in an analogous manner. z C i , z IMP i and z NC i are CES aggregates of critical, important and non-critical inputs for which wehave z C i = (cid:88) j ∈ C A − νji S νji ν , (29) z IMP i = 12 (cid:88) j ∈ IMP A − ψji S ψji ψ + 12 x cap i , (30) z NC i = (cid:88) j ∈ NC A − ζji S ζji ζ . (31)If we assume that every input is critical (i.e. the set of important and non-critical inputsis empty: a IMP i = a NC i = 0), and by taking the limits β, ν → −∞ we recover the Leontiefproduction function x inp i = min j (cid:26) S ji A ji (cid:27) . (32)If we assume that there is no critical or important inputs at all ( a C i = a IMP i = 0), taking thelimits β → −∞ and ζ → x inp i = (cid:80) j S ji a NC i . (33)The IHS1 and IHS3 production functions treat important inputs either as critical or non-critical, i.e. the set of critical inputs is again empty ( a IMP i = 0). We can approximate thesefunctions again by taking the limits β, ν → −∞ and ζ → x inp i = min (cid:26) min j ∈ C (cid:26) S ji A ji (cid:27) , (cid:80) j ∈ NC S ji a NC i (cid:27) . (34)Note that the difference between the two production functions lies in the different definition ofcritical and non-critical inputs. The functional form in Eq. (34) applies to both cases equiva-lently.The IHS2 production function where the set of important inputs is non-empty can be simi-larly approximated. In addition to the limits above, we also take the limit ψ → −∞ to obtain x inp i = min (cid:26) min j ∈ C (cid:26) S ji A ji (cid:27) ,
12 min j ∈ IMP (cid:26) S ji A ji + x cap i (cid:27) , (cid:80) j ∈ NC S ji a NC i (cid:27) . (35)48qs. (34) and (35) are not exactly identical to the IHS production functions used in the maintext (Eqs. (8) – (10)), but very similar. The only difference is that in the IHS functions non-critical inputs do not play a role for production at all, whereas here they enter the equations as alinear term. However, simulations show that this difference is practically irrelevant. Simulatingthe model with the CES-derived functions instead of the IHS production functions yield exactlythe same results, indicating that the linear term representing non-critical inputs is never abinding constraint. E Details on validation
In this appendix we provide further details about validation (Section 4 in the main paper). InAppendix E.1 we describe the data sources that we used for validation, and we explain howwe made empirical data comparable to simulated data. In Appendix E.2 we give more detailsabout the selected scenario (Section 4.3 in the main paper).
E.1 Validation data • Index of agriculture (release: 12/08/2020): • Index of production (release: 12/08/2020): • Index of construction (release: 12/08/2020): • Index of services (release: 12/08/2020):
All ONS indexes are monthly seasonally-adjusted chained volume measures, based such thatthe index averaged over all months in 2016 is 100. Although these indexes are used to proxyvalue added in UK national accounts, they are actually gross output measures, as determininginput use is too burdersome for monthly indexes.There is not a perfect correspondence between industry aggregates as considered by ONSand in WIOD. For example, the ONS only releases data for the agricultural sector as a whole,without distinguishing between crop and animal production (A01), fishing and aquaculture(A02) and forestry (A03). In this case, when comparing simulated and empirical data weaggregate data from the simulations, using initial output shares as weights. More commonly,there is a finer disaggregation in ONS data than in WIOD. For example, ONS provides separateinformation on food manufacturing (C10) and on beverage and tobacco manufacturing (C11,C12), while these three sectors are aggregated into just one sector (C10 C12) in WIOD. In thiscase, we aggregate empirical data using the weights provided in the indexes of production andservices. These weights correspond to output shares in 2016, the base year for all time series.Finally, after performing aggregation we rebase all time series so that output in February2020 takes value 100. 49 .2 Description of the selected scenario
Figure 14 shows the recovery path of all industries, both in the model and in the data. Inter-pretation is the same as in Figure 4 in the main text. For readability, industries are groupedinto six broad categories.
AC10−C12C13−C15C16 C17 C18C19C20C21C22
Model pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimistic Model optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimistic
C33D35E36E37−E39F
Model pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimistic Model optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimistic
J58J59_J60J61J62_J63 K64 K65K66L68
Model pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimistic Model optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimistic
BC23C24C25 C26 C27C28 C29C30C31_C32
Model pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimistic Model optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimistic
G45G46G47H49H50H51 H52H53I
Model pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimistic Model optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimistic
M69_M70M71M72M73 M74_M75N O84P85QR_S T
Model pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimisticModel pessimistic Model optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimisticModel optimistic
Business and financial services Professional, social and other servicesRepair, utilities, construction Trade, transports, restaurants, hotelsNon−durable production Durable production0 20 40 60 80 100 0 20 40 60 80 100020406080100020406080100020406080100
Model prediction E m p i r i c a l da t a Industry share
Month
AprilJune
Figure 14:
Comparison between model predictions and empirical data.
We plot production (grossoutput) for each of 53 industries, both as predicted by our model and as obtained from the ONS’ indexes. Eachpanel refers to a different group of industries. Different colors refer to production in April and June 2020. Blacklines connect the same industry across these three months. All sectoral productions are normalized to theirpre-lockdown levels, and each point size is proportional to the steady-state gross output of the correspondingsector.
F Sensitivity analysis
To gain a better understanding of the model behavior, we conduct a series of sensitivity analysesby showing aggregate output time series under alternative parametrizations. In particular, wevary exogenous shock inputs, the production function specification and the parameters τ , γ H , γ F and ∆ s . Supply shocks.
Figure 15(a) shows model dynamics of total output for the different supplyshock scenarios considered. It becomes clear that alternative specifications of supply shocks50an influence model results enormously. Supply shocks derived directly from the UK lockdownpolicy ( S − S ) yield a similar recovery pattern but nevertheless entail markedly different levelsof overall impacts. When initializing the model with the shock estimates from del Rio-Chanonaet al. (2020) ( S ) and Fana et al. (2020) ( S ), we obtain very different dynamics. Demand shocks.
We find that our model is less sensitive with respect to changing finaldemand shocks within plausible ranges. Here, we compare the baseline model results withalternative specifications of consumption and “other final demand” (investment, export) shocks.Instead of modifying the Congressional Budget Office (2006) consumption shocks as discussedin Section 3.2, we now also use their raw estimates. We further consider shocks of 10% toinvestment and exports which is milder than the 15% shocks considered in the main text.Figure 15(a) indicates that differences are less pronounced between the alternative demandshocks compared to the supply shock scenarios, particularly during the early phase of thelockdown. Differences of several percentage points only emerge after an extended recoveryperiod. (a) G r o ss ou t pu t ( no r m a li z ed ) S1S2 S3S4 S5S6 (b) G r o ss ou t pu t ( no r m a li z ed ) Raw, 15%Main, 15% Raw, 10%Main, 10%
Figure 15:
Sensitivity analysis with respect to supply and demand shocks.
Shocks are applied at dayone. Except for supply shocks (a) and demand shocks (b), the model is initialized as in the baseline run of themain text. Legend (b): Raw and Main indicate the estimates from Congressional Budget Office (2006) and itsadapted version used in the main text, respectively. 15% and 10% refer to the two investment/export shockscenarios.
Production function.
In Figure 16(a) and (b) we show simulation results for alternativeproduction function specifications, when using the baseline S and the more severe S supplyshock scenarios, respectively. Regardless of the supply shock scenarios considered, Leontiefproduction yields substantially more pessimistic predictions than the other production functions.For the milder baseline supply shock scenarios, aggregate predictions are fairly similar acrossthe other production functions, although we observe some differences after an extended periodof simulation. Differences between the linear and IHS production functions are larger whenconsidering the more severe shock scenario in Figure 16(b).51 a) G r o ss ou t pu t ( no r m a li z ed ) LeontiefIHS1 IHS2IHS3 Linear (b) G r o ss ou t pu t ( no r m a li z ed ) LeontiefIHS1 IHS2IHS3 Linear
Figure 16:
Sensitivity analysis with respect to production functions.
Shocks are applied at day one. (a)is based on the S and (b) on the S supply shock scenario. Otherwise, the model is initialized as in the baselinerun of the main text. In Figure 17 we explore model simulations with respect to different parametrizations of theinventory adjustment parameter τ (left column), hiring/firing parameters γ H and γ F (center leftcolumn), change in savings rate parameter ∆ s (center right column) and consumption adjust-ment speed ρ (right column) under alternative production function-supply shock combinations(panel rows). Inventory adjustment time τ . We find that the inventory adjustment time becomes a keyparameter under Leontief production and much less so under the alternative IHS3 specifica-tion. The shorter the inventory adjustment time (smaller τ ), the more shocks are mitigated.Contrary to inventory adjustment τ , model results do not change much with respect to alter-native specifications of γ H when going from Leontief production to the IHS3 function. Here,differences in model outcomes are rather due to shock severity. Model predictions are almostidentical for all choices of γ H under mild S shocks but differ somewhat for more substantial S shocks. In the S scenarios we observe that recovery is quickest for larger values of γ H (stifflabor markets), since firms would lose less productive capacity in the immediate aftermath ofthe shocks. However, this would come at the expense of reduced profits for firms which are ableto more effectively reduce labor costs for smaller values of γ H . Change in saving rate ∆ s . We find only very little variation with respect to the wholerange of ∆ s , regardless of the underlying production function and supply shock scenario. Asexpected, we find the largest adverse economic impacts in case of ∆ s = 1, i.e. when consumerssave all the extra money which they would have spent if there was no lockdown, and the mildestimpacts if ∆ s = 0. Consumption adjustment speed ρ . Similarly, the model is not very sensitive with respectto consumption adjustment speed ρ . The smaller ρ , the quicker households adjust consumptionwith respect to (permanent) income shocks. Note that parameter ρ is based on daily time scales.Economic impacts tend to be less adverse when consumers aim to keep original consumptionlevels upright (large ρ ) and more adverse if income shocks are more relevant for consumption(small ρ ). Overall, the effects are small, in particular for the S shock scenarios.52 HS3, S4IHS3, S1Leontief, S4Leontief, S10 25 50 75 1000.60.70.80.91.00.60.70.80.91.00.60.70.80.91.00.60.70.80.91.0 Days G r o ss ou t pu t ( no r m a li z ed ) t = t = t = t = t =
50 IHS3, S4IHS3, S1Leontief, S4Leontief, S10 25 50 75 1000.70.80.91.00.70.80.91.00.70.80.91.00.70.80.91.0 Days G r o ss ou t pu t ( no r m a li z ed ) g H = g H = g H = g H = g H = G r o ss ou t pu t ( no r m a li z ed ) D s = D s = .25 D s = .5 D s = .75 D s = G r o ss ou t pu t ( no r m a li z ed ) r = r = .25 r = .5 r = .75 r = Figure 17:
Results of sensitivity analysis for parameters τ , γ H , ∆ s and ρ . All plots show normalizedgross output on the y-axis and days after the shocks are applied on the x-axis. Panel rows differ with respect tothe combination of production function and supply shock scenario. Panel columns differ with respect to τ (left), γ H (center left), ∆ s (center right) and ρ (right) as indicated in the legend below each column. Except for thefour parameters, production function and supply shock scenario, the model is initialized as in the baseline run ofthe main text. In all simulations we used γ F = 2 γ H . Notation