The Inflationary Effects of Sectoral Reallocation

Board of Governors of the Federal Reserve System International Finance Discussion Papers ISSN 1073-2500 (Print) ISSN 2767-4509 (Online) Number 1369 February 2023 The Inflationary Effects of Sectoral Reallocation Francesco Ferrante, Sebastian Graves and Matteo Iacoviello Please cite this paper as: Ferrante, Ferrante, Sebastian Graves and Matteo Iacoviello (2023). “The Inflationary Effects of Sectoral Reallocation,” International Finance Discussion Papers 1369. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/IFDP.2023.1369. NOTE: International Finance Discussion Papers (IFDPs) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the International Finance Discussion Papers Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at www.ssrn.com.

The Inflationary Effects of Sectoral Reallocation⋆ Francesco Ferrantea, Sebastian Gravesa, Matteo Iacovielloa aFederal Reserve Board, United States February 13, 2023 Abstract The COVID-19 pandemic has led to an unprecedented shift of consumption from services to goods. We study this demand reallocation in a multi-sector model featuring sticky prices, input-output linkages, and labor reallocation costs. Reallocation costs hamper the increase in the supply of goods, causing inflationary pressures. These pressures are amplified by the fact that goods prices are more flexible than services prices. We estimate the model allowing for demand reallocation, sectoral productivity, and aggregate labor supply shocks. The demand reallocation shock explains a large portion of the rise in U.S. inflation in the aftermath of the pandemic. Keywords: Sectoral Reallocation, Inflation, Input-Output Models, Moment-matching exercise JEL: E10, E17, E31, E32, E37 ⋆WearegratefultoAmbrogioCesa-Bianchi,MichaelWeber,MishelGhassibe,andOmarRachedi for insightful discussions of our paper. We also thank Andrea Prestipino and Johannes Pfeifer for numerous conversations as well as seminar participants at UBC, the Midwest Macroeconomics Conference, the Federal Reserve Board, the Bank of Finland, the Paris School of Economics, the FederalReserveBankofCleveland, theEuropeanCommissionandtheDNBforhelpfulcomments. We are also grateful to Michael Weber and Raphael Schoenle for sharing data on the frequency of price adjustment across industries. All errors and omissions are our own. The views expressed in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of anyone else associated with the Federal Reserve System. Email addresses: francesco.ferrante@frb.gov (Francesco Ferrante), sebastian.h.graves@frb.gov (Sebastian Graves), matteo.iacoviello@frb.gov (Matteo Iacoviello) 1

1. Introduction The COVID-19 pandemic has led to a large, abrupt, and unprecedented increase in the demand for goods relative to services in the United States, interrupting a secular decline in the share of spending on goods. A popular narrative is that this sudden reallocation of demand has strained supply chains, leading to bottlenecks and labor shortages in a number of key sectors, thus contributing to a buildup of inflationary forces. Figure 1 illustrates the recent behavior of consumption, inflation, and employment in the U.S. economy. The share of consumption expenditures on goods rose from 31 percent in the last quarter of 2019 to more than 35 percent by the middle of 2021, and has remained high thereafter.1 Personal Consumption Expenditures inflation reached almost six percent by the end of 2021, primarily driven by a surge in goods inflation, while services inflation has been more muted. Finally, employment collapsed and rebounded, remaining significantly below the pre-pandemic trend by the end of the sample, driven by a decline in labor market participation. Figure 2 shows that these aggregate movements mask even larger movements in more disaggregated data, illustrating how the COVID-19 pandemic has been accompanied by an unprecedented increase in the dispersion of output, prices, and employment across industries. In this paper, we develop a multi-sector New Keynesian model of the U.S. economy to quantify the aggregate and cross-sectional implications of this reallocation of demand. The model features input-output linkages between sectors, heterogeneity in sectoral price rigidity, and costs of reallocating inputs across sectors.2 In particular, we assume that firms face convex hiring costs when increasing their labor input; as our model does not include capital, these hiring costs capture a variety of frictions affecting a firm’s ability to expand its productive capacity. Based on the aggregate and cross-sectional developments outlined in Figures 1 and 2, we allow for three shocks: a preference shock that alters the relative demand for goods and services; sectoral productivity shocks; and an aggregate labor supply shock. Using aggregate and cross-sectional data, we then estimate the parameters governing hiring costs and production function elasticities as well as the size of the aggregate labor supply shock. The estimated model allows us to quantify the role that each shock has played in driving aggregate and cross-sectional developments in the aftermath of the COVID-19 pandemic. 1Throughout this paper, we use data available until the first half of 2022. 2We model the industry structure after the U.S. input-output tables provided by the BEA as in BaqaeeandFarhi(2022). WecalibratetheheterogeneityinpricerigidityasinPastenetal.(2020). We estimate the cost of reallocating inputs using the strategy discussed in Section 3. 2

We study the implications of each of the three shocks individually and then examine how well the model fits the data when all the shocks occur at once. We find that the demand reallocation shock is able to explain a large portion—3.5 percentage points—of the increase in U.S. inflation post-pandemic.3 In the model, inflation occurs in response to a reallocation shock for two main reasons. First, because of the hiring costs, firms in goods-producing sectors can increase their labor input only gradually. While these firms could adjust production by using more intermediate inputs, these are only imperfect substitutes for labor, causing a slow adjustment in quantitiesandalargeriseinprices. Furthermore, sincegoodsproducedbyonesector are also used as intermediate inputs by others, the inflationary pressures propagate acrosssectorsthroughtheproductionnetwork. Incontrast, service-producingsectors reduce production swiftly, with only modest declines in prices. Second, the inflationary effects of the shift in demand are amplified by the heterogeneity in price rigidity that exists across sectors. A key feature of the data is that industries that produce goods have more flexible prices than those that produce services. We find that allowing for heterogeneity in price rigidity across sectors increases the inflationary effects of the preference shock by around 25 percent. At the industry level, we show that our demand reallocation shock is able to explain a good proportion of the cross-sectional evolution of prices and quantities since the onset of the pandemic. Not only does the shock explain why goods prices have risen more than services prices, but it also accounts for the observed heterogeneity within goods-producing and within services-producing industries, despite the fact that it affects final demand for goods and services uniformly. Both input-output linkages and sectoral heterogeneity in price stickiness contribute to this result. In the model as in the data, sectors producing goods which are directly consumed by households or selling inputs which are heavily used in the production of these goods experience a larger increase in inflation. Furthermore, sectors with more flexible prices exhibit larger price changes, all else equal. We then examine the two supply shocks. The first, sectoral productivity shocks, ismotivatedbytheincreaseinthedispersionofsector-levelvariablesshowninFigure 2. Additionally, some sectors, such as the metals or oil industry, have experienced both significant declines in production and increases in prices, which cannot be explained by demand reallocation alone. To account for this, we measure the evolution of total factor productivity at the industry level between 2019:Q4 and 2021:Q4, and feed the estimated shocks into our multi-sector model. We find that sectoral productivity shocks dramatically improve the model’s cross-sectional fit, but dampen 3As shown in Figure 1, inflation rose by 4.2 percentage points between 2019:Q4 and 2021:Q4. 3

aggregate inflation, as aggregate productivity rose above trend over this period. The second shock we consider is a reduction in aggregate labor supply, motivated by the prolonged decline in employment shown in Figure 1. We estimate the magnitude of this shock and find that it explains approximately two-thirds of the post-pandemic decline in employment. However, its effect on inflation is relatively limited: on its own, it would only increase inflation by around 1.5 percentage points, which is less than half the impact of the demand reallocation shock. When we consider the effect of all three shocks simultaneously, the estimated model can explain the majority of the rise in U.S. inflation between the end of 2019 and the end of 2021, largely driven by the demand reallocation shock.4 The model also explains a large proportion of the cross-sectional dynamics of prices and quantities: both the demand reallocation shock and the sectoral productivity shocks are important for this finding. The labor supply shock is important for explaining the persistent decline in aggregate employment, but plays a smaller role in explaining aggregate inflation and no role in accounting for the model’s cross-sectional fit. We extend our model by conduct a variety of experiments pertaining to the properties of the demand reallocation shock. We find that an unexpected reversal of the reallocation shock would be inflationary, driven by rising services prices, as services sectors struggle to increase capacity. We also consider a scenario in which households and firms are repeatedly surprised about how persistent the reallocation shock is. In such scenario, inflationary pressures are more muted, as services-producing sectors reduce output by less, and prices by more, than in our baseline assumption in which the high persistence of the shock is known immediately. We then apply our model to two episodes not directly targeted by our estimation exercise. We show that demand reallocation during the Great Recession—away from goods and towards services—would have raised inflation by around 1.5 percentage points. Finally, we show that the model can rationalize the persistence of inflation during 2022 when we allow for productivity developments that occurred in the first half of 2022, which were negative in many sectors, particularly those producing goods. In Section 2 we describe the model, which we calibrate and estimate in Section 3. Section 4 studies the cross-sectional and aggregate effects of the demand reallocation shock and the two supply shocks: sectoral productivity shocks and an aggregate labor supply shock. In Section 5 we study various extensions of the model, while Section 6 discusses sensitivity analysis. 4Duetothenon-linearitiesinherentinthemodel,thetotaleffectofthethreeshocksisnotequal to the sum of the individual effects. 4

1.1. Related Literature The model in our paper builds on the rapidly growing literature studying the role of production networks in propagating the effects of monetary policy, such as La’O and Tahbaz-Salehi (2022), Pasten et al. (2020), Ozdagli and Weber (2017) and Ghassibe (2021). In particular, Pasten et al. (2020) show that sectoral heterogeneity inpricestickinesssignificantlyamplifiestherealeffectsofmonetarypolicy.5 Weshow how heterogeneity in price rigidity amplifies the inflationary effects of a reallocation of demand from services to goods due to the fact that services-producing sectors have stickier prices than goods-producing sectors on average.6 In addition, we use the COVID-19 period to estimate production function elasticities in a multi-sector model featuring input-output linkages, and find values broadly similar to those in Atalay (2017) despite markedly different estimation strategies. Our model also relates to the literature documenting and estimating asymmetric labor adjustment costs at the firm level. Ilut et al. (2018) provide empirical evidence on the response of firms and industries to idiosyncratic shocks and find that the response of employment to positive shocks is only around 50-70 percent as large as that to negative shocks of the same size. The estimated hiring costs in our model provide asymmetric employment responses that are within this range. In using a model of production networks to understand developments since the COVID-19 pandemic, our paper also builds on Baqaee and Farhi (2022). While their quantitativeapplicationstudiestheinitiallockdownphaseofthepandemic, ourfocus is on post-lockdown dynamics, particularly on the surge in inflation that occurred in 2021. Another key difference is that they study a two-period model with no factor adjustment across sectors. In comparison, we estimate the factor adjustment costs in an infinite-horizon economy. Using this framework, we are able to study how expectations about the persistence of shocks affect labor reallocation and inflation. Recent papers have considered the implications of a demand reallocation shock such as the one that is central to our analysis. Guerrieri et al. (2021) and Fornaro and Romei (2022) study the optimal response of monetary policy to a demand reallocation shock in sticky-wage models with two periods and two sectors. Our focus is on quantifying the contribution of the demand reallocation shock to inflation, and on contrasting the reallocation shock with other competing shocks. In related, 5Pasten et al. (2021), Smets et al. (2019) and Ruge-Mucia and Wolman (2022) also study the effects of sectoral shocks in multi-sector New Keynesian models in the presence of heterogeneity in price stickiness. 6Galesi and Rachedi (2019) show that the long-run shift from goods to services has important implications for the transmission of monetary policy. 5

contemporaneous work, Anzoategui et al. (2022) show how the effects of a demand reallocation shock depend on potentially binding capacity constraints, both domestic and foreign, and di Giovanni et al. (2022) use a two-period model to quantify the contributions of different shocks to the run-up in inflation in the post-lockdown period. In their two-period model with no labor adjustment across sectors, demand reallocation shocks only cause inflation in the presence of downward nominal wage rigidity. In contrast, we study an infinite-horizon model without wage rigidity where demand reallocation shocks are inflationary due to costs of reallocating labor across sectors, whichweestimateusingaggregateandcross-sectionaldata. LikediGiovanni et al. (2022), we also find that sectoral supply shocks explain little of the increase in U.S. inflation. However, while they attribute the rise in inflation to an aggregate demand shock, we find that the reallocation of demand from services to goods is the key driver of inflation dynamics.7 2. Model Thissectiondescribesamulti-sectorNewKeynesianmodelfeaturingstickyprices and input-output linkages. Time is discrete and infinite. The economy consists of K sectors. The model contains two frictions: costs to adjusting prices and costs to reallocating labor across sectors. In order to incorporate these frictions, we assume that in each sector i = {1,...,K} there are three types of firms: a representative competitive producer, monopolistically competitive firms, and labor agencies. In each sector, the representative competitive producer aggregates the output of a continuum of monopolistically competitive firms. These firms use labor and intermediate inputs to produce their differentiated products, and set prices subject to quadratic adjustment costs. Sector-specific labor is supplied to these firms by agencies that hire labor from a representative household and face convex hiring costs. Below we describe the problem faced by each type of firm before turning to the problem of the representative household. We then set out the central bank’s monetary policy rule and the model’s market clearing conditions. 7Whilewehaveno“aggregatedemand”shockinourmodel,itispossiblethatthefiscalstimulus measuresenactedduringtheCOVID-19pandemicmayhaveaffectedthedemandforgoodsrelative to services. For example, the peak month—March 2021—for the goods share of PCE expenditures during the pandemic period coincides with the timing of the largest Economic Impact Payments. de Soyres et al. (2022) provide empirical evidence for this channel. 6

2.1. Representative Competitive Producer In each sector i, a representative competitive producer aggregates the output of a continuum of monopolistically competitive firms (indexed by s): (cid:20)(cid:90) 1 (cid:21) ϵ− ϵ 1 Yi = Yi(s) ϵ−1 ds , (1) ϵ t t 0 where ϵ is the elasticity of substitution across varieties within a sector. The solution to the competitive producer’s problem implies the following demand curve for differentiated products in each sector: (cid:18) Pi(s) (cid:19)−ϵ Yi(s) = t Yi. (2) t Pi t t 2.2. Monopolistically Competitive Firms In each sector, a continuum of firms supply differentiated products to the representative competitive producer subject to price adjustment costs. These differentiated products are produced according to the following production function: (cid:18) (cid:19) ϵY Y t i(s) = Ai t α i ϵ 1 Y (M t i(s)) ϵY ϵY −1 +(1−α i )ϵ 1 Y (Li t (s)) ϵY ϵY −1 ϵY−1 , (3) where ϵ denotes the elasticity of substitution among labor and intermediate inputs. Y In order to study sectoral productivity shocks, we allow productivity in each sector, Ai, to vary over time. Li(s) denotes labor hired by firm s in sector i at time t. t t Intermediate inputs, Mi(s), are a CES bundle of the outputs of the K sectors of the t economy: (cid:32) (cid:33) ϵM M t i(s) = (cid:88) K Γ i ϵ , M 1 j (M j i ,t (s)) ϵM ϵM −1 ϵM−1 , (4) j=1 where ϵ is the elasticity of substitution among the different inputs in each sector’s M intermediate inputs bundle. The economy’s input-output matrix is encoded in the parametersΓ (where (cid:80)K Γ = 1), whichdeterminetheimportanceoftheoutput i,j j=1 i,j of sector j as an input of production in sector i. The problem of a monopolistically competitive firm can be split into two stages: a cost minimization problem and a price-setting problem. 7

2.2.1. Cost Minimization Given the CES aggregator in equation (4), the cost minimization problem implies the following price index for intermediate inputs: (cid:32) (cid:33) 1 (cid:88) K 1−ϵM PM,i = Γ (Pj)1−ϵM . (5) t i,j t j=1 Given this price index for intermediate inputs, PM,i, and a price of labor in sector i, t PL,i, the marginal cost of production in sector i is: t 1 (cid:16) (cid:17) 1 MCi = α (PM,i)1−ϵY +(1−α )(PL,i)1−ϵY 1−ϵY . (6) t Ai i t i t t 2.2.2. Price Setting Given the marginal cost just derived, firms set prices subject to non-pecuniary, quadratic adjustment costs. The recursive form of their problem is: (cid:18) Pi(s) (cid:19)−ϵ Vi(Pi (s)) = max t Yi(Pi(s)−MCi) (7) t t−1 P t i(s) P t i t t t κ (cid:18) Pi(s) (cid:19)2 − i t PiYi +E (cid:2) M Vi (Pi (s)) (cid:3) , 2 Pi (s) t t t t+1 t+1 t−1 t−1 where κ is the sector-specific price adjustment cost, and M is the stochastic i t+1 discount factor of the representative household. The solution to the price setting problem is the following sector-level New Keynesian Phillips curve: MCi (cid:18) (Πi )2 Yi (cid:19) 1−ϵ+ϵ t −κ (Πi −1)Πi +κ E M t+1 (Πi −1) t+1 = 0, (8) Pi i t t i t t+1 Π t+1 Yi t t+1 t where Πi = P t i denote the gross inflation rate at the sector level. t Pi t−1 2.2.3. Labor Agencies In each sector, labor is supplied to the monopolistically competitive firms by a representative labor agency that hires labor from the representative household. We assume that these agencies face convex hiring costs denoted in units of labor, the size of which is key to our results and which we estimate in Section 3.8 In contrast, 8Ourformulationechoestheliteraturestudyingconvexhiringcostsinmodelsofthelabormarket, such as Merz and Yashiv (2007) and Gertler and Trigari (2009). 8

agencies are able to freely decrease employment in each sector. The recursive form of the labor agency’s problem is (cid:32) (cid:33) c (cid:18) Li (cid:19)2 Vi(Li ) = maxPL,iLi−W Li 1+1 t −1 +E (cid:2) M Vi (Li) (cid:3) , t t−1 Li t t t t t Li t >Li t−12 Li t−1 t t+1 t+1 t (9) where c is the hiring cost and 1 is a function indicating positive hiring. The Li>Li t t−1 solution to this problem is the following dynamic equation for sectoral labor demand: (cid:32) (cid:33) c (cid:18) Li (cid:19)2 (cid:18) Li (cid:19) Li PL,i = W +1 W t −1 +c t −1 t t t Li t >Li t−1 t 2 Li Li Li t−1 t−1 t−1 (cid:32) (cid:33) (cid:18) Li (cid:19)(cid:18) Li (cid:19)2 −1 E M cW t+1 −1 t+1 . (10) Li t+1 >Li t t t+1 t+1 Li Li t t This equation shows how current or future expected hiring costs introduce a wedge between the aggregate wage and the price of labor in each sector. Such a wedge generates flow dividends that are distributed to the household.9 2.3. Households A representative household consumes a bundle of goods and of services: (cid:18) Cg(cid:19)ωt (cid:18) Cs (cid:19)1−ωt C = t t . (11) t ω 1−ω t t We allow the preference parameter for goods, ω , to vary over time. The solution to t the household’s cost minimization problem implies: PgCg = ω P C , (12) t t t t t P = (Pg)ωt(Ps)1−ωt. (13) t t t Equation (12) implies that ω equals the expenditure share on goods. Figure 1 shows t that ω rose from 0.31 before the pandemic to above 0.35 in early 2021. Thus this is t the size of the shift in ω that we will study in Section 4.1. t 9A common way of introducing frictions to labor mobility assumes that the disutility of labor supplydependsbothontheaggregatequantityoflaborsuppliedanditscompositionacrosssectors, asinHorvath(2000)andBouakezetal.(2020). Suchaformulationdoesnotlenditselftostudying questions such as how the reallocation of labor depends on the expected persistence of shocks. 9

Goods consumption and services consumption are both bundles of the consumption of output from each of the K sectors: (cid:89) K (cid:18) C (cid:19)γ i g Cg = i,t , (14) t γg i=1 i (cid:89) K (cid:18) C (cid:19)γ i s Cs = i,t . (15) t γs i=1 i where (cid:80)K γg = 1 and (cid:80)K γs = 1. Again, the solution to the cost-minimization i=1 i i=1 i problem implies: K Pg = (cid:89) (Pi)γ t g , (16) t t i=1 K (cid:89) Ps = (Pi)γ t s. (17) t t i=1 Turning to the household’s dynamic problem, the household has preferences over total consumption, C , and hours worked, N : t t (cid:32) (cid:33) (cid:88) ∞ C1−γ N1+ψ U = βt t −χ t . (18) t t 1−γ 1+ψ t=0 To incorporate a labor supply shock, we allow the disutility of labor supply, χ , t to vary over time around a steady-state value χ¯. The representative household maximizes utility subject to the nominal budget constraint: P C +B = W N +(1+i )B +div , (19) t t t+1 t t t−1 t t where div denotes profits from monopolistically competitive firms and labor agent cies and B are nominal bondholdings (paying interest rate i). The solution of the t household’s problem gives the following first-order conditions: (cid:18) (cid:19) 1+i C−γ = βE C−γ t , (20) t t t+1 Π t+1 W C−γ t = χ Nψ, (21) t P t t t where Π = Pt denotes the aggregate inflation rate. t Pt−1 10

2.4. Monetary Policy and Market Clearing Monetary policy follows a Taylor rule which responds only to aggregate inflation: 1 log(1+i ) = log +ϕlogΠ . (22) t t β The model’s market clearing conditions are as follows. First, the markets for sectoral output clear when: K (cid:88) Yi = C + Mj ∀i. (23) t i,t i,t j=1 Second, the aggregate labor market clearing condition is: (cid:32) (cid:33) (cid:88) K c (cid:18) Li (cid:19)2 Li 1+1 t −1 = N . (24) t Li t >Li t−12 Li t i=1 t−1 Finally, the bond market clears when: B = 0. (25) t+1 3. Taking the Model to the Data In order to bring the model to the data, we posit that the U.S. economy has been hit by three distinct shocks during the COVID-19 pandemic. First, a demand reallocation shock—an increase in ω . Second, an aggregate labor supply shock—an t increase in χ . And finally, sectoral productivity shocks—changes in Ai across indust t tries. Wewillshowtheinclusionofthesethreeshocksallowsthemodeltoaccountfor movements in both aggregate and cross-sectional variables in the 2019:Q4-2021:Q4 period. It should be noted that by focusing on the overall changes from the end of 2019 through the end of 2021 we are abstracting from the sharp movements in macroeconomic variables that took place in 2020:Q2, in the most acute phase of the pandemic and the associated lockdown measures. Weassumethattheseshocksoccursimultaneously,andthat,followingtheshocks, the driving terms revert back to their steady-state values following AR(1) processes: ω = (1−ρ )ω¯ +ρ ω , (26) t+1 ω ω t χ = (1−ρ )χ¯+ρ χ , (27) t+1 χ χ t 11

Ai = (1−ρ )+ρ Ai. (28) t+1 A A t We proceed by externally calibrating a number of the model’s parameters, along with the size of the demand reallocation shock and the sectoral productivity shocks. We then estimate: (i) the production function elasticities, (ii) the hiring cost parameter, and (iii) the magnitude of the aggregate labor supply shock. Given the non-linearities inherent in the model—in particular the large sectoral movements induced by idiosyncratic productivity shocks and the asymmetries caused by the labor hiring cost—we estimate these parameters and show impulse response functions for versions of the model that we solve using nonlinear methods.10 3.1. Calibrated Parameters and Shocks Westudya66sectorversionofthemodel. Themodel’sinput-outputmatrix, Γ , i,j and the shares of intermediates in production, α , are calibrated using the BEA’s i input-output tables. We use the BEA’s bridge between PCE categories and NAICS industries to calibrate the sectoral consumption shares γg and γs. We label sectors i i as services-producing if more of their output is directly consumed as services than as goods. This classification leaves us with 32 services-producing sectors, 28 goodsproducing sectors, and 6 sectors that produce neither goods nor services, as none of their output is directly consumed.11 We calibrate price adjustment costs at the sectoral level using data from Pasten et al. (2020).12 We convert the frequency of price adjustment at the sector level from their paper to the value of the Rotemberg cost parameter, κ , that implies the same i slope of the New Keynesian Phillips curve. A key feature of the price adjustment data is that the prices of industries that produce goods are more flexible than those of industries that produce services. The top portion of Table 1 details the other externally calibrated parameters. The Frisch inverse labor supply elasticity parameter ψ is set at 1, and the inverse of the intertemporal elasticity of substitution parameter γ is set at 2. We assume a discount factor β of 0.995 and a response coefficient of interest rates to inflation ϕ = 1.5, consistent with the Taylor principle. The steady-state goods expenditure share ω¯ is set at 0.31 in line with its value in 2019, and the elasticity of substitution ϵ across varieties is 10. 10We solve the model using the perfect foresight solver in Dynare (version 4.5.6). Such approach has the advantage of capturing the full nonlinear dynamics of the model, albeit at the expense of abstracting from uncertainty. See Adjemian et al. (2022). 11Fewsectorsproducebothgoodsandservices: 12ofthe66sectorshavebothγg >0andγs >0. i i 12The use of the PPI data to construct their estimates of the frequency of price adjustment at the sector level is discussed in more detail in Gorodnichenko and Weber (2016). 12

Given the assumption on household preferences, the expenditure share on goods in the model is simply equal to ω . We calibrate the size of the demand reallocation t shock (∆ω = 0.045) to match the peak increase in the goods expenditure share between 2019:Q4 and 2021:Q4. We calibrate the size of the sectoral productivity shocks to match changes in sectoral TFP over the same period, the measurement of which we describe in Appendix A. We set ρ = 0.975, to mimic the slow decline in ω the goods expenditure share following its spike in 2020. We set the persistence of productivity and labor supply shocks to 0.95. 3.2. Estimated Parameters and Shocks We estimate the hiring cost c, the elasticity of substitution between intermediate inputs ϵ , and the elasticity of substitution between labor and intermediate inputs M ϵ . We also estimate the size of the labor supply shock ∆χ. We group these param- Y eters in the vector θ and estimate them by minimizing the distance between various cross-sectional and aggregate moments from data, and their model counterparts. Our cross-sectional moments are based on industry output, inflation, and employment developments. For each of the 66 sectors, we calculate the percent change in gross output between 2019:Q4 and 2021:Q4 relative to a sector-specific trend.13 We repeat the same procedure for price indexes and employment and stack these cross-sectional changes in three vectors: y , p , l . d d d Wealsotargettwoaggregatemoments, bothshowninFigure1. Between2019:Q4 and 2021:Q4, goods inflation rose by 6 percentage points, whereas services inflation rose by 1 percentage point. We target the differential rise in the two inflation rates and set ∆πG − ∆πS = 5%. Second, we target the change in total employment. d d Employment declined 4 percent relative to trend between 2019:Q4 and 2021:Q4, so that ∆L = −4%. The estimated parameters solve the following problem: d θ = argmin[ψ(θ)]′W[ψ(θ)], (29) θ 13We calculate the trend over the 2005-2019 period, as 2005 is the first year for which BEA produces quarterly GDP-by-industry data. 13

where:  σ(yg)−σ(yg (θ)) ′ d m  σ(pg)−σ(pg (θ))  d m   σ(lg)−σ(lg (θ))    d m   σ(ys)−σ(ys (θ))  d m    σ(ps)−σ(ps (θ))   d m  ψ(θ) =  σ(ls)−σ(ls (θ))  . (30)  d m   ρ(y ,y (θ))  d m    ρ(p ,p (θ))  d m    ρ(l ,l (θ))  d m    ∆L d −∆L m (θ)  (cid:0) (cid:1) (cid:0) (cid:1) ∆πG −∆πS − ∆πG(θ)−∆πS (θ) d d m m In the equation above, σ(yg), for instance, denotes the cross-sectional standard devid ation of the percent change in output for goods-producing sectors between 2019:Q4 and 2021:Q4, and σ(yg (θ)) denotes the model counterpart. By the same token, m ρ(y ,y (θ)) denotes the correlation between industry changes in output and the d m corresponding model objects, which we calculate one year after the shocks occur. We construct measures of dispersion separately for goods-producing and servicesproducing sectors as there is significant heterogeneity in the data: goods prices are much more dispersed than services prices, whereas the opposite is true for labor. This is informative for our estimation procedure. Finally, W is a weighting matrix: we use the identity matrix, implying that all moments have equal weight.14 Before turning to the parameter estimates, we discuss the relationship between these moments and the parameters that we estimate. There is clearly a direct link between the size of the labor supply shock and the decline in aggregate employment. The size of the hiring cost is closely related to difference in goods and services price inflation. As we will show in the next section, with no hiring costs there would be no change in relative prices in response to a demand reallocation shock. On the other hand, if hiring is costly, goods production will increase more slowly, and the relative price of goods will rise. Finally, the production function elasticities are important in determining how each of the shocks that hit the model propagate through the production network. The parameters ϵ and ϵ also affect how stringent hiring Y M costs are, since a high elasticity of substitution would imply that firms can avoid labor costs by using intermediate inputs. Hence, c, ϵ and ϵ jointly affect the M Y sectoral dynamics of output, prices and labor, and the cross-sectional moments from 14We calculate each of the standard deviations weighting by sectoral gross output. 14

the data help us discipline these parameters. The estimated parameters are reported in the bottom portion of Table 1. The production function elasticities are in line with the values estimated using very different approaches (e.g. Atalay, 2017). As will be discussed in Section 4.3, we find an important role for the aggregate labor supply shock in accounting for the aggregate decline in employment. The hiring costs that we estimate are relatively modest: for example, these imply that the labor agency would need to pay hiring costs of around 0.2% of its payroll in order to increase employment by 1% in a given quarter. In practice these costs are small in aggregate: when we subject the model to all shocks, the total hiring costs paid are equal to 0.15% of output in the period when the shocks occur, 0.08% of output in the next quarter, and quickly converge to zero thereafter. We discuss the robustness of the estimation strategy in Appendix B. 4. Results With the estimated parameters in hand, we now consider the role of each shock individually, before simulating the model with all three shocks turned on. 4.1. The COVID-19 Demand Reallocation Shock First, we turn off the aggregate labor supply shock (∆χ = 0) and the sectoral TFP shocks (∆Ai = 0∀i), and we consider our main experiment, which looks at the t effect of an increase in demand for goods relative to services. In order to highlight important features of the model, we contrast the effect of this shock in the baseline model with that which would occur: (i) if there were no labor adjustment costs, and (ii) if price stickiness were homogeneous across sectors. Figure 3 undertakes the first comparison and plots the response of key variables to the demand reallocation shock. The reallocation of demand leads to a large increase in goods consumption and a corresponding decline in services consumption. The dotted lines show that, absent hiring costs, these changes would offset each other leaving aggregate prices, consumption and employment unchanged. Once we introduce hiring costs, the increase in employment in goods-producing industries is much slower, constraining goods supply and resulting in a smaller increase in goods consumption compared with the frictionless model. As a consequence of the costs of increasing production, goods prices jump, resulting in year-over-year goods inflation peaking around 6 percent after one year. In contrast, employment in services-producing sectors falls immediately, as such 15

firms face no costs in reducing their workforce.15 The asymmetry caused by hiring costs is key in understanding the inflationary effects of this shock: in servicesproducing sectors, the decline in demand translates largely into a fall in quantities rather than prices. In contrast, in goods-producing sectors the increase in demand pushes up prices due to the costs firms face in increasing their capacity. While services inflation initially declines, it then also rises, peaking around 3 percent after 5 quarters. Taken together, the dynamics of sectoral inflation result in aggregate inflation peaking at 3.5 percent after one year, which represents a sizeable portion of the increase in aggregate inflation shown in Figure 1. The demand reallocation shock can also explain a roughly 1.5 percent decline in both aggregate consumption and employment in the baseline model. In Figure 4 we repeat the experiment but assuming that all sectors have the same price stickiness (equal to the average stickiness in our baseline calibration). As goodspricestendtobemoreflexiblethanservicesprices, thisassumptionraisesprice stickiness in goods-producing sectors and lowers it in services-producing sectors, on average. Higher price stickiness in the goods sector results in a lower path for goods inflation, causing a peak aggregate inflation 0.8 percentage points lower than in our baseline. Hence, heterogeneous price stickiness is an important element to explain the inflationary effects of the demand reallocation shock. Despite the simplicity of the demand reallocation shock, the model contains rich predictions on the dynamics of sectoral prices and quantities. Figure 5 shows that this relative demand shock is able to explain a good fraction of the dispersion in industry-level inflation rates and output growth. The positive correlation between inflation in the model and the data holds not only across all sectors but also within the sets of goods-producing or services-producing sectors. Both the input-output structure in the model and heterogeneity in price rigidity across sectors are important for this result, as we show in the more detail in the Appendix. For example, despite the negative shock to final demand for services, prices and quantities rise in a number of services sectors, such as the warehousing sector, which are heavily used as intermediates for goods production. 4.2. Sectoral Productivity Shocks There are a number of sectors for which price and quantity dynamics are harder to reconcile solely with the dynamics following an aggregate reallocation shock. One striking example is the “Motor Vehicle Parts and Dealer” sector, which has expe- 15Despite the absence of costs to cutting employment, labor in service sectors declines less than in the frictionless model as firms internalize the prospect of future hiring costs. 16

rienced a 40% decline in quantities and a 50% rise in prices between 2019:Q4 and 2021:Q4. Such evidence is suggestive of the importance of pandemic-related supply distributions in some sectors.16 To understand the importance of such disruptions, we now consider in isolation the role of sectoral productivity shocks. By linking industry data on employment from the BLS with data on output and material inputs from the BEA, we measure the evolution of total factor productivity at the industry level between 2019:Q4 and 2021:Q4 and feed the estimated sectoral component of the productivity series into the model. Details of our measurement of sectoral TFP are provided in Appendix A. In Appendix C we show that sectoral TFP shocks can explain a significant fraction of the cross-sectional evolution of both prices and quantities. However, their effect on aggregate inflation is actually slightly negative. This occurs as sectoral TFP growth was above trend, on average, between 2019:Q4 and 2021:Q4.17 4.3. Labor Supply Shock While the demand reallocation and sectoral productivity shocks explain a significant fraction of both sectoral and aggregate price and quantity dynamics, together they explain less than half of the decline in employment experienced in the United States. This is the motivation for introducing a negative shock to labor supply in our estimation exercise. As in a standard New Keynesian model, such a shock lowers employment and consumption, while putting upward pressure on wages and prices. In Appendix C we show that this shock leads to a rise in inflation of 1.5 percentage points, less than half of that seen in response to the demand reallocation shock. 4.4. All 3 COVID-19 Shocks Having considered the three types of shock in isolation, we now show their effects when they occur simultaneously (as assumed in our estimation procedure). Figure 6 plots the impulse response functions in this case. Overall our model suggests that these shocks are responsible for an increase in inflation of slightly less than 3.5 percentage points, close to that which was observed in the data. Thus, the deflationary effects of the sectoral productivity shocks appear to offset the inflationary effects of the labor supply shock. However, the model exhibits significant non-linearities: summing the inflationary effects of the individual shocks would lead to an increase 16Our closed-economy model abstract from disruptions to global supply chains, although such disruptions may indirectly show up as negative domestic sectoral productivity shocks. 17Our estimates of industry productivity dynamics are close to those of Fernald and Li (2022). Figure A.1 in the Appendix plots the estimated productivity shocks by sector. 17

in inflation around 30-40 percent larger than seen in Figure 6. This occurs as the negative labor supply shock reduces the expansion in hiring that occurs in goodsproducing sectors in response to the demand reallocation shock, and consequently the run-up in hiring costs that such firms face. In Appendix C.2 we provide an alternative decomposition based on considering the effect of removing shocks one at a time. Our finding that the demand reallocation shock is the key driver of inflation is robust to this approach. Turning to the cross-section, Figure 7 shows that the combination of the three shocks provides an excellent description of cross-sectional developments in prices and quantities. For example, the correlation between sectoral inflation rates in the model and the data is 0.81. Even if one is only interested in aggregate developments, we consider this to be strong evidence in favor of the channels in this paper. 5. Model Extensions In this section we undertake a number of extensions. First, we consider the implications of the demand reallocation shock under different assumptions about its persistence and how persistent it was expected to be. Next, we consider some outof-sample experiments: we study the demand reallocation that occurred around the time of the Great Recession and we finish by estimating the effect of sectoral TFP shocks that occurred during the first half of 2022. 5.1. A Reversal of the COVID-19 Demand Reallocation Shock Whatwouldhappentoinflationifdemandshiftsawayfromgoodsbacktoservices faster than anticipated? To consider such hypothesis, we perform the following exercise. Initially, the economy is hit by the baseline reallocation shock from services to goods studied in the previous section. After eight quarters, the economy is hit by an unexpected reversal in demand from goods back to services. We model such reversal by assuming that the persistence of the baseline shock unexpectedly drops from 0.975 to 0.5 in period 8. Figure 8 compares outcomes in this reversal experiment with those that occur in the baseline experiment when the demand reallocation shock is highly persistent. We find that such a reversal would raise inflation by around a percentage point relative to the no-reversal baseline. In particular, the reversal leads to renewed inflationary pressures, primarily driven by services-producing sectors which struggle to increase capacity in response to their unexpectedly fast increase in demand. 18

5.2. Unexpected Persistence of the COVID-19 Demand Reallocation Shock Our baseline experiment assumes that the agents are immediately aware of the persistence of the demand reallocation shock. An alternative hypothesis is that the persistence of the shift in demand from services to goods turned out to be higher than initially anticipated. To investigate this, we now consider a demand reallocation shock that is “unexpectedly” persistent. In particular, we assume that agents initially believe that the shock has a quarterly persistence of 0.5, even though the relative demand for goods, ω , follows the same ex post path as in our baseline expert iment. Consequently, for the first two years, agents are repeatedly surprised by the persistence of ω . After two years, we assume that agents learn the true persistence t of the shock. Figure 9 plots the response of key variables in our model to such a sequence of shocks. This shows that in such a scenario less labor is shed in services-producing sectors, while fewer employees are hired by goods-producing sectors. An implication of this reduction in reallocation is that price dispersion is higher than in the baseline. Inparticular, pricesinservices-producingsectorsfallmuchmorethaninthebaseline, as their decline in demand feeds less into quantities than it does in the baseline. The bottom-left panel of Figure 9 shows that the lower services price inflation in this scenario is largely responsible for lower total inflation. Aggregate inflation peaks at around 2.5 percent, as opposed to around 3.5 percent under our baseline assumption on expectations. On the other hand, when agents finally realize the persistence of the shock, there is a second bout of inflation, as services-producing sectors lay off workers and raise prices. 5.3. Demand Reallocation During the Great Recession Our reallocation shock is inflationary primarily due to asymmetric labor adjustment costs, regardless of whether it shifts demand from services to goods or vice versa. We prove this with an application to the Great Recession, the other recent episode with a large shift in the composition of consumption expenditures. Between 2008:Q2 and 2009:Q1, the goods expenditure share fell from 34 to 31.8 percent. We model such a shift as a shock to the relative demand for goods ω that is half the t size and the opposite sign of our baseline reallocation shock. Figure10showstheeffectsofthisshiftindemand, bothinourbaselinecalibration and in a version with homogeneous price adjustment costs. The inflationary effect of the reallocation shock during the Great Recession is proportionally smaller than in our baseline experiment, with inflation peaking at 1.4 percent. The dampened effect is explained by the heterogeneity in price adjustment costs. As goods prices are more flexible on average than those of services, heterogeneity in price stickiness amplifies 19

the effects on inflation of a shift in demand towards goods, but dampens the effects oninflationofashiftindemandtowardsservices. Despitethisdampening, ourmodel suggests that demand reallocation during the Great Recession could partly explain the “missing deflation” that has been the focus of a large literature.18 5.4. Additional Productivity Shocks during 2022 In Section 4 we considered shocks that occurred between 2019:Q4 and 2021:Q4. Absent further shocks, our model would have predicted that inflation should have declined significantly in 2022, particularly in goods-producing sectors. This is at odds with the data, as inflation remained persistently high during 2022. A number of possible explanations have been proposed for this persistence, such as renewed supply shortages caused by the war in Ukraine and continued lockdowns in China. To understand the extent to which our model can rationalize these developments, we estimate sectoral TFP shocks from 2021:Q4 to 2022:Q2 and feed these additional shocks into our model one year after the original COVID-19 shocks. While average sectoralTFPgrowthwaspositivebetween2019:Q4and2021:Q4,itturnednegativein early 2022, driven by large declines in sectors such as “Oil and Gas” and “Computer and Electronics Products”. In Figure 11 we show that feeding these additional TFP shocks into the model causes overall inflation to continue to rise for another year, and can help explaining why inflation in goods-producing sectors remained high throughout 2022. 6. Sensitivity Analysis Our finding that the demand reallocation shock was a major cause of the rise in inflation in the post-lockdown period is robust to using alternative model specifications and different estimation strategies. These specifications are described in Appendix B and briefly listed here. First, we estimate a version of the model in which we allow for firing as well as hiring costs. Firing costs are estimated to be zero, while other parameters are little affected, lending support to our baseline calibration with asymmetric labor costs. Next, we show that if we place a much smaller weight on the cross-sectional moments 18See Gilchrist et al. (2017) and Harding et al. (2022). It has to be noted that, while during the COVID-19pandemicthechangeinthegoodsexpenditureshareislikelyduetoashiftinpreferences similartoourdemandreallocationshock,theidentificationofthedriversofthedeclineinthegoods expenditure share during the Great Recession is more tenuous, as the accompanying credit crunch may have simultaneously disrupted both aggregate demand and the goods expenditure share. 20

in the estimation procedure we obtain much less precise estimates, supporting our approach of using cross-sectional information to identify the model parameters. The average price stickiness in our model is roughly in line with a Calvo-style setup in which prices adjust every two quarters, which is lower than the standard price duration that is found in many estimated New Keynesian models. Hence, we re-estimateourmodelafterscalingupthepriceadjustmentcoststomimicanaverage price duration of four quarters. This alternative estimation produces results broadly inlinewithourbaselinemodel, withthereallocationshockexplainingagoodfraction of inflation in the post-Covid period. We restrict production function elasticities, ϵ and ϵ , to be equal to 1. As ex- M Y pected,inthiscasethemodelfitdeterioratesasthemodelunderperformsinmatching cross-sectional moments. We also show that our results are robust to using a Taylor rule featuring interest rate smoothing. Finally, we show that the results change only little when we depart from Cobb-Douglas consumption preferences and use instead a more general CES specification. 7. Conclusions In this paper, we have estimated a multi-sector model with input-output linkages in order to quantify the role that demand reallocation, sector-specific disturbances, and lower aggregate labor supply have played in driving price and quantity dynamics in the U.S. economy in the aftermath of the COVID-19 pandemic. Our main finding is that the shift in consumption demand from services towards goods can explain a large proportion of the rise in U.S. inflation between 2019:Q4 and 2021:Q4. This demand reallocation shock is inflationary due to the costs of increasing production in goods-producing sectors and because such sectors tend to have more flexible prices than those producing services. The aggregate labor supply shock provides a smaller inflationary impulse, despite the fact that it explains the majority of the decline in employment. The sectoral productivity shocks actually lower inflation slightly, as average productivity grew strongly over this period. Our confidence in the model and its predictions is boosted by the fact that it provides an excellent description of cross-sectional developments in prices and quantities. We have used the model to conduct a number of experiments relating to the duration and the expected persistence of the demand reallocation shock. We have also shown that the model is able to rationalize the persistence of high inflation during 2022, as many sectors, particularly those producing goods, experienced a decline in productivity in the first half of that year. 21

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Table 1: Parameter Values Calibrated Parameters Symbol Value/Range Target/Source Inverse Elasticity of Substitution γ 2 Standard Labor Supply Disutility χ¯ 1 Normalization Inverse Labor Supply Elasticity ψ 1 Standard Taylor Rule Coefficient on Inflation ϕ 1.5 Standard Discount Factor β 0.995 Standard Elasticity Across Varieties ϵ 10 Standard Goods Expenditure Share ω¯ 0.31 BEA Intermediate Input Share (Range) α 0.11 to 0.83 BEA i Price Adjustment Cost (Range) κ 0.05 to 99.9 Pasten et al. (2020) i Reallocation Shock Persistence ρ 0.975 Goods Expenditure Share ω Labor Supply Shock Persistence ρ 0.95 Standard χ Sectoral TFP Shock Persistence ρ 0.95 Standard A Size of Reallocation Shock ∆ω 0.045 ∆ Goods Expenditure Share Sectoral TFP Shocks (Range) ∆Ai -0.29 to 0.25 Measured Sectoral TFP t Estimated Parameters Symbol Value (s.e.) Target/Source Hiring Cost c 18.8 (12.4) Estimated Elasticity Across Intermediates ϵ 0.13 (0.24) Estimated M Elasticity Between Intermediates & Labor ϵ 0.82 (0.08) Estimated Y Labor Supply Shock Size ∆χ 0.09 (0.04) Estimated The top panel shows parameters that we calibrate externally. The bottom panel shows parameters that we estimate as described in Section 3.2. For the intermediate input share, price adjustment cost, and sectoral TFP shocks we report the range across industries. Industries with lowest and highestvaluesofα are“Housing”and“Funds,Trusts,andOtherFinancialVehicles,”respectively. i Industries with lowest and highest values of κ are “Oil and Gas Extraction” and “Legal Services,” i respectively. 25

Figure1: Consumption, InflationandEmploymentintheGoodsandServicesSectors 50 50 45 45 40 40 35 35 31 31 tnecreP Goods Consumption Expenditure Share 120 120 110 110 100 100 90 90 80 80 70 70 1960m1 1980m1 2000m1 2019m12 )001=4q9102( xednI Real Consumption Expenditures Consumption (Total) Consumption Goods Consumption Services 2010q1 2015q1 2019q42021q4 10 10 8 8 6 6 4 4 2 2 0 0 -2 -2 segnahc raey-no-raeY ,tnecreP Inflation 105 105 Inflation (Total) Inflation Goods Inflation Services 100 100 95 95 90 90 85 85 2010q1 2015q1 2019q42021q4 )001=4q9102( xednI Employment Employment (Total) Employment Goods Employment Services 2010q1 2015q1 2019q42021q4 The COVID-19 pandemic led to an unprecedented increase in the demand for goods relative to services in the United States (top panels). Personal Consumption Expenditures inflation has risen, more for goods than for services (bottom left panel). Employment has initially declined before recovering, moreinthegoodsthanintheservicesector(bottomrightpanel). Inthetopleftpanel, the monthly goods share is expressed as the share in total PCE of nominal goods consumption. 26

Figure 2: Output, Prices and Employment across 66 Private Industries 190 190 160 160 130 130 100 100 70 70 40 40 )001=9102-0102( sexednI Real Gross Output Goods Industries Avg. Services Industries Avg. Goods Industries Services Industries Other Industries 2010q1 2015q1 2019q4 2021q4 220 220 190 190 160 160 130 130 100 100 70 70 40 40 )001=9102-0102( sexednI Prices Goods Industries Avg. Services Industries Avg. Goods Industries Services Industries Other Industries 2010q1 2015q1 2019q4 2021q4 140 140 120 120 100 100 80 80 60 60 40 40 )001=9102-0102( sexednI Employment Goods Industries Avg. Services Industries Avg. Goods Industries Services Industries Other Industries 2010q1 2015q1 2019q4 2021q4 Each line denotes the evolution since 2010 of the 66 private industries for which BEA publishes quarterly data on gross output, prices, and intermediate inputs. Individual industries and averages (weighted by industry gross output) are indexed to 100 in the 2010-2019 period. Employment data at the 3-digit NAICS code level are aggregated at the BEA industry level using the concordance described in https://www.uspto.gov/sites/default/files/documents/ oce-ip-economy-supplement.pdf. Variables at the industry level are detrended by calculating for each industry a log-linear time trend from 2005:Q1 through 2019:Q4. Gray lines denote sectors for which no output is directly consumed: such sectors are classified as “other.” 27

Figure 3: Aggregate Effects of the Demand Reallocation Shock Preference for Goods: t Sectoral Price Levels Sectoral Employment 5 10 s tn 4 10 io P e 3 tn e 5 tn e 5 g c c a tn e 2 re P 0 re P 0 c re1 P -5 0 -5 0 10 20 0 10 20 0 10 20 Baseline No Hiring Costs Inflation (yoy) Consumption Employment 8 15 10 s tn 6 10 io P e 4 tn e 5 tn e 5 g c c a tn 2 re P 0 re P e c 0 re 0 -5 P -2 -10 -5 0 10 20 0 10 20 0 10 20 Aggregate Goods Services This figure plots the impulse response of key variables to the demand reallocation shock that increases the value of the preference parameter for goods (ω ) in period 1. Each period is one t quarter. Solid lines denote the baseline model. Dotted lines denote the response of aggregates if there were no hiring costs. For clarity, we only plot sectoral variables in the baseline model. Gray lines denote sectors (“other” sectors) for which no output is directly consumed. 28

Figure 4: Demand Reallocation Shock: Heterogeneous vs Homogeneous Price Stickiness Preference for Goods: t Sectoral Price Levels Sectoral Employment 5 10 s tn 4 10 io P e 3 tn e 5 tn e 5 g c c a tn e 2 re P 0 re P 0 c re1 P -5 0 -5 0 10 20 0 10 20 0 10 20 Baseline Homogeneous Price Adjustment Costs Inflation (yoy) Consumption Employment 8 15 10 s tn 6 10 io P e 4 tn e 5 tn e 5 g c c a tn 2 re P 0 re P e c 0 re 0 -5 P -2 -10 -5 0 10 20 0 10 20 0 10 20 Aggregate Goods Services This figure plots the impulse response of key variables to the demand reallocation shock that increases the value of the preference parameter for goods (ω ) in period 1. Each period is one t quarter. Solidlinesdenotethebaselinemodel. Dottedlinesdenotetheresponseofvariablesifprice adjustment costs were homogeneous across industries. For clarity, we only plot sectoral variables in the baseline model. Gray lines denote sectors (“other” sectors) for which no output is directly consumed. 29

Figure 5: Model and Data: Sectoral Responses to Demand Reallocation Shock 15 10 10 Apparel le 8 le MV Dealers Warehousing d d o MV Dealers o Mining SuppoOrtil & Gas M 6 M 5 ,s e c irP y rts u d n I - 0 2 4 2 Air Trans. Warehousing PetroleuPmrimary Metal Oil & Ga ,tu p tu O y rts u d n I s -1 - 0 0 5 Ground Trans. Funds -4 -15 0 20 40 60 -50 0 50 Industry Prices, Data (% change 19Q4-21Q4) Industry Output, Data (% change 19Q4-21Q4) This figure compares the cross-sectional implication of the model with the data in response to a demand reallocation shock that increases preferences for goods. Each dot is one industry. On the x-axis we plot inflation rates (percent change in the industry chain-type price price index) and real gross output growth for the 66 private industries for which BEA publishes GDP-by-industry data. Onthey-axisweplotthemodelcounterpartsoneyearafterthereallocationshock. Servicesproducingindustriesareshowninredandgoods-producingindustriesareshowninblue. Graydots denote sectors (“other” sectors) for which no output is directly consumed. 30

Figure 6: Aggregate Effects of All Shocks Sectoral Productivity Sectoral Price Levels Sectoral Employment 20 100 15 80 10 0 60 5 tn tn tn e e e c c 40 c 0 re re re P-20 P 20 P -5 0 -10 -40 -20 -15 0 10 20 0 10 20 0 10 20 Inflation (yoy) Consumption Employment 6 10 5 s tn io 4 5 P e tn e tn e 0 g 2 c 0 c a tn re P re P e c re 0 -5 -5 P -2 -10 -10 0 10 20 0 10 20 0 10 20 Aggregate Goods Services This figure plots the impulse response of key variables to three combined shocks: (1) a demand reallocation shock that increases preferences for goods, (2) estimated sectoral TFP shocks, and (3) a negative labor supply shock. Each period is one quarter. Gray lines denote sectors (“other” sectors) for which no output is directly consumed. 31

Figure 7: Model and Data: Sectoral Responses to All Shocks 50 20 MV Dealers 40 Mining Support Apparel le le 10 Funds d Petroleum d o 30 Oil & Gaos M M ,s e 20 Primary Metal ,tu 0 Ground Trans. c p irP 10 Air Trans. tu O Oil & Gas y rts u d n I-1 0 0 y rts u d n I - - 2 1 0 0 MV Dealers -20 -30 0 20 40 60 -50 0 50 Industry Prices, Data (% change 19Q4-21Q4) Industry Output, Data (% change 19Q4-21Q4) This figure compares the cross-sectional implication of the model with the data in response to three combined shocks: (1) a demand reallocation shock that increases preferences for goods, (2) estimatedsectoralTFPshocks,and(3)anegativelaborsupplyshock. Eachdotisoneindustry. On the x-axis we plot inflation rates (percent change in the industry chain-type price price index) and real gross output growth for the 66 private industries for which BEA publishes GDP-by-industry data. On the y-axis we plot the model counterparts one year after the shocks. Services-producing industries are shown in red and goods-producing industries are shown in blue. Gray dots denote sectors (“other” sectors) for which no output is directly consumed. 32

Figure 8: Aggregate Effects of Reversal of Demand Reallocation Shock Preference for Goods: t Sectoral Price Levels Sectoral Employment 5 8 10 s4 6 tn io P e 3 tn e 4 tn e 5 g a tn e 2 c re P 0 2 c re P 0 c1 re P -2 0 -5 -4 0 10 20 0 10 20 0 10 20 Faster Reversal Baseline Inflation (yoy) Consumption Employment 6 15 10 s tn 4 10 io P e tn e 5 tn e 5 g 2 c c a tn e re P 0 re P 0 c re 0 -5 P -2 -10 -5 0 10 20 0 10 20 0 10 20 Aggregate Goods Services This figure plots the impulse response of key variables to the demand reallocation shock that increases the value of the preference parameter for goods (ω ) in period 1. The solid lines show t outcomes if the persistence unexpectedly declines from 0.95 to 0.5 after two years (denoted by the vertical line). The dotted lines shows the baseline persistence. Each period is one quarter. Gray lines denote sectors (“other” sectors) for which no output is directly consumed. 33

Figure9: AggregateEffectsofUnexpectedPersistenceofDemandReallocationShock Preference for Goods: t Sectoral Price Levels Sectoral Employment 5 15 10 s4 tn 10 io P e 3 tn e tn e 5 g a tn e 2 c re P 5 c re P 0 c re 1 0 P 0 -5 -5 0 10 20 0 10 20 0 10 20 Unexpected Persistence Baseline Inflation (yoy) Consumption Employment 8 10 8 s tn 6 5 6 io P e 4 tn e tn e 4 g c 0 c 2 a tn e 2 re P re P 0 c re P 0 -5 -2 -2 -10 -4 0 10 20 0 10 20 0 10 20 Aggregate Goods Services This figure plots the impulse response of key variables to the demand reallocation shock that increases the value of the preference parameter for goods (ω ) in period 1. The solid lines show t outcomesifagentsexpecttheshocktohavealowerpersistenceof0.5forthefirsteightquartersand thus are repeatedly surprised about its persistence. After eight quarters (denoted by the vertical line) agents learn the true persistence. The dotted lines shows the baseline persistence. Each period is one quarter. Gray lines denote sectors (“other” sectors) for which no output is directly consumed. 34

Figure 10: Demand Reallocation Shock During the Great Recession Preference for Goods: t Sectoral Price Levels Sectoral Employment 0 4 5 s tn io P e -1 tn e 2 tn e 0 g c c a tn e-2 re P 0 re P -5 c re P -2 -3 -10 0 10 20 0 10 20 0 10 20 Baseline Homogeneous Price Adjustment Costs Inflation (yoy) Consumption Employment 3 5 5 s tn 2 io P e tn e 0 tn e 0 g 1 c c a tn e re P -5 re P -5 c re 0 P -1 -10 -10 0 10 20 0 10 20 0 10 20 Aggregate Goods Services This figure plots the impulse response of key variables to the demand reallocation shock that decreases the value of the preference parameter for goods (ω ) in period 1. Each period is one t quarter. Solidlinesdenotethebaselinemodel. Dottedlinesdenotetheresponseofvariablesifprice adjustmentcostswerehomogeneousacrossindustries. Forclarity,weonlyplotsectoralvariablesin the model with heterogeneous price adjustment costs. Gray lines denote sectors (“other” sectors) for which no output is directly consumed. 35

Figure 11: Aggregate Effects of Additional TFP Shocks in 2022 Sectoral Productivity Sectoral Price Levels Sectoral Employment 20 100 15 80 10 0 60 5 tn tn tn e e e c c 40 c 0 re re re P-20 P 20 P -5 0 -10 -40 -20 -15 0 10 20 0 10 20 0 10 20 + 2022 TFP Shocks Baseline Inflation (yoy) Consumption Employment 6 10 10 s tn io 4 5 5 P e tn e tn e g 2 c 0 c 0 a tn re P re P e c re 0 -5 -5 P -2 -10 -10 0 10 20 0 10 20 0 10 20 Aggregate Goods Services Thisfigureplotstheimpulseresponseofkeyvariablestotwosetsofshocks. Thedottedlinesshows the response following the (1) demand reallocation shock, (2) estimated sectoral TFP shocks from 2019:Q4-2021:Q4and(3)thenegativelaborsupplyshock(asinFigure6). Thesolidlinesaddsthe estimatedsectoralTFPshocksfrom2021:Q4to2022Q2afterfourquarters(denotedbythevertical line). Each period is one quarter. Gray lines denote sectors (“other” sectors) for which no output is directly consumed. 36

Online Appendices Appendix A. Data Our estimation exercise uses data on 66 private industries for which the BEA publishes quarterly data on real gross output, prices, and real intermediate inputs dating back to 2005:Q1.1 The industry names, BEA codes, nominal shares of gross output in 2021, and PCE category-based expenditures allocated to each industry are listed in Table A.1. For each industry, we measure percent changes in prices, gross output, employment, and productivity between the end of 2019 and the end of 2021, relative to their pre-pandemic trend. We detrend each variable using an industry-specific trend calculated as the average growth rate for 2005-2019. The percent changes in the variables between 2019:Q4 and 2021:Q4 relative to the pre-pandemic trends are shown in Table A.2. We repeat this exercise for the period around the Russian invasion of Ukraine calculating percent changes of the variable between 2021:Q4 and 2022:Q2, and show these results in Table A.3. • Prices: We measure prices using the published BEA series on Chain-Type Price Indexes for Gross Output by Industry. • Output: We measure output using the published BEA series on chained Real Gross Output. • Employment: Seasonally-adjusted non-farm Employment data are published at the 3-digit NAICS code level by the Bureau of Labor Statistics in the monthly B-1 tables of the Employment Situation News Release.2 We aggregate thesedataattheBEAindustrylevelusingtheconcordancedescribedinhttps: //www.uspto.gov/sites/default/files/documents/oce-ip-economy-supplement. pdf.3 For the farm sector, we have no data and assume no change in employment.4 1SeetheBEAwebsite(https://www.bea.gov/data/gdp/gdp-industry)aswellasStreitwieser (2010). 2See https://www.bls.gov/ces/data/employment-situation-table-download.htm. 3As a disproportionate amount of the employment margin between 2019 and 2021 was driven bytheextensivemargin,weignorefluctuationsinmeasuredhoursandequatenumberofemployees in the data with labor input in our model. 4Thisisconsistentwithagriculturalemployment,aspublishedintheHouseholdSurvey: https: //fred.stlouisfed.org/series/LNS12034560. A.1

• Productivity: For each industry, we follow Vom Lehn and Winberry (2022) and calculate productivity using a Solow residual approach. Lacking quarterly data on the capital stock, we assume a simplified industry constant-returns-toscale production functionwith employment andintermediates inputs only. The intermediate inputs share for each industry is an average (between 2005 and 2021)oftheratioofintermediateinputstogrossoutput. Theemploymentshare is, accordingly, one minus the intermediate share. Sector level productivity is then calculated as log output minus the weighted average of log employment and log intermediates, using as weights the industry-specific shares calculated above. Figure A.1 illustrates the TFP shocks that we feed into our model for the 2019:Q4-2021:Q4 period.5 The BLS publishes annual estimates of total factor productivity at the level of three- and four-digit NAICS industries.6 We construct our own quarterly estimates since our model is quarterly. Our annualized estimates of productivity growth by industry have a high correlation with the published BLS data. For instance, when we calculate industry productivity growth in 2020-2021 relative to 2018-2019 using both measures, their correlation is 0.78. Ourcalibrationreliesonconsumptiondataforeachofthe66sectorsinthemodel. We calculate values of γg and γs using the PCE Bridge provided by the BEA, which i i allocates PCE category-level consumption expenditures to NAICS industries.7 This is possible for all industries apart from those in the wholesale/retail trade sectors. For these industries we calculate consumption expenditures from the BEA Input- Output tables and allocate all such spending to goods rather than services. This is consistent with the fact that the wholesale and retail margins reported in the PCE bridge are only present for goods spending.8 5Given that in the model we assume that productivity shocks have a quarterly autocorrelation of 0.95, we rescale the productivity shocks in period 1 so that, on average, productivity changes by the total amount that we measure in the data between 2019:Q4 and 2021:Q4, also reported in Table A.2. 6See https://www.bls.gov/news.release/prin.toc.htm and https://www.bls.gov/news. release/prin2.toc.htm 7See https://www.bea.gov/industry/industry-underlying-estimates for the PCE bridge. 8Specifically, we use the “Use of Commodities by Industries, Before Redefinitions” table to calculate consumption expenditures for the wholesale/retail trade sectors. A.2

Appendix B. Robustness to Alternative Estimation Strategies Wenowperformestimationofalternativeversionsofthemodel. TableA.4reports the estimated parameters and selected properties of each of these versions. Column 1 reports the estimated parameters and basic properties of the benchmark model. The reallocation shock can account for an increase in inflation of 3.5 percentage points, while all shocks combined lead to a total rise in inflation of 3.3 percent. Column 2 shows that when we allow for the estimation of a separate cost of cutting employment (c−), we find that this cost is estimated to be close to zero, while other parameters are largely unaffected. However, adding this extra parameter increases the uncertainty in the value of the estimated parameters. In column 3 we modify the weighting scheme so that the estimation places an arbitrarily small weight (100 times smaller) on the cross-sectional standard deviations andcorrelations. Theprecisionoftheestimatesdeteriorates, thusbolsteringourconfidence in using cross-sectional moments to infer information about the parameters of our model. The price stickiness in our model is roughly equivalent to a model with staggered price adjustment a-la Calvo in which prices change on average every 2 quarters. In column 4 we estimate a version of the model where we scale up the Rotemberg price adjustment costs so that they correspond, to a first order, to a Calvo model where prices change every 4 quarters, as in many New Keynesian models of the business cycle. While the estimated cost of increasing labor is slightly larger, and the effect of reallocation shocks is slightly smaller, the basic properties of the model are largely invarianttothismodification. Ofnote, thisversionwithhigherpricestickinessbetter matches the standard deviation of prices and output in the data, thus resulting is a slightly better overall fit. In column 5 we estimate a version where we restrict the production function elasticities, ϵ and ϵ , to be equal to 1. This version of the model fits the cross- M Y sectional moments of the data worse, but only features a slightly smaller effect of reallocation shocks on inflation. In column 6 we estimate a version of the model with persistence in the Taylor rule, of the form: 1 log(1+i ) = ρ log(1+i )+(1−ρ )(log +ϕlogΠ ) (B.1) t i t−1 i t β We re-estimate the model, setting ρ = 0.7, in line with the literature (and i leaving ϕ = 1.5). While this specification leads to less inflation overall, the demand reallocation shock remains the most important. A.3

Finally, in column 7 we estimate the model allowing for household preferences over consumption goods to depart from Cobb-Douglas: (cid:18) (cid:19) η C t = ω t η 1 (C t g) η− η 1 +(1−ω t )η 1 (C t s) η− η 1 η−1 (B.2) (cid:32) (cid:33) η η−1 C t g = (cid:88) (γ i g)η 1 (C i,t ) η− η 1 (B.3) i (cid:32) (cid:33) η η−1 C t s = (cid:88) (γ i s)η 1 (C i,t ) η− η 1 (B.4) i Wesetη = 0.75inlinewiththeestimateofAcemogluandGuerrieri(2008). With this structure it is no longer the case that ω is equal to the expenditure share on t goods. Thus we now estimate separately the size of the demand reallocation shock in order to match the rise in the goods expenditure share seen in the data9. This results in a slightly smaller demand reallocation shock ∆ = 0.042. As in column ω 4, the estimates of hiring costs and the elasticity across intermediates are higher. However, the inflationary effect of the demand reallocation shock is little changed. Appendix C. Additional Figures and Exercises FigureA.1showsthesectoralTFPshocksthatweestimatefortheperiod2019:Q4 to 2021:Q4. Figure A.2 plots the goods share of consumption expenditures at a monthly frequency, to highlight the spike in goods spending that occured in March 2021. In Figures A.4 to A.6 we plot the effects of the sectoral TFP shocks and aggregate labor supply shock individually. Figure A.7 provides further details on the evoltion of sectoral variables in response to the demand reallocation shock. Appendix C.1. A Decomposition of Cross-Sectional Implications As shown in Figure 5, a simple demand reallocation shock is able to explain a sizeable amount of the dispersion in industry-level inflation rates. In this section we compare different versions of the model in order to understand which features are key for generating this result. We consider five different versions of the model: 1. Without I-O linkages or labor adjustment costs 9We put an arbitrarily large weight on this moment to ensure that the model matches the rise exactly. A.4

2. Without I-O linkages, with homogeneous price rigidity 3. Without I-O linkages, with heterogeneous price rigidity 4. With I-O linkages, with homogeneous price rigidity 5. Baseline calibration Figure A.8 plots industry-level inflation rates in the model and the data for each of these calibrations. In the first calibration, without I-O linkages or labor adjustment costs, the model is unable to generate any dispersion in sectoral inflation rates. When we add hiring costs and homogeneous price rigidity, the model predicts little dispersion in inflation, based on only on whether the industry is a direct provider of goods or services (or both).10 If we add either heterogeneous price rigidity or I-O linkages the model predicts some dispersion in inflation rates within goods or services industries. However, the correlation in inflation rates between the model and the data is improved further when including both of these features jointly, as in our baseline calibration. This shows the importance of both the input-output structure and heterogeneity in price stickiness across sectors. We find it particularly encouraging that there is a sizeable correlation between inflation in the model and the data not only when considering all sectors but also considering the subsets of sectors that produce goods or services. This shows the important role that the input-output linkages and heterogeneous price rigidity play in the transmission of the demand reallocation shock. An alternative way of showing the importance of input-output linkages and heterogeneity in price stickiness is shown in Figures A.9 and A.10. Both in the model and in the data, prices increased more in sectors that are used more intensively, either directly or indirectly, in the production of goods, as can be computed by using the Leontief inverse matrix. Furthermore, inflation is higher (lower) in the goods (services) sectors with lower price stickiness, both in the model and in the data, supporting the important role of heterogeneous nominal rigidities across sectors. Appendix C.2. An Alternative Decomposition of Inflation Due to the non-linearities in the model, the effect on inflation of the three shocks occurring simultaneously is notably smaller than what would be predicted by summing the effects of the three shocks individually. Consequently, it is difficult to decompose overall inflation into the contributions from each shock. 10In the version of the model with no I-O linkages we recalibrate the labor adjustment cost parameter, c, in order to generate the same average difference between goods and services prices as in the baseline model. A.5

Rather than looking at the effect of each shock individually, an alternative is to look at the effect of removing each shock individually from our baseline. This allows us to ask how much lower inflation would have been had each shock not occurred.11 When we do this, we find that the peak effect on inflation is 3.2 percentage points lower without the demand reallocation shock, 0.8 percentage points higher without the sectoral TFP shocks, and 0.6 percentage points lower without the labor supply shock. Thus, the central importance of the demand reallocation shock remains in this alternative decomposition. 11We thank Mishel Ghassibe for suggesting this alternative decomposition. A.6

Table A.1: Summary Statistics for the Industries in our Model BEACode Industry OutputShare GoodsSpending ServicesSpending 111CA Farms 1.55 83,607 705 113FF Forestry,fishing,andrelatedactivities 0.15 3,603 5,765 211 Oilandgasextraction 1.94 0 0 212 Mining,exceptoilandgas 0.36 57 0 213 Supportactivitiesformining 0.32 0 0 22 Utilities 1.60 0 285,419 23 Construction 4.61 0 0 321 Woodproducts 0.32 5,458 0 327 Nonmetallicmineralproducts 0.36 5,881 4,480 331 Primarymetals 0.77 535 0 332 Fabricatedmetalproducts 1.12 17,348 463 333 Machinery 1.11 7,723 0 334 Computerandelectronicproducts 1.28 94,980 24 335 Electricalequipment,appliances,andcomponents 0.40 41,619 0 3361MV Motorvehicles,bodiesandtrailers,andparts 2.09 243,648 0 3364OT Othertransportationequipment 0.97 20,827 0 337 Furnitureandrelatedproducts 0.21 56,822 0 339 Miscellaneousmanufacturing 0.48 100,199 0 311FT Foodandbeverageandtobaccoproducts 3.11 612,836 18,393 313TT Textilemillsandtextileproductmills 0.15 23,218 0 315AL Apparelandleatherandalliedproducts 0.05 150,460 0 322 Paperproducts 0.55 19,864 0 323 Printingandrelatedsupportactivities 0.25 5,358 5 324 Petroleumandcoalproducts 2.94 176,634 0 325 Chemicalproducts 2.51 327,999 0 326 Plasticsandrubberproducts 0.75 41,173 0 42 Wholesaletrade 5.99 615,608 0 441 Motorvehicleandpartsdealers 1.11 169,781 0 445 Foodandbeveragestores 0.69 250,025 0 452 Generalmerchandisestores 0.79 230,902 0 4A0 Otherretail 3.30 874,540 0 481 Airtransportation 0.79 0 165,837 482 Railtransportation 0.23 0 1,527 483 Watertransportation 0.16 0 25,506 484 Trucktransportation 1.13 0 12,719 485 Transitandgroundpassengertransportation 0.27 0 52,324 486 Pipelinetransportation 0.15 0 0 487OS Othertransportationandsupportactivities 0.69 0 25,447 493 Warehousingandstorage 0.47 0 94 511 Publishingindustries,exceptinternet(includessoftware) 1.36 97,565 0 512 Motionpictureandsoundrecordingindustries 0.56 7,163 17,981 513 Broadcastingandtelecommunications 2.98 0 340,686 514 Dataprocessing,internetpublishing,andotherinformationservices 1.60 44,145 33,179 521CI FederalReservebanks,creditintermediation,andrelatedactivities 2.25 0 331,266 523 Securities,commoditycontracts,andinvestments 1.69 0 251,927 524 Insurancecarriersandrelatedactivities 3.75 0 430,919 525 Funds,trusts,andotherfinancialvehicles 0.33 0 157,331 HS Housing 5.85 0 2,220,452 ORE Otherrealestate 4.09 0 6,768 532RL Rentalandleasingservicesandlessorsofintangibleassets 1.23 15,318 101,274 5411 Legalservices 0.98 0 111,136 5415 Computersystemsdesignandrelatedservices 1.71 0 0 5412OP Miscellaneousprofessional,scientific,andtechnicalservices 4.94 0 73,239 55 Managementofcompaniesandenterprises 2.19 0 0 561 Administrativeandsupportservices 3.18 0 74,546 562 Wastemanagementandremediationservices 0.31 0 29,304 61 Educationalservices 1.07 0 301,718 621 Ambulatoryhealthcareservices 3.61 13,173 1,128,380 622 Hospitals 2.72 0 1,133,302 623 Nursingandresidentialcarefacilities 0.73 0 244,870 624 Socialassistance 0.63 0 148,275 711AS Performingarts,spectatorsports,museums,andrelatedactivities 0.59 0 70,352 713 Amusements,gambling,andrecreationindustries 0.45 0 205,585 721 Accommodation 0.81 0 167,673 722 Foodservicesanddrinkingplaces 2.53 0 822,730 81 Otherservices,exceptgovernment 2.12 2,089 502,347 Note: The table shows summary statistics for the industries in our model. Output share is from 2019:Q4. Goods and services spending are for the year 2019 and expressed in millions of dollars. A.7

Table A.2: Industry Summary Statistics in the 2020-2021 period %Changefrom2019:Q4to2021:Q4 BEACode Industry Share Prices Output Empl. TFP 111CA Farms 1.48 17.9 -3.8 0.0 -3.6 113FF Forestry,fishing,andrelatedactivities 0.16 3.0 10.9 -6.1 -0.1 211 Oilandgasextraction 1.63 60.2 -25.5 -17.1 -14.9 212 Mining,exceptoilandgas 0.31 4.6 -7.7 -4.8 3.4 213 Supportactivitiesformining 0.20 -3.1 -46.9 -36.9 7.7 22 Utilities 1.54 20.3 -2.0 -1.5 -6.3 23 Construction 4.38 8.6 -0.2 -1.2 -1.7 321 Woodproducts 0.30 29.5 -1.0 5.9 -3.6 327 Nonmetallicmineralproducts 0.35 5.5 3.0 -0.6 1.6 331 Primarymetals 0.65 40.0 -12.5 -4.7 -7.6 332 Fabricatedmetalproducts 1.00 14.5 -7.7 -4.4 3.7 333 Machinery 1.11 5.5 4.1 -4.6 5.8 334 Computerandelectronicproducts 1.35 8.1 5.4 1.3 -11.5 335 Electricalequipment,appliances,andcomponents 0.39 8.5 2.0 1.3 1.8 3361MV Motorvehicles,bodiesandtrailers,andparts 2.13 3.4 3.1 3.4 4.3 3364OT Othertransportationequipment 0.91 -1.0 -6.1 -2.1 -0.1 337 Furnitureandrelatedproducts 0.20 7.8 4.6 4.5 2.1 339 Miscellaneousmanufacturing 0.52 1.8 14.2 1.3 5.1 311FT Foodandbeverageandtobaccoproducts 2.88 8.0 -5.2 -2.0 3.2 313TT Textilemillsandtextileproductmills 0.14 8.6 7.2 1.6 1.5 315AL Apparelandleatherandalliedproducts 0.07 0.5 43.1 -1.3 4.1 322 Paperproducts 0.49 8.9 -5.4 0.2 0.6 323 Printingandrelatedsupportactivities 0.22 5.2 -5.0 -6.6 -1.4 324 Petroleumandcoalproducts 2.49 31.3 -13.8 -6.4 -9.7 325 Chemicalproducts 2.27 12.8 -4.9 2.7 0.9 326 Plasticsandrubberproducts 0.64 13.5 -11.5 1.7 -1.1 42 Wholesaletrade 6.31 4.9 4.5 -3.4 4.2 441 Motorvehicleandpartsdealers 0.78 46.2 -37.0 -5.1 -26.2 445 Foodandbeveragestores 0.73 2.0 8.9 0.2 7.4 452 Generalmerchandisestores 0.83 3.8 5.7 3.8 0.2 4A0 Otherretail 3.61 9.2 8.5 -1.4 2.0 481 Airtransportation 0.77 -12.4 -2.0 -0.2 -6.4 482 Railtransportation 0.23 0.2 1.3 -10.3 8.4 483 Watertransportation 0.14 8.1 -14.9 -20.3 0.8 484 Trucktransportation 1.21 13.6 9.4 -0.3 -3.2 485 Transitandgroundpassengertransportation 0.22 -5.1 -23.3 -27.0 5.4 486 Pipelinetransportation 0.14 5.2 -11.1 -6.4 -6.1 487OS Othertransportationandsupportactivities 0.79 15.7 15.5 6.8 -3.4 493 Warehousingandstorage 0.51 8.9 -0.5 18.8 -4.9 511 Publishingindustries,exceptinternet(includessoftware) 1.64 -0.4 18.1 4.9 13.5 512 Motionpictureandsoundrecordingindustries 0.58 1.2 4.5 -4.7 10.1 513 Broadcastingandtelecommunications 3.05 1.0 -0.2 -3.9 0.5 514 Dataprocessing,internetpublishing,andotherinformationservices 2.08 2.8 8.0 3.7 3.3 521CI FederalReservebanks,creditintermediation,andrelatedactivities 2.19 -2.9 0.8 2.7 15.5 523 Securities,commoditycontracts,andinvestments 1.71 8.2 2.6 0.1 0.8 524 Insurancecarriersandrelatedactivities 3.89 0.0 -1.0 -3.5 0.0 525 Funds,trusts,andotherfinancialvehicles 0.43 -3.2 30.6 0.1 13.3 HS Housing 5.76 0.6 0.0 -0.2 -0.7 ORE Otherrealestate 4.28 3.1 3.2 -0.2 1.0 532RL Rentalandleasingservicesandlessorsofintangibleassets 1.12 5.1 -9.6 -12.0 -2.0 5411 Legalservices 0.98 2.8 5.3 1.4 -1.3 5415 Computersystemsdesignandrelatedservices 1.85 0.6 -1.1 -2.3 3.6 5412OP Miscellaneousprofessional,scientific,andtechnicalservices 5.49 -1.0 8.0 1.2 4.9 55 Managementofcompaniesandenterprises 2.35 -3.4 5.0 -7.8 9.9 561 Administrativeandsupportservices 3.49 2.1 5.2 -2.9 5.7 562 Wastemanagementandremediationservices 0.32 2.4 5.1 -2.5 3.6 61 Educationalservices 1.01 1.3 -6.4 -5.9 -1.7 621 Ambulatoryhealthcareservices 3.49 2.2 -5.3 -3.5 -0.2 622 Hospitals 2.70 2.1 -2.8 -4.4 1.9 623 Nursingandresidentialcarefacilities 0.67 1.8 -8.0 -15.2 7.0 624 Socialassistance 0.63 4.7 -1.5 -10.2 2.9 711AS Performingarts,spectatorsports,museums,andrelatedactivities 0.59 0.1 -2.5 -20.7 11.0 713 Amusements,gambling,andrecreationindustries 0.37 4.4 -18.8 -14.9 -0.6 721 Accommodation 0.76 -1.4 -5.6 -29.2 17.3 722 Foodservicesanddrinkingplaces 2.61 4.9 2.9 -12.6 5.9 81 Otherservices,exceptgovernment 1.87 3.7 -9.6 -6.9 2.4 Note: The table shows summary statistics for prices, output, employment and productivity for the industries in our input-output model. Output share is from 2021:Q4. A.8

Table A.3: Industry Summary Statistics in the first half of 2022 %Changefrom2021:Q4to2022:Q2 BEACode Industry Share Prices Output Empl. TFP 111CA Farms 1.43 18.1 -2.4 0.0 -2.1 113FF Forestry,fishing,andrelatedactivities 0.16 1.8 3.1 0.5 -1.9 211 Oilandgasextraction 1.66 27.6 0.0 11.9 -11.1 212 Mining,exceptoilandgas 0.31 11.5 1.9 1.7 -4.2 213 Supportactivitiesformining 0.21 5.2 4.9 6.1 -0.8 22 Utilities 1.58 9.5 3.9 0.2 0.3 23 Construction 4.10 6.8 -5.0 1.8 -3.6 321 Woodproducts 0.28 9.2 -5.3 4.6 -4.2 327 Nonmetallicmineralproducts 0.34 3.7 -1.2 2.0 -2.1 331 Primarymetals 0.66 2.1 4.3 2.2 1.4 332 Fabricatedmetalproducts 0.96 6.4 -2.0 2.0 -3.2 333 Machinery 1.09 6.2 -1.0 2.9 -3.2 334 Computerandelectronicproducts 1.37 4.1 1.6 2.0 -7.9 335 Electricalequipment,appliances,andcomponents 0.38 6.6 -2.2 2.6 -4.8 3361MV Motorvehicles,bodiesandtrailers,andparts 2.30 2.5 8.5 0.8 1.9 3364OT Othertransportationequipment 0.93 2.5 2.7 1.1 -0.7 337 Furnitureandrelatedproducts 0.20 6.0 0.2 2.4 -2.8 339 Miscellaneousmanufacturing 0.51 4.4 -0.6 2.3 -3.3 311FT Foodandbeverageandtobaccoproducts 2.73 6.0 -4.4 2.2 -1.7 313TT Textilemillsandtextileproductmills 0.13 3.5 -0.8 2.7 -1.2 315AL Apparelandleatherandalliedproducts 0.07 3.2 7.3 4.9 -2.3 322 Paperproducts 0.46 6.7 -5.9 3.6 -3.5 323 Printingandrelatedsupportactivities 0.21 7.7 -0.3 2.8 -5.2 324 Petroleumandcoalproducts 2.52 31.8 2.0 2.2 -1.7 325 Chemicalproducts 2.16 4.4 -3.6 2.3 -5.1 326 Plasticsandrubberproducts 0.62 4.6 -1.6 3.0 -3.6 42 Wholesaletrade 6.40 4.7 1.6 2.0 -2.4 441 Motorvehicleandpartsdealers 0.78 2.9 0.5 0.8 -3.5 445 Foodandbeveragestores 0.69 5.7 -4.2 1.3 -5.0 452 Generalmerchandisestores 0.77 6.8 -6.9 2.6 -4.7 4A0 Otherretail 3.68 2.9 2.1 0.9 -2.1 481 Airtransportation 0.85 10.5 9.9 7.3 -6.9 482 Railtransportation 0.23 4.4 3.5 0.9 0.6 483 Watertransportation 0.15 3.9 6.9 5.8 0.8 484 Trucktransportation 1.16 12.4 -3.9 2.6 -7.5 485 Transitandgroundpassengertransportation 0.24 0.0 7.3 3.0 2.3 486 Pipelinetransportation 0.14 2.5 2.5 -3.1 1.3 487OS Othertransportationandsupportactivities 0.80 2.1 2.1 1.7 3.9 493 Warehousingandstorage 0.52 6.7 -1.3 1.9 -2.9 511 Publishingindustries,exceptinternet(includessoftware) 1.74 -0.7 6.1 3.8 -5.5 512 Motionpictureandsoundrecordingindustries 0.59 3.3 0.8 2.5 -3.6 513 Broadcastingandtelecommunications 3.01 2.4 -1.6 1.9 -2.9 514 Dataprocessing,internetpublishing,andotherinformationservices 2.22 0.8 2.0 2.6 -3.1 521CI FederalReservebanks,creditintermediation,andrelatedactivities 2.20 0.1 1.5 0.4 -2.3 523 Securities,commoditycontracts,andinvestments 1.67 -5.4 -2.0 0.6 -0.4 524 Insurancecarriersandrelatedactivities 3.85 0.8 -1.6 0.4 -1.9 525 Funds,trusts,andotherfinancialvehicles 0.38 1.1 -11.3 0.6 -3.1 HS Housing 5.72 1.6 0.0 0.8 -0.1 ORE Otherrealestate 4.24 2.3 -0.8 0.8 -1.2 532RL Rentalandleasingservicesandlessorsofintangibleassets 1.11 3.9 -0.1 4.9 -5.6 5411 Legalservices 0.98 -0.1 1.9 0.9 -0.3 5415 Computersystemsdesignandrelatedservices 1.89 0.3 0.4 0.7 -1.3 5412OP Miscellaneousprofessional,scientific,andtechnicalservices 5.57 1.9 1.2 1.9 -1.9 55 Managementofcompaniesandenterprises 2.35 -0.2 -0.4 0.0 0.2 561 Administrativeandsupportservices 3.59 2.3 2.1 1.5 0.6 562 Wastemanagementandremediationservices 0.33 2.2 2.3 0.9 -0.3 61 Educationalservices 1.02 0.5 1.1 1.7 -1.9 621 Ambulatoryhealthcareservices 3.50 -0.1 0.1 0.3 -0.9 622 Hospitals 2.63 1.4 -2.9 0.1 -0.2 623 Nursingandresidentialcarefacilities 0.68 0.6 2.2 0.3 0.5 624 Socialassistance 0.63 0.4 -0.1 0.3 2.5 711AS Performingarts,spectatorsports,museums,andrelatedactivities 0.64 -4.5 8.4 9.1 -0.6 713 Amusements,gambling,andrecreationindustries 0.37 1.8 0.4 2.9 -6.4 721 Accommodation 0.74 4.7 -2.8 6.4 -7.9 722 Foodservicesanddrinkingplaces 2.71 1.6 3.9 2.8 -1.6 81 Otherservices,exceptgovernment 1.84 1.8 -0.5 1.6 -0.5 Note: The table shows key summary statistics for prices, output, employment and productivity for the industries used in our input-output model. Output share is from 2022:Q2. A.9

Table A.4: Estimation Results for the Benchmark and for Alternative Models 1 2 3 4 5 6 7 Asym. No Cross Stickier Unit Persistent CES Bench. Cost Section Prices Elasticity Mon.Pol. Cons. c 18.81 18.82 45.68 38.96 32.02 19.4 41.76 (SE) 12.41 19.63 951.55 34.91 25.47 12.61 39.6 c− — 0 — — — — — (SE) — 6.21 — — — — — ϵ 0.13 0.13 0.03 1.26 1 0.17 1.87 M (SE) 0.24 0.24 21.88 0.39 — 0.24 0.41 ϵ 0.82 0.82 0.88 0.63 1 0.82 0.8 Y (SE) 0.08 0.08 9.95 0.05 — 0.08 0.07 ∆ 0.09 0.09 0.09 0.1 0.08 0.09 0.09 χ (SE) 0.04 0.05 0.41 0.04 0.04 0.04 0.04 Inflation: (∆ ) 3.5 3.5 3.8 2.8 3.4 2.1 3.4 ω Inflation: Total 3.3 3.3 3.2 2.4 2.5 2.1 2 Total Loss 100 100 — 82.06 130.44 102.33 — Note: Seetextforadescriptionofthemodels. Thetotalloss(squarednormofthedistancebetween modelanddatamoments)isnormalizedto100forthebenchmarkmodel, andexpressedrelativeto the benchmark model for the estimated versions of the model that are directly comparable to the benchmark one. A.10

Figure A.1: Sectoral TFP Shocks Accommodation Banks Publishing Funds Arts/Sports Movies Mgt. Companies Rail Trans. Mining Support Food Stores Nursing Restaruants Machinery Admin. Services Ground Trans. Misc. Manu. Misc. Services Motor Vehicles Wholesale Apparel Fabricated Metal Comp. Systems Waste Mining Data Processing Food & Bev Social Assistance Other Services Furniture Other Retail Hospitals Electrical Eq. Minerals Textiles Other Real Estate Chemicals Securities Water Trans. Paper Broadcasting Mech Stores Insurance Other Trans Eq. Forestry Ambulance Gambling Housing Plastics Legal Services Printing Construction Education Leasing Truck Trans. Other Trans. Wood Farms Warehousing Pipe Trans. Utilities Air Trans. Primary Metal Petroleum PC & Electronics Oil & Gas MV Dealers -40 -30 -20 -10 0 10 20 30 Percentage Points This bar chart shows the industry productivity shocks that we feed into our model. Servicesproducingindustriesareshowninredandgoods-producingindustriesareshowninblue. Graybars denote sectors (“other” sectors) for which no output is directly consumed. A.11

Figure A.2: Goods Share of Consumer Spending 36 36 35 35 34 34 33 33 32 32 31 31 tnecreP 2002m1 2008m1 2015m1 2019m12 2021m12 This figure plots the share of nominal consumption expenditures (PCE) that is spent on goods at a monthly frequency. Data Sources: Bureau of Economic Analysis and authors’ calculations. A.12

Figure A.3: Sectoral Price and Quantity Dynamics between 2019 and 2021 ) 4 70 Q 1 2 - 60 Oil & Gas 4 Q 9 50 1 e MV Dealers g n 40 Primary Metal a h c % 30 Petroleum Wood ( a 20 Utilities ta D PlasticFsabr C ic F h a e a te m rm d i c s M al e s tal Truck Tra O n t s h . er Trans. ,s 10 Water Trans.PFaopoedr &W CBoaenrEvesSlheterocucFutcurPusitrciriCionnatTin geil&t eOuEs xrEqttehil.leeecsr tRroentiacisl e c ir P 0 Mining Support Gambling PipLOeet N haMTes u ri E iran r O n A sd Sn A igPn t i c u s n h em gr c . cg e rin o bv aH rA t m iut c T i oi nS r lo e C a Itmr s g nsn o a s BnpoH/so c nS ci B rmu to i dsRoe a a p a ru a pa l l aaEo n ss t R .d MAM n O iir q k ilo Stcn e c Ms s s i .T ot n M W a n gy s e h s M WAt r L a s e s tioMe ao sha e c dt g t r rra nvi t e orah eg n m t au isVR s . m ll e i ca g n D M esn t a . i C ehe senl c s s F e n a i h aS o . e s ar S o t t il s m y aS c e lc o etFE . lored p ePvo S sr r a siervrtSc e oae n s iect r cts i Mo v e eseetr i r s s c iseys e ssc s i.n P Mg u a b n li u s . hing Funds Apparel y Ground Trans. r-10 ts Air Trans. u d n-20 I -50 -40 -30 -20 -10 0 10 20 30 40 50 Industry Output, Data (% change 19Q4-21Q4) This figure plots the change in prices in each sector against the change in sectoral output, from 2019:Q4to2021:Q4. Changesinbothpricesandquantitiesarecalculatedrelativetosector-specific trends. Services-producing industries are shown in red and goods-producing industries are shown in blue. Gray dots denote sectors (“other” sectors) for which no output is directly consumed. A.13

Figure A.4: Aggregate Effects of Sectoral TFP Shocks Sectoral Productivity Sectoral Price Levels Sectoral Employment 20 80 10 60 5 0 tn tn 40 tn e e e c c c 0 re P-20 re P 20 re P -5 0 -40 -20 -10 0 10 20 0 10 20 0 10 20 Inflation (yoy) Consumption Employment 2 3 0.5 s tn io 1 2 0 P e tn e tn e g 0 c c a tn re P 1 re P -0.5 e c re -1 P 0 -1 -2 0 10 20 0 10 20 0 10 20 Aggregate Goods Services This figure plots the impulse response of key variables to estimated sectoral productivity shocks (usingindustryleveldataonoutput, addedvalueandemployment)inperiod1. Eachperiodisone quarter. Gray lines denote sectors (“other” sectors) for which no output is directly consumed. A.14

Figure A.5: Model and Data: Sectoral Responses to TFP Shocks 40 20 MV Dealers Accommodation Funds 30 10 Banks le d Petroleum Oil & Ga le ds Mining Support Ground Trans. Apparel o o M 20 M 0 ,s e Primary Metal ,tu c irP 10 Air Trans. p tu O -10 Oil & Gas y rts u d n I-1 0 0 y rts u d n I - - 3 2 0 0 Petroleum MV Dealers FBuAanncdcksosmmodation -20 -40 0 20 40 60 -50 0 50 Industry Prices, Data (% change 19Q4-21Q4) Industry Output, Data (% change 19Q4-21Q4) This figure compares the cross-sectional implication of the model with the data in response to the estimatedsectoralTFPshocksattheindustrylevel. Eachdotisoneindustry. Onthex-axisweplot inflation rates (percent change in the industry chain-type price price index) and real gross output growthforthe66privateindustriesforwhichBEApublishesGDP-by-industrydata. Onthey-axis we plot the model counterparts one year after the TFP shocks. Services-producing industries are shown in red and goods-producing industries are shown in blue. Gray dots denote sectors (“other” sectors) for which no output is directly consumed. A.15

Figure A.6: Aggregate Effects of Labor Supply Shock Disutility of Labor Supply Sectoral Price Levels Sectoral Employment 10 6 0 8 4 tn e 6 tn e tn e-1 c c c re 4 re re P P2 P -2 2 0 0 -3 0 10 20 0 10 20 0 10 20 Inflation (yoy) Consumption Employment 1.5 s 0 0 tn io 1 P e tn e-1 tn e-1 g a tn 0.5 c re P c re P e c -2 -2 re 0 P -0.5 -3 -3 0 10 20 0 10 20 0 10 20 Aggregate Goods Services This figure plots the impulse response of key variables to a labor supply shock that increases the disutility of labor in period 1. Each period is one quarter. Gray lines denote sectors (“other” sectors) for which no output is directly consumed. A.16

Figure A.7: Model Implied Sectoral Dynamics (Demand Reallocation Shock) Sectoral Output Sectoral Price Levels Sectoral Employment 15 10 10 10 5 5 tn 5 tn tn e e e c c c re P 0 re P 0 re P 0 -5 -5 -10 -5 0 10 20 0 10 20 0 10 20 Sectoral Intermediate Input Sectoral Marginal Costs Sectoral Mark Ups 20 20 10 s tn 5 tn e 10 tn e 10 io P e 0 c c g re P 0 re P 0 a tn e -5 c re-10 P -10 -10 -15 0 10 20 0 10 20 0 10 20 This Figure plots the dynamic response of sectoral variables to the demand reallocation shock that increases the value of the preference parameter for goods (ω ) in period 1. Each period is one t quarter. Services-producing industries are shown in red and goods-producing industries are shown in blue. Gray lines denote sectors (“other” sectors) for which no output is directly consumed. A.17

FigureA.8: SectoralInflationResponsetoDemandReallocationShockinAlternative Models No IO, No Labor Adjustment Costs No IO, Homogeneous Price Adjustment Costs 10 10 ledoM ledoM ,secirP 5 ,secirP 5 yrtsudnI 0 c c o o r r r r ( ( a g l o l) o = d s N ) / = A N/A yrtsudnI 0 c c o o r r r r ( ( a g l o l) o = d s 0 ) . = 3 3 0.18 corr (services) = N/A corr (services)= -0.01 -20 0 20 40 60 -20 0 20 40 60 Industry Prices, Data (% change 19Q4-21Q4) Industry Prices, Data (% change 19Q4-21Q4) No IO, Heterogeneous Price Adjustment Costs IO, Homogeneous Price Adjustment Costs 10 10 ledoM ledoM ,secirP 5 ,secirP 5 yrtsudnI 0 c c o o r r r r ( ( a g l o l) o = d s 0 ) . = 4 0 0.35 yrtsudnI 0 c c o o r r r r ( ( a g l o l) o = d s 0 ) . = 4 6 0.07 corr (services)= 0.20 corr (services)= 0.36 -20 0 20 40 60 -20 0 20 40 60 Industry Prices, Data (% change 19Q4-21Q4) Industry Prices, Data (% change 19Q4-21Q4) IO, Heterogeneous Price Adjustment Costs (Baseline) 10 ledoM ,secirP 5 yrtsudnI 0 c c o o r r r r ( ( a g l o l) o = d s 0 ) . = 5 1 0.29 corr (services)= 0.45 -20 0 20 40 60 Industry Prices, Data (% change 19Q4-21Q4) This figure compares the cross-sectional implications for inflation of different models against the data between 2019:Q4 and 2021:Q4. The first panel illustrates a model without input-output linkages or hiring costs. The second panel illustrates a model with hiring costs but no inputoutput linkages and with homogeneous price stickiness across sectors. The third panel illustrates a model with heterogeneous price rigidities across sectors but without input-output linkages. The fourthpanelintroducesinput-outputlinkagesbutassumesthathomogeneouspricestickinessacross sectors. The last panel illustrates the baseline model. Services-producing industries are in red and goods-producing industries are in blue. Gray dots denote sectors (“other” sectors) for which no output is directly consumed. A.18

Figure A.9: Sectoral Inflation vs Goods Leontief (Demand Reallocation Shock) 9 70 )4 Q 8 1 2 60 -4 Q le d o M6 7 9 1 e g n a 4 5 0 0 ,s e c h c % 30 irP y 5 ( a ta 20 rts u d 4 D ,s e 10 n c I3 irP 0 y 2 rts u-10 d n I 1 -20 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Goods Leontief Goods Leontief Thisfigureplotssectoralinflationagainstsectoralexposuretogoodssector,measuredbycomputing, foreachsector,thecumulativegoodsshareofthetransposeoftheLeontiefinversematrix(asdefined inBaqaeeandFarhi(2022)). EachvalueintheLeontiefvalueisweightedbythefinalconsumption share of the specific sector. A high value of the goods Leontief means that the sector is used, directly and indirectly, as in input in many goods-producing sectors. The scatterplot in the left panel is obtained using only the estimated demand reallocation shock, and the change in sectoral prices is computed over the first year of the simulation. A.19

Figure A.10: Sectoral Inflation vs Price Stickiness (Demand Reallocation Shock) 9 70 )4 Q 8 1 2 60 -4 Q le d o M6 7 9 1 e g n a 4 5 0 0 ,s e c h c % 30 irP y 5 ( a ta 20 rts u d 4 D ,s e 10 n c I3 irP 0 y 2 rts u-10 d n I 1 -20 0 20 40 60 80 100 0 20 40 60 80 100 Price Stickiness Price Stickiness This figure plots sectoral inflation against sectoral price stickiness, measured by the size of the Rotemberg cost, in the model and in the data. The scatterplot in the left panel is obtained using only the estimated demand reallocation shock, and the change in sectoral prices is computed over the first year of the simulation. A.20