Policy Research Working Paper 10434 Labor Market Effects of Global Supply Chain Disruptions Mauricio Ulate Jose P. Vasquez Roman D. Zarate Development Economics Development Research Group May 2023 Policy Research Working Paper 10434 Abstract This paper examines the labor market consequences of recent employment as the United States is a net importer of man- global supply chain disruptions induced by COVID-19. ufactured goods, which become costlier to obtain from Specifically, it considers a temporary increase in interna- abroad. By contrast, service and agricultural employment tional trade costs similar to the one observed during the experience temporary declines. Nominal frictions lead to pandemic and analyzes its effects on labor market outcomes temporary unemployment when the shock dissipates, but using a quantitative trade model with downward nominal this depends on the degree of monetary accommodation. wage rigidities. Even omitting any health-related impacts of Overall, the shock results in a 0.14 percent welfare loss for the pandemic, the increase in trade costs leads to a tempo- the United States. The impact on labor force participation rary but prolonged decline in U.S. labor force participation. and welfare across countries varies depending on the initial However, there is a temporary increase in manufacturing degree of openness and sectoral deficits. This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at rzaratevasquez@worldbank.org. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team Labor Market Effects of Global Supply Chain Disruptions* Mauricio Ulate Jose P. Vasquez Roman D. Zarate JEL codes: F10, F11, F16, F40, F66. Keywords: Supply Chain Disruptions, Trade Costs, Downward Nominal Wage Rigidity. * Mauricio Ulate: Federal Reserve Bank of San Francisco, Jose P. Vasquez: LSE and CEPR, Roman Zarate: Development Research Group, The World Bank. We thank Marco Badilla, Lorenzo Caliendo, Juanma Castro- Vincenzi, Isabela Manelici, Joan Monras, Ishan Nath, Andres Rodriguez-Clare, Nicholas Sander and the whole department at the FRBSF for their help and useful comments. Any opinions and conclusions ex- pressed herein are those of the authors and do not necessarily represent the views of the Federal Reserve Bank of San Francisco, the Federal Reserve System, or the World Bank. 1 Introduction In the past few years, COVID-19 caused a number of disruptions in global supply chains. The pandemic strained trade flows due to port closures, reduced shipping capac- ity owing to lockdowns (for example, in China), fewer shipping workers being available for health-related reasons, and a shortage of shipping containers, among other challenges. These disruptions, in turn, caused an increase in the costs of international trade, poten- tially leading to substantial effects on production, prices, and labor markets, as well as reallocation within and across countries. This paper quantitatively studies the labor market consequences of the increased in- ternational trade costs originating from the recent global supply chain disruptions induced by COVID-19. Specifically, we analyze an x% increase in the iceberg trade costs of send- ing products across countries that reverts after τ years. In our baseline exercise, we study a 12% shock that reverts after three years, which approximates the size and duration of the trade costs shock during the COVID-19 pandemic. However, we also examine how the effects of the shock depend on its size (i.e., x = 6%, 18%, or 24%) or persistence (i.e., τ = 2, 4, 5, or 6). We employ the quantitative trade model developed by Rodriguez-Clare, Ulate, and Vasquez (2022, henceforth RUV) but with a focus on analyzing the effects of a trade-cost shock. The model features multiple sectors linked by an input-output structure, sector- level trade that satisfies the gravity equation, downward nominal wage rigidity (hence- forth DNWR), and a home-production sector that leads to an upward sloping labor supply curve. Trade takes place between regions, and workers can move across sectors in a given region subject to mobility costs. Each period, workers draw idiosyncratic shocks to the utility of working in each sector. Based on these draws, the costs of switching sectors, and expected future real income adjusted for unemployment, workers choose the sector to participate.1 We capture DNWR as in Schmitt-Grohe and Uribe (2016). This implies that the nom- 1 Ourbaseline model does not feature movement between regions in a given country, but one of our exten- sions incorporates this feature. The consequences of allowing migration across regions are very small. 1 inal wage in any period must be no less than a factor δ times the nominal wage in the previous period and that involuntary unemployment arises when wages are constrained by this lower bound.2 Given the presence of the DNWR, the model also requires a nom- inal anchor that prevents nominal wages from rising enough to make the DNWR always non-binding.3 We assume that world nominal GDP in dollars grows at a constant and ex- ogenous rate γ. This assumption captures the regularity that central banks are unwilling to allow inflation or unemployment to be too high (because of their related costs) while simul- taneously keeping our model tractable. While this nominal anchor may not capture all the complexities of the real world, it allows us to incorporate a rich trade structure with mul- tiple countries and sectors, intermediate inputs, and forward-looking mobility decisions into our trade framework while still being able to solve this otherwise-unwieldy model.4 Our quantitative analysis requires data for sector-level input-output flows as well as trade flows across all pairs of regions in our sample. We combine multiple data sources, a set of proportionality assumptions, and implications from a gravity model to construct sector-level trade flows across all region pairs in our sample. The resulting dataset con- tains 87 regions (50 U.S. states, 36 additional countries, and an aggregate rest of the world region), and 15 sectors (home production, 12 manufacturing sectors, services, and agricul- ture), for our base year of 2019. We quantify the effects of the shock in our model using the dynamic “exact-hat al- gebra” approach to counterfactual analysis (c.f., Caliendo et al., 2019). This methodology ensures that our model perfectly matches sector-level production, trade, and reallocation patterns in the base year. We then introduce an unexpected increase in trade costs that reverts after a certain number of years. Besides the myriad parameters implicitly calibrated by the exact hat algebra approach 2 See Dickens et al. (2007), Grigsby et al. (2019), and Hazell and Taska (2019) for papers that have found sup- port for the presence of DNWR in the data. Labor-market frictions in the real world might go significantly beyond DNWR, but our model uses this modeling device as a parsimonious way to capture such frictions in a rich dynamic quantitative trade model. 3 Our baseline analysis also assumes flexible exchange rates between the U.S. dollar and other countries’ currencies. However, we have also conducted an alternative analysis with fixed exchange rates, and the implications for the United States are similar. The results of this analysis are available upon request. 4 Introducing other types of nominal anchors prevents us from using the efficient Alvarez-and-Lucas type algorithm developed in RUV to deal with the DNWR, increasing the computation time by several orders of magnitude. Implementing more realistic nominal anchors is left for future research. 2 using data from the base year, we only require an explicit calibration of four parameters. Namely: the DNWR parameter δ, the growth in world nominal GDP in dollars γ, the inverse elasticity of mobility across sectors ν, and the trade elasticity 1 − σ. We normalize δ to one, indicating that nominal wages cannot fall, without loss of generality. We then set γ to 4%, in line with the relatively high nominal growth rate observed in the post-pandemic period, but we explore the robustness of our results to different values. Finally, we obtain ν directly from RUV, and we take σ from the trade literature. Our model-based analysis shows a temporary yet long-lasting decrease in U.S. labor force participation due to the shock. During the high trade cost period, engaging in the home production sector (which provides a constant utility flow) becomes more appealing, resulting in a decline in labor force participation. Once the shock dissipates, there is neg- ative pressure on nominal wages as the economy adjusts to the lower trade costs, which in the presence of DNWR can generate unemployment. The manufacturing sector, where wages increase the most during the high trade cost period, experiences the most unem- ployment when the shock dissipates. The impact of the trade cost shock on the labor market varies by sector. There is a tem- porary employment increase in manufacturing, a sector that is very tradable and where the United States is a net importer. By contrast, the service and agriculture sectors experience temporary employment reductions. We also find that the effect of the shock varies by state. States with larger service sectors (such as Alaska, Nevada, and Hawaii) tend to experience a more significant decline in labor force participation than those with larger manufacturing sectors (such as Ohio, Pennsylvania, and Wisconsin), but additional factors such as the ex- posure to other countries and states also play an important role in determining the extent of the impact. The impact of the shock on labor force participation varies internationally and de- pends on size and trade openness. On the one hand, countries like China, the United States, Brazil, and India, which are relatively large and less reliant on international trade, experience a smaller decrease in labor force participation. On the other hand, small and open countries like Ireland, Estonia, the Slovakia Republic, and Cyprus, which rely heav- ily on foreign intermediate inputs and importing/exporting, experience a more signifi- 3 cant decline in labor force participation. Furthermore, countries that are net importers in a given sector tend to increase their participation relatively more in that sector due to a cross-country expenditure-switching effect. We also investigate how different assumptions affect our conclusions. To do so, we consider alternative specifications where we vary the persistence of the shock, the size of the shock, or the nominal growth rate of world GDP in dollars. In addition, we examine how allowing for migration between U.S. states and varying the elasticity of moving across sectors change our results. Our conclusions are qualitatively robust across these different specifications. Quantitatively, one of the key lessons is that more monetary accommodation in the form of a higher γ at the time the shock disappears (but not necessarily before) can mitigate the unemployment consequences of the shock. It is important to highlight some limitations of our analysis. First, our model does not account for health-related concerns that could also affect participation decisions at the same time as the supply chain disruptions. Our quantitative results suggest that even ab- stracting from these forces, there is a long-lasting effect on labor participation. Second, our framework does not incorporate elements such as pent-up demand after post-pandemic reopening or domestic transportation disruptions, which also contributed to the recent in- crease in trade costs. Therefore, our analysis provides insights into specific aspects of the broader issue of global supply chain disruptions caused by the pandemic. Our paper contributes to the literature studying the relationship between the COVID- 19 pandemic and global supply chains, which has highlighted supply disruptions as one of the main factors explaining the decline in output and increase in inflation. For instance, LaBelle and Santacreu (2022) exploit cross-industry variation in sourcing patterns and find that exposure to supply chain disruptions is associated with higher increases in the pro- ducer price index. Similarly, Meier and Pinto (2020) analyze the impact of Chinese lock- downs on the U.S. economy, finding that sectors with higher exposure to intermediate in- puts from China experienced larger decreases in output, employment, and exports. Bona- dio et al. (2020) investigate the role of global supply chains on GDP growth during the pandemic and find that disruptions explain one-quarter of the decline in GDP. Sforza and Steininger (2020) develop a multi-sector model to show that global production linkages 4 amplified the pandemic shock. We contribute to this literature by analyzing the effect of supply disruptions on local labor markets through the lens of a state-of-the-art trade model. Our paper also relates to the vast literature that studies the impacts of trade on local labor markets using quantitative trade models. Most recent papers have focused on the effects of the rise of China’s prevalence in international trade, also known as the “China Shock” (Rodriguez-Clare et al., 2022; Galle et al., 2020; Caliendo et al., 2019; Adao et al., 2020), but other quantitative papers also examine migration shocks (Caliendo et al., 2021, 2022) or automation (Galle and Lorentzen, 2022).5 Among these papers, RUV is the closest to our work. They present a dynamic quantitative trade model with DNWR and use it to rationalize the empirical findings from the China-Shock literature. The shock itself is modeled as an increase in productivity in China from 2000 to 2007 that varies across sectors. In contrast, our paper applies the quantitative framework from RUV to study the labor market effects of the recent global supply chain disruptions, modeled as an unexpected increase in international trade costs.6 Open-economy macroeconomics papers such as Gali and Monacelli (2005, 2008) or Clarida et al. (2002) have incorporated nominal rigidities into general equilibrium models with a simplified trade structure. Schmitt-Grohe and Uribe (2016) study optimal policies in the presence of DNWR in a small open economy and Guerrieri et al. (2021) analyze monetary policy after pandemic-induced sectoral shocks in a model with DNWR and a nominal anchor similar to ours. Our contribution relative to this literature is to incorporate a hint of these important nominal elements into a rich quantitative trade model to assess the impact of trade cost shocks. The remainder of the paper is organized as follows. Section 2 provides a brief over- view of the model. Section 3 describes our data construction and baseline calibration. Sec- tion 4 presents the results of our baseline analysis for U.S. states. Section 5 focuses on how the results vary across countries. Section 6 investigates the sensitivity of our results to changes in some of the key assumptions and Section 7 concludes. 5 The list is not exhaustive. Other recent papers also study the impacts of trade shocks with unemployment effects generated via search and matching instead of DNWR (e.g. Kim and Vogel, 2020a,b; Dix-Carneiro et al., 2020; Carrere et al., 2020). 6 Our paper also adds to the rapidly growing literature in trade that discusses or incorporates nominal ele- ments (see RUV, Comin and Johnson, 2020; Costinot et al., 2022; Ahn et al., 2022; Fadinger et al., 2022). 5 2 Model Environment In order to study the effects of increases in international trade costs, we use a dynamic multi-sector quantitative trade model with nominal wage rigidities and an input-output structure based on RUV. In this section, we briefly discuss the main features of the model, relegating the details to appendix A. The model incorporates 87 regions (50 U.S. states, 36 other countries, and an aggre- gate rest of the world region) and 15 sectors (home production, 12 manufacturing sectors, services, and agriculture). The “home production” sector is meant to capture useful activ- ities conducted at home (e.g., taking care of family members, cooking, cleaning, enjoying leisure) that are not remunerated as work. In the baseline model, we assume that there is no mobility across countries or across states of the U.S. In an extension, we allow for migration across U.S. states, but this makes very little difference for any of the results. Total consumption is a Cobb-Douglas aggregate of consumption across all the mar- ket sectors with given time-invariant expenditure shares.7 As in a multi-sector Armington trade model, consumption within a given market sector is a CES aggregate of the good produced by each of the regions, with an elasticity of substitution denoted by σ. In princi- ple, each region can produce the goods in all of the sectors, but they might have very low productivity in some of these sectors. We denote the region i, sector s, and time t triad as (i, s, t). Production uses labor and intermediate inputs, but no capital. Specifically, production of the final good in (i, s, t) takes the following Cobb-Douglas form: S ,t ∏ Mi,ks,t , ϕi ,s ϕ i,ks Yi,s,t = Ai,s,t Li,s k =1 where Ai,s,t is total factor productivity in (i, s, t), Li,s,t is employment in (i, s, t), Mi,ks,t is the quantity of intermediate inputs of sector k used in (i, s, t), ϕi,s is the time-invariant labor share in (i, s), and ϕi,ks is the share of inputs that sector s uses from sector k in region i. 7 This assumption is made for tractability and does not capture changes in consumption patterns that might have occurred during the pandemic. 6 Production has constant returns to scale, i.e. ϕi,s + ∑k ϕi,ks = 1. There are iceberg trade costs τij,s,t ≥ 1 for sending the product of sector s from region i to region j at time t. These τ ’s will play an important role because they are the ones getting shocked when the economy faces an increase in trade costs generating the disruption. There is perfect competition in production. Letting Wi,s,t denote the wage in dollars in (i, s, t) and Pi,k,t denote the dollar price of the composite good of sector k, in region i, at time t, then the dollar price in region j of the (i, s, t) good is: S −1 ∏ Pi,ki,,ks ϕi,s ϕ pij,s,t = τij,s,t Ai ,s,t Wi,s,t t. k =1 This expression describes all four factors affecting the price of sending the individual good of sector s from region i to region j at time t; namely: iceberg trade costs, technology at the sector-region of origin, the wage at the sector-region of origin, and intermediate input prices (in all sectors) at the origin location. We denote the number of agents participating in (i, s, t) by ℓi,s,t , whose behavior is described below. In a standard trade model, employment in a sector-region has to equal labor supply in that sector-region, i.e. Li,s,t = ℓi,s,t . We depart from this assumption and instead follow Schmitt-Grohe and Uribe (2016) by allowing for a downward nominal wage rigidity (DNWR) specifying that the nominal wage in (i, s, t) has to be greater than δ times the nominal wage in (i, s, t − 1), that is: Wi,s,t ≥ δWi,s,t−1 . Given this rigidity, employment does not necessarily have to equal labor supply, it could be strictly below it. This is captured by the following weak inequality: L i ,s,t ≤ ℓ i ,s,t . Importantly, there can only be unemployment if the wage is at its lower bound. There- fore, the previous two inequalities are augmented by a complementary slackness condition 7 indicating that at least one of them always has to hold with equality: (ℓi,s,t − Li,s,t )(Wi,s,t − δWi,s,t−1 ) = 0. The previous equation says that wage and employment are determined by supply and demand when the wage is away from its lower bound. By contrast, when the wage lower bound is binding, the market does not clear, and there is rationing (i.e., unemployment). Returning to the determination of ℓi,s,t , agents in the model can either engage in home production (sector zero) or look for work in the labor market (sectors 1 through S). Partic- ipating in home production results in an exogenous and time-invariant real level of con- sumption which does not depend on labor market conditions. By contrast, a given market sector s > 0 yields a real level of consumption ci,s,t which is endogenous. Given the existence of downward nominal wage rigidity, agents must take into ac- count the possibility of unemployment when deciding which sector to participate in. To simplify the analysis, we assume a representative agent in each sector-region.8 Since a fraction Li,s,t /ℓi,s,t of agents is actually employed in (i, s, t), and employed agents obtain a nominal wage of Wi,s,t , the real level of consumption ci,s,t from participating in market sector s is given by: Wi,s,t Li,s,t c i ,s,t = · , Pi,t ℓi,s,t where Pi,t is the aggregate price index in region i. Agents choose their sector while facing idiosyncratic preference shocks, switching costs, and incorporating into their decision the expected future income in all sectors (i.e., the ci,s,t ’s) with perfect foresight. The idiosyncratic preference shocks are assumed to have a Gumbel distribution, making the participation decision tractable and allowing for closed- form expressions (see appendix A for additional details on the derivations). Importantly, there is an elasticity 1/ν of moving across different sectors within any given region. Since the model contains nominal elements (namely the DNWR) it is also important 8 This is equivalent to assuming that the income generated in a sector-region is equally shared between all agents in that sector-region. 8 to introduce a “nominal anchor”, preventing nominal wages from rising so much in each period as to make the DNWR always non-binding. We implement a relatively simple nom- inal rule that captures the idea that central banks are unwilling to allow inflation or unem- ployment to be too high (because of their related costs which, in the case of inflation, are outside the model) while at the same time being amenable for quantification.9 Specifically, we assume that world nominal GDP in dollars grows at a constant rate γ across years: I S I S ∑ ∑ Wi,s,t Li,s,t = (1 + γ) ∑ ∑ Wi,s,t−1 Li,s,t−1. i =1 s =1 i =1 s =1 Although this assumption is useful to solve the model, it has limitations and might not reflect the optimal monetary policy of any given country. This implies that the nominal implications of the model are to be taken with a grain of salt. Consequently, we will refrain from discussing the implications of the trade-cost shock for inflation since the model is not well suited to study this aspect. Nevertheless, the model can provide valuable insights into the behavior of relative prices, which we discuss in our results section. As mentioned above, the main objective of the paper is to examine the effects of an unanticipated trade-cost shock. To do so in a computationally tractable way, we employ a technique known as “dynamic exact hat algebra”, which allows the model to implicitly match production, trade, and reallocation patterns in a given base year. By doing so, one can then introduce a percentage change in any of the model’s fundamentals, such as trade costs, without knowing the initial levels of these fundamentals, and study the economy’s dynamic response to such a shock. To analyze the effects of the trade cost shock, we assume that the base year is 2019. At that point, the shock has not hit the economy and the model perfectly matches production, trade, and sectoral flow patterns as they occurred in the real world. Then, the shock is introduced in 2020, and the agents in the model learn the full path of the shock (recall that the agents in the model have “perfect foresight”). As the shock hits, employment, prices, production, and trade respond accordingly. 9 Thetractability of this nominal anchor allows us to solve our model using a fast contraction mapping algo- rithm in the spirit of Alvarez and Lucas (2007) developed in RUV to deal with the complementary slackness condition implied by the DNWR. A similar nominal anchor is used in Guerrieri et al. (2021). 9 3 Data, Calibration, and Shocks 3.1 Data Sources Our data construction process follows steps similar to those in RUV but uses 2019 as the base year (whereas in RUV the base year is 2000). A summary of the data-construction process is provided here, with additional details available in Appendix B. Labor, input, and consumption shares: Data from the BEA (for U.S. states) and from ICIO (OECD’s Inter-Country Input-Output Database) is used to compute the value-added share in gross output (which is used as the labor share in the model) and the input-output coef- ficients for each region. Consumption shares can be inferred based on trade flows, labor shares, and intermediate input shares. Bilateral flows: The model requires bilateral trade flows in all sectors between any pair of regions in the sample. These are constructed in 4 steps outlined in Appendix B.2. Labor flows across sectors and regions: Data for intersectoral mobility for each U.S. state is obtained from the Current Population Survey (CPS), while frictionless mobility is as- sumed for other countries. In the extension allowing for migration within the U.S., data for interstate mobility is obtained from the American Community Survey (ACS). Labor supply: Data on employment by sector (including home production) comes from the WIOD Socio Economic Accounts, the International Labor Organization, the U.S. Cen- sus, and the ACS. As in RUV, only observations for people aged between 25 and 65 are kept. Labor force participation is measured as the share of individuals in that age group who are either employed or unemployed. 3.2 Parameter Calibration Table 1 describes the parameters used in the baseline specification. Notice that γ (the nominal growth rate of world GDP in U.S. dollars) and δ (the downward nominal wage rigidity parameter) are not separately identified. For a given δ, if γ is higher, then the DNWR is less likely to bind. Likewise, for a given γ, if δ is lower, then the DNWR is less likely to bind. Therefore, we require a normalization and set δ = 1, indicating that nominal 10 Table 1: Parameter values used Parameter Value Description Source δ 1 Lower bound in DNWR Normalization γ 4% Growth rate of world nominal GDP in $ Suggestive ν 0.55 Inverse elasticity of moving across sectors RUV σ 6 Trade elasticity Trade Literature Notes: This table contains the parameter values used in the baseline specification, to- gether with their description and the source where they are taken from. wages in dollars cannot fall, and putting the burden of the nominal adjustment on γ. We set γ = 4%, due to the high nominal growth rate in the post-pandemic period. We discuss the implications of different γ’s (between 2% and 6%) in Section 6. The implications go in the direction expected, the higher the γ, the less binding the DNWR is, and the less unemployment is generated in the model. For a high γ of 6% or higher, the model has essentially the same behavior as the model without DNWR. The outcomes of the model unrelated to unemployment are only slightly affected by the choice of γ. Parameter ν for the inverse elasticity of moving across sectors is taken directly from RUV and set to 0.55. In that paper, the inverse elasticity of moving across sectors is set to match the evidence shown in Autor et al. (2013) on how more exposure to the China shock across U.S. commuting zones affects labor force participation. As we will discuss in Section 6, our results do not change substantially when using other reasonable values of ν. Finally, we set σ to 6 in all sectors, which implies a trade elasticity of -5, consistent with the trade literature (see, e.g., Costinot and Rodriguez-Clare, 2014). 3.3 Trade Shock As indicated in the introduction, the baseline exercise examines a 12% increase in the iceberg trade costs of sending products across countries that reverts after three years. We also explore, in alternative exercises described in Section 6, how the effects of the shock depend on its size (i.e., 6%, 18%, or 24% instead of 12%) or persistence (i.e., 2, 4, 5, or 6 years instead of 3). The choice of a 12% magnitude for the increase in trade costs in our baseline specifi- 11 Producer Price Index by Industry: Deep Sea Freight Transportation: Deep Sea Freight Transportation Services 380 360 340 Index Jun 1988=100 320 300 280 260 240 Jan 2015 Jan 2016 Jan 2017 Jan 2018 Jan 2019 Jan 2020 Jan 2021 Jan 2022 Shaded areas indicate U.S. recessions. Source: U.S. Bureau of Labor Statistics fred.stlouisfed.org Figure 1: PPI for deep sea freight transportation services between January 2015 and January 2022, taken directly from FRED. cation is motivated by the behavior of the producer price index for deep sea freight trans- portation services, depicted in figure 1. This index increased by approximately 12% from its pre-pandemic level of 330 to around 370 in December 2021. It is worth noting that the aforementioned producer price index may not capture the full increase in the cost of cross-border trade, as other trade cost components could have also risen. Nevertheless, iceberg trade costs in trade models also include non-physical factors such as marketing or research costs for entry into a foreign country, which may not have risen as much as physical costs. Overall, we view the 12% increase in the iceberg trade cost as a suggestive benchmark and assess the sensitivity of our results to different values of this parameter. The choice of a 3-year duration for the shock is based on current evidence suggesting that global supply chain disruptions have largely subsided by early 2023. Thus, we assume that high trade costs are in effect for 2020, 2021, and 2022, but then dissipate by 2023. 12 In Section 6, we examine how different shock duration impacts the results. We find that longer-lasting shocks lead to more severe outcomes because, given the costs of moving between sectors, it makes more sense to pay the moving cost for more extended shocks than it does for more transitory ones. 4 Baseline Results This section investigates the effects of a 12% increase in the iceberg trade costs of send- ing products across countries on labor outcomes for the United States. Our baseline exer- cise uses a model where there is no migration across U.S. states, world nominal GDP in dollars grows at 4% per year, and the trade cost shock lasts for 3 years (2020-2022). We discuss the effects on labor force participation, employment, and unemployment in the ag- gregate, as well as on labor supply to the broad sectors of manufacturing, services, and agriculture. We also assess how these effects vary across different U.S. states. International results are discussed in the next section. Figure 2 displays the effects of the shock on employment-related outcomes for the United States as a whole. The blue line depicts the cumulative percentage change in em- ployment since 2019, the green line shows the cumulative percentage change in labor sup- ply since 2019, and the red line shows the level of unemployment (in percent). We find that aggregate U.S. labor supply decreases during the years when the trade shock is active, with the largest cumulative decline of 0.7% occurring in 2022. The fall in la- bor supply occurs because, while trade costs are high, participating in the home-production sector (which offers a constant real utility flow) temporarily becomes more attractive than participating in the market sectors. This is due to the fact that high trade costs make the market sectors less productive because intermediate inputs from other countries are more expensive, which is akin to a fall in productivity. Although aggregate nominal wages in- crease at a faster-than-normal pace during the period of high trade costs, aggregate prices increase even faster, resulting in a decrease in real wages (see appendix figure C.1), which is what causes some individuals to exit the labor force. The recovery of labor supply once the shock disappears is slow, by 2027 labor supply 13 Employment, labor supply, and unemployment 0.5 0 Percentage -0.5 Employment Change Labor Supply Change Unemployment -1 2020 2025 2030 2035 Year Figure 2: Paths of relevant variables for the U.S. on aggregate. The cumulative percent- age change in employment since 2019 is in blue, the cumulative percentage change in labor supply since 2019 is in green, and the level of unemployment (in percent) is in red. The years in the x-axis go from 2019 until 2035. is still 0.2% lower than pre-shock. In the model, the costs of switching between market sectors and entering/exiting the labor force are calibrated based on pre-pandemic mobility patterns. These patterns suggest that there are substantial costs associated with reallocating across sectors, which explains why agents return to the labor force gradually. Although the pandemic may have altered the costs of switching between sectors, the model does not account for such changes.10 10 Anotherlimitation of our model is that it does not feature an income effect on labor supply, because the agents do not have a level of wealth or assets that enters their labor decision. Agents simply compare their real consumption of participating in home production (which is constant) against the real consumption they obtain from participating in a given market sector (which is given by the real wage in that sector adjusted for unemployment). Moreover, the agents cannot choose their level of employment (or their “hours”); they simply choose their sector and supply all their units of labor inelastically to that sector. 14 Unemployment is generated mostly when the shock dissipates, with the peak a-mount of unemployment of 0.32% occurring in 2023. As mentioned above, during the years with high trade costs nominal wages are increasing faster than usual, so the downward wage rigidity mostly does not bind. By contrast, when the shock dissipates nominal wages need to fall in some region-sectors.11 Consequently, those locations hit the DNWR and experi- ence some temporary unemployment. The blue line in figure 2, which shows the cumulative change in employment since 2019, is essentially the combination of the green and red lines (labor supply and unem- ployment). Importantly, even though the trough for labor supply occurs in the year 2022, the trough for employment occurs in 2023, due to the additional unemployment generated when the trade-cost shock dissipates. Figure 3 displays the cumulative percentage change since 2019 of activity (i.e., the number of people engaged) in four different broad sectors for the U.S. as a whole. Home production is depicted in blue, manufacturing in green, services in red, and agriculture in purple. While home production and manufacturing show an increase during the period when the shock is active, services and agriculture decline. The rise in home production has already been explained above, so we now focus on the employment changes in the other sectors. Several forces affect employment in each market sector. First, there is a general decrease in demand due to the aggregate fall in em- ployment (with people out of work there is less spending power). Second, intermediate inputs become more expensive, making production less efficient and decreasing labor de- mand. Third, there is an expenditure-switching effect across countries: imports become more expensive and tend to be substituted with local production, increasing labor demand in net-importing sectors. The United States is a net exporter of services and has balanced trade in agriculture, in these sectors the first two effects mentioned in the previous paragraph dominate, de- 11 Whilehigh trade costs are active, agents are flowing out of the labor force, which forces nominal wages to increase faster than usual to attain the γ growth of nominal GDP embedded in the nominal anchor. Once trade costs return to their normal level, agents flow back into the labor force, which implies nominal wages must grow more slowly than usual (or in some cases fall) to satisfy the nominal anchor. This is reminiscent of central banks around the world withdrawing monetary accommodation once the pandemic and supply disruptions subsided and the labor market normalized. 15 Change in participation by broad sector 2 Home production Manufacturing 1.5 Percentage change in participation Services Agriculture 1 0.5 0 -0.5 -1 -1.5 2020 2025 2030 2035 Year Figure 3: Paths of aggregate participation for different broad sectors in the U.S. The percentage change in home production from the baseline year of 2019 is in blue, the percentage change in labor supply to the manufacturing sector since 2019 is in green, the same concept for the service sector is in red, and for the agricultural sector is in purple. creasing participation. By contrast, the United States is a net manufacturing importer. In this sector, the expenditure-switching effect dominates and participation increases. Since manufacturing is the sector that experiences an increase in participation (and the highest increase in nominal wages) during the years when the shock is active, it is also the sector that suffers most of the unemployment when the shock dissipates. Appendix figure C.2 depicts the evolution of relative sectoral prices (nominal sectoral prices divided by the aggregate price index). Manufacturing experiences the highest in- crease in relative price (up to 4%). Agriculture’s relative price increases slightly (up to 1%), while the relative price of services decreases (up to -1%). Turning to regional results, figure 4 presents a map of the cumulative percentage 16 (-.5,0] (-.75,-.5] (-1,-.75] [-1.6,-1] Figure 4: Map for the cumulative percentage change in participation between 2019 and 2022 across U.S. states. Darker shades of blue represent smaller falls in participation. change in labor force participation between 2019 and 2022 for U.S. states. Some of the states where labor participation falls the most are Alaska, Nevada, and Hawaii, while some states where it falls the least are Pennsylvania, Ohio, and Wisconsin. While the states where participation falls the most tend to have a relatively large ser- vice sector and the ones where participation falls the least tend to have a larger manufac- turing sector, the way the shock affects each state is not immediately apparent. This is because the fall in participation and the amount of unemployment generated depend on several factors, such as the distribution of labor across sectors, deficits in the pre-pandemic period, and exposure to trade with other countries and other U.S. states, among others. 5 International Results In this section, we turn our attention to how the impacts of the trade shock vary across countries. The shock itself is uniform in how it affects the iceberg trade costs of sending products across countries. Nevertheless, countries’ exposures to the shock vary due to differences in their openness levels, size, and sectoral compositions. Figure 5 illustrates this idea by displaying the change in home production participation between 2019 and 17 Home production participation change between 2019 and 2022 14 12 Change between 2019 and 2022, in % 10 8 6 4 2 0 D R N H T N BR R SWX R N AUA L KOA D P TW T AU L T BGD SV E K oW R C C U G N BRA A S R R C N YP E D N N N L U TUS EU MN K IR PO BE ES PR E IT FR ES Z SV S IN ID H U N U L R O FI JP LT A C U G C Country Figure 5: Percentage change in home production participation between 2019 and 2022 across countries, in percent. For country abbreviation codes see appendix B.1. 2022 for all 38 countries in our sample. The figure shows that large countries such as the United States, China, Japan, Brazil, and India, which are less reliant on international trade due to the size of their domestic market, experience relatively smaller increases in home production participation due to the trade shock. In contrast, smaller and more open countries such as Ireland, Hungary, Estonia, the Slovakia Republic, and Cyprus, suffer a greater increase in home production participation (akin to a fall in the labor force). Adao, Arkolakis, and Esposito (2020) (henceforth AAE), presents a formula for the first-order approximation of the exposure of a region to a trade shock under certain simpli- fying assumptions. We use their formula to understand how regions (and therefore coun- tries) are differentially exposed to the increase in international trade costs. As expressed in equations (16) and (17) of AAE, the formula for the change in excess labor demand in 18 ˆ is given by: region i after a change in trade costs τ S η ˆ ) = (1 − σ) ∑ ℓi,s,0 θi,s (τ ˆi (τ ˆ ). s =1 In the previous expression, (1 − σ ) is the trade elasticity, ℓi,s,0 is the share of labor in market i employed in sector s in the base year (denoted with a zero even though in our implemen- ˆ ) is the shift in demand for the sector s good of tation it will be the year 2019), and θi,s (τ region i: I I ˆ) = θ i ,s ( τ ∑ rij,s,0 ˆij,s − τ ∑ λqj,s,0 τ ˆqj,s . j =1 q =1 The variable rij,s,0 denotes the share of market i’s sales in sector s that go to market j in the base year, λqj,s,0 denotes the share of market j’s purchases in sector s that come from market ˆij,s = ln(τij,s,2022 ) − ln(τij,s,2019 ) denotes the log of the change in the q in the base year, and τ iceberg trade costs between the base year and the high-trade-cost years (2020, 2021, and 2022). ˆ ) represents market i’s “revenue shock exposure”. It is the sum across sectors of ˆi (τ η ˆ ), weighted by that the shock to the demand for the good of region i in each sector, θi,s (τ sector’s share in i’s employment in the base year ℓi,s,0 . The sector-level demand shock, ˆ ), is itself the sum across destinations j of the impact of market i’s own trade shock on θ i ,s ( τ the demand for its good minus the demand shift caused by competitors’ trade shocks in that sector, weighted by the revenue importance of each destination in the base year rij,s,0 . ˆ ) can be computed with information on bilateral trade ˆi (τ Note that all components of η flows in the base year plus measures of the bilateral trade shocks. In our implementation, ˆij,s ≈ 12% if i and j are regions located in different countries, while τ τ ˆij,s = 0 if i = j or if i and j are regions of the same country (e.g., two U.S. states). The AAE exposure measure provides a useful way to assess the impact of shocks on a given region by taking into account how it competes with all other regions in all possible destination markets, including its own. If a region is in autarky, a change in the τ ’s has no ˆ ) = 0 for all s, resulting in η effect and θi,s (τ ˆ ) = 0. Regions that are more open or have ˆi (τ 19 Participation change vs exposure 14 IRL 12 10 Participation change, in % 8 CYP SVN LTU BGR 6 4 DEU ESP FRA RUS AUS 2 BRA USA CHNJPN 0 -0.5 0 0.5 1 1.5 2 AAE exposure to shock Figure 6: Scatter plot of the percentage change in home production participation be- tween 2019 and 2022 against the AAE exposure measure across countries. For country abbreviation codes see appendix B.1, for the definition of AAE exposure see the text. higher labor shares in more open sectors are more exposed to a change in trade costs. Figure 6 gives a scatter plot between the AAE exposure measure on the x-axis and the change in participation in home production between 2019 and 2022 on the y-axis. The plot reveals a tight relationship between the exposure measure and the change in participation. Although the AAE exposure measure is a first-order approximation and it does not allow for differences in labor shares or input-output coefficients, it provides a reasonably good fit. A regression of participation change on the AAE exposure plus a constant has an R- squared of 72%, and the exposure measure has a p-value substantially below 1%. The reduction in welfare due to the increase in trade costs is almost perfectly correlated 20 Manufacturing employment change between 2019 and 2022 2 0 Change between 2019 and 2022, in % -2 -4 -6 -8 -10 -12 D C N C T N R PRX C R TUN BR BEL FRA K TW E BG T LD D L D T A R P R C U oW N N G R AUA C S U P R A N E SV L U N M K KOU AN G S IR PO ES AU E IT SV Z ES BR Y S SW IN ID U N H U R O FI LT JP E N H Country Figure 7: Percentage change in manufacturing employment between 2019 and 2022 across countries, in percent. For country abbreviation codes see appendix B.1. with the fall in labor force participation between 2019 and 2022, because it is driven exactly the same factors. Appendix figure C.4 displays the welfare change across countries.12 The welfare loss for the United States is approximately 14 basis points. The minimum welfare loss of 13 basis points occurs in China, while the maximum one of 97 basis points occurs in Ireland. The unweighted average welfare loss across the 38 countries in the sample (in- cluding the “rest of the world” region) is 37 basis points, while the weighted one is 19 basis points. The fact that the unweighted welfare loss is almost twice as high as the weighted one provides another illustration that countries with smaller populations do much worse 12 The welfare change is measured as the equivalent variation in consumption required by agents in the model in the base year to be indifferent between the counterfactual economy where the trade costs increase and the baseline economy where they do not. The formula is given in RUV, it is a present value sum where we use an annual discount factor of β = 0.95. 21 in response to the shock than countries with larger populations. Turning to results in specific sectors, figure 7 illustrates the change in manufacturing employment across countries between 2019 and 2022.13 In addition to the aforementioned factors that influence the overall change in labor participation, the change in manufactur- ing employment also depends on the initial deficit in manufacturing. Countries that are net manufacturing importers, such as the United States, Great Britain, the Russian Feder- ation, or Cyprus, need to substitute foreign imports with domestic production, driving up the change in manufacturing employment. 6 Alternative Assumptions This section explores how our results change if we make different assumptions regard- ing the persistence or size of the shock or the nominal growth rate of world GDP in dollars. We also touch briefly on the consequences of allowing for migration between U.S. states or changing the elasticity of moving across sectors. To begin, we focus on persistence. Different amounts of persistence are captured by having the shock revert after 2, 4, 5, or 6 years instead of 3 years (which is the baseline as- sumption). Figure 8 illustrates the cumulative change in participation in the broad sectors of home production, manufacturing, and services (agriculture is excluded for simplicity and because it is a small sector) for different values of persistence. A higher persistence leads to a greater increase in home production and a more sub- stantial decrease in services. Manufacturing, however, is much less sensitive to changes in persistence. This is due to the fact that, out of the three factors affecting sectoral reallocation (fall in aggregate demand, lower productivity, and expenditure switching), a longer shock exacerbates the fall in aggregate demand without increasing the expenditure switching ef- fect. The amount of unemployment generated across different amounts of persistence is essentially the same (i.e., around 0.32%). We can also explore the impact of varying the size of the shock. Figure 9 depicts the 13 Similarly, appendix figures C.5 and C.6 show changes in service and agricultural employment across coun- tries between 2019 and 2022. 22 Change in home production, manufacturing, and services across persistences 2 years, Home 2 years, Manu 4 2 years, Serv 3 years, Home 3 years, Manu 3 years, Serv 3 Percentage change in participation 4 years, Home 4 years, Manu 4 years, Serv 5 years, Home 2 5 years, Manu 5 years, Serv 6 years, Home 6 years, Manu 1 6 years, Serv 0 -1 -2 2020 2025 2030 2035 Year Figure 8: Paths of aggregate U.S. participation for home production, manufacturing, and services across different values for the persistence of the shock. Blue depicts a 2- year persistence, green 3, yellow 4, orange 5, and red 6. A solid line depicts home production, a dashed line depicts manufacturing, and a line with circle markers depicts services. cumulative change in participation in home production, manufacturing, and services for four different values of the shock: 6%, 12%, 18%, and 24%. A larger shock tends to amplify the effects discussed earlier and generates more unemployment for a given value of γ (the growth rate of world nominal GDP in dollars). In turn, more unemployment discourages participation in the manufacturing sector. Next, we consider the effects of assuming different values for the annual growth rate of world nominal GDP in dollars (γ). Figure 10 depicts the cumulative change in participation in the broad sectors of home production, manufacturing, and services for different values of γ. 23 Change in home production, manufacturing, and services for different shock sizes 6% shock, Home 6 6% shock, Manu 6% shock, Serv 12% shock, Home 5 12% shock, Manu 12% shock, Serv Percentage change in participation 4 18% shock, Home 18% shock, Manu 18% shock, Serv 3 24% shock, Home 24% shock, Manu 24% shock, Serv 2 1 0 -1 -2 -3 2020 2025 2030 2035 Year Figure 9: Paths of aggregate U.S. participation for home production, manufacturing, and services across different sizes of the shock. Blue depicts a 6% shock, green 12%, orange 18%, and red 24%. A solid line depicts home production, a dashed line depicts manufacturing, and a line with circle markers depicts services. A higher γ makes the DNWR less likely to bind and decreases the unemployment generated by the shock. In addition, it leads to a smaller participation increase in home production, a larger increase in manufacturing, and a smaller fall in services. The manu- facturing sector is particularly sensitive to the value of γ (as it is to the size of the shock) because it is the sector where most of the unemployment occurs when the shock dissipates. If agents realize that a lot of unemployment will be generated, they will hesitate to go into manufacturing in the first place. The amount of unemployment generated across values of γ differs substantially. While for γ = 4% unemployment reaches 0.32% at its peak, this peak can reach 1.3% if γ = 3%, 24 Change in home production, manufacturing, and services across values of 4 = 6%, Home = 6%, Manu = 6%, Serv = 5%, Home = 5%, Manu 3 Percentage change in participation = 5%, Serv = 4%, Home = 4%, Manu = 4%, Serv 2 = 3%, Home = 3%, Manu = 3%, Serv = 2%, Home 1 = 2%, Manu = 2%, Serv 0 -1 2020 2025 2030 2035 Year Figure 10: Paths of participation for home production, manufacturing, and services across different values for the growth of world nominal GDP in dollars (γ). Blue depicts 6% growth, green 5%, yellow 4%, orange 3%, and red 2%. A solid line depicts home production, a dashed one depicts manufacturing, and a line with circle markers depicts services. and almost 3% if γ = 2%. In this sense, the model is highly non-linear due to the one-sided nature of the DNWR. More monetary policy accommodation (i.e., a higher γ) when the shock disappears can help alleviate the unemployment consequences of the shock. Allowing for migration within U.S. states has a negligible impact on the results dis- cussed so far. Note that when migration across U.S. states is allowed, there is a new elas- ticity 1/κ of moving across states that comes into play. RUV calibrate κ to 12 in order to match the evidence found by Autor et al. (2013) on how population across states responds to the China shock. Given that the population response is small, the elasticity of moving across states is calibrated to be low. Additionally, since U.S. states are similarly exposed to the shock we study, the need for reallocation is not large. 25 Finally, changes in the inverse elasticity of moving across sectors (ν) do not have a major impact on the results. Naturally, the higher the ν, the lower the elasticity with which agents move across sectors, and hence the smaller the reallocation that occurs due to the trade-cost shock. However, for reasonable values of ν between 0.35 and 0.75 (recall that the baseline value is 0.55), the results discussed above do not change substantially. 7 Conclusion In this paper, we use a dynamic quantitative trade model with an input-output struc- ture and downward nominal wage rigidity to study the effects of a 12% increase in the costs of sending products across countries that reverts after three years. This exercise is meant to capture some of the recent global supply chain disruptions caused by the COVID-19 pandemic. Our analysis reveals three main results for the United States. First, there is a tempo- rary but persistent decline in labor force participation: while the high trade cost is active, participating in the home production sector (which has a constant real utility flow) tem- porarily becomes more attractive. Second, there is a temporary increase in manufacturing employment, a highly tradable sector for which the United States is a net importer. By contrast, there are temporary reductions in service and agricultural employment. Third, unemployment is generated when the shock disappears because this is the moment when the downward nominal wage rigidity binds. The bulk of the unemployment is generated in manufacturing, where wages increase during the period of high trade costs and must decrease when the shock dissipates. In general, labor force participation tends to fall more in states with a larger service sector (such as Alaska, Nevada, and Hawaii) and less in states with larger manufacturing sectors (such as Ohio, Pennsylvania, and Wisconsin). Our country-level analysis finds that large or closed countries experience smaller de- clines in labor participation following the shock, while small or open economies experience larger ones. Although this result may seem intuitive, our model provides quantitative es- timates of the changes in participation in home production derived from a state-of-the-art trade model, as well as changes in employment in specific sectors such as manufacturing, 26 services, and agriculture. The framework we propose offers policymakers a valuable tool for estimating the potential impacts of changes in trade costs across countries or sectors lasting different amounts of time. Given the increased risk of supply chain disruptions, our model can be useful in devising effective policy responses. However, it is important to note that our model does not feature explicit costs of inflation, or other pandemic-induced issues such as pent-up demand, fiscal support, or an unanchoring of inflation expectations. 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We assume that there is no labor mobility across different coun- tries, but can allow for mobility across different states of the U.S. There are S + 1 sectors in the economy (indexed by s or k), with sector zero denoting the home production sector and the remaining S sectors being productive market sectors. In each region j and period t, a representative consumer participating in the market economy devotes all income to expenditure Pj,t Cj,t , where Cj,t and Pj,t are aggregate consumption and the price index re- spectively. Aggregate consumption is a Cobb-Douglas aggregate of consumption across the S different market sectors with expenditure shares α j,s . As in a multi-sector Armington trade model, consumption in each market sector is a CES aggregate of consumption of the good of each of the I regions, with an elasticity of substitution σs > 1 in sector s. Each region produces the good in sector s with a Cobb-Douglas production function, using labor with share ϕj,s and intermediate inputs with shares ϕj,ks , where ϕj,s + ∑k ϕj,ks = 1. TFP in region j, sector s, and time t is A j,s,t . There is perfect competition and iceberg trade costs τij,s,t ≥ 1 for exports from i to j in sector s. Intermediates from different origins are aggregated in the same way as consumption goods. Letting Wi,s,t denote the wage in region i, sector s, at time t, the price in region j of good s produced by region i at time t is then ,s,t Wi,s,t ∏ Pi,k,t , −1 ϕi ,s ϕi,ks pij,s,t = τij,s,t Ai (A1) k where Pi,k,t is the price index of sector k in region i at time t. Given our Armington assump- tion, these price indices satisfy I Pj1 −σs ,s,t = ∑ p1 −σs ij,s,t , (A2) i =1 31 with corresponding trade shares −σs p1 ij,s,t λij,s,t ≡ I 1− σ . (A3) ∑r =1 prj,s,t s Let Ri,s,t and Li,s,t denote total revenues and employment in sector s of country i, re- spectively. Noting that the demand of industry k of country j of intermediates from sector s is ϕj,sk R j,k,t and allowing for exogenous deficits, the market clearing condition for sector s in country i can be written as I S S R i ,s,t = ∑ λij,s,t α j,s ∑ Wj,k,t L j,k,t + D j,t + ∑ ϕj,sk R j,k,t , (A4) j =1 k =1 k =1 where D j,t are transfers received by region j, with ∑ j D j,t = 0. In turn, employment must be compatible with labor demand, Wi,s,t Li,s,t = ϕi,s Ri,s,t . (A5) Agents can either engage in home production or look for work in the labor market. If they participate in the labor market, they can be employed in any of the S market sectors. We let ci,0,t denote consumption associated with home production in region i, and ci,s,t denote consumption associated with seeking employment in sector s and region i at time t. We assume that ci,0,t is exogenous and does not vary over time, while – as explained further below – ci,s,t is endogenous and depends on real wages and unemployment. Additionally, we denote the number of agents that participate in region i, sector s, at time t, by ℓi,s,t . Agents are forward looking and they face a dynamic problem where they discount the future at rate β. Relocation decisions are subject to sectoral and spatial mobility costs. Specifically, there are costs φ ji,sk of moving from region j, sector s to region i, sector k. These costs are time invariant, additive, and measured in terms of utility. Additionally, agents have additive idiosyncratic shocks for each choice of region and sector, denoted by ϵi , s , t . An agent that starts in region j and sector s observes the economic conditions in all 32 labor markets and the idiosyncratic shocks, then earns real income c j,s,t and has the option to relocate. The lifetime utility of an agent who is in region j, sector s, at time t, is then: ν j,s,t = ln(c j,s,t ) + max { βE(νi,k,t+1 ) − φ ji,sk + ϵi,k,t }. ,S {i,k}iI= 1,k=0 We assume that the joint density of the vector ϵ at time t is a nested Gumbel:   ν /κ I S F (ϵ) = exp − ∑ ∑ exp (−ϵi,k,t /ν) , i =1 k =0 where κ > ν. This allows us to have different elasticities of moving across regions and sectors. Let Vj,s,t ≡ E(ν j,s,t ) be the expected lifetime utility of a representative agent in labor market j, s. Then, using γ to denote the Euler-Mascheroni constant, we have  κ ν /κ I S Vj,s,t = ln(c j,s,t ) + ln  ∑ ∑ exp 1/ν βVi,k,t+1 − φ ji,sk  + γκ . (A6) i =1 k =0 Denote by µ ji,sk|i,t the number of agents that relocate from market js to ik expressed as a share of the total number of agents that move from js to ik′ for any sector k′ . Additionally, let µ ji,s#,t denote the fraction of agents that relocate from market js to any market in i as a share of all the agents in js. As shown in RUV, these fractions are given by 1/ν exp βVi,k,t+1 − φ ji,sk µ ji,sk|i,t = 1/ν (A7) ∑S h=0 exp βVi,h,t+1 − φ ji,sh 1/ν ν/κ ∑S h=0 exp βVi,h,t+1 − φ ji,sh µ ji,s#,t = . (A8) I 1/ν ν/κ ∑m =1 ∑S h=0 exp βVm,h,t+1 − φ jm,sh The total number of agents that move from js to ik is given by µ ji,sk = µ ji,sk|i,t · µ ji,s#,t . Participation in the different labor markets evolves according to I S ℓ i ,k ,t +1 = ∑ ∑ µ ji,sk|i,t µ ji,s#,t ℓ j,s,t (A9) j =1 s =0 33 The aggregate price index in region i at time t is given by: S ∏ Pi,si,,st . α Pi,t = (A10) s =1 We assume that the income generated in a sector-region is equally shared between all participants in that sector-region. Since agents get real wage Wi,s,t / Pi,t with probability Li,s,t /ℓi,s,t if they seek employment in sector s of region i at time t, we have Wi,k,t Li,k,t c i ,k ,t = · . (A11) Pi,t ℓi,k,t We denote the number of agents that are actually employed in region i and sector k at time t with Li,k,t . In a standard trade model, labor market clearing requires that the labor used in a sector and region be equal to labor supplied to that sector, i.e. Li,k,t = ℓi,k,t . We depart from this assumption and instead follow Schmitt-Grohe and Uribe (2016) by allowing for downward nominal wage rigidity, which might lead to an employment level that is strictly below labor supply, L i ,k ,t ≤ ℓ i ,k ,t . (A12) All prices and wages up to now have been expressed in U.S. dollars. In contrast, a given region faces DNWR in terms of its local currency unit. Letting WiLCU ,k,t denote nominal wages in local currency units, the DNWR takes the following form: WiLCU LCU ,k,t ≥ δk Wi,k,t−1 , δk ≥ 0. Letting Ei,t denote the exchange rate between the local currency unit of region i and the local currency unit of region 1 (which is the U.S. dollar) in period t (in units of dollars per LCU of region i), then Wi,k,t = WiLCU ,k,t Ei,t and so the DNWR for wages in dollars entails Ei,t Wi,k,t ≥ δW . Ei,t−1 k i,k,t−1 34 Since all regions within the U.S. share the dollar as their LCU, then Ei,t = 1 and WiLCU ,k,t = Wi,k,t ∀ i ≤ M. This means that the DNWR in states of the U.S. takes the fa- miliar form Wi,k,t ≥ δk Wi,k,t−1 . For the I − M regions outside of the U.S., the LCU is not the dollar and so the behavior of the exchange rate impacts how the DNWR affects the real economy. The DNWR in dollars can then be captured using a country-specific parameter δi,k , i.e.: Wi,k,t ≥ δi,k Wi,k,t−1 , δi,k ≥ 0. (A13) The baseline model assumes that all regions outside of the U.S. have a flexible exchange rate (so the DNWR never binds). This is captured by setting δi,k = δk ∀ i ≤ M and δi,k = 0 ∀ i > M. There is also a complementary slackness condition, (ℓi,k,t − Li,k,t )(Wi,k,t − δi,k Wi,k,t−1 ) = 0. (A14) So far, we have introduced nominal elements to the model (i.e., the DNWR), but we have not introduced a nominal anchor that prevents nominal wages from rising so much in each period as too make the DNWR always non-binding. We now want to capture the general idea that central banks are unwilling to allow inflation to be too high because of its related costs. In traditional macro models, this is usually implemented via a Taylor rule, where the policy rate reacts to inflation. Instead, we use a nominal anchor that captures a similar idea in a way that naturally lends itself to quantitative implementation in our trade model. A similar nominal anchor is used in Guerrieri et al. (2021), albeit in the context of a static, closed economy model. In particular, we assume that world nominal GDP in dollars grows at a constant rate γ every year, I K I K ∑∑ Wi,k,t Li,k,t = (1 + γ) ∑ ∑ Wi,k,t−1 Li,k,t−1. (A15) i =1 k =1 i =1 k =1 The main benefit of this nominal anchor is allowing us to solve our otherwise-unwieldy model using a fast contraction-mapping algorithm in the spirit of Alvarez and Lucas (2007) that we develop to deal with the complementary slackness condition brought by the DNWR. 35 Following CDP, we can think of the full equilibrium of our model in terms of a tempo- rary equilibrium and a sequential equilibrium. In our environment with DNWR, given last period’s nominal world GDP (∑iI=1 ∑S s=1 Wi,s,t−1 Li,s,t−1 ), wages {Wi,s,t−1 }, and the current period’s labor supply {ℓi,s,t }, a temporary equilibrium at time t is a set of nominal wages {Wi,s,t } and employment levels { Li,s,t } such that equations (A1)-(A5) and (A12)-(A15) hold. In turn, given starting world nominal GDP (∑iI=1 ∑S s=1 Wi,s,0 Li,s,0 ), labor supply { ℓi,s,0 }, and wages {Wi,s,0 }, a sequential equilibrium is a sequence {ci,s,t , Vi,s,t , µ ji,sk|i,t , µ ji,s#,t , ℓi,s,t , Wi,s,t , Li,s,t , }∞ t=1 such that: (i) at every period t {Wi,s,t , Li,s,t } constitute a temporary equi- librium given ∑iI=1 ∑S s=1 Wi,s,t−1 Li,s,t−1 , {Wi,s,t−1 }, and { ℓi,s,t }, and (ii) { ci,s,t , Vi,s,t , µ ji,sk|i,t , µ ji,s#,t , ℓi,s,t }∞ t=1 satisfy equations (A6)-(A11). We are interested in obtaining the effects of the trade cost shock as it is introduced in an economy that did not previously expect this shock. In order to do this we will use the exact hat algebra methodology of Dekle et al. (2007), extended to dynamic settings by Caliendo ˆ t to denote the ratio between a relative time difference et al. (2019). Specifically, we use x ˙t in the counterfactual economy (x ′ ) and a relative time difference in the baseline economy ˙ t ), i.e. x (x ˙t ˆt = x ′ /x ˙ t for any variable x. Then we compare a counterfactual economy where the knowledge of the trade shock is unexpectedly introduced in the year 2020 (and agents have perfect foresight about the path of the shock from then on), with a baseline economy where the trade shock does not occur. B Data Construction B.1 Data Description and Sources List of sectors. We use a total of 14 market sectors. The list includes 12 manufactur- ing sectors, one catch-all services sector, and one agriculture sector (ICIO sectors D01T02, D03). We follow RUV in the selection of the 12 manufacturing sectors. These are: 1) Food, beverage, and tobacco products (NAICS 311-312, ICIO sector D10T12); 2) Textile, textile product mills, apparel, leather, and allied products (NAICS 313-316, ICIO sector D13T15); 3) Wood products, paper, printing, and related support activities (NAICS 321-323, ICIO 36 sectors D16, D17T18); 4) Mining, petroleum and coal products (NAICS 211-213, 324, ICIO sectors D05T06, D07T08, D09, D19); 5) Chemicals (NAICS 325, ICIO sectors D20, D21); 6) Plastics and rubber products (NAICS 326, ICIO sector D22); 7) Nonmetallic mineral prod- ucts (NAICS 327, ICIO sector D23); 8) Primary metal and fabricated metal products (NAICS 331-332, ICIO sectors D24, D25); 9) Machinery (NAICS 333, ICIO sector D28); 10) Computer and electronic products, and electrical equipment and appliance (NAICS 334-335, ICIO sectors D26, D27); 11) Transportation equipment (NAICS 336, ICIO sectors D29, D30); 12) Furniture and related products, and miscellaneous manufacturing (NAICS 337-339, ICIO sector D31T33). There is a 13) Services sector which includes Construction (NAICS 23, ICIO sector D41T43); Wholesale and retail trade sectors (NAICS 42-45, ICIO sectors D45T47); Ac- commodation and Food Services (NAICS 721-722, ICIO sector D55T56); transport services (NAICS 481-488, ICIO sectors D49-D53); Information Services (NAICS 511-518, ICIO sec- tors D58T60, D61, D62T63); Finance and Insurance (NAICS 521-525, ICIO sector D64T66); Real Estate (NAICS 531-533, ICIO sector D68); Education (NAICS 61, ICIO sector D85); Health Care (NAICS 621-624, ICIO sector D86T88); and Other Services (NAICS 493, 541, 55, 561, 562, 711-713, 811-814, ICIO sectors D69T75, D77T82, D90T93, D94T96, D97T98). List of economies: As in RUV, we use data for 50 U.S. states, 36 other countries and a constructed rest of the world. The list of economies is: Australia (AUS), Austria (AUT), Belgium (BEL), Bulgaria (BGR), Brazil (BRA), Canada (CAN), China (CHN), Cyprus (CYP), Czechia (CZE), Denmark (DNK), Estonia (EST), Finland (FIN), France (FRA), Germany (DEU), Greece (GRC), Hungary (HUN), India (IND), Indonesia (IDN), Italy (ITA) Ireland (IRL), Japan (JPN), Lithuania (LTU), Mexico (MEX), the Netherlands (NLD), Poland (POL), Portugal (PRT), Romania (ROU), the Russian Federation (RUS), Spain (ESP), the Slovak Republic (SVK), Slovenia (SVN), the Republic of Korea (KOR), Sweden (SWE), Taiwan, China (TWN), Turkiye (TUR), the United Kingdom (GBR), and the rest of the world (RoW). B.2 Data on Bilateral Trade For bilateral trade between countries we use the OECD’s Inter-Country Input-Output (ICIO) Database. For data on bilateral trade in manufacturing between U.S states, we com- bine the Commodity Flow Survey (CFS) with the ICIO database. The CFS records ship- 37 ments between U.S states for 43 commodities classified according to the Standard Classifi- cation of Transported Goods (SCTG). We follow CDP and use CFS tables that cross-tabulate establishments by their assigned NAICS codes against SCTG commodities shipped by es- tablishments within each of the NAICS codes. For data on bilateral trade in manufacturing and agriculture between U.S states and the rest of the countries, we follow RUV and obtain sector-level imports and exports be- tween the 50 U.S. states and the list of other countries from the Import and Export Mer- chandise Trade Statistics database, which is compiled by the U.S. Census Bureau. For data on services and agriculture expenditure and production, we use U.S. state- level services GDP from the Regional Economic Accounts of the Bureau of Economic Anal- ysis (BEA), U.S. state-level services expenditure from the Personal Consumption Expendi- tures (PCE) database of BEA and total production and expenditure in services from ICIO (for other countries). We also use the Agricultural Census and the National Marine Fish- eries Service Census to get state-level production data on crops, livestock, and seafood. For other countries we compute production and expenditure in agriculture from ICIO. For data on sectoral and regional value added share in gross output, we use data from the Bureau of Economic Analysis (BEA) by subtracting taxes and subsidies from GDP data. In the cases when gross output was smaller than value added we constrain value added to be equal to gross output. For the list of other countries we obtain the share of value added in gross output using data on value added and gross output data from ICIO. B.3 Data on Employment and Labor Flows For the case of countries, we take data on employment by country and sector from the WIOD Socio Economic Accounts (WIOD-SEA) and International Labor Organization (ILO). For the case of U.S. states, we take sector-level employment (including unemploy- ment and non-participation) from a combination of the Census and the American Com- munity Survey (ACS). As in RUV, we only keep observations with age between 25 and 65, who are either employed, unemployed, or out of the labor force. We construct a matrix of migration flows between sectors and U.S. states by combining data from the ACS and the Current Population Survey (CPS). Finally, we abstract from international migration. 38 C Additional Figures Percentage change in real wages by sector 1.5 Manufacturing Services Agriculture 1 Aggregate Percentage change 0.5 0 -0.5 -1 -1.5 2020 2025 2030 2035 Year Figure C.1: Paths of cumulative percentage change since 2019 in real wages for manu- facturing, services, agriculture, and on aggregate. 39 Percentage change in relative prices by sector 4 Manufacturing 3.5 Services Agriculture 3 Percentage change 2.5 2 1.5 1 0.5 0 -0.5 -1 2020 2025 2030 2035 Year Figure C.2: Paths of cumulative percentage change since 2019 in the relative prices of manufacturing, services, and agriculture. 40 Percentage change in real output by sector Manufacturing 1.5 Services Agriculture 1 Aggregate Percentage change 0.5 0 -0.5 -1 -1.5 -2 -2.5 2020 2025 2030 2035 Year Figure C.3: Paths of cumulative percentage change since 2019 in real output for manu- facturing, services, agriculture, and on aggregate. 41 Welfare loss across countries 1 0.9 0.8 Welfare loss from trade shock, in % 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 BRD TUN H T JP N FRR ESR SWX SVR N AUA L KO A D P TW T D L BET LTD BG E ESK GW R C C U G N SA A R S R R C N SVP PRE PON U N N L CU S EU MN AUK IR E IT Z Y IN ID H U B N U L R O FI A o C Country Figure C.4: Welfare loss from the trade shock across countries, in percent. For country abbreviation codes see appendix B.1. 42 Service employment change between 2019 and 2022 0 -1 Change between 2019 and 2022, in % -2 -3 -4 -5 -6 -7 -8 SWD C N LT T C N R EX D R C R BRN H L FRA BG K ES L G E N T TWD TU T P M A R C U oW R N SV P N D R S SA A N G E SV L U N K EU R S AN IR PO BE PR AU IT Z ES Y AU IN ID U N B U KO H L R O FI JP C U Country Figure C.5: Percentage change in service employment between 2019 and 2022 across countries, in percent. For country abbreviation codes see appendix B.1. 43 Agricultural employment change between 2019 and 2022 4 2 Change between 2019 and 2022, in % 0 -2 -4 -6 -8 -10 -12 N D N T D R BRN EX N D R BR BG L KO A C D R K R E C A L M P SW T TW T C U oW G N A SV S N TU P R C A U E N U SV L G N H K AN S EU IR PO ES BE AU PR IT Z FR ES AU Y S ID IN N U U H L R O FI LT JP C R Country Figure C.6: Percentage change agricultural employment between 2019 and 2022 across countries, in percent. For country abbreviation codes see appendix B.1. 44