Globalization, Trade Imbalances and Labor Market Adjustment

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 1310 February 2021 Globalization, Trade Imbalances and Labor Market Adjustment Rafael Dix-Carneiro, Joao Paulo Pessoa, Ricardo Reyes-Heroles, Sharon Traiberman Please cite this paper as: Dix-Carneiro,Rafael,JoaoPauloPessoa,RicardoReyes-Heroles,SharonTraiberman(2021). “Globalization, Trade Imbalances and Labor Market Adjustment,” International Finance Discussion Papers 1310. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/IFDP.2021.1310. 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.

GLOBALIZATION, TRADE IMBALANCES AND LABOR * MARKET ADJUSTMENT Rafael Dix-Carneiro, Duke University and NBER Joa˜o Paulo Pessoa, Sa˜o Paulo School of Economics Ricardo Reyes-Heroles, Federal Reserve Board Sharon Traiberman, New York University February 2, 2021 Abstract We study the role of global trade imbalances in shaping the adjustment dynamics in response to trade shocks. We build and estimate a general equilibrium, multi-country, multi-sector model of trade with two key ingredients: (a) Consumption-saving decisions in each country commanded by representative households, leading to endogenous trade imbalances; (b) labor market frictions across and within sectors, leading to unemployment dynamics and sluggish transitions to shocks. We use the estimated model to study the behavior of labor markets in response to globalization shocks, including shocks to technology, trade costs, and inter-temporal preferences (savings gluts). We find that modeling trade imbalances changes both qualitatively and quantitatively the short- and long-run implications of globalization shocks for labor reallocation and unemployment dynamics. In a series of empirical applications, we study the labor market effects of shocks accrued to the global economy, their implications for the gains from trade, and we revisit the “China Shock” through the lens of our model. We show that the US enjoys a 2.2% gain in response to globalization shocks. These gains would have been 73% larger in the absence of the global savings glut, but they would have been 40% smaller in a balanced-trade world. JEL Codes: F1, F16 Keywords: Globalization, labor markets, trade imbalances *Dix-Carneiro: rafael.dix.carneiro@duke.edu; Pessoa: joao.pessoa@fgv.br; Reyes-Heroles: ricardo.m.reyesheroles@frb.gov; Traiberman: sharon.traiberman@nyu.edu. We would like to thank seminar and conference participants for helpful feedback. Traiberman gratefully acknowledges support by Early Career Research Grant 18-156-15 from the W.E. Upjohn Institute for Employment Research. The views 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 any other person associated with the Federal Reserve System. 1

“One major contrast between most economic analyses of globalization’s impact and those of the broader public ... is the focus, or lack thereof, on trade imbalances. The public tends to see trade surpluses or deficits as determining winners and losers; the general equilibrium trade models that underlay the 1990s’ consensus gave no role to trade imbalances at all. The economists’ approach is almost certainly right for the long run ... Yet in the long run we are all dead, and rapid changes in trade balances can cause serious problems of adjustment ...” Paul Krugman, “Globalization: What Did We Miss?”1 1 Introduction A large body of evidence shows that globalization can lead to significant labor market disruption. For instance, Autor et al. (2013) show that American workers in regions facing steeper import competition from China are less likely to work in manufacturing and more likely to be unemployed.2 This work has generated considerable interest and research in understanding, modeling, and quantifying the adjustment process in response to globalization shocks.3 Yet, this literature has abstracted from modeling trade imbalances, and has been silent on how they could influence the labor market adjustment process. This gap is puzzling in light of the size and persistence of trade imbalances in the last three decades, coupled with an increased discomfort among American policy makers towards trade deficits. Indeed, there is a pervasive concern among many policy makers and the public that trade deficits are undesirable as they crowd out domestic production and are detrimental to jobs and workers.4 When trade is balanced, equilibrium forces ensure that a contraction of importcompeting sectors is met with a simultaneous expansion of export-oriented sectors. On the other hand, if globalization shocks induce countries to run trade imbalances, these shifts are no longer synchronized, affecting the dynamics of reallocation. Hence, the behavior of trade imbalances can influence the dynamics of job losses and gains, especially in the presence of unemployment and labor market frictions. In this paper, we study how endogenizing trade imbalances influences the labor market adjustment process in response to globalization. Does ignoring trade imbalances when we investigate the labor market consequences of trade shocks matter at all? How much insight do we lose in doing so? To address these questions, we build on existing models of globalization and labor market adjustment and develop an estimable, general equilibrium, multi-country, multi-sector model with three 1See Krugman (2019). 2OtherrecentpaperstyingglobalizationshockstolabormarketdisruptionsincludeDix-CarneiroandKovak(2017, 2019), Pierce and Schott (2016), Costa et al. (2016), Dauth et al. (2018), Utar (2018), among many others. 3See Artu¸c et al. (2010), Dix-Carneiro (2014), Traiberman (2019), and Caliendo et al. (2019). 4For examples of recent policy discussions, see Scott (1998), Bernanke (2005), and Navarro (2019). 2

keyingredients: (i)Consumption-savingdecisionsineachcountryaredeterminedbytheoptimizing behavior of representative households, leading to endogenous trade imbalances; (ii) Labor market frictions across and within sectors lead to unemployment dynamics, and sluggish transitions to shocks; and (iii) Ricardian comparative advantage forces promote trade but geographical barriers inhibit it. In our model, trade imbalances arise from country-level representative households making consumption and savings decisions.5 These decisions give rise to an Euler Equation that dictates how countries smooth consumption over time in response to shocks in productivity, trade costs, and inter-temporal preferences. Our approach relies neither on ad hoc rules for imbalances nor on specifying the path of imbalances exogenously, which are common in the international trade literature. Instead, our perspective builds on the workhorse model of imbalances in international macroeconomics, providing a natural benchmark for understanding how they shape the labor market adjustment process.6 Turning to production and the labor market, workers in each country are organized into the representative households. They choose in which sector to work, taking into account how their choices affect the household’s maximizing problem. Similarly, firms choose in which sector to produce, maximizing expected discounted profits. Together, a firm and worker produce tradable intermediate varieties that are aggregated into sector-level outputs used as inputs into production, or for consumption. Goods markets are perfectly competitive, but international trade is subject to trade costs. Labor markets feature two sources of frictions: (i) switching costs to moving across sectors `a la Artu¸c et al. (2010); and (ii) matching frictions within sectors `a la Mortensen and Pissarides (1994). In particular, our framework allows for job creation and destruction to respond to trade shocks, leading to rich unemployment dynamics and speaking to a key concern of the public’s anxiety over globalization.7 We estimate our model using a simulated method of moments and data from the World Input Output Database and the United States Current Population Survey. To ensure tractability of the estimation procedure, we assume the economy is in steady state and we match data moments in year 2000. The procedure conditions on the observed trade shares and allows us to estimate our parameters country by country, greatly simplifying the process. To understand the main mechanisms in our model, we first compare its response to different sets of shocks to the response of the same model under balanced trade—an assumption that most of the trade literature makes.8 We find that modeling imbalances can lead to significantly larger 5See Obstfeld and Rogoff (1995) for a survey of this approach to imbalances in international macroeconomics. 6More recent work on global imbalances builds on the standard consumption savings model by adding financial frictions (e.g., Caballero et al. (2008) and Mendoza et al. (2009)), or demographics (e.g., Barany et al. (2018)). 7Pavcnik (2017) reviews survey data showing that only 20% of Americans believe trade creates jobs, while 50% believe it destroys them. 8Specifically, under balanced trade, we impose that aggregate expenditure equals aggregate revenues for each 3

unemployment and reallocation responses to globalization shocks. To be specific, consider a hypothetical positive temporary shock to Chinese productivity. In this case, consumption smoothing leads to opposing patterns of reallocation in both the short and long run. In the short run, China saves by lending to the rest of the world, and running a trade surplus. To do so, China expands its tradable sectors while other countries contract theirs, instead expanding in nontradables. In the long run, other countries pay off their debt to China, permanently expanding their tradable sectors above their initial steady-state levels. In contrast, in a balanced-trade world, short-run reallocation is only dictated by changes in comparative advantage, while a temporary shock has no long-run effects. Because it takes time for workers to find jobs, and it takes time for firms to find workers, a magnification of reallocation induces a larger response in unemployment. Importantly, we find no systematic relationship between the response of unemployment and the sign of trade imbalances. When balanced trade is imposed, long-run allocations depend only on the final level of the shocks. On the other hand, we find that the full path of shocks matters for long-run allocations when trade imbalances are modeled. This dependence on the full path of shocks motivates us to conduct an empirical analysis where we extract the various technology, trade cost, and intertemporal preference shocks that the global economy faced between 2000 and 2014. We use the extracted shocks to answer three counterfactual questions. First, we show that the differences in predictions between our model relative to a world of balanced trade are quantitatively important in response to our extracted shocks. In our second counterfactual exercise, we study the implications of trade imbalances and labor marketfrictionsforthegainsfromtrade, typicallycomputedusingthesufficient-statisticsapproach of Arkolakis et al. (2012) and extended by Costinot and Rodr´ıguez-Clare (2014). Differences in the predicted consumption effects of trade are significant, both qualitatively and quantitatively. We show that imbalances and labor market frictions both play important roles in explaining the discrepancies. Relatedly, we compute the globalization gains accrued to each country between 2000 and 2014, and compare them to those obtained in a world without the global savings glut, or in a world with balanced trade. We show that the US enjoys a 2.2% gain in response to globalization shocks accrued to the world between 2000 and 2014. These gains would have been 73% larger in the absence of the global savings glut, but would have been 40% smaller if we had lived in a balanced-trade world. Finally, we use our model to revisit the “China shock,” which consists of: (i) the rapid increase inChinesemanufacturingproductivitysince2000; (ii)changesintradecostsoverthesametimeperiod; (iii) China’s large national savings rate (the “savings glut”).9 Aligned with previous findings, we corroborate that China contributed to the decline of the United States manufacturing sectors country in every time period. 9See Autor et al. (2016) and references therein for more discussion of the China shock. 4

between 2000 and 2014. However, this decline in manufacturing was quickly accompanied by job creation in Services and Agriculture, leading to small unemployment effects. We find that shocks to the Chinese economy had a modest effect on the US trade deficit, highlighting that the evolution of the US trade deficit is a result of the full constellation of shocks hitting the global economy. On the other hand, if we feed the model with all empirically-extracted shocks but neutralize the Chinese savings glut (China’s inter-temporal preference shocks), the trade deficit in the US would have shrunk in the short run, but would have been amplified in the long run. This amplification results in an even larger long-run contraction in manufacturing. Our paper speaks to a large literature that investigates the labor market consequences of globalization, both empirically and quantitatively. We make two contributions to this literature by incorporating both involuntary unemployment and trade imbalances into the state-of-the-art Ricardian trade model of Caliendo and Parro (2015). Broadly speaking, quantitative trade models based on Eaton and Kortum (2002) have only allowed for a non-employment option (i.e., voluntary unemployment) or have focused on steady-state analyses, ignoring transitional dynamics. Caliendo et al. (2019) is an important example of a dynamic quantitative trade model in which workers make a labor supply decision and face mobility frictions across sectors and regions. However, their model does not feature job losses and unemployment. On the other end, Carr`ere et al. (2020) and Guner et al. (2020) incorporate search frictions and unemployment into multi-sector extensions of Eaton and Kortum (2002), but do not study out-of-steady-state dynamics. In a recent exception, Rodriguez-Clare et al. (2020) incorporates wage rigidity into the model of Caliendo et al. (2019) to investigate the unemployment effects of the China Shock on local labor markets in the United States.10 Importantly, though, none of these papers model trade imbalances. We do so by incorporating the workhorse model of imbalances used in the international macroeconomics literature allowing for savings decisions by means of an international bonds market as in Reyes-Heroles (2016).11 In that regard, our paper is closely related to Kehoe et al. (2018) who explore the implications of the increase in the United States trade deficit for the secular decline in manufacturing labor over the last four decades. However, this paper does not incorporate sluggish labor market adjustment nor unemployment dynamics.12 10InadditiontothesepapersbasedontheEatonandKortummodel,HelpmanandItskhoki(2010)addlabormarket frictionstoatwo-countryMelitzmodel,andHeidandLarch(2016)addlabormarketfrictionstoanArmingtonmodel of trade. Co¸sar et al. (2016) incorporate search frictions and unemployment to an estimable small open economy Melitzmodelwithfirmdynamics,butfocusonsteady-stateanalyses. Ruggieri(2019)extendsthatmodeltostudythe transitioninresponsetotradeshocks. Similarly,HelpmanandItskhoki(2015)alsoanalyzethedynamicbehaviorofa two-countryMelitzmodelwithlabormarketfrictions. Finally,Kambourov(2009),Artuc¸etal.(2010),Dix-Carneiro (2014),andTraiberman(2019)alsostudytransitionaldynamics,butfromthelensesofsmallopeneconomymodels. 11A few papers have analyzed the consequences of current account rebalancing on labor reallocation and unemployment by considering changes in imbalances as exogenous, e.g. Obstfeld and Rogoff (2005), Dekle et al. (2007), and Eaton et al. (2013). 12In International Macroeconomics, Kehoe and Ruhl (2009), Meza and Urrutia (2011), and Ju et al. (2014) are 5

The rest of this paper is structured as follows. Section 2 outlines our model. Section 3 describes the data we use and our estimation procedure. In Section 4 we present our estimates and model fit analysis, but we also interpret the key mechanisms of the model by simulating a series of impulse response functions. Section 5 conducts a series of empirical applications of our model. We conclude and discuss future research in Section 6. 2 Model Ourmodelbuildsonexistingworkhorsemodelsofglobalization, tradeimbalancesandlabormarket adjustment. Trade imbalances are modeled according to the inter-temporal approach of Obstfeld and Rogoff (1995), and the trade bloc is based on Caliendo and Parro (2015). We adopt the framework in Artuc¸ et al. (2010) to model labor mobility frictions across sectors and the structure in Mortensen and Pissarides (1994) to model search frictions and job creation and destruction. Sections 2.1 through 2.9 formalize our model showing how these different frameworks fit together. 2.1 Environment There is no aggregate uncertainty, so that all agents have perfect foresight of aggregate variables. There are i = 1,...,N countries. Each country i has a constant labor force given by L worki ers/consumers. There are k = 1,...,K sectors. Each sector k is characterized by a continuum set of varieties j ∈ [0,1] that can be traded across countries. These varieties are then aggregated by perfectly competitive domestic firms, in each country, into non-tradable composite sector-specific intermediate goods according to: QI,t = (cid:18)(cid:90) 1 (cid:0) Qt (j) (cid:1)ε dj (cid:19)1 ε , (1) k,i k,i 0 where Qt (j) is the quantity employed of variety j in sector k and country i at time t, and σ = 1 k,i 1−ε istheelasticityofsubstitutionacrossvarietieswithinsectors. Thesecompositesector-specificgoods are solely used as intermediate inputs for the production of a final good or for the production of varieties. The price of one unit of the composite good of sector k in country i is given by the price index associated with (1), which we denote by PI,t. k,i A non-tradable final good is produced by perfectly competitive firms that aggregate sectorspecific composite goods QI,t according to: k,i K QF,t = (cid:89)(cid:16) QI,t (cid:17)µ k,i , (2) i k,i k=1 examples of the scarce work studying the interaction between the current account and labor market reallocation. 6

K (cid:80) where µ > 0 and µ = 1 ∀i. The price of one unit of the final good is given by the price k,i k,i k=1 index associated with (2), which we denote by PF,t. i 2.2 Labor Markets Workers and single-worker firms producing varieties engage in a costly search process. Firms post vacancies, butnotallofthemarefilled. Workerssearchforajob, butnotallofthemaresuccessful, leading to involuntary unemployment. Each variety j constitutes a different labor market. More precisely, the unemployment rate ut (j) is variety-specific, as is the vacancy rate vt (j). Both k,i k,i variables are expressed as a fraction of the labor force Lt (j), measured as the sum of workers k,i who are employed or unemployed and searching within sector k and variety j at time t. We impose (cid:16) (cid:17) that m ut (j),vt (j) matches are formed (as a fraction of the labor force Lt (j)), where the i k,i k,i k,i matching function m is increasing in both arguments, concave, and homogeneous of degree 1. i From now on, we drop the index j, but the reader should keep in mind that all labor market variables are country-sector-variety specific. Define labor market tightness as: vt θt ≡ k,i . (3) k,i ut k,i The fact that m has constant returns to scale allows us to write the probability that a vacancy i matches with a worker as q (θt ), for a decreasing function q , and the probability that an unemi k,i i ployed worker matches with a vacancy as θt q (θt ). We assume that workers can costlessly move k,i i k,i across varieties j within a sector, but that they face mobility costs across sectors, as we describe in the next section. 2.3 Households Countries are organized into representative families, each with a household head that, taking prices as given, determines consumption, savings, and the allocation of workers across sectors maximizing aggregate utility. We first describe the utility of individual workers, then we show how household headsaggregatemembers’utilities. Foreaseofnotation, wetemporarilyomitthecountrysubscript i and let (cid:96) index individuals. If a worker ended period t−1 unemployed in sector k she can either search in sector k at time t (at no additional cost) or incur a moving cost C and search in sector k(cid:48) at time t—so that kk(cid:48) C = 0. If a worker (cid:96) is not employed at the production stage at t, she receives preference shocks kk (cid:110) (cid:111) ωt ,k = 1,...,K for each sector at time t. After unemployed workers receive these shocks, the k,(cid:96) household head decides whether to keep each worker in the same sector and restrict him to search there at t, or to incur a mobility cost and allow him to search in another sector. The ωt shocks k,(cid:96) 7

are iid across individuals, sectors and time, and are assumed to follow a Gumbel distribution with parameters (cid:0) −γEMζ,ζ (cid:1) where γEM is the Euler-Mascheroni constant and ζ its shape parameter. This structure follows closely Artu¸c et al. (2010). After being allocated to search in sector k(cid:48) at t the unemployed worker receives unemployment utility b and matches with a firm with probability θt q(θt ). We follow Mortensen and Pissarides k(cid:48) k(cid:48) k(cid:48) (1994) and assume that once a worker and a firm match at t, a match-specific productivity for t + 1 production, xt+1, is randomly drawn from a distribution G with [0,∞) support. This (cid:96) k,i productivity is constant over time from then on. At this point, the household head or the firm can break a match if keeping it active is not optimal. Finally, at the end of every period, and following the matching process, there is an exogenous probability χ of existing matches to dissolve k (excluding new ones). Successful matches that occur at time t only start to produce at t+1, and workers employed in sector k are then paid wages denoted by wt+1(cid:0) xt+1(cid:1) . Finally, if a worker k (cid:96) produces in sector k, she receives a non-pecuniary benefit of η . Figure 1 details the timing of the k model. Section 2.5 describes the bargaining process that occurs at t and section 2.4.2 describes a the decision of firms to post vacancies at time t . c Figure 1: Timing of the Model Firms and workers Workers: consume Exogenous job bargain over wages t b Firms: post vacancies t d destruction w/ prob. χ k t−1 t a Matched Workers: Produce t c New matches t e t+1 Unemployed: learn shocks ω, occur and xt+1 ∼G (cid:96) k choose sector where to search revealed Given this setup, the period utility for individual (cid:96) at time t is, (cid:16) (cid:17) Ut(cid:0) et,kt+1,kt,ωt,ct(cid:1) = (cid:0) 1−et(cid:1) −C +b +ωt +etη +u (cid:0) ct(cid:1) , (4) (cid:96) (cid:96) (cid:96) (cid:96) (cid:96) (cid:96) (cid:96) k (cid:96) t,k (cid:96) t+1 k (cid:96) t+1 k (cid:96) t+1,(cid:96) (cid:96) k (cid:96) t (cid:96) where kt is the sector where individual (cid:96) starts period t (that sector was determined at t − 1), (cid:96) kt+1 is the t + 1 sector of choice (which is decided at time t, interim period t in Figure 1), (cid:96) b (cid:16) (cid:17) et is the employment status at the production stage (interim period t ), ωt = ωt ,...,ωt are (cid:96) b (cid:96) 1,(cid:96) K,(cid:96) idiosyncraticutilityshocksreceivedbyunemployedworkersatinterimperiodt ,andct isindividual b (cid:96) consumption. If individual (cid:96) is unemployed in sector k at t (et = 0,kt = k), the individual can (cid:96) (cid:96) switch sectors (from k to kt+1), so that mobility costs C , utility of unemployment b and (cid:96) kt,kt+1 kt+1 (cid:96) (cid:96) (cid:96) shock ωt are incurred (during period t). On the other hand, if individual (cid:96) is employed during kt+1,(cid:96) (cid:96) the production stage at t, et = 1, the worker enjoys the non-pecuniary benefit of working in sector (cid:96) kt given by η . Finally, individual (cid:96) also enjoys the utility of consumption u (cid:0) ct(cid:1) . (cid:96) kt (cid:96) (cid:96) From the perspective of the household head, the allocation of workers follows a controlled stochastic process: while the head can choose workers’ sectors given knowledge of switching costs 8

and shocks, employment itself remains a probabilistic outcome. To this end, let et (cid:0) xt+1(cid:1) ∈ {0,1} (cid:101)k (cid:96) indicatewhetherthehouseholdheadcontinuesonwithamatchattimetgivenamatchproductivity of xt+1 in sector k. Then, the probability that worker (cid:96) is employed in sector k at time t + 1, (cid:96) conditional on match productivity xt+1 and time t information (cid:0) kt,et(cid:1) is given by: (cid:96) (cid:96) (cid:96) Pr (cid:0) kt+1 = k,et+1 = 1|xt+1,kt,et(cid:1) = I (cid:0) kt = k (cid:1) et(1−χ )et (cid:0) xt+1(cid:1) (5) (cid:96) (cid:96) (cid:96) (cid:96) (cid:96) (cid:96) (cid:96) k (cid:101)k (cid:96) + (cid:0) 1−et(cid:1) I (cid:0) kt+1 = k (cid:1) θtq (cid:0) θt(cid:1) et (cid:0) xt+1(cid:1) . (cid:96) (cid:96) k k (cid:101)k (cid:96) In words, if I (cid:0) kt = k (cid:1) et = 1, then worker (cid:96) is employed in sector k at time t and the match (cid:96) (cid:96) survives with probability (1−χ ) if the family planner decides to keep the match (et (cid:0) xt+1(cid:1) = 1). k (cid:101)k (cid:96) If et = 0, that is, the worker is unemployed at t, and the planner chooses kt+1 = k, then the worker (cid:96) (cid:96) is employed in sector k at time t + 1 with probability θtq (cid:0) θt(cid:1) et (cid:0) xt+1(cid:1) . Importantly, workers’ k k (cid:101)k (cid:96) sector and employment status at t+1, kt+1 and et+1, are determined by actions taken at t. (cid:96) (cid:96) The head of the household aggregates (4) over family members and maximizes the net present value of utility subject to her budget constraint and the controlled process on employment (5). In addition to consumption and employment decisions, the household head has access to international financial markets by means of buying and selling one-period riskless bonds that are available in zero net supply around the world. One can think of international bond markets in period t as spot markets in which a family buys a piece of paper with face value of Bt+1 in exchange for a bundle of goods with the same value, and the piece of paper represents a promise to receive goods in period t + 1 with a value equal to Rt+1Bt+1. International bond markets operate without frictions, so that the nominal returns Rt+1 are equalized across countries. Finally, the household collects and aggregates profits across all firms, Πt, but takes this lump-sum payment as given. The household head chooses the path of consumption, ct, the path of sectoral choices, kt, continuation decisions, (cid:96) (cid:96) et(x), and bonds, Bt, to solve: (cid:101)k (cid:40) ∞ (cid:90) L (cid:41) (cid:88) max E (δ)tφt Utd(cid:96) , (6) 0 (cid:96) {k (cid:96) t , ,e (cid:101) t k (.),Bt,ct (cid:96) } t=0 0 subject to (5) and the budget constraint: (cid:90) L (cid:90) L (cid:32) K (cid:33) PF,t ctd(cid:96)+Bt+1−Πt−RtBt− (cid:88) I (cid:0) kt = k (cid:1) etwt (cid:0) xt(cid:1) d(cid:96) ≤ 0. (7) (cid:96) (cid:96) (cid:96) k (cid:96) 0 0 k=1 E denotes expectations with respect to future idiosyncratic shocks ω. The model has no aggregate 0 uncertainty, so that households and firms have perfect foresight of aggregate variables. δ is the discount factor, common across all countries, and φt is an inter-temporal preference shifter that 9

the household head experiences in period t.13 These shifters can differ across countries. The budget constraint states the family can buy consumption goods or bonds for next period using profits and wage income, net of interest payments (or collections) on past bonds. Let λ(cid:101) t be the Lagrange multiplier on the family’s budget constraint (7).14 The optimality condition with respect to ct is u(cid:48)(cid:0) ct(cid:1) = λ(cid:101) tPF,t, so that individual consumption is equalized across individuals within the (cid:96) (cid:96) household: ct = ct ∀(cid:96). Henceforth, we will refer to ct as per capita consumption. Armed with this (cid:96) observation, Online Appendix A shows that the labor supply decisions solving (6) subject to (7) and (5) can be decentralized and written recursively for unemployed and employed workers. We now turn to this recursive formulation. Let us return to indexing countries by i. Since workers are symmetric up to x and η in each country, we stop indexing individual workers. We denote by U(cid:101) t (ωt) the value of unemployment k,i in sector k, country i at time t conditional on shocks ωt, and by Wt (x) the value of employment k,i conditional on match-specific productivity x. If we define φ(cid:98) t+1 ≡ φt i +1 , the sector decision policy i φt i and the continuation rule et (.) must solve, conditional on shocks ωt: (cid:101)k   −C +ωt +b kk(cid:48),i k(cid:48) k(cid:48),i U(cid:101) k t ,i (ωt) = max    +θ k t (cid:48),i q (cid:16) θ k t (cid:48),i (cid:17) δφ(cid:98) t i +1(cid:82) 0 ∞ max (cid:110) W k t+ (cid:48),i 1(x),U k t+ (cid:48),i 1 (cid:111) dG k(cid:48),i (x)    , (8) k(cid:48)  (cid:16) (cid:16) (cid:17)(cid:17)  + 1−θt q θt δφ(cid:98) t+1Ut+1, k(cid:48),i k(cid:48),i i k(cid:48),i and (cid:110) (cid:111) W k t ,i (x) = λ(cid:101) t i w k t ,i (x)+η k,i +δφ(cid:98) t i +1(1−χ k,i )max W k t+ ,i 1(x),U k t+ ,i 1 +δφ(cid:98) t i +1χ k,i U k t+ ,i 1. (9) (cid:16) (cid:17) In equation (8), U k t ,i ≡ E ω U(cid:101) k t ,i (ωt) is the expected value of U(cid:101) k t ,i (ωt), integrated over ωt. The first line in this equation corresponds to the costs of switching sectors, −C +ωt , as well as kk(cid:48),i k(cid:48),i the sector-specific value of being unemployed in that sector b . The second line is the probability k(cid:48)i (cid:16) (cid:17) of finding a match θt q θt multiplied by the discounted value of the match. Note that for k(cid:48),i k(cid:48),i low values of Wt+1(x), the household head dissolves the match so that the worker obtains Ut+1. k(cid:48),i k(cid:48),i Finally, the third line is the discounted value of being unemployed next period if the worker fails to successfully match. In equation (9), wt (x) is the wage paid by a firm with match productivity x. Note that it is k,i 13As will become clear later, inter-temporal preference shocks are going to be important for our model to match the time-series behavior of final expenditures across countries in the data. The use of these shifters is common in theinternationalmacroeconomicsliterature. SeeStockmanandTesar(1995)orBaiandR´ıos-Rull(2015). However, as discussed in the introduction, the fact that these shifters lead to wedges in Euler equations implies that they can also be viewed as generated by frictions underlying asset markets that directly affect households’ aggregate saving decisions. 14In an abuse of terminology we will continue to refer to λ(cid:101)t as the Lagrange multiplier. However, the correct shadow price associated with period’s t budget constraint is given by δtφtλ(cid:101)t. 10

multipliedbythehouseholdhead’sLagrangemultiplieronthebudgetconstraintλ(cid:101) t. Todecentralize i the household’s problem, individual workers must take into account the effect of their labor supply decisions on the whole family’s utility. The second term is the non-pecuniary benefit of working in sector k in country i. The next terms are the continuation values: with probability (1−χ ) k,i the match does not exogenously dissolve and the worker continues the match; with probability χ k,i the match exogenously breaks and the worker receives the value of unemployment in k. Since ω is Gumbel distributed, the policy rule for unemployed workers can be solved analytically, so that transition rates between t and t+1 can be written as:  1/ζi  −C kk(cid:48),i +b k(cid:48),i +  exp (cid:110) (cid:111)  θ k t (cid:48),i q(θ k t (cid:48),i )δφ(cid:98) t i +1(cid:82) 0 ∞ max W k t+ (cid:48),i 1(x)−U k t+ (cid:48),i 1,0 dG k(cid:48),i (x)+δφ(cid:98) t i +1U k t+ (cid:48),i 1  st,t+1 = . (10) kk(cid:48),i  1/ζi (cid:80) K  −C kk(cid:48)(cid:48),i +b k(cid:48)(cid:48),i +  exp (cid:110) (cid:111) k(cid:48)(cid:48)=1  θ k t (cid:48)(cid:48),i q(θ k t (cid:48)(cid:48),i )δφ(cid:98) t i +1(cid:82) 0 ∞ max W k t+ (cid:48)(cid:48), 1 i (x)−U k t+ (cid:48)(cid:48), 1 i ,0 dG k(cid:48)(cid:48),i (x)+δφ(cid:98) t i +1U k t+ (cid:48)(cid:48), 1 i  2.4 Firms 2.4.1 Incumbents Firms produce by combining the labor of one single worker with composite intermediate inputs purchased from all sectors. All firms producing variety j in sector k and country i have access to common productivity zt (j) and are paid pt (j) for each unit of production. A firm producing k,i k,i variety j in sector k with match-specific productivity x and employing composite intermediate (cid:110) (cid:111)K inputs Mt obtains revenue: (cid:96),i (cid:96)=1 (cid:32) K (cid:33)(1−γ k,i ) Yt (j,x) = pt (j)zt (j)xγ k,i (cid:89)(cid:0) Mt (cid:1)ν k(cid:96),i , (11) k,i k,i k,i (cid:96),i (cid:96)=1 K (cid:80) where γ ∈ (0,1), ν > 0, and ν = 1 k,i k(cid:96),i k(cid:96),i (cid:96)=1 Firms are price takers in product and intermediate-input markets and decide on the usage of (cid:110) (cid:111)K Mt solving: (cid:96),i (cid:96)=1 (cid:32) K (cid:33)(1−γ k,i ) K St (j,x) = max pt (j)zt (j)xγ k,i (cid:89)(cid:0) Mt (cid:1)ν k(cid:96),i − (cid:88) PI,tMt , (12) k,i k,i k,i (cid:96),i (cid:96),i (cid:96),i {Mt } (cid:96),i (cid:96)=1 (cid:96)=1 where St (j,x) denotes the revenue (net of intermediate input payments) generated by the match k,i between a firm and a worker with productivity x producing variety j. One can show that: St (j,x) = wt (j)x, (13) k,i (cid:101)k,i 11

where w (cid:101)k t ,i (j) ≡ γ k,i (1−γ k,i ) 1− γk γ , k i ,i (cid:16) P k M ,i ,t (cid:17) γk γ , k i , − i 1 (cid:0) pt k,i (j)z k t ,i (j) (cid:1) γk 1 ,i , (14) K (cid:32) PI,t(cid:33)ν k(cid:96),i and PM,t ≡ (cid:89) (cid:96),i (15) k,i ν k(cid:96),i (cid:96)=1 K is the price of one unit of the intermediate input composite imt ≡ (cid:89)(cid:16) Mt (cid:17)ν k(cid:96),i in sector k and k,i (cid:96),i (cid:96)=1 country i. We assume that following entry, switching across varieties within sector is costless for firms. Hence, no arbitrage across varieties will ensure that wt (j) = wt (j(cid:48)) and pt (j)zt (j) = (cid:101)k,i (cid:101)k,i k,i k,i pt (j(cid:48))zt (j(cid:48)) ∀j,j(cid:48). Therefore, wt and pt zt do not depend on the specific variety. This implies k,i k,i (cid:101)k,i k,i k,i symmetry across varieties, allowing us to drop the index j identifying individual varieties.15 Given (cid:110) (cid:111) the expression of the surplus (13), we will henceforth refer to wt as “sectoral surpluses”. As (cid:101)k,i will become clearer in Section 2.7 these sectoral surpluses will play the same role as wages do in Caliendo and Parro (2015). We can write the value function for incumbent firms, Jt (x), as: k,i (cid:110) (cid:111) J k t ,i (x) = λ(cid:101) t i (cid:0) w (cid:101)k t ,i x−w k t ,i (x) (cid:1) +(1−χ k,i )δφ(cid:98) t i +1max J k t+ ,i 1(x),0 . (16) The first term is the firm’s current profit, and the second is the firm’s continuation value of the match.16 If Jt (x) < 0 the firm does not produce and exits. k,i 2.4.2 New Entrants Potential entrants can match with a worker by posting vacancies in k (and variety j). We assume that posting a vacancy costs κ units of the final good, and so amounts to total cost κ PF,t. k,i k,i i Vacancies are posted at the interim period t as illustrated in Figure 1. As argued above, Jt (x) is c k,i not variety specific, which means the variety distinction can also be ignored for new entrants. If a firm successfully matches with a worker at t, production starts at t+1. If we denote the expected value of an open vacancy by Vt , then: k,i  (cid:16) (cid:17) (cid:110) (cid:111)  q θt (cid:82)∞ max Jt+1(s),0 dG (s) V k t ,i = −λ(cid:101) t i κ k,i P i F,t+δφ(cid:98) t i +1  i + k, (cid:16) i 1− 0 q (cid:16) θt (cid:17)(cid:17) k, m i ax (cid:110) Vt+1,0 k (cid:111) ,i . (17) i k,i k,i 15Remember that we assume that workers face no mobility frictions across varieties within sectors. 16Firm profits are multiplied by the multiplier on the family’s budget constraint in order to keep the units, utils, consistent between the firm’s and worker’s problem. However, if one divides J k t ,i (x) by λ(cid:101)t i , then from the Euler Equationwederivebelow,itisclearthatthisformulationisequivalenttoariskneutralfirmdiscountingprofitsusing the nominal interest rate Rt+1. 12

The first term on the right hand side is the cost of posting vacancies, which is converted to utility units by the Lagrange multiplier λ(cid:101) t. The second term says that in the next period entrants match i (cid:16) (cid:17) (cid:110) (cid:111) with probability q θt and obtain the expected value of max Jt+1,0 starting in the next i k,i k,i period. If they do not match, they can post another vacancy. To close the model, we impose free entry so that Vt ≤ 0 ∀k,i,t.17 k,i 2.5 Wages The surplus of a match between a worker and a firm is defined as the utility generated by the match in excess of the parties’ outside options. Imposing the free entry condition (Vt = 0), the k,i outside option to the firm is 0, while to the worker it is Ut . Hence, the surplus of the match k,i is given by St (x) ≡ Jt (x) + Wt (x) − Ut . We assume that firms and workers engage in k,i k,i k,i k,i Nash bargaining over the surplus, with the workers’ bargaining weight given by β . This leads to k,i Jt (x) = β St (x), which combined with equations (9) and (16) imply that St , Wt , and Jt k,i k,i k,i k,i k,i k,i are increasing functions of x, implying that matches only remain active at t if x > xt where xt k,i k,i solves: St (cid:0) xt (cid:1) = Jt (cid:0) xt (cid:1) = Wt (cid:0) xt (cid:1) −Ut = 0. (18) k,i k,i k,i k,i k,i k,i k,i The wage equation resulting from Nash bargaing is: (cid:16) (cid:17) U k t ,i −δφ(cid:98) t i +1U k t+ ,i 1−η k,i wt (x) = β wt x+(1−β ) , (19) k,i k,i(cid:101)k,i k,i λ(cid:101)t i for x ≥ xt . This is similar to the standard wage equation in search models: the worker’s wage is k,i a weighted average of the surplus, and a function of their outside option. The only new term is the non-pecuniary benefit, which is subtracted from the outside option. By integrating wages across all individuals in the economy, one can solve for the family’s total wage income. 2.6 Labor Market Dynamics Since workers can switch sectors between periods t and t , the sector-specific unemployment rates a c actually differ at these two points in time within the same period. To this end, we first define the beginning of period sector-specific unemployment rate as ut−1, and labor force as Lt−1. After (cid:101)k,i k,i workers switch sectors, (measured before matching at t ), we define ut to be the share of sector-k d k,i 17Intheequilibriaweconsiderinthispaper,weverifythatthisconditionholdswithequality,bothinsteadystate and along transition paths. 13

workers searching for a job. It is given by: K (cid:80) Lt−1ut−1st,t+1 (cid:96),i (cid:101)(cid:96),i (cid:96)k,i ut = (cid:96)=1 , (20) k,i Lt k,i wherest,t+1 denotesthetransitionratefromunemploymentinsector(cid:96)tosearchinsectork between (cid:96)k,i t and t+1—see equation (10). Lt is the number of workers in sector k at t (more precisely at t ) k,i c and is equal to: Lt = Lt−1+ (cid:88) Lt−1ut−1st,t+1−Lt−1ut−1 (cid:16) 1−st,t+1 (cid:17) , (21) k,i k,i (cid:96),i (cid:101)(cid:96),i (cid:96)k,i k,i (cid:101)k,i kk,i (cid:96)(cid:54)=k (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) Outflow Inflow where the second term in the right hand side is the flow of workers into sector k and the third term is the flow of workers out of sector k. Only firms with x ≥ xt+1 produce at t+1. Therefore, the number of jobs created in sector k k,i is given by: (cid:16) (cid:16) (cid:17)(cid:17) JCt = Lt ut θt q (cid:0) θt (cid:1) 1−G xt+1 , (22) k,i k,i k,i k,i i k,i k,i k,i and the number of jobs destroyed is given by: (cid:16) (cid:16) (cid:17)(cid:17) (cid:16) (cid:17) JDt ≡ χ +(1−χ )Pr xt ≤ x < xt+1|xt ≤ x Lt−1 1−ut−1 k,i k,i k,i k,i k,i k,i k,i (cid:101)k,i   (cid:16) (cid:17) (cid:16) (cid:17)  G xt+1 −G xt  k,i k,i k,i k,i  (cid:16) (cid:17) = χ k,i +(1−χ k,i )max (cid:16) (cid:17) ,0 Lt k − ,i 1 1−u (cid:101) t k − ,i 1 , (23)  1−G xt  k,i k,i (cid:16) (cid:17) where Pr xt ≤ x < xt+1|xt ≤ x is the share of active firms above the productivity threshold k,i k,i k,i at t but below at t+1 (endogenous exit). Consequently, the rate of unemployment at the end of period t, after job creation and job destruction, is given by: Lt ut −JCt +JDt ut = k,i k,i k,i k,i . (24) (cid:101)k,i Lt k,i Equations(20)-(24)describetheevolutionoflabormarketstocksovertime. Inanygivenperiod, these stocks are bound by the labor market clearing condition: K (cid:88) Lt = L . (25) k,i i k=1 14

2.7 International Trade Our model of international trade closely follows Caliendo and Parro (2015). Varieties are traded across countries. Under the assumptions of perfect competition and iceberg trade costs, the cost of variety j from sector k produced in o can be purchased in country i at a price pt (j)dt , where k,o k,oi the first term is the price of variety j in country o and the second term is the iceberg trade cost of shipping from country o to country i. From (14) we can write: ct pt (j) = k,i , (26) k,i zt (j) k,i for each variety j and where (cid:32) wt (cid:33)γ k,i (cid:32) PM,t (cid:33)1−γ k,i ct ≡ (cid:101)k,i k,i . (27) k,i γ 1−γ k,i k,i Recall that due to the no-arbitrage condition we impose across varieties, ct is equalized within k,i sectors, so that price variation across varieties is dictated by zt (j). k,i We assume that in any country i, sector k and period t, the productivity component zt (j) k,i is independently drawn from a Frechet distribution with scale parameter At —which is country, k,i sector, and time specific—and shape parameter, λ, which is time invariant.18 Consumers buy the lowest cost variety across countries, treating the same variety from different origins as perfect substitutes. Under these assumptions, it can be shown that the resulting price index for the composite sector-specific intermediate good (1) is given by:  −1/λ N At PI,t = Γ  (cid:88) k,o  , (28) k,i k,i (cid:16) (cid:17)λ o=1 ct dt k,o k,oi where Γ is a constant. In turn, the price of the final good (2) is given by: k,i K (cid:32) PI,t(cid:33)µ k,i PF,t = (cid:89) k,i . (29) i µ k,i k=1 If we define the object Φt ≡ (cid:80) N At k,o then consumers in country i spend a share πt of k,i o=1 (ct k,o dt k,oi )λ k,oi 18The CDF for the Frechet is given by Ft (z)=exp (cid:0) −At ×z−λ(cid:1) . k,i k,i 15

their sector-k expenditures on varieties from country o given by: (cid:16) (cid:17)−λ Et At ct dt πt ≡ k,oi = k,o k,o k,oi , (30) k,oi Et Φt k,i k,i where Et = (cid:80)N Et is the total expenditure of country i on sector k varieties and Et is the k,i o=1 k,oi k,oi total expenditure of country i on sector k varieties produced by country o. Market clearing requires that total revenue Yt coming from the production of varieties in sector k and country o must be k,o equal to sales to all countries i = 1,...,N, and so: N N (cid:88) (cid:88) Yt = Et = πt Et . (31) k,o k,oi k,oi k,i i=1 i=1 LetCt ≡ L ct denotetotalconsumptionofthefinalgood. DefineEC ≡ PF,tCt astotalexpenditure i i i it i i on final goods, and let EV,t be the total expenditure of sector k in country i on vacancy posting k,i costs. We can write Et as: k,i K K Et = µ EC,t+µ (cid:88) EV,t+ (cid:88) (1−γ )ν Yt . (32) k,i k,i i k,i (cid:96),i (cid:96),i (cid:96)k,i (cid:96),i (cid:96)=1 (cid:96)=1 The right hand side represents total expenditure on sector k goods used in final consumption, vacancy posting costs, and as intermediate inputs, respectively. In turn, let It denote total disposable i income in country i, which is given by the portion of revenue that is not devoted to intermediate K (cid:16) (cid:17) good payments minus vacancy posting costs, that is, It = (cid:80) γ Yt −EV,t . Net exports are i (cid:96),i (cid:96),i (cid:96),i (cid:96)=1 then given by NXt ≡ It−EC,t, and we can rewrite (32) as: i i i (cid:32) K (cid:33) K (cid:88) (cid:88) Et = µ γ Yt −NXt + (1−γ )ν Yt . (33) k,i k,i (cid:96),i (cid:96),i i (cid:96),i (cid:96)k,i (cid:96),i (cid:96)=1 (cid:96)=1 Finally, labor market clearing dictates that total revenues coming from the production of varieties in sector k and country i is given by: Yt = w (cid:101)k t ,i Lt−1 (cid:16) 1−ut−1 (cid:17)(cid:90) ∞ s dG (s). (34) k,i γ k,i k,i (cid:101)k,i xt 1−G (cid:16) xt (cid:17) k,i k,i k,i k,i 2.8 Trade Imbalances Note that equations (31), (33) and (34) can be solved for any given values of (cid:8) NXt(cid:9) , such that i (cid:80) NXt = 0. However, these are not necessarily consistent with the household’s optimal dynamic i i 16

behavior. To this end, we turn to the determination of net exports (cid:8) NXt(cid:9) in equilibrium. The i solution to the household head’s problem (6) must satisfy the following Euler equation: u(cid:48)(ct)/PF,t i i = δφ(cid:98) t+1Rt+1, (35) u(cid:48)(ct+1)/PF,t+1 i i i and financial and goods markets in each country are linked according to: NXt = It−PF,tCt = Bt+1−RtBt. (36) i i i i i i Finally, to close this part of the model, we impose that bonds are in zero net supply, (cid:80) Bt = 0, i i and that the initial distribution of bonds is given by (cid:8) B0(cid:9) . If the model is initially in steady state, i it is easy to verify that R0 = 1. δ Having described the dynamic problem of the household, we can now discuss long-term trade imbalances in our model. To do so, consider beginning from an initial steady state. Suppose that at time t = 1, the economy unexpectedly experiences a series of shocks that end in finite time, and that a new steady state is reached at time T.19 In this case, we arrive at the following equation for the final steady-state value of deficits:20 (cid:32) T−1 T−1(cid:32) T−1 (cid:33) (cid:33) 1−δ (cid:89) (cid:88) (cid:89) NXT = − B0× Rτ + Rτ NXt . (37) i δ i i τ=1 t=1 τ=t+1 This equation shows that the behavior of long run imbalances is determined by initial wealth allocations (cid:8) B0(cid:9) and the short-run behavior of net exports (cid:8) NXt(cid:9) . This second piece is key in our i i model: if a country runs a series of trade deficits (surpluses) in the short run, even if they begin with a zero bond position, they may run trade surpluses (deficits) in perpetuity. 2.9 Equilibrium An equilibrium in this model is a set of initial steady-state allocations {L0 ,x0 ,B0,}, a fik,i k,i i nal steady-state allocations {L∞,x∞,B∞,} and sequences of policy functions for workers/firms k,i k,i i {st ,xt ,wt (x)}, value functions for workers/firms {Ut ,Wt ,Jt }, labor market tightnesses kk(cid:48),i k,i k,i k,i k,i k,i {θt }, bond decisions by the households (cid:8) Bt(cid:9) , bond returns (cid:8) Rt(cid:9) , allocations {Lt ,ut ,ct }, k,i i k,i k,i k,i (cid:110) (cid:111) profits and household consumption {Πt,Ct}, trade shares πt , sectoral surpluses {wt }, and i i k,io (cid:101)k,i (cid:110) (cid:111) price indices PI,t,PF,t such that: k,i k,i 1. Worker and firms’ value functions solve (8), (9), and (16). 19In our model, because of labor market dynamics, the final steady state is only reached in the limit, but the approximation that the final steady state is reached in finite time is exactly the one used in computation. 20We also invoke a transversality condition that lim (cid:104) (cid:81)T Rs (cid:105)−1 BT →0 ∀i. T→∞ s=1 i 17

2. The free entry condition holds in each country and sector: Vt = 0 ∀k,i,t. k,i 3. The wage equation solves the Nash bargaining problem and is given by (19). 4. Allocations and unemployment rates evolve according to (20), (21), (24). 5. Consumption and bonds decisions solve the household’s dynamic consumption-savings problem (6) subject to (5) and (7). 6. Price indices are given by equations (28) and (29). 7. Goods markets clear: equations (30)-(32) are met. K 8. Labor markets clear: (cid:80) Lt = L . k,i i k=1 N 9. Bonds market clears: (cid:80) Bt = 0. i i=1 10. The initial and final steady-state equilibria satisfy equations (A.15)-(A.36) in Online Appendix B. 3 Data and Estimation Our main source of cross-country data is the World Input Output Database (WIOD), which compiles data from individual National Accounts combined with bilateral international trade data. These data cover 56 sectors and 44 countries, including a Rest of the World aggregate, between 2000 and 2014. We divide the economy into six sectors and six countries. We consider a world comprised by the United States, China, Europe, Asia/Oceania, the Americas and the Rest of the WorldaggregateconstructedbytheWIOD.Eachcountry’seconomicactivityconsistsofsixsectors: Agriculture; Low-, Mid- and High-Tech Manufacturing; Low- and High-Tech Services. Tables I and II detail these divisions. We solve our model at the quarterly frequency. TheWIODdatasetallowustogeneratevariousmomentsthatweuseinourprocedure(detailed below) to estimate a subset of the parameters: (a) employment shares across sectors and countries; (b) average wages across sectors and countries; (c) trade shares; (d) net exports. Other moments used in the estimation procedure are obtained from ILOSTAT and the United States Current Population Survey (CPS). From ILOSTAT, we extract country-specific unemployment rates. From the CPS, we compute yearly transition rates between sectors in the United States, as well as the dispersion of wages. Table III summarizes the statistics targeted in the estimation. Table IV summarizes the parameters we need to numerically solve the model. We split them into three categories: (i) parameters that are fixed at values previously reported in the literature 18

Table I: Country Definitions 1 USA 2 China 3 Europe 4 Asia/Oceania 5 Americas 6 Rest of the World (ROW) Notes: Asia/Oceania={Australia,Japan,South Korea, Taiwan}, Americas = {Brazil, Canada, Mexico}, Rest of the World ={Indonesia, India, Russia, Turkey, Rest of the World} Table II: Sector Definitions 1 Agriculture/Mining Agriculture, Forestry and Fishing; Mining and quarrying 2 Low-Tech Manufacturing Wood products; Paper, printing and publishing; Coke and refined petroleum; Basic and fabricated metals; Other manufacturing 3 Mid-Tech Manufacturing Food, beverage and tobacco; Textiles; Leather and footwear; Rubber and plastics; Non-metallic mineral products 4 High-Tech Manufacturing Chemical products; Machinery; Electrical and optical equipment; Transport equipment 5 Low Tech Services Utilities; Construction; Wholesale and retail trade; Transportation; Accommodation and food service activities; Activities of households as employers 6 Hi Tech Services Publishing; Media; Telecommunications; Financial, real estate and business services; Government, education, health Table III: Summary of Statistics Used in the MSM Procedure Statistic Source Employment allocations across sectors and countries WIOD Average wages across sectors and countries WIOD Trade shares across country pairs and sectors WIOD Net exports across countries WIOD Unemployment rates across countries ILOSTAT Coefficient of variation of log-wages in the United States CPS Yearly transition rates between sectors and from and to unemployment for the United States CPS 19

because they are difficult to identify given the available data (Panel A); (ii) parameters that can be determined without having to solve the model (Panel B); and (iii) parameters that are estimated by the method of simulated moments, where we target the moments shown in Table III.21 As discussed in Artuc¸ et al. (2010), we are not able to separately identify ζ —the dispersion i of ω shocks—and mobility costs C without time variation in wages and transition rates across k(cid:96),i sectors. Forthisreason,wefollowArtuc¸etal.(2010)andimposeζ ,tobeequalto1.63andcommon i across countries.22 We then estimate mobility costs following the method of simulated moments procedure we describe below. Given that we solve our model at the quarterly frequency, we impose thediscountfactortobeδ = 0.9924,leadingtoanannualdiscountfactorof0.97—thesamevalueas inArtu¸cetal.(2010). Flinn(2006)discussesthedifficultyinidentifyingtheparametersofmatching functions without relying on data on vacancies. We parameterize the matching function according to Co¸sar et al. (2016): q i (θ) = (cid:0) 1+θξi (cid:1)1/ξi and impose their estimate ξ i = 1.84 to be common across countries.23 Flinn (2006) also highlights the difficulty in estimating the bargaining power parameters without firm-level data. As a result, we follow standard practice in the search literature andsetβ = 0.5(MortensenandPissarides,1999). TheFrechetscaleparameterλ = 4comesfrom k,i SimonovskaandWaugh(2014).24 Finally, weassumeindividualshavelogutilityoverconsumption, u(c) = log(c). As described in Panel B, the WIOD dataset allows us to directly extract various parameters of the model such as country-specific final expenditure shares µ , labor expenditure k,i shares γ and input-output matrices ν ; this follows from the Cobb-Douglas assumptions we k,i k(cid:96),i imposed in the production functions and on how final consumption is aggregated. We estimate the parameters described in Panel C using the method of simulated moments. Let Θ = (Θ ,...,Θ ) be the vector of these country-specific parameters. Our estimation procedure 1 N assumes that the economy is in steady state in 2000 and conditions on the observed 2000 trade shares πData and net exports NXData—so these moments are perfectly matched. Online Appendix k,oi i B summarizes the equations that must be satisfied in a steady-state equilibrium. For a given guess of Θ, we use our equilibrium equations, conditional on πData and NXData, to generate: k,oi i (a) unemployment rates across countries; (b) employment allocations and average wages across sectors and countries; (c) yearly transition rates between sectors and from and to unemployment in the United States; and (d) cross-sectional wage dispersion in the United States. The estimation procedure searches for a vector of parameters Θ that minimizes the distance between the model 21Tobeprecise,wedonottargettradesharesandnetexports,weimposethemintheestimation,sothattheyare matched exactly. 22Estimates of ζ in the literature range from 0.7 in Denmark (Traiberman, 2019) to 2.1 in Brazil (Dix-Carneiro, i 2014). The value of 1.63 in Artuc¸ et al. (2010) is well within these bounds, making it a conservative choice. In addition,Traiberman(2019)estimatesζ =1.9inDenmarkwhenthemethodinArtu¸cetal.(2010)isapplied,which i disregards worker heterogeneity and human capital accumulation. 23One convenient property of this functional form is that it always leads to q (θ) and θq (θ) to be bounded by 0 i i and 1. 24Caliendo and Parro (2015) find a similar value for λ when it is imposed to be equal across sectors: 4.55. 20

Table IV: Summary of Parameters Panel A. Fixed According to the Literature Parameter Value Description Source δ 0.9924 Discount factor Artuc¸ et al. (2010) ζ 1.63 Dispersion of ω shocks Artu¸c et al. (2010) i ξ 1.84 Matching Function Co¸sar et al. (2016) i β 0.5 Worker Bargaining Power Mortensen and Pissarides (1999) k,i λ 4 Frechet Scale Parameter Simonovska and Waugh (2014) Panel B. Estimated Outside of the Model Parameter Description Source µ Final Expenditure Shares WIOD k,i γ Labor Expenditure Shares WIOD k,i ν Input-Output Matrix WIOD k(cid:96),i Panel C. Estimated by Method of Simulated Moments Parameter Description κ Vacancy Costs (cid:101)k,i χ Exogenous Exit k,i σ2 Distribution of Match-Specific Prod. k,i η Sector-specific Utility k,i C Mobility Costs kk(cid:48) b Unemployment Utility k,i Note: Artuc¸ et al. (2010) use an annual discount factor of δ = 0.97. Since we work at the quarterly frequency, we use δ=0.971 4. The distribution of match-specific productivities is imposed to follow a log-normal distribution G ∼logN(0,σ2 ). k,i k,i generated moments and those we measure in the data. Weimposeafewrestrictionsontheparametersestimatedbythesimulatedmethodofmoments. First, theidentificationofmobilitycostsC reliesondataonbothwagesandyearlyinter-sectoral k(cid:96),i transitionrates. Althoughthesedatacanbefoundinhouseholdsurveysacrossafewofthecountries we consider, we opted to identify these parameters using transition rates for the United States only. Therefore, we impose mobility costs to be common across countries. Also for identification purposes, weneedtoimposeC = 0forallk. Second, weimposethedistributionofmatch-specific kk productivities G to follow a log-normal distribution with mean 0 and variance σ2 . We restrict k,i k,i σ2 to be the same across sectors and countries, and identify it by targeting the cross-sectional k,i coefficient of variation of log-wages in the CPS. Third, we impose that the exogenous exit rates χ k,i are decomposed into a country component χ and a sector component χ (that is, χ = χ +χ ). i k k,i i k The sector-specific component χ is identified from US transitions from sector-specific employment k tounemployment. Thecountry-specificcomponentsarethenadjustedtobettermatchthecountryspecific unemployment rates. Fourth, the utility of unemployment b is imposed to be country k,i 21

specific (that is b = b ). This parameter will be important for the model to be able to match k,i i levels of wages across countries. Finally, sector- and country-specific utility terms η help the k,i model simultaneously fit sector-specific wages and employment shares. To achieve identification, we need to impose η = 0 for some sector k (we picked k = Agriculture). k0,i 0 0 A convenient aspect of our approach is that, by conditioning on the observed 2000 trade shares (cid:80) (cid:80) and trade imbalances, and normalizing total world revenues Y = 1, we can solve for k i k,i sector-country revenues {Y } that are independent of Θ. Specifically, equations (31), (33), and k,i the normalization lead to a system of equations in {Y }, which can be solved before starting the k,i estimation procedure. Consequently, the sector- and country-specific labor demand side of the model is fixed throughout the estimation procedure, allowing the labor supply side in each country to be solved in isolation. To see this, notice that equation (34) contains revenues on the left hand side, and the right hand side only depends on country-specific sectoral variables and parameters. Therefore, in steady state, observed trade flows and trade imbalances are sufficient statistics for international linkages. This property allows us to estimate the model country by country, greatly simplifying the estimation procedure.25 Indeed, if all parameters were country specific and we had the same set of data for each country, estimation could be conducted in parallel for each country. Asafinalpoint, aconvenientaspectofconductingtheestimationconditionalontheobservedtrade shares is that we do not have to estimate the technology parameters A and trade costs d . We k,i k,oi develop algorithms to perform counterfactual responses to shocks to technology parameters and trade costs relying on the exact hat algebra approach in Dekle et al. (2007), Dekle et al. (2008) and Caliendo and Parro (2015). Although the model could be flexibly estimated country by country if we had data on yearly transitions across sectors for all countries, we impose C and σ2 to be constant across countries k(cid:96),i k,i and identified off the United States’ CPS transition rates and wage dispersion data. Therefore, we proceed in two steps. First, we estimate the model for the United States, back out C , σ2 and χ . k(cid:96) k k In a second step, we estimate the rest of the parameters in parallel, country by country, conditional on the values of C , σ , and χ that are estimated in the first step. k(cid:96) k k Atthispoint,itisworthwhilementioningthatourestimationapproach,whichdoesnotestimate A and trade costs d , cannot recover κ . Instead, we are able to recover the value of κ ≡ k,i k,oi k,i (cid:101)k,i κ PF k,i i in the 2000 steady-state equilibrium. Our counterfactual algorithms then allow κ to w (cid:101)k,i (cid:101)k,i respond to shocks, using exact hat algebra. It is also important to clarify that identifying κ is (cid:101)k,i difficult in practice. Even though the objective function is not flat with respect to κ , it tends to (cid:101)k,i be relatively flat for a wide range of values. For that reason, we follow Hagedorn and Manovskii (2008) and impose that the cost of posting one vacancy κ PF equals 0.58×w , where w is the k,i i k,i k,i 25The method of simulated moments objective function is highly non-linear and non-convex, so that global optimization routines, such as Simulated Annealing, must be applied. Breaking a large parameter vector into smaller subsets of parameters that can be estimated separately greatly simplifies the estimation procedure. 22

averagewageinsectork andincountryi. HagedornandManovskii(2008)basetheircalibrationon a combination of the labor and capital costs of posting vacancies in a single-sector search model.26 While their model and ours differ on several dimensions—e.g., we have multiple sectors and match heterogeneity—there are two reasons we turn to their calculation. First, Hagedorn and Manovskii combine micro and macro data from multiple sources, mapping their numbers to observable costs of recruitment, capital purchasing, and other costs; second, their calibration of vacancy posting costs does not rely on other parameters of the model, just observable data (e.g., the capital share of income and the unemployment rate), so that their estimate is not contaminated by the fact that our other parameters are not always estimated to be the same as Hagedorn and Manovskii’s. We impose this constraint by adding the deviations between (κ ×w )/w = (cid:0) κ ×PF(cid:1) /w (cid:101)k,i (cid:101)k,i k,i k,i i k,i and 0.58 in our method of simulated moments objective function. The full estimation algorithm is described in Online Appendix C.1. 4 Estimation Results and Mechanisms 4.1 Estimates and Model Fit The estimated parameters can be found in the Online Appendix C.7, in Tables A.1 through A.8. We first discuss the parameters that are obtained outside of the model. The Online Data Appendix detailshowthesearecomputedwithdatafromtheWIOD.TableA.1displaysthefinalexpenditure shares µ . We can separate the countries in this table in two groups with similar expenditure k,i shares: (1) United States, Europe, Asia, and Americas; and (2) China and Rest of the World. The biggest difference between these two countries is that China and the Rest of the World spend a much larger share of their disposable income on Agricultural goods and significantly lower share on High-Tech Services. Table A.2 displays the share of revenues devoted to labor payments. This share varies mostly withincountriesandacrosssectorsandrangesbetween0.24(inHigh-TechManufacturinginChina) and0.68(inHigh-TechServicesinRestoftheWorld). Finally,TableA.3displaystheaverageacross countries of the input-output matrices. As is well known, the diagonal elements tend to be larger than the off-diagonal elements. Our mobility costs are displayed in Table A.4. Artu¸c et al. (2010) express their mobility costs estimates as multiples of average wages. In contrast, in our model, workers compute their value functions and make decisions based on λ(cid:101)i × w (cid:101)k,i , and not just based on sector-specific average wages. Therefore, to make our estimates comparable to those in Artu¸c et al. (2010), we express 26Astheauthorspointout,inthesteadystateofasinglesectorsearchmodel,capitalisequivalenttointerpreting vacanciesascapitalandreinterpretingtheproductivityprocess. Inthissense,avacancyisametaphorforthewhole cost of hiring a worker—the flow cost of capital, HR efforts, etc.. We adopt a similar view in our paper, without modeling each piece. 23

Figure 2: Model Fit (a) Employment Shares ledoM 6. 4. 2. 0 (b) Unemployment Rates US China Europe Asia/Oceania Americas RoW 0 .2 .4 .6 Data ledoM 80. 60. 40. 20. US China Europe Asia/Oceania Americas RoW .02 .04 .06 .08 Data (c) Average Wages ledoM 2. 51. 1. 50. 0 (d) Transition Rates US China Europe Asia/Oceania Americas RoW 0 .05 .1 .15 .2 Data ledoM 5. 4. 3. 2. 1. 0 0 .1 .2 .3 .4 .5 Data mobility costs as multiples of λ(cid:101)US ×w US , where w US is the average wage in the US (in the data). We obtain that our estimated mobility costs across sectors (as a fraction of λ(cid:101)US × w US ) range from virtually zero to a maximum of 3.1. These numbers are of the same order of magnitude, but lower than what Artu¸c et al. (2010) estimate (in their preferred specification, mobility costs are 6 times average wages). We believe that two ingredients of our model absent from theirs, search frictions and sector-specific utility terms η , account for our lower estimates of mobility costs. k,i Indeed, Artu¸c and McLaren (2015) extends ACM to allow for η terms and also find lower moving frictions. Finally, Table A.7 shows that the values of unemployment b tend to be negative across i all countries. As the search literature has shown, a negative value of unemployment is necessary to generate the magnitudes of wage dispersion typically found in the data (e.g., Hornstein et al., 2011; Meghir et al., 2015). Figure 2 shows the model fit for the various moments we target: (a) employment shares across sectorsandcountries;(b)unemploymentratesacrosssectorsandcountries;(c)averagewagesacross sectorsandcountries; and(d)inter-sectoraltransitionratesintheUnitedStates. Asageneralrule, 24

the model matches the targeted moments well. 4.2 Impulse Response Functions Endogenizing trade imbalances as optimal inter-temporal consumption decisions implies that the dynamics of the shocks hitting the economy are key for the evolution of imbalances. Hence, in order to understand the rich mechanisms at play in our model, we study the model’s behavior in response to three sets of shocks. First, we subject the model to a tenfold increase in A , the k,China productivity location parameter in China, uniform across sectors k and lasting for five years before turning back to its original level—the magnitude of this shock is in line with the size of actual changes in Chinese productivity that we recover in section 5.1. Next, we feed the model with a tenfold permanent increase in A that happens once and for all at t = 1. Finally, we simulate k,China a slow-moving and linear increase in A that reaches a tenfold increase in 15 years. It remains k,China at that level from there on. These shocks are illustrated in Figure 3. The economy is initially in steady state, so that the shocks are unanticipated at t = 0, but their paths are fully anticipated at t = 1. To highlight the quantitative and qualitative importance of modeling trade imbalances, we study the behavior of the complete model with bonds as well as the behavior of a model without bonds, where trade is balanced in every period—that is NXt = 0 ∀i,t.27 i We start with the temporary shock depicted in Figure 3a. The evolution of net exports in Figure 4 aligns with what we would have expected from standard macroeconomic models with inter-temporal decisions. The temporary boost in productivity, and therefore income, induces China to save in the short run by running a large trade surplus. As productivity reverts back to its initial level, China sustains a permanent trade deficit of 21% of GDP, as it consumes the return on its savings. On the other hand, the remaining countries borrow from China, running trade deficits in the short run. As the productivity increase in China vanishes, all countries start to sustain permanent trade surpluses, repaying their debts to China. While these aggregate patterns are standard, this productivity shock has varied impacts on the more disaggregated economy. Specifically, the rise in productivity induces substantial labor reallocation across sectors. We summarize reallocation patterns relying on the following measure: Reallocationt = 1 (cid:88) t (cid:88) J (cid:12) (cid:12) (cid:12) Ls i,k − Ls i, − k 1(cid:12) (cid:12) (cid:12), (38) i 2 (cid:12) Ls Ls−1(cid:12) s=1k=1 i i which accumulates yearly changes in sectoral employment shares over time. Figure 5a plots the evolution of the reallocation index (38) across countries. When we consider 27To make these two cases comparable, we study the complete model responses (with trade imbalances) imposing that trade is balanced in the initial steady state. See Online Appendix C.3 for details on how we implement this procedure using exact hat algebra techniques. 25

Figure 3: Shocks to Chinese Productivity A(cid:98)k,China – Uniform Across Sectors (a) Temporary (b) Once-And-For-All (c) Slow Moving our complete model with bonds, there is an immediate and steep rise in reallocation in all countries following China’s productivity jump. After productivity returns to its initial level, reallocation continues for several years before reaching its final steady-state level. Even though we consider a uniform productivity shock across sectors, we observe substantial labor reallocation within China andwithinothercountries.28 Thereasonthatuniformproductivitychangescanhavelargeimpacts on labor reallocation is trade across countries, which adds asymmetries to how sectors respond to the same productivity shock. Our model features two sources of asymmetries. First, heterogeneity intradecostsimpliesthatthetradabilityofgoodsdiffersacrosscountriesandsectors. Asexplained by Dornbusch et al. (1977), transfers (here, net exports) across countries alter the terms of trade and therefore the allocation of economic activity within each country. Second, countries differ in their final consumption bundles which implies that the global distribution of final consumption expenditure matters for the allocation of workers across sectors. Relatedly, heterogeneity in inputoutput linkages across countries also generate changes in countries’ terms of trade and global expenditure patterns. The increase in reallocation is directly tied to an increase in unemployment in all countries, 28Note that in a closed economy without mobility costs and search frictions, we would have seen no reallocation effects given homothetic preferences and our production structure as relative prices would not change. However, the presence of heterogeneous mobility costs across sectors could lead to some reallocation effects as the option value of search would change differentially across sectors. However, based on Shimer (2005) we expect this effect to be quantitatively small. 26

Figure4: NetExportsOverGDPinResponsetoTemporaryProductivityGrowthinChina(Figure 3a) as shown in Figure 5b. This highlights a key mechanism in our model: even positive labor demand shocks can increase unemployment through asymmetric shifts in labor demand. Once again, there are two reasons this can occur. First, contracting sectors will destroy low productivity jobs, dislocating workers who must switch sectors. Second, it takes time for workers who switch into expanding sectors to find new jobs. Relatedly, that there is no systematic relationship between the response of unemployment and the sign of trade imbalances. The reason why modeling imbalances generates more reallocation is due to the richer patterns of reallocation that emerge, shown in Figures 5c (for the full model) and 5d (for balanced trade). When we consider the complete model with bonds, rising imports in the US following Chinese productivity growth do not need to be immediately met with rising exports. Instead, the US imports goods in the short run and reallocates labor to service sectors, which are less tradable. This pattern follows from homothetic preferences, and so demand for services increases when total consumption in the US rises—as this demand cannot be easily met with imports. However, if we impose balanced trade in every period, exports from the US must immediately rise to offset the increase in imports. In doing so, labor reallocates to the sector in which it has highest comparative advantage (high relative productivity coupled with lower trade costs), which is also the sector in which China has higher relative demand: Agriculture. Reallocation when trade is balanced is driven by trade costs and comparative advantage, which do not change much in response to the temporary productivity growth in China. Turning to the long run, savings and borrowing behavior leads to permanent changes in final 27

Figure 5: Labor Market Dynamics in Response to Temporary Productivity Growth in China (3a) (a) Reallocation Index (b) Unemployment (c) Labor Allocations - Full Model (d) Labor Allocations - Balanced Trade 28

steady-state bond positions across countries. These permanent shifts in the long-run allocation of wealth carry implications for steady-state labor allocations and unemployment. The sources of long-run reallocation are similar to those operating in the short run, except that the effects of the temporary shock on the distribution of bonds positions (and therefore wealth) across countries is permanent. Specifically, the US runs a large deficit in the short run, which must be paid off in the form of long-run trade surpluses. To repay its debt with China, it shifts labor back to its goods sectors which can easily ship their production internationally. In the long run, the goods sectors in the US expand relative to the initial steady state, whereas its service sectors slightly contract. These long-run effects in response to a temporary shock are in sharp contrast with those in the model with balanced trade, which predicts that long-run allocations are unchanged relative to initial ones. We next turn to the analysis of the once-and-for-all shock in Chinese productivity depicted in Figure3b. Figure6highlightsthattheeffectofthisshockonnetexportsacrosscountriesisofmuch smaller magnitude. Indeed, when an economy is subject to a permanent shock the importance of savings to smooth consumption is of second order. If labor were perfectly mobile across sectors, economies would instantaneously reallocate labor and achieve their unconstrained optimal levels of expenditure. Because labor is not perfectly mobile, we do observe imbalances arising, but these are modest. It is therefore not surprising that, in the event of once-and-for-all permanent shocks, the behavior of the model with imbalances is similar to one without imbalances.29 29However, it is worth pointing out that this prediction of the model could be different for a shock that is not uniform across sectors, or for permanent shocks to trade costs (Reyes-Heroles, 2016; Alessandria and Choi, 2019). 29

Figure 6: Net Exports Over GDP in Response to Once-and-for-all Productivity Growth in China (Figure 3b) Finally, we study the behavior of our model when we feed it with a slow increase in Chinese productivity, as is illustrated in Figure 3c. Figure 7 shows that, in this case, China heavily borrows in the short run in anticipation of its large increase in long-run productivity. All other countries lend to China by running large surpluses for over ten years. As with the temporary shock, trade imbalances greatly magnify the extent to which reallocation and unemployment respond relative to the trade balance benchmark. Figures 8a and 8b show that the short-run labor market dynamics are very different across the two models. With trade imbalances, Figure 8c shows that the US reallocates resources away from its service sectors and towards its goods sectors so that their output can be shipped to China. However, in the long run, China needs to repay its debt and so ships goods back to the US. This leads to a long-run contraction of manufacturing in the US and an expansion of the remaining sectors. Compare this behavior with the monotonic decline in manufacturing in the US if trade is imposed to be balanced in Figure 8d. The magnitude of the manufacturing contraction is also much more limited under trade balance. The main conclusion of this section is that trade imbalances can significantly amplify the reallocation and unemployment responses to temporary shocks. They can also lead to very different patternsofinter-sectoralreallocationintheshortandlongrun. However,thequantitativerelevance ofendogenizingimbalancesdependsonthenatureoftheshock,asillustratedbyouronce-and-for-all permanent shock example. This fact can be appreciated by comparing the results for the temporary and slow moving shocks. An additional important result worth pointing out from our previous analysis is that the magnitude of reallocation and unemployment responses is independent of the 30

sign of the trade imbalance. Finally, our simulations highlight that, with trade imbalances, the full path of shocks matter for the behavior of imbalances over time, but also for the determinantion of their long-run consequences. Given the importance of the path of shocks for trade imbalances and the adjustment process, we now turn to the analysis of the labor market consequences of the shocks the global economy actually experienced between 2000 and 2014. Figure 7: Net Exports Over GDP in Response to Slow Productivity Growth in China (Figure 3c) 5 Counterfactuals Section 4.2 showed that the exact path of shocks shape the magnitude and evolution of trade imbalancesovertime,directlyinfluencinglong-runoutcomesthroughchangesinthelong-runglobal distributionofbondholdings. Forthisreason, weconductanempiricalexerciseinwhichweextract the various shocks the global economy has actually experienced between 2000 and 2014. Armed with these shocks, we conduct a common exercise in the international trade literature: how do labor markets behave over time in response to the constellation of globalization shocks (i.e., shocks to productivity and trade costs)? In this exercise, we compare the labor markets responses that we obtain with our model of trade imbalances to the responses that we obtain imposing balanced trade. Having established the quantitative importance of trade imbalances for both the adjustment processandlong-runallocations,wecomparetheconsumptiongainsinresponsetochangesintrade costs in our model to those obtained in standard models of trade, as summarized by the sufficient statistic approach developped by Arkolakis et al. (2012). Next, we compute the globalization gains accrued to each country between 2000 and 2014, and compare them to those obtained in a world 31

Figure 8: Labor Market Dynamics in Response to Slow Productivity Growth in China (Figure 3c) (a) Reallocation Index (b) Unemployment (c) Labor Allocations - Full Model (d) Labor Allocations - Balanced Trade 32

withouttheglobalsavingsglut,orinaworldwithbalancedtrade(i.e.,nobonds). Finally,giventhe recent interest on the “China shock” on the US labor market, we use our extracted shocks to study the effects of shocks to the Chinese economy on the behavior of unemployment and manufacturing employment in the US. We also investigate the contribution of the “China shock” for the US trade deficit and for the trade surplus in China. 5.1 Extracting Shocks from the Data ThissectionobtainsthetimeseriesforthreesetsofshocksintheglobaleconomybetweenDecember (cid:110) (cid:111) of 2000 and December of 2014: changes in trade costs d(cid:98) t , inter-temporal preference shocks k,oi (cid:110) (cid:111) (cid:110) (cid:111) φ(cid:98) t andproductivityshocks A(cid:98) t . Wemeasurechangesintradecostsandproductivityrelative i k,i dt At to December of 2000 (which we label t = 0): d(cid:98) t = k,oi, A(cid:98) t = k,i. On the other hand, shocks k,oi d0 k,i A0 k,oi k,i to inter-temporal preferences are relative to the previous period: φ(cid:98) t+1 ≡ φt i +1 .30 i φt (cid:110) (cid:111) i (cid:110) (cid:111) WeuseWIODdatatoconstructtimeseriesoftradeshares πt ,sectoralpriceindices PI,t k,oi k,i (cid:110) (cid:111) andfinalgoodexpenditures EC,t betweenDecemberof2000andDecemberof2014. Armedwith i thesedata, wecanexploitthegravitystructureofthetradeblockofthemodel, asinHeadandRies (2001) and Eaton et al. (2016), to recover the changes in bilateral trade costs combining equations equations (28) and (30): d(cid:98) t = P(cid:98) k I , , i t (cid:32) π (cid:98)k t ,oo (cid:33)1/λ . (39) k,oi P(cid:98) k I , , o t π (cid:98)k t ,oi In turn, we rely on the Euler equation (35) and normalize φ(cid:98) t = 1 ∀t, as in Reyes-Heroles (2016), US to recover the inter-temporal preference shocks: EC,t+1 EC,t φ(cid:98) t+1 = i US for t = 1,...,T −1, (40) i EC,t EC,t+1 i US where T is the last period for which we have data, which refers to December of 2014. Note that we still need to determine φ(cid:98) T+1, but we will need to use the structure of the model to do so, as this i value will depend on the model-implied steady-state value for final good expenditures EC,∞. i (cid:110) (cid:111) Finally, we recover the productivity shocks A(cid:98) t using: k,i πt A(cid:98) t k,i = (cid:16) (cid:98)k,ii (cid:17)λ (cid:0) (cid:98) ct k,i (cid:1)λ . (41) P(cid:98) I,t k,i 30WeimposeA(cid:98)t k,i =A(cid:98)T k,i andd(cid:98)t k,oi =d(cid:98)T k,oi forallt>T,whereT isthelastperiodforwhichwehavedata(T =14 andreferstoDecember2014). Wealsoimposeandφ(cid:98)t i =1forallt>T+1—asexplainedbelow,thevalueofφ(cid:98)T i +1 =1 is set to gauge the model-implied steady-state value for final consumption expenditures EC,∞. i 33

Given that ct depends on wt , which has no data counterpart, we need to use the full structure (cid:98)k,i (cid:101)k,i of the model to recover the sequence of productivity shocks. Online Appendix C.6 details the (cid:110) (cid:111) (cid:110) (cid:111) algorithm to recover the shocks A(cid:98) t as well as φ(cid:98) T+1 using the full structure of the model. k,i i To be able to recover the full set of shocks the economy experienced between 2000 and 2014, we (cid:110) (cid:111) (cid:110) (cid:111) assume the economy faces no additional shocks after 2015. That is, the values for At , dt k,i k,oi and (cid:8) φt(cid:9) are imposed to be constant from 2015 onwards.31 i Figure 9a shows an increase in productivity all over the world. In particular, China has experienced large increases in productivity, especially in manufacturing sectors.32 Other emerging economies—which comprise the bulk of the Americas and the Rest of the World aggregate—also experiencedimpressiveproductivitygrowth,whilegrowthwasmoremutedforadvancedeconomies. Turning to trade costs, we first construct a summary statistic to capture this large object. We focus on the average import cost for each country-sector pair, weighted by their initial steady state import shares: π0 d t = (cid:88) k,oi d(cid:98) t . (42) k,i 1−π0 k,oi o(cid:54)=i k,ii Figure 9b plots this index for each country and sector. In general, import trade costs are declining for the United States and Asia, and approximately flat in Europe (with some heterogeneity across sectors). Perhaps surprisingly, starting after the 2008 financial crisis and concurrent collapse in trade, initially falling import trade costs in China begin to revert and are actually larger by the end of the sample. This estimate of changes in trade costs reflects the fall in the share of trade in output, as documented in Bems et al. (2013). The sources for these increasing frictions are myriad, and include policy changes in countries like China, as well as changes in supply chain management, and other reasons. That said, our measures of frictions are a standard, straightforward, measure of the implied barriers to trade. Finally, we turn to our measure of shocks to inter-temporal preferences, which are presented in Figure 10. The shocks in the US are normalized to 1 in every period. In Europe and Asia (except China), the discount factor shocks fluctuate around 1, suggesting little persistent deviations in consumption behavior from what would be expected with a simple consumption smoothing model. On the other hand, China, the Americas, and the aggregated remaining countries (Rest of the World) exhibit persistent shocks to their inter-temporal preferences, suggesting increased patience over the period we consider. These persistent deviations are often referred to as the “global savings 31We also assume the economy is in steady state in 2000 and fully anticipates the full set of current and future shocks in 2001. (cid:110) (cid:111) 32While we plot changes in the productivity location parameters A(cid:98)t k,i , this is not directly comparable to productivity in the classic sense of a Solow Residual. In order to make sense of the magnitudes, note that TFP growth, defined as (cid:98) ct k,i /P(cid:98) k I , , i t, can be expressed as (A(cid:98)t k,i /π (cid:98)k t ,ii )1/λ. Therefore, using our recovered values for A(cid:98)t k,i , data on changesintradeshares,andimposingλ=4,themagnitudeforactualannualizedTFPgrowthinChinarangesfrom 3to5%peryear,dependingonthesector—whichisinlinewithgrowthaccountingestimatesdiscussedinZhu(2012). 34

Figure 9: Extracted Globalization Shocks (a) Productivity Shocks A(cid:98)t k,i t (b) Trade-Weighted Import Costs d (See Equation (42)) k,i 35

glut.”33 It is important to recognize that there are rich dynamics to consumption in the real world, reflecting preferences, frictions, and other factors. We are agnostic on the exact theory, instead summarizing the effect of these channels with the φ(cid:98) t shocks. This is useful because it allows i us to ask counterfactual questions about the dynamics of globalization shocks without the global savings glut, without having to specify what policy or change in deep parameters to achieve this—a useful benchmark to compare against the usual assumption in trade of no consumption smoothing whatsoever. Figure 10: Extracted Inter-Temporal Preference Shocks φ(cid:98) t i To extract the shocks the global economy experienced between 2000 and 2014, we have solely reliedondataontradeshares,sectoralprices,andaggregatefinalexpendituresacrosscountries. We havenotusedinformationonlaborallocationsortradeimbalances. Itisthereforenaturaltoaskhow the model-implied behavior of labor allocations and trade imbalances compare to those in the data. A note of caution before we proceed with this comparison: given our perfect foresight assumption, once we feed the shocks into the model, responses at impact are large as agents (suddenly) fully anticipate the path of future shocks. That said, Figure 11 compares labor allocations in the United States in our model (Panel a) to labor allocations in the data (Panel b). Our model replicates the decline of manufacturing as a whole, the expansion of services, and the decline and rebound of agriculture. The magnitudes in our model are compressed, but we believe this is explained by 33The large trade surplus that China has been running since the early 2000s is a puzzle for models in which the main driving forces are productivity shocks. For instance, as argued by Song et al. (2011), financial frictions within China are key drivers of the Chinese savings glut. Our inter-temporal preference shocks constitute a reduced-form waytoallowthemodeltomatchthetimeseriesbehaviorofChineseaggregateexpendituresandtherestoftheworld. 36

pre-existing trends driving the decline of manufacturing as well as the fact that we impose that the inter-temporal shocks φ(cid:98) t revert to 1 after 2014. The latter observation is important as individuals i in the model anticipate the end of the savings glut years before the end of our sample period, leading to some rebalancing happening before 2014. This observation is also important to explain the strong rebound of Low-Tech Manufacturing, for which we do not find support in the data. To verify the plausibility of this explanation, we simulated the same shocks we extracted with one difference: we keep the φ(cid:98) t shocks fixed at their 2012 to 2014 averages for 15 more years (that is, i until 2029). Indeed, not only the magnitude of the downsize of manufacturing that we obtain is larger than what is depicted in Figure 11a, but also Low-Tech steadily contracts until 2014. Figure 11: Comparing Labor Allocations in the Model and Data (a) Model (b) Data Figure 12 compares the model-implied trade imbalances in the US and China to those in the data. The model is able to capture the large surplus in China as well as the persistent deficit in the US. However, the model misses the behavior of Chinese imbalances in the beginning of the period. This happens as China anticipates its massive shocks that are coming (both large increases in productivity and shocks to inter-temporal preferences), which leads to large unemployment in the short run. In turn, this implies an initial production shortage and trade deficits. 5.2 Global Technology and Trade Shocks Ourfirstcounterfactualexercisefocusesonthegeneralequilibriumeffectsofchangesinproductivity and trade costs since 2000, with no shocks to inter-temporal preferences. In particular, we focus (cid:110) (cid:111) (cid:110) (cid:111) on the consequences of our extracted series of A(cid:98) t and d(cid:98) t above. Our goal is to isolate the i k,oi quantitative significance of globalization on labor market outcomes in a setting where workers smooth their consumption over time. As we will show, the shocks we recover from the data have significant impacts on global imbalances, which has implications for adjustment dynamics, unemployment, wages, and, ultimately, consumption. Before discussing results, it is helpful to contrast our approach with standard practice. There 37

Figure 12: Comparing Net Exports in the Model and Data (a) Model (b) Data are two typical approaches to dealing with imbalances in the quantitative trade literature. The first approach involves fixing imbalances in the data, or assuming balanced trade period by period. This method has been employed in both static models (e.g., Eaton and Kortum (2002) and Dekle et al. (2007)) and dynamic models (e.g., Dix-Carneiro (2014) and Traiberman (2019)). The use of this method in dynamic models is a particularly strong assumption, since it implicitly imposes that workers and governments have no access to borrowing or savings mechanisms. The second approach, involves assigning ownership shares of capital or fixed factors to agents at an initial point, and fixing these shares over time and in counterfactuals. Although this procedure does not follow from optimizing behavior, this method has been used in Caliendo et al. (2019), allowing for imbalances to change as returns to fixed factors change. If returns to capital increase while those to labor decline, this implies that workers have access to some social insurance. Nevertheless, agents are prevented from buying or selling shares in response to the shocks they face.34 To be able to compare the implications of the globalization shocks in our model of trade imbalances relative to a model without imbalances, we start both models from a steady steady with trade balance—that is NXt = 0 ∀i at t = 0, see Online Appendix C.3 for details on our procedure, i which is based on exact hat algebra. Figure 13 shows that the globalization shocks we feed into the model can lead to substantial imbalances in the short run. These predictions range from a trade deficit in China of up to 65% of GDP to a trade surplus in Asia close to 20%. The US runs a short-run surplus amounting to close to 10% of GDP. As expected from previous literature, if we purge the model of the inter-temporal preference shocks, we see China running a large trade deficit in the short run. This is not surprising in light of our discussion in section 4.2 as Chinese productivity strongly and steadily increases between 2000 and 2014, more than in other countries. 34Theseapproximationsmaybereasonableinasituationwhereimbalancesaresmallalongthetransitionpathfrom oneequilibriumtothenext. Thiswouldbethecase,forexample,iftheprimaryforceforchangesinimbalanceswere shockstoaggregateconsumption,andorthogonaltotradeshocks(i.e.,ifimbalancesweredrivenbyφ(cid:98)t i ). Nevertheless, these are imperfect if the path and magnitude of trade shocks lead to large changes in consumption and savings, which we show is the case below. 38

Figure 13: Net Exports Over GDP in Response to Global Technology and Trade Shocks We learned in our analysis of section 4.2 that trade imbalances can amplify the amount of reallocation in the economy relative to a model where trade is balanced. Our empirical exercise corroboratesthisfinding,asweillustrateinFigure14a. Thebehaviorofunemploymentisalsoquite different, and driven by a larger amount of reallocation. Figures 13 and 14b also show that the responses of unemployment are not systematically related to the sign of imbalances. Importantly, Figures 14c and 14d highlight the importance of modeling trade imbalances in understanding the adjustment process in response to globalization shocks. A model that imposes trade balance often predicts opposing patterns of short-run reallocation. For example, our model with imbalances predicts that the globalization shocks would lead to an expansion of all manufacturing sectors in the US in the short run, but a contraction in the long run. On the other hand, trade balance would lead to a monotonic decline of High-Tech Manufacturing and a long-run expansion of Low-Tech Manufacturing. Other countries also display drastically different patterns of adjustment in both the short and long runs. 5.3 Trade Costs and Imbalances The previous section established that empirically-extracted shocks can lead to significant trade imbalances,andthataccountingfortheseimbalancescansubstantiallyaltertheadjustmentprocess relative to a balanced-trade world. This section studies the implications of both trade imbalances and labor market frictions for the consumption gains from trade, and for how these compare with thewidelyusedsufficient-statisticsapproachbasedonArkolakisetal.(2012), henceforthACR.Our model nests the Ricardian model considered in ACR, but violates two of their key assumptions: (i) 39

Figure 14: Labor Market Dynamics in Response to Global Technology and Trade Shocks (a) Reallocation Index (b) Unemployment (c) Labor Allocations - Full Model (d) Labor Allocations - Balanced Trade 40

no labor market frictions; and (ii) no trade imbalances. Concretely, we consider the changes in trade costs between 2000 and 2014 we obtain in Section 5.1, purging the model of shocks to inter-temporal preferences and to productivity. In this case, the implied gains from trade following Costinot and Rodr´ıguez-Clare (2014), who extend the ACR formula to allow for input-output linkages, is given by: K K W(cid:99) i ACR,Static = (cid:89)(cid:89) π (cid:98)k − ,i µ i j,iℵ jk,i /λ , (43) j=1k=1 where all of the changes are between final and initial steady states and ℵ is the j,kth element jk,i of the Leontief Inverse of the input-output matrix in country i. We obtain π solving our full (cid:98)k,ii model. To perform the comparison between consumption gains in our model and those using the ACR formula, we first focus on the change in steady-state consumption given by our framework. Given the static nature of the ACR model, we believe this is a more direct comparison between our predictions for the gains from trade. Figure15adisplaysthecomparisonbetweenthelong-runACRgainsinconsumption(bluebars) and the long-run gains we obtain in our model (red bars). Overall, these gains are quite different. The ACR formula predicts that the US endures a 0.6% loss in response to the changes in trade costs the global economy experiences, whereas our model predicts that the US experiences a gain of 0.9%. OurconclusionsdifferstarklyinChina, wheretheACRformulapredictsagainofalmost3%, but our model predicts a long-run loss of 0.7%. These numbers differ because of both labor market frictions and long-run trade imbalances that arise in our model. The latter figures depend on the full path of shocks fed into the model, and not just the initial and final levels of trade costs—as do the ACR gains. Figure 16 shows the long-run trade imbalances that arise in our model. They are particularly important in China, Asia, and the Rest of the World. Given the dynamic nature of our model, we define the dynamic consumption gains from trade as the ratio between the level of constant consumption that would yield the same net present value consumption that unfolds along the transition path and the initial steady-state consumption. Mathematically: (cid:40) ∞ (cid:41) (cid:88) W(cid:99)i ≡ exp (1−δ) δtlog(C i t)−log(C i SS0) . (44) t=0 Similarly, we can also calculate “ACR Dynamic” gains from trade, by taking the net present value of the static gains calculated by (43) in every period. More precisely:   ∞ K K W(cid:99) i ACR,Dynamic = (1−δ) (cid:88) δt  (cid:89)(cid:89) (π (cid:98)k t ,ii )−µj,iℵ jk,i /λ  (45) t=0 j=1k=1 41

where πt is the change in trade shares between periods 0 and t, computed using our full model. (cid:98)k,ii Figure 15: Shocks in Trade Costs and the Consumption Gains from Trade (a) Long-Run Gains from Trade (b) Dynamic Gains from Trade Notes: InPanel(a),thebluebars,“ACR,”refertotheconsumptiongainscomputedusingequation(43);theredbars,“Full Model,”refertothechangeinsteady-stateconsumptiongivenbyourfullmodelwithtradeimbalances. InPanel(b),theblue bars,“ACR,”refertothepresentvalueofgainscalculatedbyusingequation(45);theredbars,“FullModel,”refertothe presentvalueofgainsoverthetransitioninthefullmodelwithtradeimbalances,usingequation(44). Inallcases,πt is (cid:98)k,ii obtainedbysimulatingourfullmodelinitializedwithNXt=0∀iatt=0 i Figure 15b compares the consumption gains predicted by the “dynamic ACR” formula (45) to the dynamic gains computed according our model (44). Although predictions are now similar for China and Europe, they are quite different for the remaining countries. For example, Asia enjoys a consumption gain of almost 2.5% according to the dynamic ACR formula, whereas our model predicts an essentially zero gain. Also noteworthy, the Rest of the World gains by almost 2% according to our model, but by less than 0.5% according to the dynamic ACR formula. In a series of exercises available upon request, we investigate the separate role of trade imbalances and labor market frictions behind the discrepancies between the predictions of the ACR formula and those of our model. To that end, we simulate our model under balanced-trade and still find significant differences between the gains predicted by our model and those by the ACR formula. We conclude that both trade imbalances and labor market frictions are important contributors to the divergences we document. 5.4 Globalization Gains The previous section compared how the consumption gains in our model compare with those from the ACR formula in response to shocks in trade costs alone. We now ask by how much countries benefittedfromallglobalizationshocksduringtheperiodweconsider,whichincludeshockstotrade costs, technology and inter-temporal preferences. To that aim, we adopt the following procedure. For each country at a time, we neutralized the shocks it experienced between 2000 and 2014, while 42

Figure 16: Steady-Sate Changes in Net Exports in Response to Shocks in Trade Costs feeding the model with the path of shocks faced by the remaining countries. For example, to assess the effects of globalization on US consumption, we set all US shocks to 1, but we keep shocks to remaining countries at the values we recovered in Section 5.1. Table V displays the results. The first column shows that all countries benefitted from globalization. China benefitted the most, with consumption gains reaching 6.6%. The Americas and Asia/Oceania gained the least: 0.03%. The magnitude of gains can be significantly affected if we impose trade balance: the second column showsthatgainsintheUSarereducedfrom2.2%to1.3%. Finally,weinvestigatetheeffectofintertemporalshocksinthethirdandfourthcolumns(withandwithouttradeimbalances, respectively). If we shut down the global savings glut, welfare in the US is significantly higher, reaching 3.8%. We conclude observing that even though our results are consistent with the belief that the global savings glut was detrimental to the US, balancing trade would lead to an even worse situation. 5.5 The China Shock As a final application of our model, we investigate the role of China on the adjustment of the labor market in the US. This topic has attracted much academic interest since the work of Autor et al. (2013) and Pierce and Schott (2016). We compare the behavior of our model when we feed it with all of the shocks we recovered in Section 5.1 (which we label as the Benchmark counterfactual) to the behavior of the model when (a) shocks to China are set to be equal to the average of shocks experienced by the remaining countries; and when (b) we neutralize China’s savings glut by setting φ(cid:98) t = 1 for all t.35 In these simulations, trade imbalances in the initial steady state are set at China NXt=0 = NXData, that is, the level of trade imbalances in the data in 2000. i i 35Shockstointer-temporalpreferencesandtheirinteractionwithstandardshocksinproductivitiesandtradecosts differentiate these counterfactual experiments from Caliendo et al. (2019) and Ada˜o et al. (2020). 43

Table V: Globalization Consumption Gains Over 2000-2014 Complete Model Balanced Trade Country Complete Model Balanced Trade φ(cid:98) t = 1 ∀i,t φ(cid:98) t = 1 ∀i,t i i United States 1.022 1.013 1.038 1.013 China 1.066 1.067 1.056 1.067 Europe 1.015 1.015 1.025 1.016 Asia/Oceania 1.003 1.021 0.997 1.021 Americas 1.003 1.006 1.002 1.006 Rest of the World 1.052 1.045 1.037 1.045 Notes: EachrowdisplaysW(cid:99)i (seeequation(44))inresponsetoextractedshockstoallothercountrieswhenown country shocks are neutralized. Third and fourth columns impose φ(cid:98)t i = 1 ∀i,t, neutralizing all inter-temporal preferenceshocks. TomaketheCompleteModelexercisescomparablewiththeBalancedTradeones,weinitialize the Complete Model with NXt =0 for t=0. i We first analyze the situation where shocks to China between 2000 and 2014 are imposed to be equaltotheaverageofshocksacrossalloftheremainingcountries.36 Theobjectiveistounderstand the behavior of the global economy in a counterfactual world where Chinese fundamentals evolved like those of an average country. The red dashed line in Figure 17a shows that China runs a much more modest trade surplus over time compared to the Benchmark illustrated by the blue solid line. Interestingly, Figure 17b shows that the behavior of the US trade deficit is barely affected if shocks to China are set to other countries’ averages. This result suggests that the evolution of the US trade deficit between 2000 and 2014 was not greatly influenced by the extraordinary shocks China experienced over this period. Instead, the evolution of the trade deficit in the US was primarily dictated by the full constellation of shocks that the global economy experienced over the 2000’s. This result highlights an important advantage of our multi-country model relative to two-country models, where changes in the trade balance in one country are mirrored in the other. Figure 18 describes the impact of the China shock on sectoral reallocation in the US. The red dashed line shows that if shocks to China had behaved in an ordinary way between 2000 and 2014, thecontractioninMid-andHigh-TechManufacturingwouldhavebeenlesspronounced. Theeffect of the China shock on employment in Low-Tech Manufacturing is not as visible, but the dashed red line is consistently above the solid blue line, showing that shocks to the Chinese economy led to mild contractions in employment in the sector (or prevented stronger growth in the long run). In contrast, employment in Agriculture and Services (particularly Low-Tech Services) moved in opposite directions, quickly absorbing workers displaced from Manufacturing. Figure 19a shows that the behavior of unemployment with the China shock (solid blue line) or without it (dashed 36ShockstotradecostsfromcountryitoChinaaresettobeequaltoaweightedaverageofshocksbetweencountry i and all other countries—weights are given by country sizes L . Shocks to trade costs from China to country i are i set to be equal to the weighted average of shocks between all remaining countries and country i. 44

Figure 17: The China Shock: Net Exports (a) NX / GDP in the China (b) NX / GDP in the US Notes: “AllShocks”: modelisfedwithallshocksrecoveredinsection5.1. “ChinaReceivesWorldAvg. Shocks”: model isfedwithallshocksrecoveredinsection5.1,withtheexceptionofChina. ForChina,productivityandinter-temporal productivityshocksbetween2000and2014areimposedtobeequaltotheaverageoftheseshocksacrossallthe remainingcountries. ShockstotradecostsfromcountryitoChinaaresettobeequaltoaweightedaverageofshocks betweencountryiandallothercountries—weightsaregivenbycountrysizesLi. ShockstotradecostsfromChinato countryiaresettobeequaltotheweightedaverageofshocksbetweenallremainingcountriesandcountryi. “All Shocksbutφ(cid:98)China =1”: modelisfedwithallshocksrecoveredinsection5.1butChina’ssavingsglutbysetting φ(cid:98)t =1forallt. t=0correspondstoyear2000. t=14correspondsto2014,thelastyearofdataweemployedto China extracttheshocks. red line) is very similar. Indeed, in either case, the unemployment rate reaches a maximum of 3.14%. It is important to highlight that the small response of US unemployment in Figure 19a is not a mechanical feature of our model. Indeed, Figures 5b, 8b and 14b show substantial changes in the unemployment rate in the US and other countries in response to other shocks we simulate. Further insights can be obtained if we study the behavior of sectoral unemployment. Consider the “All Shocks” counterfactual, where we feed the model with all the shocks we extracted in Section 5.1. Figure 19b shows that the response of sectoral unemployment rates is considerably larger than the aggregate response. Specifically, aggregate unemployment ranges from 3.06% to 3.14% in response to the extracted shocks. At the sectoral level, unemployment within the manufacturing sectors repond more strongly and range between 3.65% and 4.35% and unemployment within agriculture varies between 2.6% and 3.4%. However, unemployment within the service sectors are essentially unresponsive to the shocks. Therefore, given that 86% of workers are initially in services, the effect oftheseshocksonUSunemploymentismuted. Ontheotherhand,aggregateunemploymentranges from 6.5% to 12.5% in Europe and from 3.5% and 14% in China, showing that the model is capable of producing substantial unemployment responses to global shocks. It is also instructive to compare the behavior of the model when it is subjected to all the global shocks we extracted in Section 5.1 (the Benchmark) to its behavior when we subject it with the 45

Figure 18: The China Shock: Labor Allocations in the US Notes: “AllShocks”: modelisfedwithallshocksrecoveredinsection5.1. “ChinaReceivesWorldAvg. Shocks”: modelisfed withallshocksrecoveredinsection5.1,withtheexceptionofChina. ForChina,productivityandinter-temporalproductivity shocksbetween2000and2014areimposedtobeequaltotheaverageoftheseshocksacrossalltheremainingcountries. ShockstotradecostsfromcountryitoChinaaresettobeequaltoaweightedaverageofshocksbetweencountryiandall othercountries—weightsaregivenbycountrysizesLi. ShockstotradecostsfromChinatocountryiaresettobeequalto theweightedaverageofshocksbetweenallremainingcountriesandcountryi. “AllShocksbutφ(cid:98)China =1”: modelisfed withallshocksrecoveredinsection5.1butChina’ssavingsglutbysettingφ(cid:98)t =1forallt. t=0correspondstoyear China 2000. t=14correspondsto2014,thelastyearofdataweemployedtoextracttheshocks. same shocks but remove China’s saving glut (that is, we set φ(cid:98) t = 1 for all t). The yellow China dotted line in Figure 17a shows that, in the absence of China’s savings glut, China would have run a massive trade deficit in the short run, reaching 75% of GDP.37 These large short-run deficits are then accompanied by large permanent trade surpluses in the long run, surpassing 10% of GDP. The evolution of the dotted yellow line is unsurprising in light of our our discussion in Section 4.2, and, more specifically, given Figure 7. In anticipation of a much higher level of productivity in the future (see Figure 9a), China borrows greatly in the short run to smooth consumption over time. 37In our model, in the absence of shocks to inter-temporal preferences, countries perfectly smooth consumption expenditure over time. This fact gives rise to a surge in imbalances that is not in line with what we observe in the data. There is ample evidence that the world is far from perfect consumption smoothing or risk sharing as documented and analyzed in Heathcote and Perri (2014). 46

Figure 19: The China Shock: Unemployment in the US (b) Sectoral Unemployment (a) Aggregate Unemployment Notes: Panel(a)—“AllShocks”: modelisfedwithallshocksrecoveredinsection5.1. “ChinaReceivesWorldAvg. Shocks”: modelisfedwithallshocksrecoveredinsection5.1,withtheexceptionofChina. ForChina,productivityandinter-temporal productivityshocksbetween2000and2014areimposedtobeequaltotheaverageoftheseshocksacrossalltheremaining countries. ShocksintradecostsfromcountryitoChinaaresettobeequaltothesimpleaverageofshocksbetweencountryi andallothercountries. ShockstotradecostsfromcountryitoChinaaresettobeequaltoaweightedaverageofshocks betweencountryiandallothercountries—weightsaregivenbycountrysizesLi. ShockstotradecostsfromChinatocountry iaresettobeequaltotheweightedaverageofshocksbetweenallremainingcountriesandcountryi. “AllShocksbut φ(cid:98)China =1”: modelisfedwithallshocksrecoveredinsection5.1butChina’ssavingsglutbysettingφ(cid:98)t China =1forallt. t=0correspondstoyear2000. t=14correspondsto2014,thelastyearofdataweemployedtoextracttheshocks. Panel(b) —Behaviorofsectoralunemploymentratesinresponseto“AllShocks”. This debt must be repaid in the form of large surpluses in the long run. This result illustrates the quantitatively important role of shocks to inter-temporal preferences φ(cid:98) t not only in offsetting China these large short-run trade deficits, but also in turning them into surpluses.38 NeutralizingtheChinesesavingsglutalsohasimportanteffectsonthedynamicsoftheUStrade deficit. The yellow dotted line in Figure 17b shows that the US trade deficit would be significantly smaller in the short run. However, the trade deficit would stabilize at a larger value in the long run (5% of GDP) as China runs a permanent large trade surplus. This result highlights that, even in the absence of the China’s savings glut, consumption smoothing motives in the global economy would lead to a large trade surplus in China in the long run (north of 10% of GDP) as the trade deficit in the US deteriorates to 5% of GDP. The dotted yellow and solid blue lines in Figure 18 show interesting consequences of China’s savings glut on the size of the manufacturing sector in the US. The Chinese savings glut was responsible for large declines in US manufacturing in the short run. This behavior is consistent across all three manufacturing sectors. However, absent the Chinese savings glut, manufacturing employment in the US would be substantially lower in the long run as China runs a permanently large trade surplus, and the US runs a permanently large trade deficit.39 38IfweabstractfromintertemporalpreferenceshocksinChina,ourresultisinlinewiththe“allocationpuzzle”in open economy macroeconomics which states that aggregate net capital inflows tend to be negatively correlated with productivity growth across developing countries (Gourinchas and Rey, 2014). In line with this puzzle, our intertemporal preference shifters could be interpreted as arising from the public sector’s expenditure decisions (Gourinchas and Jeanne, 2013; Aguiar and Amador, 2011; Alfaro et al., 2008). 39These results are in line with the findings of Kehoe et al. (2018) on the effects of the savings glut on structural 47

We now turn to the welfare consequences of the China shock. Specifically, we use equation (44) to compute the welfare effects of the shocks we recover in Section 5.1 (Benchmark), relative to the counterfactuals where (a) shocks to China are set to be equal to the average shocks experienced by the remaining countries: W(cid:99) Benchmark/W(cid:99) (a) ; and where (b) we neutralize China’s savings glut by i i setting φ(cid:98) t = 1 for all t: W(cid:99) Benchmark/W(cid:99) (b) . By doing so, we are capturing the effect of China’s China i i shocks relative to a situation where the Chinese fundamentals behaved similarly to the average global economy (excluding China), and relative to a situation where China did not experience a savings glut. Table VI: Global Consumption Gains of the China Shock (2000-2014) Panel A. W(cid:99) Benchmark/W(cid:99) (a) i i Country Complete Model Balanced Trade US 1.001 1.012 Europe 1.001 1.003 Asia 1.004 0.994 Americas 1.001 1.001 Rest of the World 1.005 1.031 Panel B. W(cid:99) Benchmark/W(cid:99) (b) i i Country Complete Model Balanced Trade US 0.997 1.000 Europe 0.998 1.000 Asia 0.998 1.000 Americas 1.003 1.000 Rest of the World 1.010 1.000 Notes: Changes in welfare obtained using equation (44). W(cid:99)i Benchmark referstoallshocksextractedinSection5.1fedintothe model. W(cid:99) (a)referstothesesameshocks,butChina’sshocksatsetto i theaverageofshocksinremainingcountries. W(cid:99) (b)referstoallshocks i extracted in Section 5.1 fed into the model, but φ(cid:98)t China = 1 for all t. To make the Complete Model exercises comparable with the Balanced Trade ones, we initialize the Complete Model with NXt = 0 i for t=0. Panel A of Table VI shows the effect of the China shock relative to a situation where China experienced shocks set to the average of the remaining countries. The first column displays the consumption effects of the China shock in our complete model with trade imbalances. The second column shows the consumption effects if we impose trade balance period by period. First, note that all countries benefitted from the extraordinary shocks accrued to China. However, these consumption effects were all very small. Interestingly, the welfare effects of the China shock in the change in the US. 48

US and the Rest of the World would be significantly higher if trade balanced every period. Panel B shows the effect of the Chinese savings glut. Our model predicts that the US, Europe, and Asia were negatively affected by the large shocks to inter-temporal preferences in China, but that these effects were, again, very mild. The exception is the Rest of the World, that actually benefits from theChinesesavingsglut. TheChinesesavingsglutwouldhavehadvirtuallynoconsumptioneffects around the world under balanced trade. 6 Conclusion There is a widespread concern among policy makers that, as globalization brings disruption to the labor market, growing trade deficits can accentuate job losses and the decline of manufacturing. Given how persistent these concerns have been in the past four decades, it is surprising that trade economiststypicallyabstractfromtradeimbalanceswhentheystudythelabormarketconsequences of globalization shocks. This paper fills this gap by extending the workhorse model of trade (Eaton and Kortum, 2002, and Caliendo and Parro, 2015) to allow for inter-sectoral mobility costs (as in Artu¸cetal.,2010),searchfrictions(asinMortensenandPissarides,1999),andtradeimbalances(as in Reyes-Heroles, 2016). In short, we extend the state-of-the-art model of trade with the workhorse models for mobility frictions, unemployment and trade imbalances. We estimate the model using data from the WIOD, ILOSTAT, and the US CPS. Our estimation method conditions on trade shares and net exports and can be performed country by country. Even though the parameter space is large, the country by country estimation allows us to break a large optimization problem into smaller ones. After analyzing impulse response functions to hypothetical shocks, we find that: (i) incorporating trade imbalances has the potential to significantly magnify the effect of globalization shocks on inter-sectoral reallocation and unemployment; (ii) reallocation paths can be substantially different if we allow for trade imbalances compared to balanced trade—specifically, sectors that expand in the short run with trade imbalances can instead contract with balanced trade; (iii) the behavior of trade imbalances and of the labor market depends on the whole path of shocks; (iv) the response of unemployment to globalization shocks is not related to sign of imbalances. In particular, temporary shocks can have important persistent long-run effects in our model, but none if we impose balanced trade. This motivates us to empirically extract the path of shocks the global economy actually experienced between 2000 and 2014 using standard methods from the international trade and macro literatures. We conduct a standard exercise in the international trade literature and subject the model to the empirically-extracted global technology and trade cost shocks. Aligned with our impulse response function analyses, we find that allowing for trade imbalances have a first order effect on 49

the behavior of labor markets around the world. Next, we investigate how the gains from trade in ourmodelcomparewiththoseobtainedusingtheinfluentialsufficient-statisticsapproachpioneered by Arkolakis et al. (2012). We find that both trade imbalances and labor market frictions can lead to substantial discrepancies between the gains from trade in our model relative to those in the literature on quantitative models of trade, which is summarized in Costinot and Rodr´ıguez-Clare (2014). Not only there are differences in the magnitude of the gains, but also on their signs. Relatedly, we assess, for each country, the gains from globalization between 2000 and 2014. Our model predicts that the US has enjoyed a gain of 2.2% in response to globalization shocks over this period. Our estimates suggest that these gains would have been 73% larger in the absence of the global savings glut. However, in a world where balanced trade is imposed, the US would have experienced 40% smaller gains. We also use our model to investigate the impact of the “China Shock” on the US trade deficit and labor market. Consonant with previous literature, we find that shocks to the Chinese economy contributed to the decline of manufacturing in the US, especially Mid-Tech and High-Tech Manufacturing. However, other sectors of the economy quickly absorbed workers from these sectors, leading to small effects on unemployment. We also find that shocks to the Chinese economy had only a modest effect on the evolution of the US trade deficit, highlighting that the evolution of the US trade deficit was mostly driven by the full constellation of shocks the global economy experienced. Interestingly, if China had not experienced its savings glut, the US trade deficit would have been smaller in the short run, but larger in the long run. Our work shows that carefully modeling imbalances can have quantitatively important implications for the adjustment process in response to globalization shocks and opens important questions forfuturework. Giventheimportanceofimbalancesforthereallocationprocess, anaturalquestion to address next is to quantitatively characterize how trade imbalances shape the inequality effects of trade. Our model can be extended to allow heterogeneous workers, so this is a natural next step. In addition, we also hope to be able to add endogenous capital accumulation decisions and capitalskill complementarity, generating rich mechanisms linking globalization to the skill premium as in Reyes-Heroles et al. (2020). Finally, an interesting extension of our framework would allow workers to make borrowing and savings decisions at the individual level, which will aggregate into global imbalances. Even though this is a hard problem, especially regarding estimation, we believe that our method of simulated moments that can be performed country by country (conditional on trade shares and imbalances) can be applied to this situation. 50

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Online Appendix, Not for Publication A Decentralizing the Labor Supply Decision in the Household Problem This Section shows that the labor supply decision solving (6) subject to (7) and (5) can be decentralized to individual workers solving equations (5) and (9). The Lagrangian of problem (6), (7) and (5) is  ∞ (cid:104) (cid:16) (cid:17)(cid:105)     (cid:80) δtφt Lu (cid:0) ct (cid:96) (cid:1) −λ(cid:101) t(cid:0) LPF,tct (cid:96) +Bt+1−Πt−RtBt(cid:1) +    L = E 0          (cid:82) 0 L    t= t (cid:80) ∞ = 0 0    δtφt    (cid:0) e 1 t (cid:96) η − kt e + t (cid:96) (cid:1) λ(cid:101) (cid:16) t − (cid:18) C (cid:80) K k (cid:96) t, I k (cid:96) t+ (cid:0) 1 k (cid:96) t + +1 ω = (cid:96) t ,k (cid:96) k t+ (cid:1) 1 e + t (cid:96) w b k t k (cid:96) t (cid:0) + x 1 t (cid:96) (cid:17) (cid:1) (cid:19) +          d(cid:96)          (A.1) (cid:96) k=1 Because each worker is infinitesimal, and the allocation of one worker does not interfere with the allocation/utility of other individual workers (conditional on aggregates), maximizing   (cid:0) 1−et(cid:1) (cid:16) −C +ωt +b (cid:17) +  (cid:90) 0 L   (cid:88) t ∞ =0 δtφt  et (cid:96) η kt + (cid:96) λ(cid:101) t (cid:18) (cid:80) K k (cid:96) t, I k (cid:96) t+ (cid:0) 1 k (cid:96) t+1 = (cid:96),k (cid:96) k t+ (cid:1) 1 et (cid:96) w k t k (cid:96) t (cid:0) + x 1 t (cid:96) (cid:1) (cid:19)     d(cid:96) (A.2) (cid:96) k=1 means maximizing each individual term. Therefore, the planner solves, for each individual, the recursive problem:  (cid:0) 1−et(cid:1) (cid:16) −C +ωt +b (cid:17) +etη      (cid:96) k (cid:96) t,k (cid:96) t+1 (cid:96),k (cid:96) t+1 k (cid:96) t+1 (cid:96) k (cid:96) t     Lt W (cid:0) k (cid:96) t,et (cid:96) ,xt (cid:96) ,ω (cid:96) t(cid:1) = kt+ m 1,e a t+ x 1(.) +λ(cid:101)t (cid:80) K I (cid:0) k (cid:96) t = k (cid:1) et (cid:96) w k t (cid:0) xt (cid:96) (cid:1) +  , (A.3) (cid:96) (cid:101)k    δφ(cid:98) t+1E k t = L 1 t W +1(cid:0) k (cid:96) t+1,et (cid:96) +1,xt (cid:96) +1,ω (cid:96) t+1(cid:1)    where φ(cid:98) t+1 ≡ φt+1 . φt Denote by Ft the set of information at t. So, E (.) = E (cid:0) .|Ft(cid:1) . For an unemployed worker in sector t k at time t, kt = k, et = 0: (cid:96) (cid:96) Lt W (cid:0) k (cid:96) t = k,et (cid:96) = 0,xt (cid:96) ,ω (cid:96) t(cid:1) = max −C kk(cid:48) +ω (cid:96) t ,k(cid:48) +b k(cid:48) +δφ(cid:98) t+1E t Lt W +1(cid:0) k(cid:48),et (cid:96) +1,xt (cid:96) +1,ω (cid:96) t+1(cid:1) . k(cid:48),{et+1(.)} (cid:101)k (A.4)

Using the law of iterated expectations we obtain: Lt (cid:0) kt = k,et = 0,xt,ωt(cid:1) = max −C +ωt +b W (cid:96) (cid:96) (cid:96) (cid:96) kk(cid:48) (cid:96),k(cid:48) k(cid:48) k(cid:48),{et+1(.)} (cid:101)k +δφ(cid:98) t+1E (cid:8) E (cid:2) Lt+1(cid:0) k(cid:48),1,xt+1,ωt+1(cid:1) |xt+1,Ft(cid:3) ×Pr (cid:0) kt+1 = k(cid:48),et+1 = 1|xt+1,Ft(cid:1) |Ft(cid:9) W (cid:96) (cid:96) (cid:96) (cid:96) (cid:96) (cid:96) +δφ(cid:98) t+1E (cid:8) E (cid:2) Lt+1(cid:0) k(cid:48),0,xt+1,ωt+1(cid:1) |xt+1,Ft(cid:3) ×Pr (cid:0) kt+1 = k(cid:48),et+1 = 0|xt+1,Ft(cid:1) |Ft(cid:9) W (cid:96) (cid:96) (cid:96) (cid:96) (cid:96) (cid:96) = max −C +ωt +b kk(cid:48) (cid:96),k(cid:48) k(cid:48) k(cid:48),{et+1(.)} (cid:101)k +δφ(cid:98) t+1θ k t (cid:48) q (cid:0) θ k t (cid:48) (cid:1) E (cid:8) Lt W +1(cid:0) k(cid:48),1,xt (cid:96) + (cid:48) 1,ω (cid:96) t+1(cid:1) e (cid:101) t k + (cid:48) 1(cid:0) xt (cid:96) +1(cid:1) |Ft(cid:9) +δφ(cid:98) t+1E (cid:8)(cid:0) 1−θ k tq (cid:0) θ k t (cid:48) (cid:1) e (cid:101) t k + (cid:48) 1(cid:0) xt (cid:96) +1(cid:1)(cid:1) Lt W +1(cid:0) s(cid:48),0,xt (cid:96) +1,ω (cid:96) t+1(cid:1) |Ft(cid:9) (A.5) For an employed worker in sector k, kt = k, et = 1: (cid:96) (cid:96) Lt W (cid:0) k (cid:96) t = k,et (cid:96) = 1,xt (cid:96) ,ω (cid:96) t(cid:1) = max λ(cid:101) tw k t (cid:0) xt (cid:96) (cid:1) +η k +δφ(cid:98) t+1E t Lt W +1(cid:0) k,et (cid:96) +1,xt (cid:96) ,ω (cid:96) t+1(cid:1) {et+1(.)} (cid:101)k = max λ(cid:101) tw k t (cid:0) xt (cid:96) (cid:1) +η k {et+1(.)} (cid:101)k (cid:26) E (cid:2) Lt+1(cid:0) k,1,xt,ωt+1(cid:1) |kt+1 = k,,et+1 = 1,xt+1,Ft(cid:3) × (cid:27) +δφ(cid:98) t+1E W Pr (cid:0) kt (cid:96) +1 (cid:96) = k,et (cid:96) +1 = 1|xt+ (cid:96) 1,Ft(cid:1) |Ft (cid:96) (cid:96) (cid:96) (cid:96) (cid:26) E (cid:2) Lt+1(cid:0) k,0,xt,ωt+1(cid:1) |kt+1 = k,et+1 = 0,xt+1,Ft(cid:3) × (cid:27) +δφ(cid:98) t+1E W Pr (cid:0) kt (cid:96) +1 = (cid:96) k,et+ (cid:96) 1 = 0|xt+ (cid:96) 1,Ft(cid:1) |Ft (cid:96) (cid:96) (cid:96) (cid:96) = max λ(cid:101) tw k t (cid:0) xt (cid:96) (cid:1) +η k {et+1(.)} (cid:101)k (cid:20) et+1(cid:0) xt(cid:1) Lt+1(cid:0) k,1,xt,ωt+1(cid:1) (cid:21) +δφ(cid:98) t+1(1−χ k )E + (cid:0) 1− (cid:101)k et+1(cid:0) x (cid:96) t(cid:1)(cid:1) W Lt+1(cid:0) k,0, (cid:96) xt, (cid:96) ωt+1(cid:1) |Ft (cid:101)k (cid:96) W (cid:96) (cid:96) +δφ(cid:98) t+1χ k E (cid:2) Lt W +1(cid:0) k,0,xt (cid:96) ,ω (cid:96) t+1(cid:1) |Ft(cid:3) (A.6) Make the following definitions U(cid:101) t(cid:0) ωt(cid:1) ≡ Lt (cid:0) kt = k,et = 0,xt,ωt(cid:1) , and k (cid:96) W (cid:96) (cid:96) (cid:96) (cid:96) Wt(x) ≡ Lt (cid:0) kt = k,et = 1,x,ωt(cid:1) . (A.7) k W (cid:96) (cid:96) (cid:96) U(cid:101) t(cid:0) ωt(cid:1) is the value of unemployment in sector k, conditional on the preference shocks ωt, and k (cid:96) (cid:96) Wt(x) is the value of a job with match productivity x. Note that Lt (cid:0) kt = k,et = 0,xt,ωt(cid:1) does k W (cid:96) (cid:96) (cid:96) (cid:96) not depend on xt and Lt (cid:0) kt = k,et = 1,x,ωt(cid:1) does not depend on ωt. Rewrite U(cid:101) t(cid:0) ωt(cid:1) as (cid:96) W (cid:96) (cid:96) (cid:96) (cid:96) k (cid:96) U(cid:101) k t(cid:0) ω (cid:96) t(cid:1) = max −C kk(cid:48) +ω (cid:96) t ,k(cid:48) +b k(cid:48) k(cid:48),{et+1(.)} (cid:101)k (cid:90) +δφ(cid:98) t+1θ k t (cid:48) q (cid:0) θ k t (cid:48) (cid:1) W k t+ (cid:48) 1(x)e (cid:101) t k + (cid:48) 1(x)dG k(cid:48) (x) (cid:16) (cid:17) +δφ(cid:98) t+1(cid:0) 1−θ k t (cid:48) q (cid:0) θ k t (cid:48) (cid:1) Pr (cid:0) e (cid:101) t k + (cid:48) 1(cid:0) xt (cid:96) +1(cid:1) = 1 (cid:1)(cid:1) E ω U(cid:101) k t+ (cid:48) 1(cid:0) ω (cid:96) t+1(cid:1) , (A.8)

and so: U(cid:101) k t(cid:0) ω (cid:96) t(cid:1) = max −C kk(cid:48) +ω (cid:96) t ,k(cid:48) +b k(cid:48) k(cid:48),{et+1(.)} (cid:101)k (cid:90) (cid:32) Wt+1(x)et+1(x)+ (cid:33) +δφ(cid:98) t+1θ k t (cid:48) q (cid:0) θ k t (cid:48) (cid:1) E ω (cid:16) U(cid:101) k t+ (cid:48) 1 k(cid:48) (cid:0) ω (cid:96) t+1(cid:1) (cid:101) (cid:17)k(cid:48) (cid:0) 1−e (cid:101) t k + (cid:48) 1(x) (cid:1) dG k(cid:48) (x) (cid:16) (cid:17) +δφ(cid:98) t+1(cid:0) 1−θ k t (cid:48) q (cid:0) θ k t (cid:48) (cid:1)(cid:1) E ω U(cid:101) k t+ (cid:48) 1(cid:0) ω (cid:96) t+1(cid:1) . (A.9) Now, wewrite Wt(x) as: k W k t(x) = max λ(cid:101) tw k t (x)+η k {et+1(.)} (cid:101)k +δφ(cid:98) t+1(1−χ k )e (cid:101) t k +1(x)W k t+1(x) (cid:16) (cid:17) +δφ(cid:98) t+1(cid:0) 1−(1−χ k )e (cid:101) t k +1(x) (cid:1) E U(cid:101) k t+1(cid:0) ω (cid:96) t+1(cid:1) , (A.10) and so W k t(x) = max λ(cid:101) tw k t (cid:0) xt (cid:96) (cid:1) +η k {et+1(.)} (cid:101)k (cid:16) (cid:16) (cid:17)(cid:17) +δφ(cid:98) t+1(1−χ k ) e (cid:101) t k +1(x)W k t+1(x)+ (cid:0) 1−e (cid:101) t k +1(x) (cid:1) E ω U(cid:101) k t+1(cid:0) ω (cid:96) t+1(cid:1) (cid:16) (cid:17) +δφ(cid:98) t+1χ k E ω U(cid:101) k t+1(cid:0) ω (cid:96) t+1(cid:1) . (A.11) It is now clear that the optimal policy et+1(.) is: (cid:101)k (cid:40) (cid:16) (cid:17) (cid:41) et+1(x) = 1 if W k t+1(x) > E ω U(cid:101) k t+1(cid:0) ω (cid:96) t+1(cid:1) . (A.12) (cid:101)k 0 otherwise (cid:16) (cid:17) Define U k t ≡ E ω U(cid:101) k t(cid:0) ω (cid:96) t(cid:1) . We therefore have the following Bellman equations:  max−C +b +ωt  kk(cid:48) k(cid:48) (cid:96),k(cid:48) k(cid:48) U k t = E ω   +δφ(cid:98) t+1θ k t (cid:48) q (cid:0) θ k t (cid:48) (cid:1)(cid:82) max (cid:8) W k t+ (cid:48) 1(x),U k t+ (cid:48) 1(cid:9) dG k(cid:48) (x)   (A.13) +δφ(cid:98) t+1(cid:0) 1−θt q (cid:0) θt (cid:1)(cid:1) Ut+1 k(cid:48) k(cid:48) k(cid:48) W k t(x) = λ(cid:101) tw k t (x)+η k +δφ(cid:98) t+1(1−χ k ) (cid:0) max (cid:8) W k t+1(x),U k t+1(cid:9)(cid:1) +δφ(cid:98) t+1χ k U k t+1 (A.14)

B Steady State Equilibrium In this section we derive the equations characterizing the steady state equilibrium. The key conditions that we impose is that variables are constant over time, inflows of workers into each sector equal outflows, and job destruction rates equal job creation rates. We also impose that the preference shifters (cid:8) φt(cid:9) are constant and equal to 1 in the long run. i Wage Equation (1−β )(1−δ)U −(1−β )η k,i k,i k,i k,i w (x) = β w x+ (A.15) k,i k,i(cid:101)k,i λ(cid:101)i Firms’ value function 1−β k,i (cid:0) (cid:1) J k,i (x) = 1−(1−χ )δ λ(cid:101)i w (cid:101)k,i x−x k,i (A.16) k,i Probability of filling a vacancy κ PF 1−δ(1−χ ) q (θ ) = k,i i × k,i (A.17) i k,i (cid:0) (cid:1) w δ(1−β )I x (cid:101)k,i k,i k,i k,i where (cid:0) (cid:1) (cid:90) xmax(cid:0) (cid:1) I x ≡ s−x dG (s) (A.18) k,i k,i k,i k,i x k,i Unemployed workers’ Bellman equation U = ζ log   (cid:88) exp    −C kk(cid:48),i +b k(cid:48),i +θ k(cid:48),i κ k w (cid:101) (cid:48), k i (cid:48) P ,i i F ×λ(cid:101)i w (cid:101)k(cid:48),i(1− β k β (cid:48) k ,i (cid:48),i ) +δU k(cid:48),i      (A.19) k,i i  ζ   i  k(cid:48)   Transition rates   exp  −C k(cid:96),i +b (cid:96),i +θ (cid:96),i κ(cid:96) w(cid:101) ,i (cid:96) P ,i i F ×λ(cid:101)iw (cid:101)(cid:96),i(1− β(cid:96) β , (cid:96) i ,i ) +δU (cid:96),i    ζi    s = (A.20) k(cid:96),i  κ PF β  (cid:80) exp    −C kk,i +b k,i +θ k,i k w(cid:101) ,i k,i i ×λ(cid:101)iw (cid:101)k,i(cid:18) 1− k β , k i ,i (cid:19)+δU k,i    k   ζi     Steady-state unemployment rates χ k,i u = (A.21) k,i (cid:0) (cid:0) (cid:1)(cid:1) θ q (θ ) 1−G x +χ k,i i k,i k,i k,i k,i

Trade + Price System Input Bundle Price K (cid:32) PI (cid:33)ν k(cid:96),i PM = (cid:89) (cid:96),i (A.22) k,i ν k(cid:96),i (cid:96)=1 Domestic Sectoral Output Price (cid:18) w (cid:19)γ k,i (cid:32) PM (cid:33)1−γ k,i (cid:101)k,i k,i c = (A.23) k,i γ 1−γ k,i k,i Price of Composite Sector-Specific Intermediate Good  −1/λ N P k I ,i = Γ k,i (cid:88) (c A d k,j )λ  (A.24) j=1 k,j k,ji where Γ is a sector and country specific constant. k,i Price of Final Consumption Good K (cid:32) PI (cid:33)µ ki PF = (cid:89) k,i (A.25) i µ k,i k=1 Trade Shares A (c d )−λ k,o k,o k,oi π = , (A.26) k,oi Φ k,i where N (cid:88) Φ = A (c d )−λ. (A.27) k,i k,o k,o k,oi o=1 Zero net flows condition (cid:32) K (cid:33)K (cid:88) (L .u ) = s L u = s(cid:48)(L .u ) (A.28) i i (cid:96)k,i (cid:96),i (cid:96),i i i i (cid:96)=1 k=1 Product market clearing Gross Output (cid:90) xmax s γ Y = w L (1−u ) dG (s) (A.29) k,o k,o (cid:101)k,o k,o k,o (cid:0) (cid:1) k,o 1−G x x k,i k,o k,o = w (cid:101)k,o L(cid:101)k,o (A.30) Expenditure with Vacancies EV = κ PFθ u L (A.31) k,o k,o o k,o k,o k,o

Market Clearing System N (cid:88) Y = π E (A.32) k,o k,oi k,i i=1 (cid:32) K (cid:33) K (cid:88) (cid:88) E = µ γ Y + (1−γ )ν Y −µ NX (A.33) k,i k,i (cid:96),i (cid:96),i (cid:96),i (cid:96)k,i (cid:96),i k,i i (cid:96)=1 (cid:96)=1 Normalization: World total revenue is the numeraire N K (cid:88)(cid:88) Y = 1 (A.34) k,i i=1k=1 Final Good Consumption Expenditure K K (cid:88) (cid:88) EC = γ Y − EV −NX (A.35) i k,i k,i k,i i k=1 k=1 Lagrange multipliers L i λ(cid:101)i = EC (A.36) i

C Solution Methods This Section presents the different algorithms we developped to estimate the model and to perform counterfactual simulations. Section C.1 details the estimation algorithm and Section C.2 obtains expressions for simulated moments. Section C.3 outlines an exact hat alebra algorithm to compute changes in the steady state equilibrium in response to shocks in trade costs, productivities or net exports. Section C.4 develops the algorithm solving for the transition path of our complete model with trade imbalances. Section C.5 adapts this algorithm to the case where we have exogenous deficits. Finally, Section C.6 outlines the procedure we use in Section 5.1 to extract the shocks in trade costs, productivities and inter-temporal shocks. C.1 Estimation Algorithm (cid:16) (cid:17) Define I (x) ≡ (cid:82)xmax(s−x)dG (s). Imposing G ∼ logN 0,σ2 and a bit of algebra leads k,i x k,i k,i k,i to: (cid:16) (cid:17) (cid:136) G (x) = Φ lnx k,i σ k,i (cid:18) (cid:19) (cid:136) I (x) = exp σ k 2 ,i Φ (cid:16) σ − lnx (cid:17) −xΦ (cid:16) −lnx (cid:17) k,i 2 k,i σ σ k,i k,i (cid:18) (cid:19) (cid:136) I (0) = exp σ k 2 ,i k,i 2 (cid:18) (cid:19) (cid:136) (cid:82)xmax s dG (s) = exp (cid:18) σ k 2 ,i (cid:19) Φ σ k,i − ln σ x k k ,i ,i x k,i 1−G k,i (x k,i ) k,i 2 Φ (cid:18) − lnxk,i (cid:19) σk,i Note: The estimation procedure we describe takes trade shares πData and net exports NXData as k,oi i given. Step 1: Solve for {Y } using: k,i N K N (cid:88)(cid:88) (cid:88) Y = πData(µ γ +(1−γ )ν )Y − πDataµ NX k,o k,oi k,i (cid:96),i (cid:96),i (cid:96)k,i (cid:96),i k,oi k,i i i=1(cid:96)=1 i=1 N K (cid:88)(cid:88) Y = 1 k,o o=1k=1 The rest of the procedure conditions on these values of {Y }. k,i κ PF Step 2: Guess model parameters Ω. We treat κ ≡ k,i i as parameters to be estimated. (cid:101)k,i w (cid:101)k,i

Step 3: Define (1−(1−χ )δ)κ k,i (cid:101)k,i (cid:36) ≡ k,i δ(1−β ) k,i If (1−(1−χ k,i )δ)κ (cid:101)k,i = (cid:36) k,i ≥ 1, the free entry condition cannot be satisfied—I is decreasing. δ(1−β k,i )I k,i (0) I k,i (0) k,i Abort the procedure and highly penalize the objective function. Step 4: Find xub such that (1−(1−χ k,i )δ)κ (cid:101)k,i = 1 ⇐⇒ I (cid:16) xub (cid:17) = (cid:36) . If along the algorithm k,i δ(1−β )I (xub) k,i k,i k,i k,i k,i k,i x goes above xub, we update it to be equal to xub (minus a small number). k,i k,i k,i (cid:8) (cid:9) Step 5: Guess {L }, and x k,i k,i (cid:0) (cid:1) (cid:0) (cid:1) Step 6: Compute I x , G x , θ and u . k,i k,i k,i k,i k,i k,i (cid:18) (cid:19) (cid:136) θ = q−1 (cid:36) k,i where q−1(y) = (cid:16) 1−yξi (cid:17)1/ξi k,i i I k,i (x k,i ) i yξi (cid:136) u = χ k,i k,i θ k,i qi (θ k,i )(1−G k,i (x k,i ))+χ k,i (cid:110) (cid:111) Step 7: Compute L(cid:101)k,i (cid:90) xmax s L(cid:101)k,i ≡ L k,i (1−u k,i ) (cid:0) (cid:1) dG k,i (s) 1−G x x k,i k,i k,i (cid:16) (cid:17) = L (1−u )exp (cid:32) σ k 2 ,i (cid:33) Φ σ k,i − ln σ x k, k i ,i k,i k,i 2 (cid:16) lnx (cid:17) Φ − k,i σ k,i Step 8: Compute {w } (cid:101)k,i γ Y k,i k,i w = (cid:101)k,i L(cid:101)k,i (cid:110) (cid:111) Step 9: Compute EV k,i EV = κ w θ u L k,i (cid:101)k,i(cid:101)k,i k,i k,i k,i Step 10: Compute (cid:8) EC(cid:9) i K K (cid:88) (cid:88) EC = γ Y − EV −NX i k,i k,i k,i i k=1 k=1 (cid:110) (cid:111) Step 11: Compute λ(cid:101)i L i λ(cid:101)i = EC i Step 12: Obtain {U }. k,i

(cid:136) Step 12a: Guess (cid:8) U0(cid:9) ki (cid:136) Step 12b: Compute until convergence    Ug+1 = ζ log (cid:88) K exp   −C k(cid:96),i +b (cid:96),i +θ (cid:96),i κ (cid:101)(cid:96),i λ(cid:101)i w (cid:101)(cid:96),i(1− β (cid:96) β ,i (cid:96),i ) +δU (cid:96),i −δU k g ,i   +δUg k,i i  ζ  k,i  i  (cid:96)=1   Step 13: Update {L }. k,i (cid:136) Step 13a: Given knowledge of {U }, compute transition rates s . k,i k(cid:96),i exp (cid:40) −C k(cid:96),i +b (cid:96),i +θ (cid:96),i κ (cid:101)(cid:96),i λ(cid:101)iw (cid:101)(cid:96),i1− β(cid:96) β , (cid:96) i ,i +δU (cid:96),i (cid:41) ζi s = k(cid:96),i  β  (cid:80) −C kk,i +b k,i +θ k,i κ (cid:101)k,i λ(cid:101)iw (cid:101)k,i1− k β ,i +δU k,i  exp k,i k  ζi  (cid:136) Step 13b: Find y such that i (cid:0) I −s(cid:48)(cid:1) y = 0 i i (cid:136) Step 13c: Find allocations L k,i L u = ϕy k,i k,i k,i ⇒ L = ϕy /u k,i k,i k,i (cid:124) (cid:123)(cid:122) (cid:125) y (cid:101)k,i ⇒ L(cid:48)1 = ϕy(cid:48) 1 = L i K×1 (cid:101)k,i K×1 i L i ⇒ ϕ = y(cid:48) 1 (cid:101)k,i K×1 (L )(cid:48) = ϕy k,i (cid:101)k,i Lnew = (1−λ )L +λ (L )(cid:48) k,i L k,i L k,i (cid:8) (cid:9) Step 14: Update x . k,i Note that in equilibrium: λ(cid:101)i w (cid:101)k,i x k,i = (1−δ)U k,i −η k,i (A.37) So, we update x according to: k,i (1−δ)U −η (cid:0) (cid:1)(cid:48) k,i k,i x = k,i λ(cid:101)i w (cid:101)k,i (cid:110) (cid:111) xnew = min (1−λ )x +λ (cid:0) x (cid:1)(cid:48) ,xub k,i x k,i x k,i k,i

(cid:13)(cid:110) (cid:111)(cid:13) (cid:13)(cid:110) (cid:111)(cid:13) Step15: ArmedwithLnew andxnew gotoStep6until(cid:13) Lnew −L (cid:13) → 0and(cid:13) xnew −x (cid:13) → k,i k,i (cid:13) k,i k,i (cid:13) (cid:13) k,i k,i (cid:13) 0. (cid:13)(cid:110) (cid:111)(cid:13) Note that (cid:13) xnew −x (cid:13) → 0 does not imply that (A.37) is satisfied. Therefore, we penalize (cid:13) k,i k,i (cid:13) deviations from (A.37) in the objective function. Step 16: Generate moments, compute Loss Function, guess new parameter set Ω and go to Step 3, until objective function is minimized. Note: Given that we condition on the trade shares πData, we can estimate the model country by k,oi country, separately. However, in practice, we will first estimate the model for the US and obtain all of the US specific parameters. Next, armed with US-specific mobility costs C and sector-specific kk(cid:48) exogenousexitcomponentsχ (wewillimposeχ = χ +χ ), weestimatetheremainingcountries’ k k,i i k parameters separately, in parallel. C.2 Expressions for Simulated Moments C.2.1 Employment Shares L (1−u ) k,i k,i emp = k,i K (cid:80) L (1−u ) k,i k,i k=1 C.2.2 National Unemployment Rate K (cid:80) L u k,i k,i unemp = k=1 i K (cid:80) L k,i k=1 C.2.3 Sector-Specific Average Wages w (x) = (1−β )w x +β w x k,i k,i (cid:101)k,i k,i k,i(cid:101)k,i (cid:82)xmaxw (s)dG (s) x k,i k,i w = k,i k,i (cid:0) (cid:1) 1−G x k,i k,i (cid:90) xmax s = (1−β )w x +β w dG (s) k,i (cid:101)k,i k,i k,i(cid:101)k,i (cid:0) (cid:1) k,i 1−G x x k,i k,i k,i (cid:16) (cid:17) = (1−β )w x +β w exp (cid:32) σ k 2 ,i (cid:33) Φ σ k,i − ln σ x k, k i ,i k,i (cid:101)k,i k,i k,i(cid:101)k,i 2 (cid:16) lnx (cid:17) Φ − k,i σ k,i

C.2.4 Sector-Specific Variance of Wages (cid:82)∞ (w (s)−w )2dG (s) x k,i k,i k,i σ2 = k,i w,k,i 1−G (cid:0) x (cid:1) k,i k,i  (cid:18) (cid:19)2 (cid:82) x ∞ k,i s−exp (cid:18) σ k 2 2 ,i (cid:19) Φ Φ σ (cid:18) k − ,i − ln l x n σ k x k ,i k ,i (cid:19) ,i  dG k,i (s) = (β w )2× σk,i k,i(cid:101)k,i (cid:0) (cid:1) 1−G x k,i k,i  (cid:16) lnx (cid:17)  (cid:16) lnx (cid:17)2 Φ 2σ − k,i Φ σ − k,i = (β k,i w (cid:101)k,i )2×  exp (cid:0) 2σ k 2 ,i (cid:1) (cid:16) k,i lnx σ k (cid:17) ,i −exp (cid:0) σ k 2 ,i (cid:1)  (cid:16) k,i lnx σ k, (cid:17) i    Φ − k,i Φ − k,i σ σ k,i k,i C.2.5 Transition Rates Note that the transition rates in equation (10) are transitions from unemployment in sector k to search in sector k(cid:48) within period t. There are no data counterfactuals for this variable. However, we can construct a matrix with transition rates between all possible (model) states between time t and time t+N (where N is even)—where variables are measured at the t stage (which is the a production stage). From this matrix, we can obtain N-period transition rates between all states observed in the data (employment in each of the sectors and unconditional unemployment). First, we obtain the one-year transition matrix st,t+1 between states {u ,...,u ,1,...,K}. Here, we abuse (cid:101) (cid:101)1 (cid:101)K notation to mean u as sector-k unemployment at the very beginning of a period. (cid:101)k The one-year transition rate between sector-(cid:96) unemployment and sector-k unemployment is given by: (cid:16) (cid:16) (cid:16) (cid:17)(cid:17)(cid:17) st,t+1 = st,t+1 1−θt q (cid:0) θt (cid:1) 1−G xt+1 , (A.38) (cid:101)u u ,i (cid:96)k,i k,i i k,i k,i k,i (cid:101)(cid:96)(cid:101)k thatis,asharest ofindividualsstartingperiodtunemployedinsector(cid:96)choosetosearchinsector (cid:96)k,i (cid:16) (cid:16) (cid:17)(cid:16) (cid:16) (cid:17)(cid:17)(cid:17) k. A fraction 1−θt q θt 1−G xt+1 of those do not find a match that survives k,i i k,i k,i k,i until t + 1. Similarly, the one-year transition rate between sector-(cid:96) unemployment and sector-k employment is given by: (cid:16) (cid:16) (cid:17)(cid:17) st,t+1 = st,t+1θt q (cid:0) θt (cid:1) 1−G xt+1 (cid:101)u k,i (cid:96)k,i k,i i k,i k,i k,i (cid:101)(cid:96) = st,t+1−st,t+1 . (A.39) (cid:96)k,i (cid:101)u u ,i (cid:101)(cid:96)(cid:101)k According to the timing assumptions of the model, the one-year transition rate between employment in sector k and employment in sector k(cid:48) is zero if k (cid:54)= k(cid:48). However, the persistence rate of employment in sector k is given by the probability that a match does not receive a death shock timesthe probabilitythat thematch isnotdissolvedbecausethe thresholdforproductionincreases in the following period: (cid:40) 0 if k (cid:54)= k(cid:48) st,t+1 = (cid:16) (cid:17) . (A.40) (cid:101)kk(cid:48),i (1−χ )Pr x ≥ xt+1|x ≥ xt if k = k(cid:48) k,i k,i k,i Finally, the one-year transition rate between sector-k employment and unemployment in sector (cid:96)

is given by: (cid:40) 0 if k (cid:54)= (cid:96) st,t+1 = (cid:16) (cid:17) . (A.41) (cid:101)ku (cid:101)(cid:96) ,i χ k,i +(1−χ k,i )Pr x < xt k + ,i 1|x ≥ xt k,i if k = (cid:96) That is, if a worker is employed in sector k at t, she cannot start next period unemployed in sector (cid:96) if k (cid:54)= (cid:96). Otherwise, workers transition between sector k employment to sector k unemployment if their match is hit with a death shock or if their employer’s productivity goes below the threshold for production at t+1. We can now write the N-period transition matrix as: st,t+N = st+k−1,t+k ×...×st+1,t+2×st,t+1, (A.42) (cid:101) (cid:101) (cid:101) (cid:101) and we can write transition rates between unemployment u and sector-k employment between t (cid:101) and t+N as: K (cid:80) Lt−1ut−1st,t+N (cid:96),i (cid:101)(cid:96),i (cid:101)u ,k (cid:101)(cid:96) st,t+N = (cid:96)=1 . (A.43) (cid:101)u (cid:101) ,k,i (cid:80) K Lt−1ut−1 (cid:96),i (cid:101)(cid:96),i (cid:96)=1 Finally, we can write transition rates between sector-k employment and unemployment u as: (cid:101) K st,t+N = 1− (cid:88) st,t+N. (A.44) (cid:101)k,u,i (cid:101)k,k(cid:48),i (cid:101) k(cid:48)=1 1-period transition rates (cid:0) (cid:0) (cid:0) (cid:1)(cid:1)(cid:1) s = s 1−θ q (θ ) 1−G x (cid:101)u (cid:101)(cid:96) u (cid:101)k ,i (cid:96)k,i k,i i k,i k,i k,i (cid:0) (cid:0) (cid:1)(cid:1) s = s θ q (θ ) 1−G x (cid:101)u (cid:101)(cid:96) k,i (cid:96)k,i k,i i k,i k,i k,i (cid:26) 0 if (cid:96) (cid:54)= k s = (cid:101)(cid:96)k,i (1−χ ) if (cid:96) = k (cid:96),i (cid:26) 0 if (cid:96) (cid:54)= k s = (cid:101)(cid:96)u (cid:101)k ,i χ if (cid:96) = k k,i N-period transition rates from and to unconditional unemployment: sN (cid:101) K (cid:80) L u sN (cid:96),i (cid:96),i(cid:101)u ,k,i (cid:101)(cid:96) sN = (cid:96)=1 (cid:101)u (cid:101) ,k,i K (cid:80) L u (cid:96),i (cid:96),i (cid:96)=1 K (cid:88) sN = 1− sN . (cid:101)k,u,i (cid:101)k,(cid:96),i (cid:101) (cid:96)=1

C.3 Algorithm: Steady-State Equilibrium Following Shock (cid:110) (cid:111) (cid:110) (cid:111) (cid:110) (cid:111) (cid:110) (cid:111) Consider shocks A0 → A1 , d0 → d1 , (cid:8) NX0(cid:9) → (cid:8) NX1(cid:9) k,i k,i k,oi k,oi i We will be using 0 superscripts to denote the initial steady state, and 1 superscripts to denote the final steady state. (cid:110) (cid:111) (cid:110) (cid:111) (cid:110) (cid:111) (cid:110) (cid:111) Start from estimated Steady State: L0 , x0 , w0 , π0 k,i k,i (cid:101)k,i k,oi Note that π0 = πData k,oi k,oi We also have κ0 = κ k,i P i F,0 , but we do not know (cid:110) PF,0 (cid:111) (cid:101)k,i w0 i (cid:101)k,i Denote relative changes in variable a by a = a1 (cid:98) a0 (cid:110) (cid:111) (cid:110) (cid:111) Step 1: Guess L1 and x1 k,i k,i (cid:110) (cid:111) Step 2: Guess w1 (cid:101)k,i (cid:136) Step 2a: Compute w(cid:98) (cid:101)k,i = w w (cid:101)k 1 0 ,i and iteratively solve for P(cid:98) k I ,i and (cid:98) c k,i using the system (cid:101)k,i (cid:98) c k,i = (cid:16) w(cid:98) (cid:101)k,i (cid:17)γ k,i(cid:89) K (cid:16) P(cid:98) (cid:96) I ,i (cid:17)(1−γ k,i )ν k(cid:96),i (cid:96)=1 (cid:32) N (cid:33)−1/λ (cid:88) (cid:16) (cid:17)−λ P(cid:98) k I ,i = π k 0 ,oi A(cid:98)k,o (cid:98) c k,o d(cid:98)k,oi o=1 (cid:136) Step 2b: Compute P(cid:98) F : k,i K P(cid:98) F = (cid:89)(cid:16) P(cid:98) I (cid:17)µ ki i k,i k=1 (cid:136) Step 2c: Compute π : (cid:98)k,oi (cid:32) (cid:33)−λ (cid:98) c k,o d(cid:98)k,oi π (cid:98)k,oi = A(cid:98)k,o P(cid:98) I k,i (cid:136) Step 2d: Compute

– π1 = π0 π k,oi k,oi(cid:98)k,oi – κ1 ≡ κ k,i P i F,1 = κ k,i P i F,0P i F,1w (cid:101)k 0 ,i = κ0 P(cid:98)i F (cid:101)k,i w (cid:101)k 1 ,i w (cid:101)k 0 ,i P i F,0w (cid:101)k 1 ,i (cid:101)k,iw(cid:98)(cid:101)k,i Step 3: If κ1 × 1−δ(1−χ k,i ) ≥ 1 abort, set x1 such that κ1 × 1−δ(1−χ k,i ) = 1−ε and (cid:101)k,i δ(1−β )I (x1 ) k,i (cid:101)k,i δ(1−β )I (x1 ) k,i k,i k,i k,i k,i k,i go back to Step 1 with this new guess. If κ1 × 1−δ(1−χ k,i ) < 1, proceed to Step 4. (cid:101)k,i δ(1−β )I (x1 ) k,i k,i k,i Step 4: Compute 1−δ(1−χ ) q (cid:0) θ1 (cid:1) = κ1 × k,i i k,i (cid:101)k,i (cid:16) (cid:17) δ(1−β )I x1 k,i k,i k,i   1−δ(1−χ ) θ k 1 ,i = q i −1 κ (cid:101) 1 k,i × (cid:16) k,i (cid:17) δ(1−β )I x1 k,i k,i k,i χ u1 = k,i k,i (cid:16) (cid:17)(cid:16) (cid:16) (cid:17)(cid:17) θ1 q θ1 1−G x1 +χ k,i i k,i k,i k,i k,i (cid:110) (cid:111) Step 5: Solve system in Y1 k,o N (cid:32) (cid:32) K (cid:33) K (cid:33) N (cid:88) (cid:88) (cid:88) (cid:88) Y1 = π1 µ γ Y1 + (1−γ )ν Y1 − π1 µ NX1 k,o k,oi k,i (cid:96),i (cid:96),i (cid:96),i (cid:96)k,i (cid:96),i k,oi k,i i i=1 (cid:96)=1 (cid:96)=1 i=1 N K (cid:88)(cid:88) Y1 = 1 k,i i=1k=1 (cid:110) (cid:111) Step 6: Compute L(cid:101) 1 k,i L(cid:101) 1 k,i ≡ L1 k,i (cid:0) 1−u1 k,i (cid:1) (cid:90) xmax s (cid:16) (cid:17) dG k,i (s) x1 1−G x1 k,i k,i k,i (cid:18) (cid:19) lnx1 (cid:32) (cid:33) Φ σ − k,i σ2 k,i σ = L1 (cid:0) 1−u1 (cid:1) exp k,i k,i k,i k,i 2 (cid:18) lnx1 (cid:19) Φ − k,i σ k,i (cid:110) (cid:111) Step 7: Update w1 (cid:101)k,i γ Y1 (cid:0) w1 (cid:1)new = k,i k,i (cid:101)k,i L(cid:101) 1 k,i (cid:110) (cid:111) Go back to Step 2a and repeat until converegence of w1 . (cid:101)k,i

Step 8: Compute EV,1 = κ1 w1 θ1 u1 L1 k,i (cid:101)k,i(cid:101)k,i k,i k,i k,i K K EC,1 = (cid:88) γ Y1 − (cid:88) EV,1−NX1 i k,i k,i k,i i k=1 k=1 Step 9: Obtain Lagrange Multipliers L λ(cid:101) 1 = i i EC,1 i Step 10: Compute Bellman Equations    U1 = ζ log (cid:88) exp   −C kk(cid:48),i +b k(cid:48),i +θ k 1 (cid:48),i κ (cid:101) 1 k(cid:48),i λ(cid:101) 1 i w (cid:101)k 1 (cid:48),i(1− β k β (cid:48) k ,i (cid:48),i ) +δU k 1 (cid:48),i    k,i i  ζ   i  k(cid:48)   (cid:110) (cid:111) Step 11: Update L1 . k,i (cid:110) (cid:111) (cid:136) Step 11a: Given knowledge of U1 , compute transition rates s1 . k,i k(cid:96),i   exp −C k(cid:96),i +b (cid:96),i +θ (cid:96) 1 ,i κ (cid:101) 1 (cid:96),i λ(cid:101)1 i w (cid:101)(cid:96) 1 ,i(1− β(cid:96) β , (cid:96) i ,i ) +δU (cid:96) 1 ,i  ζi  s1 = k(cid:96),i  β  (cid:80) exp   −C kk,i +b k,i +θ k 1 ,i κ (cid:101) 1 k,i λ(cid:101)1 i w (cid:101)k 1 ,i (cid:18) 1− k β , k i ,i (cid:19)+δU k 1 ,i   k   ζi   (cid:136) Step 11b: Find y such that i (cid:16) (cid:17) I − (cid:0) s1(cid:1)T y = 0 i i (cid:136) Step 11c: Find allocations L k,i L1 u1 = ϕy k,i k,i k,i ⇒ L1 = ϕy /u1 k,i k,i k,i (cid:124) (cid:123)(cid:122) (cid:125) y (cid:101)k,i ⇒ (cid:0) L1(cid:1)T 1 = ϕyT 1 = L i K×1 (cid:101)k,i K×1 i L i ⇒ ϕ = yT 1 (cid:101)k,i K×1

(cid:0) L1 (cid:1)(cid:48) = ϕy k,i (cid:101)k,i (cid:0) L1 (cid:1)new = (1−λ )L1 +λ (cid:0) L1 (cid:1)(cid:48) k,i L k,i L k,i (cid:110) (cid:111) Step 12: Update x1 . k,i Note that in equilibrium: λ(cid:101) 1 i w (cid:101)k 1 ,i x1 k,i = (1−δ)U k 1 ,i −η k,i So, we update x1 according to: k,i (1−δ)U1 −η (cid:0) x1 (cid:1)(cid:48) = k,i k,i k,i λ(cid:101)1 i w (cid:101)k 1 ,i (cid:110) (cid:111) (cid:0) x1 (cid:1)new = min (1−λ )x1 +λ (cid:0) x1 (cid:1)(cid:48) ,xub k,i x k,i x k,i k,i (cid:16) (cid:17)new (cid:16) (cid:17)new (cid:13)(cid:110)(cid:16) (cid:17)new (cid:111)(cid:13) Step 13: Armed with L1 and x1 go to Step 2 until (cid:13) L1 −L1 (cid:13) → 0 and k,i k,i (cid:13) k,i k,i (cid:13) (cid:13)(cid:110)(cid:16) (cid:17)new (cid:111)(cid:13) (cid:13) x1 −x1 (cid:13) → 0. (cid:13) k,i k,i (cid:13)

C.4 Algorithm: Out-of-Steady-State Transition (cid:110) (cid:111) Inner Loop: conditional on paths for expenditures EC,t —determined in the Outer Loop i below. Consider paths (cid:110) At (cid:111)TSS and (cid:110) dt (cid:111)TSS with A0 = 1 and d0 = 1. Also, consider paths k,i o,i,k k,i o,i,k t=0 t=0 (cid:8) φt i (cid:9)T t= S 0 S with φ0 i = 1 and φ(cid:98) t i = 1 for T ≤ t ≤ T SS , for some T << T SS . (cid:110) (cid:111) (cid:110) (cid:111) Step 0: Given paths EC,t , compute paths λ(cid:101) t : λ(cid:101) t = Li i i i EC,t i Step 1: Guess paths (cid:110) wt (cid:111)TSS for each sector k and country i. (cid:101)k,i t=1 Step 2: Compute xT k, S i S consistent with w (cid:101)k T , S i S and λ(cid:101) T i SS. Obtain θ k T , S i S, U k T , S i S, s k T (cid:96) S , S i ,TSS+1 and π k T , S o S i . (cid:136) Step 2a: Compute w(cid:98) (cid:101)k,i = w (cid:101) w k T 0 , S i S , A(cid:98)k,i = A A T k 0 , S i S and d(cid:98)k,i = d d 0 T o, S i, S k. Iteratively solve for P(cid:98) k I ,i and (cid:101)k,i k,i o,i,k c using the system (cid:98)k,i (cid:98) c k,i = (cid:16) w(cid:98) (cid:101)k,i (cid:17)γ k,i(cid:89) K (cid:16) P(cid:98) (cid:96) I ,i (cid:17)(1−γ k,i )ν k(cid:96),i (cid:96)=1 (cid:32) N (cid:33)−1/λ (cid:88) (cid:16) (cid:17)−λ P(cid:98) k I ,i = π k 0 ,oi A(cid:98)k,o (cid:98) c k,o d(cid:98)k,oi o=1 (cid:136) Step 2b: Compute P(cid:98) F : k,i K P(cid:98) F = (cid:89)(cid:16) P(cid:98) I (cid:17)µ ki i k,i k=1 (cid:136) Step 2c: Compute (cid:32) (cid:33)−λ (cid:98) c k,o d(cid:98)k,oi π (cid:98)k,oi = A(cid:98)k,o P(cid:98) I k,i And obtain πTSS = π0 π k,oi k,oi(cid:98)k,oi (cid:136) Step 2d: Compute – κTSS = κ0 P(cid:98)i F (cid:101)k,i (cid:101)k,iw(cid:98)(cid:101)k,i (cid:110) (cid:111) (cid:136) Step 2e: Guess xTSS k,i (cid:136) Step 2f: Compute   1−δ(1−χ ) θ k T , S i S = q i −1 κ (cid:101) T k, S i S × δ(1−β )I (cid:16) k x ,i TSS (cid:17) k,i k,i k,i

(cid:136) Step 2g: Compute Bellman Equations    UTSS = ζ log (cid:88) exp   −C kk(cid:48),i +b k(cid:48),i +θ k T (cid:48) S ,i Sκ (cid:101) T k(cid:48) S ,i Sλ(cid:101) T i SSw (cid:101)k T (cid:48) S ,i S (1− β k β (cid:48) k ,i (cid:48),i ) +δU k T (cid:48) S ,i S   k,i i  ζ   i  k(cid:48)   (cid:136) Step 2h: Compute (cid:16) xTSS (cid:17)(cid:48) = (1−δ)U k T , S i S −η k,i k,i λ(cid:101) T i SSw (cid:101)k T , S i S (cid:16) (cid:17)(cid:48) (cid:136) Step 2i: Update xTSS = (1−λ )xTSS +λ xTSS , for a small step size λ , and go back to k,i x k,i x k,i x Step 2d until convergence. (cid:136) Step 2j: Compute sTSS,TSS+1 kk(cid:48) exp (cid:40) −C k(cid:96),i +b (cid:96),i +θ (cid:96) T , S i Sκ (cid:101) T (cid:96), S i Sλ(cid:101) T i SSw (cid:101)(cid:96) T , S i S 1− β(cid:96) β , (cid:96) i ,i +δU (cid:96) T , S i S (cid:41) ζi sTSS,TSS+1 = k(cid:96),i (cid:80) exp  −C kk,i +b k,i +θ k T , S i Sκ (cid:101) T k, S i Sλ(cid:101) T i SSw (cid:101)k T , S i S 1− β k β , k i ,i +δU k T , S i S   k  ζi  Step 3: Obtain series (cid:110) πt (cid:111)TSS , (cid:110) κt (cid:111)TSS . Define xt ≡ xt . k,oi (cid:101)k,i (cid:98) x0 t=0 t=0 (cid:136) Step 3a: For t = 1,...,T SS −1 compute w(cid:98) (cid:101) t k,i = w w (cid:101)k t 0 ,i and iteratively solve for P(cid:98) k I , , i t and (cid:98) ct k,i using (cid:101)k,i the system (cid:98) ct k,i = (cid:16) w(cid:98) (cid:101) t k,i (cid:17)γ k,i(cid:89) K (cid:16) P(cid:98) (cid:96) I , , i t (cid:17)(1−γ k,i )ν k(cid:96),i (cid:96)=1 (cid:32) N (cid:33)−1/λ P(cid:98) k I , , i t = (cid:88) π k 0 ,oi A(cid:98) t k,o (cid:16) (cid:98) ct k,o d(cid:98) t k,oi (cid:17)−λ o=1 (cid:136) Step 3b: Compute P(cid:98) k F ,i ,t for t = 1,...,T SS −1: K P(cid:98) F,t = (cid:89)(cid:16) P(cid:98) I,t (cid:17)µ ki i k,i k=1 (cid:136) Step 3c: Compute πt for t = 1,...,T −1: (cid:98)k,oi SS (cid:32) (cid:33)−λ π (cid:98)k t ,oi = A(cid:98) t k,o (cid:98) ct k P , (cid:98) o d I (cid:98) , t k t ,oi k,i (cid:136) Step 3d: Compute or t = 1,...,T −1: SS

– πt = π0 πt k,oi k,oi(cid:98)k,oi – κt ≡ κ k,i P i F,t = κ k,i P i F,0 P i F,t w (cid:101)k 0 ,i = κ0 P(cid:98) i F,t (cid:101)k,i w (cid:101)k t ,i w (cid:101)k 0 ,i P i F,0w (cid:101)k t ,i (cid:101)k,i w(cid:98)(cid:101) t k,i Step 4: Given knowledge of w (cid:101)k T , S i S, λ(cid:101) T i SS and xT k, S i S (and therefore J k T , S i S (s)), start at t = T SS −1 and sequentially compute (backwards) for each t = T −1,...,1 SS (cid:136) Step 4a: Given w (cid:101)k t ,i , xt k + ,i 1, κ (cid:101) t k,i , λ(cid:101) t i and J k t+ ,i 1(s) compute θ k t ,i . If λ(cid:101)t i κ (cid:101) t k,i w (cid:101)k t ,i ≤ 1 then δφ(cid:98) t i +1(cid:82) x x t m + a 1 xJ k t+ ,i 1(s)dG k,i (s) k,i   θt = q−1  λ(cid:101) t i κ (cid:101) t k,i w (cid:101)k t ,i  k,i i δφ(cid:98) t i +1(cid:82) x x t m + a 1 xJ k t+ ,i 1(s)dG k,i (s) k,i If λ(cid:101)t i κ (cid:101) t k,i w (cid:101)k t ,i > 1, it is not possible to satisfy Vt = 0, so that Vt < 0 and δφ(cid:98) t i +1(cid:82) x x t m + a 1 xJ k t+ ,i 1(s)dG k,i (s) k,i k,i k,i θt = 0. k,i (cid:136) Step4b: Givenxt+1,Wt+1(x) = β k,i Jt+1(x)+Ut+1 (forx ≥ xt+1),θt ,Ut+1 computeUt . k,i k,i 1−β k,i k,i k,i k,i k,i k,i k,i (cid:16) (cid:16) (cid:17)(cid:17) Noticethat (cid:82)xmaxWt+1(s)dG (s) = β k,i (cid:82)xmaxJt+1(s)dG (s)+ 1−G xt+1 Ut+1 xt k + ,i 1 k,i k,i 1−β k,i xt k + ,i 1 k,i k,i k,i k,i k,i so that:    −C +b  kk(cid:48),i k(cid:48),i  Ut = ζ log    (cid:88) exp      +δφ(cid:98) t i +1θ k t (cid:48),i q i (cid:16) θ k t (cid:48),i (cid:17) 1− β k β , k i ,i (cid:82) x x t k m + ,i a 1 xJ k t+ ,i 1(s)dG k,i (s)+δφ(cid:98) t i +1U k t+ (cid:48),i 1         k,i i  ζ    i   k(cid:48)           (cid:136) Step 4c: Given Jt+1(x), wt , Ut , Ut+1 and xt+1 compute Jt (x) k,i (cid:101)k,i k,i k,i k,i k,i J k t ,i (x) = (1−β k,i )λ(cid:101) t i w (cid:101)k t ,i x+(1−β k,i )η k,i (cid:16) (cid:17) (cid:110) (cid:111) −(1−β k,i ) U k t ,i −δφ(cid:98) t i +1U k t+ ,i 1 +(1−χ k,i )δφ(cid:98) t i +1max J k t+ ,i 1(x),0 (cid:16) (cid:17) (cid:136) Step 4d: Solve for xt : Jt xt = 0 k,i k,i k,i Step 5: Compute transition rates (cid:110) st,t+1 (cid:111)TSS−1 for all countries i according to: kk(cid:48),i t=1 (cid:40) (cid:41) −C +b + kk(cid:48),i k(cid:48),i st,t+1 = exp δφ(cid:98) t i +1θ k t (cid:48),i q(θ k t (cid:48),i ) 1− β k β (cid:48) k ,i (cid:48),i (cid:82) x x t k m + (cid:48), a 1 i xJ k t+ (cid:48),i 1(x)dG k(cid:48),i (x)+δφ(cid:98) t i +1U k t+ (cid:48),i 1 . kk(cid:48),i (cid:40) −C +b + (cid:41) (cid:80) kk(cid:48)(cid:48),i k(cid:48)(cid:48),i k(cid:48)(cid:48) exp δφ(cid:98) t i +1θ k t (cid:48)(cid:48),i q(θ k t (cid:48)(cid:48),i ) 1− β k β (cid:48) k (cid:48), (cid:48) i (cid:48),i (cid:82) x x t k m + (cid:48)(cid:48) a 1 ,i xJ k t+ (cid:48)(cid:48), 1 i (x)dG k(cid:48)(cid:48),i (x)+δφ(cid:98) t i +1U k t+ (cid:48)(cid:48), 1 i

Step 6: Start loop over t going forward (t = 0 to t = T −1) SS Initial conditions: we know ut=−1 = ut=0, Lt=−1 = Lt=0, and θt=0 from the initial steady state (cid:101)k,i k,i k,i k,i k,i (cid:110) (cid:111) (cid:110) (cid:111) computation. Obtain ut and Lt using flow conditions and sequences θt , xt . (cid:101)k,i k,i k,i k,i (cid:136) Step 6a: Compute (cid:16) (cid:16) (cid:17)(cid:17) JCt = Lt ut θt q (cid:0) θt (cid:1) 1−G xt+1 k,i k,i k,i k,i i k,i k,i k,i   (cid:16) (cid:17) (cid:16) (cid:17)  G xt+1 −G xt  k,i k,i k,i k,i  (cid:16) (cid:17) JD k t ,i = χ k,i +(1−χ k,i )max (cid:16) (cid:17) ,0 Lt k − ,i 1 1−u (cid:101) t k − ,i 1  1−G xt  k,i k,i Lt ut −JCt +JDt ut = k,i k,i k,i k,i (cid:101)k,i Lt k,i (cid:136) Step 6b: Compute Lt+1 = Lt +IFt+1−OFt+1, k,i k,i k,i k,i where IFt+1 = (cid:88) Lt ut st+1,t+2, k,i (cid:96),i(cid:101)(cid:96),i (cid:96)k,i (cid:96)(cid:54)=k and (cid:16) (cid:17) OFt+1 = Lt ut 1−st+1,t+2 . k,i k,i(cid:101)k,i kk,i (cid:136) Step 6c: Compute K (cid:80) Lt ut st+1,t+2 (cid:96),i(cid:101)(cid:96),i (cid:96)k,i ut+1 = (cid:96)=1 k,i Lt+1 k,i (cid:136) Step 6d: Compute L(cid:101) t k + ,i 1 = Lt k,i (cid:0) 1−u (cid:101) t k,i (cid:1) (cid:90) ∞ s (cid:16) (cid:17) dG k,i (s) xt+1 1−G xt+1 k,i k,i k,i (cid:18) (cid:19) lnxt+1 (cid:32) (cid:33) Φ σ − k,i σ2 k,i σ = Lt (cid:0) 1−ut (cid:1) exp k,i k,i k,i (cid:101)k,i 2 (cid:18) lnxt+1 (cid:19) Φ − k,i σ k,i (cid:136) Step 6e: Compute expenditure with vacancies EV,t+1 = κt+1wt+1θt+1ut+1Lt+1 k,i (cid:101)k,i (cid:101)k,i k,i k,i k,i

(cid:110) (cid:111) (cid:136) Step 6f: Solve for Yt+1 in the system k,i K Et+1 = µ EC,t+1+ (cid:88)(cid:16) µ EV,t+1+(1−γ )ν Yt+1 (cid:17) . k,i k,i i k,i (cid:96),i (cid:96),i (cid:96)k,i (cid:96),i (cid:96)=1 N (cid:88) Yt+1 = πt+1Et+1. k,o k,oi k,i i=1 (cid:136) Step 6g: Compute (cid:16) wt+1 (cid:17)(cid:48) = γ k,i Y k t , + i 1 (cid:101)k,i L(cid:101) t+1 k,i (cid:18) (cid:26) (cid:27)(cid:19) (cid:110) (cid:111) (cid:16) (cid:17)(cid:48) Step 7: Compute distance dist wt , wt (cid:101)k,i (cid:101)k,i (cid:16) (cid:17)(cid:48) (cid:136) Step 7b: Update wt = (1−λ )wt +λ wt t = 1,...,T , for a small step size λ . (cid:101)k,i w (cid:101)k,i w (cid:101)k,i SS w (cid:110) (cid:111) (cid:136) Step 7c: At this point, we have a new series for wt – go back to Step 2 until convergence (cid:101)k,i (cid:110) (cid:111) of wt . (cid:101)k,i Step 8: Compute disposable income (cid:8) It(cid:9)TSS i t=1 K It = (cid:88)(cid:16) γ Yt −EV,t (cid:17) i (cid:96),i (cid:96),i (cid:96),i (cid:96)=1 Outer Loop: iteration on (cid:8) NXt(cid:9) i Step 0: Impose a change in a subset of parameters that happens at t = 0, but between t and t . c d That is, the shock occurs after production, workers’ decisions of where to search and after firms post vacancies at t = 0. Impose a large value for T . Assume that for t ≥ T the system will SS SS I have converged to a new steady state. World expenditure with final goods (cid:80) EC,t is normalized i i=1 to 1 for every t. Step 1:Startwithestimatedstateequilibriumatt = 0. Rememberthatweusedthenormalization I K I K (cid:80) (cid:80) (cid:80) (cid:80) Y = 1 during the estimation procedure. Change the normalization from Y = 1 k,i k,i i=1k=1 i=1k=1 I (cid:110) (cid:111) (cid:110) (cid:111) (cid:110) (cid:111) to (cid:80) EC = 1. Nominal variables to be renormalized: Y0 , w0 , EC,0 , (cid:8) NX0(cid:9) . i k,i (cid:101)k,i i i i=1 I Step 2: Obtain B0 with respect to the normalization (cid:80) EC = 1. Equation (37) gives us: i i i=1 NX0 B0 = i i (cid:0) 1− 1(cid:1) δ

I Step 3: Make initial guess for NXTSS (with respect to the normalization (cid:80) EC = 1). i i i=1 Step 4: Compute steady state equilibrium at T , conditional on NXTSS, and the change in SS i parameter values. I K (cid:136) Step 4a: Notice that the steady-state algorithm uses the normalization (cid:80) (cid:80) Y = 1. Nork,i i=1k=1 I K malize NXTSS with respect to normalization (cid:80) (cid:80) Y = 1. To perform such normalization, i k,i i=1k=1 (cid:110) (cid:111) use revenue YTSS obtained in the initial steady state if this is the first outer loop iteration, k,i (cid:110) (cid:111) otherwise use revenue YTSS obtained in Step 6 below. k,i I K (cid:136) Step4b: Aftercomputingthefinalsteadystate,changethenormalizationfrom (cid:80) (cid:80) Y = k,i i=1k=1 I 1 to (cid:80) EC = 1 using (cid:8) EC(cid:9) obtained in Step 3a. Nominal variables to be renormalized: i i i=1 (cid:110) (cid:111) (cid:110) (cid:111) (cid:110) (cid:111) (cid:110) (cid:111) YTSS , wTSS , EC,TSS , NXTSS . k,i (cid:101)k,i i i Step 5: Start at t = T −1 and go backward until t = 1 and sequentially compute: SS (cid:80)N EC,t+1 Rt+1 = 1 i=1 φ(cid:98) i t i +1 = 1 (cid:88) N E i C,t+1 , δ (cid:80)N EC,t δ φ(cid:98) t+1 i=1 i i=1 i EC,t+1 EC,t = i i δφ(cid:98) t+1Rt+1 i (cid:110) (cid:111) to obtain paths for (cid:8) Rt(cid:9) and EC,t . Note that, because B1 is decided at t = 0, before the shock, i i R1 = R0 = 1. δ (cid:110) (cid:111) Step 6: Solve for the out-of-steady-state dynamics conditional on aggregate expenditures EC,t . i Step 7: Usingthepathfordisposableincome (cid:8) It(cid:9)TSS obtainedinStep6andequation(7)compute: i t=1 (cid:0) NXt(cid:1)(cid:48) = It−EC,t for 1 ≤ t < T i i SS (cid:16) NXTSS (cid:17)(cid:48) = − 1−δ 1 (cid:32) B0+ TS(cid:88)S−1(cid:32) (cid:89) t (Rτ)−1 (cid:33) (cid:0) NXt(cid:1)(cid:48) (cid:33) i δ (cid:32)TS(cid:89)S−1 (Rτ)−1 (cid:33) i t=1 τ=1 i τ=1 Step 8: Compute (cid:18) (cid:26) (cid:27)(cid:19) (cid:110) (cid:111) (cid:16) (cid:17)(cid:48) dist NXTSS , NXTSS i i

Step 9: Update NXTSS i (cid:16) (cid:17)(cid:48) NXTSS = (1−λ )NXTSS +λ NXTSS , i o i o i (cid:110) (cid:111) for a small step size λ Go back to Step 4 until convergence of NXTSS . o i

C.5 Algorithm: Out-of-Steady-StateTransition, ExogenousDeficits(NoBonds) Consider paths (cid:110) At (cid:111)TSS and (cid:110) dt (cid:111)TSS with A0 = 1 and d0 = 1. Also, consider paths k,i o,i,k k,i o,i,k t=0 t=0 (cid:8) φt i (cid:9)T t= S 0 S with φ0 i = 1 and φ(cid:98) t i = 1 for T ≤ t ≤ T SS , for some T << T SS . We condition on an exogenous path for (cid:8) NXt(cid:9)TSS. i t=1 Step 1: Guess paths (cid:110) λ(cid:101) t (cid:111)TSS for each country i. i t=1 Step 2: Guess paths (cid:110) wt (cid:111)TSS for each sector k and country i. (cid:101)k,i t=1 Step 3: Compute xT k, S i S consistent with w (cid:101)k T , S i S and λ(cid:101) T i SS. Obtain θ k T , S i S, U k T , S i S, s k T (cid:96) S , S i ,TSS+1 and π k T , S o S i . (cid:136) Step 3a: Compute w(cid:98) (cid:101)k,i = w (cid:101) w k T 0 , S i S , A(cid:98)k,i = A A T k 0 , S i S and d(cid:98)k,i = d d 0 T o, S i, S k. Iteratively solve for P(cid:98) k I ,i and (cid:101)k,i k,i o,i,k c using the system (cid:98)k,i (cid:98) c k,i = (cid:16) w(cid:98) (cid:101)k,i (cid:17)γ k,i(cid:89) K (cid:16) P(cid:98) (cid:96) I ,i (cid:17)(1−γ k,i )ν k(cid:96),i (cid:96)=1 (cid:32) N (cid:33)−1/λ (cid:88) (cid:16) (cid:17)−λ P(cid:98) k I ,i = π k 0 ,oi A(cid:98)k,o (cid:98) c k,o d(cid:98)k,oi o=1 (cid:136) Step 3b: Compute P(cid:98) F : k,i K P(cid:98) F = (cid:89)(cid:16) P(cid:98) I (cid:17)µ ki i k,i k=1 (cid:136) Step 3c: Compute (cid:32) (cid:33)−λ (cid:98) c k,o d(cid:98)k,oi π (cid:98)k,oi = A(cid:98)k,o , P(cid:98) I k,i and obtain πTSS = π0 π k,oi k,oi(cid:98)k,oi (cid:136) Step 3d: Compute – κTSS = κ0 P(cid:98)i F (cid:101)k,i (cid:101)k,iw(cid:98)(cid:101)k,i (cid:110) (cid:111) (cid:136) Step 3e: Guess xTSS k,i (cid:136) Step 3f: Compute   1−δ(1−χ ) θ k T , S i S = q i −1 κ (cid:101) T k, S i S × δ(1−β )I (cid:16) k x ,i TSS (cid:17) k,i k,i k,i

(cid:136) Step 3g: Compute Bellman Equations    UTSS = ζ log (cid:88) exp   −C kk(cid:48),i +b k(cid:48),i +θ k T (cid:48) S ,i Sκ (cid:101) T k(cid:48) S ,i Sλ(cid:101) T i SSw (cid:101)k T (cid:48) S ,i S (1− β k β (cid:48) k ,i (cid:48),i ) +δU k T (cid:48) S ,i S   k,i i  ζ   i  k(cid:48)   (cid:136) Step 3h: Compute (cid:16) xTSS (cid:17)(cid:48) = (1−δ)U k T , S i S −η k,i k,i λ(cid:101) T i SSw (cid:101)k T , S i S (cid:16) (cid:17)(cid:48) (cid:136) Step 3i: Update xTSS = (1−λ )xTSS +λ xTSS , for a small step size λ , and go back to k,i x k,i x k,i x Step 2d until convergence. (cid:136) Step 3j: Compute sTSS,TSS+1 kk(cid:48) exp (cid:40) −C k(cid:96),i +b (cid:96),i +θ (cid:96) T , S i Sκ (cid:101) T (cid:96), S i Sλ(cid:101) T i SSw (cid:101)(cid:96) T , S i S 1− β(cid:96) β , (cid:96) i ,i +δU (cid:96) T , S i S (cid:41) ζi sTSS,TSS+1 = k(cid:96),i (cid:80) exp  −C kk,i +b k,i +θ k T , S i Sκ (cid:101) T k, S i Sλ(cid:101) T i SSw (cid:101)k T , S i S 1− β k β , k i ,i +δU k T , S i S   k  ζi  Step 4: Obtain series (cid:110) πt (cid:111)TSS , (cid:110) κt (cid:111)TSS . Define xt ≡ xt . k,oi (cid:101)k,i (cid:98) x0 t=0 t=0 (cid:136) Step 4a: For t = 1,...,T SS −1 compute w(cid:98) (cid:101) t k,i = w w (cid:101)k t 0 ,i and iteratively solve for P(cid:98) k I , , i t and (cid:98) ct k,i using (cid:101)k,i the system (cid:98) ct k,i = (cid:16) w(cid:98) (cid:101) t k,i (cid:17)γ k,i(cid:89) K (cid:16) P(cid:98) (cid:96) I , , i t (cid:17)(1−γ k,i )ν k(cid:96),i (cid:96)=1 (cid:32) N (cid:33)−1/λ P(cid:98) k I , , i t = (cid:88) π k 0 ,oi A(cid:98) t k,o (cid:16) (cid:98) ct k,o d(cid:98) t k,oi (cid:17)−λ o=1 (cid:136) Step 4b: Compute P(cid:98) k F ,i ,t for t = 1,...,T SS −1: K P(cid:98) F,t = (cid:89)(cid:16) P(cid:98) I,t (cid:17)µ ki i k,i k=1 (cid:136) Step 4c: Compute πt for t = 1,...,T −1: (cid:98)k,oi SS (cid:32) (cid:33)−λ π (cid:98)k t ,oi = A(cid:98) t k,o (cid:98) ct k P , (cid:98) o d I (cid:98) , t k t ,oi k,i (cid:136) Step 4d: Compute or t = 1,...,T −1: SS

– πt = π0 πt k,oi k,oi(cid:98)k,oi – κt ≡ κ k,i P i F,t = κ k,i P i F,0 P i F,t w (cid:101)k 0 ,i = κ0 P(cid:98) i F,t (cid:101)k,i w (cid:101)k t ,i w (cid:101)k 0 ,i P i F,0w (cid:101)k t ,i (cid:101)k,i w(cid:98)(cid:101) t k,i Step 5: Given knowledge of w (cid:101)k T , S i S, λ(cid:101) T i SS and xT k, S i S (and therefore J k T , S i S (s)), start at t = T SS −1 and sequentially compute (backwards) for each t = T −1,...,1 SS (cid:136) Step 5a: Given w (cid:101)k t ,i , λ(cid:101) t i , xt k + ,i 1, κ (cid:101) t k,i and J k t+ ,i 1(s) compute θ k t ,i . If λ(cid:101)t i κ (cid:101) t k,i w (cid:101)k t ,i ≤ 1 then δφ(cid:98) t i +1(cid:82) x x t m + a 1 xJ k t+ ,i 1(s)dG k,i (s) k,i   θt = q−1  λ(cid:101) t i κ (cid:101) t k,i w (cid:101)k t ,i  k,i i δφ(cid:98) t i +1(cid:82) x x t m + a 1 xJ k t+ ,i 1(s)dG k,i (s) k,i If λ(cid:101)t i κ (cid:101) t k,i w (cid:101)k t ,i > 1, it is not possible to satisfy Vt = 0, so that Vt < 0 and δφ(cid:98) t i +1(cid:82) x x t m + a 1 xJ k t+ ,i 1(s)dG k,i (s) k,i k,i k,i θt = 0. k,i (cid:136) Step5b: Givenxt+1,Wt+1(x) = β k,i Jt+1(x)+Ut+1 (forx ≥ xt+1),θt ,Ut+1 computeUt . k,i k,i 1−β k,i k,i k,i k,i k,i k,i k,i (cid:16) (cid:16) (cid:17)(cid:17) Noticethat (cid:82)xmaxWt+1(s)dG (s) = β k,i (cid:82)xmaxJt+1(s)dG (s)+ 1−G xt+1 Ut+1 xt k + ,i 1 k,i k,i 1−β k,i xt k + ,i 1 k,i k,i k,i k,i k,i so that:    −C +b  kk(cid:48),i k(cid:48),i  Ut = ζ log    (cid:88) exp      +δφ(cid:98) t i +1θ k t (cid:48),i q i (cid:16) θ k t (cid:48),i (cid:17) 1− β k β , k i ,i (cid:82) x x t k m + ,i a 1 xJ k t+ ,i 1(s)dG k,i (s)+δφ(cid:98) t i +1U k t+ (cid:48),i 1         k,i i  ζ    i   k(cid:48)           (cid:136) Step 5c: Given λ(cid:101) t i , J k t+ ,i 1(x), w (cid:101)k t ,i , θ k t ,i , δ, U k t ,i , U k t+ ,i 1 and xt k + ,i 1 compute J k t ,i (x) J k t ,i (x) = (1−β k,i )λ(cid:101) t i w (cid:101)k t ,i x+(1−β k,i )η k,i (cid:16) (cid:17) (cid:110) (cid:111) −(1−β k,i ) U k t ,i −δφ(cid:98) t i +1U k t+ ,i 1 +(1−χ k,i )δφ(cid:98) t i +1max J k t+ ,i 1(x),0 (cid:16) (cid:17) (cid:136) Step 5d: Solve for xt : Jt xt = 0 k,i k,i k,i Step 6: Compute transition rates (cid:110) st,t+1 (cid:111)TSS−1 for all countries i according to: kk(cid:48),i t=1 (cid:40) (cid:41) −C +b + kk(cid:48),i k(cid:48),i st,t+1 = exp δφ(cid:98) t i +1θ k t (cid:48),i q(θ k t (cid:48),i ) 1− β k β (cid:48) k ,i (cid:48),i (cid:82) x x t k m + (cid:48), a 1 i xJ k t+ (cid:48),i 1(x)dG k(cid:48),i (x)+δφ(cid:98) t i +1U k t+ (cid:48),i 1 . kk(cid:48),i (cid:40) −C +b + (cid:41) (cid:80) kk(cid:48)(cid:48),i k(cid:48)(cid:48),i k(cid:48)(cid:48) exp δφ(cid:98) t i +1θ k t (cid:48)(cid:48),i q(θ k t (cid:48)(cid:48),i ) 1− β k β (cid:48) k (cid:48), (cid:48) i (cid:48),i (cid:82) x x t k m + (cid:48)(cid:48) a 1 ,i xJ k t+ (cid:48)(cid:48), 1 i (x)dG k(cid:48)(cid:48),i (x)+δφ(cid:98) t i +1U k t+ (cid:48)(cid:48), 1 i

Step 7: Start loop over t going forward (t = 0 to t = T −1) SS Initial conditions: we know ut=−1 = ut=0, Lt=−1 = Lt=0, and θt=0 from the initial steady state (cid:101)k,i k,i k,i k,i k,i (cid:110) (cid:111) (cid:110) (cid:111) computation. Obtain ut and Lt using flow conditions and sequences θt , xt . (cid:101)k,i k,i k,i k,i (cid:136) Step 7a: Compute (cid:16) (cid:16) (cid:17)(cid:17) JCt = Lt ut θt q (cid:0) θt (cid:1) 1−G xt+1 k,i k,i k,i k,i i k,i k,i k,i   (cid:16) (cid:17) (cid:16) (cid:17)  G xt+1 −G xt  k,i k,i k,i k,i  (cid:16) (cid:17) JD k t ,i = χ k,i +(1−χ k,i )max (cid:16) (cid:17) ,0 Lt k − ,i 1 1−u (cid:101) t k − ,i 1  1−G xt  k,i k,i Lt ut −JCt +JDt ut = k,i k,i k,i k,i (cid:101)k,i Lt k,i (cid:136) Step 7b: Compute Lt+1 = Lt +IFt+1−OFt+1, k,i k,i k,i k,i where IFt+1 = (cid:88) Lt ut st+1,t+2, k,i (cid:96),i(cid:101)(cid:96),i (cid:96)k,i (cid:96)(cid:54)=k and (cid:16) (cid:17) OFt+1 = Lt ut 1−st+1,t+2 . k,i k,i(cid:101)k,i kk,i (cid:136) Step 7c: Compute K (cid:80) Lt ut st+1,t+2 (cid:96),i(cid:101)(cid:96),i (cid:96)k,i ut+1 = (cid:96)=1 k,i Lt+1 k,i (cid:136) Step 7d: Compute L(cid:101) t k + ,i 1 = Lt k,i (cid:0) 1−u (cid:101) t k,i (cid:1) (cid:90) ∞ s (cid:16) (cid:17) dG k,i (s) xt+1 1−G xt+1 k,i k,i k,i (cid:18) (cid:19) lnxt+1 (cid:32) (cid:33) Φ σ − k,i σ2 k,i σ = Lt (cid:0) 1−ut (cid:1) exp k,i k,i k,i (cid:101)k,i 2 (cid:18) lnxt+1 (cid:19) Φ − k,i σ k,i and Y k t , + i 1 = w (cid:101)k t+ ,i 1L(cid:101) t k + ,i 1

(cid:136) Step 7e: Compute expenditure with vacancies EV,t+1 = κt+1wt+1θt+1ut+1Lt+1 k,i (cid:101)k,i (cid:101)k,i k,i k,i k,i (cid:136) Step 7f: Compute EC,t+1 = Li i λ(cid:101) t+1 i (cid:110) (cid:111) (cid:136) Step 7g: Solve for Yt+1 in the system k,i K Et+1 = µ EC,t+1+ (cid:88)(cid:16) µ EV,t+1+(1−γ )ν Yt+1 (cid:17) . k,i k,i i k,i (cid:96),i (cid:96),i (cid:96)k,i (cid:96),i (cid:96)=1 N (cid:88) Yt+1 = πt+1Et+1. k,o k,oi k,i i=1 (cid:110) (cid:111) (cid:136) Step 7h: Normalize Yt+1 to make sure it sums to 1 across sectors and countries. k,i (cid:136) Step 7i: Compute (cid:16) wt+1 (cid:17)(cid:48) = γ k,i Y k t , + i 1 (cid:101)k,i L(cid:101) t+1 k,i (cid:32) (cid:33) Step 8: Compute dist (cid:110) wt (cid:111)TSS , (cid:26) (cid:16) wt (cid:17)(cid:48) (cid:27)TSS (cid:101)k,i (cid:101)k,i t=1 t=1 (cid:16) (cid:17)(cid:48) Step 9: Update wt = (1−α )wt +α wt for t = 1,...,T , for a small step size α , and (cid:101)k,i w (cid:101)k,i w (cid:101)k,i SS w (cid:110) (cid:111) go back to Step 3 until convergence of wt (cid:101)k,i Step 10: Compute disposable income (cid:8) It(cid:9)TSS i t=1 K It = (cid:88)(cid:16) γ Yt −EV,t (cid:17) i (cid:96),i (cid:96),i (cid:96),i (cid:96)=1 Step 11: Update (cid:110) EC,t (cid:111)TSS using i t=1 EC,t = It−NXt i i i (cid:16) (cid:17)(cid:48) Step 12a: Compute λ(cid:101) t i = E L C i ,t for all t = 1,...,T SS i (cid:32) (cid:33) (cid:136) Step 12b: Compute dist (cid:110) λ(cid:101) t (cid:111)TSS , (cid:26) (cid:16) λ(cid:101) t (cid:17)(cid:48) (cid:27)TSS i i t=1 t=1 (cid:16) (cid:17)(cid:48) (cid:136) Step 12c: Update λ(cid:101) t i = (1−α λ )λ(cid:101) t i +α λ λ(cid:101) t i for t = 1,...,T SS , for a small step size α λ , and (cid:110) (cid:111) go back to Step 2 until convergence of λ(cid:101) t . i

C.6 Algorithm: Recovering Shocks InnerLoop: conditionalonpathsforexpenditures (cid:110) EC,t (cid:111)TSS andshocks (cid:110) φ(cid:98) t (cid:111)TSS , (cid:110) d(cid:98) t (cid:111)TSS i i k,i t=1 t=2 t=1 A TSS and A(cid:98)k,i ≡ A k 0 ,i – determined in the Outer Loop below. k,i As before, we denote changes relative to t = 0 by xt = xt . This loop conditions on data on (cid:98) x0 (cid:110) (cid:111)T (cid:110) (cid:111)T π (cid:98)k t ,oi and P(cid:98) k I , , i t , where T is the last period we have data on these variables. We assume t=1 t=1 d TSS t = 0 is the estimated steady state. Define d(cid:98)k,i ≡ d o 0 ,i,k. o,i,k (cid:110) (cid:111) (cid:110) (cid:111) Step 1: Given paths EC,t , compute paths λ(cid:101) t : λ(cid:101) t = Li . i i i EC,t i Step 2: Guess paths (cid:110) wt (cid:111)TSS for each sector k and country i. (cid:101)k,i t=1 Step 3: Compute xT k, S i S consistent with w (cid:101)k T , S i S and λ(cid:101) T i SS. Obtain θ k T , S i S, U k T , S i S, s k T (cid:96) S , S i ,TSS+1 and π k T , S o S i . (cid:136) Step 3a: Compute w(cid:98) (cid:101)k,i = w (cid:101) w k T 0 , S i S . Iteratively solve for P(cid:98) k I ,i and (cid:98) c k,i using the system (cid:101)k,i (cid:98) c k,i = (cid:16) w(cid:98) (cid:101)k,i (cid:17)γ k,i(cid:89) K (cid:16) P(cid:98) (cid:96) I ,i (cid:17)(1−γ k,i )ν k(cid:96),i (cid:96)=1 (cid:32) N (cid:33)−1/λ (cid:88) (cid:16) (cid:17)−λ P(cid:98) k I ,i = π k 0 ,oi A(cid:98)k,o (cid:98) c k,o d(cid:98)k,oi o=1 (cid:136) Step 3b: Compute P(cid:98) F : k,i K P(cid:98) F = (cid:89)(cid:16) P(cid:98) I (cid:17)µ ki i k,i k=1 (cid:136) Step 3c: Compute (cid:32) (cid:33)−λ (cid:98) c k,o d(cid:98)k,oi π (cid:98)k,oi = A(cid:98)k,o P(cid:98) I k,i And obtain πTSS = π0 π k,oi k,oi(cid:98)k,oi (cid:136) Step 3d: Compute – κTSS = κ0 P(cid:98)i F (cid:101)k,i (cid:101)k,iw(cid:98)(cid:101)k,i (cid:110) (cid:111) (cid:136) Step 3e: Guess xTSS k,i

(cid:136) Step 3f: Compute   1−δ(1−χ ) θ k T , S i S = q i −1 κ (cid:101) T k, S i S × δ(1−β )I (cid:16) k x ,i TSS (cid:17) k,i k,i k,i (cid:136) Step 3g: Compute Bellman Equations    UTSS = ζ log (cid:88) exp   −C kk(cid:48),i +b k(cid:48),i +θ k T (cid:48) S ,i Sκ (cid:101) T k(cid:48) S ,i Sλ(cid:101) T i SSw (cid:101)k T (cid:48) S ,i S (1− β k β (cid:48) k ,i (cid:48),i ) +δU k T (cid:48) S ,i S   k,i i  ζ   i  k(cid:48)   (cid:136) Step 3h: Compute (cid:16) xTSS (cid:17)(cid:48) = (1−δ)U k T , S i S −η k,i k,i λ(cid:101) T i SSw (cid:101)k T , S i S (cid:16) (cid:17)(cid:48) (cid:136) Step 3i: Update xTSS = (1−λ )xTSS +λ xTSS , for a small step size λ and go back to k,i x k,i x k,i x Step 2d until convergence. (cid:136) Step 3j: Compute sTSS,TSS+1 kk(cid:48) exp (cid:40) −C k(cid:96),i +b (cid:96),i +θ (cid:96) T , S i Sκ (cid:101) T (cid:96), S i Sλ(cid:101) T i SSw (cid:101)(cid:96) T , S i S 1− β(cid:96) β , (cid:96) i ,i +δU (cid:96) T , S i S (cid:41) ζi sTSS,TSS+1 = k(cid:96),i (cid:80) exp  −C kk,i +b k,i +θ k T , S i Sκ (cid:101) T k, S i Sλ(cid:101) T i SSw (cid:101)k T , S i S 1− β k β , k i ,i +δU k T , S i S   k  ζi  Step 4: Obtain series (cid:110) πt (cid:111)TSS and (cid:110) κt (cid:111)TSS . k,oi (cid:101)k,i t=T+1 t=1 (cid:136) Step 4a: For t = T +1,...,T do: SS Compute w(cid:98) (cid:101) t k,i = w w (cid:101)k 0 t ,i and iteratively solve for P(cid:98) k I , , i t and (cid:98) ct k,i using the system (cid:101)k,i (cid:98) ct k,i = (cid:16) w(cid:98) (cid:101) t k,i (cid:17)γ k,i(cid:89) K (cid:16) P(cid:98) (cid:96) I , , i t (cid:17)(1−γ k,i )ν k(cid:96),i , (cid:96)=1 (cid:32) N (cid:33)−1/λ P(cid:98) k I , , i t = (cid:88) π k 0 ,oi A(cid:98)k,o (cid:16) (cid:98) ct k,o d(cid:98)k,oi (cid:17)−λ . o=1 (cid:136) Step 4b: Compute P(cid:98) k F ,i ,t for t = 1,...,T SS −1 (remember P(cid:98) k I , , i t is data for t = 1,...,T): K P(cid:98) F,t = (cid:89)(cid:16) P(cid:98) I,t (cid:17)µ ki i k,i k=1

(cid:136) Step 4c: Compute πt and πt for t = T +1,...,T −1. (cid:98)k,oi k,oi SS For t = 1,...,T −1 do: SS First Case: If t ≤ T then πt is data, so do: (cid:98)k,oi πt = π0 πt k,oi k,oi(cid:98)k,oi End of First Case Second Case if t ≥ T +1 do: (cid:32) (cid:33)−λ π (cid:98)k t ,oi = (cid:16) A(cid:98) t k,o (cid:17)(cid:48) (cid:98) ct k P , (cid:98) o d I (cid:98) , t k t ,oi k,i πt = π0 πt k,oi k,oi(cid:98)k,oi End of Second Case (cid:136) Step 4d: Compute for t = 1,...,T −1 SS – κt ≡ κ k,i P i F,t = κ k,i P i F,0 P i F,t w (cid:101)k 0 ,i = κ0 P(cid:98) i F,t (cid:101)k,i w (cid:101)k t ,i w (cid:101)k 0 ,i P i F,0w (cid:101)k t ,i (cid:101)k,i w(cid:98)(cid:101) t k,i Step 5: Given knowledge of w (cid:101)k T , S i S, λ(cid:101) T i SS and xT k, S i S (and therefore J k T , S i S (s)), start at t = T SS −1 and sequentially compute (backwards) for each t = T −1,...,1 SS (cid:136) Step 5a: Given w (cid:101)k t ,i , xt k + ,i 1, κ (cid:101) t k,i , λ(cid:101) t i and J k t+ ,i 1(s) compute θ k t ,i . If λ(cid:101)t i κ (cid:101) t k,i w (cid:101)k t ,i ≤ 1 then δφ(cid:98) t i +1(cid:82) x x t m + a 1 xJ k t+ ,i 1(s)dG k,i (s) k,i   θt = q−1  λ(cid:101) t i κ (cid:101) t k,i w (cid:101)k t ,i  k,i i δφ(cid:98) t i +1(cid:82) x x t m + a 1 xJ k t+ ,i 1(s)dG k,i (s) k,i If λ(cid:101)t i κ (cid:101) t k,i w (cid:101)k t ,i > 1, it is not possible to satisfy Vt = 0, so that Vt < 0 and δφ(cid:98) t i +1(cid:82) x x t m + a 1 xJ k t+ ,i 1(s)dG k,i (s) k,i k,i k,i θt = 0. k,i (cid:136) Step5b: Givenxt+1,Wt+1(x) = β k,i Jt+1(x)+Ut+1 (forx ≥ xt+1),θt ,Ut+1 computeUt . k,i k,i 1−β k,i k,i k,i k,i k,i k,i k,i (cid:16) (cid:16) (cid:17)(cid:17) Noticethat (cid:82)xmaxWt+1(s)dG (s) = β k,i (cid:82)xmaxJt+1(s)dG (s)+ 1−G xt+1 Ut+1 xt k + ,i 1 k,i k,i 1−β k,i xt k + ,i 1 k,i k,i k,i k,i k,i so that:    −C +b  kk(cid:48),i k(cid:48),i  Ut = ζ log    (cid:88) exp      +δφ(cid:98) t i +1θ k t (cid:48),i q i (cid:16) θ k t (cid:48),i (cid:17) 1− β k β , k i ,i (cid:82) x x t k m + ,i a 1 xJ k t+ ,i 1(s)dG k,i (s)+δφ(cid:98) t i +1U k t+ (cid:48),i 1         k,i i  ζ    i   k(cid:48)          

(cid:136) Step 5c: Given Jt+1(x), wt , Ut , Ut+1 and xt+1 compute Jt (x) k,i (cid:101)k,i k,i k,i k,i k,i J k t ,i (x) = (1−β k,i )λ(cid:101) t i w (cid:101)k t ,i x+(1−β k,i )η k,i (cid:16) (cid:17) (cid:110) (cid:111) −(1−β k,i ) U k t ,i −δφ(cid:98) t i +1U k t+ ,i 1 +(1−χ k,i )δφ(cid:98) t i +1max J k t+ ,i 1(x),0 (cid:16) (cid:17) (cid:136) Step 5d: Solve for xt : Jt xt = 0 k,i k,i k,i Step 6: Compute transition rates (cid:110) st,t+1 (cid:111)TSS−1 for all countries i according to: kk(cid:48),i t=1 (cid:40) (cid:41) −C +b + kk(cid:48),i k(cid:48),i st,t+1 = exp δφ(cid:98) t i +1θ k t (cid:48),i q(θ k t (cid:48),i ) 1− β k β (cid:48) k ,i (cid:48),i (cid:82) x x t k m + (cid:48), a 1 i xJ k t+ (cid:48),i 1(x)dG k(cid:48),i (x)+δφ(cid:98) t i +1U k t+ (cid:48),i 1 . kk(cid:48),i (cid:40) −C +b + (cid:41) (cid:80) kk(cid:48)(cid:48),i k(cid:48)(cid:48),i k(cid:48)(cid:48) exp δφ(cid:98) t i +1θ k t (cid:48)(cid:48),i q(θ k t (cid:48)(cid:48),i ) 1− β k β (cid:48) k (cid:48), (cid:48) i (cid:48),i (cid:82) x x t k m + (cid:48)(cid:48) a 1 ,i xJ k t+ (cid:48)(cid:48), 1 i (x)dG k(cid:48)(cid:48),i (x)+δφ(cid:98) t i +1U k t+ (cid:48)(cid:48), 1 i Step 7: Start loop over t going forward (t = 0 to t = T −1) SS Initial conditions: we know ut=−1 = ut=0, Lt=−1 = Lt=0, and θt=0 from the initial steady state (cid:101)k,i k,i k,i k,i k,i (cid:110) (cid:111) (cid:110) (cid:111) computation. Obtain ut and Lt using flow conditions and sequences θt , xt . (cid:101)k,i k,i k,i k,i (cid:136) Step 7a: Compute (cid:16) (cid:16) (cid:17)(cid:17) JCt = Lt ut θt q (cid:0) θt (cid:1) 1−G xt+1 k,i k,i k,i k,i i k,i k,i k,i   (cid:16) (cid:17) (cid:16) (cid:17)  G xt+1 −G xt  k,i k,i k,i k,i  (cid:16) (cid:17) JD k t ,i = χ k,i +(1−χ k,i )max (cid:16) (cid:17) ,0 Lt k − ,i 1 1−u (cid:101) t k − ,i 1  1−G xt  k,i k,i Lt ut −JCt +JDt ut = k,i k,i k,i k,i (cid:101)k,i Lt k,i (cid:136) Step 7b: Compute Lt+1 = Lt +IFt+1−OFt+1, k,i k,i k,i k,i where IFt+1 = (cid:88) Lt ut st+1,t+2, k,i (cid:96),i(cid:101)(cid:96),i (cid:96)k,i (cid:96)(cid:54)=k and (cid:16) (cid:17) OFt+1 = Lt ut 1−st+1,t+2 . k,i k,i(cid:101)k,i kk,i

(cid:136) Step 7c: Compute K (cid:80) Lt ut st+1,t+2 (cid:96),i(cid:101)(cid:96),i (cid:96)k,i ut+1 = (cid:96)=1 k,i Lt+1 k,i (cid:136) Step 7d: Compute L(cid:101) t k + ,i 1 = Lt k,i (cid:0) 1−u (cid:101) t k,i (cid:1) (cid:90) ∞ s (cid:16) (cid:17) dG k,i (s) xt+1 1−G xt+1 k,i k,i k,i (cid:18) (cid:19) lnxt+1 (cid:32) (cid:33) Φ σ − k,i σ2 k,i σ = Lt (cid:0) 1−ut (cid:1) exp k,i k,i k,i (cid:101)k,i 2 (cid:18) lnxt+1 (cid:19) Φ − k,i σ k,i (cid:136) Step 7e: Compute expenditure with vacancies EV,t+1 = κt+1wt+1θt+1ut+1Lt+1 k,i (cid:101)k,i (cid:101)k,i k,i k,i k,i (cid:110) (cid:111) (cid:136) Step 7f: Solve for Yt+1 in the system k,i K Et+1 = µ EC,t+1+ (cid:88)(cid:16) µ EV,t+1+(1−γ )ν Yt+1 (cid:17) . k,i k,i i k,i (cid:96),i (cid:96),i (cid:96)k,i (cid:96),i (cid:96)=1 N (cid:88) Yt+1 = πt+1Et+1. k,o k,oi k,i i=1 (cid:136) Step 7g: Compute (cid:16) wt+1 (cid:17)(cid:48) = γ k,i Y k t , + i 1 (cid:101)k,i L(cid:101) t+1 k,i (cid:18) (cid:26) (cid:27)(cid:19) (cid:110) (cid:111) (cid:16) (cid:17)(cid:48) Step 8: Compute distance dist wt , wt (cid:101)k,i (cid:101)k,i (cid:16) (cid:17)(cid:48) (cid:136) Step 8b: Update wt = (1−λ )wt +λ wt t = 1,...,T , for a small step size λ . (cid:101)k,i w (cid:101)k,i w (cid:101)k,i SS w (cid:110) (cid:111) (cid:136) Step 8c: At this point, we have a new series for wt – go back to Step 3 until convergence (cid:101)k,i (cid:110) (cid:111) of wt . (cid:101)k,i Step 9: Compute disposable income (cid:8) It(cid:9)TSS i t=1 K It = (cid:88)(cid:16) γ Yt −EV,t (cid:17) i (cid:96),i (cid:96),i (cid:96),i (cid:96)=1

(cid:26) (cid:27) (cid:16) (cid:17)(cid:48) Step 10: Compute A(cid:98) t . k,i t wt For t = 1,...,T compute w(cid:98) = (cid:101)k,i, obtain ct : (cid:101)k,i w0 (cid:98)k,i (cid:101)k,i (cid:98) ct k,i = (cid:16) w(cid:98) (cid:101) t k,i (cid:17)γ k,i(cid:89) K (cid:16) P(cid:98) (cid:96) I , , i t (cid:17)(1−γ k,i )ν k(cid:96),i , (cid:96)=1 (cid:16) (cid:17)(cid:48) and compute A(cid:98) t : k,i (cid:16) A(cid:98) t k,i (cid:17)(cid:48) = (cid:16) π (cid:98)k t ,ii (cid:17)λ (cid:0) (cid:98) ct k,i (cid:1)λ . P(cid:98) I,t k,i For t ≥ T +1 set: (cid:16) (cid:17)(cid:48) (cid:16) (cid:17)(cid:48) A(cid:98) t = A(cid:98) T k,i k,i (cid:26) (cid:27) (cid:16) (cid:17)(cid:48) Feed outer loop with A(cid:98) TSS . k,i Outer Loop: iteration on (cid:8) NXt(cid:9) i (cid:110) (cid:111)T Step 0: Compute changes in trade costs d(cid:98) t : k,oi t=1 d(cid:98) t = (cid:32) π (cid:98)k t ,oo (cid:33)1/λ P(cid:98) k I , , i t k,oi π (cid:98)k t ,oi P(cid:98) k I , , o t Set d(cid:98) t = d(cid:98) T for t > T. k,oi k,oi Step 1:Startwithestimatedstateequilibriumatt = 0. Rememberthatweusedthenormalization I K I K (cid:80) (cid:80) (cid:80) (cid:80) Y = 1 during the estimation procedure. Change the normalization from Y = 1 k,i k,i i=1k=1 i=1k=1 I (cid:110) (cid:111) (cid:110) (cid:111) (cid:110) (cid:111) to (cid:80) EC = 1. Nominal variables to be renormalized: Y0 , w0 , EC,0 , (cid:8) NX0(cid:9) . i k,i (cid:101)k,i i i i=1 Step 2: Compute EC,t = E i C,0(E(cid:98) i C,t) Data for t = 1,...,T where EC,0 is aggregate consumption i N i (cid:80)EC,0(E(cid:98) C,t) i i Data i=1 (cid:16) (cid:17) expenditure in the estimated steady state, and E(cid:98) C,t comes from the data. i Data Step 3: Normalize φ(cid:98) t = 1 for t = 2,...,T −1. This yields US EC,t+1 Rt+1 = US for t = 1,...,T −1 δEC,t US (cid:110) (cid:111)T Obtain remaining shocks φ(cid:98) t using i t=2 EC,t+1 φ(cid:98) t+1 = i for t = 1,...,T −1 i δEC,tRt+1 i

Set φ(cid:98) t = 1 for t ≥ T +2. The value of φ(cid:98) T+1 will depend on EC,TSS and will be recovered in Step 7. i i i Note: the value of φ(cid:98) t=1 does not matter. Individuals made decisions at t = 0 assuming φ(cid:98) t=1 = 1, i i as the economy was assumed to be in steady state at t = 0. I Step 4: Obtain B0 with respect to the normalization (cid:80) EC = 1. Equation (37) gives us: i i i=1 NX0 B0 = i i (cid:0) 1− 1(cid:1) δ I Step 5: Make initial guess for NXTSS (with respect to the normalization (cid:80) EC = 1) and for i i i=1 A(cid:98) TSS = A(cid:98) T ≡ AT k,i. k,i k,i A0 k,i Step 6: Compute steady state equilibrium at T SS , conditional on NX i TSS, A(cid:98) T k, S i S and d(cid:98) T k, S o S i . I K (cid:136) Step 6a: Notice that the steady-state algorithm uses the normalization (cid:80) (cid:80) Y = 1. Nork,i i=1k=1 I K malize NXTSS with respect to normalization (cid:80) (cid:80) Y = 1. To perform such normalization, i k,i i=1k=1 (cid:110) (cid:111) use revenue YTSS obtained in the initial steady state if this is the first outer loop iteration, k,i (cid:110) (cid:111) otherwise use revenue YTSS obtained in Step 9 below. k,i I K (cid:136) Step6b: Aftercomputingthefinalsteadystate,changethenormalizationfrom (cid:80) (cid:80) Y = k,i i=1k=1 I 1 to (cid:80) EC = 1 using (cid:8) EC(cid:9) obtained in Step 3a. Nominal variables to be renormalized: i i i=1 (cid:110) (cid:111) (cid:110) (cid:111) (cid:110) (cid:111) (cid:110) (cid:111) YTSS , wTSS , EC,TSS , NXTSS . k,i (cid:101)k,i i i  (cid:18) (cid:19)  EC,0 E i C,2000+t for t = 0,...,T, as in Step 0 Step 7: Set EC,t = i EC,2000 i i Data  EC,TSS for t = T +1,...,T i SS Note: φ(cid:98) t = 1 for t ≥ T +2 ⇒ EC,t = EC,TSS for at t ≥ T +1 (Euler Equation) i i i Step 8: Compute φ(cid:98) T+1, imposing φ(cid:98) T+1 = 1: i US EC,TSS φ(cid:98) T+1 = i , i δRT+1EC,T i EC,TSS RT+1 = US . δEC,T US We now have a full path for (cid:110) φ(cid:98) t (cid:111)TSS . i t=2

Step9: Solvefortheout-of-steady-statedynamicsconditionalonaggregateexpenditures (cid:110) EC,t (cid:111)TSS , i t=0 on preference shifters (cid:110) φ(cid:98) t (cid:111)TSS and steady-state productivity shocks (cid:110) A(cid:98) TSS (cid:111) . i k,i t=2 Step 10: Using the path for disposable income (cid:8) It(cid:9)TSS obtained in Step 9 and equation (7) i t=1 compute: (cid:0) NXt(cid:1)(cid:48) = It−EC,t for 1 ≤ t < T i i SS (cid:16) NXTSS (cid:17)(cid:48) = − 1−δ 1 (cid:32) B0+ TS(cid:88)S−1(cid:32) (cid:89) t (Rτ)−1 (cid:33) (cid:0) NXt(cid:1)(cid:48) (cid:33) i δ (cid:32)TS(cid:89)S−1 (Rτ)−1 (cid:33) i t=1 τ=1 i τ=1 Step 11: Compute (cid:18) (cid:26) (cid:27)(cid:19) (cid:110) (cid:111) (cid:16) (cid:17)(cid:48) dist NXTSS , NXTSS and i i (cid:18) (cid:26) (cid:27)(cid:19) (cid:110) (cid:111) (cid:16) (cid:17)(cid:48) dist A(cid:98) TSS , A(cid:98) TSS , k,i k,i (cid:26) (cid:27) (cid:16) (cid:17)(cid:48) using the values of A(cid:98) TSS obtained in Step 9. k,i Step 12: Update NXTSS i (cid:16) (cid:17)(cid:48) NXTSS = (1−λ )NXTSS +λ NXTSS i o i o i and A(cid:98) TSS k,i (cid:16) (cid:17)(cid:48) A(cid:98) T k, S i S = (1−λ A )A(cid:98) T k, S i S +λ A A(cid:98) T k, S i S for small step sizes λ and λ . o A (cid:110) (cid:111) (cid:110) (cid:111) Go back to Step 6 until convergence of NXTSS and A(cid:98) TSS . i k,i

C.7 Parameter Estimates In this section, we display the complete set of parameter estimates. Table A.1: Final Expenditure Shares µ k,i Sector ↓ Country → USA China Europe Asia/Oceania Americas ROW Agr. 0.01 0.12 0.02 0.01 0.02 0.09 LT Manuf. 0.03 0.02 0.04 0.03 0.04 0.03 MT Manuf. 0.05 0.11 0.08 0.07 0.1 0.11 HT Manuf. 0.1 0.15 0.11 0.1 0.11 0.1 LT Serv. 0.3 0.35 0.34 0.38 0.33 0.39 HT Serv. 0.51 0.25 0.41 0.41 0.4 0.29 Table A.2: Labor Shares in Production γ k,i Sector ↓ Country → USA China Europe Asia/Oceania Americas ROW Agr. 0.45 0.58 0.56 0.54 0.62 0.67 LT Manuf. 0.37 0.25 0.32 0.35 0.28 0.27 MT Manuf. 0.33 0.28 0.31 0.37 0.32 0.28 HT Manuf. 0.39 0.24 0.33 0.32 0.31 0.25 LT Serv. 0.61 0.37 0.49 0.54 0.56 0.48 HT Serv. 0.62 0.55 0.63 0.67 0.67 0.68

Table A.3: Input-Output Table – Average Across Countries 1 (cid:80) ν N i k(cid:96),i User ↓ Supplier → Agr. LT Manuf. MT Manuf. HT Manuf. LT Serv. HT Serv. Agr. 0.267 0.079 0.118 0.138 0.26 0.139 (0.056) (0.019) (0.036) (0.029) (0.06) (0.07) LT Manuf. 0.195 0.376 0.043 0.081 0.223 0.082 (0.047) (0.064) (0.009) (0.015) (0.041) (0.04) MT Manuf. 0.222 0.066 0.287 0.106 0.225 0.095 (0.034) (0.017) (0.04) (0.022) (0.052) (0.044) HT Manuf. 0.022 0.157 0.067 0.463 0.184 0.106 (0.018) (0.022) (0.015) (0.052) (0.044) (0.05) LT Serv. 0.057 0.136 0.105 0.101 0.343 0.259 (0.042) (0.03) (0.027) (0.034) (0.073) (0.11) HT Serv. 0.007 0.076 0.033 0.11 0.267 0.507 (0.005) (0.023) (0.019) (0.071) (0.069) (0.171) Note: Standard Deviation of ν across countries. k(cid:96) Table A.4: Mobility Costs Estimates C k(cid:96) From ↓ / To → Agr. LT Manuf. MT Manuf. HT Manuf. LT Serv. HT Serv. Agriculture 0 0.825 1.560 0.454 0.189 1.676 LT Manufacturing 0.414 0 0.005 0.000 0.799 2.034 MT Manufacturing 2.033 0.000 0 0.002 0.866 2.646 HT Manufacturing 0.015 0.001 0.003 0 0.276 0.917 LT Services 0.268 0.972 1.221 0.466 0 0.002 HT Services 0.790 1.826 2.150 1.201 0.004 0 Table A.5: Sector-Specific Utility and Variance Estimates η ,σ2 k,i k,i Sector ↓ / Country → USA China Europe Asia/Oceania Americas ROW Agriculture 0 0 0 0 0 0 LT Manuf. -0.383 -0.943 -0.428 -0.521 -0.588 -0.316 MT Manuf. 0.026 -0.566 -0.245 -0.229 -0.195 -0.072 HT Manuf. -0.551 -1.557 -0.743 -0.607 -1.292 -0.934 LT Services 0.085 -0.454 -0.382 -0.236 -0.405 -0.588 HT Services -0.052 -0.467 -0.603 -0.518 -0.894 -1.011 σ2 0.727 US

Table A.6: Exogenous Death Rates Estimates χ = χ +χ k, i k USA 0.026 China 0.022 Country Europe 0.054 Component χ Asia/Oceania 0.021 i Americas 0.027 ROW 0.020 Agriculture 0 Low Tech Man 0.005 Sector Med Tech Man 0.014 Component χ High Tech Man 0.002 k Other Services 0.008 Hi Tech Services -0.001 Table A.7: Unemployment Utility b = b k,i i USA -14.4 China -12.7 Europe -7.1 Asia/Oceania -8.5 Americas -8.6 ROW -14.9 Table A.8: Vacancy Posting Costs Estimates κ (cid:101)k,i Sector ↓ / Country → USA China Europe Asia/Oceania Americas ROW Agriculture 0.539 0.450 0.451 0.664 0.451 0.452 LT Manuf. 0.632 0.810 0.681 0.865 0.809 0.583 MT Manuf. 0.472 0.615 0.549 0.660 0.540 0.447 HT Manuf. 0.698 0.984 0.821 0.922 1.076 0.830 LT Services 0.449 0.617 0.592 0.660 0.649 0.639 HT Services 0.511 0.674 0.672 0.840 0.872 0.813