Globalization, Trade Imbalances and Labor Market Adjustment

February 10, 2021 at 03:38 pm

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, Joao Paulo Pessoa, Ricardo Reyes-Heroles, Sharon Traiberman (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 stimu-late 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 atwww.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library atwww.ssrn.com.

GLOBALIZATION, TRADE IMBALANCES AND LABORMARKET 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.reyes-heroles@frb.gov; Traiberman: sharon.traiberman@nyu.edu. We would like to thank seminar and conference partici-pants 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.

"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 unem-ployed.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 import-competing 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 adjust-ment 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 adjust-ment and develop an estimable, general equilibrium, multi-country, multi-sector model with three

1 SeeKrugman (2019).
2 Other recent papers tying globalization shocks to labor market disruptions includeDix-Carneiro and Kovak (2017,

2019),Pierce and Schott (2016),Costa et al. (2016),Dauth et al. (2018),Utar (2018), among many others.

3 SeeArtu¸c et al. (2010),Dix-Carneiro (2014),Traiberman (2019), andCaliendo et al. (2019).
4 For examples of recent policy discussions, seeScott (1998),Bernanke (2005), andNavarro (2019).

key ingredients: (i) Consumption-saving decisions in each country are determined by the optimizing 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 con-sumption 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 mar-ket 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 laArtu¸c et al. (2010); and (ii) matching frictions within sectors `a laMortensen andPissarides (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

5 SeeObstfeld and Rogoﬀ (1995) for a survey of this approach to imbalances in international macroeconomics.
6 More recent work on global imbalances builds on the standard consumption savings model by adding ﬁnancial frictions (e.g.,Caballero et al. (2008) andMendoza 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.
8 Speciﬁcally, under balanced trade, we impose that aggregate expenditure equals aggregate revenues for each

unemployment and reallocation responses to globalization shocks. To be speciﬁc, consider a hypo-thetical 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 inter-temporal 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 market frictions for the gains from trade, typically computed using the suﬃcient-statistics approach ofArkolakis et al. (2012) and extended byCostinot 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 in Chinese manufacturing productivity since 2000; (ii) changes in trade costs over the same time pe-riod; (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.

9 SeeAutor et al. (2016) and references therein for more discussion of the China shock.

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 glob-alization, 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 Ri-cardian trade model ofCaliendo and Parro (2015). Broadly speaking, quantitative trade models based onEaton 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.Caliendoet 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) andGuner et al. (2020) incorporate search frictions and unemployment into multi-sector extensions ofEaton 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 ofCaliendo 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 inReyes-Heroles (2016).11 In that regard, our paper is closely related toKehoe 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

10 In addition to these papers based on the Eaton and Kortum model,Helpman and Itskhoki (2010) add labor market frictions to a two-country Melitz model, andHeid and Larch (2016) add labor market frictions to an Armington model of trade.Co¸sar et al. (2016) incorporate search frictions and unemployment to an estimable small open economy Melitz model with ﬁrm dynamics, but focus on steady-state analyses.Ruggieri (2019) extends that model to study the transition in response to trade shocks. Similarly,Helpman and Itskhoki (2015) also analyze the dynamic behavior of a two-country Melitz model with labor market frictions. Finally,Kambourov (2009),Artuc¸ et al. (2010),Dix-Carneiro (2014), andTraiberman (2019) also study transitional dynamics, but from the lenses of small open economy models.

11 A few papers have analyzed the consequences of current account rebalancing on labor reallocation and unem-ployment by considering changes in imbalances as exogenous, e.g.Obstfeld and Rogoﬀ (2005),Dekle et al. (2007), andEaton et al. (2013).

12 In International Macroeconomics,Kehoe and Ruhl (2009),Meza and Urrutia (2011), andJu et al. (2014) are

The rest of this paper is structured as follows. Section2 outlines our model. Section3 describes the data we use and our estimation procedure. In Section4 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. Section5 conducts a series of empirical applications of our model. We conclude and discuss future research in Section6.

2 Model

Our model builds on existing workhorse models of globalization, trade imbalances and labor market adjustment. Trade imbalances are modeled according to the inter-temporal approach ofObstfeldand Rogoﬀ (1995), and the trade bloc is based onCaliendo and Parro (2015). We adopt the framework inArtuc¸ et al. (2010) to model labor mobility frictions across sectors and the structure inMortensen and Pissarides (1994) to model search frictions and job creation and destruction. Sections2.1 through2.9 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 Li work-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:

Z 1

1 ε

I,t Qk,i =

Qk,i (j)t

(1)

where Qkt ,i (j) is the quantity employed of variety j in sector k and country i at time t, and σ =

1 1−ε

is the elasticity of substitution across varieties within sectors. These composite sector-speciﬁc goods 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 PkI,,it.

A non-tradable ﬁnal good is produced by perfectly competitive ﬁrms that aggregate sector-speciﬁc composite goods QIk,,ti according to:

QF,t = YK QI,t i k,i k=1

µk,i ,

(2)

examples of the scarce work studying the interaction between the current account and labor market reallocation.

K where µk,i > 0 and P µk,i =1 ∀i. The price of one unit of the ﬁnal good is given by the price k=1 index associated with (2), which we denote by PiF,t.

2.2 Labor Markets

Workers and single-worker ﬁrms producing varieties engage in a costly search process. Firms post vacancies, but not all of them are ﬁlled. Workers search for a job, but not all of them are successful, leading to involuntary unemployment. Each variety j constitutes a diﬀerent labor market. More precisely, the unemployment rate ukt ,i (j) is variety-speciﬁc, as is the vacancy rate vkt ,i (j). Both variables are expressed as a fraction of the labor force Lkt ,i (j), measured as the sum of workers who are employed or unemployed and searching within sector k and variety j at time t. We impose that mi ukt ,i (j) ,vkt ,i (j) matches are formed (as a fraction of the labor force Ltk,i (j)), where the matching function mi is increasing in both arguments, concave, and homogeneous of degree 1.

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:

t θk,i ≡

vk,i t uk,i .

(3)The fact that mi has constant returns to scale allows us to write the probability that a vacancy matches with a worker as qi(θkt ,i), for a decreasing function qi, and the probability that an unem-ployed worker matches with a vacancy as θkt ,iqi(θkt ,i). We assume that workers can costlessly move 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 heads aggregate members' utilities. For ease of notation, we temporarily omit the country subscript i and let ` 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 Ckk0 and search in sector k0 at time t- so that Ckk = 0. If a worker ` is not employed at the production stage at t, she receives preference shocks

k,`,k =1 ,...,K for each sector at time t. After unemployed workers receive these shocks, the 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 ω kt ,` shocks

ω t

are iid across individuals, sectors and time, and are assumed to follow a Gumbel distribution with parameters −γEM ζ,ζ where γEM is the Euler-Mascheroni constant and ζ its shape parameter. This structure follows closelyArtu¸c et al. (2010).

After being allocated to search in sector k0 at t the unemployed worker receives unemployment utility bk0 and matches with a ﬁrm with probability θkt 0q(θkt 0). We followMortensen and Pissarides (1994) and assume that once a worker and a ﬁrm match at t, a match-speciﬁc productivity for t + 1 production, x`t+1, is randomly drawn from a distribution Gk,i with [0,∞ ) support. This 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 χk of existing matches to dissolve (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 wkt+1 x`t+1 . Finally, if a worker produces in sector k, she receives a non-pecuniary beneﬁt of ηk . Figure1 details the timing of the model. Section2.5 describes the bargaining process that occurs at ta and section2.4.2 describes the decision of ﬁrms to post vacancies at time tc.

Figure 1: Timing of the Model

Firms and workers	Workers: consume	Exogenous job
bargain over wages	tb	Firms: post vacancies	destruction w/ prob. χk

t − 1

Matched Workers: Produce Unemployed: learn shocks ω, choose sector where to search

New matches occur and xt`+1 ∼ G k revealed

t +1

Given this setup, the period utility for individual ` at time t is,

U`t e`t ,k`t+1,k`t ,ω `t,c`t = 1 − e`t

−Ckt ,kt+1 + bkt+1 + ω kt+1 ,`

+ e`t ηk`t + u c`t ,

(4)

where k`t is the sector where individual ` starts period t (that sector was determined at t − 1),

t+1 k`

is the t + 1 sector of choice (which is decided at time t, interim period tb in Figure1),e`t is the employment status at the production stage (interim period tb), ω `t =

ω t

1,`,...,ω Kt ,` are

idiosyncratic utility shocks received by unemployed workers at interim period tb, and c`t is individual consumption. If individual ` is unemployed in sector k at t (e`t =0 ,k`t = k), the individual can switch sectors (from k to k`t+1), so that mobility costs Ckt ,kt+1 , utility of unemployment bkt+1 and

` `

shock ω kt t+1 ,` are incurred (during period t). On the other hand, if individual ` is employed during

the production stage at t, e`t = 1, the worker enjoys the non-pecuniary beneﬁt of working in sector k`t given by ηkt . Finally, individual ` also enjoys the utility of consumption u c`t .

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

and shocks, employment itself remains a probabilistic outcome. To this end, let ekt e

xt`+1

∈{ 0,1}

conditional on match productivity x`t+1 and time t information k`t ,e` is given by:indicate whether the household head continues on with a match at time t given a match productivity of x`t+1 in sector k. Then, the probability that worker ` is employed in sector k at time t +1, t

Pr k`

t+1

t+1 = k,e`

t+1 =1 |x`

,k`,e` = I k`t = k e`t (1 − χk ) ekt

x`t+1

(5)

+ 1 − e`t I k`t+1 = k θkt q θkt ekt x`t+1 .

In words, if I k`t = k e`t = 1, then worker ` is employed in sector k at time t and the matchsurvives with probability (1 − χk ) if the family planner decides to keep the match (et

t+1 ek x`

= 1).

is employed in sector k at time t + 1 with probability θk q θk ek x` . Importantly, workers' sector and employment status at t +1, k`t+1 and e`t+1, are determined by actions taken at t.

If e`t = 0, that is, the worker is unemployed at t, and the planner chooses k`t+1 = k, then the worker t t et t+1

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 B t+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+1B t +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, Π t, but takes this lump-sum payment as given. The household head chooses the path of consumption, ct`, the path of sectoral choices, k`t , continuation decisions, ekt (x), and bonds, B t, to solve: e

)

(

∞

Z L

max

(δ)t φt

U`td` , (6)

{kt ,et (.),Bt ,ct` }

`, ek

t=0

subject to (5) and the budget constraint:

Z L

P F,t

ct`d` + B t+1 − Π t − RtB t −

I k`t = k

et t t `wk x`

d` ≤ 0. (7)

k=1

E0 denotes expectations with respect to future idiosyncratic shocks ω . The model has no aggregate 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 thatthe 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 usingproﬁts and wage income, net of interest payments (or collections) on past bonds. Let λt be the Lagrange multiplier on the family's budget constraint (7).14 The optimality condition with respect

to ct` is u0 ct` = λt P F,t, so that individual consumption is equalized across individuals within the household: c`t = ct ∀`. Henceforth, we will refer to ct as per capita consumption. Armed with this observation, Online AppendixA 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 eachcountry, we stop indexing individual workers. We denote by Ukt,i(ω t) the value of unemployment in sector k, country i at time t conditional on shocks ω t, and by Wkt,i (x) the value of employment

conditional on match-speciﬁc productivity x. If we deﬁne φi

bt+1 ≡ φit+1

φt i

, the sector decision policyand the continuation rule ekt (.) must solve, conditional on shocks ω t: e

Uk,i(ω t ) = max k0

    

−Ckk0,i + ω k0 + bk0,i

+θk ,iqt 0

t 0 θk ,i

δφi

bt+1 R ∞ 0

max

t+1 t+1

Wk0,i (x) ,Uk0,i

k0,i

(x)

    
, (8)
+ 1 − θkt 0,iqt 0 θk ,i
δφi
bt+1U t+1
k0,i ,
and
on
t Wk,i
(x )= λe itwkt ,i (x )+ ηk,i + δφi
bt+1
(1 − χk,i) max
t+1 Wk,i
(x) ,Uk,i
t+1
bt+1 + δφi
t+1 χk,iUk,i
. (9)In equation (8), Ukt,i ≡ Eω
e t (ω t) Uk,i
is the expected value of Uekt,i(ω t), integrated over ω t. Theﬁrst line in this equation corresponds to the costs of switching sectors, −Ckk0,i + ω kt 0,i, as well as the sector-speciﬁc value of being unemployed in that sector bk0i. The second line is the probability
of ﬁnding a match θkt 0,iq
t
multiplied by the discounted value of the match. Note that for
θk0,i
low values of Wkt+0,i1 (x), the household head dissolves the match so that the worker obtains Ukt+0,i1. Finally, the third line is the discounted value of being unemployed next period if the worker fails to successfully match.
In equation (9), wkt ,i (x) is the wage paid by a ﬁrm with match productivity x. Note that it is
13 As 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 the international macroeconomics literature. SeeStockman and Tesar (1995 )orBai and R´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.
14 In an abuse of terminology we will continue to refer to λt as the Lagrange multiplier. However, the correct
e
shadow price associated with period's t budget constraint is given by δt φt λt.
e

multiplied by the household head's Lagrange multiplier on the budget constraint λit. To decentralize 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 − χk,i) the match does not exogenously dissolve and the worker continues the match; with probability χk,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
−Ckk0,i + bk0,i+
exp
o
n

θt k0,i
q(θt k0,i
)δφt+1
R
∞
bi
max
t,t+1 skk0,i
0
W t+1 k0,i
(x) − Ukt+0,i1 ,0 dG
k0,i
(x )+ δφi
bt+1 U t+1 k0,i

=
1/ζi . (10)
K
-  
−C kk00,i + bk00,i+
-  
  P exp
  o
  n
  t t t+1 R ∞
  k00=1
  
  θk00,i q(θk00,i )δφi
  b
  0
  max Wk00,i (x) − Uk00,i ,0 dG k00,i (x )+ δφit+1
  t+1 t+1
  b
  t+1 Uk00,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 zkt ,i (j) and are paid ptk,i (j) for each unit of production. A ﬁrm producing variety j in sector k with match-speciﬁc productivity x and employing composite intermediate inputs n M`t,io K obtains revenue: `=1
  K
  ! (1−γk,i )
  Y
  Ykt,i (j,x )= pkt ,i (j) zkt ,i (j) xγk,iMt `,i
  νk`,i
  ,
  (11)
  `=1
  K where γk,i ∈ (0,1), νk`,i > 0, and P `=1
  νk`,i =1
  Firms are price takers in product and intermediate-input markets and decide on the usage of n M t o K
  `,i
  solving:
  `=1
  K
  ! (1−γk,i )
  K
  X
  Y
  Skt ,i (j,x ) = max
  t t pk,i (j) zk,i
  (j) xγk,i
  Mt `,i
  νk`,i
  −
  I,t t P`,i M`,i ,
  (12)
  {M`,i }
  t
  `=1
  `=1
  where Skt ,i (j,x) denotes the revenue (net of intermediate input payments) generated by the match between a ﬁrm and a worker with productivity x producing variety j. One can show that:
  t Sk,i
  (j,x )= wt ek,i (j) x,
  (13)

where

γk,i −1

1−γk,i wekt ,i (j) ≡ γk,i (1 − γk,i ) γk,i

P M,t k,i

γk,i

pkt ,i (j) zkt ,i (j) γk,i ,

(14)

K and PkM,i,t ≡ Y `=1

I,t ! νk`,i

P`,i

(15)

νk`,i

≡ YK

νk`,i

is the price of one unit of the intermediate input composite imtk,i

t M`,i

in sector k and

`=1

country i. We assume that following entry, switching across varieties within sector is costless forﬁrms. Hence, no arbitrage across varieties will ensure that wk,i (j )=w

ekt ,i (j 0) and pk,i(j)zk,i(j )=tt

pk,i(j 0)zk,i (j 0) ∀j,j 0. Therefore, wt symmetry across varieties, allowing us to drop the index j identifying individual varieties.15 Given

ek,i and pkt ,izkt ,i do not depend on the speciﬁc variety. This implies

the expression of the surplus (13), we will henceforth refer to

twk,i

as "sectoral surpluses". As

will become clearer in Section2.7 these sectoral surpluses will play the same role as wages do inCaliendo and Parro (2015).

We can write the value function for incumbent ﬁrms, Jkt ,i (x), as:

o
t	Jkt+,i 1 (x) ,0 .	(16)
Jk,i

bt+1

(x )= λe it wk,ix − wkt ,i (x ) +(1 − χk,i) δφi

maxThe ﬁrst term is the ﬁrm's current proﬁt, and the second is the ﬁrm's continuation value of the match.16 If Jkt ,i (x)< 0 the ﬁrm does not produce and exits.

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 κk,i units of the ﬁnal good, and so amounts to total cost κk,iPiF,t. Vacancies are posted at the interim period tc as illustrated in Figure1. As argued above, Jkt ,i(x )is 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 Vkt,i, then:





t Vk,i

= −λe itκk,iPiF,t

+ δφi

t+1

t θk,i

R ∞

max

t+1 Jk,i

(s) ,0 dGk,i (s)





(17)

+ 1 − q

θt k,i

max n V t+1,0o k,i

15 Remember that we assume that workers face no mobility frictions across varieties within sectors.
16 Firm 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 Jkt ,i (x ) by λt

e i , then from the Euler

Equation we derive below, it is clear that this formulation is equivalent to a risk neutral ﬁrm discounting proﬁts using the nominal interest rate Rt+1 .

The ﬁrst term on the right hand side is the cost of posting vacancies, which is converted to utilityunits by the Lagrange multiplier λit. The second term says that in the next period entrants match

with probability qi

t θk,i

and obtain the expected value of max Jk,i ,0

t+1

starting in the nextperiod. If they do not match, they can post another vacancy. To close the model, we impose free entry so that Vkt,i ≤ 0 ∀k,i,t.17

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 (Vkt,i = 0), the outside option to the ﬁrm is 0, while to the worker it is Ukt,i. Hence, the surplus of the match is given by Skt ,i (x) ≡ Jkt ,i (x )+ Wkt,i (x) − Ukt,i. We assume that ﬁrms and workers engage in Nash bargaining over the surplus, with the workers' bargaining weight given by βk,i. This leads to Jkt ,i (x )= βk,iSkt ,i (x), which combined with equations (9 ) and (16) imply that Skt ,i , Wkt,i, and Jkt ,i are increasing functions of x, implying that matches only remain active at t if x>x kt ,i where xkt ,i solves:

t t t t t t t

Sk,i xk,i = Jk,i xk,i = Wk,i xk,i − Uk,i =0.

(18)The wage equation resulting from Nash bargaing is:

− ηk,i wkt ,i (x )= βk,iwkt ,ix +(1 − βk,i) , t

t Uk,i

− δφt+1 bi

t+1 Uk,i

(19)

e λi

for x ≥ xkt ,i. This is similar to the standard wage equation in search models: the worker's wage is 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 ta and tc, the sector-speciﬁc unemployment rates 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 ukt−,i1, and labor force as Lkt−,i1. After e

workers switch sectors, (measured before matching at td), we deﬁne ukt ,i to be the share of sector-k

17 In the equilibria we consider in this paper, we verify that this condition holds with equality, both in steady state and along transition paths.

workers searching for a job. It is given by:

t−1ut−1 t,t+1 L`,i e`,i s`k,i

uk,i = , t

`=1

(20)

Lk,i

where st`,kt,+i 1 denotes the transition rate from unemployment in sector ` to search in sector k between t and t + 1- see equation (10). Lkt ,i is the number of workers in sector k at t (more precisely at tc) and is equal to:

t t−1 Lk,i = Lk,i

t−1ut−1 t,t+1 L`,i e`,i s`k,it−1ut−1 − Lk,i ek,it,t+1 1 − skk,i

(21)

`=6 k

|{z}

Outﬂow

|{z}

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 ≥ xkt+,i1 produce at t + 1. Therefore, the number of jobs created in sector k is given by:

t t t t t JCk,i = Lk,iuk,iθk,iqi θk,i

1 − Gk,i xtk+,i1

, (22)and the number of jobs destroyed is given by:

JDk,i ≡ χk,i +(1 − χk,i )Pr xkt ,i ≤ x<x kt+,i1|xkt ,i ≤ xt

t−1 Lk,i

1 − ut−1 ek,i



 

Gk,it+1 xk,i

− Gk,it xk,i

 

=  χk,i +(1 − χk,i) max
,0

t−1 Lk,i
1 − ut−1 ek,i
, (23)

1 − Gk,it xk,i

where Pr xkt ,i ≤ x<x kt+,i1|xkt ,i ≤ x is the share of active ﬁrms above the productivity threshold 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:
et uk,it t t t = Lk,iuk,i − JCk,i + JDk,i .
Lt k,i
(24)Equations (20)-(24) describe the evolution of labor market stocks over time. In any given period, these stocks are bound by the labor market clearing condition:
K
X
Lk,i = L i.
t
(25)
k=1

2.7 International Trade

Our model of international trade closely followsCaliendo 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 pkt ,o (j) dkt ,oi, where 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:

t pk,i (j )=

ck,i t zk,i (j ),

(26)for each variety j and where

! γk,i

t ck,i ≡

wk,i γk,i

M,t Pk,i

! 1−γk,i

(27)

1 − γk,i

Recall that due to the no-arbitrage condition we impose across varieties, ckt ,i is equalized within sectors, so that price variation across varieties is dictated by zkt ,i (j).

We assume that in any country i, sector k and period t, the productivity component zkt ,i (j) is independently drawn from a Frechet distribution with scale parameter Akt ,i- which is country, 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

PkI,,it =Γ k,it Ak,o

 

 
, (28)
o=1
t t ck,odk,oi
where Γk,i is a constant. In turn, the price of the ﬁnal good (2) is given by:
K
P F,t = YI,t ! µk,i Pk,i
If we deﬁne the object Φtk,i
i
N
t
≡ P
Ak,o
(ct
dt
o=1
k,o k,oi
. (29)
µk,i
k=1
)
λ
then consumers in country i spend a share πkt ,oi of
18 The CDF for the Frechet is given by Fkt,i (z ) = exp −Ak,i × z−λ .
t

their sector-k expenditures on varieties from country o given by:

−λ

t πk,oi ≡

t Ek,oi t Ek,i =

At ct dt k,o k,o k,oi

t Φk,i

(30)P N where Ekt ,i = o=1 Ekt ,oi is the total expenditure of country i on sector k varieties and Ekt ,oi is the total expenditure of country i on sector k varieties produced by country o. Market clearing requires that total revenue Ykt,o coming from the production of varieties in sector k and country o must be equal to sales to all countries i =1 ,...,N , and so:

t Yk,o =t Ek,oi =t t πk,oiEk,i.

(31)

i=1

Let Cit ≡ Licit denote total consumption of the ﬁnal good. Deﬁne EiCt ≡ P F,t Cit as total expenditure on ﬁnal goods, and let EkV,,it be the total expenditure of sector k in country i on vacancy posting costs. We can write Ekt ,i as:

Kt C,t Ek,i = µk,iEi

+ µk,i `=1

V,t E`,i

(1 − γ`,i) ν`k,iY`,i .

(32)

`=1

The right hand side represents total expenditure on sector k goods used in ﬁnal consumption, va-cancy posting costs, and as intermediate inputs, respectively. In turn, let Iit denote total disposable income in country i, which is given by the portion of revenue that is not devoted to intermediate

good payments minus vacancy posting costs, that is, Iit =

V,t γ`,iY`,i − E`,it

. Net exports are

`=1 then given by NX it ≡ Iit − EiC,t , and we can rewrite (32) as:

Ek,i = µk,it t γ`,iY`,i − N Xi

(1 − γ`,i) ν`k,iY`,i .

(33)

`=1

Finally, labor market clearing dictates that total revenues coming from the production of varieties in sector k and country i is given by:

Z ∞

twk,i

t−1 1 − ut−1

Yk,i = γk,i Lk,iek,i

dGk,i (s).

(34)

xt k,i

1 − Gk,ixt k,i

2.8 Trade Imbalances

Note that equations (31 ),(33 ) and (34) can be solved for any given values ofN Xi , such that

i NX it = 0. However, these are not necessarily consistent with the household's optimal dynamicbehavior. To this end, we turn to the determination of net exports

N Xi

in equilibrium. Thesolution to the household head's problem (6) must satisfy the following Euler equation:

u0(ci

t)/P F,t

= δφt+1Rt+1, b

u0(ci

t+1)/P F,t+1 i

(35)and ﬁnancial and goods markets in each country are linked according to:

NX it = Iit − P

iF,tCit = Bit+1 − RtBt

(36)

Finally, to close this part of the model, we impose that bonds are in zero net supply, i Bit =0, and that the initial distribution of bonds is given by Bi0 . If the model is initially in steady state, it is easy to verify that R0 = 1δ.

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

0 × T −1Rτ + T −1

T −1

1 − δ

NX iT = −

Rτ ! NXt i

(37)

τ =1

t=1

τ =t+1

This equation shows that the behavior of long run imbalances is determined by initial wealthallocations Bi and the short-run behavior of net exports N Xi . This second piece is key in our 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 {Lk0,i,xk0,i,Bi0,} , a ﬁ-nal steady-state allocations {L∞k,i,x∞k,i,Bi∞ ,} and sequences of policy functions for workers/ﬁrms {skt k0,i,xkt ,i,wkt ,i(x)}, value functions for workers/ﬁrms {Ukt,i,Wkt,i,Jkt ,i}, labor market tightnesses

{θkt ,i}, bond decisions by the households

, bond returns	Rt	, allocations {Ltk,i,uk,i,ck,i},
n	o

t t

proﬁts and household consumption {Π it,Cit}, trade shares

t πk,io

, sectoral surpluses {wtek,i}, and

price indices

P I,t,P F,t k,i k,i

such that:

1. Worker and ﬁrms' value functions solve (8 ),(9), and (16).

19 In 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.

i−1

20 We also invoke a transversality condition that limT →∞

T s=1

Bi → 0 ∀ i.

2. The free entry condition holds in each country and sector: Vkt,i =0 ∀k,i,t.
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 prob-lem (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.

8. Labor markets clear:

Lk,i = Li.

k=1

9. Bonds market clears: Bit =0.
i=1
10. The initial and ﬁnal steady-state equilibria satisfy equations (A.15)-(A.36) in Online Ap-pendixB.

3 Data and Estimation

Our main source of cross-country data is the World Input Output Database (WIOD), which com-piles 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 World aggregate constructed by the WIOD. Each country's economic activity consists of six sectors: Agriculture; Low-, Mid- and High-Tech Manufacturing; Low- and High-Tech Services. TablesI andII detail these divisions. We solve our model at the quarterly frequency.

The WIOD dataset allow us to generate various moments that we use in our procedure (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. TableIII 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 literatureTable 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
2 Low-Tech Manufacturing
3 Mid-Tech Manufacturing
4 High-Tech Manufacturing
5 Low Tech Services
6 Hi Tech ServicesAgriculture, Forestry and Fishing; Mining and quarrying Wood products; Paper, printing and publishing;

Coke and reﬁned petroleum; Basic and fabricated metals; Other manufacturing

Food, beverage and tobacco; Textiles;

Leather and footwear; Rubber and plastics; Non-metallic mineral products

Chemical products; Machinery;

Electrical and optical equipment; Transport equipment Utilities; Construction; Wholesale and retail trade; Transportation; Accommodation and food service activities; Activities of households as employers

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 TableIII.21

As discussed inArtuc¸ et al. (2010), we are not able to separately identify ζi- the dispersion of ω shocks- and mobility costs Ck`,i without time variation in wages and transition rates across sectors. For this reason, we followArtuc¸ et al. (2010) and impose ζi, to be equal to 1.63 and common 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 the discount factor to be δ =0 .9924, leading to an annual discount factor of 0.97- the same value as inArtu¸c et al. (2010).Flinn (2006) discusses the diﬃculty in identifying the parameters of matching functions without relying on data on vacancies. We parameterize the matching function according toCo¸sar et al. (2016): qi (θ )= 1+ θξi 1/ξi and impose their estimate ξi =1 .84 to be common across countries.23Flinn (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 and set βk,i =0 . 5(Mortensen and Pissarides,1999). The Frechet scale parameter λ = 4 comes fromSimonovska and Waugh (2014).24 Finally, we assume individuals have log utility over consumption, 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 µk,i, labor expenditure shares γk,i and input-output matrices νk`,i; this follows from the Cobb-Douglas assumptions we 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 1,...,ΘN ) be the vector of these country-speciﬁc parameters. Our estimation procedure assumes that the economy is in steady state in 2000 and conditions on the observed 2000 trade shares πkD,oaita and net exports NX iData- so these moments are perfectly matched. Online AppendixB 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 πkD,oaita and NX iData, to generate: (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

21 To be precise, we do not target trade shares and net exports, we impose them in the estimation, so that they are matched exactly.

22 Estimates of ζi in the literature range from 0.7 in Denmark (Traiberman,2019) to 2.1 in Brazil (Dix-Carneiro,2014). The value of 1.63 inArtuc¸ et al. (2010) is well within these bounds, making it a conservative choice. In addition,Traiberman (2019) estimates ζi =1 .9 in Denmark when the method inArtu¸c et al. (2010) is applied, which disregards worker heterogeneity and human capital accumulation.

23 One convenient property of this functional form is that it always leads to qi (θ) and θqi (θ) to be bounded by 0 and 1.

24Caliendo and Parro (2015) ﬁnd a similar value for λ when it is imposed to be equal across sectors: 4.55.

Table IV: Summary of Parameters

Panel A. Fixed According to the LiteratureParameter δ ζi ξi βk,i λ

ValueDescription

Source

0.9924 Discount factor
Artuc¸ et al. (2010)
1.63 Dispersion of ω shocks
Artu¸c et al. (2010)
1.84 Matching Function
Co¸sar et al. (2016)
0.5 Worker Bargaining Power
Mortensen and Pissarides (1999)
4 Frechet Scale Parameter

Simonovska and Waugh (2014)

Panel B. Estimated Outside of the ModelParameter

µk,i γk,i νk`,i

Description	Source
Final Expenditure Shares	WIOD
Labor Expenditure Shares	WIOD
Input-Output Matrix	WIOD

Panel C. Estimated by Method of Simulated Moments
Description
Vacancy Costs
κk,i
Exogenous Exit
χk,i
2	Distribution of Match-Speciﬁc Prod.
σk,i
Sector-speciﬁc Utility
ηk,i
Mobility Costs
Ckk0
Unemployment Utility
bk,i

Parameter

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 .97 41 . The distribution of match-speciﬁc productivities is imposed to follow a log-normal distribution Gk,i ∼ log N (0,σk2,i ).

generated moments and those we measure in the data.

We impose a few restrictions on the parameters estimated by the simulated method of moments.

First, the identiﬁcation of mobility costs Ck`,i relies on data on both wages and yearly inter-sectoral transition rates. Although these data can be found in household surveys across a few of the countries 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, we need to impose Ckk = 0 for all k. Second, we impose the distribution of match-speciﬁc productivities Gk,i to follow a log-normal distribution with mean 0 and variance σk2,i. We restrict σk2,i to be the same across sectors and countries, and identify it by targeting the cross-sectional coeﬃcient of variation of log-wages in the CPS. Third, we impose that the exogenous exit rates χk,i are decomposed into a country component χi and a sector component χk (that is, χk,i = χi + χk ).

The sector-speciﬁc component χk is identiﬁed from US transitions from sector-speciﬁc employment to unemployment. The country-speciﬁc components are then adjusted to better match the country-speciﬁc unemployment rates. Fourth, the utility of unemployment bk,i is imposed to be countryspeciﬁc (that is bk,i = bi). This parameter will be important for the model to be able to match levels of wages across countries. Finally, sector- and country-speciﬁc utility terms ηk,i help the model simultaneously ﬁt sector-speciﬁc wages and employment shares. To achieve identiﬁcation, we need to impose ηk0 ,i = 0 for some sector k0 (we picked k0 = Agriculture).

A convenient aspect of our approach is that, by conditioning on the observed 2000 trade shares

and trade imbalances, and normalizing total world revenues

ki Yk,i

= 1, we can solve forsector-country revenues {Yk,i} that are independent of Θ. Speciﬁcally, equations (31 ), (33), and the normalization lead to a system of equations in {Yk,i}, which can be solved before starting the 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.

As a ﬁnal point, a convenient aspect of conducting the estimation conditional on the observed trade shares is that we do not have to estimate the technology parameters Ak,i and trade costs dk,oi . We develop algorithms to perform counterfactual responses to shocks to technology parameters and trade costs relying on the exact hat algebra approach inDekle et al. (2007),Dekle et al. (2008) andCaliendo 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 Ck`,i and σk2,i to be constant across countries 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 Ck`, σk2 and χk.

In a second step, we estimate the rest of the parameters in parallel, country by country, conditional on the values of Ck`, σk , and χk that are estimated in the ﬁrst step.

At this point, it is worthwhile mentioning that our estimation approach, which does not estimate

Ak,i and trade costs dk,oi, cannot recover κk,i. Instead, we are able to recover the value of κk,i ≡ e

κk,i PiF in the 2000 steady-state equilibrium. Our counterfactual algorithms then allow κ

e k,i

wk,i

respond to shocks, using exact hat algebra. It is also important to clarify that identifying κk,i is e

diﬃcult in practice. Even though the objective function is not ﬂat with respect to κk,i, it tends to e

be relatively ﬂat for a wide range of values. For that reason, we followHagedorn and Manovskii (2008) and impose that the cost of posting one vacancy κk,iPiF equals 0.58 × wk,i, where wk,i is the

25 The method of simulated moments objective function is highly non-linear and non-convex, so that global opti-mization 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.

average wage in sector k and in country i.Hagedorn and Manovskii (2008) base their calibration on 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 (κk,i × wk,i) /wk,i = κk,i × PiF

/wk,i

and 0.58 in our method of simulated moments objective function. The full estimation algorithm is described in Online AppendixC.1.

4 Estimation Results and Mechanisms

4.1 Estimates and Model Fit

The estimated parameters can be found in the Online AppendixC.7, in TablesA.1 throughA.8. We ﬁrst discuss the parameters that are obtained outside of the model. The Online Data Appendix details how these are computed with data from the WIOD. TableA.1 displays the ﬁnal expenditure shares µk,i. We can separate the countries in this table in two groups with similar expenditure 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.

TableA.2 displays the share of revenues devoted to labor payments. This share varies mostly within countries and across sectors and ranges between 0.24 (in High-Tech Manufacturing in China) and 0.68 (in High-Tech Services in Rest of the World). Finally, TableA.3 displays the average across 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 TableA.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 λi × wk,i, and not just based on sector-speciﬁc average e

wages. Therefore, to make our estimates comparable to those inArtu¸c et al. (2010), we express

26 As the authors point out, in the steady state of a single sector search model, capital is equivalent to interpreting vacancies as capital and reinterpreting the productivity process. In this sense, a vacancy is a metaphor for the whole 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.

Figure 2: Model Fit

(a) Employment Shares

(b) Unemployment Rates

(d) Transition Rates

mobility costs as multiples of λ US × wUS, where wUS is the average wage in the US (in the data).

We obtain that our estimated mobility costs across sectors (as a fraction of λ US × wUS) range from virtually zero to a maximum of 3.1. These numbers are of the same order of magnitude, but lower than whatArtu¸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 ηk,i, account for our lower estimates of mobility costs. Indeed,Artu¸c and McLaren (2015) extends ACM to allow for η terms and also ﬁnd lower moving frictions. Finally, TableA.7 shows that the values of unemployment bi tend to be negative across 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 sectors and countries; (b) unemployment rates across sectors and countries; (c) average wages across sectors and countries; and (d) inter-sectoral transition rates in the United States. As a general rule,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 Ak,China, the 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 section5.1. Next, we feed the model with a tenfold permanent increase in Ak,China that happens once and for all at t = 1. Finally, we simulate a slow-moving and linear increase in Ak,China that reaches a tenfold increase in 15 years. It remains at that level from there on. These shocks are illustrated in Figure3. 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 NX it =0 ∀i,t.27

We start with the temporary shock depicted in Figure3a. The evolution of net exports in Figure4 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:

XJX

Reallocationi = 12

Ls i,k s

s−1 Li,k − ,

LiLi

s−1

(38)

s=1 k=1

which accumulates yearly changes in sectoral employment shares over time.

Figure5a plots the evolution of the reallocation index (38) across countries. When we consider

27 To 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 AppendixC.3 for details on how we implement this procedure using exact hat algebra techniques.

Figure 3: Shocks to Chinese Productivity Ak,China - Uniform Across Sectors

(a) Temporary

(b) Once-And-For-All

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 and within other countries.28 The reason that uniform productivity changes can have large impacts 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 in trade costs implies that the tradability of goods diﬀers across countries and sectors. As explained byDornbusch 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 input-output 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,

28 Note 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 onShimer (2005) we expect this eﬀect to be quantitatively small.

Figure 4: Net Exports Over GDP in Response to Temporary Productivity Growth in China (Figure3a)

as shown in Figure5b. This highlights a key mechanism in our model: even positive labor de-mand 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 Figures5c (for the full model) and5d (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 ﬁnalFigure 5: Labor Market Dynamics in Response to Temporary Productivity Growth in China (3a)

(a) Reallocation Index

(b) Unemployment

(d) Labor Allocations - Balanced Trade

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. Figure6 highlights that the eﬀect of this shock on net exports across countries is of much 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

29 However, 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).

Figure 6: Net Exports Over GDP in Response to Once-and-for-all Productivity Growth in China (Figure3b)

Finally, we study the behavior of our model when we feed it with a slow increase in Chinese productivity, as is illustrated in Figure3c. Figure7 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. Figures8a and8b show that the short-run labor market dynamics are very diﬀerent across the two models. With trade imbalances, Figure8c 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 Figure8d. 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 real-location and unemployment responses to temporary shocks. They can also lead to very diﬀerent patterns of inter-sectoral reallocation in the short and long run. However, the quantitative relevance of endogenizing imbalances depends on the nature of the shock, as illustrated by our once-and-for-all permanent shock example. This fact can be appreciated by comparing the results for the tempo-rary 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 thesign 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 (Figure3c)

5 Counterfactuals

Section 4.2 showed that the exact path of shocks shape the magnitude and evolution of trade imbalances over time, directly inﬂuencing long-run outcomes through changes in the long-run global distribution of bond holdings. For this reason, we conduct an empirical exercise in which we extract 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 process and long-run allocations, we compare the consumption gains in response to changes in trade 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 worldFigure 8: Labor Market Dynamics in Response to Slow Productivity Growth in China (Figure3c)

(a) Reallocation Index

(b) Unemployment

(d) Labor Allocations - Balanced Trade

without the global savings glut, or in a world with balanced trade (i.e., no bonds). Finally, given the 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

This section obtains the time series for three sets of shocks in the global economy between December

of 2000 and December of 2014: changes in trade costs

dk,oi

, inter-temporal preference shocks

non

bt φi

and productivity shocks

At bk,i

. We measure changes in trade costs and productivity relativeto inter-temporal preferences are relative to the previous period: φi

t	t
to December of 2000 (which we label t = 0): dk,oi	= dk,oi	Ak,i	. On the other hand, shocks
d0	A0
k,oi	k,i

bt+1 ≡ φit+1

, At bk,i =

φt i

onon

We use WIOD data to construct time series of trade shares

t πk,oi

, sectoral price indices

I,t Pk,i

and ﬁnal good expenditures

E C,t i

between December of 2000 and December of 2014. Armed withthese data, we can exploit the gravity structure of the trade block of the model, as inHead and Ries (2001) andEaton et al. (2016), to recover the changes in bilateral trade costs combining equations equations (28 ) and (30):

P I,tt

! 1/λ

b dk,oi

k,i

P I,t bk,o

πk,oo πt bk,oi

(39)In turn, we rely on the Euler equation (35) and normalize φ Ut S =1 ∀t , as inReyes-Heroles (2016), to recover the inter-temporal preference shocks:

bb φi

t+1

C,t+1

C,t

ECU,tS+1 for t =1 ,...,T − 1,

(40)

C,tE US

where T is the last period for which we have data, which refers to December of 2014. Note that westill need to determine φiT +1, but we will need to use the structure of the model to do so, as this value will depend on the model-implied steady-state value for ﬁnal good expenditures EiC,∞ .

Finally, we recover the productivity shocks

Ak,i

using:

bt Ak,i

= b

πk,ii

t ck,i

(41)

I,t

Pk,i

30 We impose Akt ,i = A and dtk,oi = dbkT,oi for all t>T , where T is the last period for which we have data (T =14

bk,i

and refers to December 2014). We also impose and φbti = 1 for all t>T +1- as explained below, the value of φT +1 =1 is set to gauge the model-implied steady-state value for ﬁnal consumption expenditures EiC,∞ .

Given that ck,i depends on w of the model to recover the sequence of productivity shocks. Online AppendixC.6 details the

ekt ,i, which has no data counterpart, we need to use the full structure

algorithm to recover the shocks

At bk,i

as well as

bT +1 φi

using the full structure of the model.

To be able to recover the full set of shocks the economy experienced between 2000 and 2014, weassume the economy faces no additional shocks after 2015. That is, the values for and φit are imposed to be constant from 2015 onwards.31

n	o n
,	t
dk,oi

t Ak,i

Figure9a shows an increase in productivity all over the world. In particular, China has ex-perienced 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 experienced impressive productivity growth, while growth was more muted for advanced economies.

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

t k,i

= X

k,oio=6 i

1 − π0 k,ii

bt dk,oi

(42)Figure9b 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 inBems 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 Figure10. 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

31 We also assume the economy is in steady state in 2000 and fully anticipates the full set of current and future shocks in 2001.

32 While we plot changes in the productivity location parameters

Ak,i

, this is not directly comparable to pro-ductivity in the classic sense of a Solow Residual. In order to make sense of the magnitudes, note that TFP growth,deﬁned as ck,i /Pk,i , can be expressed as (Ak,i /πk,ii Therefore, using our recovered values for At changes in trade shares, and imposing λ = 4, the magnitude for actual annualized TFP growth in China ranges from 3 to 5% per year, depending on the sector- which is in line with growth accounting estimates discussed inZhu (2012).

b I,t

bt bt )1 /λ.

bk,i , data on

Figure 9: Extracted Globalization Shocks

(a) Productivity Shocks Akt ,i

(b) Trade-Weighted Import Costs dtk,i (See Equation (42))

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, insteadsummarizing the eﬀect of these channels with the φit shocks. This is useful because it allows 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 φit

To extract the shocks the global economy experienced between 2000 and 2014, we have solely relied on data on trade shares, sectoral prices, and aggregate ﬁnal expenditures across countries. We have not used information on labor allocations or trade imbalances. It is therefore natural to ask how 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, Figure11 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

33 The 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 bySong et al. (2011), ﬁnancial frictions within China are key drivers of the Chinese savings glut. Our inter-temporal preference shocks constitute a reduced-form way to allow the model to match the time series behavior of Chinese aggregate expenditures and the rest of the world.

pre-existing trends driving the decline of manufacturing as well as the fact that we impose that theinter-temporal shocks φit revert to 1 after 2014. The latter observation is important as individuals 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 φit shocks ﬁxed at their 2012 to 2014 averages for 15 more years (that is, until 2029). Indeed, not only the magnitude of the downsize of manufacturing that we obtain is larger than what is depicted in Figure11a, but also Low-Tech steadily contracts until 2014.

Figure 11: Comparing Labor Allocations in the Model and Data

(a) Model

(b) Data

Figure12 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

Our ﬁrst counterfactual exercise focuses on the general equilibrium eﬀects of changes in productivity and trade costs since 2000, with no shocks to inter-temporal preferences. In particular, we focus

onon

on the consequences of our extracted series of

At bi

and

bt dk,oi

above. Our goal is to isolate thequantitative 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. ThereFigure 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) andDekleet al. (2007)) and dynamic models (e.g.,Dix-Carneiro (2014) andTraiberman (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 inCaliendo 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 im-balances relative to a model without imbalances, we start both models from a steady steady with trade balance- that is NX it =0 ∀i at t = 0, see Online AppendixC.3 for details on our procedure, which is based on exact hat algebra. Figure13 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 section4.2 as Chinese productivity strongly and steadily increases between 2000 and 2014, more than in other countries.

34 These approximations may be reasonable in a situation where imbalances are small along the transition path from one equilibrium to the next. This would be the case, for example, if the primary force for changes in imbalances wereshocks to aggregate consumption, and orthogonal to trade shocks (i.e., if imbalances were driven by φit ). 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.

Figure 13: Net Exports Over GDP in Response to Global Technology and Trade Shocks

We learned in our analysis of section4.2 that trade imbalances can amplify the amount of reallocation in the economy relative to a model where trade is balanced. Our empirical exercise corroborates this ﬁnding, as we illustrate in Figure14a. The behavior of unemployment is also quite diﬀerent, and driven by a larger amount of reallocation. Figures13 and14b also show that the responses of unemployment are not systematically related to the sign of imbalances. Importantly, Figures14c and14d 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, and that accounting for these imbalances can substantially alter the adjustment process 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 the widely used suﬃcient-statistics approach based on Arkolakis et al. (2012), henceforth ACR. Our model nests the Ricardian model considered in ACR, but violates two of their key assumptions: (i)Figure 14: Labor Market Dynamics in Response to Global Technology and Trade Shocks

(a) Reallocation Index

(b) Unemployment

(d) Labor Allocations - Balanced Trade

no labor market frictions; and (ii) no trade imbalances.

Concretely, we consider the changes in trade costs between 2000 and 2014 we obtain in Section5.1, purging the model of shocks to inter-temporal preferences and to productivity. In this case, the implied gains from trade followingCostinot and Rodr´ıguez-Clare (2014), who extend the ACR formula to allow for input-output linkages, is given by:

W ACR, Static = Y

π−µj,i ℵ jk,i /λ, bk,ii

(43)

j=1k=1

where all of the changes are between ﬁnal and initial steady states and ℵ jk,i is the j,kth element of the Leontief Inverse of the input-output matrix in country i. We obtain πk,ii solving our full b

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.

Figure15a displays the comparison between the long-run ACR gains in consumption (blue bars) 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%. Our conclusions diﬀer starkly in China, where the ACR formula predicts a gain of almost 3%, 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. Figure16 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:

)

(

∞

Wi ≡ exp (1 − δ) X δt log(Cit) − log(Ci ) .

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:





∞

WiACR, Dynamic

=(1 − δ)



(πk,ii)− µj,i ℵ jk,i /λ b



(45)

t=0

j=1k=1

where πkt ,ii is the change in trade shares between periods 0 and t, computed using our full model.

Figure 15: Shocks in Trade Costs and the Consumption Gains from Trade

(a) Long-Run Gains from Trade

(b) Dynamic Gains from Trade

Notes: In Panel (a), the blue bars, "ACR," refer to the consumption gains computed using equation (43); the red bars, "Full Model," refer to the change in steady-state consumption given by our full model with trade imbalances. In Panel (b), the blue bars, "ACR," refer to the present value of gains calculated by using equation (45); the red bars, "Full Model," refer to the present value of gains over the transition in the full model with trade imbalances, using equation (44). In all cases, πkt ,ii is b

obtained by simulating our full model initialized with NX it =0 ∀ i at t =0

Figure15b 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 beneﬁtted from all globalization shocks during the period we consider, which include shocks to trade 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, whileFigure 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 Section5.1. TableV 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 shows that gains in the US are reduced from 2.2% to 1.3%. Finally, we investigate the eﬀect of inter-temporal shocks in the third and fourth columns (with and without trade imbalances, 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 ofAutor et al. (2013) andPierce and Schott (2016). We compare the behavior of our model when we feed it with all of the shocks we recovered in Section5.1 (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

φCt hina = 1 for all t.35 In these simulations, trade imbalances in the initial steady state are set at

N Xi

t=0

Data = N Xi

, that is, the level of trade imbalances in the data in 2000.

35 Shocks to inter-temporal preferences and their interaction with standard shocks in productivities and trade costs diﬀerentiate these counterfactual experiments fromCaliendo et al. (2019) andAda˜o et al. (2020).

Table V: Globalization Consumption Gains Over 2000-2014

Country

Complete ModelBalanced TradeComplete Model φbit =1 ∀i,tBalanced Trade φbti =1 ∀i,t

United States China Europe Asia/Oceania Americas

1.022

1.013

1.038 1.013

1.066

1.067

1.056 1.067

1.015

1.025 1.016

1.003

1.021

0.997 1.021

1.003

1.006

1.002 1.006

Rest of the World

1.052

1.045

1.037 1.045

Notes: Each row displays Wi (see equation (44)) in response to extracted shocks to all other countries when own

country shocks are neutralized. Third and fourth columns impose φit =1 ∀ i,t, neutralizing all inter-temporal preference shocks. To make the Complete Model exercises comparable with the Balanced Trade ones, we initialize the Complete Model with NX it =0for t =0.

We ﬁrst analyze the situation where shocks to China between 2000 and 2014 are imposed to be equal to the average of shocks across all of the remaining countries.36 The objective is to understand 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 Figure17a shows that China runs a much more modest trade surplus over time compared to the Benchmark illustrated by the blue solid line. Interestingly, Figure17b 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.

Figure18 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, the contraction in Mid- and High-Tech Manufacturing would have been less pronounced. The eﬀect 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. Figure19a shows that the behavior of unemployment with the China shock (solid blue line) or without it (dashed

36 Shocks to trade costs from country i to China are set to be equal to a weighted average of shocks between country i and all other countries- weights are given by country sizes Li . Shocks to trade costs from China to country i are set to be equal to the weighted average of shocks between all remaining countries and country i.

Figure 17: The China Shock: Net Exports

(a) NX / GDP in the China

(b) NX / GDP in the US

Notes: "All Shocks": model is fed with all shocks recovered in section5.1. "China Receives World Avg. Shocks": model is fed with all shocks recovered in section5.1, with the exception of China. For China, productivity and inter-temporal productivity shocks between 2000 and 2014 are imposed to be equal to the average of these shocks across all the remaining countries. Shocks to trade costs from country i to China are set to be equal to a weighted average of shocks between country i and all other countries- weights are given by country sizes Li . Shocks to trade costs from China to country i are set to be equal to the weighted average of shocks between all remaining countries and country i. "AllShocks but φChina = 1": model is fed with all shocks recovered in section5.1 but China's savings glut by setting

φCt hina = 1 for all t. t = 0 corresponds to year 2000. t = 14 corresponds to 2014, the last year of data we employed to extract the shocks.

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 Figure19a is not a mechanical feature of our model. Indeed, Figures5b,8b and14b 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 Section5.1.

Figure19b 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 of these shocks on US unemployment is muted. On the other hand, aggregate unemployment ranges 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 theFigure 18: The China Shock: Labor Allocations in the US

Notes: "All Shocks": model is fed with all shocks recovered in section5.1. "China Receives World Avg. Shocks": model is fed with all shocks recovered in section5.1, with the exception of China. For China, productivity and inter-temporal productivity shocks between 2000 and 2014 are imposed to be equal to the average of these shocks across all the remaining countries. Shocks to trade costs from country i to China are set to be equal to a weighted average of shocks between country i and all other countries- weights are given by country sizes Li . Shocks to trade costs from China to country i are set to be equal tothe weighted average of shocks between all remaining countries and country i. "All Shocks but φC hina = 1": model is fed

with all shocks recovered in section5.1 but China's savings glut by setting φCt hina = 1 for all t. t = 0 corresponds to year 2000. t = 14 corresponds to 2014, the last year of data we employed to extract the shocks.

same shocks but remove China's saving glut (that is, we set φCt hina = 1 for all t). The yellow dotted line in Figure17a 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 Section4.2, and, more speciﬁcally, given Figure7. In anticipation of a much higher level of productivity in the future (see Figure9a), China borrows greatly in the short run to smooth consumption over time.

37 In 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 inHeathcote and Perri (2014).

Figure 19: The China Shock: Unemployment in the US

(a) Aggregate Unemployment

(b) Sectoral Unemployment

Notes: Panel (a) - "All Shocks": model is fed with all shocks recovered in section5.1. "China Receives World Avg. Shocks": model is fed with all shocks recovered in section5.1, with the exception of China. For China, productivity and inter-temporal productivity shocks between 2000 and 2014 are imposed to be equal to the average of these shocks across all the remaining countries. Shocks in trade costs from country i to China are set to be equal to the simple average of shocks between country i and all other countries. Shocks to trade costs from country i to China are set to be equal to a weighted average of shocks between country i and all other countries- weights are given by country sizes Li . Shocks to trade costs from China to country i are set to be equal to the weighted average of shocks between all remaining countries and country i. "All Shocks but φChina = 1": model is fed with all shocks recovered in section5.1 but China's savings glut by setting φCt hina = 1 for all t.

t = 0 corresponds to year 2000. t = 14 corresponds to 2014, the last year of data we employed to extract the shocks. Panel (b) - Behavior of sectoral unemployment rates in response to "All Shocks".

This debt must be repaid in the form of large surpluses in the long run. This result illustrates thequantitatively important role of shocks to inter-temporal preferences φCt hina not only in oﬀsetting these large short-run trade deﬁcits, but also in turning them into surpluses.38

Neutralizing the Chinese savings glut also has important eﬀects on the dynamics of the US trade deﬁcit. The yellow dotted line in Figure17b 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 Figure18 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

38 If we abstract from intertemporal preference shocks in China, our result is in line with the "allocation puzzle" 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 intertem-poral preference shifters could be interpreted as arising from the public sector's expenditure decisions (Gourinchasand Jeanne,2013;Aguiar and Amador,2011;Alfaro et al.,2008).

39 These results are in line with the ﬁndings ofKehoe et al. (2018) on the eﬀects of the savings glut on structural

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 Section5.1 (Benchmark), relative to the counterfactuals where (a) shocks to China are set to be equal to the average shocks experienced by the remaining countries: WiBenchmark /Wc i(a); and where (b) we neutralize China's savings glut by

setting φbCt hina = 1 for all t: Wc iBenchmark /Wi(b). By doing so, we are capturing the eﬀect of China's 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. WiBenchmark c

/Wc i(a)

Country

Complete ModelBalanced TradeUS 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. WiBenchmark c

/Wc i(b)

Country US Europe Asia Americas

Rest of the World

Complete Model	Balanced Trade
0.997	1.000
0.998	1.000
0.998	1.000
1.003	1.000
1.010	1.000

Notes: Changes in welfare obtained using equation (44).

Wi refers to all shocks extracted in Section5.1 fed into the

Benchmark

model. Wi(a) refers to these same shocks, but China's shocks at set to

the average of shocks in remaining countries. Wi(b) refers to all shocks

extracted in Section5.1 fed into the model, but φCt hina = 1 for all t. To make the Complete Model exercises comparable with the Bal-anced Trade ones, we initialize the Complete Model with NX it =0 for t =0.

Panel A of TableVI 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.

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 the Chinese savings glut. The Chinese savings glut would have had virtually no consumption eﬀects 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 economists typically abstract from trade imbalances when they study the labor market consequences of globalization shocks. This paper ﬁlls this gap by extending the workhorse model of trade (Eatonand Kortum,2002, andCaliendo and Parro,2015) to allow for inter-sectoral mobility costs (as inArtu¸c et al.,2010), search frictions (as inMortensen and Pissarides,1999), and trade imbalances (as inReyes-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) incorporat-ing 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, tem-porary 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 onthe behavior of labor markets around the world. Next, we investigate how the gains from trade in our model compare with those obtained using the inﬂuential suﬃcient-statistics approach pioneered byArkolakis 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 inCostinot 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 Man-ufacturing. 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 experi-enced. 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 implica-tions for the adjustment process in response to globalization shocks and opens important questions for future work. Given the importance of imbalances for the reallocation process, a natural question 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 capital-skill complementarity, generating rich mechanisms linking globalization to the skill premium as inReyes-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.

References

Ad˜ao, Rodrigo, Costas Arkolakis, and Federico Esposito, "General Equilibrium Eﬀects in

Space: Theory and Measurement," Technical Report 2020.

Aguiar, Mark and Manuel Amador, " Growth in the Shadow of Expropriation *," The Quar-terly Journal of Economics, 06 2011, 126 (2), 651-697.

Alessandria, George A and Horag Choi, "The dynamics of the US trade balance and real exchange rate: The J curve and trade costs?," Technical Report, National Bureau of Economic Research 2019.

Alfaro, Laura, Sebnem Kalemli-Ozcan, and Vadym Volosovych, "Why Doesn't Capital

Flow from Rich to Poor Countries? An Empirical Investigation," The Review of Economics and Statistics, 2008, 90 (2), 347-368.

Arkolakis, Costas, Arnaud Costinot, and Andr´es Rodr´ıguez-Clare, "New trade models, same old gains?," American Economic Review, 2012, 102 (1), 94-130.

Artu¸c, Erhan and John McLaren, "Trade policy and wage inequality: A structural analysis with occupational and sectoral mobility," Journal of International Economics, 2015, 97 (2), 278-294.

Artu¸c, Erhan, Shubham Chaudhuri, and John McLaren, "Trade Shocks and Labor Ad-justment: A Structural Empirical Approach," American Economic Review, June 2010, 100 (3), 1008-45.

Autor, David H., David Dorn, and Gordon H. Hanson, "The China Syndrome: Local

Labor Market Eﬀects of Import Competition in the United States," American Economic Review, October 2013, 103 (6), 2121-68.

, , and , "The China Shock: Learning from Labor-Market Adjustment to Large Changes in Trade," Annual Review of Economics, 2016, 8 (1), 205-240.

Bai, Yan and Jos´e-V´ıctor R´ıos-Rull, "Demand Shocks and Open Economy Puzzles," American

Economic Review, May 2015, 105 (5), 644-49.

Barany, Zsoﬁa, Nicholas Coeurdacier, and St´ephane Guibaud, "Capital Flows in an Aging

World," 2018.

Bems, Rudolfs, Robert C. Johnson, and Kei-Mu Yi, "The Great Trade Collapse," Annual

Review of Economics, 2013, 5 (1), 375-400.

Bernanke, Benjamin S., "The Global Saving Glut and the U.S. Current Account Deﬁcit," Speech presented at the Sandridge Lecture, Virginia Association of Economists, Richmond, VA, March 10 2005.

Caballero, Ricardo J., Emmanuel Farhi, and Pierre-Olivier Gourinchas, "An Equilibrium

Model of "Global Imbalances" and Low Interest Rates," American Economic Review, March 2008, 98 (1), 358-93.

Caliendo, Lorenzo and Fernando Parro, "Estimates of the Trade and Welfare Eﬀects of

NAFTA," Review of Economic Studies, 2015, 82 (1), 1-44.

, Maximiliano Dvorkin, and Fernando Parro, "Trade and Labor Market Dynamics: General Equilibrium Analysis of the China Trade Shock," Econometrica, 2019, 87 (3), 741-835.

Carr`ere, C´eline, Anja Grujovic, and Fr´ed´eric Robert-Nicoud, "Trade and Frictional Un-employment in the Global Economy," Journal of the European Economic Association, 01 2020. jvz074.

Co¸sar, A. Kerem, Nezih Guner, and James Tybout, "Firm Dynamics, Job Turnover, and

Wage Distributions in an Open Economy," American Economic Review, March 2016, 106 (3), 625-63.

Costa, Francisco, Jason Garred, and Jo˜ao Paulo Pessoa, "Winners and losers from a commodities-for-manufactures trade boom," Journal of International Economics, 2016, 102 ,50 - 69.

Costinot, Arnaud and Andr´es Rodr´ıguez-Clare, "Trade Theory with Numbers: Quantifying the Consequences of Globalization," in "Handbook of International Economics," Vol. 4, Elsevier, 2014, pp. 197-261.

Dauth, Wolfgang, Sebastian Findeisen, and Jens Suedekum, "Adjusting to Globalization in Germany," IZA DP No. 11299, IZA 2018.

Dekle, Robert, Jonathan Eaton, and Samuel Kortum, "Unbalanced Trade," American

Economic Review, May 2007, 97 (2), 351-355.

, , and , "Global rebalancing with gravity: Measuring the burden of adjustment," IMF Staﬀ Papers, 2008, 55 (3), 511-540.

Dix-Carneiro, Rafael, "Trade Liberalization and Labor Market Dynamics," Econometrica, 2014, 82 (3), 825-885.

and Brian K. Kovak, "Trade Liberalization and Regional Dynamics," American Economic Review, October 2017, 107 (10), 2908-46.

and , "Margins of labor market adjustment to trade," Journal of International Economics, 2019, 117, 125 - 142.

Dornbusch, R., S. Fischer, and P. A. Samuelson, "Comparative Advantage, Trade, and

Payments in a Ricardian Model with a Continuum of Goods," The American Economic Review, 1977, 67 (5), 823-839.

Eaton, Jonathan and Samuel Kortum, "Technology, Geography, and Trade," Econometrica, 2002, 70 (5), 1741-1779.

, , and Brent Neiman, "On Deﬁcits and Unemployment," Revue ´economique, 2013, 64 (3), 405-420.

, , , and John Romalis, "Trade and the Global Recession," American Economic Review, November 2016, 106 (11), 3401-38.

Flinn, Christopher J., "Minimum Wage Eﬀects on Labor Market Outcomes under Search,

Matching, and Endogenous Contact Rates," Econometrica, 2006, 74 (4), 1013-1062.

Gourinchas, Pierre-Olivier and H´el`ene Rey, "Chapter 10 - External Adjustment, Global

Imbalances, Valuation Eﬀects," in Gita Gopinath, Elhanan Helpman, and Kenneth Rogoﬀ, eds., Handbook of International Economics, Vol. 4 of Handbook of International Economics, Elsevier, 2014, pp. 585 - 645.

and Olivier Jeanne, "Capital Flows to Developing Countries: The Allocation Puzzle," The Review of Economic Studies, 02 2013, 80 (4), 1484-1515.

Guner, Nezih, Alessandro Ruggieri, and James Tybout, "Training, Oﬀshoring, and the Job

Ladder," Technical Report, Pennsylvania State University 2020.

Hagedorn, Marcus and Iourii Manovskii, "The Cyclical Behavior of Equilibrium Unemploy-ment and Vacancies Revisited," American Economic Review, September 2008, 98 (4), 1692-1706.

Head, Keith and John Ries, "Increasing Returns versus National Product Diﬀerentiation as an Explanation for the Pattern of U.S.-Canada Trade," American Economic Review, September 2001, 91 (4), 858-876.

Heathcote, Jonathan and Fabrizio Perri, "Chapter 9 - Assessing International Eﬃciency," in

Gita Gopinath, Elhanan Helpman, and Kenneth Rogoﬀ, eds., Handbook of International Eco-nomics, Vol. 4 of Handbook of International Economics, Elsevier, 2014, pp. 523 - 584.

Heid, Benedikt and Mario Larch, "Gravity with unemployment," Journal of International

Economics, 2016, 101 , 70 - 85.

Helpman, Elhanan and Oleg Itskhoki, "Labour Market Rigidities, Trade and Unemployment,"

The Review of Economic Studies, 07 2010, 77 (3), 1100-1137.

and , "Trade Liberalization and Labor Market Dynamics with Heterogeneous Firms," Tech-nical Report 2015.

Hornstein, Andreas, Per Krusell, and Giovanni L. Violante, "Frictional Wage Dispersion in Search Models: A Quantitative Assessment," American Economic Review, December 2011, 101 (7), 2873-98.

Ju, Jiandong, Kang Shi, and Shang-Jin Wei, "On the connections between intra-temporal and intertemporal trades," Journal of International Economics, 2014, 92, S36 - S51. 36th Annual NBER International Seminar on Macroeconomics.

Kambourov, Gueorgui, "Labour Market Regulations and the Sectoral Reallocation of Workers:

The Case of Trade Reforms," The Review of Economic Studies, 10 2009, 76 (4), 1321-1358.

Kehoe, Timothy J and Kim J Ruhl, "Sudden stops, sectoral reallocations, and the real ex-change rate," Journal of Development Economics, 2009, 89 (2), 235-249.

Kehoe, Timothy J., Kim J. Ruhl, and Joseph B. Steinberg, "Global Imbalances and

Structural Change in the United States," Journal of Political Economy, 2018, 126 (2), 761-796.

Krugman, Paul, "Globalization: What Did We Miss?," in Luis Catao and Maury Obstfeld, eds.,

Meeting Globalization's Challenges, Princeton University Press, 2019, pp. 113-120.

Meghir, Costas, Renata Narita, and Jean-Marc Robin, "Wages and Informality in Devel-oping Countries," American Economic Review, April 2015, 105 (4), 1509-46.

Mendoza, Enrique G., Vincenzo Quadrini, and Jos´e-V´ıctor R´ıos-Rull, "Financial Inte-gration, Financial Development, and Global Imbalances," Journal of Political Economy, 2009, 117 (3), 371-416.

Meza, Felipe and Carlos Urrutia, "Financial liberalization, structural change, and real ex-change rate appreciations," Journal of International Economics, 2011, 85 (2), 317-328.

Mortensen, Dale T. and Christopher A. Pissarides, "Job Creation and Job Destruction in the Theory of Unemployment," The Review of Economic Studies, 07 1994, 61 (3), 397-415.

and , "Unemployment Responses to 'Skill-Biased' Technology Shocks: The Role of Labour Market Policy," The Economic Journal, 1999, 109 (455), 242-265.

Navarro, Peter, "A Tariﬀ Issue on Which Free and Fair Traders Can Agree," Wall Street Journal,

May 2019.

Obstfeld, Maurice and Kenneth Rogoﬀ, "The Intertemporal Approach to the Current Ac-count," Handbook of International Economics, 1995, 3, 1731-99.

and , "Global current account imbalances and exchange rate adjustments," Brookings papers on economic activity, 2005, 2005 (1), 67-146.

Pavcnik, Nina, "The Impact of Trade on Inequality in Developing Countries," Working Paper

23878, National Bureau of Economic Research September 2017.

Pierce, Justin R. and Peter K. Schott, "The Surprisingly Swift Decline of US Manufacturing

Employment," American Economic Review, July 2016, 106 (7), 1632-62.

Reyes-Heroles, Ricardo, "The Role of Trade Costs in the Surge of Trade Imbalances," Technical

Report 2016.

, Sharon Traiberman, and Eva Van Leemput, "Emerging Markets and the New Geography of Trade: The Eﬀects of Rising Trade Barriers," IMF Economic Review, 2020, 68, 456-508.

Rodriguez-Clare, Andres, Mauricio Ulate, and Juan Pablo Vasquez, "New Keynesian

Trade: Understanding the Employment and Welfare Eﬀects of Sectoral Shocks," Technical Re-port, University of California at Berkeley 2020.

Ruggieri, Alesandro, "Trade and labour market institutions: A tale of two liberalizations,"

Research Paper 2019/15, University of Nottingham 2019.

Scott, Robert E., "Causes of the Trade Deﬁcit and Its Implications for the U.S. Economy:

Hearing Before the Committee on Finance, US Senate," 105th Congress. Testimony of Robert E. Scott 1998.

Shimer, Robert, "The Cyclical Behavior of Equilibrium Unemployment and Vacancies," Ameri-can Economic Review, March 2005, 95 (1), 25-49.

Simonovska, Ina and Michael E Waugh, "The elasticity of trade: Estimates and evidence,"

Journal of International Economics, 2014, 92 (1), 34-50.

Song, Zheng, Kjetil Storesletten, and Fabrizio Zilibotti, "Growing Like China," American

Economic Review, February 2011, 101 (1), 196-233.

Stockman, Alan C. and Linda L. Tesar, "Tastes and Technology in a Two-Country Model of the Business Cycle: Explaining International Comovements," The American Economic Review, 1995, 85 (1), 168-185.

Traiberman, Sharon, "Occupations and Import Competition: Evidence from Denmark," Amer-ican Economic Review, December 2019, 109 (12), 4260-4301.

Utar, Hale, "Workers beneath the Floodgates: Low-Wage Import Competition and Workers'

Adjustment," The Review of Economics and Statistics, 2018, 100 (4), 631-647.

Zhu, Xiaodong, "Understanding China's Growth: Past, Present, and Future," Journal of Eco-nomic Perspectives, November 2012, 26 (4), 103-24.

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 decen-tralized to individual workers solving equations (5 ) and (9).

The Lagrangian of problem (6 ),(7 ) and (5 )is

 

∞

δtφtLu c

t `

− λt LP F,tc`t + B t+1 − Π t − RtBt

t=0

 





  

L = E0

∞

1 − et `

−C

R L



 

 
δtφt
kt ,k
t+1 + ω `t,k
t+1 + b
k
t+1
`
`
`
+
(A.1)
 
 
 
 
d`
t=0
P et`ηk`t + λt
e
k`
t+1
= k et`wkt x`t

k=1I
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
 


Z L
∞
1 − e`
t
−C
kt ,k
X
δtφt
K`
t t+1 + ω `,k `
t+1 + b `
kt+1 + `
-  
-  
-  
-  
  d`
  (A.2)
  P
  0
  t=0
  et`ηk`t + λt
  e
  k`
  t+1
  = k et`wkt x`t
  k=1I
  means maximizing each individual term. Therefore, the planner solves, for each individual, the recursive problem:
  -  
  t 1 − e`
  −C kt ,kt+1 ` `
  t + ω `,k
  t+1 + b k `
  t+1 `
  + etη ` kt `
  -  
    LW k`,e`,x`,ω `t
    tttt
    =max
    +λ K I k`t = k et`wkt xt` +
    ,
    (A.3)
    e t P
    t+1 k`
    t+1 ,ek e
    (.)
    
    δφt+1EtLW
    k=1 t+1
    k`t+1,e`t+1,x`t+1 ,ω `t+1
    
    b
    φt+1 where φt+1 ≡ .
    b
    φt
    Denote by F t the set of information at t. So, Et (. )= E .|F t . For an unemployed worker in sector k at time t, k`t = k, e`t =0:
    LW k`t = k,e`t =0 ,x`t ,ω `t =t
    max
    − C
    t
    kk0 + ω `,k0 + bk0
    k0,{et+1 (.)}
    ek
    + δφt+1EtLt+1 b
    k0,e`t+1,x`t+1 ,ω `t+1
    W
    .
    (A.4)

Using the law of iterated expectations we obtain:

LW k`t = k,e`t =0 ,x`t ,ω `t =t

max

k0,{et+1 (.)}

− C kk0 + ω `,k0 + bk0

+ δφt+1E E LWt+1 k0,1,x`t+1,ω `t+1 |x`

+ δφt+1E E LWt+1 k0,0,x`t+1 ,ω `

t+1

max

t − Ckk0 + ω `,k0 + bk0

k0,{et+1 (.)}

|x`

t+1,Ft t+1,Ft

+ δφt+1 t

θk0

q θt k0

Lt+1

+ δφt+1E

1 − θkq

t et+1 t+1

k0,1,x`0

t+1,ω t+1 ` LWt+1

et+1 ek0

θk0

s0,0,x`

ek0

For an employed worker in sector k, k`t = k, e`t =1:

LWt

k`t = k,e`t =1 ,x`t ,ω `t =

max λtwk x` {et+1 (.)}

{et+1 (.)}e ek

+ δφt+1E

{et+1 (.)}e ek

+ δφt+1 (1 − χk )E

+ δφt+1χkE LW

Make the following deﬁnitions

Ukt ω `t ≡L Wt

× Pr × Pr

kt+1 t+1 `

= k0,e` ,F = k0,e` ,F

=1 |x` =0 |x`

t+1 t t+1 t

xt+1 `

|F t

t+1 ,ω `t+1

max wk

+ ηk + δφt+1EtLWt+1 k,e`t+1,x`t ,ω `t+1

λt t

t x`

E LW

t+1

E LW

+ ηkk,1,xt ,ω `t+1

Pr k`

t+1

k,0,xt ,ω `t+1	\|kt+1
`	`
\|F t

Pr k`

max

λtwk x` + ηk

` t+1

= k,e`

t+1

t+1 = k,e`

|kt+1 ` t+1

= k,,e

t+1 =1 ,xt+1,F t ×

t+1,Ft =1 |x`

= k,e

t+1 =0 ,xt+1,F t × `

t+1,Ft =0 |x`

|F t

et+1 ek

et+1 + 1 − ek

x` LW k,1,xt ,ω `t+1

t+1

k,0,x`,ω `t+1 |F

t+1

xt ` t

Lt+1

|F |F

` k,0,xt ,ω `t+1 |F t

t t

(A.5)

(A.6)

k`t = k,e`t =0 ,x`t ,ω `t , and

Wkt (x) ≡L Wt

k`t = k,e`t =1 ,x,ω `t .

(A.7)

Uk ω `tt

is the value of unemployment in sector k, conditional on the preference shocks ω `t, andWkt (x) is the value of a job with match productivity x. Note that LWt

t t t k` = k,e` =0 ,xt`,ω ` does

not depend on x`t and LWt k`t = k,e`t =1 ,x,ω `t does not depend on ω `t. Rewrite Uk ω

Uk ω` =

max	− C	t
kk0 + ω `,k0 + bk0
k0,{et+1 (.)}
Z

+ δφt+1 t

θk0

q θt k0

W t+1 k0

(x) et+1 (x) dG ek0

t `

(x)

+ δφt+1 b

t 1 − θk0q

t θk0

et+1 ek0

t+1 x`

Uk0

e t+1

t+1 ω`

,(A.8)

and so:

Uk ω` =

max	− C	t
kk0 + ω `,k0 + bk0
k0,{et+1 (.)}

+ δφt+1 t

+ δφt+1 b

Now, wewrite Wkt (x) as:and so

W t+1 k0

(x) et+1 (x )+

θk0

q θt k0

Eω

t 1 − θk0q

Wkt (x )=

t θk0

Eω

max λtwkt (x )+ ηk {et+1 (.)}

+ δφt+1 (1 − χk ek

Uk0

U t+1 ek0

) et+1

(x) Wkt+1 (x)

+ δφt+1 1 − (1 − χk ek

Wkt (x )=

max λtwkt x`t + ηk {et+1 (.)}

+ δφt+1 (1 − χk

+ δφt+1χk Eω

ek0

t+1

) et+1

ω`

t+1 1 − et+1

t+1 ω`

(x) E Uk

e t+1

ω`

t+1

dGk0 (x)

(x)

(A.9)

(A.10)

)

et+1 ek

(x) Wkt+1 (x )+1 − et+1 (x) E ek

e t+1

ω`

t+1

ω`

t+1

(A.11)It is now clear that the optimal policy ekt+1 (.) is:

(

)

t+1 ek e

Deﬁne Ukt ≡ Eω

1if Wkt+1 (x) >Eω

Ukt+1

(x )=

t+1 ω`

0 otherwise

Uk ω

t `

. We therefore have the following Bellman equations:

(A.12)



Ukt = Eω

 

+δφt+1 b

Wkt (x )= λt wkt (x )+ ηk + δφ

bt+1

max − Ckk0 + bk0 + ω `t,k0 k0

t k0

q θt k0

max

t+1

Wk0

(x) ,Ukt+0 1 dG

+δφt+1 b

t 1 − θk0q

t θk0

t+1

Uk0

(1 − χk ) max Wkt+1 (x) ,U t+1 k



(x)

 
(A.13)
+ δφt+1 b
χkU
t+1 k
(A.14)

B Steady State Equilibrium

In this section we derive the equations characterizing the steady state equilibrium. The key con-ditions 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 prefer-

ence shifters

t φi

are constant and equal to 1 in the long run.

Wage Equation

wk,i (x )= βk,iwk,ix + (1 − βk,i )(1 − δ) Uk,i − (1 − βk,i) ηk,i

(A.15)

e λi

Firms' value function

1 − βk,i

Jk,i (x )= λiwk,i x − xk,i 1 − (1 − χk,i)δ

(A.16)

Probability of ﬁlling a vacancy

1 − δ (1 − χk,i)

qi (θk,i )= κkw,iPiF × ek,i

(A.17)

δ (1 − βk,i) Ik,ixk,i

where

Z xmax

Ik,i xk,i ≡ xk,is − xk,i dGk,i ( s)

(A.18)

Unemployed workers' Bellman equation



  

−Ckk0,i + bk0,i + θk0,i κk0,i Pi × λi ek0,i + δUk0,i

βk0,i

wk0,iζi

(1−β

Uk,i = ζi log

 

exp

k0,i

)

   

 
(A.19)
k0
-  
-  
  Transition rates
  
  
  F
  -  
  −Ck`,i +b`,i +θ`,i κ`,iPie ×λi e `,i +δU`,i
  w
  β`,i
  -  
    w`,i ζi
    e
    exp
    (1 −β`,i )
    -  
    -  
      sk`,i =
      (A.20)P exp
      k
      -     
      F κk,i Pi
      ×λiw e
      βk,i
      e
      +δUk,i
      −Ckk,i +bk,i +θ k,i
      k,ie wk,i
      1−βk,i
      ζi
      -     
        Steady-state unemployment rates
        χk,iuk,i =
        (A.21)
        θk,iqi (θk,i) 1 − Gk,i xk,i
        + χk,i

Trade + Price System Input Bundle Price

Domestic Sectoral Output Price

Pk,i = Y `=1

MPI ! νk`,i `,i

νk`,i

wk,i γk,i

γk,i

PM k,i

ck,i =

1 − γk,i

Price of Composite Sector-Speciﬁc Intermediate Good



Pk,i =Γ k,i X

k,jj=1 (ck,j dk,ji)

where Γk,i is a sector and country speciﬁc constant.

Price of Final Consumption Good

Trade Shares

where

Zero net ﬂows condition

(Li.ui )=

Product market clearing Gross Output

PiF = YK

k=1

πk,oi = Ak,o (ck,odk,oi)−λ ,N

Φk,i = X o=1

Ak,o (ck,odk,oi)−λ .

`=1

s`k,iL`,iu`,i

γk,oYk,o = wk,oLk,o (1 − uk,o)Z

Expenditure with Vacancies

! 1−γk,i

 −1/λ

λ 

I Pk,i µk,i

µki

Φk,i

! K

k=1

= si0 (Li.u i)

xmax

xk,o

= wk,oLk,o

1 − Gk,i x

V F

Ek,o = κk,oPo θk,ouk,oLk,o

(A.22)

(A.23)

(A.24)

(A.25)

(A.26)

(A.27)

(A.28)

sdGk,o ( s)

(A.29)

k,o

(A.30)

(A.31)

Market Clearing System

Yk,o =

πk,oiEk,i

i=1

Ek,i = µk,i

γ`,iY`,i

(1 − γ`,i) ν`k,iY`,i − µk,iN Xi

`=1

Normalization: World total revenue is the numeraire

i=1 k=1

(A.32)

(A.33)

Yk,i =1

Final Good Consumption Expenditure

Ei =

γk,iYk,i −

k=1

Ek,i − N Xi

(A.34)

(A.35)

Lagrange multipliers

λi = LCi

(A.36)

C Solution Methods

This Section presents the diﬀerent algorithms we developped to estimate the model and to perform counterfactual simulations. SectionC.1 details the estimation algorithm and SectionC.2 obtains expressions for simulated moments. SectionC.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. SectionC.4 develops the algorithm solving for the transition path of our complete model with trade imbalances. SectionC.5 adapts this algorithm to the case where we have exogenous deﬁcits. Finally, SectionC.6 outlines the procedure we use in Section5.1 to extract the shocks in trade costs, productivities and inter-temporal shocks.

C.1 Estimation Algorithm

Deﬁne Ik,i (x) ≡ Rxxmax (s − x) dG k,i (s). Imposing Gk,i ∼ log N to:

2 0,σk,i

and a bit of algebra leadsGk,i (x )=Φ

ln x

k,i

Ik,i (x ) = exp

2 σk,i

Φ σ

k,i −

ln x σk,i

− xΦ

ln x − σk,i

Ik,i (0) = exp

2 σk,i

ln xk,i

R xmax xk,i

dGk,i (s ) = exp

2 σk,i

σk,i −

σk,i

1−G s k,i (xk,i )

− ln xk,i σk,i

Note: The estimation procedure we describe takes trade shares πkD,oaita and net exports NX iData as given.

Step 1: Solve for {Yk,i} using:

Yk,o =

Data πk,oi

(µk,iγ`,i +(1 − γ`,i) ν`k,i) Y`,i −

Data πk,oi µk,iN Xi

i=1 `=1

i=1

Yk,o =1 o=1 k=1

The rest of the procedure conditions on these values of {Yk,i}.

Step 2: Guess model parameters Ω. We treat κk,i ≡ as parameters to be estimated.

κk,i PiF

e k,i

Step 3: Deﬁne

$ k,i ≡ (1 − (1 − χk,i) δ) κk,i e

δ (1 − βk,i)

If = I$ k,i ≥ 1, the free entry condition cannot be satisﬁed- Ik,i is decreasing. Abort the procedure and highly penalize the objective function.

(1−(1−χk,i )δ)κk,i

δ(1−βk,i )Ik,i (0)

k,i (0)

Step 4: Find xku,bi such that =1⇐⇒

(1−(1−χk,i )δ)κk,i

δ( 1−β

Ik,iub xk,i

= $ k,i. If along the algorithm

k,i )Ik,i (xku,bi )

xk,i goes above xku,bi, we update it to be equal to xku,bi (minus a small number).

Step 5: Guess {Lk,i}, and

xk,iStep 6: Compute Ik,i xk,i , Gk,i xk,i , θk,i and uk,i.

−1 θk,i = qi

$ k,iIk,i (xk,i )

where qi−1 (y )=

χk,i

uk,i =

θk,i qi (θk,i )(1−Gk,i (xk,i ))+χ k,i

1/ξi

1−yξiyξi

Step 7: Compute

Lk,i

Lk,i ≡ Lk,i (1 − uk,i)Z

xmax

xk,i

= Lk,i (1 − uk,i) exp

1 − Gk,i xk,i

dGk,i (s)

ln xk,i

! Φ

σ2 k,i

σk,i −

k,i

Φ − ln xk,i σk,i

Step 8: Compute {wk,i}

γk,iYk,iwk,i =

Lk,i

Step 9: Compute

V Ek,iV

Ek,i = κk,iwk,iθk,iuk,iLk,i

Step 10: Compute

Ei =

Ek,i − N XiV

γk,iYk,i −

k=1

Step 11: Compute

one λi

Step 12: Obtain {Uk,i}.

λi =

EC i

Step 12a: Guess

Uki

Step 12b: Compute until convergence



g+1 Uk,i

= ζi log

 

`=1

Step 13: Update {Lk,i}.

  

exp

−Ck`,i + b`,i + θ`,iκ`,iλiw`,i

β`,i

(1−β`,i ) + δU`,i − δUk,i

ζi

 

Step 13a: Given knowledge of {Uk,i}, compute transition rates sk`,i.

   

 
g + δUk,i
-  
  (
  )
  w
  β`,i
  −Ck`,i +b`,i +θ`,i κ`,i λi e `,i 1−β`,i +δU`,i
  e
  e
  exp
  ζisk`,i =
  -  
  P
  k
  βk,i
  e
  −Ckk,i +bk,i +θk,i κk,i λi wk,i 1−βk,i +δUk,i
  ee
  exp
  -  
    ζi
    
    
    Step 13b: Find yi such that
    ˆ
    I − si0 yi =0
    Step 13c: Find allocations Lk,i
    ˆ
    Lk,iuk,i = ϕy k,i
    ⇒
    Lk,i = ϕy k,i/uk,i
    |{z}
    yk,i
    e
    ⇒
    L0 i1K ×1
    = ϕ y0 ek,i1K ×1 = Li
    Li
    ⇒ ϕ =
    new Lk,i
    0 yk,i1K ×1
    e
    (Lk,i)0 = ϕyk,i e
    =(1 − λL) Lk,i + λL (Lk,i)0
    Step 14: Update
    xk,i
    .
    Note that in equilibrium:So, we update xk,i according to:
    e λiwk,ixk,i =(1 − δ) Uk,i − ηk,i
    e
    xk,i 0 = (1 − δ) Uk,i − ηk,i
    xkn,eiw = min
    λiwk,i
    (1 − λx) xk,i + λx xk,i
    0
    ub
    ,xk,i
    e
    (A.37)
    e
    on

onon

Step 15: Armed with Lkn,eiw	new	xnew
Lk,i	k,i
0.

new

and xk,i go to Step 6 until

− Lk,i

→ 0 and

− xk,i

→

Note that

new xk,i

− xk,i

→ 0 does not imply that (A.37) is satisﬁed. Therefore, we penalizedeviations 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 πkD,oaita, we can estimate the model country by 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 Ckk0 and sector-speciﬁc exogenous exit components χk (we will impose χk,i = χi + χk ), we estimate the remaining countries' parameters separately, in parallel.

C.2 Expressions for Simulated Moments

C.2.1 Employment Shares
empk,i =
KLk,i
(1 − uk,i)
P
Lk,i (1 − uk,i k=1
)
C.2.2 National Unemployment Rate
K
P
unempi =
Lk,iuk,i k=1
K
P
Lk,i k=1
C.2.3 Sector-Speciﬁc Average Wages

wk,i (x ) = (1 − βk,i) wk,ixk,i + βk,iwk,ix

R xmax wk,i (s) dGk,i (s)wk,i =xk,i1 − Gk,i xk,i

xmax

=(1 − βk,i) wk,ixk,i + βk,iw

ek,i

(s)

1 − Gk,i xk,i dGk,i

xk,i

ln xk,i

! Φ

2 σk,i

σk,i −

k,i

=(1 − βk,i) wk,ixk,i + βk,iwk,i exp

Φ − ln xk,i σk,i

C.2.4 Sector-Speciﬁc Variance of Wages

Rx∞k,i (wk,i (s) − wk,i)2 dGk,i (s)

2 σw,k,i =

1 − Gk,i xk,i  2



R ∞

 s − exp

2 σk,i

ln xk,i σk,i −ln xσk,i



xk,i

dGk,i (s)

Φ −

k,i σk,i

=( βk,iwk,i)2 × e

1 − Gk,i xk,i



ln xk,i



ln xk,i



Φ 2σk,i −

σk,i −

=( βk,iwk,i

e )2 ×

 

exp 2σ2 k,i

σk,i

− exp

σk,i

σk2,i





 
Φ − ln xk,i σk,i
Φ − ln xk,i σk,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 k0 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 ta stage (which is the 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 {u1,...,uK ,1,...,K } .Here, we abuse notation to mean uk as sector-k unemployment at the very beginning of a period.
eee
e
The one-year transition rate between sector-` unemployment and sector-k unemployment is given by:
t,t+1
se ` ek eu u ,i
= s
t,t+1 `k,i
t t 1 − θk,iqi θk,i
1 − Gk,it+1 xk,i
, (A.38)that is, a share s`tk,i of individuals starting period t unemployed in sector ` choose to search in sector
k. A fraction 1 − θkt ,iqi θkt ,i 1 − Gk,i
t+1
of those do not ﬁnd a match that survives
xk,i
until t + 1. Similarly, the one-year transition rate between sector-` unemployment and sector-k employment is given by:
t,t+1
t,t+1 t t
t+1
= s`k,i θk,iqi θk,i
xk,i
se`
1 − Gk,i
eu k,i
= st,t+1 − st,t+1 `k,i eu` e k ,i
e u
.
(A.39)
According to the timing assumptions of the model, the one-year transition rate between em-ployment in sector k and employment in sector k0 is zero if k 6= k0. However, the persistence rate of employment in sector k is given by the probability that a match does not receive a death shock times the probability that the match is not dissolved because the threshold for production increases in the following period:
(
0if k 6= k0
st,t+1 ekk0,i
=
.
(A.40)
(1 − χk,i )Pr x ≥ xt+1|x ≥ xtk,ik,i
if k = k0
Finally, the one-year transition rate between sector-k employment and unemployment in sector `

is given by:

(

st,t+1 eku ,i e`

0if k 6= ` χk,i +(1 − χk,i )Pr x<x tk+,i1|x ≥ xtk,i

(A.41)if k = `

That is, if a worker is employed in sector k at t, she cannot start next period unemployed in sector ` if k 6= `. 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)

eeee

and we can write transition rates between unemployment u and sector-k employment between t e

and t + N as:

t−1ut−1 t,t+N

`=1L`,i e`,i su` ,k e

st,t+N eu,k,i e

= .

(A.43)

t−1ut−1 L`,i e`,i

`=1

Finally, we can write transition rates between sector-k employment and unemployment u as: e

st,t+N

ek,u,i e

=1−

st,t+N. ek,k0,i

(A.44)

k0=1

1-period transition rates

eu` e k ,i = s`k,i 1 − θk,iqi (θk,i) 1 − Gk,i xk,iu

eu` k,i = s`k,iθk,iqi (θk,i) 1 − Gk,i xk,i

0if ` 6= k

s`k,i =

(1 − χ`,i ) if ` = k

s e`uk ,i e

0if ` 6= k χk,i if ` = k

N -period transition rates from and to unconditional unemployment: sN e

`=1L`,iu`,i eu` ,k,i

Nsu,k,i = e

L`,iu`,i `=1

sk,u,i e

=1 − X

Nsk,`,i.

`=1

C.3

Algorithm: Steady-State Equilibrium Following Shock

Consider shocks

o n
0	1	,	0	1
Ak,i	Ak,i	dk,oi	dk,oi

→

, NX0 →

NX1 i

We will be using 0 superscripts to denote the initial steady state, and 1 superscripts to denote the ﬁnal steady state.

Start from estimated Steady State:

Note that πk0,oi = πkD,oaita

o n

Lk,i

0 xk,i

We also have κk0,i = , but we do not know

F,0 κk,i Pi

w0 e k,i

Denote relative changes in variable a by a = b

oo no n

w0 ek,i

π0 k,oi

PiF,0

a1 a0

Step 1: Guess

non

Lk,i

and

1 xk,i

Step 2: Guess

wk,i

Step 2a: Compute wk,i = wwk0,i and iteratively solve for Pk,i and ck,i using the system e k,i

bIb

Step 2b: Compute PkF,i :

γk,i YK

bck,i = w e

−γ

k,i )νk`,i

b k,i

P`,i (1

`=1

I Pk,i =

−1/λ

−λ

0 πk,oiAk,o

b ck,o dk,oi

o=1

Step 2c: Compute πk,oi:

Step 2d: Compute

PbiF = YK

k=1

b πk,oi = Ak,o

PI bk,i

µki

! −λ

b bck,odk,oi

IPk,i

π1 k,oi

= π0 k,oi

πk,oi

e - κk,i ≡ = P F,0 = κ0

F,1 κk,i PiF,0 κk,i Pi

F,1

0 wk,i

w1 e k,iw0 e k,i

iw1 e k,i

e k,i

wk,i

1−δ(1−χk,i )

Step 3 : If κk1,i × ≥ 1 abort, set xk1,i such that κ1

δ(1−β k,i )I k,i (x1 )

1−δ(1−χk,i )k,i

ek,i × δ(1−β k,i )I k,i (x1 )

=1 − ε and

k,i

1−δ(1−χk,i )

go back to Step 1 with this new guess. If κk1,i ×< 1, proceed to Step 4.

Step 4: Compute

δ(1−β k,i )I k,i (x1 )k,i

1 qi θk,i

1 − δ (1 − χk,i)

= κ1 ek,i ×

δ (1 − βk,i) Ik,i

1 xk,i



−1

1 − δ (1 − χk,i)

θk,i = qi

1 uk,i =

 κk,i × e

δ (1 − βk,i) Ik,i





1 xk,i

χk,i

1 θk,i

θ1 k,i

1 − Gk,i

1 xk,i

+ χk,i

Step 5: Solve system in

Yk,o

Yk,o =

i=1

Step 6: Compute

1 πk,oi

µk,i

1 γ`,iY`,i

(1 − γ`,i) ν`k,iY`,i

−

πk,oiµk,iN Xi

`=1

i=1

Yk,i =1

i=1 k=1

Lk,i

xmax

1 − uk,i

Lk,i ≡ Lk,i

1 xk,i

1 = Lk,i

1 − uk,i exp

1 − Gk,i

2 σk,i

Step 7: Update

wk,i

new

1 γk,iYk,iwk,i

Go back to Step 2a and repeat until converegence of

sdGk,i (s)

1 xk,i

1 ln xk,i

! Φ

σk,i −

k,i

1 − ln xk,i

σk,i

1 k,i

wk,i

Step 8: Compute

Ek,i = κk,iwk,iθk,iuk,iLk,i

C,1

=Step 9: Obtain Lagrange Multipliers

V,1

k=1

Step 10: Compute Bellman Equations

Uk1,i = ζi log

1 γk,iYk,i −

V,1 Ek,i

1 − N Xi

k=1

e 1 = λi

E C,1 i



 

  

κ10 λ1 e 10

βk0,i

−Ckk0,i + bk0,i + θk ,i e k ,i e i wk ,i + δUk10,i

(1−βk0,i )

exp

   

 
ζi
-  
-  
  Step 11: Update
  on
  1
  Lk,i
  .
  n
  o
  Step 11a: Given knowledge of
  1
  Uk,i
  , compute transition rates sk1`,i .
  ˆ
  -  
  exp
  −Ck`,i +b`,i +θ1
  κ1 e 1 w1
  β`,i
  1
  `,i e `,i λi e `,i (1−β`,i ) +δU`,i
  -  
    ζi
    
    
    1 sk`,i =
    
    -  
    P
    k
    −Ckk,i +bk,i +θ1 k,i
    κ1
    1
    βk,i
    e
    k,i e 1w λi e k,i
    +δU
    1 k,i
    1−βk,i
    exp
    
    -  
      ζi
      -  
      -  
        Step 11b: Find yi such that
        ˆ
        1 T
        I − si
        yi =0
        Step 11c: Find allocations Lk,i
        ˆ
        1
        1
        Lk,iuk,i = ϕy k,i
        ⇒
        1
        1
        Lk,i = ϕy k,i/uk,i
        1 T
        ⇒
        Li
        |{z}
        yk,i
        e
        1K ×1
        = ϕ yT ek,i1K ×1 = Li
        Li
        ⇒ ϕ =
        T yk,i1K ×1
        e

1	0	= ϕyk,i
Lk,i	e

new

Lk,i

=(1 − λL) Lk1,i + λL Lk1,i

Step 12: Update

1 xk,i

Note that in equilibrium:So, we update xk1,i according to:

λe i wk,ixk,i =(1 − δ) Uk,i − ηk,i e

1 xk,i

(1 − δ) Uk1,i − ηk,i

e 1w 1 λi ek,i

1 xk,inew

= min (1 − λx) xk1,i + λx xk1,i

ub o ,xk,i

Step 13: Armed with

Lk,inew

and

new
1	1	1
xk,i	Lk,i	− Lk,i

new

go to Step 2 until

→ 0 and

new

1 xk,i

1 − xk,i

→ 0.

C.4

Algorithm: Out-of-Steady-State Transition

Inner Loop: conditional on paths for expenditures below.

Consider paths n Atk,i

φt i

o TSS

t=0

and n dto,i,kE C,t i

- determined in the Outer Loop

o TSS

t=0

with A0k,i = 1 and d0o,i,k = 1. Also, consider pathsTt=S0S with φ0i = 1 and φbti = 1 for T ≤ t ≤ TSS , for some T<<> SS.

Step 0: Given paths

E C,t i

Step 1: Guess paths n wt ek,i

, compute paths

λt ei

e t = : λiLi

E C,t i

o TSS

t=1

for each sector k and country i.

Step 2: Compute xTk,SiS consistent with wTSS and λe Ti SS . Obtain θkT,SiS

TSSTSS ,TSS +1

ek,i

, Uk,i , sk`,iTSS and πk,oi .

Step 2a: Compute

wk,i = wewkT0 ,Si S b

ck,i

using the system

Step 2b: Compute PkF,i :

, A

bk,i = ATk,SiS

A0 k,i

and dk,i

= dTSS o,i,k . Iteratively solve for Pk,i and

e k,id0 o,i,k

γk,i YK

bck,i = w e

−γ

k,i )νk`,i

b k,i

P`,i (1

`=1

I Pk,i =

−1/λ

−λ

0 πk,oiAk,o

b ck,o dk,oi

o=1

Step 2c: Compute

PI bk,i

µki

PbiF = YK

k=1

b πk,oi = Ak,o

! −λ

b bck,odk,oi

Pk,i

And obtain πkT,SoSi = πk0,oi

Step 2d: Compute

πk,oi

- κk,i

e TSS = κ0

e k,i

Step 2e: Guess

wk,i

TSS xk,i

Step 2f: Compute





TSS = qi

−1

κTSS × 

θk,i

 e k,i

1 − δ (1 − χk,i)

δ (1 − βk,i) Ik,iTSS xk,i

Step 2g: Compute Bellman Equations



Uk,i

  

TSS = ζi log

−Ckk0,i + bk0,i + θk0,i e k0,i ei

TSS κTSS λTSS e TSS wk0,i

βk0,i

(1−βk0,i )

+ δU T0SS

k ,i

 

exp

   

 
ζi
k0
-  
-  
  Step 2h: Compute
  ˆ
  0
  (1 − δ) UkT,SiSTSS xk,i
  =Step 2i: Update xkT,SiS =(1 − λx) xTk,SiS + λx Step 2d until convergence.
  ˆ
  − ηk,i
  λi
  e TSS wTSS
  ek,iTSS xk,i
  0 , for a small step size λx, and go back to
  Step 2j: Compute skTkS0S ,TSS +1
  ˆ
  (
  )
  TTSS SS λei
  TSS we `,i
  β`,i
  −Ck`,i +b`,i +θ`T,Si S κ
  e `,i
  1−β
  `,i
  +δU
  TSS `,i
  exp
  ζiTSS ,TSS +1 sk`,i
  =
  -  
  P
  k
  TSS
  −Ckk,i +bk,i +θk,iTSS κk,i
  e
  λi
  e
  TSSTSS wk,i
  e
  1−βk,i
  βk,iT +δU SS k,i
  exp
  -  
    ζi
    
    
    o TSS , n κt
    Step 3: Obtain series n πkt ,oi
    ˆ
    e k,i
    o TSS . Deﬁne xt ≡ xx0t .
    t=0
    t=0
    Step 3a: For t =1 ,...,TSS − 1 compute w the system
    t b k,i = and iteratively solve for PkI,,it and c
    e
    t bck,i =t
    γk,i YK
    b
    wk,i
    e
    `=1
    XN
    I,t
    0 t
    Pk,i =
    b
    πk,oiAk,o
    b
    o=1
    Step 3b: Compute PkF,i,t for t =1 ,...,TSS − 1:
    b
    ˆ
    b
    t wk,i
    w0 e k,i
    e
    b
    bkt ,i using
    I,t
    (1−γk,i )νk`,i
    b
    P`,i
    !
    −1/λ
    −λ
    tt
    bb
    ck,odk,oi
    YK
    PiF,t
    b
    =
    k=1
    Step 3c: Compute πt
    bk,oi
    for t =1 ,...,TSS − 1:
    I,t
    µki
    b
    Pk,i
    ˆ
    t
    tb πk,oi = Ak,o
    b
    Step 3d: Compute or t =1 ,...,TSS − 1:
    ct bt bk,odk,oi
    P
    b
    I,t k,i
    ! −λ
    ˆ

πt k,oi

= π0

πt k,oi bk,oi

F,t κk,i PiF,0 κk,i PiF,t

wk,i

- κk,i ≡ = P F,0 wtPi

F,t

= κk,i wb t

e k,i

e k,iie k,i

b k,i

Step 4: Given knowledge of wTSS , λi

ek,i

e TSS and xTSS (and therefore JkT,SiS (s)), start at t = TSS − 1

k,i

and sequentially compute (backwards) for each t = TSS − 1,...,1

ˆ Step 4a: Given wt

t+1, κt

ek,i, xk,ie k,i, λi k,i

e t and J t+1 (s) compute θkt ,i .

λi δφt+1 R xmax

e t κet t

k,i we k,i

(s) ≤ 1 then

i t+1 xk,i

Jkt+,i1 (s)dG

k,i





t −1 θk,i = qi

λtκt wt e i e k,i ek,i



δφi

t+1 R xmax

xt+1 J k,i

t+1 k,i

(s) dGk,i (s)

λi δφt+1 R xmax

e t κet t k,i we k,i

(s) > 1, it is not possible to satisfy Vkt,i = 0, so that Vkt,i< 0 and

i t+1 xk,i

Jkt+,i1 (s)dG

k,i

t θk,i =0.

Step 4b: Given xkt+,i1, Wkt+,i 1 (x )= 1−βkβ,ki ,i Jkt+,i 1 (x)+Ukt+,i 1 (for x ≥ xtk+,i1), θkt ,i, Ukt+,i 1 compute Ukt,i.

Notice that R xmax Wkt+,i 1 (s) dGk,i (s )= xt+1 Jkt+,i 1 (s) dGk,i (s)+ 1 − Gk,i xkt+,i1

so that:

Ukt,i = ζi log

βk,ixt+1 k,i

1−βk,i

R xmax

k,i

t+1 Uk,i

     



 

exp

−Ckk0,i + bk0,i

+δφt+1 t 0 bi

θk ,i

qi θt 0

k ,i

1−βk,i

βk,i

R xmax J t+1

xt+1 k,iζi

k,i

(s) dGk,i (s )+ δφi

bt+1U t+1 k0,i



         

Step 4c: Given Jkt+,i 1 (x), wt

t t+1 ek,i, Uk,i, Uk,i

and xk,i compute Jkt ,i (x)

t+1

Jkt ,i (x ) = (1 − βk,i) λitwkt ,ix +(1 − βk,i) ηk,i e

− (1 − βk,i) Uk,i − δφit+1

Step 4d: Solve for xkt ,i: Jkt ,i

Step 5: Compute transition rates n stk,kt+0,i1o TSS −1 for all countries i according to: t=1

exp

tt xk,i

(

t+1	t+1	(x) ,0
Uk,i	Jk,i
)

+(1 − χk,i) δφit+1 max

δφi

t+1 t t

θk0,iq(θk0,i) 1−β0k0,i

−Ckk0,i + bk0,i+ βk ,i R xmax Jkt+0,i1 (x) dGk0,i(x )+ δφit+1

xt+1 k0,i

t+1 Uk0,i

st,t+1 kk0,i

= .

(

k00 exp

δφt+1 bi

βk00,i

θk ,iq(θk ,i) 1−β

−Ckk00,i + bk00,i+

)

R xmax J t+1 xt+1

t 00

k00,ik00,i

k00,i (x) dG

k00,i

(x )+ δφi

bt+1U t+1 k00,i

Step 6: Start loop over t going forward (t =0 to t = TSS − 1)

Initial conditions: we know ukt=,i−1 e

t=0 t=−1 = uk,i , Lk,i

= Lkt=,i0, and θkt=,i0 from the initial steady statecomputation. Obtain ukt ,i and Lkt ,i using ﬂow conditions and sequences e

n	o n
,	t
xk,i

t θk,i

Step 6a: Compute

t t t t t JCk,i = Lk,iuk,iθk,iqi θk,i



JDkt ,i =  χk,i +(1 − χk,i) max

1 − Gk,i

 



k,ixt+1 k,i

1 − Gk,i

− Gk,it xk,i

xt k,i

t−1	1 − ut−1
Lk,i	ek,i

t uek,i =

t t t t Lk,iuk,i − JCk,i + JDk,i

t+1 xk,i

 
,0



Lt k,i
Step 6b: Compute
ˆ
t+1 Lk,it t+1 − OF t+1 = Lk,i + IFk,i k,i
where
,
t+1 IFk,i
=
X
`=6 kt t t+1,t+2
L`,iu`,is`k,i
and
,
e
OFkt+,i 1 = Lk,iuk,it
e
tt+1,t+2 1 − skk,i
.
Step 6c: Compute
ˆ
K
P
t+1 uk,it ut
t+1,t+2
L`,i e`,is`k,i
=
`=1
t+1 Lk,i
Step 6d: Compute
ˆ
Z ∞
t+1
Lk,i
e
t = Lk,i
1 − ut ek,i
t+1 xk,i
t = Lk,i
1 − ut ek,i
expStep 6e: Compute expenditure with vacancies
ˆ
V,t+1 Ek,i
sdGk,i (s)
1 − Gk,it+1 xk,i
t+1 ln xk,i
! Φ
2 σk,i
2
σk,i −
Φ
t+1 − ln xk,i
σk,i
e t+1wt+1 t+1 t+1 t+1 = κk,i ek,i θk,i uk,i Lk,i
σk,i

Step 6f: Solve for

t+1 Yk,i

in the system

Kt+1 Ek,i

C,t+1 = µk,iEi

V,t+1 µk,iE`,i

t+1 +(1 − γ`,i) ν`k,iY`,i

`=1

t+1 Yk,o

t+1 t+1 πk,oi Ek,i .

i=1

0 =Step 6g: Compute

e t+1 wk,i

t+1 γk,i Yk,i

Lt+1

k,i

t o

Step 7: Compute distance dist

wk,i

t ek,i

Step 7b: Update wkt ,i =(1 − λw ) wkt ,i + λw

t wk,i

t =1 ,...,TSS , for a small step size λw.

Step 7c: At this point, we have a new series for

wk,i

- go back to Step 2 until convergence

eon

twk,i

Step 8: Compute disposable income

It TSSi

t=1

Ii =

t V,t γ`,iY`,i − E`,i

`=1

Outer Loop: iteration on

N Xi

Step 0: Impose a change in a subset of parameters that happens at t = 0, but between tc and td. 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 TSS . Assume that for t ≥ TSS the system will

I have converged to a new steady state. World expenditure with ﬁnal goods P EiC,t is normalized i=1

to 1 for every t.

Step 1: Start with estimated state equilibrium at t = 0. Remember that we used the normalization

I	K	I	K
P	P	P	P

Yk,i = 1 during the estimation procedure. Change the normalization from Yk,i =1

i=1k=1

n o n C,0o

Ei = 1. Nominal variables to be renormalized:

0 o , n w0 Yk,i ek,i

, Ei

N Xi .

i=1k=1 0

i=1

Step 2: Obtain Bi0 with respect to the normalization i=1

Ei = 1. Equation (37) gives us:

Bi =

N Xi

1 − 1δ

Step 3: Make initial guess for NX iTSS (with respect to the normalizationEi = 1).

i=1

Step 4: Compute steady state equilibrium at TSS , conditional on NX iTSS , and the change in parameter values.

Step 4a: Notice that the steady-state algorithm uses the normalization

Yk,i = 1. Nor-

i=1k=1
malize NX iTSS	with respect to normalization	Yk,i = 1. To perform such normalization,
n	o

i=1k=1
use revenue	TSS	obtained in the initial steady state if this is the ﬁrst outer loop iteration,
Yk,i

otherwise use revenue

TSS

Yk,i

obtained in Step 6 below.

Step 4b: After computing the ﬁnal steady state, change the normalization from

i=1k=1
1 to	Ei	= 1 using	Ei	Nominal variables to be renormalized:
n	o n	o n

TSS .

i=1

obtained in Step 3a.

o n
TSS	wTSS	,
Yk,i	ek,i

C,TSS

N Xi

Step 5: Start at t = TSS − 1 and go backward until t = 1 and sequentially compute:

Rt+1 = 1 δ

C,t+1

Eit+1 i=1 = 1 b

φiI

Yk,i =N

C,t+1

N C,t i=1 Ei

Eit+1

i=1

b φi

C,t+1

EC,t = i

δφt+1Rt+1 b

to obtain paths for R1 = R0 = 1δ.

and

E C,t i

. Note that, because Bi1 is decided at t = 0, before the shock,Step 6: Solve for the out-of-steady-state dynamics conditional on aggregate expenditures

E C,t i

Step 7: Using the path for disposable income	It	TSS	obtained in Step 6 and equation (7) compute:
i	t=1

for 1 ≤ t<> SS

N Xi

t 0

= Iit − E

C,t

N Xi

TSS

Step 8: Compute

0 + TSS −1

1 − δ

= −

TSS −1

τ =1

(Rτ )−1

NXt

(Rτ )−1

t=1

τ =1

dist

N Xi

TSS o

N Xi

TSS

Step 9: Update NX iTSS

N XiTSS =(1 − λo) NX iTSS + λo N Xi

TSS

for a small step size λo Go back to Step 4 until convergence of

N Xi

TSS .

C.5

Algorithm: Out-of-Steady-State Transition, Exogenous Deﬁcits (No Bonds)

o TSS

Consider paths n Atk,i

φt i

and n dto,i,k

o TSS

t=0

with A0k,i = 1 and d0o,i,k = 1. Also, consider paths

t=0

Tt=S0S with φ0i = 1 and φbti = 1 for T ≤ t ≤ TSS , for some T<<> SS.

We condition on an exogenous path for NXt TSS .

t=1

Step 1: Guess paths n λto TSS for each country i.

t=1

Step 2: Guess paths n wt ek,i

o TSS

t=1

for each sector k and country i.

Step 3: Compute xTk,SiS consistent with wTSS and λe Ti SS . Obtain θkT,SiS

TSSTSS ,TSS +1

ek,i

, Uk,i , sk`,iTSS and πk,oi .

Step 3a: Compute

wk,i = wewkT0 ,Si S b

ck,i

using the system

Step 3b: Compute PkF,i :

, A

bk,i = ATk,SiS

A0 k,i

and dk,i

= dTSS o,i,k . Iteratively solve for Pk,i and

e k,id0 o,i,k

γk,i YK

bck,i = w e

−γ

k,i )νk`,i

b k,i

P`,i (1

`=1

I Pk,i =

−1/λ

−λ

0 πk,oiAk,o

b ck,o dk,oi

o=1

Step 3c: Compute

PI bk,i

µki

PbiF = YK

k=1

b πk,oi = Ak,o

! −λ

b bck,odk,oi

Pk,iand obtain πkT,SoSi = πk0,oiπk,oi b

Step 3d: Compute

- κk,i

e TSS = κ0

e k,i

Step 3e: Guess

wk,i

TSS xk,i

Step 3f: Compute



TSS = qi

−1

κTSS × 

θk,i

 e k,i

1 − δ (1 − χk,i)

δ (1 − βk,i) Ik,i



TSS xk,i

Step 3g: Compute Bellman Equations



Uk,i

  

TSS = ζi log

−Ckk0,i + bk0,i + θk0,i e k0,i ei

TSS κTSS λTSS e TSS wk0,i

βk0,i

(1−βk0,i )

+ δU T0SS

k ,i

 

exp

   

 
ζi
k0
-  
-  
  Step 3h: Compute
  ˆ
  0
  (1 − δ) UkT,SiSTSS xk,i
  =Step 3i: Update xkT,SiS =(1 − λx) xTk,SiS + λx Step 2d until convergence.
  ˆ
  − ηk,i
  λi
  e TSS wTSS
  ek,iTSS xk,i
  0 , for a small step size λx, and go back to
  Step 3j: Compute skTkS0S ,TSS +1
  ˆ
  (
  )
  TTSS SS λei
  TSS we `,i
  β`,i
  −Ck`,i +b`,i +θ`T,Si S κ
  e `,i
  1−β
  `,i
  +δU
  TSS `,i
  exp
  ζiTSS ,TSS +1 sk`,i
  =
  -  
  P
  k
  TSS
  −Ckk,i +bk,i +θk,iTSS κk,i
  e
  λi
  e
  TSSTSS wk,i
  e
  1−βk,i
  βk,iT +δU SS k,i
  exp
  -  
    ζi
    
    
    o TSS , n κt
    Step 4: Obtain series n πkt ,oi
    ˆ
    e k,i
    o TSS . Deﬁne xt ≡ xx0t .
    t=0
    t=0
    Step 4a: For t =1 ,...,TSS − 1 compute w the system
    t b k,i = and iteratively solve for PkI,,it and c
    e
    t bck,i =t
    γk,i YK
    b
    wk,i
    e
    `=1
    XN
    I,t
    0 t
    Pk,i =
    b
    πk,oiAk,o
    b
    o=1
    Step 4b: Compute PkF,i,t for t =1 ,...,TSS − 1:
    b
    ˆ
    b
    t wk,i
    w0 e k,i
    e
    b
    bkt ,i using
    I,t
    (1−γk,i )νk`,i
    b
    P`,i
    !
    −1/λ
    −λ
    tt
    bb
    ck,odk,oi
    YK
    PiF,t
    b
    =
    k=1
    Step 4c: Compute πt
    bk,oi
    for t =1 ,...,TSS − 1:
    I,t
    µki
    b
    Pk,i
    ˆ
    t
    tb πk,oi = Ak,o
    b
    Step 4d: Compute or t =1 ,...,TSS − 1:
    ct bt bk,odk,oi
    P
    b
    I,t k,i
    ! −λ
    ˆ

πt k,oi

= π0

πt k,oi bk,oi

F,t κk,i PiF,0 κk,i PiF,t

wk,i

- κk,i ≡ = P F,0 wtPi

F,t

= κk,i wb t

e k,i

e k,iie k,i

b k,i

Step 5: Given knowledge of wTSS , λi

ek,i

e TSS and xTSS (and therefore JkT,SiS (s)), start at t = TSS − 1

k,i

and sequentially compute (backwards) for each t = TSS − 1,...,1

ˆ Step 5a: Given wt

e t, xt+1, κt t+1 ek,i, λi k,i e k,i and Jk,i

λi δφt+1 R xmax

e t κet t

(s) compute θkt ,i .

k,i we k,i

(s) ≤ 1 then

i t+1 xk,i

Jkt+,i1 (s)dG

k,i



t −1 θk,i = qi

λtκt wt e i e k,i ek,i



δφi



t+1 R xmax

xt+1 J k,i

t+1 k,i

(s) dGk,i (s)

λi δφt+1 R xmax

e t κet t k,i we k,i

(s) > 1, it is not possible to satisfy Vkt,i = 0, so that Vkt,i< 0 and

i t+1 xk,i

Jkt+,i1 (s)dG

k,i

t θk,i =0.

Step 5b: Given xkt+,i1, Wkt+,i 1 (x )= 1−βkβ,ki ,i Jkt+,i 1 (x)+Ukt+,i 1 (for x ≥ xtk+,i1), θkt ,i, Ukt+,i 1 compute Ukt,i.

Notice that R xmax Wkt+,i 1 (s) dGk,i (s )= xt+1 Jkt+,i 1 (s) dGk,i (s)+ 1 − Gk,i xkt+,i1

so that:

Ukt,i = ζi log

βk,ixt+1 k,i

1−βk,i

R xmax

k,i

t+1 Uk,i

     



 

−Ckk0,i + bk0,i

+δφt+1 t 0 bi

θk ,i

qi θt 0

k ,i

1−βk,i

βk,i

R xmax J t+1

xt+1 k,iζi

k,i

(s) dGk,i (s )+ δφi

bt+1U t+1 k0,i

exp



         

Step 5c: Given λit, Jkt+,i 1 (x), wt

t t t+1

e ek,i, θk,i, δ, Uk,i, Uk,i

and xk,i compute Jkt ,i (x)

t+1

Jkt ,i (x ) = (1 − βk,i) λitwkt ,ix +(1 − βk,i) ηk,i e

− (1 − βk,i) Uk,i − δφit+1

t+1 Uk,i

+(1 − χk,i) δφit+1 max

t+1 Jk,i

(x) ,0

Step 5d: Solve for xkt ,i: Jkt ,i

t xk,i

Step 6: Compute transition rates n stk,kt+0,i1o TSS −1 for all countries i according to: t=1

exp

(

)

δφi

t+1 t t

θk0,iq(θk0,i) 1−β0k0,i

−Ckk0,i + bk0,i+ βk ,i R xmax Jkt+0,i1 (x) dGk0,i(x )+ δφit+1

xt+1 k0,i

t+1 Uk0,i

st,t+1 kk0,i

= .

(

k00 exp

δφt+1 bi

βk00,i

θk ,iq(θk ,i) 1−β

−Ckk00,i + bk00,i+

)

R xmax J t+1 xt+1

t 00

k00,ik00,i

k00,i (x) dG

k00,i

(x )+ δφi

bt+1U t+1 k00,i

Step 7: Start loop over t going forward (t = 0 to t = TSS − 1)Initial conditions: we know ukt=,i−1 e

t=0 t=−1 = uk,i , Lk,i

= Lkt=,i0, and θkt=,i0 from the initial steady statecomputation. Obtain ukt ,i and Lkt ,i using ﬂow conditions and sequences e

n	o n
,	t
xk,i

t θk,i

Step 7a: Compute

t t t t t JCk,i = Lk,iuk,iθk,iqi θk,i



JDkt ,i =  χk,i +(1 − χk,i) max

1 − Gk,i

 



k,ixt+1 k,i

1 − Gk,i

− Gk,it xk,i

xt k,i

t−1	1 − ut−1
Lk,i	ek,i

t uek,i =

t t t t Lk,iuk,i − JCk,i + JDk,i

t+1 xk,i

 
,0



Lt k,i
Step 7b: Compute
ˆ
t+1 Lk,it t+1 − OF t+1 = Lk,i + IFk,i k,i
where
,
t+1 IFk,i
=
X
`=6 kt t t+1,t+2
L`,iu`,is`k,i
and
,
e
OFkt+,i 1 = Lk,iuk,it
e
tt+1,t+2 1 − skk,i
.
Step 7c: Compute
ˆ
K
P
t+1 uk,it ut
t+1,t+2
L`,i e`,is`k,i
=
`=1
t+1 Lk,i
Step 7d: Compute
ˆ
Z ∞
t+1
t = Lk,i
s
Lk,i
e
1 − ut ek,i
t+1 xk,i
1 − Gk,i
! Φ
t = Lk,i
1 − ut ek,i
exp
2 σk,i
2
Φ
and Y t+1 = wt+1 e t+1 k,i ek,i Lk,i
dGk,i (s)
t+1 xk,i
t+1 ln xk,i
σk,i −
σk,it+1 − ln xk,i
σk,i

Step 7e: Compute expenditure with vacancies

V,t+1 Ek,i

e t+1wt+1 t+1 t+1 t+1 = κk,i ek,i θk,i uk,i Lk,i

Step 7f: Compute EiC,t+1 =

Step 7g: Solve for

t+1 Ek,i

Step 7h: Normalize

Step 7i: Compute

Step 8: Compute dist

Li λt+1

t+1 Yk,i

in the system

C,t+1 = µk,iEi

t+1 Yk,o

t+1 Yk,i

to make sure it sums to 1 across sectors and countries.

e t+1 wk,i

0 =

t+1 γk,i Yk,i

Lt+1

k,io TSS

n wt ek,i

wt ek,i

t=1

Step 9: Update wkt ,i =(1 − αw ) wkt ,i + αw

go back to Step 3 until convergence of

`=1

V,t+1 µk,iE`,i

t+1 +(1 − γ`,i) ν`k,iY`,i

t+1 t+1 πk,oi Ek,i .

i=1

TSS

t=1

twk,i

for t =1 ,...,TSS , for a small step size αw , and

twk,i

Step 10: Compute disposable incomeStep 11: Update n EiC,to TSS using t=1

It TSSi

t=1

Ii =

t V,t γ`,iY`,i − E`,i

`=1

C,t

= Iit − NX it

Step 12a: Compute

e λi

= for all t =1 ,...,TSSStep 12b: Compute distStep 12c: Update λ

E C,t

n λto TSS

t=1 ,

e it =(1 − αλ) λit + αλ

go back to Step 2 until convergence of

TSS

t ei

t=1

λt

for t =1 ,...,TSS , for a small step size αλ, and

ne λi

C.6

Algorithm: Recovering Shocks

to T SS

Inner Loop: conditional on paths for expenditures n EiC,to TSS and shocks φi t=1

and Ak,i ≡ - determined in the Outer Loop below.

o Tn

d bk,it

t=2 ,

t=1

ATSS k,i

k,i

As before, we denote changes relative to t = 0 by xt = xx0t . This loop conditions on data on b

n πt bk,oi

o T

t=1

and n P I,to T

k,i

, where T is the last period we have data on these variables. We assume

t=1

t = 0 is the estimated steady state. Deﬁne dk,i ≡ .

Step 1: Given paths

E C,t i

Step 2: Guess paths n wt ek,i

dTSS o,i,k

o,i,k

, compute paths

λt ei

e t = : λiLi

EC,t .

o TSS

t=1

for each sector k and country i.

Step 3: Compute xTk,SiS consistent with wTSS and λe Ti SS . Obtain θkT,SiS

TSSTSS ,TSS +1

ek,i

, Uk,i , sk`,iTSS and πk,oi .

Step 3a: Compute

wk,i = wewkT0 ,Si S b

. Iteratively solve for Pk,i and ck,i using the system

e k,i

γk,i YK

bck,i = w e

−γ

k,i )νk`,i

b k,i

P`,i (1

`=1

I Pk,i =

−1/λ

−λ

0 πk,oiAk,o

b ck,o dk,oi

o=1

Step 3b: Compute PkF,i :

Step 3c: Compute

PI bk,i

µki

PbiF = YK

k=1

b πk,oi = Ak,o

! −λ

b bck,odk,oi

Pk,i

And obtain πkT,SoSi = πk0,oi

Step 3d: Compute

πk,oi

- κk,i

e TSS = κ0

e k,i

Step 3e: Guess

wk,i

TSS xk,i

Step 3f: Compute



TSS = qi

−1

1 − δ (1 − χk,i)



κTSS × 

θk,i

 e k,i

δ (1 − βk,i) Ik,iTSS xk,i

Step 3g: Compute Bellman Equations



Uk,i

  

TSS = ζi log

−Ckk0,i + bk0,i + θk0,i e k0,i ei

TSS κTSS λTSS e TSS wk0,i

βk0,i

(1−βk0,i )

+ δU T0SS

k ,i

 

exp

   

 
ζi
k0
-  
-  
  Step 3h: Compute
  ˆ
  0
  (1 − δ) UkT,SiSTSS xk,i
  =Step 3i: Update xkT,SiS =(1 − λx) xTk,SiS + λx Step 2d until convergence.
  ˆ
  − ηk,i
  λi
  e TSS wTSS
  ek,iTSS xk,i
  0 , for a small step size λx and go back to
  Step 3j: Compute skTkS0S ,TSS +1
  ˆ
  (
  )
  TTSS SS λei
  TSS we `,i
  β`,i
  −Ck`,i +b`,i +θ`T,Si S κ
  e `,i
  1−β
  `,i
  +δU
  TSS `,i
  exp
  ζiTSS ,TSS +1 sk`,i
  =
  -  
  P
  k
  TSS
  −Ckk,i +bk,i +θk,iTSS κk,i
  e
  λi
  e
  TSSTSS wk,i
  e
  1−βk,i
  βk,iT +δU SS k,i
  exp
  -  
    ζi
    
    
    Step 4: Obtain series n πkt ,oi
    ˆ
    o TSS
    t=T +1
    and n κtStep 4a: For t = T +1 ,...,TSS do:Compute
    o TSS .
    e k,i
    t=1
    wt
    b k,i
    t = wk,i and iteratively solve for Pk,i
    w0 e k,i
    e
    b I,t and c
    bkt ,i using the system
    e
    bt ck,i
    wt
    γk,i YK
    =
    P I,t b`,i
    (1−γk,i )νk`,i ,
    b k,i
    e
    `=1
    XN
    I,t
    !
    −1/λ
    −λ
    0 πk,oiAk,ot
    Pk,i =
    b
    b
    b ck,odk,oi
    .
    b
    o=1
    Step 4b: Compute PkF,i,t for t =1 ,...,TSS − 1 (remember PkI,,it is data for t =1 ,...,T ):
    bb
    ˆ
    YK
    PiF,t
    b
    =
    k=1
    I,t
    µki
    b
    Pk,i

Step 4c: Compute πt bk,oi

For t =1 ,...,TSS − 1 do: First Case: If t ≤ T then πtEnd of First Case

bk,oi

Second Case if t ≥ T +1do:End of Second Case

and πkt ,oi for t = T +1 ,...,TSS − 1.

is data, so do:

t 0 t

πk,oi = πk,oiπk,oi

πk,oi

t Ak,o

t 0 t

πk,oi = πk,oiπk,oi

Step 4d: Compute for t =1 ,...,TSS − 1

F,t κk,i PiF,0 κk,i PiF,t

wk,i

- κk,i ≡ = P F,0 wtct bt bk,odk,oi

! −λ

I,t

Pk,i

F,t

= κk,i wb t

e k,i

e k,iie k,i

b k,i

Step 5: Given knowledge of wTSS , λi

ek,i

e TSS and xTSS (and therefore JkT,SiS (s)), start at t = TSS − 1

k,i

and sequentially compute (backwards) for each t = TSS − 1,...,1

Step 5a: Given wt

t+1, κt

ek,i, xk,ie k,i, λi k,i

e t and J t+1 (s) compute θkt ,i .

λi δφt+1 R xmax

e t κet t k,i we k,i

(s) ≤ 1 then

i t+1 xk,i

Jkt+,i1 (s)dG

k,i





t −1 θk,i = qi

λtκt wt e i e k,i ek,i



δφi

t+1 R xmax

xt+1 J k,i

t+1 k,i

(s) dGk,i (s)

λi δφt+1 R xmax

e t κet t k,i we k,i

(s) > 1, it is not possible to satisfy Vkt,i = 0, so that Vkt,i< 0 and

i t+1 xk,i

Jkt+,i1 (s)dG

k,i

t θk,i =0.

Step 5b: Given xkt+,i1, Wkt+,i 1 (x )= 1−βkβ,ki ,i Jkt+,i 1 (x)+Ukt+,i 1 (for x ≥ xtk+,i1), θkt ,i, Ukt+,i 1 compute Ukt,i.

Notice that R xmax Wkt+,i 1 (s) dGk,i (s )= xt+1 Jkt+,i 1 (s) dGk,i (s)+ 1 − Gk,i xkt+,i1

so that:

Ukt,i = ζi log

βk,ixt+1 k,i

1−βk,i

R xmax

k,i

t+1 Uk,i

     



 

−Ckk0,i + bk0,i

+δφt+1 t 0 bi

θk ,i

qi θt 0

k ,i

1−βk,i

βk,i

R xmax J t+1

xt+1 k,iζi

k,i

(s) dGk,i (s )+ δφi

bt+1U t+1 k0,i

exp



         

Step 5c: Given Jkt+,i 1 (x), wt

t t+1 ek,i, Uk,i, Uk,i

and xk,i compute Jkt ,i (x)

t+1

Jkt ,i (x ) = (1 − βk,i) λitwkt ,ix +(1 − βk,i) ηk,i e

− (1 − βk,i) Uk,i − δφit+1

Step 5d: Solve for xkt ,i: Jkt ,i

Step 6: Compute transition rates n stk,kt+0,i1o TSS −1 for all countries i according to: t=1

t xk,it

(

t+1	t+1	(x) ,0
Uk,i	Jk,i
)

+(1 − χk,i) δφit+1 max

exp

δφi

t+1 t t

θk0,iq(θk0,i) 1−β0k0,i

−Ckk0,i + bk0,i+ βk ,i R xmax Jkt+0,i1 (x) dGk0,i(x )+ δφit+1

st,t+1 kk0,i

= .

(

xt+1 k0,i

−Ckk00,i + bk00,i+

k00 exp

δφt+1 bi

θk ,iq(θk ,i) 1−β

βk00,i

R xmax J t+1 xt+1

t 00

k00,i (x) dG

t 00

k00,i

k00,ik00,i

Step 7: Start loop over t going forward (t =0 to t = TSS − 1)

Initial conditions: we know ukt=,i−1 e

t=0 t=−1 = uk,i , Lk,i

= Lkt=,i0, and θkt=,i0 from the initial steady statecomputation. Obtain ukt ,i and Lkt ,i using ﬂow conditions and sequences e

t+1 Uk0,i

(x )+ δφi

bt+1U t+1 k00,i

n	o n
,	t
xk,i

t θk,i

)

Step 7a: Compute

t t t t t JCk,i = Lk,iuk,iθk,iqi θk,i



JDkt ,i =  χk,i +(1 − χk,i) max

1 − Gk,i

 



k,ixt+1 k,i

1 − Gk,i

− Gk,it xk,i

xt k,i

t−1	1 − ut−1
Lk,i	ek,i

t uek,i =

t t t t Lk,iuk,i − JCk,i + JDk,i

t+1 xk,i

 
,0



Lt k,i
Step 7b: Compute
ˆ
t+1 Lk,it t+1 − OF t+1 = Lk,i + IFk,i k,i
where
X
t+1 IFk,i
=
t t t+1,t+2
L`,iu`,is`k,i
`=6 k
and
ttOFkt+,i 1 = Lk,iuk,i
,
e
e
t+1,t+2 1 − skk,i
,.

Step 7c: Compute

t+1 uk,it ut

t+1,t+2

L`,i e`,is`k,i

`=1

t+1 Lk,i

Step 7d: Compute

Z ∞

t+1

Lk,i

t = Lk,i

1 − ut ek,i

t+1 xk,i

t = Lk,i

1 − ut ek,i

expStep 7e: Compute expenditure with vacancies

sdGk,i (s)

1 − Gk,it+1 xk,i

t+1 ln xk,i

! Φ

2 σk,i

σk,i −

t+1 − ln xk,i

σk,i

V,t+1 Ek,i

e t+1wt+1 t+1 t+1 t+1 = κk,i ek,i θk,i uk,i Lk,i

Step 7f: Solve for

t+1 Yk,it+1 Ek,i

Step 7g: Compute

C,t+1 = µk,iEi

e t+1 wk,i

Step 8: Compute distance distin the system

V,t+1 µk,iE`,i

t+1 +(1 − γ`,i) ν`k,iY`,i

`=1

t+1 Yk,o

t+1 t+1 πk,oi Ek,i .

i=1

0 =

t+1 γk,i Yk,i

Lt+1

k,i

t o

wk,i

t ek,i

Step 8b: Update wkt ,i =(1 − λw ) wkt ,i + λw

wk,i

eee

Step 8c: At this point, we have a new series fort =1 ,...,TSS , for a small step size λw.

twk,i

- go back to Step 3 until convergence

twk,i

Step 9: Compute disposable income

It TSSi

t=1

Ii =

`=1

t V,t γ`,iY`,i − E`,i

Step 10: Compute

Ak,i

For t =1 ,...,T compute wand compute

Ak,i

For t ≥ T + 1 set:

t b k,i

e = , obtain ct

t wk,i

w0 e k,i

bk,i:bt ck,i

γk,i YK

P I,t b`,i

(1−γk,i )νk`,i ,

b k,i

`=1

bt Ak,i

0 =

πt bk,ii

ck,i

I,t

Pk,i

t Abk,i

Ak,i

Feed outer loop with

TSS

Ak,i

Outer Loop: iteration on

N Xi

Step 0: Compute changes in trade costs n dtk,oiSet dt

o Tb

t=1

! 1/λ

I,t

b
bt	πk,oo	Pk,i
dk,oi	πt	P I,t
bk,oi	bk,o

bT bk,oi = dk,oi

for t>T.

Step 1: Start with estimated state equilibrium at t = 0. Remember that we used the normalization

I K

P P

i=1k=1

Yk,i = 1 during the estimation procedure. Change the normalization from Yk,i =1 i=1k=1

Ei = 1. Nominal variables to be renormalized:

i=1

Step 2: Compute E

E C,0 E C,t

C,t i

( bi = for t =1 ,...,T where EiC,0 is aggregate consumption

)DataN

C,0 ( b C,t )

Data

i=1Ei

expenditure in the estimated steady state, and

n o n C,0o

0 o , n w0 Yk,i ek,iE C,t

iData

Step 3: Normalize φ Ut S = 1 for t =2 ,...,T − 1. This yields

, Ei

N Xi .

comes from the data.

C,t+1

Rt+1 = E US

for t =1 ,...,T − 1

I K

P P

C,t δE US

Obtain remaining shocks n φto T t=2

using

b φi

t+1

EiC,t+1 t+1 for t =1 ,...,T − 1

C,t δEi R

Set φbti = 1 for t ≥ T +2 . The value of φT +1 will depend on EiC,TSS and will be recovered in Step 7.

Note: the value of φbit=1 does not matter. Individuals made decisions at t = 0 assuming φi

as the economy was assumed to be in steady state at t =0.

bt=1 =1,

Step 4: Obtain Bi0 with respect to the normalization P	EC	= 1. Equation (37) gives us:
i
i=1
I

N Xi

Bi =

1 − 1δ

Step 5: Make initial guess for NX iTSS (with respect to the normalization

ATSS	bT	≡ Ak,i
bk,i	= Ak,i	A0
k,i

i=1

= 1) and for

Step 6: Compute steady state equilibrium at TSS , conditional on NX iTSS	bTSS	and dTSS
, Ak,i
I	K
P	P

bk,oi .

Step 6a: Notice that the steady-state algorithm uses the normalizationYk,i = 1. Nor-

i=1k=1
malize NX iTSS	with respect to normalization	Yk,i = 1. To perform such normalization,
n	o

i=1k=1
use revenue	TSS	obtained in the initial steady state if this is the ﬁrst outer loop iteration,
Yk,i

otherwise use revenue

TSS

Yk,i

obtained in Step 9 below.

Step 6b: After computing the ﬁnal steady state, change the normalization from

Yk,i =

i=1k=1
1 to	Ei	= 1 using	Ei	Nominal variables to be renormalized:
n	o n	o n

TSS ,

i=1

obtained in Step 3a.

oo n

wTSS ek,i

C,TSSYk,i

N Xi

TSS .

 

Step 7: Set EiC,t =

C,2000+t

C,0

E C,2000 i



Note: φit = 1 for t ≥ T +2⇒ Eifor t =0 ,...,T , as in Step 0

Data

C,tC,T

SS for t = T +1 ,...,TSS

= EiC,TSS for at t ≥ T + 1 (Euler Equation)Step 8: Compute φT +1 , imposing φ US

bT +1 =1:

Ei = ,

C,TSS

b φi

T +1

δRT +1Ei

C,TSSRT +1 = E US

C,T

C,T δE US

We now have a full path for n φto TSS .

t=2

Step 9: Solve for the out-of-steady-state dynamics conditional on aggregate expenditures n EiC,to TSS , t=0

on preference shifters

to TSS φi

and steady-state productivity shocks

t=2

Step 10:	It	TSS
i	t=1
compute:

C,t

Using the path for disposable income

N Xi

TSS

Step 11: Compute

t 0

N Xi

= Iit − E

obtained in Step 9 and equation (7)

for 1 ≤ t<> SS

TSS o bk,i

0 + TSS −1

1 − δ

= −

(Rτ )−1

NXt

TSS −1

τ =1

(Rτ )−1

t=1

τ =1

dist

N Xi

TSS o

N Xi

TSS

andusing the values of

ATSS b

k,i

Step 12: Update NX iTSS

dist

TSS o

Ak,i

A TSS bk,i

obtained in Step 9.

N Xi

TSS =(1 − λo) NX iTSS

+ λo N Xi

TSS

and Ak,i

TSS

for small step sizes λo and λA.

bTSS

Ak,i

=(1 − λA) ATSS + λA

Go back to Step 6 until convergence of

bTSS

bk,i

Ak,i

NX TSS i

and

Ak,i

bTSS .

C.7 Parameter Estimates

In this section, we display the complete set of parameter estimates.

Table A.1: Final Expenditure Shares µk,i

Sector ↓ Country →	USA	China	Europe	Asia/Oceania
Agr.	0.01	0.12	0.02	0.01
LT Manuf.	0.03	0.02	0.04	0.03
MT Manuf.	0.05	0.11	0.08	0.07
HT Manuf.	0.1	0.15	0.11	0.1
LT Serv.	0.3	0.35	0.34	0.38
HT Serv.	0.51	0.25	0.41	0.41
Sector ↓ Country →
Agr.
LT Manuf.
MT Manuf.
HT Manuf.
LT Serv.
HT Serv.

Americas	ROW
0.02	0.09
0.04	0.03
0.1	0.11
0.11	0.1
0.33	0.39
0.4	0.29
Table A.2: Labor Shares in Production γk,i
Americas	ROW
0.62	0.67
0.28	0.27
0.32	0.28
0.31	0.25
0.56	0.48
0.67	0.68

USA

ChinaEuropeAsia/Oceania

0.45

0.58

0.56 0.54

0.37

0.25

0.32 0.35

0.33

0.28

0.31 0.37

0.39

0.24

0.33 0.32

0.61

0.37

0.49 0.54

0.62

0.55

0.63 0.67

Table A.3: Input-Output Table - Average Across Countries

i νk`,i

LT Serv.	HT Serv.
0.26	0.139
(0.06)	(0.07)
0.223	0.082
(0.041)	(0.04)
0.225	0.095
(0.052)	(0.044)
0.184	0.106
(0.044)	(0.05)
0.343	0.259
(0.073)	(0.11)
0.267	0.507
(0.069)	(0.171)
Note: Standard Deviation of νk` across countries.
Table A.4: Mobility Costs Estimates Ck`
LT Serv.	HT Serv.
0.189	1.676
0.799	2.034
0.866	2.646
0.276	0.917
0	0.002
0.004	0
ROW
0
-0.316
-0.072
-0.934
-0.588
-1.011

User ↓ Supplier → Agr.

Agr.

LT Manuf.

MT Manuf.

HT Manuf.

LT Manuf.

MT Manuf.

HT Manuf.

(0.056)

0.195

0.267

(0.019)

0.376

0.079

0.118 (0.036) 0.043

(0.047)

0.138 (0.029) 0.081

(0.064)

(0.009) (0.015)
0.222
0.066
0.287
(0.034)
0.106
(0.017)
(0.04) (0.022)

0.022

0.157

0.067

(0.018)

(0.022) (0.015)
LT Serv.
0.463
(0.052)
0.057
0.136
0.105
(0.042)
(0.03) (0.027)

0.101

(0.034)

HT Serv.

0.007

0.076 (0.023)

0.033 (0.019)

0.11

(0.005)

(0.071)From ↓ / To → Agriculture

Agr.

LT Manuf.

MT Manuf.

HT Manuf.

0.825

LT Manufacturing MT Manufacturing HT Manufacturing LT Services

HT Services

0.414 0

1.560 0.454

0.005 0.000

2.033 0.015 0.268 0.790

0.000 0.001 0.972 1.826

0 0.002

0.003

1.221 0.466

2.150 1.201

Table A.5: Sector-Speciﬁc Utility and Variance Estimates ηk,i,σk2,iSector ↓ / Country → Agriculture

LT Manuf. MT Manuf. HT Manuf. LT Services HT Services

USA

China

Europe

Asia/Oceania 0

Americas 0

-0.383

-0.943

-0.428

-0.521 -0.588
0.026
-0.566
-0.245
-0.229 -0.195
-0.551
0.085
-1.557
-0.743
-0.607 -1.292
-0.454
-0.382
-0.236 -0.405
-0.052
-0.467
-0.603
-0.518 -0.894

2 σ US

0.727

Table A.6: Exogenous Death Rates Estimates χk, = χi + χk

USA	0.026
China	0.022
Country	Europe	0.054
Component χi	Asia/Oceania	0.021
Americas	0.027
ROW	0.020
Agriculture	0
Low Tech Man	0.005
Sector	Med Tech Man	0.014
Component χk	High Tech Man	0.002
Other Services	0.008
Hi Tech Services	-0.001

Table A.7: Unemployment Utility bk,i = biUSA -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 κk,i e

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

Attachments

Original document
Permalink

Disclaimer

Board of Governors of the Federal Reserve System published this content on 10 February 2021 and is solely responsible for the information contained therein. Distributed by Public, unedited and unaltered, on 10 February 2021 20:37:05 UTC.

Assa Abloy: targets maintained, but share price declines	05:32am	CF
ARCELORMITTAL : Oddo BHF confirms its recommendation on the stock	05:32am	CF
South Africa's unemployment rate rises to 32.9% in first quarter	05:31am	RE
U.K. Sells GBP600 Million in March 2073 Index-Linked Gilt	05:29am	DJ
NHTSA - Opens Preliminary Evaluation Into Estimated 444 Waymo Vehicles Due To ADS Behavior	05:27am	RE
ANALYST RECOMMENDATIONS : Nike, Roblox, Starbucks, Walmart, Deckers Outdoor...	05:26am
Alcon: surrounded after its quarterly results	05:21am	CF
BAYER AG : Deutsche Bank reaffirms its Neutral rating	05:21am	ZD
Poujoulat: outlook more uncertain, share price falls	05:21am	CF
ADESSO : Berenberg maintains a Buy rating	05:19am	ZD
OPEC to issue May oil market report at 1000 GMT	05:18am	RE
RHEINMETALL AG : Receives a Buy rating from Barclays	05:18am	ZD
India's PVR Inox posts wider-than-expected Q4 loss on weak demand	05:16am	RE
News Highlights : Top Company News of the Day - Tuesday at 5 AM ET	05:16am	DJ
News Highlights : Top Global Markets News of the Day - Tuesday at 5 AM ET	05:15am	DJ

Stock Market News in real time

Globalization, Trade Imbalances and Labor Market Adjustment

All News: More news

Headlines

Most Read News

of ﬁnding a match θkt 0,iq	t	multiplied by the discounted value of the match. Note that for
θk0,i

k. A fraction 1 − θkt ,iqi θkt ,i 1 − Gk,i	t+1	of those do not ﬁnd a match that survives
xk,i