Offshore Production and Business Cycle Dynamics with Heterogeneous Firms

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 995r December 2012 Offshore Production and Business Cycle Dynamics with Heterogeneous Firms Andrei Zlate NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at www.ssrn.com.

Offshore Production and Business Cycle Dynamics  with Heterogeneous Firms Andrei Zlate Federal Reserve Board December 2012 Abstract Cross-country variation in production costs encourages firms to relocate production to other countries, a process known as offshoring through vertical foreign direct investment (FDI). To examine the effect of offshoring through vertical FDI on the international transmission of business cycles, I propose a model that distinguishes between fluctuations in the number of offshoring firms (the extensive margin) and in the value added per offshoring firm (the intensive margin) as separate transmission mechanisms. In the model, firms face a sunk cost to enter the domestic market, and an additional fixed cost to produce offshore. The offshoring decision depends on the firm-specific productivity and on fluctuations in the relative cost of effective labor. The model replicates the procyclical pattern of offshoring, as well as the dynamics along its extensive and intensive margins, which I document using data from U.S. manufacturing and Mexico's maquiladora sector. In addition, offshoring enhances the comovement of output across countries, in line with existing empirical evidence. The result is closely related to the dynamics of offshoring along its extensive and intensive margins. JEL classification: F23, F41 Keywords: offshore production; extensive margin; heterogeneous firms; firm entry; business cycle dynamics; terms of labor.  I thank Fabio Ghironi, James Anderson and Susanto Basu for their guidance, as well as George Alessandria, Richard Arnott, David Arseneau, Marianne Baxter, Michele Cavallo, Matteo Iacoviello, Federico Mandelman, Fernando Parro, Joel Rodrigue, Vitaliy Strohush and Linda Tesar for helpful suggestions, and Quoctrung Bui for his excellent research assistance. Participants at the 2012 Dynare Conference at the Swiss National Bank, the 2012 Midwest Macro Meetings, the 2011 Asian Meeting of the Econometric Society, the 2010 Winter Meeting of the Econometric Society, the 2009 SCIEA meeting of the Federal Reserve, the Federal Reserve Board, the 2009 International Economics and Finance Society/ASSA meeting, and the Green Line Macro Workshop at Boston College/Boston University provided helpful comments.  Contact email: Andrei.Zlate@frb.gov, phone: (202) 452-3542. The author is a staff economist in the Division of International Finance, Board of Governors of the Federal Reserve System, 20th and C Street NW, Washington, D.C. 20551 U.S.A. The views in this paper are solely the responsibility of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System.

1 Introduction Firms often establish production a¢ liates at foreign locations to bene(cid:133)t from relatively lower productioncosts,aprocessknownintheinternationaleconomicsliteratureaso⁄shoringthrough vertical foreigndirectinvestment(FDI).1 Unlikeo⁄shoringthroughhorizontal FDI,underwhich (cid:133)rms relocate production abroad to gain access to the local market, the type of o⁄shoring that I model is motivated by cross-country di⁄erences in the cost of e⁄ective labor, as foreign a¢ liates produce goods that are shipped for consumption back to their home country.2 The number of o⁄shoring (cid:133)rms (the extensive margin) and the value added per o⁄shoring (cid:133)rm (the intensive margin) (cid:135)uctuate over the business cycle, and thus a⁄ect output, prices and wages in the home and the foreign economies. In addition, since the o⁄shore production is part of the aggregate output of the foreigneconomybut is a⁄ectedbydemandfromhome, o⁄shoringthroughvertical FDI has potential implications for the comovement of output between the economies involved. Tomotivatethemodelofo⁄shoringproposedbythispaper,Idocumentempiricallythebusiness cycle (cid:135)uctuations of o⁄shoring through vertical FDI, with particular focus on its extensive and intensive margins, using time series data on U.S. manufacturing and Mexico(cid:146)s maquiladora sector as an example.3 The data show that both the total value added o⁄shore and the number of maquiladora plants (a proxy for the extensive margin) are procyclical with the U.S. manufacturing output (see Figure 3, panels 1 and 3), and that the o⁄shoring sector comoves more closely with U.S. manufacturing than does Mexico(cid:146)s total manufacturing output. In addition, 1"O⁄shoring" refers to the activity of (cid:133)rms that relocate certain stages of production to foreign countries. In contrast, "outsourcing" refers to (cid:133)rms that purchase intermediates from una¢ liated suppliers, located either at home or abroad, rather than producing them in house (see Helpman, 2006). 2Helpman, Melitz and Yeaple (2004) model exports and horizontal FDI as alternative internationalization strategies for multinational (cid:133)rms. Contessi (2010) analyzes this trade-o⁄in a business cycle framework. Also see Helpman (1984). 3Themaquiladora sectorinMexicoconsistsofmanufacturingplantsthatimportintermediategoods,process them, andexporttheresultingoutput, thusaccomodatingtheo⁄shoringactivitiesofU.S.manufacturing(cid:133)rms. 1

the o⁄shoring dynamics di⁄er across the total value added and the number of plants: The total value added in Mexico comoves contemporaneously with U.S. manufacturing, whereas the number of maquiladora plants lags the expansions and contractions in U.S. manufacturing by about one year. This pattern highlights the gradual adjustment of the extensive margin of o⁄shoring in response to shocks in the home economy, and thus its role in the propagation of shocks across countries. This evidence adds to existing empirical studies showing that (cid:135)uctuations in the extensive margin of o⁄shoring have substantial macroeconomic e⁄ects. Bergin, Feenstra and Hanson (2009) (cid:133)nd that the extensive margin accounts for about one-third to one-half of the adjustment of Mexico(cid:146)s maquiladora employment. In addition, Kurz (2006) shows that, although o⁄shoring is undertaken by only a small fraction of U.S. manufacturing (cid:133)rms, the o⁄shoring (cid:133)rms are larger and more productive than their domestically-oriented counterparts. This (cid:133)nding helps explain why the o⁄shoring activities of just a subset of (cid:133)rms can have important macroeconomic implications for the economies involved. The combined empirical evidence suggeststhatmodellingtheextensivemarginofo⁄shoringinaframeworkwithheterogeneous(cid:133)rms can provide new insights on the channels and the timing at which shocks are transmitted across economies. Motivatedbytheseobservations,Iexaminethebusinesscycledynamicsofo⁄shoringthrough vertical FDI, and study the e⁄ect of o⁄shoring on aggregate dynamics and the macroeconomic interdependence across countries. For this purpose, I build a two-country (i.e. North and South), dynamic stochastic general equilibrium model that rationalizes the (cid:133)rms(cid:146)decision to relocate production o⁄shore. The key model ingredients are endogenous (cid:133)rm entry in the home country, (cid:133)rm heterogeneity in labor productivity, and endogenous o⁄shoring. Firm entry in 2

the home country is subject to a sunk cost re(cid:135)ecting headquarter activities at home. Following entry in the North, each (cid:133)rm can use either domestic or foreign labor in producing for the home market. The use of foreign labor involves the establishment of an o⁄shore plant, and is subject to (cid:133)xed and trade costs every period.4 Since (cid:133)rms are heterogeneous in productivity, the decision to produce o⁄shore is (cid:133)rm-speci(cid:133)c; despite the lower cost of e⁄ective labor abroad (de(cid:133)nedastherealwagenormalizedbyaggregateproductivity), onlythemoreproductive(cid:133)rms can a⁄ord the (cid:133)xed and trade costs associated with o⁄shoring. The cross-country asymmetry in the cost of e⁄ective labor also implies that o⁄shoring takes place one-way; only some of the Northern (cid:133)rms have an incentive to produce o⁄shore, whereas all Southern (cid:133)rms produce at home. The results are as follows. First, the model generates a procyclical pattern of o⁄shoring, and dynamics along its extensive and intensive margins that are consistent with the data from U.S. manufacturing and Mexico(cid:146)s maquiladora sector. In the model, the fraction of o⁄shoring (cid:133)rms every period depends on the (cid:135)uctuations in the relative cost of e⁄ective labor across countries. A positive shock to aggregate productivity in the North encourages domestic (cid:133)rm entry, and causes the home wage to persist above aggregate productivity, as labor demand increases to accommodate (cid:133)rm entry requirements. Importantly, due to (cid:133)rm entry in the North, the increase in the cost of e⁄ective labor in is gradual, which in turn triggers a gradual increase in the number of o⁄shoring (cid:133)rms (the extensive margin), like in the data. Second, as a result of these dynamics, o⁄shoring is highly correlated with home output, and a greater prevalence of o⁄shoring enhances the comovement of output across countries. The increase in output in the North (generated by a country-speci(cid:133)c shock to aggregate productivity) and 4This paper assumes a one-to-one correspondence between a (cid:133)rm, a variety, and an o⁄shore plant. 3

also in the South (caused by the increase in Northern demand for o⁄shored varieties and the relocation of production to the South) enhance output comovement. The result is consistent with the empirical evidence in Burstein, Kurz, and Tesar (henceforth BKT, 2008), who show that country pairs with larger shares of o⁄shoring-related trade in bilateral trade exhibit larger correlations of manufacturing output. Thispaperaddstotheinternationalmacroeconomicsliteratureono⁄shoring,whichdoesnot fullycapturethebusinesscycledynamicsofo⁄shoringalongitsextensivemargin. BKTpropose a model in which production sharing enhances the comovement of output, but in which the location of production is (cid:133)xed (thus abstracting from the extensive margin), and comovement results from a very low elasticity of substitution between the country-speci(cid:133)c goods in the vertically-integratedsector. Inthemodelproposedhere, o⁄shoringenhancesthecomovementof output through a mechanism that is di⁄erent from BKT: The elasticity of substitution between varieties produced domestically and o⁄shore is set at relatively high level that is consistent with (cid:133)rm-level studies, and hence the intensive margin plays a smaller role in comovement. Instead, output comovement is closely linked to procyclical (cid:133)rm entry in the North, the appreciation of the terms of labor, and in turn the adjustment of the o⁄shoring along both its extensive and intensive margins. Arkolakis and Ramanarayanan (2009) build a model with two stages of production, in which heterogeneity in production e¢ ciency gives rise to vertical specialization acrosscountries, andoutputcomovementisrelatedtothetransferofproductivitygainsthrough the imports of cheaper intermediate goods. In comparison, my model examines o⁄shoring in a one-stage production setting, in which (cid:133)rm heterogeneity gives rise to intertemporal dynamics of o⁄shoring along its two margins that are consistent with the data, which in turn generate procyclical o⁄shoring and output comovement. Bergin, Feenstra and Hanson (BFH, 2011) 4

study the importance of o⁄shoring in amplifying the transmission of shocks across countries, in a model in which the number of o⁄shoring (cid:133)rms adjusts instantly, rather than gradually over time as in the data, in response to simultaneous shocks in the home and foreign economies. However, while BFH study the impact of o⁄shoring on output volatility, this paper focuses on output comovement and the intertemporal dynamics of o⁄shoring.5 More generally, this paper is related to a growing body of macroeconomic literature that focuses on endogenous (cid:133)rm entry and adjustments along the extensive margin of exports (but not of o⁄shoring). For example, Ghironi and Melitz (2005) study the export decision of (cid:133)rms in the presence of (cid:133)xed exporting costs, in a framework with endogenous (cid:133)rm entry and heterogeneous (cid:133)rms.6 Alessandria and Choi (2007) analyze the extensive margin of exports in a model with sunk exporting costs and (cid:133)xed continuation costs that explains the "exporter hysteresis" behavior.7 The model implications are robust in the presence of endogenous labor supply and physical capital accumulation. With endogenous labor supply, the response of o⁄shoring is similar, but stronger than in the baseline model. Following a positive shock to productivity the North, (cid:133)rm entry(cid:150)andhencelabordemand(cid:150)increasesbymorethaninthebaselinemodel, asnew(cid:133)rmsare attracted by the increased supply of more productive labor, and the larger market size arising from higher labor income. In turn, the terms of labor appreciate by more in the quarters after the shock, thus enhancing the (cid:133)rms(cid:146)incentive to relocate production o⁄shore. The addition of physical capital dampens but does not reverse the dynamics of o⁄shoring. Since investment 5Also see Arseneau and Leduc (2011), who study o⁄shoring as an outside option in wage negotiations by multinational(cid:133)rms,andhighlightitse⁄ectonwagesandlabormarketallocationsinatwo-countrylaborsearch model. In addition, Ottaviano, Peri and Wright (2012) analyze the impact of a reduction in the costs of o⁄shoring and immigration on employment, in a multi-sector model with a continuum of tasks in each sector, and heterogeneity in the immigrant workers(cid:146)productivity and in the o⁄shoring costs across tasks. 6See Fattal Jaef and Lopez (2012), who examine the implications of (cid:133)rm entry and (cid:133)rm exporting costs like in Ghironi and Melitz (2005) in the presence of physical capital and endogenous labor supply. Also see Farhat (2009) for a similar study under various assumptions for labor supply. 7"Exporter hysteresis" refers to the behavior of (cid:133)rms that continue to serve the foreign market even after a real exchange rate appreciation reduces their export competitiveness. 5

in physical capital and (cid:133)rm entry are substitutes, a positive shock to aggregate productivity in the North leads to slower (cid:133)rm entry, and therefore to a slower increase in the marginal cost of production relative to the South. However, (cid:133)rm entry and production costs are still procyclical, resulting in a gradual increase in the number of o⁄shoring (cid:133)rms and the total value added o⁄shore. The rest of the paper is organized as follows: Section 2 introduces the baseline model. Section 3 translates the model with heterogeneous (cid:133)rms into an equivalent framework with two representative (cid:133)rms that produce domestically and o⁄shore, and describes the baseline model calibration. Section 4 presents the alternative models with elastic labor supply and physical capital. Section 5 presents the results, including the business cycle dynamics of o⁄shoring, the dynamics of its two margins, and the relation between o⁄shoring and output comovement. Section 6 concludes with a summary and possible extensions of the model. 2 Model of O⁄shoring with Heterogeneous Firms The model consists of two economies, North and South. Each economy includes one representative household and a continuum of (cid:133)rms that are monopolistically competitive and heterogeneous in labor productivity. Each (cid:133)rm produces a di⁄erent variety of goods, and the Northern (cid:133)rms have the option to produce either domestically or o⁄shore in order to serve their home market. This section describes the problem of the representative household and the (cid:133)rms in the North under (cid:133)nancial autarky, while the Appendix presents the model version with international trade in bonds.8 Agents in the South face a similar problem, except for that all 8I use "(cid:133)nancial autaky" to refer to the absence of international bond or stock trading. However, the characterization of o⁄shoring as a type of foreign direct investment, with the Northern household investing in (cid:133)rms that may produce abroad, could be considered a form of (cid:133)nancial integration. 6

Southern (cid:133)rms produce domestically due to the steady-state asymmetry in the marginal cost of production across countries, which is higher in the North. Variables for the Southern economy are marked with a star superscript. 2.1 Household(cid:146)s Problem The representative household in the North maximizes the expected lifetime utility subject to a budget constraint: max E 1(cid:12)s tCs 1 (cid:0) (cid:13) ; where (cid:12) (0;1) is the subjective discount f Bt+1;xt+1 g(cid:20) t s=t (cid:0) 1 (cid:0) (cid:13) (cid:21) 2 P factor, C is aggregate consumption, and (cid:13) > 0 is the inverse of the inter-temporal elasticity of t substitution. The budget constraint is: (v +d )N x +(1+r )B +w L v (N +N )x +B +C : (1) t t t t t t t > t t E;t t+1 t+1 t e e e The representative household starts every period with share holdings x in a mutual fund of t N (cid:133)rms whose average market value is v , as in Ghironi and Melitz (2005), and also with real t t bond holdings B .9 It receives dividends equal to the average (cid:133)rm pro(cid:133)t d in proportion with t e t the number of (cid:133)rms N . It also receives interest r B on bond holdings, aend the real wage w t t t t for the amount of labor L 1 supplied inelastically. (The alternative models in Section 4 allow (cid:17) for endogenous labor supply, and also for households to invest in physical capital, which is used in production by (cid:133)rms). The representative household purchases two types of assets every period. First, it purchases x shares in a mutual fund of Northern (cid:133)rms that includes: (i) a number of N incumbent t+1 t 9Inthebaselinemodel,inwhichstocksandbondsarenottradedacrosscountries,theequilibriumconditions for stock and bond holdings are x = x = 1 and B = B = 0. Bond holdings play a role in the model t t+1 t t+1 version with (cid:133)nancial integration, described in the Appendix, in which the representative household buys riskfree, country-speci(cid:133)c bonds in the presence of quadratic adjustment costs for bond holdings. 7

(cid:133)rms that produce either domestically or o⁄shore at time t, and (ii) a number of N new E;t (cid:133)rms that enter the market in period t. On average, each (cid:133)rm is worth its market value v , which is equal to the net present value of the expected stream of future pro(cid:133)ts. (The t mechanisms driving the number of incumbent (cid:133)rms, the number of new entrants and the (cid:133)rms(cid:146) e market value are discussed in Section 2.2 below.) The household also purchases the risk-free bond B denominated in units of the Northern consumption basket. Finally, the household t+1 purchases the consumption basket C : t (cid:18) (cid:18) 1 (cid:0) 2zV;t 3 1 1 (cid:18) 1 (cid:18) 1 (cid:18) 1 C t = 6 y D;t (!) (cid:0)(cid:18) d! + y V;t (!) (cid:0)(cid:18) d! + y H(cid:3);t (!) (cid:0)(cid:18) d! 7 ; (2) 6 7 6 6 z Z min z Z V;t z Z H(cid:3);t 7 7 6 7 6 6 ! 2 (cid:10)N t N ! 2 (cid:10)N t S ! 2 (cid:10)S t S 7 7 4| {z } | {z } | {z } 5 which includes varieties produced by the Northern (cid:133)rms either domestically (! (cid:10)NN) or 2 t o⁄shore (! (cid:10)NS), and also varieties produced by the Southern exporting (cid:133)rms (! (cid:10)SS); 2 t 2 t (cid:18) > 1 is the symmetric elasticity of substitution across varieties. As described in Sections 2.2 and 2.3 below, [z ; ) is the support interval for the idiosyncratic productivity of Northern min 1 (cid:133)rms, and z is the endogenous productivity cuto⁄above which (cid:133)rms produce o⁄shore for the V;t home market.10 Since the number of (cid:133)rms is time-variant and (cid:133)rms re-optimize their o⁄shoring and exporting strategies every period, the composition of the consumption basket changes over time. I use the home consumption basket C as the numeraire good, so that the price index in t 1 the North is 1 = (cid:26) (!)1 (cid:18)d! 1 (cid:18), where ! (cid:10)NN (cid:10)NS (cid:10)SS, and (cid:26) (!) is the real price t (cid:0) (cid:0) 2 t [ t [ t t 10Asexplainedlate(cid:2)rR,onlythemore(cid:3)productive(cid:133)rms,whoseidiosyncraticproductivityislargerthanthecuto⁄ levels z and z , engage in o⁄shoring and exporting, respectively. In the South, [z ; ) is the support V;t H;t m(cid:3)in 1 interval for the idiosyncratic productivity of Southern (cid:133)rms, and z is the endogenous productivity cuto⁄of H(cid:3);t Southern exporters. 8

of each variety expressed in units of the North consumption basket. The (cid:133)rst-order conditions generate the Euler equations for bonds and stocks: C (cid:13) = (cid:12)(1+r )E C (cid:13) ; (3) t(cid:0) t+1 t t(cid:0)+1 C(cid:2) (cid:3) (cid:13) t+1 (cid:0) v = (cid:12)(1 (cid:14))E (d +v ) ; (4) t t t+1 t+1 (cid:0) C " (cid:18) t (cid:19) # e e e where (cid:14) is the exogenous rate of (cid:133)rm exit every period, described next. 2.2 Firm Entry and Exit Firmentry(i.e. thecreationofnew(cid:133)rmsinthehomeeconomy)takesplaceeveryperiodinboth the North and the South, as in Ghironi and Melitz (2005). In the North, (cid:133)rm entry requires a sunk entry cost equal to f units of Northern e⁄ective labor, which re(cid:135)ects headquarter E activities in the home country (such as research and development).11 After paying the sunk entry cost, each (cid:133)rm is randomly assigned an idiosyncratic labor productivity factor z that is drawnindependentlyfromacommondistributionG(z)withsupportovertheinterval[z ; ), min 1 and which the (cid:133)rm keeps for the entire duration of its life. The N (cid:133)rms created at time t do not produce until t + 1. Also, irrespective of their E;t idiosyncratic productivity, all (cid:133)rms (cid:150)including the new entrants (cid:150)are subject to a random exit shock that occurs with probability (cid:14) at the end of every period. Thus, the law of motion for the number of producing (cid:133)rms is: N = (1 (cid:14))(N +N ). t+1 t E;t (cid:0) The potential entrant (cid:133)rms anticipate their expected post-entry value v , which depends t on the expected stream of future pro(cid:133)ts d , the stochastic discount factor, and the exogenous t e 11The sunk entry cost is equivalent to f w =Z units of the Northern consumption basket. E t te 9

probability (cid:14) of exit every period. The forward iteration of the Euler equation for stocks (4) generates the following expression for the expected post-entry value of the average (cid:133)rm: v = E 1 [(cid:12)(1 (cid:14))]s t C s (cid:0) (cid:13) d : (5) t t (cid:0) s (cid:0) C ( s=t+1 (cid:18) t(cid:19) ) X e e Thus, every period, the unbounded pool of potential entrant (cid:133)rms face a trade-o⁄between the sunk entry cost and the expected stream of future monopolistic pro(cid:133)ts. In equilibrium, (cid:133)rm entry takes place until the expected value of the average (cid:133)rm is equal to the sunk entry cost expressed in units of the Northern consumption basket: v = f wt: t EZt e 2.3 Markets and Production Strategies Every period t, the active (cid:133)rms N choose the destination market(s) that they serve and the t location of production every period, as follows: 1. All (cid:133)rms serve their home market. For this purpose, the Northern (cid:133)rms can produce either at home or o⁄shore. O⁄shoring o⁄ers the advantage of a lower production cost, but is subject to (cid:133)xed and trade costs every period. Importantly, given that this paper focuses on o⁄shoring through vertical FDI, the (cid:133)rms(cid:146)choice between producing at home or o⁄shore concerns the output intended for the home market only, and is not guided by access to the foreign market. 2. A subset of (cid:133)rms from each economy also serve the foreign market. Since the channel of o⁄shoring through horizontal FDI is beyond the scope of this paper, the (cid:133)rms serving the foreign market use exclusively home labor in production, and export their varieties 10

subject to a per-period (cid:133)xed cost as in Ghironi and Melitz (2005).12 Each of these two problems (cid:150)the o⁄shoring decision of (cid:133)rms serving their home market, as well as the exporting decision of (cid:133)rms serving the foreign market (cid:150)are described below. 2.3.1 Firms Serving the Domestic Market: Domestic vs. O⁄shore Production This section illustrates the mechanisms of domestic and o⁄shore production as alternative choices for the Northern (cid:133)rms that produce for the home market. Every period, the (cid:133)rm with labor productivity z must choose one of the two possible production strategies: (a) Produce domestically: y (z) = Z zl , with output as a function of the aggregate D;t t t productivity in the North Z , the (cid:133)rm-speci(cid:133)c labor productivity z, and domestic labor l . t t (b) Alternatively, produce o⁄shore: y (z) = Z zl : Thus, the Northern (cid:133)rm producing V;t t(cid:3) t(cid:3) o⁄shore uses Southern labor l and becomes subject to the aggregate productivity of the South t(cid:3) Z , but is able to carry its own idiosyncratic labor productivity z abroad. (cid:3) Undermonopolisticcompetition, the(cid:133)rmwithidiosyncraticproductivityz solvesthepro(cid:133)tmaximization problem for the alternative scenarios of domestic and o⁄shore production: w t max d (z) = (cid:26) (z)y (z) y (z); (6) D;t D;t D;t D;t (cid:0) Z z (cid:26)D;t(z) t f g w Q w Q max d (z) = (cid:26) (z)y (z) (cid:28) t(cid:3) t y (z) f t(cid:3) t ; (7) V;t V;t V;t V;t V (cid:0) Z z (cid:0) Z (cid:26)V;t(z) t(cid:3) t(cid:3) f g where (cid:26) (z) and (cid:26) (z) are the prices associated with each of the two production strategies, D;t V;t expressed in units of the North consumption basket; w and w are the real wages in the North t t(cid:3) 12Thus, one useful feature of the model is that, when o⁄shoring is removed, the model revisits Ghironi and Melitz (2005), which serves as a basis of comparison for some key results. 11

and the South; and Q is the real exchange rate.13 t The cost of producing one unit of output either domestically or o⁄shore varies not only with the cost of e⁄ective labor w =Z and w Q =Z across countries, but also with the idiosyncratic t t t(cid:3) t t(cid:3) labor productivity z across (cid:133)rms. In addition, the Northern (cid:133)rms producing o⁄shore incur a (cid:133)xed cost equal to f units of Southern e⁄ective labor, which re(cid:135)ects the building and V maintenanceoftheo⁄shoreproductionfacility,14 andalsoanicebergtradecost(cid:28) > 1associated with the shipping of goods produced o⁄shore back to the parent country.15 The demand for the variety of (cid:133)rm z produced either domestically or o⁄shore is y (z) = D;t (cid:26) (z) (cid:18)C or y (z) = (cid:26) (z) (cid:18)C respectively, where C is the aggregate consumption in D;t (cid:0) t V;t V;t (cid:0) t t the North. Pro(cid:133)t maximization implies the equilibrium prices (cid:26) (z) = (cid:18) wt and (cid:26) (z) = D;t (cid:18) 1Ztz V;t (cid:0) (cid:18) (cid:28)w t(cid:3) Qt for the alternative scenarios of domestic and o⁄shore production. The corresponding (cid:18) 1 Z z (cid:0) t(cid:3) pro(cid:133)ts, expressed in units of the aggregate consumption basket C ; are: t 1 d (z) = (cid:26) (z)1 (cid:18)C ; (8) D;t D;t (cid:0) t (cid:18) 1 w Q d (z) = (cid:26) (z)1 (cid:18)C f t(cid:3) t : (9) V;t V;t (cid:0) t V (cid:18) (cid:0) Z t(cid:3) When deciding upon the location of production every period, the (cid:133)rm with productivity z compares the pro(cid:133)t d (z) that it would obtain from domestic production with the pro(cid:133)t D;t d (z) that it would obtain from producing the same variety o⁄shore. As a particular case, I V;t de(cid:133)ne the productivity cuto⁄level z on the support interval [z ; ), so that the (cid:133)rm at the V;t min 1 13The real exchange rate Q = P " =P is the ratio between the price indexes in the South and the North t t(cid:3) t t expressed in the same currency, where " is the nominal exchange rate. t 14The (cid:133)xed o⁄shoring cost is equivalent to f w =Z units of the Southern consumption basket. V t(cid:3) t(cid:3) 15For every (cid:28) > 1 units produced o⁄shore, only one unit arrives in the North for consumption, with the di⁄erence lost due to trade barriers, transportation and insurance costs (Anderson and Wincoop, 2004). 12

cuto⁄obtains equal pro(cid:133)ts from producing domestically or o⁄shore: z = z d (z) = d (z) : (10) V;t D;t V;t f j g The model implies that only the relatively more productive Northern (cid:133)rms (cid:133)nd it pro(cid:133)table to produce their varieties o⁄shore. Despite the lower cost of e⁄ective labor in the South, only (cid:133)rms with idiosyncratic productivity above the cuto⁄ level (z > z ) obtain bene(cid:133)ts from V;t o⁄shoring that are large enough to cover the (cid:133)xed and iceberg trade costs. This implication is consistent with the empirical evidence in Kurz (2006), who shows that the U.S. plants and (cid:133)rms using imported components in production are larger and more productive than their domestically-oriented counterparts, as the larger idiosyncratic productivity levels allow them to cover the (cid:133)xed costs of o⁄shoring.16 In addition, the productivity cuto⁄z reacts to (cid:135)uctuations in the relative cost of e⁄ective V;t labor across countries, and thus a⁄ects the extensive margin of o⁄shoring over the business cycle. For any given level of (cid:133)rm-speci(cid:133)c productivity, a relatively lower cost of e⁄ective labor abroad implies lower prices, higher revenues, and higher pro(cid:133)ts from o⁄shoring, and therefore leads to a larger fraction of o⁄shoring (cid:133)rms in equilibrium. This implication is consistent with the empirical evidence on the determinants of o⁄shoring in Hanson, Mataloni, and Slaughter (2005), who show that U.S. multinationals attract larger shares of their foreign a¢ liates(cid:146)s sales when the latter bene(cid:133)t from lower trade costs and lower wages abroad. 16A useful implication of the model is that more productive (cid:133)rms have larger output and revenue. Given (cid:18) two (cid:133)rms with idiodsyncratic productivity z > z , their output and pro(cid:133)t ratios are y(z2) = z2 > 1 and 2 1 y(z1) z1 d(z2) = z2 (cid:18) (cid:0) 1 > 1 (also see Melitz, 2003). This is consistent with the empirical evidence th (cid:16) at (cid:17) (cid:133)rms using d(z1) z1 imported(cid:16)inp(cid:17)uts in production are not only more productive, but also have larger revenues and employ more workers (Kurz, 2006). 13

In equilibrium, the existence of productivity cuto⁄z requires a cross-country asymmetry V;t in the cost of e⁄ective labor, which ensures that some of the Northern (cid:133)rms have an incentive to produce o⁄shore. To illustrate this point, I re-write the per-period pro(cid:133)ts from domestic and 1 (cid:18) 1 (cid:18) o⁄shore production as d (z) = M wt (cid:0) z(cid:18) 1 and d (z) = M (cid:28)w t(cid:3) Qt (cid:0) z(cid:18) 1 f w t(cid:3) Qt, D;t t Zt (cid:0) V;t t Z t(cid:3) (cid:0) (cid:0) V Z t(cid:3) (cid:16) (cid:17) (cid:16) (cid:17) where M t (cid:17) 1 (cid:18) 1 (cid:18) (cid:18) 1 (cid:0) (cid:18) C t measures the size of the Northern market. Figure 1 plots the two (cid:0) (cid:0) (cid:1) pro(cid:133)ts as functions of the idiosyncratic productivity parameter z(cid:18) 1 over the support interval (cid:0) [z ; ). The vertical intercept is zero for domestic production; it is equal to the negative of min 1 the (cid:133)xed cost ( f w t(cid:3) Qt) for o⁄shoring. In this framework, the productivity cuto⁄ z exists (cid:0) V Z t(cid:3) V;t in equilibrium if the pro(cid:133)t function from o⁄shoring is steeper than the pro(cid:133)t function from domestic production, slope d (z) > slope d (z) : When this condition is met, o⁄shoring V;t D;t f g f g generates larger pro(cid:133)ts than domestic production for the subset of (cid:133)rms with idiosyncratic productivity z along the upper range of the support interval (z > z ). The inequality of pro(cid:133)t V;t slopes is equivalent to (cid:28)TOL < 1; with the "terms of labor" TOL = Qtw t(cid:3) =Z t(cid:3) de(cid:133)ned as the t t wt=Zt ratio between the cost of e⁄ective labor in the South and the North expressed in the same currency. The condition implies that the e⁄ective wage in the South must be su¢ ciently lower than in the North, so that the di⁄erence covers the (cid:133)xed and iceberg trade cost ((cid:28) > 1), and thus provides an incentive for some of the Northern (cid:133)rms to produce o⁄shore. (Note that an appreciation of the terms of labor for the North is equivalent to a decline in TOL .) The model t calibration and the magnitude of macroeconomic shocks ensure that this condition is satis(cid:133)ed every period.17 17Asecondcondionnecessarytoavoidthecornersolutionwhenall(cid:133)rmswouldproduceo⁄shoreisd (z )> D;t min d (z ). It ensures that z >z in all periods. V;t min V;t min 14

2.3.2 Exporting Firms In addition to serving their domestic market, (cid:133)rms from each economy can choose to serve the foreign market through exports, as in Ghironi and Melitz (2005). In the North, the (cid:133)rm with idiosyncratic productivity z would use an amount of domestic labor l (z) to produce for the H;t Southern market, y (z) = Z zl (z). The Southern (cid:133)rms that choose to export to the North H;t t H;t face a similar problem. Pro(cid:133)tmaximizationimpliesthefollowingequilibriumprice: (cid:26) (z) = (cid:18) (cid:28) wtQ(cid:0)t 1 andpro(cid:133)t H;t (cid:18) 1 (cid:3) Ztz (cid:0) function: d (z) = 1(cid:26) (z)1 (cid:18)C Q f wt for the Northern exporter with productivity factor H;t (cid:18) H;t (cid:0) t(cid:3) t (cid:0) HZt z, where C is aggregate consumption in the South. Producing for the foreign market generates t(cid:3) additional pro(cid:133)ts, but involves a (cid:133)xed exporting cost equal to f units of Northern e⁄ective H labor, and also an iceberg trade cost (cid:28) . The model implies that only the subset of Northern (cid:3) (cid:133)rms with idiosyncratic labor productivity above the productivity cuto⁄z (cid:133)nd it pro(cid:133)table H;t toproduceinNorthandexporttotheSouthernmarket, astheycana⁄ordthe(cid:133)xedandiceberg trade costs of exporting. Thus, the time-varying productivity cuto⁄for exporters is: z = inf z d (z ) > 0 : (11) H;t H;t V;t f j g 2.3.3 O⁄shoring and Exporting Firms In the stylized model of vertical FDI proposed in this paper, the o⁄shoring and exporting activities of Northern (cid:133)rms are driven by separate objectives, namely by selling to the home vs. foreign markets respectively. In an alternative model, o⁄shoring (cid:133)rms could also sell to the foreign market (cid:150)in addition to the home market (cid:150)if given the opportunity, either directly by engaging in export-substituting horizontal FDI as in Helpman, Melitz and Yeaple 15

(2004), or indirectly by re-routing the varieties through the home country. However, such a setup would provide di⁄erent incentives to the o⁄shoring (cid:133)rms, and would have di⁄erent macroeconomic implications than o⁄shoring through vertical FDI, which is the focus of this paper. This choice is guided by a number of reasons, including that vertical FDI is the type of o⁄shoring associated with the maquiladora stylized facts presented earlier. In addition, o⁄shoring through vertical FDI is associated with the empirical relation between o⁄shoringrelated trade and output comovement documented in BKT, since it boosts trade rather than substitutes it (see Ramondo and Rodriguez-Clare, 2012). Finally, with o⁄shoring through vertical FDI, the o⁄shoring output is part of the foreign economy but is a⁄ected by demand in home, which has important implications for output comovement. One implication from the family of models with heterogeneous (cid:133)rms is that (cid:133)rms self-select themselves into exporting and o⁄shoring activities from the higher end of the productivity distribution. Thus, in this model, there are cases in which the o⁄shoring and exporting operations are undertaken by (cid:133)rms with similar productivity, although these activities target di⁄erent markets.18 The implication is consistent with empirical evidence that both exporting and importing (cid:133)rms are relatively more productive (Bernard, Jensen, Redding, Schott, 2007), and also that exporting and o⁄shoring activities may occur simultaneously within the same (cid:133)rm (Kurz, 2006). It is also consistent with (cid:133)rms whose globalization strategy involves o⁄shoring to a low-wage country at the same time with producing in the home base for reasons other than vertical integration, such as diversifying supply chain risks and reducing inventory costs (Economist, 2011). 18A model with heterogeneous (cid:133)rms that combines o⁄shoring through vertical FDI (as in this paper) with exports and horizontal FDI (as in Helpman, Melitz and Yeaple, 2004) would yield a similar implication when the productivity cuto⁄for vertical FDI is below that for horizontal FDI. 16

3 Aggregation over Heterogeneous Firms This section translates the model with a continuum of heterogeneous (cid:133)rms into an equivalent framework with two average representative Northern (cid:133)rms that produce domestically and o⁄shore, respectively, for their domestic market. Since o⁄shoring takes place one-way, there is only one representative Southern (cid:133)rm that produces for the South market. In addition, one representative (cid:133)rm in each economy produces domestically for the export market. 3.1 Average Firm Productivity Levels Domestic vs. o⁄shore production: First I describe the average productivity levels of the two representative Northern (cid:133)rms that produce domestically and o⁄shore for the Northern market. Figure 2 plots the density of the (cid:133)rm-speci(cid:133)c labor productivity levels z over the support interval [z ; ). Every period t, there are N (cid:133)rms from the North with idiosynmin D;t 1 cratic productivity factors below the o⁄shoring cuto⁄ (z < z ) that produce domestically; V;t their average productivity is z . There are also N (cid:133)rms with productivity factors above the D;t V;t cuto⁄ (z > z ) that choose to produce o⁄shore; their average productivity is z . Since the V;t e V;t (cid:133)rm-speci(cid:133)c labor productivity levels z are random draws from a common distribution G(z) e with density g(z), I compute the two average productivity levels as: 1 1 zV;t (cid:18) 1 (cid:18) (cid:0) 1 1 (cid:0) 1 1 z = z(cid:18) 1g(z)dz and z = z(cid:18) 1g(z)dz : (12) D;t 2G(z ) (cid:0) 3 V;t 21 G(z ) (cid:0) 3 V;t V;t Z (cid:0) Z zmin 6 zV;t 7 e 4 5 e 4 5 I assume that the (cid:133)rm-speci(cid:133)c labor productivity draws z are Pareto-distributed, with p.d.f. g(z) = kzk =zk+1 and c.d.f. G(z) = 1 (z =z)k over the support interval [z ; ). Using min (cid:0) min min 1 this assumption, I derive analytical solutions for the average productivity levels of the two 17

representative Northern (cid:133)rms that produce domestically and o⁄shore as functions of the timevariant productivity cuto⁄z :19 V;t 1 z = (cid:23)z z z V k (cid:0) ;t ((cid:18) (cid:0) 1) (cid:0) z m k (cid:0) in ((cid:18) (cid:0) 1) (cid:18) (cid:0) 1 and z = (cid:23)z ; (13) D;t min V;t zk zk V;t V;t " V;t (cid:0) min # e e 1 wheretheproductivitycuto⁄isz = z (N =N )(1=k),andtheparametersare(cid:23) k (cid:18) (cid:0) 1 V;t min t V;t (cid:17) k ((cid:18) 1) (cid:0) (cid:0) h i and k > (cid:18) 1.20 Since o⁄shoring takes place one-way, from the North to the South, the South- (cid:0) ern (cid:133)rms serve their domestic market exclusively through domestic production. Their average productivity is constant, z = (cid:23)z , as it covers the entire support interval [z ; ). D(cid:3) m(cid:3)in m(cid:3)in 1 e Exporting (cid:133)rms: Under the Pareto assumption, the average productivity levels of the exporting (cid:133)rms in each economy are as in Ghironi and Melitz (2005): 1=k N 1=k N t D(cid:3);t z = (cid:23)z and z = (cid:23)z : (14) H;t min N H(cid:3);t m(cid:3)in N (cid:18) H;t(cid:19) H(cid:3);t! e e 3.2 Average Prices and Pro(cid:133)ts Using the average productivity levels for the domestic, o⁄shoring and exporting (cid:133)rms de(cid:133)ned in Section 3.1, I translate the model of o⁄shoring in terms of three representative Northern (cid:133)rms: oneproducesdomestically, anotherproduceso⁄shore(eachservingtheNorthernmarket), while a third (cid:133)rm produces domestically and exports to the Southern market. There are only two representative Southern (cid:133)rms: one produces for the local market, and the other exports to the 19The derivations are shown in the Technical Appendix available online. 20I use the Pareto c.d.f. G(z ) = 1 (z =z )k and the share of Northern (cid:133)rms producing o⁄shore V;t min V;t (cid:0) N =N = 1 G(z ) to write the productivity cuto⁄ as z = z (N =N )(1=k). The share of Northern V;t t V;t V;t min t V;t (cid:0) (cid:133)rms producing domestically is N =N = G(z ). Parameter k re(cid:135)ects the dispersion of the productivity D;t t V;t draws: A relatively larger k implies a smaller dispersion and a higher concentration of productivities z towards the lower productivity bound z . min 18

North. The average prices and pro(cid:133)ts for each representative (cid:133)rm are in Table 1. Using the property that the Northern (cid:133)rm at the productivity cuto⁄ z is indi⁄erent V;t between the two production strategies, I derive the following relationship between the average pro(cid:133)ts of the two representative (cid:133)rms that produce domestically and o⁄shore:21 k z (cid:18) 1 (cid:18) 1 w Q d = V;t (cid:0) d + (cid:0) f t(cid:3) t : (15) V;t D;t V k ((cid:18) 1) z k ((cid:18) 1) Z (cid:0) (cid:0) (cid:18) D;t(cid:19) (cid:0) (cid:0) t(cid:3) e e e In addition, using the property that the (cid:133)rm at the productivity cuto⁄z obtains zero pro(cid:133)ts H;t from exporting, the average pro(cid:133)ts from exports are as in Ghironi and Melitz (2005): (cid:18) 1 w (cid:18) 1 w d = (cid:0) f t and d = (cid:0) f t(cid:3) : (16) H;t k ((cid:18) 1) H Z (cid:3)H;t k ((cid:18) 1) H(cid:3) Z t t(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) e e Price indexes and total pro(cid:133)ts The consumption price indexes in the North and the South are functions of the average prices of varieties available in each economy: 1 = N D;t ((cid:26) D;t )1 (cid:0) (cid:18) +N V;t ((cid:26) V;t )1 (cid:0) (cid:18) +N H(cid:3);t (cid:26) (cid:3)H;t 1 (cid:0) (cid:18) : (17) (cid:0) (cid:1) 1 = N D(cid:3);t e(cid:26) (cid:3)D;t 1 (cid:0) (cid:18) +N H;t (e(cid:26) H;t )1 (cid:0) (cid:18): e (18) (cid:0) (cid:1) e e Finally, total pro(cid:133)ts are based on the average pro(cid:133)ts and the number of (cid:133)rms in each economy: N d = N d +N d +N d : (19) t t D;t D;t V;t V;t H;t H;t N de = N de +N ed : e (20) D(cid:3);t t D(cid:3);t (cid:3)D;t H(cid:3);t (cid:3)H;t 21See the Technical Appendix availaeble onlineefor details. e 19

3.3 Aggregate Accounting and the Current Account Aggregate output is equal to the sum of labor income and stock dividends that households in each economy obtain every period, Y = w L + N d and Y = w L + N d : Thus, the t t t t t(cid:3) t(cid:3) (cid:3) D(cid:3);t (cid:3)t value added o⁄shore, VA t = N V;t (cid:18) (cid:18)(cid:0)(cid:28) 1 ((cid:26) V;t )1 (cid:0) (cid:18)C t +f V e w Z t(cid:3) Qt , de(cid:133)ned as the waege income of t(cid:3) h i Southern workers employed for the production and (cid:133)xed cost activities in the o⁄shoring sector, e is part of the Southern output.22 The pro(cid:133)ts of Northern (cid:133)rms that produce o⁄shore are part of the Northern output. Under (cid:133)nancial autarky in the markets for bonds and stocks, aggregate accounting implies that households spend their income from labor and stock holdings on consumption and investment in new (cid:133)rms, C +N v = Y and C +N v = Y : t E;t t t t(cid:3) E(cid:3);t t(cid:3) t(cid:3) The current account in the North is: e e CA t = N H;t ((cid:26) H;t )1 (cid:0) (cid:18)C t(cid:3) Q t + N V;t d V;t (cid:0) N V;t ((cid:26) V;t )1 (cid:0) (cid:18)C t (cid:0) N H(cid:3);t (cid:26) (cid:3)H;t 1 (cid:0) (cid:18) C t (a) Exports (b) Repatriated pro(cid:133)ts (c) Value added o⁄shore (d) Imports(cid:0)ofSou(cid:1)thern varieties e e e e (21) | {z } | {z } | {z } | {z } Under(cid:133)nancialautarky, thebalancedcurrentaccountcondition(CA = 0)impliesthatthesum t of (a) exports by Northern (cid:133)rms to the South and (b) repatriated pro(cid:133)ts of o⁄shore a¢ liates must be equal to the sum of (c) the value added o⁄shore imported by the North and (d) the imports of varieties produced by the Southern (cid:133)rms.23 3.4 Summary of Baseline Model The baseline model with (cid:133)nancial autarky for the Northern economy is characterized by 16 equations in 16 endogenous variables: N , N , N , N , N , d , d , d , d , z , z , t D;t V;t H;t E;t t D;t V;t H;t D;t V;t 22The inclusion of the (cid:133)xed cost in VA has minimal implications for the value added dynamics (see Figure t e e e e e e D.3 in the Technical Appendix online). 23Inthecasewithinternationaltradeinbonds,thecurrentaccountbalanceequalsthechangeinbondholdings (see the Appendix). 20

z , v , r , w and C . Since the Southern (cid:133)rms do not produce in the high-cost North, the H;t t t t t Southern economy is described by only 11 equations in 11 endogenous variables; there are no e e Southern counterparts for N , N , d , z and z .24 Finally, the real exchange rate Q and t V;t V;t D;t V;t t the current account equation close thee model. e e 3.5 Calibration Iuseastandardquarterlycalibrationbysettingthesubjectiverateof timediscount(cid:12) = 0:99 to match an average annualized interest rate of 4 percent. The coe¢ cient of relative risk aversion is (cid:13) = 2. Following Ghironi and Melitz (2005), the intra-temporal elasticity of substitution is (cid:18) = 3:8, and the probability of (cid:133)rm exit is (cid:14) = 0:025, which matches annual 10 percent job destruction in the United States. AssummarizedinTable2, theParetodistributionparameterk, theicebergtradecost(cid:28), and the (cid:133)xed costs of o⁄shoring (f ) and exporting (f and f ) are calibrated so that the model V H H(cid:3) in steady state matches the importance of o⁄shoring for the Mexican economy, as illustrated by three empirical moments: (1) The maquiladora value added represents about 20 percent of Mexico(cid:146)s manufacturing GDP (Bergin et al., 2009), vs. 20 percent in the model in steady state; (2) The maquiladora sector provided about 55 percent of Mexico(cid:146)s manufacturing exports on average from 2000 to 2006 (INEGI, 2008), compared to about 60 percent in the model; (3) The maquiladora sector accounts for about 25 percent of Mexico(cid:146)s manufacturing employment (Bergin et al., 2009), vs. 20 percent in the model. To this end, I set k = 4:2, (cid:28) = 1:2, f = 0:095, f = 0:040 and f = 0:025. Without loss of generality, the lower bound of the V H H(cid:3) 24The model summary is in the Appendix, and the asymmetric steady-state solution is available in the Technical Appendix. Note that the average labor productivity of the representative Southern (cid:133)rm producing for the domestic market (z ) is constant over time. Variables N , r , N and r are predetermined. D(cid:3) D;t t t(cid:3) t(cid:3) e 21

support interval for (cid:133)rm-speci(cid:133)c productivity in the North and the South is z = z = 1. min m(cid:3)in To obtain an asymmetric cost of e⁄ective labor across countries in steady state, the sunk entry cost, which re(cid:135)ects headquarter costs sensitive to the regulation of starting a business in the (cid:133)rms(cid:146)country of origin, is set to be larger in the South than in the North (f = 4f and E(cid:3) E f = 1). As a result, the steady-state number of (cid:133)rms, the labor demand and the e⁄ective E wage are relatively lower in the South. The calibration re(cid:135)ects the considerable variation in the monetary cost of starting a business across economies, which was 2.8 times higher in Mexico than in the United States in purchasing power parity terms in 2010 (World Bank, 2011). The asymmetric sunk entry costs, along with the values for k, (cid:28), f , f and f V H H(cid:3) discussed above, generate a steady-state value for the terms of labor that is less than unit (TOL = Qw (cid:3) =Z (cid:3) = 0:75). In other words, the steady-state cost of e⁄ective labor in the South is w=Z 75 percentofthecostofe⁄ectivelaborintheNorth. Thus, thecalibrationprovidesanincentive for some of the Northern (cid:133)rms to produce o⁄shore in steady state.25 4 Alternative Models This section presents the alternative models with endogenous labor supply and investment in physical capital. 25The resulting steady-state fraction of the Northern (cid:133)rms that use foreign labor (N =N) is 1 percent; the V fraction of exporting (cid:133)rms (N =N) is 9 percent. Since o⁄shoring is modelled in an asymmetric two-country H frameworkthat abstracts from the trade of U.S.(cid:133)rms with the rest of the world otherthan Mexico, the steadystate values reported above are less than their empirical counterparts. In the data, 14 percent of the U.S. (cid:133)rms (other than domestic wholesalers) used imported inputs in 1997 (Bernard, Jensen, Redding and Schott, 2007); 21percentoftheU.S.manufacturingplantswereexportersin1992(Bernard,Eaton,JensenandKortum,2003). 22

4.1 Endogenous Labor Supply With endogenous labor supply, the representative household in the North maximizes the expected lifetime utility max E 1(cid:12)s tU(C ;L ) ; with the discount factor (cid:12) (0;1). The t (cid:0) s s f Lt;xt;Bt g(cid:20) s=t (cid:21) 2 period utility function takes the fo P rm: U (C ;L ) = lnC (cid:31)L1 t + ; in which C denotes cont t t t (cid:0) 1+ t sumption, L is the variable labor supply, > 0 is the inverse elasticity of labor supply, t and (cid:31) > 0 is the weight on the disutility from labor. In the North, the Euler equation for 1= bonds is: C 1 = (cid:12)(1+r )E C 1 ; the equation for labor supply is: L = wt , t(cid:0) t+1 t t(cid:0)+1 t (cid:31)Ct (cid:16) (cid:17) (cid:2) (cid:3) and the equation for aggregate accounting changes to incorporate endogenous labor supply: C +N v = w L +N d . The corresponding equations for the South are similar.26 t E;t t t t t t e e 4.2 Physical Capital The model with physical capital includes four new variables and four new equations for each economy. For the North, K is the stock of physical capital, I is investment in physical capital, t t rk is the gross return from capital, and (cid:21) is the multiplier on the new equation of capital t t accumulation, which takes the form: (cid:25)k I 2 K = (1 (cid:14)k)K +I I t 1 : t+1 t t t 1 (cid:0) (cid:0) 2 (cid:0) (cid:18) I t 1 (cid:0) (cid:19) (cid:0) where (cid:25)k denotes an investment adjustment cost. In addition, the budget constraint of the representative household becomes: (v +d )N x +w L+rkK v (N +N )x +C +I : t t t t t t t > t t E;t t+1 t t 26In a robustness check, to mute the income e⁄ect on labor supply, I use preferences as in Greenwood, e Hercowitz and Hu⁄man (GHH, 1988), with e U (C ;L ) = 1 C (cid:31)L1 t + e1 (cid:0) (cid:13) 1 . The equation for labor t t t 1 (cid:13) t (cid:0) 1+ (cid:0) 1= (cid:0) (cid:20)(cid:16) (cid:17) (cid:21) supply becomes L = wt . t (cid:31) (cid:16) (cid:17) 23

Thus, the (cid:133)rst-order conditions for capital and investment are: (cid:21) = (cid:12)E C (cid:13)rk +(cid:12)(1 (cid:14)k)E [(cid:21) ]; t t t(cid:0)+1 t+1 (cid:0) t t+1 C t(cid:0) (cid:13) = (cid:21) t (cid:2) 1 (cid:0) (cid:25)k (cid:3) It It 1 (cid:0) 1 +(cid:12)E t (cid:21) t+1 (cid:25) 2 k It It 1 2 (cid:0) 1 : (cid:0) (cid:20) (cid:18) (cid:0) (cid:19)(cid:21) h (cid:16) (cid:17)i (cid:16) (cid:17) Theequationforaggregateaccountingisadjustedtoincludetheinvestmentandgrossreturn from physical capital: N d +w L+rkK = N v +C +I : Importantly, the composite good t t t t t E;t t t t that incorporates domestiec, o⁄shored and foreign varieties is used for both consumption and e (cid:18) investment: C t +I t = zV;t y D;t (!) (cid:18) (cid:0)(cid:18) 1 d! + 1y V;t (!) (cid:18) (cid:0)(cid:18) 1 d! + 1 y H(cid:3);t (!) (cid:18) (cid:0)(cid:18) 1 d! (cid:18) (cid:0) 1 : "zmin zV;t z H(cid:3);t # R R R For each variety z; production is a function of labor and capital, and takes the form y (z) =Z z[l (z)]1 (cid:11)[k (z)](cid:11) for domestic production, and y (z) =Z z[l (z)]1 (cid:11)[k (z)](cid:11) for D;t t t (cid:0) t V;t t(cid:3) t(cid:3) (cid:0) t(cid:3) (cid:11) o⁄shoring. The corresponding prices are (cid:26) D;t (z) = (cid:18) (cid:18) 1Z 1 tz 1 wt (cid:11) 1 (cid:0) (cid:11) r (cid:11) t k if variety z is pro- (cid:0) (cid:0) duced at home, and (cid:26) (z) = (cid:18) (cid:28)Qt w t(cid:3) 1 (cid:0) (cid:11) r t(cid:3) k (cid:11) if it i (cid:0) s o⁄s (cid:1) hore (cid:16) d. (cid:17) In addition, (cid:133)rm entry V;t (cid:18) 1Z z 1 (cid:11) (cid:11) (cid:0) t(cid:3) (cid:0) (cid:16) (cid:17) (cid:16) (cid:17) in the North implies a sunk cost activity that requires e⁄ective units of domestic labor and (cid:11) capital, and thus is equal to fE wt 1 (cid:0) (cid:11) r t k units of the North consumption basket. Also, Zt 1 (cid:11) (cid:11) (cid:0) (cid:16) (cid:17) (cid:0) (cid:1) o⁄shoring implies a (cid:133)xed cost activity that requires e⁄ective units of foreign labor and capital, 1 (cid:11) (cid:11) and thus is equal to fV w t(cid:3) (cid:0) r t(cid:3) k units of the South consumption basket. Similarly, the Z 1 (cid:11) (cid:11) t(cid:3) (cid:0) (cid:16) (cid:17) (cid:16) (cid:17) (cid:11) (cid:133)xed cost of exporting is fH wt 1 (cid:0) (cid:11) r t k : Thus, the market clearing condition for the stock Zt 1 (cid:11) (cid:11) (cid:0) (cid:16) (cid:17) (cid:0) (cid:1) of capital in the North incorporates capital used by the (cid:133)rms producing domestically for the home and foreign market, as well as capital used for the sunk entry cost and (cid:133)xed exporting cost activities: f f (cid:11)w 1 (cid:11) E H t (cid:0) K = N k +N k +(N +N ) : t D;t D;t H;t H;t E;t Z H;t Z (1 (cid:11))rk t t (cid:20) (cid:0) t (cid:21) e e 24

The market clearing condition for the South is similar, but also includes capital used by the o⁄shoring (cid:133)rms from North for production and (cid:133)xed cost activities in the South. Finally, in the presence of physical capital, the terms of labor TOL = Qtw t(cid:3) =Z t(cid:3) are no longer t wt=Zt an adequate measure of the relative cost of production across countries. Instead, I de(cid:133)ne the "terms of production" as the ratio between the marginal cost of production in the South and the North expressed in units of the same currency: TOP = Qt(w t(cid:3) )1 (cid:0) (cid:11)(r t(cid:3) k)(cid:11) =Z t(cid:3): The model of t (wt)1 (cid:0) (cid:11)(r t k)(cid:11) =Zt o⁄shoring with physical capital is summarized in Table A.3 of the Appendix. 4.3 Calibration of alternative models In the model with elastic labor supply, the elasticity of labor supply is 1= = 1 in both the North and the South, as in Farhat (2009), and the weight on the disutility from labor is set at (cid:31) = 0:9208 in the North and (cid:31) = 0:9466 in the South, so that labor supply in state state (cid:3) matches that in the baseline model, L = L = 1.27 (cid:3) In the model with physical capital, the coe¢ cient on capital in production and sunk/(cid:133)xed cost activities is set at (cid:11) = 0:37 in both economies, so that the share of capital in aggregate income (which includes income from capital, labor as well as (cid:133)rm pro(cid:133)ts) is about 0:3. The (cid:133)xed costs of o⁄shoring and exporting are re-set at f = 0:44, f = 0:032 and f = 0:027, V H H(cid:3) so that trade openness in the North and the South, as well as the importance of o⁄shoring for the Southern economy (i.e. 22 percent of GDP, 57 percent of exports, and 21 percent of employment) are similar to the baseline model. Since investment in physical capital and (cid:133)rm entryaresubstituteoptionsfortheNorthernhousehold, theirrelativevolatilityhasanon-trivial e⁄ect on model implications (see Fattal Jaef and Lopez, 2012). Therefore, the adjustment cost 27With GHH preferences, the inverse inter-termporal elasticity of substitution is (cid:13) =1; the inverse elasticity of labor supply is =1, and the weights are (cid:31)=2:451 and (cid:31) =1:481 so that, in steady state, L=L =1. (cid:3) (cid:3) 25

of investment in physical capital is set at (cid:25)k = (cid:25) k = 1:35, so that the volatility of (cid:133)rm entry (cid:3) matches that of investment in physical capital, as in the data.28 5 Results 5.1 O⁄shoring to Mexico(cid:146)s Maquiladora Sector This section describes empirically the cyclicality of o⁄shoring motivated by lower production costs, usingdatafromU.S.manufacturingandMexico(cid:146)smaquiladorasectorasanexample. The empirical exercise will be useful to assess the model implications, which are described next. Mexico(cid:146)s maquiladorasectorrepresentsanappropriateempirical setuptostudythecyclicality of o⁄shoring motivatedbylowerproduction costs, due to its direct links to U.S. manufacturing and the absence of local consumption in Mexico. The maquiladora sector consists of plants that import inputs, process them, and export the resulting output back to the country of origin (see Gruben, 2001). Although only a subset of the maquiladora plants are U.S.-owned, most of them accommodate the o⁄shoring operations of U.S. (cid:133)rms: The maquiladoras import most of their production inputs from the United States (82 percent), and likewise export most of their output to the United States (90 percent; see Hausman and Haytko, 2003; Burstein, Kurz and Tesar, 2008). The maquiladora value added is part of Mexico(cid:146)s manufacturing output. Empirical cross-correlations Mexico(cid:146)s manufacturing production and, in particular, the maquiladora value added are strongly correlated with the U.S. manufacturing production. Panel1ofFigure3plotsthedetrendedseriesforMexico(cid:146)smaquiladorarealvalueadded(dashed 28Using the data on new establishments from the Business Dynamics Statistics of the U.S. Census Bureau, Fattal Jaef and Lopez (2012) show that (cid:133)rm entry is at least as volatile as investment. 26

line), Mexico(cid:146)s manufacturing industrial production (Mex IP, dotted line), and the U.S. manufacturing industrial production (US IP, solid line), for the interval from 1990:Q1 to 2006:Q4 for which the maquiladora data are available.29 The chart shows that the U.S. recessions in 1990 and 2001, as well as the expansion throughout the late 1990s were associated with similar developments in Mexico. Also, during the 1994-95 (cid:133)nancial crisis in Mexico, the decline in the maquiladora value added was less pronounced than the drop in Mexico(cid:146)s manufacturing IP, as the o⁄shoring sector bene(cid:133)ted from its direct links with U.S. manufacturing. In panel 2, the cross-correlations show that Mexico(cid:146)s maquiladora value added comoves more closely with the U.S. manufacturing IP than does Mexico(cid:146)s total manufacturing IP: the contemporaneous correlation between the maquiladora value added the U.S. manufacturing IP (0.69) is larger than the correlation between the Mexican and U.S. manufacturing IP (0.58). Panel 3 of Figure 3 plots the detrended series for the number of maquiladora plants in Mexico (dashed line) (cid:150)which is a proxy for the extensive margin of o⁄shoring (cid:150)and also the U.S. manufacturing IP(solid line). The cross-correlations in panel 4 showthat the contemporaneous correlation is positive, and that the U.S. manufacturing IP leads the number of maquiladora plants by about four quarters. The result suggests that the extensive margin of o⁄shoring adjustsgraduallyovertime,whereasthemaquiladoravalueaddediscontemporaneouslycorrelated with the U.S. manufacturing IP.30 29The data are seasonally adjusted, converted in natural logs, and expressed in deviations from a Hodrick- Prescott trend. The maquiladora series were discontinued at the end of 2006. 30These results are consistent with the empirical impulse responses of o⁄shoring to Mexico (including the extensive margin) from the structural VAR model discussed in Section C the Technical Appendix avilable online. 27

5.2 Impulse Responses To illustrate the model implications for o⁄shoring, I log-linearize the model around the steady state, and compute the impulse responses to a transitory one-percent increase in aggregate productivity in the North. Aggregate productivity follows the autoregressive process logZ = t+1 (cid:26)logZ +u , with persistence (cid:26) = 0:9. t t Figure 4 shows the impulse responses of the baseline model of o⁄shoring (thick solid lines), and compares them with the impulse responses from two alternative models: (i) a model of o⁄shoring in which the productivity cuto⁄ is (cid:133)xed, so that the fraction of o⁄shoring (cid:133)rms is constantoverthebusinesscycle(thinsolidlines);31 and(ii)theextremecasewithnoo⁄shoring, which revisits the model with exports only in Ghironi and Melitz (2005) (dashed lines).32 For each variable, the horizontal axis illustrates quarters after the initial shock, and the vertical axis shows the percent deviations from the original steady state in each quarter. The intensive margin In the baseline model (thick solid lines), on impact, the increase in aggregate labor productivity in the North generates a proportional increase in the real wage (w ). The increase in demand for aggregate consumption, which includes varieties produced t both domestically and o⁄shore as imperfect substitutes, causes an immediate increase in the valueaddedpero⁄shoring(cid:133)rm(theintensivemargin).33 Inturn, sincetheincreaseinaggregate productivityintheNorthisnotreplicatedintheSouth,theexcessdemandforSoutherne⁄ective 31In the alternative model with (cid:133)xed productivity cuto⁄, the fraction of o⁄shoring (cid:133)rms is constant, but the number of o⁄shoring (cid:133)rms varies over time due to (cid:133)rm entry in the parent country. During expansions in the North,thenewentrantsthatdrawidiosyncraticproductivityfactorsabovethecuto⁄startbyproducingdirectly o⁄shore. However, none of the (cid:133)rms that initially produce at home can relocate o⁄shore when the terms of labor appreciate. 32In the alternative model with exports only (Ghironi and Melitz, 2005), I set f =0:0330 and f =0:0315 H H(cid:3) so that the fraction of Northern exporting (cid:133)rms (9 percent) and that of Southern exporting (cid:133)rms (53 percent) match the corresponding steady-state values from the baseline model with o⁄shoring. 33The immediate increase in the intensive margin would be stronger with a lower elasticity of substitution between varieties produced domestically and o⁄shore (see Figure D.2 in the Technical Appendix online). 28

laborcausestherealwageintheSouth(w )torise,andthetermsoflabor TOL = Qtw t(cid:3) =Z t(cid:3) to t(cid:3) t wt=Zt (cid:16) (cid:17) depreciate (increase) on impact. As a result, the number of o⁄shoring (cid:133)rms (N ) falls initially, V;t due to the increase in the cost of e⁄ective labor o⁄shore and the (cid:133)xed cost of o⁄shoring, both of which are sensitive to the e⁄ective wage in the South. However, the increase in value added per o⁄shoring (cid:133)rms (the intensive margin) more than o⁄sets the initial decline in the number of o⁄shoring (cid:133)rms (the extensive margin), and thus the total value added o⁄shore increases on impact. The extensive margin In the quarters after the shock, the role of the two margins in drivingtheprocyclicalpatternofo⁄shoringisreversed: theextensivemarginincreasesgradually over time, while the intensive margin declines. As aggregate productivity in the North persists above its steady state, the larger market size encourages (cid:133)rm entry, as shown by the gradual increase in the number of incumbent (cid:133)rms (N ). In turn, (cid:133)rm entry leads to an increase in t demand for Northern labor, which causes the cost of e⁄ective labor to appreciate gradually in the North relative to the South. In Figure 4, this appreciation is visible as the real wage in the North declines more slowly than aggregate productivity after the initial shock, and thus the terms of labor appreciate (fall) relative to their steady-state level. Following the appreciation of the terms of labor, the number of o⁄shoring (cid:133)rms (N ) increases gradually like in the data, V;t as some of the more productive Northern (cid:133)rms relocate production to the South, while the intensive margin declines. Thus, the increase in the extensive margin more than o⁄sets the intensive margin decline, reinforcing the procyclical pattern of o⁄shoring in the quarters after the shock. The total value added o⁄shore (VA ) increases by more under the baseline model of o⁄t 29

shoring (thick solid line) than in the alternative model of o⁄shoring in which the productivity cuto⁄ is (cid:133)xed (thin solid line). Thus, 20 quarters after the shock, roughly one quarter of the increase in the total value added o⁄shore is due to the extensive margin adjustment. In the South, the initial jump in the real wage, caused by the increase in o⁄shoring along its intensive margin, is followed by an additional increase which occurs gradually over time, as some of the more productive Northern (cid:133)rms relocate production to the South. Since the increase in o⁄shoring along its extensive margin transfers some of the upward pressure from the domestic to the foreign wage, the terms of labor appreciate by less (declines by less) in the baseline model of o⁄shoring (thick solid line) than in the alternative model with no o⁄shoring as in Ghironi and Melitz (2005) (dashed line). International bond trading Figure 5 shows the impulse responses for the model with international bond trading (thin solid lines), which in general are similar to those from the baseline model (thick lines). One di⁄erence is that, following the positive technology shock in the North, the terms of labor do not depreciate (rise) on impact, and hence the number of o⁄shoring (cid:133)rms does not fall, while the total value added o⁄shore rises on impact by more than under (cid:133)nancial autarky. The reason is that, since the Southern household lends to the North, (cid:133)rm entry rises more strongly in the North and falls by more in the South, thus placing more upward pressure on the North wage and less on the South wage. Elastic labor supply Figure 6 shows the impulse responses to the positive shock to productivity in the North for the model with elastic labor supply (the thin solid lines, in green), and compares them to those for the baseline model with (cid:133)xed labor supply (the thick solid lines, in black). With elastic labor supply, the response of o⁄shoring is similar to the 30

baseline model, but is stronger in the quarters after the shock. On impact, the equilibrium real wage in the North rises along with aggregate productivity, like in the baseline model. Although dampened somewhat by the income e⁄ect, labor supply rises in response to the higher wage. However, labor demand rises by even more than in the baseline model, re(cid:135)ecting the stronger entry of new (cid:133)rms attracted by the increased supply of more productive labor, and also by the larger market size resulting from higher labor income. Thus, the immediate wage response is similar to that from the baseline model. In the quarters after the shock, the number of incumbent (cid:133)rms in the North increases by more than in the baseline model, boosting the demand for labor. In contrast, labor supply falls below its steady-state level due to the income e⁄ect associated with higher consumption. As a result, the terms of labor appreciate by more, and hence the number of o⁄shoring (cid:133)rms and the value added o⁄shore increase by more than in the baseline model. The e⁄ect is even stronger for a higher elasticity of labor supply (see the dashed lines, with 1= = 3).34 Physical capital Figure 7 shows the impulse responses for the model with physical capital. For comparability with the baseline model, the (cid:133)gure presents two versions of the model with physical capital: one in which the share of capital in production follows the standard calibration ((cid:11) = (cid:11) = 0:37, thick lines), and another in which the share of capital is set arbitrarily (cid:3) low ((cid:11) = (cid:11) = 0:01, thin lines). The latter case resembles the baseline model, since investment (cid:3) in physical capital represents a very small share of aggregate income. The presence of physical capital dampens but does not reverse the dynamics of o⁄shoring. 34Theresultalsoholdswhentheincomee⁄ectisshutdownusingpreferencesasinGreenwood,Hercowitzand Hu⁄man (1988). As shown in Figure D.4 of the Technical Appendix, without the income e⁄ect, the increase in labor supply is still o⁄set by the increase in labor demand, which mirrors the stronger rise in (cid:133)rm entry relative to the baseline model. In turn, following the initial depreciation, the terms of labor appreciate over time relative to the steady-state level, providing an incentive for (cid:133)rms to relocate production o⁄shore. Overall, the total value added o⁄shore rises on impact, and continues to rise in the following quarters. 31

On impact, (cid:133)rm entry rises by less with the standard calibration than in the baseline-like case, since investment in physical capital substitutes (cid:133)rm entry to some extent, as in Fattal Jaef and Lopez(2012). Also, inthequartersaftertheshock, thenumberofincumbent(cid:133)rmsintheNorth increases by less with physical capital, given the slower pace of (cid:133)rm entry, which in turn causes the terms of production to appreciate (fall) by less relative to the baseline model. However, the presence of physical capital does not reverse the procyclicality of (cid:133)rm entry, which still places appreciation pressure on the marginal cost of production in the North relative to the South. As a result, the terms of production fall below their steady-state level. Although more slowly, the number of o⁄shoring (cid:133)rms and the total value o⁄shore increase gradually in the quarters following the shock, like in the baseline model. 5.3 Business Cycles: Data and Model This section presents the contemporaneous and cross-correlations between output in the North and the o⁄shoring sector generated by the model, and compares them to the empirical correlations of o⁄shoring from the United States to Mexico discussed in Section 5.1. Aggregate productivities Z and Z follow the bivariate autoregressive process: t t(cid:3) logZ (cid:26) (cid:26) logZ (cid:24) t Z ZZ t 1 t 2 3 = 2 (cid:3) 32 (cid:0) 3+2 3; (22) logZ (cid:26) (cid:26) logZ (cid:24) 6 t(cid:3) 7 6 Z (cid:3) Z Z (cid:3) 76 t(cid:3) 1 7 6 t(cid:3) 7 6 7 6 76 (cid:0) 7 6 7 4 5 4 54 5 4 5 with persistence parameters (cid:26) and (cid:26) < 1, spillovers (cid:26) and (cid:26) 0, and normally- Z Z ZZ Z Z > (cid:3) (cid:3) (cid:3) distributed, zero-mean technology shocks (cid:24) and (cid:24) . To compute the correlations of key model t t(cid:3) variables, the bivariate productivity process is calibrated for the United States and Mexico, based on the Solow residual estimates for the two economies at quarterly frequency over the 32

interval 1987:Q1 to 2003:Q2. For each economy, the natural logarithm of the Solow residual is computed as ln(cid:21) = lny (1 (cid:11) )lnk (cid:11) lnn; using seasonally-adjusted aggregate data on (cid:21) (cid:21) (cid:0) (cid:0) (cid:0) output (y), the capital stock (k) and employment (n) obtained from Silos (2007) for the United States, and Aguiar and Gopinath (2007) for Mexico.35 Following Heathcote and Perri (2002), I use the seemingly unrelated regression procedure to estimate the persistence and spillover parameters from the Solow residuals, as well as the variance-covariance matrix of the shocks.36 In line with these estimates, the productivity process is calibrated to be more persistent in the United States than in Mexico ((cid:26) = 0:996 > (cid:26) = 0:951), and the spillovers from Mexico Z Z (cid:3) to the United States to be close to zero ((cid:26) = 0:003), in contrast with the positive U.S.-to- ZZ (cid:3) Mexico spillovers ((cid:26) = 0:049). I also set the variance of shocks at 0:009532 and covariance Z Z (cid:3) at 0:242172 10 4; which implies a correlation of 0:267. (cid:0) (cid:3) 5.3.1 Contemporaneous correlations Table 3 shows the empirical and model correlations of: (1) output in the North and the South Corr(Y ;Y ), (2) output in the North and the value added o⁄shore Corr(Y ;VA ), and (3) R R(cid:3) R R output in the North and the number of o⁄shoring plants Corr(Y ;N ), obtained with the R V bivariate productivity process calibrated for the United States and Mexico.37 In the model, the contemporaneous correlation between output in the North and the value added o⁄shore is larger than the correlation between total output in the North and the South, 35Silos (2007) uses (cid:11) =0:64 for the United States; Aguiar and Gopinath (2007) use (cid:11) =0:68 for Mexico. (cid:21) (cid:21) 0:996 (0:014) 0:003 (0:015) 36The estimates of persistence and spillover parameters are A = ; standard 0:049 (0:040) 0:951 (0:040) (cid:20) (cid:21) errors are reported in parantheses. Also, var((cid:24) )=0:00512, var((cid:24) )= 0:01402 and corr((cid:24) ;(cid:24) )=0:267: t t(cid:3) t t(cid:3) 37The cross-country correlations are computed using output and the value added o⁄shore de(cid:135)ated by the average price indexes in each economy, since the empirical price de(cid:135)ators are best represented by the average priceindexP ratherthanthewelfare-basedpriceindexP (seeGhironiandMelitz,2007). Forinstance,output t t 1 in the North is de(cid:135)ated as Y =P Y =P = N +N +N 1 (cid:18) Y , using the decomposition of the price R;t t t t D;t V;t H(cid:3);t (cid:0) t e 1 index into its (i) variety and (ii) average e price(cid:0)components: P t = (cid:1)N D;t +N V;t +N H(cid:3);t 1 (cid:0) (cid:18) P t . (cid:0) (cid:1) e 33

Corr(Y ;VA ) > Corr(Y ;Y ). This result is consistent with the empirical correlations pre- R R R R(cid:3) sentedincolumn1(anddiscussedinSection5.1), whichshowthatthemaquiladoravalueadded comoves more closely with the U.S. manufacturing output than does Mexico(cid:146)s total manufacturing output. Notably, the ranking of the two correlations is preserved when the correlation of shocks and the productivity spillovers are shut down in the bivariate productivity process (see Table D.7 of the Technical Appendix). More, the correlation between output in the North and the number of o⁄shoring plans (the extensive margin of o⁄shoring) is positive like in the data, Corr(Y ;N ) > 0.38 R V Intuitively, in the model, the value added o⁄shore (which is part of the South output) is procyclical and strongly correlated with output in the North, as a result of the extensive and intensive margin dynamics of o⁄shoring described in Section 5.2. However, an increase in aggregate productivity in the North weakens the economic activity elsewhere in the South, given that (cid:133)rm pro(cid:133)ts and (cid:133)rm entry are dampened in the relatively less productive economy, which partially o⁄sets the positive e⁄ect from o⁄shoring on output comovement.39 In addition, o⁄shoring reduces the pro(cid:133)ts of Southern exporters, as it transfers some of the upward wage pressure from the North to the South. As a result, the correlation between total output in the North and the South is lower than the correlation between output in the North and the value added o⁄shore. The ranking of correlations is also robust for the alternative models with international bond trading, elastic labor supply and physical capital, also shown in Table 3. With bond trading, the correlations of the value added o⁄shore and the number of o⁄shoring (cid:133)rms with output 38Note that the positive spillover from the North to the South productivity dampens the initial depreciation of the terms of labor, which in turn dampens the initial decline in the extensive margin. 39See the impulse responses in Figures D.5 and D.6, in which the magnitude of shocks and persistence of productivity are calibrated for the United States and Mexico, but the correlation of shocks and productivity spillovers are set to zero. 34

in the North are larger than in (cid:133)nancial autarky: Since a positive shock to productivity in the North has a more muted initial e⁄ect on the terms of labor, the the number of o⁄shoring (cid:133)rms and the value added o⁄shore exhibit positive and larger initial responses than in (cid:133)nancial autarky, as discussed earlier (see Figure 5). Also, with elastic labor supply, the cross-country correlation of output is smaller than in the baseline model, given the divergent responses of labor supply and labor income across countries. 5.3.2 Cross-correlations This section analyzes the model cross-correlations for each of the following four indicators with lags and leads of output in the North: (i) the total output in the South; (ii) the o⁄shoring value added inthe South; (iii) the numberof Northern (cid:133)rms that produce o⁄shore, as anindicatorfor the extensive margin of o⁄shoring; and (iv) the value added per o⁄shoring (cid:133)rm, as an indicator for the intensive margin. For each indicator, Figure 8 plots the cross-correlations implied by the model, and compares them to their empirical counterparts. To compute the model cross-correlations, I simulate series of the productivity shocks (cid:24) and t (cid:24) for a length of 68 periods (which coincides with the length of the maquiladora data series t(cid:3) discussed in Section 5.1), using the baseline calibration of the bivariate productivity process for the United States and Mexico. Then the series of simulated shocks are fed into the model, and thecross-correlationsoftheHP-(cid:133)lteredsimulatedseriesarecomputedformodelvariables. This procedure is repeated 5,000 times, and the average moments across simulations are reported in Figure 8.40 First, the model cross-correlations of total output in the South with output in the North 40The contemporaneous correlations based on model simulations should be very close to the theoretical correlations reported in Table 3, but not necesarely identical. 35

(panel 1), and the cross-correlations of the o⁄shoring value added with output in the North (panel 2) are tent-shaped, with the positive peak happening contemporaneously like in the data. More, as already discussed, the o⁄shoring value added comoves more closely with output in the North than does the total Southern output. Second, themodelissuccessfulincapturingthedelayedadjustmentintheextensivemargin, as it generates inter-temporal dynamics for the number of o⁄shoring (cid:133)rms that are consistent with those from the data. In panel 3, the cross-correlations of the number of o⁄shoring (cid:133)rms with lags and leads of the Northern output are S-shaped, rather than tent-shaped like in panels 1 and 2. In general, they peak for the Northern output lagged by about three quarters, like in the data. The result arises from the property that, following a productivity increase in the North, domestic(cid:133)rmentrycausesthetermsoflabortoappreciategradually, whichinturnleads to a gradual increase in the number of o⁄shoring (cid:133)rms. The delayed response of the extensive margin is stronger with elastic labor supply, due to the greater appreciation of the terms of labor discussed before, but somewhat weaker with physical capital, due to the substitution between investment and (cid:133)rm entry. Third, regarding the intensive margin (panel 4), the correlations between the value added per o⁄shoring (cid:133)rm and lagged Northern output are negative as in the data, both in the baseline model, as well as with elastic labor supply and physical capital. The result arises from the property that, in response to a positive shock to productivity in the North, the initial increase in value added per o⁄shoring (cid:133)rm is followed by a decline below its steady-state level, which explainsthenegativecorrelationsbetweentheintensivemarginandlaggedoutputintheNorth. 36

5.4 O⁄shoring and Output Comovement Thissectionexaminestherelationshipbetweeno⁄shoringandoutputcomovementgeneratedby the model with heterogeneous (cid:133)rms, and compares it to the empirical evidence from BKT, who document the positive relation between the share of o⁄shoring-related trade in bilateral trade and output comovement across countries. Using annual data on manufacturing value added andtradefortheUnitedStatesand34tradingpartners, BKTestimateequation(23)inacrosssectional framework, in which the dependent variable is the correlation between manufacturing output in the United States and output in each of its trading partners over 1983-2005, while the explanatory variables are the o⁄shoring intensity of bilateral trade (the (cid:133)rst variable), and the reliance on exports to the United States for each trading partner (the second variable):41 affilsales mftgEXP j j Correlation = (cid:11)+(cid:12) +(cid:12) +" : (23) US;j 1 2 j mftgEXP mftgVA (cid:18) j(cid:19) (cid:18) j (cid:19) The estimation results in BKT indicate a positive link between the correlation of output and the share of o⁄shoring in bilateral trade: (cid:12) = 0:746 is statistically signi(cid:133)cant at the 5 percent 1 level, whereas (cid:12) = 0:140 is not statistically signi(cid:133)cant. 2 To analyze the implications of the model of o⁄shoring with heterogeneous (cid:133)rms for output comovement, Iusealternativecalibrationsforthe(cid:133)xedcostsofo⁄shoringandexportingtovary thesteady-stateshareofo⁄shoringinSouthernexports, whileholdingtheshareof total exports in output (cid:133)xed for both countries.42 For each alternative calibration, output correlations are 41See BKT for details. The o⁄shoring intensity of bilateral trade is measured as the sales of U.S. foreign a¢ liates back to the United States expressed as a share of country j(cid:146)s total exports to the United States. The reliance on exports to the United States is measured as a share of country j(cid:146)s manufacturing output. 42To obtain this result, I vary f [0:045; 0:405], f [0:005; 0:071] and f [0:016; 0:038], and select V 2 H 2 H(cid:3) 2 the calibrations that closely match the steady-state share of exports in output from the baseline calibration (0:26 0:0015fortheNorth,0:44 0:0015fortheSouth),whileallowingfortheshareofo⁄shoring-relatedtrade (cid:6) (cid:6) in Southern exports to vary from about 0:45 to 0:70. 37

computed with the bivariate productivity process calibrated for the United States and Mexico. The results in Figure 9 show that larger shares of o⁄shoring in Southern exports (on the horizontal axis) are associated with larger correlations of output (on the vertical axis), in line with the empirical evidence. The results hold both for the baseline model with (cid:133)nancial autarky and with international bond trading (panel a), and also for the alternative models with endogenous labor supply and physical capital (panel c). To quantify the model implications, the regression of output correlations (on the vertical axis in Figure 9) on a constant term and the share of o⁄shoring in Southern exports (on the horizontal axis) generates the slope estimates (cid:12) = 0:44 for the baseline model with (cid:133)nancial autarky, and (cid:12) = 0:39 for international bond trading. In each case, the slopes from the model aremorethanhalfoftheempiricalestimatesfromBKT.Theslopeissmallerfortradeinbonds, since a greater prevalence of o⁄shoring increases the pro(cid:133)tability of Northern (cid:133)rms, which in turn enhances cross-border lending in response to an aggregate productivity increase in the North, and thus o⁄sets some of the extra comovement from o⁄shoring. The slope is somewhat less steep with elastic labor supply ((cid:12) = 0:26); is steeper with physical capital ((cid:12) = 0:71), when o⁄shoring a⁄ects a larger share of aggregate income in the north (i.e. not only labor income, but also the return from capital). The result also holds when, in the baseline model, the productivity shocks and persistence in the bivariate productivity process (22) are calibrated for the United States and Mexico as before, but with the shock correlations and productivity spillovers set to zero (panel b in Figure 9). As expected, the levels and the slopes of output correlations are somewhat lower than before ((cid:12) = 0:29 under (cid:133)nancial autarky and (cid:12) = 0:12 for international bond trading), but still positive. 38

Note that, while the model of endogenous o⁄shoring with heterogeneous (cid:133)rms is consistent with the empirical evidence in BKT, the comovement of output is generated by a mechanism thatisdi⁄erentfromBKT.Asalreadydiscussed,themodelinBKTabstractsfromtheextensive margindynamics, andoutputcomovementresultsfromarelativelylowelasticityofsubstitution between country-speci(cid:133)c goods in the vertically-integrated sector. In contrast, in the model of o⁄shoring with heterogeneous (cid:133)rms presented here, the the elasticity of substitution between home and o⁄shore varieties is set at a relatively high level, and hence the intensive margin plays a smaller role. Instead, output comovement arises from the procyclical pattern of (cid:133)rm entry in the North, the procyclical appreciation of the terms of labor, and in turn the adjustment of the o⁄shoring along both its extensive and intensive margins, as shown in Sections 5.2 and 5.3 above. 6 Conclusion This paper examines the e⁄ect of o⁄shoring motivated by lower production costs on the crosscountry transmission of business cycles, in a model with endogenous (cid:133)rm entry, heterogeneous (cid:133)rms, and endogenous o⁄shoring. The model implications are consistent with the empirical pattern of o⁄shoring undertaken by the U.S. multinational (cid:133)rms in Mexico. First, the model generates a procyclical pattern of o⁄shoring, which arises from the gradual adjustment in o⁄shoring along its extensive margin and the immediate adjustment along the intensive margin in response to shocks in the home economy, like in the data. Second, the o⁄shoring sector comoves more closely with home output than does the total output of the foreign economy. Third, o⁄shoring enhances the comovement of output between the economies involved. Impor- 39

tantly, these results are closely related to the procyclical (cid:133)rm entry in the home economy, the procyclical appreciation of the terms of labor, and the extensive and intensive margin dynamics of o⁄shoring. The model of o⁄shoring with heterogeneous (cid:133)rms built here is useful to study a number of issues related to the international mobility of production and labor. Thus, the framework is useful to analyze the e⁄ect of o⁄shoring on employment dynamics in the home and foreign economies. In addition, o⁄shoring has important implications for production costs, prices and the real exchange rates, and thus the model is useful to study the impact of o⁄shoring on the Balassa-Sameulson e⁄ect. Nonetheless, the interaction between o⁄shore production and labor migration across tradable and non-tradable sectors represents a topic with rich policy implications. References [1] Aguiar, Mark and Gita Gopinath. 2007. "Emerging Market Business Cycles: The Cycle Is the Trend." Journal of Political Economy, 155(1): 62-102. [2] Alessandria, George and Horag Choi. 2007. "Do Sunk Costs of Exporting Matter for Net Export Dynamics?" Quarterly Journal of Economics, 122(1): 289-336. [3] Anderson, James and Erik van Wincoop. 2004. "Trade Costs." Journal of Economic Literature, 42(3): 691-751. [4] Arkolakis, Costas and Ananth Ramanarayanan. 2009. "Vertical Specialization and International Business Cycle Synchronization." Scandinavian Journal of Economics, 111(4): 655-680. [5] Arseneau, David and Sylvain Leduc. 2011. "Threatening to O⁄shore in a Search Model of the Labor Market," Federal Reserve Board, mimeo. [6] Bergin, Paul R.; Robert C. Feenstra; and Gordon H. Hanson. 2009. "Outsourcing and Volatility: Evidence from Mexico(cid:146)s Maquiladora Industry." American Economic Review, 99 (4): 1664-1671. 40

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A Model Summary A.1 O⁄shoring with Financial Autarky Table A.1 Euler equation, bonds C (cid:13) = (cid:12)(1+r )E C (cid:13) t(cid:0) t+1 t t(cid:0)+1 C t(cid:3)(cid:0) (cid:13) = (cid:12) 1+r t(cid:3)+1 E(cid:2) t C t(cid:3)+(cid:0)(cid:3) 1 (cid:13) (cid:13) Euler equation, stocks v = (cid:12)(1 (cid:0)(cid:14))E (cid:1)Ct+1 (cid:2)(cid:0) (d(cid:3) +v ) t (cid:0) t Ct t+1 t+1 (cid:20) (cid:21) (cid:16) (cid:17) (cid:13) v = (cid:12) (1 (cid:14) )E C t(cid:3)+1 (cid:0)e(d +v ) et(cid:3) (cid:3) (cid:0) (cid:3) t C t(cid:3) (cid:3)t+1 e t(cid:3)+1 (cid:20) (cid:21) (cid:16) (cid:17) Free entry v et = fE Z w t t e e f w v = E(cid:3) t(cid:3) t(cid:3) Z e t(cid:3) Law of motion, total number of (cid:133)rms N = (1 (cid:14))(N +N ) t+1 t E;t e (cid:0) N = (1 (cid:14))(N +N ) D(cid:3);t+1 (cid:0) D(cid:3);t E(cid:3);t Aggregate accounting C +N v = w L+N d t E;t t t t t C +N v = w L +N d t(cid:3) E(cid:3);t t(cid:3) t(cid:3) (cid:3) eD(cid:3);t (cid:3)t e Consumption price index 1 = N D;t ((cid:26) D;t )1 (cid:0) (cid:18) +N V;t ((cid:26) Ve;t )1 (cid:0) (cid:18) +N H(cid:3);t (cid:26) (cid:3)H;t 1 (cid:0) (cid:18) e 1 = N D(cid:3);t (cid:26) (cid:3)D;t 1 (cid:0) (cid:18) +N H;t ((cid:26) H;t )1 (cid:0) (cid:18) (cid:0) (cid:1) e e e Total pro(cid:133)ts N d = N(cid:0) d (cid:1) +N d +N d t t D;t D;t V;t V;t H;t H;t e e N d = N d +N d D(cid:3) e;t (cid:3)t D(cid:3) e;t (cid:3)D;t H(cid:3) e;t (cid:3)H;t e Total number of (cid:133)rms (North) N = N +N t e D;t eV;t e (cid:18) 1 O⁄shoring pro(cid:133)ts link (North) d = k zV;t (cid:0) d + (cid:18) 1 f w t(cid:3) Qt V;t k (cid:0) ((cid:18) (cid:0) 1) zD;t D;t k (cid:0) ((cid:0)(cid:18) (cid:0) 1) V Z t(cid:3) Export pro(cid:133)ts link d = (cid:18) 1 f (cid:16) wt (cid:17) eH;t k ((cid:0)(cid:18) 1) HeZt e (cid:0) (cid:0) d = (cid:18) 1 f w t(cid:3) e (cid:3)H;t k (cid:0) ((cid:0)(cid:18) (cid:0) 1) H(cid:3) Z t(cid:3) 1 Avrg. prod. of domestic producers (North) ze = (cid:23)z z z V k (cid:0);t ((cid:18) (cid:0) 1) (cid:0) z m k (cid:0)in ((cid:18) (cid:0) 1) (cid:18) (cid:0) 1 D;t min V;t zk zk (cid:20) V;t(cid:0) min (cid:21) 1=k Avrg. prod. of o⁄shore producers (North) z = (cid:23)z Nt eV;t min NV;t (cid:16) (cid:17)1=k Avrg. productivity of exporters z = (cid:23)z Nt e H;t min NH;t (cid:16)N (cid:17)1=k z = (cid:23)z D(cid:3);t eH(cid:3);t m(cid:3)in N H(cid:3);t Balanced trade N ((cid:26) )1 (cid:16)(cid:18)C Q (cid:17) +N d = H;t H;t (cid:0) t(cid:3) t V;t V;t e = N V;t ((cid:26) V;t )1 (cid:0) (cid:18)C t +N H(cid:3);t e (cid:26) (cid:3)H;t 1 (cid:0) (cid:18) C t e (cid:0) (cid:1) e e 43

A.2 O⁄shoring with International Bonds In the model version with (cid:133)nancial integration, international asset markets are incomplete, as the representative household in each economy holds risk-free, country-speci(cid:133)c bonds from both the North and the South. Each type of bonds provides a real return denominated in units of the issuing country(cid:146)s consumption basket. Quadratic costs of adjustment for bond holdings ensure stationarity for the net foreign assets in the presence of temporary shocks. The representative household in the North maximizes inter-temporal utility subject to: (d +v )N x +w L+(1+r )B +(1+r )Q B +T (24) t t t t t t h;t t(cid:3) t f;t t (cid:25) (cid:25) > e C t e+v t (N t +N E;t )x t+1 +B h;t+1 + (B h;t+1 )2 +Q t B f;t+1 + Q t (B f;t+1 )2; 2 2 e where r and r are the rates of return of the North and South-speci(cid:133)c bonds; (1+r )B and t t(cid:3) t h;t (1 + r )Q B denote the principal and interest income from each type of bonds; (cid:25) (B )2 t(cid:3) t f;t 2 h;t+1 and (cid:25)Q (B )2 are the adjustment costs for each type of bond holdings; T is the fee rebate. 2 t f;t+1 t Setting (cid:25) = 0:005, the two Euler equations for bonds are added to the baseline model: C (cid:13) t+1 (cid:0) 1+(cid:25)B = (cid:12)(1+r )E ; (25) h;t+1 t+1 t C " (cid:18) t (cid:19) # Q C (cid:13) t+1 t+1 (cid:0) 1+(cid:25)B = (cid:12)(1+r )E : (26) f;t+1 t(cid:3)+1 t Q C " t (cid:18) t (cid:19) # 44

For the Southern representative household, the Euler equations for bonds are: Q C (cid:13) 1+(cid:25)B = (cid:12) (1+r )E t t(cid:3)+1 (cid:0) ; (27) h(cid:3);t+1 (cid:3) t+1 t Q C " t+1 (cid:18) t(cid:3) (cid:19) # C (cid:13) 1+(cid:25)B = (cid:12) (1+r )E t(cid:3)+1 (cid:0) : (28) f(cid:3);t+1 (cid:3) t(cid:3)+1 t C " (cid:18) t(cid:3) (cid:19) # The market clearing conditions for bonds are: B +B = 0 and B +B = 0: (29) h;t+1 h(cid:3);t+1 f;t+1 f(cid:3);t+1 Thus, (cid:133)nancial integration through trade in bonds adds four new variables (B ;B ;B ; h;t f;t h(cid:3);t B ) and six new equations (25, 26, 27, 28, and the two equations under 29) while removing f(cid:3);t the original two Euler equations from the baseline model with (cid:133)nancial autarky. Also, the new expressions for aggregate accounting in the North and the South are: C +N v +B +Q B = w L+N d +(1+r )B +(1+r )Q B ; (30) t E;t t h;t+1 t f;t+1 t t t t h;t t(cid:3) t f;t C +N v e+Q 1B +B = w L +Ne d +(1+r )Q 1B +(1+r )B : (31) t(cid:3) E(cid:3);t t(cid:3) (cid:0)t h(cid:3);t+1 f(cid:3);t+1 t(cid:3) (cid:3) D(cid:3);t (cid:3)t t (cid:0)t h(cid:3);t t(cid:3) f(cid:3);t e e Finally, the balanced current account condition is replaced by the balance of international payments equation, which shows that the current account balance (trade balance plus repatriated pro(cid:133)ts plus investment income) equals the negative of the (cid:133)nancial account balance (the change in bond holdings): TB + N d +r B +r Q B = (B B )+Q (B B ) (32) t V;t V;t t h;t t(cid:3) t f;t h;t+1 (cid:0) h;t t f;t+1 (cid:0) f;t Repatriated pro(cid:133)ts Income from bonds Change in bond holdings e | {z } | {z } | {z } 45

A.3 O⁄shoring with Physical Capital Table A.3 Euler equation, bonds C (cid:13) = (cid:12)(1+r )E C (cid:13) t(cid:0) t+1 t t(cid:0)+1 C t(cid:3)(cid:0) (cid:13) = (cid:12) 1+r t(cid:3)+1 E(cid:2) t C t(cid:3)+(cid:0)(cid:3) 1 (cid:13) (cid:13) Euler equation, stocks v = (cid:12)(1 (cid:0)(cid:14))E (cid:1)Ct+1 (cid:2)(cid:0) (d(cid:3) +v ) t (cid:0) t Ct t+1 t+1 (cid:20) (cid:21) (cid:16) (cid:17) (cid:13) v = (cid:12) (1 (cid:14) )E C t(cid:3)+1 (cid:0)e(d +v ) et(cid:3) (cid:3) (cid:0) (cid:3) t C t(cid:3) (cid:3)t+1 e t(cid:3)+1 (cid:20) (cid:21) (cid:16) (cid:17) 2 Law of motion, capital K e t+1 = (1 (cid:0) (cid:14)k)K t +I t (cid:0) (cid:25) 2 kI t (cid:0) e1 It It 1 e (cid:0) 1 (cid:0) 2 K = (1 (cid:14)k)K +I (cid:25)kI (cid:16) I t(cid:3) 1 (cid:17) t(cid:3)+1 (cid:0) t(cid:3) t(cid:3) (cid:0) 2 t(cid:3) (cid:0) 1 I t(cid:3) 1 (cid:0) (cid:0) F.O.C. capital (cid:21) = (cid:12)E C (cid:13)rk +(cid:12)(1 (cid:14)k)E (cid:16) [(cid:21) ] (cid:17) t t t(cid:0)+1 t+1 (cid:0) t t+1 (cid:21) (cid:3)t = (cid:12)E t (cid:2)C t(cid:3)+(cid:0)1 (cid:13)r t(cid:3)+ k 1 (cid:3) +(cid:12)(1 (cid:0) (cid:14)k)E t (cid:21) (cid:3)t+1 2 F.O.C. investment C t(cid:0) (cid:13) = (cid:21) t (cid:2)1 (cid:0) (cid:25)k I (cid:3) t It 1 (cid:0) 1 +(cid:12)E t (cid:2) (cid:21) t+ (cid:3) 1 (cid:25) 2 k It It 1 (cid:0) 1 (cid:0) (cid:20) (cid:18) (cid:0) (cid:19)(cid:21) h (cid:16) (cid:17)i (cid:16) (cid:17) 2 C t(cid:3)(cid:0) (cid:13) = (cid:21) (cid:3)t 1 (cid:0) (cid:25)k I t I (cid:3) t(cid:3) 1 (cid:0) 1 +(cid:12)E t (cid:21) (cid:3)t+1 (cid:25) 2 k I t I (cid:3) t(cid:3) 1 (cid:0) 1 (cid:0) (cid:20) (cid:18) (cid:0) (cid:19)(cid:21) h (cid:16) (cid:17)i (cid:16) (cid:17) 1 (cid:11) Capital market clearing K = N k +N k +(N fE +N fH) (cid:11)wt (cid:0) t D;t D;t H;t H;t E;tZt H;tZt (1 (cid:0) (cid:11))r t k 1 (cid:11) K = N k +N k +N k +(N f E(cid:3) h +N fV i +N f H(cid:3) ) (cid:11)w t(cid:3) (cid:0) t(cid:3) D(cid:3);teD(cid:3);t V;te (cid:11) V(cid:3);t H(cid:3);t H(cid:3);t E(cid:3);t 1 Z t(cid:3) (cid:11) V;t (cid:11) Z t(cid:3) H(cid:3);tZ t(cid:3) (1 (cid:0) (cid:11))r t k (cid:3) Free entry v t = f Z E t 1 w (cid:0) e t (cid:11) 1 (cid:0) (cid:11) r (cid:11) t k e and v t(cid:3) = e Z f E(cid:3) t(cid:3) 1 w (cid:0) t(cid:3) (cid:11) (cid:0) r (cid:11) t k (cid:3) h i (cid:16) (cid:17) (cid:16) (cid:17) (cid:16) (cid:17) Law of motion, (cid:133)rms N = ((cid:0)1 (cid:1)(cid:14))(N +N ) and N = (1 (cid:14))(N +N ) e t+1 (cid:0) t E;t e D(cid:3);t+1 (cid:0) D(cid:3);t E(cid:3);t Aggregate accounting N v +C +I = N d +w L+rkK E;t t t t t t t t t N v +C +I = N d +w L +rk K E(cid:3);t t(cid:3) t(cid:3) t(cid:3) eD(cid:3);t (cid:3)t t(cid:3) (cid:3) t(cid:3) t(cid:3) e Cons. price index 1 = N D;t ((cid:26) D;t )1 (cid:0) (cid:18) +N V;te ((cid:26) V;t )1 (cid:0) (cid:18) +N H(cid:3);t (cid:26) (cid:3)H;t 1 (cid:0) (cid:18) e 1 = N D(cid:3);t (cid:26) (cid:3)D;t 1 (cid:0) (cid:18) +N H;t ((cid:26) H;t )1 (cid:0) (cid:18) (cid:0) (cid:1) e e e Total pro(cid:133)ts N d = N(cid:0) d (cid:1) +N d +N d t t D;t D;t V;t V;t H;t H;t e e N d = N d +N d D(cid:3) e;t (cid:3)t D(cid:3) e;t (cid:3)D;t H(cid:3) e;t (cid:3)H;t e No. of (cid:133)rms (North) N = N +N t e D;t eV;t e (cid:18) 1 1 (cid:11) (cid:11) O⁄shoring pro(cid:133)ts link d = k zV;t (cid:0) d + (cid:18) 1 fVQt w t(cid:3) (cid:0) r t(cid:3) k V;t k (cid:0) ((cid:18) (cid:0) 1) zD;t D;t k (cid:11)(cid:0) ((cid:0)(cid:18) (cid:0) 1) Z t(cid:3) 1 (cid:0) (cid:11) (cid:11) 1 (cid:11) (cid:11) Export pro(cid:133)ts link d eH;t = k (cid:0) (cid:18) ((cid:0)(cid:18) (cid:0) 1 1) (cid:16)f Z H t e 1 w(cid:17) (cid:0) t (cid:11) 1 (cid:0) e (cid:11) r (cid:11) t k and d (cid:3)H;t (cid:16) = k (cid:0) (cid:18) ( (cid:17) (cid:0)(cid:18) (cid:0) 1 1) f Z (cid:16) H t(cid:3) 1 (cid:17)w (cid:0) t(cid:3) (cid:11) (cid:0) r (cid:11) t(cid:3) k Avrg. productivity ze = (cid:23)z z (cid:0)z V k (cid:0);t ((cid:18) (cid:0) (cid:1)1) (cid:0) z m k(cid:16) (cid:0)in ((cid:18) (cid:0) (cid:17)1) (cid:18) (cid:0) 1 1 (deomestic (cid:133)rms) (cid:16) (cid:17) (cid:16) (cid:17) D;t min V;t zk zk (cid:20) V;t(cid:0) min (cid:21) 1=k Avrg. productivity z = (cid:23)z Nt (o⁄shoring (cid:133)rms) eV;t min NV;t Avrg. productivity z = (cid:23)z (cid:16) Nt (cid:17)1=k and z = (cid:23)z N D(cid:3);t 1=k (exporters) e H;t min NH;t H(cid:3);t m(cid:3)in N H(cid:3);t Balanced trade N H;t ((cid:26) H;t )1 (cid:0) (cid:16)(cid:18)C t(cid:3) Q (cid:17) t4 + 6 N V;t d V;t = N V;t ((cid:26) V;t (cid:16) )1 (cid:0) (cid:18)C (cid:17) t +N H(cid:3);t (cid:26) (cid:3)H;t 1 (cid:0) (cid:18) C t e e (cid:0) (cid:1) e e e e

Tables and Figures Table 1. Average prices and pro(cid:133)ts Firm Origin Production Market Average prices Average pro(cid:133)ts 1. North North North (cid:26) D;t = (cid:18) (cid:18) 1Zt w zD t ;t d D;t = 1 (cid:18) (cid:26) D;t 1 (cid:0) (cid:18) C t (cid:0) 2. South South South e (cid:26) (cid:3)D;t = (cid:18) (cid:0) (cid:18) 1Z t(cid:3) e w z D t(cid:3) ;t(cid:3) d e (cid:3)D;t = 1 (cid:18) (cid:0) e (cid:26) (cid:3)D;t (cid:1) 1 (cid:0) (cid:18) C t(cid:3) 3. North South North e (cid:26) V;t = (cid:18) (cid:0) (cid:18) 1 (cid:28) Z w t e (cid:3) t(cid:3) z Q V; t t d eV;t = 1 (cid:18) (cid:0)(cid:26) e V;t (cid:1) 1 (cid:0) (cid:18) C t (cid:0) f V w Z t(cid:3) Q t(cid:3) t 4. North North South e (cid:26) H;t = (cid:18) (cid:0) (cid:18) 1 (cid:28) (cid:3) w Ze t t Q zH (cid:0)t ; 1 t d eH;t = 1 (cid:18) (cid:0) e (cid:26) H;t (cid:1) 1 (cid:0) (cid:18) C t(cid:3) Q t (cid:0) f H w Zt t 5. South South North e (cid:26) (cid:3)H;t = (cid:18) (cid:0) (cid:18) 1 (cid:28) Z w t(cid:3) t(cid:3) z Q H e (cid:3) t ;t d e (cid:3)H;t = 1 (cid:18) (cid:0) e (cid:26) (cid:3)H;t (cid:1) 1 (cid:0) (cid:18) C t Q (cid:0)t 1 (cid:0) f H(cid:3) Z w t t(cid:3) (cid:3) (cid:0) (cid:1) e e e e Table 2. Calibration parameters and steady-state targets Calibration parameters: Steady-state targets: Data Model Pareto distribution coe⁄. k = 4:2 Maquila. VA in Mex. manufacturing 20% 20% Iceberg trade cost (cid:28) = 1:2 Maquila. share in Mexican exports 55% 61% Fixed o⁄shoring cost f = 0:095 Maquila. share in manuf. employment 25% 20% V Fixed exporting cost, North f = 0:040 H Fixed exporting cost, South f = 0:025 H(cid:3) Table 3. Cross-country contemporaneous correlations Data Baseline Alternative models Correlations: Bonds Elastic L Capital US IP, Mexico IP 0:58 0:33 0:32 0:13 0:34 US IP, maquiladora value added 0:69 0:75 0:98 0:60 0:81 US IP, maquiladora plants 0:33 0:23 0:94 0:15 0:32 47

Tables and Figures Figure 1: The firm-specific productivity cutoff z . V,t d (z) V d(z) d (z) D 0 z min θ-1 z V,t θ-1 z θ-1 Figure 2: Average labor productivity for Northern firms ~ ~ that produce domestically (z ) and offshore (z ) for the North market. D,t V,t 48

Tables and Figures Figure 3: Business cycle dynamics in Mexico’s maquiladora sector. Data sources: Federal Reserve Board (for the U.S. manufacturing IP), Haver Analytics (for Mexico’s manufacturing IP) and INEGI (for the maquiladora data). Note: The data are seasonally adjusted, converted in natural logs, and expressed in deviations from a Hodrick-Prescott trend. See the Technical Appendix for details. 49

Tables and Figures Figure 4: Impulse responses to a one-percent shock to aggregate productivity in the North, with persistence ρ = 0.9, baseline model with financial autarky. Note: the impulse responses correspond to: (1) the baseline model of offshoring (thick solid line); (2) alternative model with fixed productivity cutoff (thin solid line); (3) alternative model with no offshoring (dashed line). 50

Tables and Figures Figure 5: Impulse responses to a one-percent shock to aggregate productivity in the North, with persistence ρ = 0.9, financial autarky vs. international bond trading. 51

Tables and Figures Figure 6: Impulse responses to a one-percent shock to aggregate productivity in the North, with persistence ρ = 0.9, fixed vs. elastic labor supply. 52

Tables and Figures Figure 7: Impulse responses to a one-percent shock to aggregate productivity in the North, with persistence ρ = 0.9, alternative model with physical capital. 53

Tables and Figures Figure 8: Cross-correlations, data vs. model. Note: the black line (circle marks) denotes the empirical cross-correlations, and the shaded area represents the 90 percent confidence bands. The red line (star marks) denotes the crosscorrelations from the baseline model with financial autarky; the green line (triangle marks) denotes the model cross-correlations with elastic labor supply; the blue line (cross marks) denotes the model cross-correlations with physical capital. For data sources, see the notes to Figure 3. 54

Tables and Figures Figure 9: Offshoring and output comovement. (a) Baseline TFP calibration (b) Baseline TFP persistence and shocks, but zero spillovers and uncorrelated shocks 55

Tables and Figures (c) Baseline TFP calibration, alternative models with elastic labor supply and capital 56