Headquarters Gravity

Transcription

1 Headquarters Gravity Zi Wang Shanghai University of Finance and Economics October 24, 2017 Abstract This paper examines the impacts of multinational enterprises (MNEs) on international trade. I document a novel fact that Chinese affiliates of foreign MNEs concentrate their exports in markets close to their headquarters. I incorporate this headquarters gravity into a multi-country general equilibrium model with trade and multinational production (MP). I structurally estimate key model parameters about headquarters gravity using Chinese firm data and calibrate the general equilibrium model to aggregate trade and MP data. I then use the model to quantify the empirical relevance of headquarters gravity and show that (1) headquarters gravity accounts for 30% of MNEs contribution to international trade, (2) headquarters gravity is essential to understanding the relocation of MNEs activities following trade liberalization, and (3) ignoring headquarters gravity leads to sizable underestimation of the welfare gains for developed countries from China s openness. Keywords: Multinational Firms; Export; Production Relocation; Welfare JEL classification: F12, F23, O19. I am grateful to Steve Yeaple for his continuous guidance and support. I thank Jonathan Eaton, Felix Tintelnot, James Tybout, and Stefania Garetto for extensive discussions and in-depth comments. I also thank Kala Krishna, Pol Antras, Paul Grieco, Eduardo Morales, Kamran Bilir, Lorenzo Caliendo, Fernando Parro, Costas Arkolakis, Michael Peters, Ferdinando Monte, Davin Chor, Sam Asher, Melanie Morten, Jing Zhang, Nick Ryan, Jianpeng Deng, and seminar participants at the Penn State University (Sept 2015), for helpful comments. All errors are my own. School of International Business Administration, Shanghai University of Finance and Economics, 100 Wudong Road, Shanghai, China, address: wang.zi@mail.shufe.edu.cn. Telephone: The online appendix and replication files can be downloaded from my website

2 1 Introduction Promoting exports is challenging for most if not all countries. In particular, most of the local firms neither are productive enough nor have sufficient marketing networks to access the export market. In contrast, the affiliates of foreign multinational enterprises (MNEs) have not only better production but also better trading technologies. Indeed, MNEs are the largest players in international trade. Their export share is even larger than their production share in host countries, as Figure 1 illustrates. Therefore, understanding the exporting behaviors of these large MNEs is key to understanding the consequences of globalization and the gains from openness. This paper starts by documenting a novel fact about MNEs exporting behaviors using a newly-combined Chinese firm-level database: Chinese affiliates of foreign MNEs are more likely to export and to export more to markets that are closer to their headquarters countries. I name this market bias of MNE affiliates as headquarters gravity. In this paper, I incorporate headquarters gravity into a multicountry general equilibrium model with trade and multinational production (MP), using Chinese firm data to estimate key model parameters about headquarters gravity and aggregate trade and MP data to calibrate the general equilibrium model. I then use the model to quantify the relocation of MNEs activities following trade liberalization, showing that headquarters gravity is essential to replicate actual MP relocation in the data. Finally, I explore the welfare implications of headquarters gravity by quantifying the impacts of China s openness over [Figure 1 about here.] Traditionally, gravity models of international trade have emphasized trade frictions between exporting and importing countries (see Anderson and Wincoop (2003), Eaton and Kortum (2002), Melitz (2003), and Eaton, Kortum, and Kramarz (2011)). Headquarters gravity implies that, in the presence of MP, the locations of headquarters are also important in shaping bilateral trade flows. For example, a large fraction of Chinese exports to Canada is contributed by Chinese affiliates of the U.S. MNEs that have an advantage in serving the 2

3 Canadian market. Therefore, an effective way to promote Chinese exports to Canada is to attract more MNEs from the U.S. The standard gravity trade models cannot capture this third-country effect. My model extends the firm export model developed by Eaton, Kortum, and Kramarz (2011) by incorporating MP and export platforms. In the model, a firm can endogenously decide its global production sites and the export destinations for each of its affiliates. The novel ingredient of the model is that an affiliate s export cost to a market depends on both the proximity of this market is to its production location (gravity) and to its headquarters (headquarters gravity). 1 An appealing feature of the model is that it is designed to capture MNEs export behaviors in micro data but still delivers tractable gravity equations for aggregate trade and MP flows. The structural equations for the exports of MNE affiliates are directly amenable for estimating headquarters gravity using Chinese firm data, whereas gravity equations for aggregate trade and MP flows are convenient for calibrating the model to aggregate data. The newly-combined Chinese firm data is ideal for analyzing the exporting behaviors of MNE affiliates. I observe destination-specific exports for almost all manufacturing firms that operated in China in the year 2001, combined with their nationalities. This rich data permits estimation in which parameters about headquarters gravity are recovered transparently through structural equations of MNEs exports in the model. The main empirical challenge is that both productivities and headquarters gravity affect MNEs exports. The identification comes from the fact that productivity affects affiliate sales in all markets, but headquarters gravity is headquarter-destination-specific. Therefore, I control firms productivities by their sales in China and recover headquarters gravity from the correlation between firm exports and the proximity of the destination to headquarters countries. The estimation results show that foreign MNE affiliates do face much lower export costs to countries close to their head- 1 Following the tradition in trade literature, I rationalize headquarters gravity by the structure of trade costs. There is an extensive literature that rationalizes gravity equations by bilateral trade frictions. See Anderson and Wincoop (2004) for literature review. It is reasonable to think that gravity equations are driven by demand factors. However, demand and supply factors cannot be separately identified in the standard trade model with constant markups. 3

4 quarters countries: doubling the physical distance between the headquarter and destination countries will, ceteris paribus, increase the iceberg trade costs by 4.4%. Armed with the structural estimates of headquarters gravity, I calibrate the full set of trade and MP frictions by fitting equilibrium outcomes to aggregate data on bilateral trade and MP flows. To highlight the importance of headquarters gravity, I also calibrate a gravity-only model in which all MNE affiliates are imposed to have the same export costs with local firms. The out-of-sample predictions suggest that the gravity-only model fails to capture key features of MNEs exports in the data. With the calibrated model in hand, I quantify the implications of headquarters gravity by counterfactual experiments. First, the world manufacturing trade volume in 2001 would decrease by 12.7% if the affiliates of foreign MNEs incurred the same export costs with local firms. Furthermore, the world manufacturing trade volume in 2001 would decrease by 42.7% if MP was prohibited. Therefore, MNEs advantage in market access accounted for 30% of their contribution to international trade, whereas 70% of MNEs contribution to international trade was attributed to their productivity advantage. Headquarters gravity is particularly important to the exports from developing to developed countries. Without headquarters gravity, the manufacturing exports from developing to developed countries would decrease by 17.6%, whereas the manufacturing exports from developed to developing countries would decrease by only 13.8%. In the absence of marketing networks brought by foreign MNEs, it will be even more challenging for developing countries to make sales in developed markets. Second, ignoring headquarters gravity will lead to a misunderstanding of the spatial reallocation of MNEs activities following trade liberalization. To see this, I reduce the iceberg export cost from China to the U.S. by 10% in both the baseline and gravity-only model. In the presence of headquarters gravity, this trade liberalization will attract more MNEs originating from countries close to the U.S. to set affiliates in China. Comparing the counterfactual predictions to actual changes, I show that the baseline model can replicate key moments of MP relocation in the data, whereas the gravity-only model fails to do 4

5 so. Therefore, headquarters gravity is essential to understanding the relocation of MNEs activities in the data. Third, I quantify the welfare implications of China s trade and MP liberalization between 2001 and The results show that ignoring headquarters gravity leads to sizable underestimation of the welfare gains from China s openness for developed countries. On the one hand, the gravity-only model underestimates the sales expansion of Chinese affiliates of MNEs from developed countries following China s openness. On the other hand, in the presence of headquarters gravity, MNEs from developed countries can serve their home countries and countries close to their home countries by their Chinese affiliates with low trade costs. This benefits consumers in developed countries by providing them with the low-priced made-in-china, a large fraction of which is made by Chinese affiliates of foreign MNEs. This result suggests that any policy aiming to restrict trade and FDI with China, a manufacturing center for firms from all over the world, should be cautious about its negative impacts on firms and consumers in developed countries. Ample policy practices in developing countries support the key mechanism of the model. It is well-documented that poor countries face higher costs to export relative to rich countries (see Waugh (2010)). This was true for China before it joined WTO. In order to implement the reform and openness strategy, Chinese governments heavily subsidized foreign MNEs, including enterprises from Hong Kong, Macau, and Taiwan, by tax reduction and cheap land and labor supply. The international marketing networks of these foreign MNEs were crucial for China s export expansion in 1990s and early 2000s. This paper contributes to the literature about the MNEs advantage in serving their home countries. Cosar et al. (2015) emphasize the preference for home brands as a driver of MNEs home market advantage. This paper complements theirs by suggesting that consumers prefer not only home brands but also brands originating from countries close to their home countries. Head and Mayer (2015) use detailed production and trade data in the global car market and find that, regardless of production site, it is more difficult to make sales in markets that are geographically separated from the brand s headquarters. I generalize their 5

6 argument to aggregate trade flows and discuss the general equilibrium effects of this new margin of multinational sales. I also build on and contribute to quantitative studies that focus on the gains from trade and MP. Irarrazabal, Moxnes, and Opromolla (2013) develop a structural model that extends Helpman, Melitz, and Yeaple (2004) and estimate the model using Norwegian firm-level data and quantify the welfare gains from MP. However, their paper ignores export platform sales and thus omits headquarters gravity. Ramondo and Rodriguez-Clare (2013) develop a multicountry model with trade and MP, finding that the gains from trade can be twice as large if MP is taken into consideration. Arkolakis et al. (2017) further introduce firm entry and cross-country profit flows generated by MNEs to quantify the asymmetric impacts of MP liberalization on source and host countries. Tintelnot (2017) quantifies the impacts of export platforms in a model that incorporates cannibalization within MNEs and fixed costs of building affiliates. These three models assume that foreign affiliates face the same export costs with local firms. Therefore, they cannot capture the headquarters gravity found in the micro data, which is shown to be quantitatively important in welfare analysis. This paper also enhances our understanding of cross-border knowledge transfer led by MNEs. Previous papers focus on MNEs transferring production technologies to their affiliates (see MacGrattan and Prescott (2009) and Burstein and Monge-Naranjo (2009)). This paper provides evidence suggesting that the parents transfer not only production but also trading technologies to their affiliates. By exploring the impacts of headquarters locations on affiliate exports, I shed light on informational and marketing frictions in international trade documented in Arkolakis (2010) and Allen (2014). Unlike domestic firms whose production sites and headquarters are located in the same country, MNEs produce outside home countries, enabling us to disentangle the standard gravity that depends on the proximity between production and destination countries from the headquarters gravity. Structural estimates suggest these informational and marketing costs of international trade are substantial and quantitatively important. The rest of the paper is organized as follows. In Section 2, I describe the data I use 6

7 and document novel facts about exports by Chinese affiliates of foreign MNEs. In Section 3, I introduce my model setup and discuss key model assumptions. In Section 4, I define and characterize the general equilibrium, delivering structural equations for estimation. In Section 5, I identify and estimate key model parameters about headquarters gravity using Chinese firm data. Section 6 calibrates the general equilibrium model. Section 7 presents general equilibrium counterfactuals. Section 8 concludes. 2 Data and Empirical Evidence 2.1 Data To understand the export behaviors of multinational affiliates operating in China, I merge three sets of micro data. First, the Annual Survey of Chinese Manufacturing (ASCM), collected by the Chinese National Bureau of Statistics, provides firm-level operation characteristics such as sales, capital, employment, and expenditure on intermediates for all state-owned manufacturing firms and other manufacturing firms whose annual sales exceed 5 million RMB (about 0.6 million dollars). The manufacturers excluded from ASCM are small and unlikely to be engaged in international trade. Therefore, ASCM covers the majority of Chinese manufacturing exporters. Second, I supplement ASCM with firm-level exports by destination from Chinese Customs Records (CCR). CCR documents transaction-level exports with destination country, the 8- digit HS code, export mode (ordinary or processing trade), export value and quantity. CCR is merged with ASCM by firms contact information such as name, address, zip code, and phone number. Finally, to understand the impact of headquarter locations on affiliates sales, I need to observe the nationalities of foreign affiliates operating in China. This information is rare for most of the commonly-used firm-level trade data sets. I collect this information from the Foreign-Invested Enterprise Survey in China (FIESC). It covers all foreign-invested firms in China in 2001 (not only for manufacturing firms), with names and nationalities of their 7

8 foreign investors. Moreover, FIESC can be merged with ASCM by numeric firm identifiers. The combined Chinese firm data is ideal for studying export-platform FDI. First, China is a major exporter and FDI receiver in the world, with a large number of export destinations and countries of origin. Second, the data covers almost all Chinese manufacturing firms with their exports by destination and their nationalities. I am not aware of comparable data in other countries. Boehm et al. (2015) links restricted U.S. Census Bureau microdata to firms international ownership structure. However, they focus on the imported inputs of the U.S. affiliates of foreign MNEs instead of exploring their export behaviors. Now I turn to describing two empirical regularities in the combined Chinese firm data. The first confirms the MNEs export advantage in the literature, whereas the second motivates a novel ingredient that I argue should be included in the quantitative framework. 2.2 Fact 1: Export-advantage of Chinese affiliates of foreign MNEs MNE affiliates are large producers and exporters in host countries. As illustrated in Figure 1, in 2001 foreign MNE affiliates accounted for 23% of Chinese manufacturing plants but 35% of manufacturing sales and 77% of manufacturing exports. [Table 1 about here.] The MNEs export advantage in aggregate data may come from their productivity advantages. To control for productivity effects, I regress firms export decisions (both intensive and extensive margins) on a dummy for foreign MNEs and several observed firm characteristics. Table 1 shows that after controlling for observed firm characteristics such as value-added, employment, and capital stock, the Chinese affiliates of foreign MNEs are still more much likely to export and to export more than Chinese domestic firms. 2.3 Fact 2: Headquarters Gravity The combined Chinese firm data allows me to link a firm s export destinations to the location of its headquarters. To fix the idea of this linkage, I compare the sales distribution of 8

9 two plants operating in China with similar sizes and products but different countries of origin: Philips from the Netherlands and Nitto Denko from Japan. Table 2 shows that the exports of Philips (China) are concentrated in European countries such as Germany, the Netherlands, France, and Italy. In contrast, the exports of Nitto Denko (China) are concentrated in Asian-Pacific markets. This example suggests the importance of headquarter locations to affiliates export destinations. [Table 2 about here.] The home market bias found in individual firms sales also exists in aggregate MP sales. Table 3 illustrates the sales distribution of foreign MNEs in China across destinations. By construction, if the affiliates exports are independent from their headquarter locations, then the shares should be identical in a row. However, in Table 3 the diagonal dominates, suggesting a strong bias of the sales of MNE affiliates towards their headquarters countries, which is consistent with the home market advantage of MNE sales found in many industries. 2 Table 3 provides the first evidence of the home market advantage in aggregate multinational sales. Moreover, the sales of MNE affiliates are also biased towards the destination markets close to their headquarters countries. Take Korean and Dutch firms as an example. Korean firms in China have 16.2% of their exports to Japan (among ten destinations in Table 3) but only 3.2% to Germany. In contrast, Dutch firms in China have 12.9% of their exports to Germany but only 5.8% to Japan. This suggests that the home market advantage of MNE sales does not only hold in headquarters countries but also in the markets close to headquarters countries. [Table 3 about here.] [Table 4 about here.] To control for affiliate- and destination-specific factors, I regress firms export destination choices (both intensive and extensive margins) on the distance measures between headquarters countries and destinations. I use affiliate fixed effects to control for productivities and 2 See Cosar et al. (2015) for the car industry. 9

10 other affiliate characteristics. Since all affiliates produce in China, the standard gravity can be controlled by destination fixed effects. Following Morales, Sheu, and Zahler (2015), I measure the distance between headquarters country i and destination n by log of physical distance (log(dist in )), dummy for common language (lang in ), dummy for similar GDP per capita (sgdp in ), 3 and dummy for the headquarters country itself (1{i = n}). Table 4 provides evidence of the pattern named headquarters gravity : controlling for standard gravity terms and affiliate characteristics, a Chinese affiliate of foreign MNE is more likely to export and to export more to the destination markets closer to their headquarters countries. In addition to the headquarters country itself, a Chinese affiliate of foreign MNE is more likely to export to countries that are physically closer to, use the same language as, or have similar development levels to its headquarters country. For intensive margin, physical distance and similar GDP per capita are insignificant, which is mainly due to the endogenous selection of exporters. In the structural estimation, I will show that after controlling for export entry, the intensive margin of headquarters gravity is significant. I also estimate aggregate headquarters gravity by regressing the aggregate sales of Chinese affiliates of MNEs from country i to market n on destination fixed effects (controlling for the standard gravity), origin fixed effects (controlling for origin s productivity), and distance measures between headquarters countries and destination markets. The results are reported in the last column of Table 4. The aggregate headquarters gravity is sizable: doubling the physical distance between the headquarters country and the destination market will, ceteris paribus, lowering the aggregate trade value by about 20%. 2.4 What drives the MNEs Market Bias? Headquarters gravity suggests that a firm s capability of making sales is destinationspecific and depends on its country of origin. It is consistent with the idea long noticed by the marketing literature that firms can hardly achieve significant sales in markets far 3 Following the definition of the World Bank, I divide countries into four income groups based on GDP per capita: low income for < $756, lower middle for [$756, $2995], upper middle for [$2996, $9265], and high for $9266. Countries belonging to the same group are regarded as having similar GDP per capita. 10

11 away from their headquarters. Bronnenberg, Dhar, and Dube (2009) find that a brand s market shares are systematically higher in markets closer to its city of origin, regardless of production locations. They argue that this is due to the persistence of consumers perceived quality of brands. To shed more light on the driving forces of headquarters gravity, I estimate it using more disaggregate trade data, dividing the firm export sales into (1) homogeneous and differentiated goods; 4 (2) ordinary and processing trade; and (3) final goods and intermediates. 5 The results in Table 5 show that headquarters gravity is more pronounced in ordinary trade, trade of final goods, and trade of differentiated goods. The sales of these goods rely heavily on marketing networks and brand reputation, which suggests that headquarters gravity is likely to be driven by MNEs advantage in market access to countries near their headquarters. Moreover, the evidence suggests that headquarters gravity is more than merely vertical integration. [Table 5 about here.] 3 Theoretical Framework I present a quantifiable multi-country model of global production and sales. I first give a brief overview of the model. I then discuss preferences and technologies in detail later in the paper. Firms set their headquarters in country i after paying fixed entry costs. There is free entry of firms. Post entry, each firm decides its production locations, possibly in multiple countries, after paying a fixed MP cost in each production location. For model tractability, I assume that each production site produces a distinctive variety. After choosing their production sites, firms observe their core productivities. Firms that draw low core productivities may 4 The classification of homogeneous and differentiated goods is based on Rauch (1999). I treat both organized exchange and reference-priced goods in Rauch (1999) as homogeneous goods. 5 For each two-digit HS industry, I calculate the share of intermediates in Chinese exports from the World Input-Output Table in I define the industries with a final good share greater than.4 as final good industries. 11

12 not be able to produce in some of their production sites, which reflects self-selection into MP. Then each affiliate decides its export destinations based on its productivity and trade costs. The novel element of the model is that the export cost of a MNE affiliate does not only depend on the proximity of the destination to its production location (gravity), but also on the proximity of the destination to its headquarters (headquarters gravity). This novel element allows the model to capture micro patterns of MNEs exports. Moreover, each affiliate draws destination-specific entry and demand shocks. These shocks rationalize the fact that there is not a perfect pecking order of MNEs export entry observed in Chinese data. 6 In a nutshell, this model is designed to capture headquarters gravity found in micro data while remaining tractable for calibration using aggregate trade and MP data. 3.1 Preferences Consider a world consisting of N countries in which the representative household has a standard CES preference over a continuum of final varieties: U i = [ q i (ω) σ 1 σ ω Ω i dω] σ σ 1, σ > 1, (1) where Ω i is the set of varieties available to consumers in country i. I use i, l, n, and k to denote countries. These preferences are assumed to be common worldwide. There is a unique primary factor of production, labor, which commands a wage w i in country i. Country i is endowed with workers L i. Each worker supplies her one unit of labor inelastically. Workers within a country are identical ex ante. 6 See evidence for imperfect pecking order in the online appendix. 12

13 3.2 Technology and Geography The differentiated final varieties are produced by firms under monopolistic competition. Production of final varieties requires labor and the composite final good aggregated by Equation (1). Each firm can potentially be a multinational firm, with headquarters in one country and production affiliates in multiple countries. Specifically, firm ν can set its headquarters in country i after incurring a fixed entry cost equal to f e units of labor in country i. Post entry, firm ν originating from country i draws its core productivity ϕ i (ν) from a Pareto distribution: P rob{ϕ i (ν) ϕ} = F i (ν) = 1 T i ϕ θ, ϕ T 1 θ i > 0, θ > max{σ 1, 1}. As in Tintelnot (2017), firms can produce in their affiliates outside their headquarters countries and use these affiliates as export platforms after incurring fixed MP costs. A key feature of the equilibrium will be determining the locations of production and the destination of sales. It is well-known that solving the firm s production sites and sales destinations simultaneously is challenging. 7 I make the following two assumptions to simplify the firm s problem and make the general equilibrium model tractable. First, I assume that in each of its affiliate firm ν produces a distinctive variety of final goods ω. This assumption delivers closed-form gravity equations of aggregate trade and MP flows and greatly simplifies the quantitative framework. Without loss of generality, I assume that each firm can build at most one affiliate in each country. Second, I assume that, unlike Tintelnot (2017), firm ν decides its potential production sites and pays for fixed MP costs before observing its core productivity. To establish an affiliate in country l, firm ν originated in country i incurs a fixed MP cost f il ψ l (ν) in units of labor in country i, with f il being common across firms from i producing in l and ψ l (ν) being a firm-location-specific shock. The firm-location-specific shock ψ l (ν) is drawn from Pareto 7 See discussions in Tintelnot (2017) and Head and Mayer (2015). 13

14 distribution: P rob{ψ l (ν) ψ} = 1 ψ ɛ, ψ 1. Firm ν can use its core productivity in all of its affiliates. However, producing outside of the headquarters countries incurs efficiency losses. 8 I assume that firm ν from country i incurs an iceberg MP costs γ il 1 for producing in country l, with γ ii being normalized into 1. Final varieties can be traded internationally subject to trade costs, and the structure of trade costs is crucial for my model to rationalize headquarters gravity. I assume that firms originating from country i incur both an iceberg shipping cost τ ln 1 and iceberg marketing cost ζ in 1 to serve country n from their affiliates in country l. While the iceberg shipping cost τ ln represents the standard trade barriers between exporting and importing countries, the iceberg marketing cost ζ in is a novel element of my model. This new trade friction captures the cost increase in serving the markets far away from a firm s headquarters, which, for instance, includes building marketing networks, establishing brand reputation, and understanding consumers tastes. Subject to iceberg MP and trade costs, the affiliate in l owned by firm ν originating from i incurs a unit cost c iln (ν) to serve market n: c iln (ν) = γ ilτ ln ζ in w β l P 1 β l, (2) ϕ i (ν) where P l is the standard ideal price index associated with (1) and β (0, 1] is the share of labor in final good production. Motivated by the fact that only a small fraction of firms export, I assume that firm ν originating from country i incurs a fixed cost χ ln (ν)e s ln Em in in units of labor in country n to serve n from its affiliate in country l. The fixed export costs are a combination of shipping costs Eln s, which depend on trade frictions between production and destination countries, and marketing costs E m in, which depend on the proximity between headquarters and destination 8 See discussions in Keller and Yeaple (2013) for the gravity of knowledge associated with MNEs activities. 14

15 countries. χ ln (ν) is an affiliate-destination-specific entry shock. Furthermore, firm ν faces an affiliate-destination-specific demand shock ξ ln (ν), which can rationalize its sales across destinations. Idiosyncratic shocks (χ ln (ν), ξ ln (ν)) are i.i.d. across affiliates and destinations. Figure 2 summarizes trade and MP frictions in the model: [Figure 2 about here.] The timing of events of the model is summarized in Figure 3: [Figure 3 about here.] 3.3 Discussion of Assumptions A number of aspects of the model setup are worth discussing. First, I assume that each affiliate produces a distinctive variety. This assumption eliminates cannibalization effects within MNEs and thus the proximity-concentration trade-off emphasized in the literature (see Helpman, Melitz, and Yeaple (2004)). This is mainly due to data limitation. Without observing the operation of MNE affiliates in countries other than China, cannibalization effects within MNEs cannot be identified. Furthermore, this assumption simplifies the model greatly, leading to a transparent empirical framework in which I can separate the structural estimation of headquarters gravity using micro data with the calibration of other parameters using macro data. Finally, MNEs tend to produce multiple products and may site very different operations in different locations, which reduces the degree of cannibalization. A natural question is how the elimination of cannibalization would affect the structural estimation. I show in the online appendix that my estimates of headquarters gravity in the model without cannibalization are the lower bound of the estimates. In a model with cannibalization, it is unlikely for a MNE to serve markets close to its headquarters from its affiliates distant from its headquarters. Doing so will steal the market of its own affiliates. Therefore, to rationalize the observed affiliate exports, we need even stronger headquarters gravity. Indeed, a model with cannibalization but without headquarters gravity predicts an export pattern of MNE affiliates that is inconsistent with what I have observed in the data. 15

16 Second, the assumption that firms choose their potential production sites before drawing their core productivities is crucial for having closed-form gravity equations. 9 In a dynamic world, the MP entry costs tend to be sunk while productivity evolves over time. My timing assumption captures this feature in a static world. Moreover, this timing assumption does not rule out the self-selection into MP emphasized in the literature. Although a firm decides its potential production sites without knowing its core productivity, it may not operate in some of its potential production sites if it draws a low productivity. So a more productive firm is still more likely to be a realized MNE. Third, I rationalize headquarters gravity entirely by the cost structure. It is reasonable to think that at least some dimensions of headquarters gravity are driven by demand factors. However, under the CES preferences, models that put headquarters gravity on the demand side are isomorphic to my current setup. Head and Mayer (2015) have a very detailed discussion about this issue. With richer data including quantities and prices, it is possible to separate supply and demand factors of headquarters gravity. 10 This is not the focus of this paper. Finally, the structure of trade and MP frictions summarized by Figure 2 is similar to the one in Head and Mayer (2015). My work departs from theirs in two aspects. First, they do not allow firms to choose their production sites. Second, they do not allow fixed trade costs. Both aspects will be shown to be quantitatively relevant. 4 Equilibrium In this section, I define and characterize the general equilibrium of the model. Based on the timing of events illustrated by Figure 3, I solve the equilibrium in three steps. First, I solve the firms export decisions conditional on their production sites. Second, I characterize 9 Suppose that firms observe their core productivities before choosing their potential production sites. Then the solution of firms production sites depends on both core productivities and idiosyncratic shocks of fixed MP costs. There are no closed-form expressions for aggregate trade and MP flows since the MP entry conditions are too complicated. 10 Cosar et al. (2017) have decomposed MNEs home market advantage into supply and demand factors using detailed price and quantity data of global car markets. 16

17 the choice of production sites. Third, I aggregate the firm decisions and solve for the general equilibrium. I then emphasize the importance of headquarters gravity by discussing its implications for bilateral trade flows and gains from openness. 4.1 Firm Exports conditional on Production Sites In this subsection I solve the firm s export destinations and sales given their production sites. The structural equations that characterize affiliates export entry and sales will be used to estimate headquarters gravity. Suppose that firm ν orginated from country i has established an affiliate in country l and paid the fixed export costs to serve country n. Then its sales can be given by the standard results of monopolistic competition: x iln (ν) = ξ ln (ν) [ σc iln (ν)] 1 σ P σ 1 n X n, σ := σ σ 1, (3) where X n is the total expenditure of destination n and ξ ln (ν) is the affiliate-destinationspecific demand shock. The sales in Equation (3) will be realized if and only if the profits exceed the fixed export cost w n χ ln (ν)e s ln Em in, which can be formalized as 1 σ x iln(ν) w n χ ln (ν)e s ln Em in. Equivalently, firm ν originating from country i will serve country n from its affiliate in country l if and only if: [ ] ϕ i (ν) ϕ σwn E s 1 ln iln(η ln (ν)) := Em σ 1 in [ σγil τ η ln (ν)pn σ 1 ln ζ in w β l X P 1 β l ], (4) n where η ln (ν) := ξ ln(ν) χ ln (ν) is a composite export entry shock. By construction (η ln(ν), ξ ln (ν)) is i.i.d. across firms and countries. For tractability, I further assume that the entry and demand shocks are drawn from a bivariate lognormal distribution with the variances being σ 2 η and σ 2 ξ and the correlation coefficient being ρ ξη. Equation (4) and (3) characterize, respectively, the export entry condition and the export sales. As mentioned above, these two equations will be utilized to structurally estimate headquarters gravity, ζ in and E m in, from Chinese firm data. According to Equation (4), the 17

18 export condition relates to both ζ in and E m in while, according to Equation (3), the export sales conditional on entry do not rely on fixed marketing cost E m in. Therefore, using firm-level data on export entry and sales, I can separately identify ζ in and E m in. 4.2 Production sites Each firm decides its optimal production sites by comparing the expected operational profit in each host country with its fixed MP cost there. Before the realization of ϕ, ξ, and η, the expected sales of firm originating from i producing in l to market n can be expressed as x iln = Λ 1 T i [γ il τ ln ζ in w β l P 1 β l ] θ [ wn E s ln Em in Pn σ 1 X n ] θ (σ 1) σ 1 P σ 1 n X n, (5) where Λ 1 = θ σ θ θ (σ 1) σ σ 1 θ (σ 1) 0 cost associated with x iln has a share θ (σ 1) θσ of x iln. ξη θ (σ 1) σ 1 dg(ξ, η). Moreover, the expected fixed export 0 Since in each affiliate the firm produces a distinctive variety, the firm will produce in a country if the expected operational profit exceeds the fixed MP cost. Then firm ν originating from country i will produce in country l if and only if ψ l (ν) ψ il := θσ σ 1 w i f il n x iln. (6) Furthermore, I assume that f il is large enough so that ψ il 1 for all i, l. The expected sales in Equation (5) will be realized if and only if Equation (6) holds. Therefore, before the realization of ψ, the expected total sales of an affiliate in country l owned by firm ν from country i is ( θσ x il = σ 1 w i f il n x iln ) ( ) ɛ x iln. (7) n Notice that Equation (7) can be derived directly from the distribution of ψ and the cutoff in Equation (6). Moreover, the expected fixed MP cost associated with x il has a share of x il. ɛ σ 1 ɛ+1 θσ 18

19 4.3 General Equilibrium Consider now the general equilibrium of the model. The measure of firms originating from i producing in l is determined by the measure of firms originating from i, M i, and the MP entry condition (6): [ ] ɛ S il = Λ 2 M 1 1+ɛ i [w i f il ] ɛ 1+ɛ 1+ɛ X iln, Λ 2 = n [ σ 1 θσ ] ɛ 1+ɛ, (8) where X iln is the aggregate sales of firms originating from i to n from their affiliates in l. Conditional on MP entry, the expected sales have been given by Equation (5). Therefore, the aggregate trilateral trade flow is: X iln = S il x iln. (9) The ideal price index is standard in monopolistic competition: P θ n [ ] θ (σ 1) wn σ 1 = Λ 1 Ψ n, Ψ n = X n i,l { S il T i γ il τ ln ζ in w β l P 1 β l } θ [E s lne m in] θ (σ 1) σ 1. (10) Labor income comes from production, marketing, and creating affiliates and firms: ( w l L l = β 1 1 ) X iln + σ n i θ (σ 1) θσ i k X ikl + σ 1 θσ X lkn. (11) The total expenditure is equal to the sum of wage income and intermediate expenditure n k X l = w l L l + (1 β)(1 1 σ ) i X iln. (12) n Finally, free entry implies that M i w i f e = 1 σ ɛ θσ X iln. (13) n l 19

20 Then the general equilibrium can be defined as follows: Definition 1 Given the preferences, technology, and geographical frictions, the equilibrium consists of {w i, X i, P i, M i, S il } such that: 1. The measure of firms originating from i and producing in l, S il, satisfies Equation (8). 2. The price index P n satisfies Equation (10). 3. Total expenditure X l satisfies Equation (12). 4. The wage w l satisfies the labor market clearing condition (11). 5. The measure of firms M i is derived by the free entry condition (13). 4.4 Gravity In this section we explore the implications of my model for the aggregate volume of bilateral trade and MP. Using Equation (5) and aggregating across firms, I obtain the following expression for the aggregate sales of firms originating from country i to n from their affiliates in l: { X iln = S il T i γ il τ ln ζ in w β l P 1 β l } θ [E s lnein] m θ (σ 1) σ 1 1 Ψ n X n. (14) The trilateral trade flows X iln are not observed in aggregate data for many countries. Instead, we observe bilateral trade flows X T R ln := i X iln across countries. I then re-express trilateral trade flows in Equation (14) into bilateral trade flows that are standard in gravity equations. Proposition 2 (Gravity and Headquarters Gravity) Aggregate bilateral trade flows can 20

21 be expressed as log ( X T R ln ) ) = θ log (w β l P 1 β l + log }{{} Exporter Fixed Effect ( + log i ( Xn Ψ n ) }{{} Importer Fixed Effect T i (γ il ζ in ) θ S il (Ein) m θ (σ 1) σ 1 } {{ } Third-country effects via MP θ (σ 1) θ log τ ln log Eln s }{{ σ 1 } ). Bilateral trade barrier (15) Moreover, if ζ in = E m in = 1, then log ( ) Xln T R = θ log (w β l P 1 β l i T i S il γ θ il ) } {{ } Exporter Fixed Effect ( ) Xn θ (σ 1) θ log τ ln log Eln s Ψ }{{ n σ 1 }}{{} Importer Fixed Effect Bilateral trade barrier (16) + log Proof. Summing the log of Equation (14) along i leads to Equation (15). Inserting ζ in = Ein m = 1 into Equation (15) leads to Equation (16). Equation (15) resembles a standard gravity equation relating bilateral trade flows to an exporter fixed effect (here the factor prices in exporting countries), an importer fixed effect (here the total expenditure and a multilateral resistance term), and the bilateral trade costs between exporting and importing countries. However, due to headquarters gravity, there is an additional term entering into Equation (15), representing third-country effects via MP. This term can be understood through a simple example. Suppose that the exporting country l is China and the importing country n is Canada. Then a large fraction of Chinese exports to Canada is contributed by Chinese affiliates of the U.S. MNEs who have an advantage in serving the Canadian market. The standard gravity models can hardly capture this third-country effect. Take an analogy from physics. The standard gravity equation suggests that the center of gravity for exporters lies in their production locations. The new third-country effects in Equation (15) suggests that, for MNEs, the center of gravity lies somewhere in between their production locations and their headquarters. The sales of MNE affiliates are then biased by 21

22 the center of gravity towards their headquarters. Equation (16) further shows that this new term of third-country effects does not exist in the MP models without headquarters gravity. If multinational affiliates face the same trade costs with local firms, the third-country effect will be absorbed by the exporter s fixed effect. In the absence of headquarters gravity, MP only affects the technology the exporting countries get access to. The standard gravity equation for aggregate bilateral trade flows still holds. In sum, in the presence of MP and headquarters gravity, the standard gravity equation is not sufficient to characterize bilateral trade flows across countries. Third-country effects led by headquarters gravity have to be considered. 4.5 Gains from Openness Through the lens of my model, countries are connected by trade and MP. How would opening to trade and MP affect a country s welfare? The following proposition applies the sufficient statistics approach developed by Arkolakis et al. (2012). For any variable y, I denote y as the level of y after openness and ŷ = y /y. Proposition 3 Suppose that β = 1. Let W i := w i /P i be the real wage in country i. Let λ iln := X iln /X n. Let Y f i := n,l X iln and Y f ii := n X iin. Then Ŵ i = ˆλ 1 θ iii (Ŷ f i ˆX i ) 1 θ 1 1+ɛ ( Ŷ f ii ˆX i ) 1 θ ɛ 1+ɛ. (17) Moreover, let W Aut i be the real wage in country i under autarky, then W i W Aut i = λ 1 θ iii ( Y f i X i ) 1 θ 1 1+ɛ ( Y f ii X i ) 1 θ ɛ 1+ɛ. (18) Proof. See the online appendix. The first term on the right-hand-side of Equation (17) characterizes welfare gains from 22

23 consuming and producing more varieties in the open economy. Unlike pure trade models, here the sufficient statistics for the gains from openness depend on the expenditure share of the goods that are originating from, produced in, and consumed by country i, λ iii. Similar to Ramondo and Rodriguez-Clare (2013) and Arkolakis et al. (2017), MP can potentially lead to much larger gains from openness than the ones under pure trade models. As mentioned above, for most countries λ iii is not directly observed in the macro data and depends heavily on headquarters gravity. Therefore, I bring my model to the micro data and estimate headquarters gravity and λ iii structurally. 5 Structural Estimation In this section, I estimate key model parameters, the iceberg and fixed marketing costs, using Chinese firm-level data in To do so, I re-express export entry decisions in Equation (4) and export sales in Equation (3) in terms of observables. After controlling for productivity and standard gravity, the iceberg marketing cost ζ in and fixed marketing cost E m in can be separately identified by affiliate-level intensive and extensive margins of exports. The extensive margin depends on both variable and fixed marketing costs, whereas conditional on entry the intensive margin depends only on variable marketing costs. Based on this identification strategy, I first estimate the extensive margin to deliver an entry hurdle which combines variable and fixed marketing costs. Firms with productivities higher than this entry hurdle will export to a certain market. Second, I estimate iceberg marketing cost from export sales conditional on export entry. My estimation procedures are similar to the Heckman two-step approach developed by Irarrazabal, Moxnes, and Opromolla (2013). My approach departs from theirs by controlling for export entry non-parametrically, which is more robust with mis-specification. In Section 6, I embed structural estimates into the general equilibrium model and calibrate the general equilibrium model to aggregate trade and MP data for 34 major economies. I take two parameters from the literature: the elasticity of substitution σ = 4 from 23

24 Arkolakis et al. (2017) and the value-added share β = 0.35 from Johnson and Moxnes (2013). 5.1 Affiliate-Level Extensive Margin for Exports The extensive margin of affiliates exports is characterized by Equation (4). Notice that the productivity ϕ i (ν) in Equation (4) is unobserved. But it can be expressed as a function of sales in China, x ill (ν). Substituting ϕ i (ν) with x ill (ν), Equation (4) can be rewritten as log(x ill (ν)) + log(η ln(ν)) H iln, n l = CHN, (19) where H iln = log σ + log(w n ElnE s in) m + (σ 1) log(ζ }{{} in ) (σ 1) log(ζ il ) }{{} Fixed Export Cost Iceberg Headquarters Gravity [log(x n Pn σ 1 /X l P σ 1 l ) (σ 1) log(τ ln )], }{{} Export Sales Potential and η ln (ν) = η ln(ν)/ξ ll (ν) is a compound entry shock. Equation (19) means that an affiliate in China from country i will serve market d if its sales in China plus an affiliate-destination-specific shock exceeds an entry hurdle H dni. Therefore, the entry hurdle H iln characterizes how likely an affiliate will export to a market, given its sales in China. H iln consists of three parts. First it increases with respect to the fixed trade cost. Second it increases with respect to the iceberg marketing cost. Third it decreases with respect to the export sales potential. By construction log(ηln (ν)) is drawn from a normal distribution with mean 0 and standard deviation σ η = ση 2 + σξ 2. Therefore, Θ 1 = {H iln, σ η } can be estimated by a ML estimator with the following likelihood function: l 1 (Θ 1 ) = n l i ν [1 y iln (ν)] log{φ[ H iln log x ill (ν) σ η ]}+y iln (ν) log{1 Φ[ H iln log x ill (ν) ]}, σ η (20) 24

25 where y iln (ν) = 1 indicates that affiliate ν enters market n and Φ[.] is the c.d.f. of the standard normal distribution. The entry hurdle H iln is estimated as a headquarters-destination fixed effect in Probit Equation (20). The entry hurdle H iln is identified by the mean sales in China for those firms from country i who serve market n. With a higher entry hurdle H iln, firms from country i have to be more productive to serve market n. The standard deviation of the compound entry shock, σ η, is recovered from the coefficient of the sales in China in Probit Equation (20). The model implies that the firm with larger sales in China are more likely to export to all destination countries. This selection is disturbed by compound entry shocks. With σ η = 0, the export entry is entirely decided by sales in China. The estimation on Probit Equation (20) shows that the coefficient of log(x ill ) is with standard error This implies that the standard deviation of the compound entry shock η is σ η = Figure 4 illustrates the estimated entry hurdle, H iln, with respect to the distance between source country i and destination n. It shows that foreign MNEs in China must be larger in terms of their sales in China to serve markets more distant from their headquarters. This relationship exists even if I exclude the case with i = n. Notice that H iln is the headquartersdestination fixed effect in Probit Equation (20). The patterns in Figure 4 are entirely datadriven since I do not impose any restrictions on H iln. Similar patterns hold for cultural and economic distances. MNE affiliates face low entry hurdles to markets that share common languages or have similar development levels with their headquarters countries. Moreover, MNE affiliates have stronger advantage in entering their home markets. [Figure 4 about here.] [Figure 5 about here.] 25

26 5.2 Parametrization and Estimation on Iceberg Marketing Costs In this subsection, I estimate ζ di from the export sales conditional on entry. Notice that ffiliate ν from country i will serve market n if and only if log(x ill (ν)) + log(ηln (ν)) H iln. I define an affiliate-specific entry hurdle as H iln (ν) = H iln log(x ill (ν)). I parametrize ζ in as a function of observed gravity variables: log(ζ in ) = ρ ζ,1 log(dist in ) + ρ ζ,2 lang in + ρ ζ,3 sgdp in + ρ ζ,4 self in + ρ ζ,5 self in 1{i = USA} + ρ ζ,6 self in 1{i = JPN/KOR} := ρ ζ D in. where 1{i = USA} and 1{i = JPN/KOR} are dummies for the source country as the U.S. and Japan/Korea respectively. Then conditional on η ln (ν) H iln (ν), the export sales can be given by log ( ) xiln (ν) = (σ 1)ρ ζ D in + ι il + κ ln + log(ξ x ill (ν) ln(ν)), (21) where ι il = (σ 1) log(ζ il ) and κ ln = log(x n Pn σ 1 /X l P σ 1 l ) (σ 1) log(τ ln ), and ξln (ν) = ξ ln (ν)/ξ ll (ν). Notice that Equation (21) only holds for affiliates with η ln (ν) H iln (ν). Therefore if cov(η, ξ ) 0, then the OLS estimator of ρ ζ from Equation (21) will be inconsistent. It is straightforward to show that if cov(η, ξ ) > 0 then the OLS estimator of ρ ζ will be biased towards 0. I leave the details of this proof in the online appendix. To correct the selection bias, I insert the estimated affiliate-specific entry hurdle into Equation (21) with a general functional form: log ( ) xiln (ν) = (σ 1)ρ ζ D in + ι il + κ ln + m( x ill (ν) H iln (ν)) + u iln (ν), (22) where m(.) is a general-form function and u iln (ν) is the measurement error. Then I use Robinson (1988) semiparametric estimator to estimate Equation (22). The details of this estimator are presented in the online appendix. 26

27 [Table 6 about here.] The left column of table 6 presents the results of the semiparametric estimator. ρ ζ are statistically significant and with expected signs. The estimates suggest that the MNE affiliates have an advantage in serving markets close to their headquarters: the iceberg export cost of a foreign affiliate in China to its headquarters country is, ceteris paribus, 46% lower than to any other country. If the distance between the headquarters and destination countries doubles, the affiliate s export cost would increase by 4.4%. The similar income level between the headquarters and destination countries would decrease the affiliate s export cost by 13%. The coefficient of the shared language between the headquarters and destination countries is negative as expected but not statistically significant. Moreover, the U.S. and Japanese/Korean firms in China are substantially different in terms of home market advantage. The Japanese/Korean firms incur much lower costs to export back to home market than the U.S. firms do. It is consistent with the prevalence of horizontal MP in the U.S. MNEs found by Ramondo et al. (2016). Comparing to the U.S. MNEs, Japanese and European MNEs are more likely to conduct vertical MP and export platforms. Allowing this heterogeneity improves my model fit. To show the importance of controlling for selection, I also estimate Equation (22) by using OLS estimator without controlling for H dni (ν). The result is presented on the right column of Table 6. The OLS estimator without controlling entry hurdles biases the estimates of ρ ζ towards 0, which suggests that cov(η, ξ ) > Imputation of the Fixed Export Costs With the estimated entry hurdle H iln and iceberg headquarters gravity term ζ in, I can compute the fixed export cost E s ln Em in directly by log(e s lne m in) = H iln (σ 1) log(ζ in ) + ι in + κ ln log σ log w n, where the wage w n is approximated by GDP per capita in 2001 from Penn World Table. 27

28 However, these estimates give me only E s ln Em in for l = CHN. To impute E s ln Em in for all (i, l, n) triples, I parameterize it as log(e s lne m in) = ρ E,1 log(d in ) + ρ E,2 log(d ln ) + v iln, n l = CHN, (23) where v iln is an exogenous measurement error. I estimate Equation (23) by OLS estimator. The result is presented in Table 7. Similar to ζ in, the estimates on E m in suggest headquarters gravity being substantial. [Table 7 about here.] To check the quality of imputation, I compare the estimated entry hurdle H iln with the entry hurdle imputed by Equation (23). Overall the imputation works well. See the online appendix for details. 5.4 Shock Parameters The observed export sales (relative to sales in China) are drawn from a truncated lognormal distribution which depends on shock parameters {σ ξ, σ η, ρ ξη }. I utilize this truncated lognormal distribution to back out shock parameters by ML estimator. The derivation of the likelihood function is tedious and relegated to the online appendix. The variance of demand shock σ 2 ξ is identified by the variance of firms export sales that cannot be explained by the firms sales in China. Given the firm s sales in China, the firm s export sales would be more dispersed if σ ξ is larger. Notice that this effect exists even without selection. In contrast, the correlation between demand and entry shock, ρ ξη, affects the mean of export sales through selection. Conditional on entry, the mean of export sales would increase with respect to ρ ξη. This conditional mean identifies the correlation term ρ ξη. The estimation results are shown in Table 8. The results confirms that cov(η, ξ ) = σξ 2 + ρ ξησ ξ σ η > 0. [Table 8 about here.] 28

29 Notice that ξ is an idiosyncratic demand shock and η is the ratio of ξ to an idiosyncratic fixed export cost shock χ. The correlation between log(η) and log(ξ) is close to 1, which implies that the variation of idiosyncratic demand shocks is much higher than the variation of fixed export cost shocks. This result further implies that the variation of export entry across firms is primarily driven by the demand shock. The shocks estimated from Chinese data are much larger than the estimates from French data in Eaton, Kortum, and Kramarz (2011) but similar to the estimates from Norwegian data of Irarrazabal, Moxnes, and Opromolla (2013). 6 Calibration Armed with the structural estimates in Section 5, I calibrate the general equilibrium model to aggregate trade and MP data. The world I target to consists of 34 economies in In the following subsections, I first calibrate the productivity dispersion parameter θ and MP cost dispersion ɛ. Then I calibrate trilateral trade shares, λ iln := X iln /X n. 6.1 Calibrating θ and ɛ The dispersion parameter of firm productivity, θ, is calibrated from the dispersion of the domestic sales for Chinese local firms. Let α = θ. The model shows that the domestic sales for Chinese local firms is σ 1 log(x lll (ν)) = δ(ν) + log ξ(ν) + Φ l, where Φ l = X l P σ 1 l σ 1 σ (w β l P 1 β l ) 1 σ, δ follows an exponential distribution with parameter α, and log ξ follows a left-truncated normal distribution. 11 These economies are Australia, Austria, Belgium, Bulgaria, Brazil, Canada, China, Czech, Germany, Denmark, Spain, Finland, France, Britain, Greece, Hungary, Indonesia, India, Ireland, Italy, Japan, Korea, Lithuania, Mexico, the Netherlands, Poland, Portugal, Romania, Russia, Slovakia, Sweden, Turkey, Taiwan, and the U.S. 29

30 For the domestic sales I ignore the selection of exporters, assuming log ξ is symmetrically distributed 12. The property of exponential distribution indicates that mean(log(x lll )) median(log(x lll )) = 1 log(2). α Therefore, θ σ 1 = Since σ = 4, θ = ɛ characterizes the elasticity of multinational production with respect to fixed MP costs. In equilibrium, the fixed MP cost has a share of ɛ 1+ɛ in MP sales. Tintelnot (2017) has estimated the fixed MP costs in a structural model, showing that the fixed MP costs account for 5% to 25% of the MP sales in different countries. As a result, I calibrate ɛ = 0.2. The robustness tests show that ɛ does not affect my main quantitative results. 6.2 Calibrating Trilateral Trade Share The trilateral trade share, λ iln := X iln /X n, is crucial for conducting counterfactual experiments. However, it is not observed in the macro data for most of the countries. Instead, I observe MP from i to l as a share of l s production, λ MP il = n X iln, trade i,n X i ln from l to n as a share of n s expenditure on goods produced at n, λ T R ln = i X iln i X inn, and the total expenditure in country n, X n. In this section, I am going to calibrate λ iln from these observables by gravity equation (14). Let T il = (S il T i ) 1 θ γ il w β l P 1 β l. Then λ iln can be rewritten as λ iln = T θ il τ θ ln ζ θ in [Es ln Em in] θ (σ 1) σ 1 θ i,l T i l τ θ l n ζ θ i n [E l nei m θ (σ 1) n ] σ 1. (24) ζ in, E s ln, and Em in have been estimated in Section 5. Therefore, {λ iln } can be expressed in terms of { T il, τ ln }. Moreover, λ MP il and λ T R ln can be expressed by λ iln and X n : λ T R ln = i λ iln i λ inn, λ MP il = n λ ilnx n i,n λ i lnx n. (25) 12 The imputed entry hurdle for local firms in the domestic market, H nnn, is very low. Therefore assuming log ξ is symmetrically distributed does not affect the result. 30

31 With data on λ MP il and λ T R ln, { T il, τ ln } can be computed by solving Equation (25). Then λ iln is derived from Equation (24). I refer to the case in which ζ in and E m in are estimated in Section 5 as the Baseline case. I focus primarily on manufacturing sectors. The bilateral manufacturing trade flows in 2001 (including the domestic production) come from the World Input-Output Database (WIOD). The bilateral manufacturing MP flows in 2001 come from Ramondo, Rodriguez- Clare, and Tintelnot (2017). To explore the general equilibrium effects of headquarters gravity, I also calibrate {λ iln } in the case where ζ in = E m in = 1 for all (i, n). In this case, only standard gravity terms matter for bilateral trade volume. I refer this case as the Gravity-only case. Notice that both the baseline case and the gravity-only case can match bilateral trade and MP shares perfectly, but they generate different trilateral trade shares {λ iln }. 6.3 Out-of-Sample Predictions In this subsection I provide additional validity for my model using data moments that my calibration does not targets to. I compute the following normalized global sales of MNEs in China in the calibrated model and in Chinese firm data: X iln X iln = ( i X i ln) (, n X iln ) l = CHN. (26) By Equation (14), if ζ in = E m in = 1 for all (i, n), the normalized global sales of MNEs in China can be expressed as X iln X iln = ( i X i ln) ( n X iln ) = [ i S i lt i γ θ i l 1 ] [ n τ ln (Eln s ) θ (σ 1) σ 1 ], (27) X n Ψ n which is constant over (i, n). Notice that I have utilized Chinese firm data to estimate ζ in and E m in but not to calibrate the general equilibrium. Figure 6 compares the normalized sales of MNEs in China in 31

32 the data and in the calibrated model (both baseline and gravity-only). It shows that the baseline predicts the normalized sales of MNEs in China well, while the gravity-only model, as predicted by Equation (27), fails to make a sensible prediction. [Figure 6 about here.] I have abstracted cannibalization within MNEs from my model. Concerning the model predictions, a natural question is: Does cannibalization within MNEs help explaining the normalized global sales of MNEs in China? I calibrate the model developed by Arkolakis et al. (2016) to bilateral trade and MP flows. Their model incorporates within-firm cannibalization effects into a multi-country general equilibrium model. Then I compute the model-generated normalized global sales of MNEs that produce in China and compute it to the Chinese data. The result shows that X iln generated by their model is negatively correlated with its data counterparts. Therefore, cannibalization within MNEs does not help explaining headquarters gravity found in the micro data. See the details of calibration and predictions in the online appendix. 7 General Equilibrium Counterfactuals With the calibrated model in hand, I conduct counterfactual analysis. First, following Dekle, Eaton, and Kortum (2008) I show that the counterfactual changes of equilibrium outcomes can be solved given the calibrated trade and MP shares, elasticity parameters, and exogenous parameter changes. Then in each counterfactual, I compute the changes of equilibrium outcomes using this algorithm. To illustrate the importance of headquarters gravity, I contrast the counterfactual predictions of the baseline model with the gravity-only model. 7.1 Exact Hat Algebra Computing the general equilibrium is challenging due to the high-dimensionality of {γ il, f il, τ ln }. Following Dekle, Eaton, and Kortum (2008), I can compute changes of equilib- 32

33 rium outcomes from observed shares and parameter changes. Given data (λ iln, X n ), elasticity parameters (θ, σ, ɛ, β), and exogenous changes (ˆγ il, ˆf il, ˆτ ln, Ês ln, ˆζ in, Êm in, ˆT i, ˆL i ), the equilibrium changes (ŵ i, ˆP i, ˆX i, ˆM i, Ŝil) can be computed by the following system of equations: First, I combine exogenous changes of trade and MP frictions into: ˆµ iln := ˆγ ilˆτ ln ˆζin, Ê iln := Ês lnêm in. (28) Then changes of trilateral trade shares can be expressed as ˆλ iln = Ŝ il ˆTi {ˆµ iln ŵ β l ˆP 1 β l k,m λ kmnŝkm ˆT k {ˆµ kmn ŵ β m } θ Ê θ (σ 1) σ 1 iln 1 β ˆP m } θ (σ 1) θê σ 1 kmn. (29) Changes in price indices are then [ ] θ (σ 1) ˆP n θ ŵn σ 1 = ˆX n λ iln Ŝ il ˆTi {ˆµ iln ŵ β l i,l ˆP 1 β l } θ Ê θ (σ 1) σ 1 iln. (30) Changes in the MP entry can be expressed as Ŝ il = ˆM ] 1 ɛ 1+ɛ 1+ɛ i [ŵ i ˆfil Current account balance requires that [ ( ˆλ iln ˆXn n λ iln X n k λ ilkx k ) ] ɛ 1+ɛ. (31) ˆX l = w ll l ŵ l ˆLl + (1 β)(1 1 X l σ ) i n ˆλ iln ˆXn λ iln X n X l. (32) Labor market clearing delivers ŵ l ˆLl = β + σ 1 θσ ( 1 1 ) σ n n l i λ iln X n θ (σ 1) ˆλ iln ˆXn + w l L l θσ ˆλ iln ˆXn λ iln X n w i L i. i k ˆλ ikl ˆXl λ ikl X l w l L l (33) 33

34 Finally, free entry condition implies that ˆM i ŵ i = n λ iln X n ˆλ iln ˆXn k,m λ. (34) ikmx m l 7.2 The Trade Effects of Headquarters Gravity As mentioned at the beginning of this paper, MNEs are the largest players in international trade. Why do they account for a substantial fraction of international trade? Is it due to their size or productivity? Or is it due to their advantage in accessing international markets, which has been carefully estimated in this paper? To answer these questions, I conduct two counterfactuals based on the baseline model. First, I shut down headquarters gravity by imposing foreign MNE affiliates to have the same export costs with local firms, i.e. ˆµ iln = ζ ln ζ in and Êiln = Em ln E m in for all n l. 13, which will be referred as the No HG scenario. Second, I shut down MP by setting γ il = for i l, which will be referred as the No MP scenario. The aggregate trade effect of headquarters gravity turns out to be substantial: eliminating headquarters gravity would decrease the world manufacturing trade in 2001 by 12.7%, whereas shutting down MP would decrease the world manufacturing trade in 2001 by 42.7%. As a result, headquarters gravity accounts for about 30% of the MNEs contribution to international trade. The remaining 70% of the MNEs contribution to international trade is due to their productivity advantage. Headquarters gravity not only affects the volumes but also directions of trade flows. Based on R&D share in GDP, I divide countries into two groups: innovative and less innovative. 14 According to Arkolakis et al. (2017), innovative countries are rich and more likely to be home countries for MNEs, whereas less innovative countries include many developing countries and are more likely to be host countries for MNEs. Table 9 shows that headquar- 13 Headquarters gravity implies that local firms have an advantage in serving host countries. In this exercise I do not allow foreign affiliates to face the same costs in marketing to the host countries as local firms face. Otherwise it gives them an additional advantage in serving the host markets, which is equivalent to MP liberalization. 14 Innovative countries turn out to be rich developed countries, including Japan, the Netherlands, Finland, Denmark, United States, Germany, France, Sweden, United Kingdom, Belgium, Canada, Korea, and Austria. 34

35 ters gravity is particularly important for exports from less innovative countries to innovative countries. Without affiliates of foreign MNEs and their access to export markets, it would be very challenging for those less innovative (often developing) countries to make sales in rich developed countries. [Table 9 about here.] The trade effects of headquarters gravity and MP could be seen more clearly from Figure 7, which illustrates the counterfactual changes of Chinese exporting sales by destination. Eliminating headquarters gravity will switch Chinese manufacturing exports from developed countries to developing countries. [Figure 7 about here.] Headquarters gravity suggests that, for host countries, inward MP and exports are complements. How large is this complementarity? I quantify it by shutting down MP under both the baseline model and the gravity-only model. It turns out that shutting down MP in the baseline model will reduce the world manufacturing trade by, as mentioned above, 42.7%, whereas doing so in the gravity-only model will only reduce the world manufacturing trade by 6.2%. This strong complementarity implies that attracting inward MP, especially MNEs from large markets, is an effective way to promote exports. This type of policy is indeed widely accepted in practice. 7.3 Spatial Reallocation of MNEs Activities Multinational production is the first-order phenomenon in globalization. How MNEs relocate their activities following trade liberalization thus has first-order impacts on manufacturing production across countries. To understand the implications of headquarters gravity for the relocation of MNEs activities after trade liberalization, I first conduct a stylized counterfactual experiment by reducing the iceberg trade cost from China to the U.S. by 10%. Then I test the empirical relevance of these implications by comparing the counterfactual predictions to actual changes in the data. 35

36 7.3.1 MP Relocation after Trade Liberalization To understand MP relocation after trade liberalization, I reduce the iceberg export cost from China to the U.S., τ CHN,USA, by 10% and measure how MNEs from different source countries adjust the sales of their Chinese affiliates. I conduct trade liberalization in both the baseline and gravity-only models. This trade liberalization makes China a better export platform to the U.S. Therefore, in the presence of headquarters gravity, MNEs originating from countries close to the U.S. substantially increase their production in China following trade liberalization (see Table 10), whereas MNEs from countries far away from the U.S. respond very little to this trade liberalization. In contrast, the gravity-only model predicts that MNEs from different source countries will uniformly increase their production in China following trade liberalization. [Table 10 about here.] In sum, headquarters gravity suggests a complementarity between a country s inward MP and its exports. The decline of Chinese export costs to the U.S. will stimulate the expansion of Chinese affiliates of MNEs from countries close to the U.S. A natural question is how relevant this new complementarity is in the data. To answer this question, I will compare the counterfactual predictions to actual changes observed in the data Comparing Counterfactual Predictions to Actual Changes It is challenging to compare counterfactual predictions to actual changes since in reality many exogenous changes occur simultaneously. Following the standard procedures in the literature, I calibrate the actual changes in trade and MP costs from the data, compute counterfactual changes in trade and MP flows, and compare the key moments of counterfactual changes to their data counterparts. By Equation (24), I compute { T il, τ ln } from the baseline model to match bilateral trade and MP flows in 2001 and 2007 separately. These are the two years when I have access to 36

37 bilateral trade and MP flows across countries. 15 I set headquarters gravity as its level in By doing this, I calibrate the changes in trade costs, ˆτ ln, from the observed changes in trade flows. Then by assuming that changes in iceberg MP cost, ˆγ il, are symmetric, the first-order approximation leads to ˆγ il = Til Tli. T ii Tll Inserting the calibrated (ˆγ il, ˆτ ln ) into the system of equations delivered by the exacthat algebra, I then compute the counterfactual changes predicted by my model. I conduct this counterfactual experiment in both the baseline and the gravity-only models. Notice that there were changes other than trade and MP liberalization between 2001 and So my model cannot perfectly replicate actual changes. To explore the complementarity between inward MP and exports suggested by headquarters gravity, I construct the following indices using bilateral MP flows, Xil MP, and trade flows, X T R ln :16 Ẑ MP il Ẑ T R ln = = k i ˆX MP 1 log (dist ki ) ( ) ( ˆXMPkl ), l kl k ˆXMP k l X T R ln ( n X T R ln ) ( l X T R l n ), (35) where ẐMP il and ẐT R ln reveals the liberalization of MP to country l from countries close to country i reveals the liberalization of exports from country l to country i. Three points worth discussion. First, I use the inverse of distance as the weight in computing ẐMP il. Countries closer to country i will have larger weights in computing ẐMP il. Second, when computing Ẑil MP, I do not include country i itself. Third, the aggregate terms in the denominator are included to control for the size changes of source and host countries. Then I run the following regression using the actual and counterfactual changes in trade 15 Bilateral trade and MP flows in 2001 have been used to calibrate the baseline model. The bilateral trade flows in 2007 come from WIOT database. The bilateral MP flows in 2007 are imputed from the changes in FDI stocks from UNCTAD. The details are presented in the online appendix. 16 Xil MP is the total production in country l of the MNEs from country i. Xln T R is the exports from country l to country n. 37

38 and MP flows: log (ẐMP il ) = β 0 + β COM log ) R (ẐT li + v il, i l. (36) If β COM > 0, the expansion of exports from country l to country i is associated with the expansion of MP sales in country l from countries close to country i, which is consistent with what I have found in the stylized counterfactual experiment. [Table 11 about here.] The results are shown in Table 11. The estimated β COM is significantly positive in the data, which suggests that trade liberalization from country l to i indeed stimulates MP flows to country l from countries close to country i. The counterfactual predictions by the baseline model replicate this pattern, whereas the gravity-only model generates β COM that is much smaller than the one from the data. Therefore, headquarters gravity is essential to understanding the relocation of MNEs activities in the data. 7.4 Welfare Implications of China s Openness The ultimate goal of my multi-country general equilibrium model is to quantify the welfare implications of trade and MP liberalization. In this subsection, I quantify the welfare impacts of China s integration into the world economy, which has been regarded as the most important event of globalization in recent years. China joined WTO at the end of 2001, triggering a series of events that accelerate China s openness to trade and MP. This provides a natural shock that has profound welfare implications on China and other countries. In the previous subsection, I have calibrated the changes in iceberg MP and trade costs, (ˆγ il, ˆτ ln ), between 2001 and To isolate the impacts of China s trade and MP liberalization, I set (ˆτ CHN,n, ˆτ l,chn, ˆγ i,chn, ˆγ CHN,l ) as calibrated, 17 keeping all other trade and MP costs in their 2001 level. Starting with the The average of ˆτ CHN,n, ˆτ l,chn, and ˆγ i,chn are, respectively, 0.76, 0.94, and The details of calibrated trade and MP liberalization are presented in the online appendix. 38

39 world economy, the model delivers counterfactual changes led by China s trade and MP liberalization. Similar to what I have done previously, I conduct this counterfactual experiment in the baseline and gravity-only models. The welfare implications of China s trade and MP liberalization between 2001 and 2007 are shown in Table 12. First, contrary to popular fear, the integration of China into the world economy has benefited all countries in this exercise. 18 Second, rich innovative countries gain more from China s openness than developing countries. Third, with the emergence of China as a world manufacturing center, rich innovative countries are increasingly specialized in innovation. 19 Fourth, headquarters gravity is quantitatively important to the welfare implications of China s openness. [Table 12 about here.] Figure 8 shows the importance of headquarters gravity in quantifying welfare gains from China s openness. Ignoring headquarters gravity leads to sizable underestimation of the welfare gains from China s openness for rich innovative countries. For example, in the baseline model, China s openness raises the Japanese real wage by 1.87%, whereas in the gravity-only model without headquarters gravity, the Japanese real wage increases by only 1.24%. Another example is the U.S. In the baseline model, the U.S. gains 1.44% in terms of real wage from China s openness, whereas in the gravity-only model it only gains 0.97%. [Figure 8 about here.] [Figure 9 about here.] Why does ignoring headquarters gravity lead to underestimation of gains from China s openness for developed countries? First, the gravity-only model underestimates the increase of firm masses in developed countries following China s openness. This can be seen clearly from Figure 9. In the presence of headquarters gravity, the liberalization of China s exports 18 The magnitude of welfare gains from China s openness in this exercise is comparable to the ones estimated in Arkolakis et al. (2017). 19 Following Arkolakis et al. (2017), I define innovation as creating new firms. 39

40 to, for example, the U.S. will stimulate the expansion of MP to China from countries close to the U.S., which will further stimulate firm entry in these countries. In contrast, the gravity-only model predicts a uniform increase in MP to China from all countries after trade liberalization, which leads to the bias shown in Figure 9. Second, the gravity-only model underestimates the decline of prices in developed countries following China s openness. In the presence of headquarters gravity, MNEs from developed countries expanded their production in China after the liberalization of China s exports, utilizing cheap Chinese labor to serve their home countries and countries close to their home countries with low trade costs. Through this channel, consumers in developed countries benefit from the low-priced made-in-china, a large fraction of which is made by Chinese affiliates of foreign MNEs. Consequently, headquarters gravity is important to understanding the welfare impacts of China s openness, especially the impacts on firms and consumers in developed countries. If a developed country plans to restrict its trade and FDI with China, it should be aware of the negative impacts on its own firms and consumers. 8 Conclusion My paper enhances our understanding of MNEs export behaviors by (1) documenting a novel fact named headquarters gravity by which MNE affiliates are more likely to make sales in markets closer to their headquarters countries and (2) estimating headquarters gravity from micro data and quantifying its impacts on trade, production, and welfare. My quantitative exercises suggest that (1) headquarters gravity accounts for a large fraction of international trade, especially exports from developing to developed countries, (2) headquarters gravity is essential to understanding the relocation of MNEs activities following trade liberalization and (3) ignoring headquarters gravity will lead to sizable underestimation of the welfare gains from China s openness for developed countries. By discussing the advantage of MNE affiliates in accessing international markets, I iden- 40

41 tify a new type of knowledge transferred by MNEs to host countries: trading technologies. Traditionally, the literature emphasizes the production technologies brought by MNE affiliates from their parents, which are universally applicable to serve all markets. In contrast, utilizing detailed information about the headquarters locations and exporting destinations of MNE affiliates, I have identified destination-specific trading technologies brought by foreign MNEs, which have been ignored by the literature. For model tractability and transparent estimation using the data I have, I have abstracted within-firm cannibalization away from my model. Being important as itself, cannibalization can be re-introduced and identified using richer data that contains information on MNE affiliates in countries other than China. Finally, in this model, I rationalize headquarters gravity entirely by variable and fixed marketing costs. As mentioned before, headquarters gravity could also have been loaded onto preferences. With more detailed information on MNEs global sales and pricing, I can extend my model to separately identify the demand and supply factors of headquarters gravity. This will further improve our understanding of the MNEs global operations. 41

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47 Figure 1: Foreign MNE Manufacturers in Host Countries (Notes: Data for OECD countries is from FATS. Chinese data is constructed from various sources which will be described in the data section. All data is for the year 2001.) 47

48 Figure 2: Spatial Frictions Shaping Global Production and Sales 48

49 Figure 3: Timing of events 49

50 (a) All (b) Without i = n Figure 4: Entry Hurdle w.r.t. Distance between Headquarters and Destination (Note: Entry hurdle H iln is defined in Equation (19) as a cutoff of the sales in China above which an affiliate from country i and located in China would export to market n. The gray area is the 95 percent confident interval.) 50

51 Figure 5: Entry Hurdle w.r.t. Social and Economic Distances (Note: Entry hurdle H iln is defined in Equation (19) as a cutoff of the sales in China above which an affiliate from country i and located in China would export to market n. The box covers the 25th percentile to the 75th percentile. The median is marked in the box.) 51

52 (a) Baseline (b) Gravity-only Figure 6: Normalized Global Sales of MNEs in China: Model vs Data (Note: Normalized global sales are computed by Equation (26). All variables are in logs. Regressing log X iln from Chinese firm data on the one from the baseline model delivers a coefficient equal to 1.02 with standard error.16.) 52

53 Figure 7: Counterfactual Switching of Chinese Export Destination (Note: No HG refers to the counterfactual exercise in which ˆµ iln = ζ ln ζ in and Êiln = Em ln E for all n l. in m No MP refers to the counterfactual exercise in which γ il = for all i l.) 53