Immigration, Trade and Productivity in Services: Evidence from U.K. Firms

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1 Immigration, Trade and Productivity in Services: Evidence from U.K. Firms Gianmarco I.P. Ottaviano (LSE) Giovanni Peri (UC Davis) Greg C. Wright (UC Merced) August 18, 2014 Abstract This paper explores the impact of immigrants on the imports, exports and productivity of firms producing services in the U.K. Immigrants may substitute for imported intermediate inputs (offshore production) and they may affect the productivity of the firm as well as its export behavior. The first effect can be understood as the re-assignment of productive tasks between offshore and immigrant workers, the second can be seen as a productivity or cost cutting effect due to immigration, and the third as the effect of immigrants on specific trade costs. We test the predictions of our model using immigration shocks across U.K. labor markets, instrumented with an enclave-based instrument that distinguishes between aggregate and bilateral immigration, as well as immigrant diversity. We find that immigrants increase overall productivity in serviceproducing firms, revealing a cost cutting impact on these firms. Immigrants also reduce country-specific offshoring costs, indicative of a reallocation of tasks and, finally, they increase country-specific exports, implying an important role in reducing communication and trade costs. Key Words: Immigration, Services Trade JEL Codes: F16, F10, F22, F23 Gianmarco I.P. Ottaviano, Department of Economics, London School of Economics and Political Science, Houghton Street, London, WC2A 2AE, U.K. g.i.ottaviano@lse.ac.u.k. Giovanni Peri, Department of Economics, UC Davis, One Shields Avenue, Davis, CA gperi@ucdavis.edu. Greg C. Wright, Department of Economics, University of California, Merced, 5200 North Lake Dr., Merced, CA gwright4@ucmerced.edu. This paper was written as part of the project Europe s Global Linkages and the Impact of the Financial Crisis: Policies for Sustainable Trade Capital Flows and Migration funded by the Volkswagen Foundation. 1

2 1 Introduction The connection between immigration and productivity, and immigration and trade, has been the focus of active research for several years. Several papers have analyzed the role of immigrants, especially highly educated ones, in promoting skill diversity, with potentially positive productivity effects (Ottaviano and Peri 2005, Ortega and Peri 2013, Brunow, Trax and Sudekum 2013). Other papers have focused on the role of immigrants in promoting specialization and the division of jobs along the manual to complex task spectrum (Peri and Sparber 2009, Damuri and Peri, 2014). Within this literature researchers have recognized that immigrants may be substitutes for the performance of tasks offshore (Ottaviano et al 2013), thereby generating a cost-reduction effect that may increase the firm s productivity in the same way as offshoring does (Grossman and Rossi-Hansberg 2009). To the extent that this substitution effect exists, it will produce a negative correlation between the employment of immigrants and imports of intermediate goods (i.e., offshoring) by the firm. A separate branch of the literature has analyzed, instead, the effect of immigrants in promoting goods exports via the reduction of bilateral trade costs, by enhancing information flows, trust and linkages between countries (see Felbermayr, Grossman and Kohler 2012 for a review of this literature). Most of the literature described above has analyzed trade in goods and, as a result, has focused narrowly on firms in the manufacturing sector. To the best of our knowledge, no paper has analyzed the impact of immigration on the imports, exports and productivity of firms who trade in services. While immigrants origincountry networks may lower the costs of both goods and services trade, selling services in foreign markets may require overcoming additional barriers. For instance, selling business services abroad may require an understanding of the idiosyncrasies of country-specific business culture, while selling legal services may require an understanding of the differences in each country s legal systems. In this sense, trade in services may necessitate a complex understanding of a foreign market, and immigrants may facilitate that understanding. It is also worth noting that immigrants may generate larger productivity gains in services relative to goods. Since services are often knowledge-intensive, and individuals knowledge is inherently imperfectly substitutable 1 (see Garicano and Rossi-Hansberg, 2014), the new ideas and solutions to problems that immigrants bring are likely to complement native knowledge in the provision of services, above and beyond the complementarities that have been shown to arise in goods production (e.g., see Ottaviano and Peri, 2012). In this paper, we jointly analyze the impact of an increase in total immigration, as well as of immigration from specific countries, on productivity and we tie these flows to the firm s bilateral imports and exports of services with those countries. In doing so, we are able to separately estimate three effects of immigration: the first is a productivity effect, due to overall cost-reduction in production, the second is an import substitution effect, due to the relative reduction in the cost of performing some tasks by immigrants relative to performing 1 As Garicano and Rossi-Hansberg (2014) note, having 10 workers who cannot solve a problem is no better than having 5. 2

3 them offshore, and the third is an export promotion effect of immigrants, due to a reduction in bilateral trade costs. We do this in the context of the U.K., a country that is both the world s second most popular immigrant destination (in absolute numbers) and the second largest service trader (in value). Just in 2013, approximately half a million immigrants arrived in the U.K. 2 As shown in Figure 1, during the period we examine immigrants were distributed across U.K. labor markets (Travel to Work areas or TTWA for short) in very different proportions of the local labor supply, generating significant geographic heterogeneity in the supply of their specific skills. At the same time, services exports and imports accounted for 9.4 percent and 7.4 percent of U.K. GDP, respectively. Figure 2 shows the volume of trade by type of aggregate service in which U.K. firms are active. Various types of Business Services and Royalties/Licensing constitute the bulk of value of UK import and export of services. 3 In the empirics we exploit data covering U.K. firms over which links information on firms producing and exporting services with information on the destination of the exports and origin of the imports for each firm. We then link this firm data with data from the U.K. Quarterly Labour Force Survey that describes worker characteristics in the local labor markets (defined as travel-to-work areas, or TTWAs). We consider the inflow of new immigrants in a TTWA as a shock in the immigrant supply in the local labor market. We address two primary questions in this paper: first, does increased immigration to an area affect the level of services imports (offshoring) from and exports to the country of origin of immigrants? For instance, services imported by U.K. firms (e.g. accounting, technical, or computer services) could be reassigned from the remote location to in-house provision if the individuals performing them immigrate to the U.K. Figure 3 presents a correlation that is consistent with this notion. The figure plots the change in the share of immigrant employment across TTWA-sector and country of origin cells against imports of services by local firms in the sector-ttwa from the same country. The existing negative and significant relationship between them is consistent with substitutability between the two. Conversely, some services that are exported, especially those requiring knowledge of the language, institutional settings or norms of a country, could be exported more efficiently if some individuals from the country migrate and work in the U.K. Figure 4 provides a stylized fact consistent with this idea. The figure shows a positive relationship between the change in the share of immigrants in a labor market-country of origin cell and the change in bilateral exports (to the same country) of services from the same labor market. The second question we address is whether the aggregate (rather than bilateral) presence and diversity of immigrants affects labor productivity in the service-producing firm, thereby inducing firms to export or import more to all markets. Figures 5 and 6 show that there is indeed a positive relationship between the immigrant 2 Source: Office of National Statistics. 3 See Table 1 for a more detailed list of services included in the analysis. 3

4 share in a local labor market and aggregate exports and imports of services. Motivated by these stylized facts, we develop a simple model in which the presence of immigrants may have three effects. First, they may substitute for offshore workers and, therefore, for the imports of services. Second, they may increase firm productivity by reducing the labor costs faced by the firm. Finally, they may reduce the specific cost of exporting to their country of origin, by improving communication and delivery of the service. The offshore-substitution effect and the export promotion effect are very likely to be country-specific, due to the specificity of traded services. The overall productivity effects, instead, are generated by immigrants more generally, and potentially by their overall diversity. Hence we can distinguish between these effects by exploring the impact of an exogenous increase in the number and diversity of immigrants on the productivity of the firm and, separately, the effect of an increase in immigrants from a specific country on the level of imports and exports from those countries. The literature has thus far not attempted to separate these effects from one another, and we believe that the exercise may be particularly relevant for the case of service-producing firms. Our main findings can be summarized as follows: (i) there is a bilateral import-substitution effect of immigrants; (ii) there is a bilateral export-promotion effect of immigrants, particularly for language-intensive and institutional-knowledge intensive services; (iii) there is a positive productivity effect of aggregate immigration that, in some cases, is associated with country-of-origin diversity. The rest of the paper is organized as follows: Section 2 reviews the related literature and Section 3 describes the data we use. Section 4 presents some basic facts regarding immigration and services trade in the U.K. Section 5 presents a model and discusses the predictions that the model generates. Section 6 presents the main results and Section 7 provides some concluding remarks. 2 Related Literature Beginning with Gould (1994) and Head and Ries (1998), a large literature has explored the effect of immigration on bilateral trade flows, typically finding an important role for immigrants in facilitating trade with their country of origin i.e., immigration and trade (especially exports) are typically found to be complements. In particular, immigrants are found to reduce barriers to exports by facilitating communication between firms and reducing set up costs in the destination country (Rauch and Trindade, 2002). Immigrants may at the same time demand goods and services from their home countries, leading to an increase in imports. Putting these ideas together, many researchers have looked for an asymmetric effect of immigrants on trade, biased toward a relative increase in imports. However, it has recently been pointed out (see Ottaviano, et al, 2013) that when a good is part of a production chain, such that firms must decide whether to produce the good locally or overseas (offshore), overseas workers and immigrants may be substitutes in production. Increased immigration may reduce imports of intermediate goods. On the whole then, it is not clear whether one should expect an asymmetric effect on 4

5 trade due to immigrants. In terms of the economic magnitudes involved, immigrants seem to generate a substantial amount of trade on average. For instance, Genc, et al (2011) perform a meta-analysis of this literature and conclude that a 10 percent increase in the number of immigrants to a country increases the volume of trade by 1.5 percent. At the same time, the literature finds that the immigrant-trade relationship may be very different depending on the type of good being traded (Rauch and Trindade, 2002) and on the initial stock of immigrants (Gould, 1994), among other dimensions. For our purposes, it is important to note that the effects on services trade are mostly unexplored. 4 A more recent branch of the literature has estimated the productivity impact of immigrants. In this framework productivity gains may arise simply from the cost-savings realized from hiring lower-cost immigrant workers (if a firm can discriminate wages of natives and immigrants). Beyond this, several studies also find evidence suggestive that the change in skill mix in a local labor market due to immigration may induce firms to adopt new production techniques that use the immigrant labor factor intensively and these new techniques may generate productivity gains (Beaudry and Green (2003, 2005); Beaudry, et al (2010); Caselli and Coleman (2006)). Another channel through which immigration may foster productivity gains is through increased competition or specialization of production activities between natives and immigrants. Peri (2012) estimates the long-run impact of immigration in U.S. states and finds a positive effect on state-level TFP that can be explained in large part by increased specialization. Similarly, estimates from Ottaviano, et al (2013) suggest a positive, short-run productivity effect at the industry level. On the other hand, Brunow, Trax and Sudekum (2013) find little direct impact of immigrants in Germany on firm-level productivity, though they do find an effect that operates through immigrant diversity. Similarly, Paserman (2013) exploits the mass migration of high skilled workers from the Soviet Union to Israel in the 1990s, finding no overall productivity effects related to the immigrant share, though he does find a positive effect in high-tech industries. 3 Data Our dataset combines U.K. data on workers, firms and trade in services over the period These data are collectively compiled from three sources: the Quarterly Labour Force Survey (QLFS), the Annual Respondent s Database (ARD) and the International Trade in Services (ITIS) dataset. The QLFS is a one percent sample of individuals in the U.K. and it includes a variety of demographic, education and work-related information, including the geographic location and industry in which an individual works. The ARD provides information on U.K. businesses and is the U.K. equivalent of the U.S. Longitudinal Respondents Database. It is administered by the Office of National Statistics and the data are drawn from the Annual Business Inquiry. The 4 An exception is Gheasi, et al (2011) who explore the impact of immigrants on tourism. 5

6 data consist of the full population of large businesses (those with more than 100 or 250 employees depending on the year) as well as a random sample of smaller businesses. 5 The ARD includes many firm-level variables and, for our purposes, the most relevant will be the total value of imports and exports of services by the firm, as well as the 4-digit industry and geographic location of the firm. We can also control for various firm features such as capital expenditures and employment. The ITIS dataset consists of firm-level information on the value of imports and exports of services by country of origin/destination and by service type, details that are missing from the aggregate trade values provided by the ARD. The ITIS includes information on producer services and excludes travel and transport, higher education, the financial sector and the public sector, each of which are covered in other surveys that are, unfortunately, not available to researchers. We link the ARD with the ITIS via the common establishment identifier in both datasets, and we link this combined dataset with the QLFS by the travel-to-work area (TTWA) and one-digit sector of the establishments and workers. Though we could link these datasets at a more disaggregate level (we could do so by 4-digit industry, for instance), because the QLFS is a one percent sample of workers we need to be sure there are an adequate number of workers in each cell. By matching at the one-digit sector level we ensure that each cell contains at least 1000 immigrant hours worked from each of the top 20 immigrant origin countries, thereby alleviating concerns about measurement error and the related attenuation bias 6. We will then focus on the impact of immigrants from these specific countries when analyzing any bilateral effects. Ultimately, the final dataset encompasses workers from 142 countries (though the bilateral analysis focuses on the top 20) located across 243 TTWAs, working within 6 one-digit industries and trading with 180 countries (again, bilateral effects are constrained to the top 20 countries of immigrant origin) over 7 years. We will exploit firm-by-year level variation in our dependent variables and TTWA-sector-by-year level variation in the immigration regressors. There are 309,930 year-firm combinations and 640,054 year-firm-origin combinations. In addition, there are 11,649 export bilateral matches i.e., instances in which a cell contains an immigrant from, and some firm s export services to, a particular country. In our empirical analysis we will also distinguish between broad categories of services, in which the categories are defined in order to account for the different ways in which service provision interacts with immigrant workers. Specifically, we categorize service output as belonging to one of three categories: Technical-Financial, Legal and Related, or Language-Human Resources. Table 1 lists how each detailed service type is categorized in one of these three broad categories. The idea is that immigrants may facilitate or, alternatively, substitute for trade in services when language or culture is an important aspect of the service provision, and we refer to these services as Language-Human Resource (LHR) intensive services. Similarly, when service provision relies on country-specific 5 For a comprehensive description of this dataset, see Criscuolo, Haskel and Martin (2003). 6 Aydemir and Borjas (2011) show that attenuation bias can be an important concern when estimating the impact of immigrants on native labor market outcomes with cells of small size. 6

7 norms and institutions, immigrant workers may be particularly strong substitutes or complements these are what we call Legal and Related (LR) services. Finally, Technical-Financial (TF) services may be relatively unaffected by country-specific knowledge so that immigrants are not cost-reducing for firms when trading these service types. Finally, we also collect information on services trade barriers from the OECD. 7 Since the bulk of U.K. exports are with OECD countries, these measures will serve as useful proxies for the overall barriers faced by U.K. firms in exporting services to foreign markets and will serve as an important proxy of import and export costs. 4 Stylized Facts on Services Trade and Immigration To illustrate some important features of service production and trade, that will inform the development of our model, we augment the stylized facts presented in the introduction with some additional facts. Around 8 percent of firms trade in services. For those that export, the mean export-to-sales ratio is 30 percent and the corresponding number for imports is 10 percent. Despite these relatively small shares, services traders are an important part of the economy, accounting for 22.5 percent of total employment and 30 percent of value added. Figures 7 and 8 document the primary destinations and source countries for service imports and exports and here we see the dominant role of the U.S. and, unsurprisingly, a strong role for the large E.U. countries. This pattern is not unlike the one for goods 8 In fact, the cross-section of services traders displays much of the same pattern of heterogeneity as goods traders. In particular, a very few firms are responsible for the bulk of services trade, and within firms the volume of trade is positively associated with firm size and productivity. Along the extensive margin larger and more productive firms are much more likely to trade in services, and to trade with more countries and in a wider variety of services. At the same time, on average, a service exporting firm sells 68 percent of their output to a single market, while importing 76 percent from a single market. Even more starkly, a single service type accounts for 95 percent of exports and 86 percent of imports for the average service trading firm (see Breinlich and Criscuolo, 2010). Each of these facts is broadly consistent with the characteristics of good trading firms, as evidenced by the literature. Hence firm heterogeneity, the presence of an important intensive and extensive margin of trade and the concentration in one foreign market are feature that motivate the structure of our model below, partly inspired to good production and trade. Immigration to the U.K. was significant over the period 1999 to This phase of large immigration inflows began in the early 1990s when there was a sharp uptick in the number of immigrants to the U.K.. 7 See for more information 8 For additional facts with respect to services trade, see Breinlich and Criscuolo (2010). 7

8 Importantly, looking over the period 1990 to 2005 twice as many immigrants worked in professional and managerial occupations relative to other less skilled occupations. Immigrants, that is, worked in occupations that are used relatively intensively in the provision of services. In terms of policy events, it is important to note that in 2004 several Eastern European countries joined the European Union and their workers gained access to UK labor markets. This partly altered the composition of new immigrants, tilting it toward the less skilled. 9 In addition, there was an expansion of the points-based immigration system in 2002 by the U.K. government in order to target highly skilled immigrants, a policy that provided a route to U.K. citizenship for both high-skilled workers and their spouses and children. Part of the aggregate variation in immigration inflows and countries of origin that we exploit is due to these policies. In Figure 9 we document the cross-sectional distribution of immigrants across education groups during our period, along with the native distribution. We can see that, as it has already been documented for the United States (e.g. Ottaviano and Peri 2012), that UK immigrants are polarized in their educational attainment relative to natives, and they are over-represented among highly and less educated groups, while under-represented in the intermediate education groups. 5 The Model In this section we present a model of immigration and international trade in services in which firms are heterogeneous in their productivities, as in Melitz (2003). Although heterogeneous firm models have typically been motivated by stylized facts that are based on goods producers, in the previous section we noted the wide-ranging similarities between goods producers and services producers. Most importantly, services traders are like goods traders larger and more productive than non trading firms. Moreover the most productive firms sell a wider variety of services in a greater number of markets. These facts, along with the relationships depicted in Figures 3 to 6, motivate the model presented here. There are two symmetric countries trading goods and services with each other and two types of workers who are the natives of the two countries. The expatriated natives of a country are the immigrants to the other country. Natives inelastically supply an efficiency unit of labor when employed in their country of origin and 1/µ units when emigrated, with µ > 1 due to migration frictions. To analyze the effects of an exogenous migration shock through comparative statics, the numbers of workers of the two types and their distribution between countries are taken as given. In particular, there are L workers of each type and a share λ (0, 1) of them reside in their countries of origin. Accordingly, each country is endowed with λl units of native labor and (1 λ)l/µ units of immigrant labor. By increasing the number of efficiency units of immigrant labor, lower µ captures an absolute and relative increase in immigrant labor supply. This is the immigration shock whose effects we are going to analyze. 9 These facts come from the U.K. International Passenger Survey. Similar facts are also reported in Hatton (2005). 8

9 All workers share the same preferences and the two countries have access to the same technologies, which will support a unique symmetric equilibrium. Preferences are captured by a Cobb-Douglas utility function defined over an aggregate good M and services Q: U = Q α M 1 α with α (0, 1). Good M is freely traded between countries and is produced under perfect competition through a constant-returns-to-scale technology that employs one efficiency unit of labor per unit of output. The two worker types are perfectly substitutable in the production of M and this good is chosen as numeraire. Free trade and marginal cost pricing then pin down also the equilibrium wage per efficiency unit to one for both worker types. Services Q are provided in two stages: an intermediate upstream stage U and a final downstream stage D. 5.1 Final Services There is a continuum of horizontally differentiated D-services with constant elasticity of substitution δ > 1. Their CES quantity and price indices are [ Q = Ω ] δ Q(ω) δ 1 δ 1 δ dω and [ P = P (ω) 1 δ dω Ω ] 1 1 δ (1) where Q(ω) is the quantity of D-service ω, P (ω) is its price, and Ω is the endogenous set of D-services available. D-services are provided under monopolistic competition and increasing returns to scale. Input requirements are met in terms of two types of horizontally differentiated U-services, associated with the two worker types. Entry and exit of heterogeneous D-providers are modeled as in Melitz (2003). There is a large pool of potential entrants that are ex ante identical. Entry in either country requires a sunk input requirement f E incurred in terms of native U-services. The provision of a D-service then faces a fixed input requirement f, also incurred in terms of native U-services, and a marginal input requirement 1/ϕ, incurred in terms of a CES composite of native and immigrant U-services with elasticity of substitution between them equal to σ > δ > 1. Accordingly, the total cost facing a D-provider with efficiency ϕ is C(ϕ) = p o f + p Q(ϕ) ϕ 9

10 where p is the exact price index associated with the CES composite of native and immigrant U-services p = ( p 1 σ o + p 1 σ ) 1 1 σ a (2) with p o and p a denoting the prices of native and immigrant U-services. D-services can also be exported incurring a fixed export cost p a f X paid in terms of immigrant U-services and a per-unit iceberg trade cost requiring τ > 1 units to be sent for a unit to reach destination. A D-provider s efficiency ϕ is determined upon entry as a random draw from a Pareto distribution with c.d.f. and support ϕ [ϕ M, ). G(ϕ) = 1 ( ϕm ϕ ) k (3) k > δ 1 is the concentration parameter of the Pareto distribution: larger k reduces the variability of efficiency draws away from the lower bound ϕ M. All D-entrants draw their efficiency levels simultaneously and the outcomes are common knowledge. They then decide whether to provide their final services or exit the market. The Law of large numbers implies that for all variables ex ante means and ex post averages coincide. Profit maximization by a D-provider with efficiency ϕ entails that the delivered prices of its final service to domestic and foreign customers are equal to P d (ϕ) = δ p δ 1 ϕ, P x (ϕ) = δ p δ 1 ϕ τ (4) with associated revenues R d (ϕ) = αep δ 1 ( P d (ϕ) ) 1 δ, R x (ϕ) = αep δ 1 (P x (ϕ)) 1 δ (5) and profits Π d (ϕ) = Rd (ϕ) δ p o f, Π x (ϕ) = Rx (ϕ) δ p a f X (6) As exit is free, provision to a given market is chosen only by entrants who can make non-negative profits in that market. For the domestic market, these are the entrants whose efficiency does not fall short of the domestic cutoff efficiency level ϕ d such that Π d (ϕ d ) = 0: marginal providers must be indifferent between serving the domestic market or not. Analogously, exporters are entrants whose efficiency does not fall short of the export cutoff efficiency level ϕ x such that Π x (ϕ x ) = 0: marginal exporters must be indifferent between exporting or 10

11 not. Given that Π d (ϕ d ) = 0 and Π x (ϕ x ) = 0 imply ϕ x ϕ d = τ ( ) 1 pa δ 1 f X p o f (7) assuming that parameter value are such that the right hand side of (7) is larger than one ensures that only the most efficient D-providers also export. As entry is free too, potential entrants must be indifferent between entering or not. Indifference requires their expected profit [ 1 G ( ϕ d)] Π to exactly match the sunk entry cost p o f E so that ( ) ϕ d k Π = p o f E (8) ϕ M where Π is the expected value of a D-provider s total profit Π d (ϕ) + Π x (ϕ) from (6) conditional on its efficiency being above the relevant cutoffs [ Π = δ 1 ( k δ + 1 p of 1 + τ k pa f X p o f ) 1 k ] δ 1 (9) Ex post this is also D-providers average profit as well as the profit of the D-provider of average efficiency. With free entry, expenditures E on D-services are fully absorbed by D-providers revenue R. This pins down the mass ( numbers ) of D-providers located in each country to N d = δ 1 E k Π (10) as R = N d R with R = k/(δ 1)Π denoting average revenue. Taken together, (8) and (9) imply that the equilibrium domestic cutoff equals { ϕ d δ 1 f = ϕ M k δ + 1 f E [ 1 + τ k ( pa p o f X f ) 1 k δ 1 ]} 1 k (11) with the corresponding export cutoff ϕ x determined by (7). In turn, the equilibrium values of ϕ d, ϕ x and N d determine the associated numbers of exporters N x = ( ϕ d /ϕ x) k N d and entrants N e = ( ϕ M /ϕ d) k N d. The price index of D-services (1) can be finally restated as { [ P = δ p k δ 1 ϕ d k δ + 1 N d 1 + τ k ( pa f X p o f ) 1 k ]} 1 1 δ δ 1 (12) 11

12 5.2 Intermediate Services U-services are provided under perfect competition and constant returns to scale. They can be traded between countries facing an iceberg trade friction ρ > 1. U-services of a given type are provided only by workers of the same type. U-services of the same type are horizontally differentiated. They have unit mass and constant elasticity of substitution ε > σ: U-services of the same type are better substitutes than U-services of different types. The price indices of native U-services provided to a country by native and foreign workers are p o = p a = [ 1 0 [ 1 0 ] 1 p o (υ) 1 ε 1 ε dυ ] 1 p a (ν) 1 ε 1 ε dυ (13) Following Eaton and Kortum (2002), for each native U-service υ (foreign U-service ν), the output levels per efficiency unit z d o(υ) and z x o (υ) (z d o(υ) and z x o (υ)) of native (foreign) resident labor and native (foreign) expatriated labor are determined as independent random draws from two identical Frechet distributions with c.d.f. F (z) = e z θ for z [0, ). The random variables Z, whose realizations determine z, has mean e γ/θ (where γ = 0.57 is the Euler Constant) while ln Z has standard deviation π/(θ 6) (with π ). Accordingly, θ > 0 is the concentration parameter of the Frechet distribution: larger θ reduces the variability of efficiency draws away from a larger mode. This parameter captures the heterogeneity of worker types efficiency in providing U-services, as parameter k does for D-provider efficiency under the Pareto distribution. As U-services can be traded, each of them can be alternatively sourced domestically or imported ( offshored ) depending on which option is the cheaper. Marginal cost pricing under perfect competition entails [ ] 1 p o (υ) = min zo(υ) d, ρµ zo x (υ) [ ] µ p a (ν) = min za(ν) d, ρ za(ν) x where the presence of µ is explained by the fact that, due to the migration friction, one unit of output requires µ efficiency units of expatriated labor. Under (??), the Law of large numbers implies that the share of imported native U-services provided by native expatriates is π X o = µ θ ρ θ 1 + µ θ ρ θ 12

13 Analogously the share of imported foreign U-services provided by foreign natives ( offshore worker ) equals π X a = ρ θ µ θ + ρ θ (14) As for the price indices (13), they can be expressed as p o = η [ 1 + µ θ ρ θ] 1 θ (15) p a = η [ µ θ + ρ θ] 1 θ 1 1 ε with η = [Γ (1 (ε 1)/ε)] and where Γ ( ) is the Gamma function. The marginal cost of D-providers (2) can then be rewritten as p = η { [(1 + µ θ σ 1 ρ θ) θ + ( µ θ + ρ σ 1 θ) θ ] θ } 1 θ σ 1 (16) Finally, due to the fact that there is free entry in all activities and the Law of large numbers holds for all services, income consists only of labor income: E = λl + (1 λ)l/µ. This closes the characterization of the general equilibrium of the economy. 6 Comparative Statics and Empirical Predictions The model matches the stylized facts highlighted in Section 4. In particular, only a small fraction of D-service providers export. On average, exporters are more efficient and larger in terms of revenues than non-exporters. Even though exporters are a small fraction of service providers, they generate a large fraction of industry revenues. Though small in number, the largest exporters account for the largest fraction of exports. More specifically, the model also generates several additional predictions on the effects of an increase in immigrant labor supply (lower µ) that we can bring to further empirical investigation. According to (15) and (16), as µ falls the price indices p o, p a and p also fall. However, the price index p a of foreign U-services D- providers use for their owns exports falls faster than the price index p of U-services they use for providing their services, and this falls faster than the price index p o of native services used for entry and distribution in the domestic market. Hence, the relative price p a /p o of imported foreign U-service decreases. First, in terms of imports, as shown by (14), the contraction of p a /p o implies that the share π X a of imported foreign U-services (and, thus, also the probability that ex ante a D-provider imports foreign services) falls. In other words, as immigrant labor supply rises, the extensive margin of imports by D-providers shrinks. 13

14 Moreover, as the value of D-providers imports of U-services is ( ) θ ( ) ε 1 ( µ r X po p = ρ p a p o ) σ 1 ( ) δ 1 P E p with θ + 1 > ε > σ > δ > 1, smaller µ implies smaller r X : as immigrant labor supply rises, also the intensive margin of imports by D-providers shrinks. Second, in terms of provision, by (11), smaller p a /p o implies that both the cutoff efficiency ϕ d and the 1 average efficiency ϕ d δ 1 = [k/ (k + 1 δ)] ϕ d of D-providers increase. Due to a selection effect, as immigrant labor supply rises, D-service providers become on average more efficient. Moreover, given (7), the ratio ϕ x / ϕ d between the average efficiencies of exporting and purely domestic D-providers decreases. Third, in terms of exports, lower ϕ x /ϕ d implies that the share of D-providers that export rises. In other words, as immigrant labor supply rises, the extensive margin of exports by D-providers widens (and so does the probability that ex ante a D-provider exports). As for the intensive margin, in order to understand the behavior of individual exports, one has to account for the selection effect that, through higher ϕ d, pushes the aggregate price index P down. Given (5), the value of exports by a D-provider with efficiency ϕ is R x (ϕ) = αep δ 1 δ ( δ τ 1 δ p δ 1 ϕ ) 1 δ When P is hold constant, R x (ϕ) is a decreasing function of p and, therefore, a decreasing function of µ. Hence, controlling for the selection effect, as immigrant labor supply rises, the intensive margin of exports by D- providers widens. When instead the selection effect is not controlled for, lower P more than offsets the fall in p. The D-provider s value of export becomes R x (ϕ) = αp o fτ 1 δ ( ϕ ϕ d ) δ 1 which is a decreasing function of µ as it is cheaper for domestic competitors to enter (higher ϕ d ) and provide their services (lower p o ). Also average exports are a decreasing function of µ as it is cheaper for other exporters to sell abroad (lower p a ) R x = k k δ + 1 αp af X 7 Main Empirical Predictions Our two-country model has assumed only one export destination/import origin and, accordingly, only one immigrant group per country. This has been instrumental to obtain a rich set of empirical predictions on the effects of immigrant labor supply on the efficiency and the import-export behavior of heterogeneous service 14

15 providers. In approaching the data, we have now to account for several export destinations, several import origins and, most crucially, several immigrant groups. This is straightforward to do in the case of imports and exports whereas, in the case of service providers efficiency, we will investigate the possible role of heterogeneity among immigrant groups by introducing a measure of country of birth diversity. The main questions that we explore in the empirical section are: 1. Is there a productivity effect associated with the share of immigrants in total employment and their diversity in a TTWA-sector? 2. Is there a substitution effect associated with immigrants such that the share of immigrants from country i in local employment reduces imports from ( offshoring to) country i? Note that, as in the model, the primary margin of substitution is between immigrants and offshore workers then the increase in immigrant share should not affect native employment. 3. Is there a reduction in export costs due to immigrants, such that the share of immigrants from country j in local employment positively affects exports to country j? Furthermore, we can exploit differences in the type of services being traded in order to test two additional implications of the logic of the model. First, the substitution of immigrants for offshoring should be greater the stronger is the relevance of linguistic, cultural or, more generally, country-specific skills that are associated with the provision of the service. Similarly, these effects may be stronger where there is a larger linguistic or cultural difference between country i and j. Second, the export effect of immigrants should also be stronger for services that have a strong country-specific component. 8 Empirical Strategy We adopt two main specifications in order to test the three results from the model above. We test Proposition 1, which states that immigration into sector-ttwa j in period t may raise the total labor productivity and total value of exports of local firm i in that sector-ttwa, through the following regression: ln(y) ikt = φ i + θ t + ξ st + ξ at + β 1 ImmShr kt + β 2 ImmDiv kt + β x ln X ijkt + ɛ ijkt (17) The units of observation are firms in TTWA-Sector cells in each year. In (17) the outcome y ikt can be either the labor productivity or the value of exports of firm i belonging to area-sector cell k in year t. ImmShr kt is the share of immigrants in TTWA-sector cell k; ImmDiv kt is a measure of country of birth immigrant diversity in cell k; X ijkt is a set of firm-level control variables; φ i and θ t are firm and year fixed effects, respectively; ξ st are sector-by-year fixed effects and ξ at is a TTWA-by-year effect; and the term ɛ ijkt captures zero-mean idiosyncratic errors. We cluster standard errors at the TTWA-sector level, the level of variation of our regressors of interest. 15

16 The coefficients of interest are β 1 and β 2. These capture the aggregate effect on labor productivity and export intensity of the share of immigrants and of their diversity. When these coefficients are positive and significant it indicates that immigrants produce a cost saving effect due to reallocation of tasks and/or a productivity effect due to the diversity of their skills. The second and third implications are tested by running the following regression: ln(y) n ikt = φ i + θ t + ξ st + ξ at + γ nt + β 1 ImmShr kt + β 2 ImmDiv kt + β 3 ImmShr n kt + τ jn + β x ln X ijkt + ɛ ijkt (18) In this case the units of observation are firm-by-export destination cells. In (17) the outcome y n ikt can be either the value of intermediate imports of firm i from country n (to test Proposition 2) or the value of exports from firm i to country n in year t (to test Proposition 3). ImmShr kt is the share of immigrants in TTWAsector cell k; ImmDiv kt is a measure of country of birth immigrant diversity in cell k; we now also include ImmShrkt n, which is the employment share of workers from country n in area-sector cell k. X ijkt is a set of firm-level control variables; φ i and θ t are firm and year fixed effects, respectively; ξ st are sector-by-year fixed effects and ξ at is a TTWA-by-year effect; and now we also include γ nt, a destination-country specific annual trend. Export barriers to services trade, denoted by τ jn, are also included in the regression, and in doing so we use the OECD services trade barriers described above. In this case, while the coefficients β 1 and β 2 reflect the overall productivity effect due to immigrants on the imports and exports of the firm (depending on the left-hand side variable included), the coefficient β 3 now captures the effect of immigrants in replacing imported intermediates (i.e. offshore workers from exporting countries) or in reducing exporting costs. Hence the size and significance of these coefficients collectively allow us to test Propositions 2 and 3 from the model. 8.1 Identification and Instrumental Variable Strategy While we control for an array of fixed effects especially sector-year, TTWA-year and firm effects aimed at capturing unobservable local shocks and firm heterogeneity, the presence of unobservable shocks still threatens proper identification. If the inflow of immigrants in a TTWA-sector in a year is driven by a demand shock (in that sector-locality) and such a shock is correlated with the outcome yikt n then the estimated coefficients β 1, β 2 and β 3 may be inconsistent. In order to address this issue we construct instruments for the share of immigrants in a cell. The instrument that we use to isolate exogenous variation in the share of immigrant hours worked in a cell extends the method proposed by Altonji and Card (1991) and Card (2001). Specifically, we exploit the fact that foreigners from different countries have increased or decreased their relative presence in the U.K. according to changes in the cost of migrating and other factors that are specific to their countries of origin. In short, variation in the initial presence of immigrants from different countries who are working in a TTWA-sector cell 16

17 makes firms in that cell more or less subject to shifts in origin-specific cost and push factors. Using these two facts we impute the population of immigrant groups across these cells over time. Formally, we start with the average share of immigrant workers, by country of origin, working in each TTWA-sector in 1997, and we augment this share by the aggregate growth rate of the specific immigrant group s population to the U.K. relative to total U.K. population growth. In so doing we obtain IMMIV n jt the imputed number of immigrants from country n in cell j at time t. Summing across immigrant groups within a TTWA-sector cell, we obtain the imputed share of foreign-born in employment in that cell. We call this measure IMMIV jt and note that it varies across TTWA-sector cells and time.** 10 ** Its value relative to total employment in the cell will be the instrument for the immigrant share. Ultimately, because of localized ethnic networks (Bartel, 1989), we expect that the initial distribution of immigrants will be a strong predictor of future immigration flows into a TTWA-sector cell. To check that the constructed instrument is not correlated with some of the outcomes in the pre-1999 period we regress the growth in imputed immigrant share over , which constitutes our instrument, on the growth of native employment and wages across TTWA cells in the pre-period, We find no significant correlation between these variables. 9 Empirical Results In this section we present the results from estimating specifications (17) and (18) and in particular we report the coefficients β 1, β 2 and β 3 in tables that share a similar structure. We first present the impact of immigrants and their country of birth diversity on the productivity of the firm and on variables that should be correlated with productivity at the firm level (capital and employment). We then analyze how, controlling for this firm-level productivity effect, bilateral immigration affects bilateral offshoring and exports. 9.1 Immigrants and Firm Productivity If firms produce differentiated services, a greater variety of locally available skills can increase their productivity. Or, if workers specialize in tasks according to their relative ability, a broader variety of abilities could increase specialization and productivity. On the other hand, if differences in the place of birth of workers leads to costly coordination problems, then the increased presence of immigrants may cause a reduction in productivity.** 11 ** Using variation in immigrant shares across labor markets (represented by TTWA-sector cells), instrumented with the imputed value obtained from the pre-determined distribution of immigrants interacted with aggregate 10 This index is similar to the constructed shift-share instrument often used in studies of immigration in local labor markets (e.g., Card, 2001; Card and DiNardo, 2000; Peri and Sparber, 2009). **We could cite also Ottaviano and Peri, 2005 and 2006.** 11 On this maybe we could cite: Kahane, Leo, Neil Longley, and Robert Simmons. The effects of coworker heterogeneity on firm-level output: assessing the impacts of cultural and language diversity in the National Hockey League. Review of Economics and Statistics 95, no. 1 (2013):

18 flows by country of origin, we estimate the impact of the immigrant share on firm productivity. Table 2 presents the results from three specifications of the estimating equation (17) that include different combinations of fixed effects. Throughout, we always include firm fixed effects and always cluster standard errors at the sector-ttwa level, which is the level of variation of the explanatory variables in each of the specifications based on (17). The results, presented in Table 2, indicate that immigration inflows led to an increase in firm gross value added per worker (our measure of productivity), where a one percent increase in the share of immigrants in a cell led to a one to two percent increase in firm labor productivity. In contrast, while the OLS results suggest an association between immigrant diversity and firm productivity, the 2SLS estimates are not significant. 12 Table 3 then repeats specification (17) with firm investments in plant, machinery and equipment capital as the dependent variable. The estimates are positive and significant, though economically small, suggesting that the labor productivity gains may, in small part, accrue via an increase in the capital stock. Finally, Table 4 puts native employment on the left hand side and finds a small, positive and significant effect, suggesting that the labor productivity gains may also manifest in part through increased employment within the firm. 9.2 Immigrants and bilateral offshoring Table 5 presents the results of specification (2) where the dependent variable is firm imports of services. Both OLS and 2SLS results indicate a negative and significant effect of immigrants on bilateral services offshoring, suggesting that offshore workers and immigrants from the particular offshore country are substitutes. Moreover, the aggregate productivity effects are positive and significant, consistent with an overall cost savings effect that generates an increase in imports more broadly. Beyond these effects there is also a positive effect of immigrant (country-of-origin) diversity on firm imports. In terms of economic significance, the results suggest an important role for each channel. Over a period in which the overall share of immigrants in a sector-ttwa cell increased by an average of 0.3 percent per year, the 2SLS estimates indicate that these inflows raised the volume of services imports by an average of around 6 percent per year, clearly a large effect. The bilateral and diversity effects were also important. Bilateral offshoring rose by about one percent per year due to the rising immigration share while offshoring increased by about 0.3 percent per year due to increased immigrant diversity. Table 6 estimates the same specification (2) where the dependent variable is now more narrowly focused on each of the groups of services defined above. Columns (1)-(3) present estimates with respect to TF services, columns (4)-(6) focus on LR services and columns (7)-(9) focus on LHR services. The bilateral effects are negative and significant and of similar magnitude for LR and LHR services, and are unimportant for TF Services. These results fit an intuitive story in which immigrants substitute for foreign service provision when the services are intensive in language, cultural and institutional content. The estimates suggest that TF services, 12 We also note that the power in the first stage is significant, as evidenced by the reported F-statistics. 18

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