Firm-embedded Productivity and Cross-country Income Differences

Firm-embedded productivity and cross-country income differences Abstract We measure the contribution of firm-embedded productivity to cross-country income differences. By firm-embedded productivity we refer to the components of productivity that differ across firms and that can be transferred internationally, such as blueprints, management practices, and intangible capital. Our approach relies on microlevel data on the cross-border operations of multinational enterprises (MNEs). We compare the market shares of the exact same MNE in different countries and document that they are about four times larger in developing than in high-income countries. This finding indicates that MNEs face less competition in less-developed countries, suggesting that firm-embedded productivity in those countries is scarce. We propose and implement a new measure of firm-embedded productivity based on this observation. We find a strong positive correlation between our measure and output per-worker across countries. In our sample, differences in firm-embedded productivity account for roughly a third of the cross-country variance in output per-worker. 1 Introduction Differences in Total Factor Productivity (TFP) account for about half of the cross-country differences in income per-capita.1 Understanding TFP differences is thus at the center of Development Economics. A common view is that aggregate productivity is partly determined by knowledge and expertise that is embedded in individual firms in the form of blue-prints, management practices, and other intangible capital.2 This view has motivated a wide array of policies that promote firm-embedded productivity around the world, ranging from tax-incentives for R&D to incubator programs for startups.3 More recently, randomized control trials have shown that micro-level interventions fostering different aspects of firm-embedded productivity can improve firm outcomes.4 Nonetheless, the Macro Development literature has been silent on the aggregate contribution of firm-embedded productivity to cross-country income differences.5 This paper introduces and implements a framework for measuring the contribution of firm-embedded productivity to cross-country income differences. By ‘firm-embedded productivity’ we refer to the components of productivity that are specific to the firm and that can be transferred internationally. We contrast these components with ‘countryembedded factors’, which are available to all firms producing in a country and are internationally immobile, such as natural amenities, infrastructure, and workers’ quality. As noted by Burstein and Monge-Naranjo (2009), separating between these two components is challenging, as different combinations of firm-embedded productivity and countryembedded factors can result in the same level of output per-worker. Our approach overcomes this challenge by bringing to bear firm-level data on the crossborder operations of multinational enterprises (MNEs). We compare the market shares of the exact same MNE in different countries and document that they are roughly four times larger in developing than in high-income countries. We propose and implement a new measure of firm-embedded productivity based on this observation. Our central idea is that MNEs should have larger market shares in countries where aggregate firmembedded productivity is relatively scarce, as they face less competition in those coun1 See Hall and Jones (1999) and Caselli (2016). Prescott and Visscher (1980), Klette and Kortum (2004), Atkeson and Kehoe (2005), Bloom and Van Reenen (2007), and McGrattan and Prescott (2009). 3 See the policy report by Atkin et al. (2019) for a review. 4 For example, Giné and Yang (2009) and Atkin et al. (2017a) facilitate technology adoption at the firm level; Bloom et al. (2013) and Brooks et al. (2018) improve management practices; Cai and Szeidl (2017) and Atkin et al. (2017b) provide intangible capital in the form of business networks and market access. 5 Burstein and Monge-Naranjo (2009) is a notable exception that we discuss below. 2 See 1 tries. The observed differences in MNE market shares are indicative of large differences in the firm-embedded productivity of the competitors that MNEs face in each country. We develop this logic in a development accounting framework and measure aggregate firm-embedded productivity using data on market shares of the foreign affiliates of MNEs that simultaneously operate in multiple countries. The framework assumes that producers in a country are heterogeneous in their production efficiency and product quality (what we call ’firm-embedded productivity’), but access the same country-embedded factors and set a constant markup over their marginal cost. Thus, the market share of a MNE in a country is determined by the MNE’s productivity relative to the aggregate firmembedded productivity in the country.6 MNEs can transfer their productivity around the world but face different competitors in each country where they operate. Differences in market shares of the same MNE in different countries pin-down the difference in aggregate firm-embedded productivity between those countries. We attribute the residual differences in income per-capita across countries to differences in country-embedded factors. Of course, MNEs may not be able to fully transfer their productivity across countries. We allow for imperfect technology transfers by assuming that MNEs can only use a fraction of their productivity when operating abroad. This is the standard assumption in the multinational production literature when modeling imperfect technology transfers, home-bias in preferences, and other costs that are specific to MNEs. Under this assumption, the market share of a MNE can be relatively low in a country both if aggregate firm-embedded productivity in that country is high, or if the MNE faces large transfer costs. We control for these transfer costs in two straightforward ways. First, we focus on the cross-country variation in the market shares of MNE’s foreign affiliates (not parent firms), so we control for MNE-specific transfer costs that are common across foreign destinations. Second, we control for the country-pair specific component of the transfer costs using a gravity specification that follows Waugh (2010).7 We implement our framework using data on MNE revenues from ORBIS, a worldwide 6 The model does not take into account that, given their relatively large market shares, MNEs may be able to set higher markups in developing countries. Higher markups would push down MNEs market shares in these countries, so that the observed market shares would understate the true differences in competition and firm-embedded productivity across countries. 7 The gravity specification assumes that bilateral costs are a function of bilateral distance, country-pair specific taxes and subsidies for MNEs, and other country-pair specific characteristics, and it is common in the International Trade and Multinational Production literature. Waugh (2010) also controls for sourcespecific costs using fixed effects. Section 5 shows that our results are robust to using alternative gravity controls. 2 dataset maintained by Bureau van Dijk. The main advantage of ORBIS is the scope and accuracy of its ownership information: it details the full list of direct and indirect subsidiaries and shareholders of each company in the dataset, along with a company’s global ultimate owner and other companies in the same corporate family. This information allows us to build ownership links between affiliates of the same MNE, including cases where the affiliates and the parent are in different countries. We build these links at the firm-sector level to ensure that the affiliates in our comparisons are producing similar goods and services across countries. We focus on destinations where ORBIS has the most extensive coverage, so that our sample is mainly comprised of Eastern and Western European countries.8 Since ORBIS does not cover the universe of firms, we take aggregate revenues at the country-sector level from KLEMS and OECD when computing market shares. We note that, while ORBIS may have limited coverage of small firms in some countries, it has very good coverage of MNEs in the countries in our sample. We estimate the key structural equation from our model, which states that the log of a MNE market share in a country and sector can be written as the sum of: (i) a MNEsector component; (ii) a destination-sector component; and (iii) the transfer costs. We fit a two-way fixed-effect specification to measure cross-country differences in firm-embedded productivity from the estimated destination-sector fixed effects. The OLS estimates of the destination-sector-specific components of the market shares are unbiased if the assignment of MNEs to destination countries is exogenous with respect to the error term. This is the case if selection of MNEs into destinations is driven by firm characteristics (e.g. productivity) and by destination-country characteristics (e.g. market size).9 Thus, the fact that MNEs are larger and more productive than domestic firms, and the fact that ORBIS may not cover the universe of MNEs, do not bias our estimates of the destinationsector fixed effects. These estimates are identified from variation in market shares within MNEs across countries, rather than from variation across MNEs. In contrast, these estimates would be biased if the assignment of MNEs to destination countries were driven by firm-destination characteristics, such as firm-destination-specific transfer costs. We address this and other selection concerns in detail in Section 5.2, and show that our main results are unchanged if we focus on subsamples of firms that are more likely to satisfy this exogeneity assumption. We find that for the average country in our sample, firm-embedded productivity is 0.20 8 Our sample of destination countries also includes Japan, Korea, and Mexico. In contrast, every country in the world is potentially a source of MNEs in our data. 9 These assumptions hold in the workhorse models of multinational production in the tradition of Helpman et al. (2004). 3 log points lower than in France, our reference country.10 The relative importance of the differences in firm-embedded productivity varies considerably across countries. For example, firm-embedded productivity in Italy is 0.28 log-points higher than in Greece, accounting for three quarters of the observed differences in output per-worker between these two countries. In contrast, firm-embedded productivity is similar for Greece and Bulgaria, though output per-worker in Greece is 0.5 log points higher than in Bulgaria due to the difference in country-embedded factors between these countries. We show that there is a strong positive correlation between firm-embedded productivity and output per-worker. It is worth noting that while the development accounting literature documents a positive correlation between TFP and output per-worker, it computes TFP as a residual using data on output per-worker. In contrast, we directly measure a component of TFP (firm-embedded productivity) using data on MNE market shares, and show that this component is strongly correlated with independent measures of output per-worker. In fact, differences in firm-embedded productivity account for about onethird of the cross-country variance in output per-worker. We also show a positive correlation between firm-embedded productivity and measures of firm innovation and management practices across countries. In contrast, firm-embedded productivity is uncorrelated with a country’s physical and human capital, and with measures of infrastructure and governance. Next, we study cross-country differences in firm-embedded productivity at the sector level. The cross-country differences in firm-embedded productivity are larger in Manufacturing than in Services, but so are the cross-country differences in output per-worker. Remarkably, the contribution of firm-embedded productivity to the cross-country variance in output per-worker ends up being roughly a third in these two broad sectors. We further show that the foreign output of a country’s MNEs is concentrated in sectors where the country’s firm-embedded productivity is relatively high. For example, Japan and Finland have a particularly large stock of firm-embedded productivity in Manufacturing, and the foreign output of the MNEs from these countries is also concentrated in the Manufacturing sector. In contrast, Latvia and Lithuania have relatively more firm-embedded productivity in Services, and the foreign output of the MNEs from these countries is concentrated in the Service sector. Finally, we evaluate the sources of the observed cross-country differences in firm-embedded productivity along two dimensions. First, we evaluate if these differences stem from ag10 We use France as our reference country since it has the best coverage among the rich countries in ORBIS. 4 gregate scale (or variety) effects by focusing on the component of firm-embedded productivity that is orthogonal to a country’s population, thus removing scale effects from our measure. We show that there is still a very strong correlation between this residualized component of firm-embedded productivity and output per-worker. Second, we separately compute differences in firm-embedded productivity across domestic firms and across the foreign affiliates of the MNEs that operate in each country. Differences in firm-embedded productivity across domestic firms account for roughly 88 percent of the observed differences in firm-embedded productivity across countries, while differences across the foreign affiliates of MNEs account for the remaining 12 percent. Related literature: Our paper is closely related to Burstein and Monge-Naranjo (2009), who separate firm-embedded productivity from country-embedded factors using aggregate data on Foreign Direct Investment (FDI) stocks and the equilibrium conditions of a structural model of MNE location choices. Their framework is based on the Lucas ‘span of control’ model and assumes that firm-embedded productivity is a rival factor, so that each firm (or manager) must choose only one country where to produce. Under these assumptions, firm-embedded productivity can be recovered from aggregate data using a non-arbitrage condition that equates after-tax managerial profits across countries. In contrast, our approach treats firm-embedded productivity as a non-rival factor that can be used simultaneously in many countries, and is based on firm-level data on MNE operations in multiple countries rather than on a structural model of MNE location choices. In that sense, our approach is similar to that in Hendricks and Schoellman (2018), who exploit the idea that workers can take their human capital with them when moving to a foreign country. Using data on wage gains upon migration, they tease out the role of human-capital in explaining cross-country income differences. More broadly, our paper is related to the extensive literature on development accounting, which measures the contribution of factors of production to cross-country income differences directly and computes TFP as a residual (see Caselli 2005 for a survey). This literature has focused on improving measures of factor stocks to better account for differences in productivity embodied in physical and human capital (recent examples are Hendricks and Schoellman, 2018, Lagakos et al., 2018 and Caunedo and Keller, 2020). We contribute to this literature by proposing a measure of the productivity that is embodied in firms. In doing so, we provide a direct measure of one of the components of TFP, firm-embedded productivity, using data on MNEs. Finally, our paper is related to the large literature studying technology transfers through 5 MNEs. One branch of the literature uses parent-affiliate matched data to estimate how productivity and shocks are transmitted within the MNE (see e.g. Cravino and Levchenko 2017 and Bilir and Morales 2020). In contrast, our focus is on measuring the contribution of firm-embedded productivity in explaining cross-country income differences. A different branch of the literature parameterizes structural models of MNE location choices to measure their contribution to welfare and TFP (see e.g. Ramondo and Rodriguez-Clare 2013, Irarrazabal et al. 2013, Alviarez 2019 and Arkolakis et al. 2018). Our measurement strategy is based on parent-affiliate matched data rather than on the general equilibrium conditions of a structural model. The rest of the paper is organized as follows. Section 2 presents the accounting framework. Section 3 describes the data and our empirical strategy. Section 4 presents the quantitative results. Section 5 collects robustness exercises, and Section 6 concludes. 2 Accounting framework In this section, we first develop a stylized framework that formalizes our definition of firm-embedded productivity and shows how it can be measured using firm-level data on the cross-border operations of MNEs. Next, we present a quantitative version of this framework that allows for multiple sectors and factors of production. 2.1 A model economy Preliminaries: We consider a world economy consisting of N countries indexed by i and n. Each country is populated by a continuum of differentiated intermediate good producers that are owned by firms from different source countries. We refer to a firm that simultaneously operates in multiple countries as a MNE. Factor markets are competitive and integrated within countries. Intermediate goods cannot be traded internationally. In each country, intermediates are aggregated into a final tradable good by a competitive producer. 6 Technologies: The production function for the final good in each country n is given by " Yn = ∑ i Z ω ∈Ωin [ Qin (ω ) Yin (ω )] ρ −1 ρ # dω ρ ρ −1 , (1) where Yin (ω ) is the output of firm ω from source country i operating in country n, and ρ ≥ 1 is the elasticity of substitution across intermediate goods. Ωin denotes the set of firms from country i that are active in country n. Qin (ω ) is a shifter for firm ω, which we interpret as product quality. Note that the idiosyncratic quality Qin (ω ) can differ across production locations. The production function for intermediate goods is Yin (ω ) = Zn Xin (ω ) Lin (ω ) , (2) where Lin (ω ) is the number of workers employed by firm ω in country n. The productivity of the firm depends on a country-specific component, Zn , and a firm-specific component, Xin (ω ). Following Burstein and Monge-Naranjo (2009) we refer to Zn as “country-embedded productivity”, as it captures factors that affect all firms in a country and are not internationally mobile, such as infrastructure, institutions, workers’ quality, and natural amenities. In contrast, Xin (ω ) is idiosyncratic to firm ω, and like product quality, can differ across production locations. It is useful to define Ain (ω ) ≡ [ Qin (ω ) × Xin (ω )]ρ−1 . In what follows, we will refer to Ain (ω ) as “firm-embedded productivity”. It captures production, managerial, and marketing know-how that is specific to the firm. In contrast to country-embedded productivity, firm-embedded productivity can be transferred internationally within the boundaries of the firm. We assume that firm-embedded productivity can be transferred imperfectly across countries, so that the productivity of an MNE from country i when it operates in country n is Ain (ω ) = Ai (ω ) × exp (−κin (ω )) , (3) with κii (ω ) = 0. Here, Ai (ω ) is the productivity embedded in MNE ω in its home country i, and κin (ω ) is a technology transfer cost that captures the degree to which firmembedded productivity can be moved from i to n. If κin (ω ) = 0, the MNE can use the same Ai (ω ) in all the countries where it produces. 7 Aggregate output and TFP: Aggregate output can be written as 1 ρ −1 Yn = Zn Φn Ln , (4) where Φn ≡ ∑ i Z ω ∈Ωin Ain (ω ) dω (5) denotes aggregate firm-embedded productivity in country n, which is the sum of the productivity embedded in the firms that produce in country n. In what follows, we use lowercase to denote the log of a variable, and use yn ≡ ln [Yn /Ln ] to denote the log of output per-worker. Using Equation (4), we can thus write yn = zn + 1 φn . ρ−1 (6) Equation (6) states that cross-country differences in output per-worker arise from differences in country-embedded productivity, zn , and differences in aggregate firm-embedded productivity, φn . Clearly, the same level of yn can be achieved with different combinations of zn and φn , so that these two terms cannot be separated using only aggregate data. Next, we show how to use micro-level data on the cross-border operations of MNEs to separate φn from zn . 2.2 Decomposing cross-country differences in output per-worker We now show how cross-country differences in φn can be computed using firm-level data on market shares. From the demand functions implied by Equation (1), we can write the revenue of MNE ω from country i producing in country n, relative to the sum of the revenues of all firms producing in n, as Sin (ω ) ≡ Pin (ω ) Yin (ω ) A (ω ) = in . Φn ∑i ω ∈Ωin Pin (ω ) Yin (ω ) dω R (7) A MNE market share in a country depends on its productivity, Ain (ω ), relative to the productivity embedded in all firms operating in that country, Φn . Intuitively, MNEs should have larger market shares in countries where aggregate firm-embedded productivity is 8 relatively low, since they face less competition in those countries. We build on this intuition to identify cross-country differences in Φn . Substituting Equation (3) in (7), the market share in logs is sin (ω ) = ai (ω ) − κin (ω ) − φn . (8) Equation (8) shows that if technology transfer costs do not vary across foreign destinations, κin (ω ) = κi (ω ), cross-country differences in market shares across affiliates of the same MNE pin-down differences in φn . In this case, one could regress firm-level market shares on MNE- and destination-level dummies, and use the destination dummies to recover cross-country differences in φn . The MNE-level dummies would capture differences in ai (ω ) − κi (ω ) across MNEs, while the cross-country variation in shares within an MNE would identify the differences in φn . After obtaining cross-country differences in φn , differences in zn can be computed as residuals from Equation (6). This two-way fixed-effect approach constitutes the basis of our estimation strategy described in Section 3.2. In the more general case where technology transfer costs vary across destinations, differences in market shares across affiliates of the same MNE are not enough to identify differences in aggregate firm-embedded productivity. As Equation (8) makes clear, this is because the market share of an affiliate can be relatively low in country n if either firmembedded productivity is relatively large in country n, high φn , or if the costs to transfer technology are large, high κin (ω ). Section 3.2 shows how, if we observe market shares for MNEs from multiple source countries and into multiple destinations, we can identify differences in φn by imposing assumptions on the structure of κin (ω ) that are common in the International Trade and Multinational Production literature. Discussion: Two remarks are in order. First, Equation (7) relies on the assumption that the allocation of resources across firms is efficient. We note that, if as documented by Bento and Restuccia (2017) and Fattal Jaef (Forthcoming), size-dependent distortions are more prevalent in less developed countries -for example if larger firms are taxed more or have higher markups in developing countries-, then these distortions would push down MNE market shares in less developed countries. In this case our procedure would underestimate the contribution of firm-embedded productivity to cross country income differences. 9 Second, country-embedded productivity, Zn , does not affect the MNE market share Sin (ω ) in Equation (7), since it proportionally affects all the firms producing in n. This follows from the assumption that Zn and Xin (ω ) enter log-linearly into the production function in Equation (2). Section 5.2 and Appendix B show that this functional form provides a good approximation of the data. Together with the assumption on transfer costs in Equation (3), the log-linearity assumption also implies that country-embedded factors that have different effect across domestic vs. foreign firms -such as regulations that apply only to foreign firms- would be captured in κin (ω ).11 2.3 Quantitative model We now extend our framework to incorporate additional sectors and factors of production.12 We assume that in each country there are J sectors indexed by j, and that a competitive producer of final goods aggregates sectorial output according to Yn = ∏ h j i j θn Yn , (9) j j j j where Yn denotes the final output from sector j and θn ∈ [0, 1] with ∑ j θn = 1. Sectorial output is produced by aggregating intermediate goods, " j Yn = ∑ i Z h j ω ∈Ωin j j Qin (ω ) Yin (ω ) i ρ j −1 ρj ρj # ρ j −1 dω , (10) j where Yin (ω ) is the output of intermediate-good producer firm ω from country i in sector j j. Qin (ω ) denotes product quality of firm ω from country i in sector j. Intermediate goods in each sector are produced with a Cobb-Douglas technology, j j j j j j j Yin (ω ) = Zn Xin (ω ) Hin (ω )1−α Kin (ω )α , j (11) j where α j ∈ [0, 1]. The variables Hin (ω ) and Kin (ω ) denote the effective units of labor 11 That is, our model is isomorphic to assuming a production function given by Yin (ω ) = Z̃in (ω ) Xii (ω ) Lin (ω ) , with Z̃in (ω ) ≡ κin (ω ) Zn . 12 The framework incorporates physical and human capital. Appendix C shows that our approach and results do not change if we incorporate intermediate inputs in production, and recalibrate the model’s parameters accordingly. 10 and capital employed by firm ω in country n and sector j. h i ρ j −1 j j j As in the previous section, we define Ain (ω ) ≡ Qin (ω ) × Xin (ω ) with j Ain (ω ) = j Ai (ω ) × exp  j −κin  (ω ) . (12) Aggregate output in each sector satisfies i j h iα j h i 1 h j j j j 1− α j j j Kn , Yn = Zn Φn ρ −1 H̄n Ln j j (ω ) dω is the aggregate firm-embedded productivity in sector j A ω ∈Ωin in j j the number of workers employed in sector j, and H̄n ≡ j and country n, Ln denotes  R j j ∑i ω ∈Ω j Hin (ω ) dω /Ln are the units of effective labor per-worker (average human where Φn ≡ ∑i R in j capital) in sector j, and Kn is the physical capital employed in sector j. Output per-worker in sector j can be written as j Yn j Ln h j where Z̃n ≡ j Zn i 1 1− α j j H̄n  j Kn j Yn  αj 1− α j j j j = Z̃n Φ̃n , , Φ̃n ≡ h j Φn iβj (13) , and β j ≡ j 1 1 . 1− α j ρ j −1 In an abuse of j notation, in what follows we will refer both to Φ̃n and Φn as firm-embedded productivity. j We refer to Z̃n as country-embedded factors, as it includes physical and human capital, j in addition to the country-embedded productivity Zn . Aggregate output per worker can be written as Yn = Z̃n Φ̃n , Ln with Φ̃n ≡ θ̄n H̄n 13 θ̄ h Kn Yn i αn 1− α n  n j β n ρ n −1 β j ρ j −1 i j θn ∏ j Φ̃n h j ≡ ∏ j θn h j ∏ j Zn h 1− α j 1− α n i j θn 1− α n i 1− α j h , βn ≡ αn j j αn ≡ ∑ j θn α j , ρn ≡ ∑ j θn ρ j , and Z̃ n ≡ .13 Here Ln and Kn denote the number of workers and capiθ αj 1 1 1− α n ρ n −1 , (14) j iα j  1−nαn is a country-specific constant. 11  tal stock in country n, and H̄n ≡ ∑ j ∑i R j ω ∈Ωin j Hin  (ω ) dω /Ln is the average human capital in n. Applying logs to Equation (14), we can thus write yn = z̃n + φ̃n . (15) We can compute the terms in Equation (15) following steps analogous to those described in Section 2.2. In particular, the (log) market-share of MNE ω operating in country n and sector j is j j j j sin (ω ) = ai (ω ) − κin (ω ) − φn . (16) j A MNE share in a sector depends on its productivity, ai (ω ), relative to the productivity j of all firms in the sector, φn . As explained in the previous section, we can use differences in sectorial market shares across affiliates of the same MNE that are located in different j countries to pin-down differences in φn . These differences can be aggregated to obtain j β ρ −1 j φ̃n = ∑ j θn βnj ρnj −1 φn . Once φ̃n is calculated, z̃n can be computed as a residual from Equation (15). Finally, our development-accounting exercise evaluates the contribution of firm-embedded productivity to the cross-country variance of output per-worker. We follow the variance decomposition in Klenow and Rodriguez-Clare (1997) and compute cov(yn , z̃n ) cov(yn , φ̃n ) + = 1. var (yn ) var (yn ) (17) The next section explains how we implement this variance decomposition in our data. 3 3.1 Data and empirical strategy Data description This section describes our data. We refer the reader to Appendix A for details. Our firm-level data come from ORBIS, a worldwide dataset maintained by Bureau van 12 Dijk that includes comprehensive information on firm’s revenue and employment. ORBIS includes information on both listed and unlisted firms collected from various countryspecific sources, such as national registries and annual reports. The main advantage of ORBIS is the scope and accuracy of its ownership information: it details the full lists of direct and indirect subsidiaries and shareholders of each company in the dataset, along with a company’s global ultimate owner and other companies in the same corporate family. This information allows us to build links between affiliates of the same MNE, including cases in which the affiliates and the parent are in different countries. We specify that a parent should own at least 50 percent of an affiliate to identify an ownership link between two firms. The main variable used in our analysis is the revenue (turnover) of each firm. We use data for the year 2016, which is the year with the largest coverage in ORBIS. We focus on a subset of destination countries for which aggregate revenues by foreign-firms in ORBIS account for at least 20 percent of the aggregate revenues by foreign-firm reported by OECD/Eurostat.14 In addition, we exclude Ireland, Luxembourg, and Switzerland from our sample as MNE revenues in these countries are particularly sensitive to profitshifting strategies. In contrast, every country in the world is a potential source country for the MNEs in ORBIS, so that our sample of source countries is much larger than our sample of destination countries.15 Figure 1 shows our sample of destination countries and reports, for each destination, the ratio of the foreign-firm revenues in ORBIS to the foreign-firm revenues as reported by OECD/Eurostat. The original unit of observation in ORBIS is a tax-identification number. Often, affiliates or plants, located in different addresses within the same country and belonging to the same corporate group, are registered with different tax identification numbers. We aggregate revenues of all firms in ORBIS that belong to the same corporate group and that operate in the same country and 2-digit NAICS sector. Our unit of observation is then a corporate group-country-sector triplet. For example, ORBIS shows multiple taxids belonging to Renault in Germany in the Transportation and Equipment sector. We aggregate the revenues of those affiliates to obtain Renault’s total revenues in this sector in Germany. We then compute market shares by dividing the revenues of each corporate group-country-sector by the aggregate revenues in each country-sector. Data on aggre14 OECD Activity of Multinational Enterprises (AMNE) database and the Eurostat Foreign Affiliate Statis- tics database. 15 Our sample of source countries includes the United States, China, and Canada, among others. As destinations, these countries have very low or inexistent coverage in ORBIS, and thus they are not included in our sample of destination countries. 13 Figure 1: Data coverage: foreign-MNE revenues. Slovenia Romania Portugal France Estonia Bulgaria Belgium Austria Czech Rep. Italy Sweden UK Croatia Poland Spain Korea Slovakia Netherlands Greece Hungary Latvia Lithuania Finland Denmark Germany Japan Mexico 0 .2 .4 .6 .8 1 Notes: Ratio of total foreign-affiliate revenues in ORBIS to total foreign-affiliate revenues reported by OECD/Eurostat, for each country in our sample. gate revenues are from EU KLEMS and OECD, since ORBIS not always covers the population of firms in each country-sector pair. Finally, we define a MNE as all the tax id’s that belong to the same corporate group. Our procedure compares affiliates of the MNE Renault in the Transportation and Equipment sector located in different countries, and separately compares affiliates of Renault’s in, e.g., the Retail sector across countries. We obtain aggregate output per-worker from the Penn World Tables (9.1), and measure output-per-worker in international dollars at the sector level using data on output perworker from EU KLEMS and the PPP conversion factor from the Penn World Tables (9.1). 3.2 Empirical strategy This section describes how we measure cross-country differences in firm-embedded productivity using firm-level data on the activity of MNEs across countries. Our strategy builds on Equation (16) and imposes structure on the technology transfer costs following a long tradition in International Economics that approximates trade and multinational production costs using observable variables. 14 We assume that technology transfer costs are given by j j j j j κin (ω ) =Oi + Dn + Bin + ε in (ω ) . (18) The assumption states that technology transfer costs in each sector can be additively j j decomposed into origin- and destination-specific components, Oi and Dn , a bilateral j j component, Bin , and a MNE-destination-sector specific component, ε in (ω ). In addition, we assume that the bilateral component is symmetric and a log-linear function j of observable characteristics, such as bilateral distance and sharing a language, Bin = j j χd distin + χl langin . Substituting Equation (18) into (16), we obtain the estimating equation j j j j j j sin (ω ) = δi (ω ) + An + ψd distin + ψl langin + ein (ω ) . j (19) j Here, δi (ω ) are MNE-sector fixed effects. An denotes a set of dummies that take the value of 1 if the destination country is n and the sector is j. We estimate Equation (19) by Ordinary Least Squared (OLS) using the sample of the MNE foreign affiliates in the ORBIS data -MNEs in their home country are not included. The regression identifies the MNEj sector fixed effect, δi (ω ), from the within-MNE average market share across destinations, in each sector j, controlling for destination characteristics and the bilateral component of j the technology transfer costs. Similarly, the destination effects An are identified from the average market shares of the foreign affiliates that operate in each country n and sector j, controlling for within-MNE characteristics and the bilateral component of the technology j transfer costs. The residual ein (ω ) is (the negative of) the MNE-destination-sector specific component of the technology transfer costs. The OLS estimates of the destination-sector-specific components of the market shares, j An , are unbiased if the assignment of MNEs to destination countries is exogenous with j respect to the error term, ein (ω ). This is the case in the workhorse models of multinational production in the tradition of Helpman et al. (2004), where selection is driven by firm characteristics (e.g. productivity) and by destination-country characteristics (e.g. market size), not by firm-destination characteristics. For the reminder of this section, we assume that MNEs do not select into countries based j on firm-destination characteristics, ε in (ω ). In Section 5.2, we show that our main results are robust to reestimating Equation (19) using subsamples of MNEs that are more likely to satisfy this exogeneity assumption. 15 3.3 Cross-country differences in MNE market shares In what follows, we use the notation ∆xn ≡ xn − xr to express the difference of a variable in country n with respect to France, our reference country. Using data on sectorial expenj j j j diture shares in each country, θn , our OLS estimates of ∆An , and defining ∆xn ≡ ∑ j θn ∆xn as the aggregate across sectors, we compute the aggregate destination-country effects as ∆An ≡ ∑ θn ∆An . j j (20) j The aggregate country effect ∆An captures the (log of the) average MNE market share in each destination relative to France, after controlling for the MNE-sector fixed effects and the bilateral variables. Figure 2 reports exp(∆An ). On average, MNE market shares are larger in less developed countries. Differences between developed and developing countries are enormous: MNE market shares are about three and a half times larger in Greece and Portugal, and about twelve times larger in Estonia and Lithuania, compare to their market shares in France. In contrast, MNEs have similar market shares in the UK, Germany, and France. Appendix Figure A1 reports standard errors for our estimates of ∆An , and shows that these dummies are tightly estimated and exhibit substantial variation across countries. j The R-squared of the regression is 0.72.16 The country-sector dummies ∆An and the j MNE-sector dummies δi (ω ) account respectively for 0.27 and for 0.45 of the total variance j of sin (ω ) in Equation (19). Appendix Figure A1 also shows that we obtain very similar estimates if we use data on employment shares or data on value-added shares as the dependent variables in Equation (19).17 16 Appendix Table A1 reports the OLS coefficients on bilateral distance and common language, j j ψd and ψl , for each sector. Appendix B presents additional statistics on our two-way fixed effect estimator. 17 In the model, revenue shares, employment shares, and value-added shares coincide, so that in theory any of these shares can be used for our estimation. We use revenue shares for our baseline estimates since ORBIS has a more complete coverage of revenues than of employment and value-added. Using employment data alleviates concerns about profit-shifting strategies by MNEs. 16 Figure 2: Market shares of foreign MNE affiliates, relative to France. Note: The figure shows exp(∆An ), calculated using Equation (20) and the OLS estimates of Equation (19). The x-axis reports the output per-worker of each country, relative to France, from Penn World Tables (9.1). 3.4 Interpreting differences in MNE market shares j j We calculate the differences in ∆φn using our estimated country-sector effects, ∆An . In our model, these effects correspond to j ∆An =− h j ∆φn j + ∆Dn j i , (21) which conflates firm-embedded productivity ∆φn and the destination effects of the techj nology transfer costs ∆Dn . For our baseline results, the identification strategy follows j Waugh (2010), and assumes that costs have an origin-specific, ∆Oi 6= 0 , but not destinationj specific, component, ∆Dn = 0. In that case, the country dummies can be interpreted as j j j ∆An = −∆φn , and the MNE-level dummies, δi (ω ), would absorb the origin-specific j component of the technology transfer cost, ∆Oi . But what if this identification assumpj j tion is not satisfied, ∆Dn 6= 0? If ∆Dn is high for low income countries (i.e. it is harder to j transfer technology into less developed countries), then cov(∆yn , ∆Dn ) ≤ 0. This inequalj ity implies that our baseline estimates of ∆φn based on Equation (21) would understate the contribution of aggregate firm-embedded productivity to the cross-country variance 17 of output per-worker, cov  j ∆yn , −∆An  = cov  j ∆yn , ∆φn j + ∆Dn  ≤ cov  j ∆yn , ∆φn  . (22) j Section 5 presents a robustness exercise that allows for ∆Dn > 0. Those results are remarkably similar to our baseline results. 3.4.1 Parameterization Finally, as shown in Section 2.3, to evaluate the contribution of aggregate firm-embedded productivity to cross-country income differences we need to aggregate our sectoral estimates and assign values to the model parameters. Taking logs of Equation (13), and using j j our baseline identification assumption so that ∆An = −∆φn , yields j j j ∆yn = − β j ∆An + ∆z̃n . Here β j ≡  ρj − 1  1 − αj −1 is a composite elasticity and can be estimated from an OLS j ∆yn j regression of on ∆An . Unfortunately, these estimates would not be consistent unless j j ∆An is orthogonal to ∆z̃n . A concern would be that policies that encourage accumulation j of country-embedded factors, captured by ∆z̃n , would also improve firm-embedded proj j ductivity, ∆φn . One way to deal with this concern is to control for factors included in ∆z̃n that simultaneously affect the accumulation of firm-embedded productivity, such as human capital and the capital-output ratio, the quality of institutions, and the infrastructure in country n. In particular, we estimate j j j j j j ∆yn = b0 +b1 ∆An + b2 ∆Cn + un , (23) where Cn is a vector of country-specific controls. Table 1 reports these estimates. Columns (1), (4) and (7) respectively show the results for the pooled sample of sectors, Manufacturing sectors, and Services sectors, estimated under the restriction that b1 is the same in all sectors (see Appendix Table A2 for results j on estimating b1 for each sub-sector in Manufacturing and Services). The coefficients on b1 are precisely estimated around -0.20 in the three samples. As shown in Columns (2), (5) and (8), we estimate very similar values when we control for the (log of the relative) capital-output ratio and the (log of the relative) average years of schooling, and also in 18 Columns (3), (6) and (9) when controlling for measures of country’s governance and infrastructure.18 Overall, we cannot reject the null hypothesis that β = 0.2 in any of these samples. For a labor share of 1 − α = 2/3, our estimate implies a value of ρ = 8.5, which is within the range of estimates used to match the average markup in the United States (see e.g. Edmond et al. 2018 and Baqaee and Farhi 2020). j Using β = 0.2 and the restriction that ∆Dn = 0, we get our baseline estimates of aggregate firm-embedded productivity as ∆φ̃n = − β∆An , where ∆An is obtained from aggregating the OLS estimates in Equation (19) according to Equation (20).19 We calculate ∆z̃n as a residual using data on income per worker. 4 Quantitative results This section combines the estimates from Equation (21) with our elasticity estimates from Section 3.4.1 to decompose differences in output per-worker across countries into aggregate firm-embedded productivity and country-embedded factors. Figure 3 plots the result of this decomposition (see Appendix Table A5 for the exact numbers). The x-axis shows the log-difference in output per-worker in each country relative to France, ∆yn . In the y-axis, the red circles show the difference in firm-embedded productivity in each country relative to France, ∆φ̃n , while the blue squares show the differences in countryembedded factors relative to France, ∆z̃n . For the average country, firm-embedded productivity is 0.20 log points lower than in France. There is, however, wide variation across countries. For some of the large developed nations in our sample, such as Germany and Korea, firm-embedded productivity is the same as in France, whereas in Japan it is somewhat larger (0.09 log-difference). In contrast, firm-embedded productivity is quite low in the Baltic Republics of Lithuania, Latvia, and Estonia. 18 Our measure of infrastructure is the number of mobile cellular subscriptions per-capita, from the World Development Indicators. Our estimates are unchanged if we use alternative measures of infrastructure, such as the number of fixed broadband subscriptions per-capita or the electric power consumption percapita. 19 In a one-sector model, estimating Equation (23) without controlling for ∆C would yield β = n cov(∆An ,∆yn ) − var(∆A ) . Using this expression to calculate ∆φ̃n = − β∆An , the second term of the variance den cov(∆y ,∆φ̃ ) cov(∆y ,∆A ) cov(∆A ,∆y )cov(∆y ,∆A ) n n n n n n n n = − β var(∆y = , composition in Equation (17) would boil down to var(∆y var (∆An )var (∆yn ) n) n) which corresponds to the R-squared of a regression of ∆yn on ∆An , and which does not depend on the model parameters. Rather than focusing exclusively on this R-squared, we parameterize β to evaluate the decomposition for each individual country in our sample. 19 Table 1: Estimating the composite elasticity β All sectors j ∆An (1) (2) (3) (4) (5) (6) (7) (8) (9) -0.199*** -0.197*** -0.189*** -0.203*** -0.196*** -0.193*** -0.194*** -0.193*** [0.0267] [0.0261] [0.0282] [0.0338] [0.0372] [0.0340] [0.0342] [0.0342] [0.0386] ∆hn 0.381*** 0.275* 0.496** 0.297 0.195 0.121 [0.115] [0.157] [0.165] [0.167] [0.122] [0.128] 0.244 -0.168 0.774 0.144 -0.0915 -0.456 [0.385] [0.522] [0.494] [0.751] [0.301] [0.423] ∆Governancen 0.479 ∆In f rastructuren R-squared Service sectors -0.194*** ∆[k n − yn ] Observations Manufacturing sectors 0.780 0.348 [0.350] [0.432] [0.219] 0.117 0.00421 0.197 [0.390] [0.385] [0.380] 445 445 445 158 158 158 161 161 161 0.334 0.393 0.422 0.397 0.513 0.581 0.420 0.447 0.482 Notes: The table reports the OLS estimates from Equation (23). ∆ [k n − yn ] denotes the capital-output ratio, ∆hn denotes human capital from the Penn World Tables (9.1). ∆Governancen is an aggregate indicator of governance averaging the six Worldwide Governance Indicators (WGI): (1) rule of law, (2) voice and accountability, (3) political stability and absence of violence, (4) government effectiveness, (5) regulatory quality, and (6) control of corruption. ∆In f rastructuren is measured by the number of mobile cellular subscriptions per-capita. Sector fixed effects are included and standard errors are clustered by country and sector (in parentheses). 20 The relative importance of the differences in firm-embedded productivity and countryembedded factors also varies considerably across countries. For example, Italy and Slovenia –both EU members– have similar levels of country-embedded factors. However, Italy has more firm-embedded productivity, which generates significant differences in output per-worker between these two countries. In contrast, firm-embedded productivity is similar for Slovenia and Bulgaria, though output per-worker is much higher in Slovenia due to a large difference in country-embedded factors between these two countries. For countries such as Spain and the Netherlands, with roughly the same level of output per-worker, our decomposition indicates that while for Netherlands firm-embedded productivity is 0.15 log-point lower than for Spain, that negative difference is compensated by an advantage of equal magnitude in country-embedded factors. Our measure of aggregate firm-embedded productivity is strongly correlated with output per-worker. As we noted in the Introduction, while the development accounting literature documents a positive correlation between TFP and output per-worker, it computes TFP as a residual using output per-worker data. In contrast, we directly measure one component of TFP (firm-embedded productivity) and show that this component is strongly correlated with independent measures of output per-worker. Furthermore, we compute the share of the cross-country variance in output per-worker accounted for aggregate firm-embedded productivity and country-embedded factors, in the spirit of Klenow and Rodriguez-Clare (1997). The contribution of aggregate firm-embedded productivity corresponds to the slope of a bivariate OLS regression of ∆φ̃n on ∆yn , which is reported in Figure 3. Differences in ∆φ̃n account for roughly a third of the cross-country variance in output per-worker; differences in country-embedded factors account for the remaining two thirds. Correlation with country characteristics: Table 2 evaluates how our measures of firmembedded productivity and country-embedded factors correlate with country characteristics. In particular, we regress output per-worker, firm-embedded productivity, and country-embedded factors on a country’s capital-output ratio, human capital, measures of governance and infrastructure, and the number of patent applications per capita. The table shows that differences in firm-embedded productivity are uncorrelated with physical and human capital (Column 3), and with Governance and Infrastructure (Column 4), but strongly correlated with the number of patent applications per capita (Column 4). In contrast, differences in country-embedded factors are significantly correlated with physical and human capital (Column 5), and Governance (Column 6), but they are uncor21 0.5 Figure 3: Dev. accounting: firm-embedded productivity vs country-embedded factors. 0.0 JP KR EELT ∆ϕ̃n, ∆z̃n MX SI SK PT RO PT RO SK SI LV HU -0.5 BG HU LV EELT HR PL CZGR GR CZPL HR GB GB KR JP DK AT SE FINL BE DEIT FR ES ES IT DE BE NL AT FISE DK BG -1.0 MX ∆ϕ̃n: 0.34 (0.10) ∆z̃n: 0.66 (0.10) -1.0 -0.8 -0.6 ∆yn -0.4 -0.2 0.0 Notes: Each circle (square) represents a country’s firm-embedded productivity (country-embedded factors) relative to France. The figure plots the decomposition in Equation (15), where ∆yn is plotted in the x-axis and ∆z̃n and ∆φ̃n are plotted in the y-axis. The legend reports the slopes of a bivariate OLS regression of ∆φ̃n on ∆yn . related with the number of patent applications per capita (Column 6). These results are reassuring since, as explained in Section 2.3, cross-country differences in factors should be captured by our measure of country-embedded factors, and not by our measure of firm-embedded productivity.20 Finally, we relate our measure of firm-embedded productivity with an index of Management Practices from the World Management Survey. Unfortunately, this index is only available for 12 countries in our sample, and thus we cannot include it in the regressions in Table 2. Figure 4 shows the raw correlation between these two variables. The figure shows that, despite the sample size, there is a strong positive correlation between the index of management practices and our measure of firm embedded productivity. In contrast, Management Practices are not significatively correlated with our measure of ∆z̃n . 20 The measures of Governance and Infrastructure are those used in Section 3.4.1. with other measures. 22 We obtain similar results Table 2: Correlations with country characteristics ∆yn dep. var. ∆ [k n − yn ] ∆hn (1) 0.379** [0.179] 0.772* [0.424] ∆Governancen ∆In f rastructuren ∆patents( pc)n Obs. R-squared 27 0.201 ∆φ̃n (2) 0.183 [0.187] -0.157 [0.630] 0.689* [0.385] -0.0643 [0.597] 0.0841** [0.0366] 27 0.525 (3) -0.045 [0.094] -0.019 [0.274] 27 0.007 (4) -0.0496 [0.103] -0.331 [0.213] -0.134 [0.205] -0.101 [0.338] 0.110*** [0.0211] 27 0.610 ∆z̃n (5) 0.428*** [0.127] 0.792** [0.350] 27 0.358 (6) 0.232** [0.103] 0.174 [0.525] 0.823*** [0.235] 0.0365 [0.319] -0.0264 [0.0262] 27 0.637 Notes: The table reports the OLS estimates from Equation (23). ∆ [k n − yn ] denotes the capital-output ratio, ∆hn denotes human capital from the Penn World Tables (9.1). ∆Governancen is an aggregate indicator of governance averaging the six Worldwide Governance Indicators (WGI): (1) rule of law, (2) voice and accountability, (3) political stability and absence of violence, (4) government effectiveness, (5) regulatory quality, and (6) control of corruption. ∆In f rastructuren is measured by the number of mobile cellular subscriptions per-capita. ∆patents( pc)n denotes the total number of patent applications per capita from the World Development Indicators. Sector fixed effects are included and standard errors are clustered by country and sector (in parentheses). 23 .2 Figure 4: Firm-embedded productivity and management practices. JP DE IT 0 FR GB ES MX -.2 ∆ϕ̃n PL SE PT -.4 GR R2:0.286 -.08 -.04 0 Average Management Practices .04 Notes: Each circle represents a country’s firm-embedded productivity relative to France. The figure plots the the average management practices score from the World Management Survery in the x-axis and ∆φ̃n are plotted in the y-axis. The legend reports the R-squared of a bivariate OLS regression of ∆φ̃n and country’s management practices score. 4.1 Sector-level decompositions We now decompose differences in output per-worker in Manufacturing and Services by aggregating our sectoral estimates of the country effects into those two broad sectoral categories. Figure 5 reports the results. Even though firm-embedded productivity for the average country (relative to France) is similar for Manufacturing and Services (-0.18 vs -0.20 logpoints), the cross-country differences are larger in Manufacturing. The cross-country differences in output per-worker are also larger in Manufacturing than in Services, so the contribution of firm-embedded productivity to cross-country income differences ends up being roughly one third for both sectors. There is substantial variation across countries. For example, Japan, Korea, and Germany have relative high levels of firm-embedded productivity in Manufacturing, but their firm-embedded productivity in Services is similar to that of other developed countries. Firm-embedded productivity is lower than countryembedded factors, relative to France, in Services sectors for all countries, except for Germany, Mexico, and Hungary. Manufacturing presents much more heterogeneity than services, with less developed countries having higher firm-embedded productivity than more developed countries, and vice-versa. 24 Figure 5: Dev. accounting: Manufacturing and Services 0.5 Services 0.5 Manufacturing DK BE NL JP HR HR EE LV PT CZ HU RO SI LT PL MX ∆ϕ̃n: 0.34 (0.09) ∆z̃n: 0.66 (0.09) -1.0 BG -1.2 0.0 DK -0.8 -0.4 ∆yn 0.0 BG HU BG HU -0.5 LV EE -1.0 BG RO CZ HU SK ∆ϕ̃n, ∆z̃n PL SI PT DK LT GR IT FI GB ES FR KR ES GB DE NL FI BE IT SEAT GR JP LT MX -0.5 ∆ϕ̃n, ∆z̃n 0.0 BE NL SEAT KR DE 0.4 FI SE AT PL IT IT SI DE FR CZ GR EEHR ES SK GB JP ESDE GB KR RO LVMX PL PT RO KR AT GR SE PT NL FI DK SK CZ SI MX HR LV EE LT BE ∆ϕ̃n: 0.32 (0.09) ∆z̃n: 0.68 (0.09) -0.8 -0.6 -0.4 -0.2 ∆yn 0.0 0.2 0.4 Notes: Each circle (square) represents a country’s firm-embedded productivity (country-embedded factors). j The figures plot the decomposition in Equation (15) at the sectoral level. ∆yn is plotted in the x-axis and j j ∆z̃n and ∆φ̃n are plotted in the y-axis for j =Manufacturing (left panel) and j =services (right panel). We can further decompose differences in output per-worker within each sub-sector in Manufacturing and each sub-sector in Services. Appendix Figures A2 and A3 show these results. The figures show a very strong correlation between our sectoral measures of firmembedded productivity and output per-worker at the sector level. Finally, we evaluate if the observed differences in aggregate firm-embedded productivity arise from differences in the sectoral composition of output across countries. With this in mind, we compute a measure of aggregate firm-embedded productivity that aggregates sectoral differences using the output shares of our reference country (France), j j ∆φ̃nw ≡ ∑ j θr ∆φ̃n . Figure 6 shows that this measure and our baseline measure are very close to each other, indicating that cross-country differences in aggregate firm-embedded productivity are not driven by cross-country differences in sectoral output shares. Withinsector differences in firm-embedded productivity across countries overwhelmingly create the observed aggregate differences. 4.2 Firm-embedded productivity and comparative advantage An extensive literature in International Trade studies the sources of comparative advantage by relating the sectorial concentration of a country’s exports to factor endowments, 25 0.5 Figure 6: Differences in firm-embedded productivity within and between sectors. 0.0 JP KR ∆ϕ̃n, ∆ϕ̃n ω MX HU HU BG LV LV EELT EELT -0.5 -1.0 PL PL RO PT RO GR PT CZGR CZ SK HR SK SI HR MX JP KR GB DEIT IT DE FR ES ES BE BE AT NL AT FISE NL SE FI DK DK ∆ϕ̃n: 0.34 (0.10) ω ∆ϕ̃n : 0.36 (0.09) -1.0 -0.8 -0.6 ∆yn -0.4 -0.2 0.0 Notes: The figure plots the decomposition in Equation (15), where ∆yn is plotted in the x-axis and ∆φ̃w n ≡ j j j j ˜ ∑ j θr ∆φ̃n and ∆φn ≡ ∑ j θn ∆φ̃n are plotted in the y-axis. The legend reports the slopes of a bivariate OLS regression of ∆φ̃n (rest. ∆φ̃nw ) on ∆yn . Each circle (square) represents a country. technologies, financial conditions, or institutions.21 In this section, we evaluate how sectorial differences in firm-embedded productivity and in country-embedded factors shape the sectorial concentration of the foreign output of a country’s MNEs. The notion that MNEs can use their idiosyncratic productivity around the world while countryembedded factors are immobile suggests that only the former should affect the activities of MNEs when producing abroad. With this in mind, we correlate sectoral differences in firm-embedded productivity in a country with the sectoral concentration of the foreign output of the MNEs from that country (referred to as ’outward MNE sales’). We measure this sectoral concentration usj ing a Revealed Comparative Advantage (RCA) index for outward MNE sales. Let Rn,row j (Rr,row ) denote the total revenues of MNEs from country n (reference country, r) in the 21 A non-exhaustive list of recent papers includes Bernhofen and Brown (2004), Romalis (2004), Levchenko (2007), Nunn (2007), Costinot et al. (2012), Levchenko and Zhang (2016), and Hanson et al. (2015). 26 rest of the world.22 We define the RCA index for outward MNE sales as   j0 j R R / 0 ∑ n,row n,row j j . ∆rcan ≡ ln  j j0 Rr,row / ∑ j0 Rr,row (24) j j ∆rcan is defined in logs and takes France as the reference country. Thus, ∆rcan > 0 when the share of sector j in outward MNE sales is larger for MNEs from country n than for j MNEs from France. Note that, while ∆φ̃n is measured with data on market shares of j foreign MNEs in country n, ∆rcan is measured with data on sales of country n’s MNEs in foreign countries, so that the two measures do not need to be correlated. Figure 7 compares the relative differences in firm-embedded productivity in manufacturing vs. services, ∆φ̃nman − ∆φ̃nserv , to the differences in revealed comparative advantage in manufacturing and services for outward MNE sales, ∆rcaman − ∆rcaserv n n . There is a strong positive relation between differences in firm-embedded productivity and differences in the RCA index for outward MNE sales across countries. For example, Japan and Finland have a particularly large stock of firm-embedded productivity in Manufacturing, and the outward sales of the MNEs from these countries are concentrated in the Manufacturing sector. In contrast, Latvia and Lithuania have relatively more firm embedded productivity in Services, and the sales of the MNEs from these countries in the rest of the world are also concentrated in the Service sector. We observe similar patterns across disaggregated 2-digit sectors. Table 3 shows the results j of regressing our sectorial measure of comparative advantage, ∆rcan , on our measures j j of sectorial firm-embedded productivity and country embedded factors, ∆φ̃n and ∆z̃n . Columns (1), (4) and (7) show a strong correlation between a country’s sectorial firmembedded productivity and its comparative advantage.23 In contrast, Columns (2), (5) and (8) show no correlation between sectorial country-embedded factors and a country’s comparative advantage. Columns (3), (6), and (9) reports similar results when countryembedded factors and firm-embedded productivity are simultaneously included in the regression. These results are in line with the notion that firm-embedded productivity is transferable 22 Using ∑n0 6=n R j the notation from j j Pnn0 (ω ) Ynn0 (ω ) dω. Section 2 these ω ∈Ω 0 nn 23 This result is in line with the findings in Alviarez (2019), revenues correspond to j Rn,row ≡ who using sectoral-level data shows a positive correlation between the bilateral sales of affiliates of foreign MNEs in a sector and the RCA index for sectoral TFP in the source country of the MNE. 27 1.0 Figure 7: Sectorial firm-embedded productivity and outward MNE sales. FI BE HU SE AT JP ∆rcamanuf,n-∆rcaserv,n -2.0 -1.0 0.0 IT FR PL GB DE DK SI CZ SK GR PT HR ES RO LT -3.0 LV 4.59 (1.59), R2: 0.29 -0.2 0.0 ∆ϕ̃manuf,n-∆ϕ̃serv,n 0.2 0.4 Notes: The x-axis reports the difference in our measure of firm-embedded productivity in manufacturing j vs. services, relative to France. The y-axis reports the difference in the ∆rcan index defined in Equation (24), between j = Manufacturing and j = Services. across countries and a source of advantage for MNEs operating abroad. Country embedded factors, which are immobile across countries, do not appear to shape the sectorial concentration of a country’s MNEs. 4.3 Contribution of domestic and foreign firms This section further decomposes the sources of the cross-country differences in firmembedded productivity by considering the origin of the firms in each country. In particular, differences in firm-embedded productivity may arise both from cross-country differences in the productivity embedded in all domestic firms, and from differences in the productivity embedded in the foreign affiliates operating in each country. We write the market share of domestic firms in country n and in sector j as j Snn j where Φnn ≡ R ≡ Z j Ωnn j Snn (ω )dω j j Ωnn j = Φnn j Φn , (25) Ann (ω ) dω is the productivity embedded in domestic firms in country 28 Table 3: Sectorial firm-embedded productivity and comparative advantage. j dep. var. ∆rcan All sectors (1) j ∆φ̃n (2) 2.63*** [0.663] j ∆z̃n Observations R-squared Manufacturing sectors (3) (4) 3.23*** [0.836] 4.14** [1.326] 0.17 [0.469] 0.83 [0.501] 313 0.001 313 0.094 313 0.072 (5) (6) (7) 5.48*** [1.075] 3.07** [0.906] 1.51 [0.927] 2.49** [0.823] 121 0.056 121 0.274 121 0.138 Service sectors (8) 2.84** [0.812] -0.76 [0.527] 132 0.063 (9) 132 0.023 -0.19 | [0.645] 132 0.064 Notes: Each j corresponds to a NAICS 2-digit sector. ’All sectors’ include sectors those in Manufacturing, Services, and others. Standard errors are clustered by country and sector (in parentheses). n. Similarly, the market share of foreign firms in country n is given by j S Fn j where Φ Fn ≡ ∑i6=n R ≡ ∑ Z j i 6=n Ωin j Sin (ω )dω j = Φ Fn j Φn , (26) j j Ωin Ann (ω ) dω denotes the productivity embedded in foreign firms j operating in country n. From the definition of Φn , and using lowercase to denote logs, we can write the first-order approximation h i j j j j j ∆φn = Srr ∆φnn + 1 − Srr ∆φFn , (27) j where Srr refers to the market share of domestic firms in the reference country r (and sector j). Finally, aggregating across sectors we obtain ∆φ̃n =∑ j j j θn Srr ∆φ̃nn j j j h j 1 − Srr i j ∆φ̃Fn , (28) j j | +∑ j θn {z } ∆φ̃nn | {z ∆φ̃Fn } j where ∆φ̃nn ≡ β j ∆φnn and ∆φ̃Fn ≡ β j ∆φFn . Equation (28) shows the contributions of domestic firms (∆φ̃nn ) and foreign firms (∆φ̃Fn ) to the observed differences in aggregate firm-embedded productivity (∆φ̃n ). To measure j j these contributions, we first use domestic shares Snn from the data, our estimates of Φn , 29 0.2 Figure 8: Aggregate firm-embedded productivity: domestic vs foreign firms. 0.0 JP SK ∆ϕ̃nn, ∆ϕ̃Fn -0.2 EE LV HU G SIBHR LT CZ NLRO AT SE FIPT GR DK -0.4 LT LV SK IT DE FRDE IT ES GB ES GB JP AT GR RO SE FIPT NL HR SIBG PL BE BEPL DK CZ HU -0.6 EE ∆ϕ̃nn: 0.88 (0.03) ∆ϕ̃Fn: 0.12 (0.03) -0.6 -0.4 ∆ϕ̃n -0.2 0.0 Notes: Brown circles and green squares, respectively, report ∆φ̃nn and ∆φ̃Fn defined in Equation (28). j and Equation (25) to compute Φnn . Similarly, we use the revenue share of foreign firms in j j j country n, S Fn , together with the estimates of Φn , and Equation (26), to compute Φ Fn . We j then aggregate across sectors using sectoral shares θn and the reference-country sectoral j revenue share for their domestic firms, Srr . Figure 8 shows the two terms in the right-hand side of Equation (28). The average country has a 0.21 log-point difference relative to France regarding domestic firm-embedded productivity, while the gap for foreign firms is only 0.04. Differences in aggregate firmembedded productivity for domestic firms account for 88 percent of the cross-country differences in aggregate firm-embedded productivity. Differences in the productivity embedded in the foreign affiliates of MNEs are very small across countries, with some developing countries having better foreign MNE affiliates than developed countries. Countries such as Latvia, Estonia, and Slovakia have less productivity embedded in domestic firms than most of the more developed countries in our sample. However, these countries foreign firms that are as productive as the ones located in Finland, the Netherlands, or Austria. Finally, this decomposition attributes, for instance, all the difference in aggregate firm-embedded productivity between France and Poland, observed in Figure 3, to domestic firms. 30 4.4 Firm-embedded productivity and scale effects A recurring theme in the International Trade and Growth/Development literatures is that aggregate scale or variety effects may be important for TFP (see e.g. Krugman 1980, Jones 1995, and Hsieh and Klenow 2009). In this section we decompose cross-country differences in aggregate firm-embedded productivity into differences in the average productivity embedded in each firm, and differences in the number of firms across countries. In particular, we can write the differences in firm-embedded productivity as ∆φ̃n = β∆mn + ∆φ̄n , | {z } |{z} Scale (29) Average where ∆mn denotes the log-difference in the aggregate number of firms across sectors, and ∆φ̄n ≡ ∆φ̃n − β∆mn is the log-difference in the average firm-embedded productivity relative to France. Computing the scale term in Equation (29) is not straightforward, since comparable data on the number of firms across countries are not readily available.24 This problem is compounded by the fact that, in our framework, a firm corresponds to all the tax-identification numbers belonging to the same ultimate owner. In contrast, in most existing datasets, establishments and firms are not recorded by their ultimate owner. Notice that this challenge cannot be overcome by counting the firms in our dataset, since ORBIS does not cover the population of firms in each country and the coverage differs across countries. With this in mind, we assume that there is a log-linear relation between the scale effect and the population in a country, ∆mn = λ × ∆popn , (30) where we continue to use lowercase to denote logs, and where popn is the log of the population population in country n. This relation is a standard feature of many models of scale economies, such as Krugman (1980). Replacing Equation (30) into (29), we fit the regression given by ∆φ̃n = b × ∆popn + ε n . 24 The definition of what constitutes a ’firm’ differs across country-sources. For example, the minimum number of employees for an establishment or firm to be counted in surveys varies across countries. 31 0.2 Figure 9: Dev. accounting: average firm-embedded productivity. 0.0 KR JP HU RO PL ∆ϕ̅n BG -0.2 -0.4 PT IT FI BE AT SI DE LV HR EE FR SK ES GR GB CZ SE NL DK LT MX ∆ϕ̅n: 0.16 (0.03) -1.0 -0.8 -0.6 -0.4 ∆yn -0.2 0.0 0.2 0.4 Notes: Each circle represents a country. The y-axis plots the residual of a regression of firm-embedded productivity, ∆φ̃n , on the log of population. The x-axis plots the residual of a regression of the log of income per capita, yn , on the log of population. Under the assumption that the average firm-embedded productivity ∆φ̄n is orthogonal to the country’s population, the error term can be interpreted as ε n = ∆φ̄n . If the average firm-embedded productivity in a country increased with population, the residual ε n would understate the differences in average firm-embedded productivity across countries, since it would capture only the part of average firm-embedded productivity that is orthogonal to population. Figure 9 shows a very strong correlation between our measure of average firm-embedded productivity ∆φ̄n and output per-worker (also residualized by population).25 The slope in this figure is flatter but more precisely estimated than the slope between ∆φ̃n and ∆yn . in Figure 3. The cross-country variation in firm-embedded productivity that is not driven by the country’s scale accounts for 16 percent of the cross-country variance in income per-worker, almost half of the variation accounted for our aggregate measure of firmembedded productivity ∆φ̃n . the slope of this relation corresponds to the slope of a regression of ∆yn on ∆φ̃n that also controls for ∆popn . 25 Thus, 32 5 Robustness This section presents several robustness exercises. First, we show how to estimate firmembedded productivity under alternative assumptions on the technology transfer costs. Second, we evaluate potential selection concerns. Third, we evaluate the log-linearity assumption on the production function. Finally, we repeat our analysis using alternative samples, finer sectoral disaggregations, and other gravity controls. 5.1 Alternative assumptions on the technology transfer costs j Our baseline estimates for ∆φn were derived under the assumption that technology transj fer costs could have an origin-specific, but not a destination-specific component, ∆Dn = 0, as specified in Equation (21). As explained in Section 3.2, if this assumption does not hold, and if it is harder to transfer technology to less developed countries, our baseline estimates would understate the contribution of firm-embedded productivity to the crosscountry variance of output per-worker. j j We now show how to estimate ∆φn when ∆Dn 6= 0. We use data on market shares of both affiliates and parent firms of MNEs, and assume that costs have a destination-specific, but j no origin-specific, component, ∆On = 0, as in Eaton and Kortum (2002). In particular, we estimate j j j j j j j sin (ω ) = δi (ω ) + An + Pn + ψd distin + ψl langin + ein (ω ) . (31) j Here, An is a set of dummies that take the value of 1 if the destination country is n and the j firm is an affiliate, i 6= n, in sector j, while Pn is a set of dummies that take the value of 1 if the destination country is n and the firm is a parent, i = n, in sector j. In this specification, j j the dummies An are still given by Equation (21), while the dummies Pn are h i j j j ∆Pn = − ∆φn − ∆On . j j (32) If ∆On = 0, ∆Pn can be interpreted as the inverse of the firm-embedded productivity in country n relative to France. If the assumption is not satisfied and the origin-specific j component of the transfer cost is higher for low income countries, cov(∆y j n , ∆On ) ≤ 0, estimates based on Equation (32) would overstate the contribution of firm-embedded pro- 33 0.5 Figure 10: Alternative assumptions on the technology transfer costs. GB 0.0 KR KR ∆ϕ̃n MX BG -1.0 -0.5 BG MX HU HU LV EE LV EELT LT RO GR PL SK PT RO PT SK SI SI PL CZGR HR HR JP JP GB DE DEIT IT FR NL ES ES SE BE AT NL AT FISE FI DK DK ∆Dn=0: 0.34 (0.10) (baseline) ∆On=0: 0.50 (0.11) -1.0 -0.8 -0.6 ∆yn -0.4 -0.2 0.0 Notes: Each circle (square) represents a country. The figure plots the decomposition in Equation (15), where ∆yn is plotted in the x-axis and ∆φ̃n is plotted in the y-axis. The legends report the slopes of a bivariate OLS j j regression of ∆φ̃n on ∆yn under the assumption that ∆Dn = 0 (baseline) and ∆On = 0. Standard errors are in parenthesis. ductivity to the cross-country variance of output per-worker,       j j j j cov ∆yn , −∆Pn = cov ∆yn , ∆φn − ∆On ≥ cov ∆yn , ∆φn . (33) Hence, while our baseline estimates yield a lower bound to the contribution of differences in firm-embedded productivity to cross-country differences in income, this alternative specification yields an upper bound to that contribution. Figure 10 compares our baseline estimates with those based on Equations (32) and (31) j and the restriction that ∆On = 0. The two alternative identification assumptions on transfer costs yield similar estimates for aggregate firm-embedded productivity, relative to France, for each country. Appendix Figure A4 shows that the OLS estimates from Equation (31) are less precise than our baseline estimates, as the number of MNE foreign affiliates in our data far exceeds the number of MNE parent firms. For the average country, this alternative estimate of ∆φn is -0.19 log-points, relative to France, while our baseline estimate is -0.20. One of the largest differences is observed for Mexico where aggregate firm-embedded productivity, relative to France, is estimated to be -0.42 when we assume j j that ∆On = 0 and -0.11 when we alternative assume that ∆Dn = 0. 34 5.2 Selection based on MNE-destination specific characteristics The OLS estimates of the destination-sector-specific components of the market shares are unbiased if the assignment of MNEs to destination countries is exogenous with respect to the error term in Equation (19). This is the case if selection is driven by firm characteristics and by destination-country characteristics, but not by firm-destination characteristics. In contrast, the estimates are biased if MNE-destination specific transfer costs drive the assignment of MNEs to countries -that is, if selection is based on match-specific effects-. If the relatively unproductive MNEs enter unattractive locations only when their j MNE-destination specific component of the transfer cost ε in (ω ) is low, then the average j of ε in (ω ) across the MNEs that choose to enter each destination would vary across n and j thus it would be captured by the country effects An . To assess the severity of this potential bias, we follow the literature on two-way matching (Abowd et al., 1999) and analyze the residuals from estimating our baseline specification in Equation (19) by OLS. If the assignment of MNEs to countries is driven by MNEdestination specific transfer costs, we should expect these costs to be on average lower j -low ε in (ω )- for low-productivity MNEs in unattractive markets. In contrast, highly proj ductive MNEs are more likely to enter these markets irrespective of their ε in (ω ). If this is the case, our specification should underestimate market shares for low-productivity j MNEs in unattractive markets, as it does not take into account that the ε in (ω )’s can systematically vary with firm productivity among the MNEs that choose to enter any given market. We evaluate this implication in Figure 12a, which plots the mean standardized residuals, j j j s (ω )−ŝ (ω ) êin (ω ) = in σs in , against deciles of estimates of the MNE-sector fixed effects, δ j (ω ), and deciles of market popularity. Our measure of market popularity is calculated using data from OECD-Eurostat on the number of foreign MNEs operating in a country-sector pair. Indeed, we tend to see positive residuals for the less productive MNEs (decile 1 of the MNE-sector fixed effect) in less popular markets (decile 1 of market popularity). In contrast, we overestimate the market shares of the most productive MNEs (decile 10 of the MNE-sector fixed effect) in these markets. The residuals are very close to zero in the remaining bins of the figure, indicating that technology transfer costs do not vary systematically across MNEs and locations in those bins. With this concern in mind, we proceed to re-estimate Equation (19) using alternative subsamples, restricted to exclude the MNEs at the extremes of the market-share distribution. 35 Figure 11: OLS Residuals. (a) By MNE-sector and market popularity. (b) By MNE-sector and country-embedded factors. Notes: Deciles are calculated within sectors. Market popularity refers to the number of foreign MNEs in a j country-sector pair, from OECD-Eurostat. Country-embedded factor refers to estimates of Z̃n . Concretely, we restrict the sample to subsets of MNEs that lie within the 2nd to 9th, 3rd to 8th, 4th to 7th deciles, or 5th and 6th deciles, of the MNE-sector fixed effect distribution within a sector. Alternatively, we also apply our estimation procedure to subsamples of MNEs that operate in at least 3, 5, or 10 countries. These are large MNEs that are unlikely to select into destination markets due to the MNE-destination specific component of the technology transfer costs. Table 4 shows that the contribution of firm-embedded productivity to the cross-country variance in output per-worker is very similar to our baseline in all these subsamples. 5.3 Production function assumptions A related concern with our baseline estimation pertains the separability between firmembedded productivity and country-embedded factors. Our model assumes a production function that is log-linear in firm-embedded productivity and the country embedded factors. This separability is inherited by the aggregate production function, which is linear in z̃n and φ̃n . But if, for instance, high productivity MNEs do relatively better in countries with high country-embedded factors, the assumption would not longer hold, and our procedure would underestimate market shares for high productivity MNEs in markets with high z̃n . We evaluate this implication in Figure 12b, which plots the mean standardized residuals, 36 Table 4: Contribution of firm-embedded productivity, restricted samples. cov(∆yn ,∆φ̃n ) var (∆yn ) Baseline 0.34 (0.10) I. Keeping MNEs with MNE-sector FE belonging to: 2nd to 9th Decile 3rd to 8th Decile 4th to 7th Decile 5th to 6th Decile 0.32 (0.10) 0.31 (0.11) 0.31 (0.11) 0.37 (0.12) II. Keeping MNEs operating in: at least 3 countries at least 5 countries at least 10 countries 0.32 (0.10) 0.28 (0.08) 0.32 (0.08) Notes: Slopes of a bivariate OLS regression of ∆φ̃n on ∆yn . MNE-sector fixed effect, for each sector, estimated using Equation (19) by OLS. Standard errors are in parenthesis. j j êin (ω ) = j sin (ω )−ŝin (ω ) , σs against deciles of estimates of the MNE-sector fixed effects, δ j (ω ), j and deciles of estimates of the country-embedded factors z̃n . We see positive residuals for the less productive MNEs (decile 1 of the MNE-sector fixed effect) in countries with lower j z̃n (decile 1 of country-embedded factors). We actually overestimate the market shares of the most productive MNEs (decile 10 of the MNE-sector fixed effect) in these countries. The residuals are very close to zero in the remaining bins of the figure, indicating that the log-linearity assumption is not systematically violated in those bins. Table 4 shows that the contribution of firm-embedded productivity to the cross-country variance in output per-worker is very similar when estimated in subsamples of MNE that are not at the extremes of the fixed-effects distribution. Appendix B presents additional test that support our linearity assumption. 5.4 Additional robustness exercises This section briefly describes additional robustness exercises, which are collected in Table 5. First, we consider sectors at the 4-digit NAICS (336 sectors), rather than the 2-digit NAICS classification. Second, we exclude the Health, Education, and Real Estate sectors from our sample, as the government has a large participation in theses sectors in some 37 Table 5: Contribution of firm-embedded productivity, additional robustness. cov(∆yn ,∆φ̃n ) var (∆yn ) Baseline 0.34 (0.10) Aggregation at 4-digit NAICS industries Excluding Real Estate, Health, and Education Excluding MNEs that do not appear in ORBIS every year between 2010-2016 Controlling for differences in GDP per-worker between source and host country Controlling for bilateral tax treaties (BTT) between source and host country Excluding gravity variables 0.38 (0.11) 0.32 (0.10) 0.39 (0.09) 0.34 (0.10) 0.35 (0.10) 0.29 (0.11) Notes: Slopes of a bivariate OLS regression of ∆φ̃n on ∆yn . Bilateral tax treaties data comes from UNCTAD International Investment Agreements. Standard errors are in parenthesis. countries in our sample. Third, we repeat our analysis for firms that appear in ORBIS in every year between 2010 and 2016, as these are arguably the years when the ORBIS data are of the highest quality (see Appendix Table A4 for results by year). Fourth, we include the difference between the income per-capita of the source and the host country among our gravity controls, and an indicator variable for the existence of a bilateral tax treaty between the source and host country, which allow foreign-owned subsidiaries to avoid or mitigate double taxation. Finally, we repeat our analysis without any gravity control. The results of our decomposition for all these alternative specifications are remarkably close to our baseline result. 6 Conclusion This paper measures cross-country differences in firm-embedded productivity and their contribution to cross-country income differences. Our key insight is that, if MNEs can use their idiosyncratic productivity around the world, but they must use the factors from the countries where they produce, differences in the market shares of the same MNE across countries can be used to measure cross-country differences in firm-embedded productivity. We implement this idea in an accounting framework and measure firm-embedded productivity using firm-level revenue data on MNEs that produce in multiple countries. While our sample of developing countries is limited to those in Eastern Europe and Mexico, our new procedure can be easily applied to more countries as new affiliate-parent matched data become available. 38 Our results indicate that cross-country differences in firm-embedded p roductivity are large, accounting for roughly one-third of the observed differences in output per-worker across the countries in our sample. This suggests that micro-level interventions and policies that foster firm-embedded productivity can play an important role in closing crosscountry income differences. 39