Offshoring and Labor Share in Manufacturing Industries in Developed Countries

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1 JOB MARKET PAPER Offshoring and Labor Share in Manufacturing Industries in Developed Countries Ilhyun Cho University of California, Davis November 28, 2016 Abstract This paper studies the effect of offshoring on the relative share of income going to labor and capital. It introduces offshoring in a model of heterogeneous firms with two intermediate inputs. The intermediate inputs are produced with CES technology using two factors of production: labor and capital. Given the direction of labor-saving technical change, offshoring decreases the relative demand for labor, which thereby decreases labor share. Empirical studies of the World Input-Output Database (WIOD) show that in manufacturing industries in developed countries, the share of imported intermediate inputs, especially those that originate in developing countries, negatively affects labor share. JEL Classification: F14, F16, J20 Keywords: labor share, offshoring I thank Deborah Swenson, Robert Feenstra, Giovanni Peri, Alan Taylor, and Katheryn Russ for their guidance. I also thank Jaerim Choi, Chi-Yuan Tsai, Keita Oikawa, and seminar participants at UC Davis. All errors are my own. Department of Economics, University of California, Davis. ihcho@ucdavis.edu 1

2 1 Introduction Contrary to conventional wisdom, labor share is not unchanging; instead, it has declined globally since the 1980s (Karabarbounis and Neiman, 2014; Stockhammer, 2013; EC, 2007; Rodriguez and Jayadev, 2013). In the meantime, and concurrent with declining trends in labor share, offshoring has been rising. Offshoring has received attention for explaining the increase in inequality between labor groups (high-skilled and low-skilled labor), which has been a significant change since the early 1980s (Feenstra and Hanson, 2001). Inequality between labor groups contributed to the increase in overall income inequality, but decreasing labor share, too, played a role. Piketty and Goldhammer (2014) show that across time and space, incomes from capital are distributed more unequally than those of labor. Atkinson (2009) finds that economic inequality in developed countries arises primarily because nonlabor income is much more unevenly distributed than labor income. These findings indicate that declining labor share might be an important cause of rising income inequality (Checchi and GARCÍA-PEÑALOSA, 2010). However, the impact of offshoring on the distribution between labor and capital has received less attention. To fill the gap, this paper studies the effect of offshoring on the relative share of income that goes to labor. This study is motivated by the distinctive patterns and trends in manufacturing indus- Labor share Offshoring Scource: Calculations based on World Input Output Database Figure 1: Manufacturing Industries in Developed Countries 1

3 Labor share Offshoring Labor share Offshoring Year Year Labor share Offshoring Labor share Offshoring Offshoring to developed Offshoring to developing Offshoring to developed Offshoring to developing Notes: Offshoring = offshoring to developed + offshoring to developing Scource: Calculations based on World Input Output Database Notes: Offshoring = offshoring to developed + offshoring to developing Scource: Calculations based on World Input Output Database (a) Manufacturing sector (b) Non-manufacturing sector Figure 2: Labor Share and Offshoring Trends, Developed Countries tries seen in developed countries. Figure 1 presents a scatter plot between labor share and offshoring for 14 manufacturing industries in 21 developed countries during the period of 1995 to Each point represents an observation at the country-industry-year level. Offshoring is measured as the share of imported intermediate inputs in total purchases of intermediate inputs. 1 The data show that labor share and offshoring are negatively correlated. Compared to non-manufacturing industries and the developing country cases, this pattern is distinctive. 2 Aggregating each country s labor share and offshoring, 3 Figure 2 depicts the trends for the aggregate labor share and offshoring for developed countries. Foreign intermediate inputs are split into two origins: developed countries and developing countries. Offshoring to developed and developing countries represents the share of intermediate inputs imported from developed countries and developing countries, respectively. The sum of the two is equal to overall offshoring. Prior to the financial crisis of 2008, the aggregate labor share trended downward while aggregate offshoring trended upward. In the manufacturing sector, the aggregate labor share declined from in 1995 to in Although Germany and the United States contributed most strongly to the aggregate declining trend of labor, most 1 See the empirical study for data and definition of variables. 2 See Figure 7 in the Appendix for non-manufacturing industries and cases for developing countries. 3 All values are converted to US dollar and are aggregated. 2

4 Value share (%) Labor share (%) Change Impact due to: % of total Total Between Within Impact Non-manufacturing Manufacturing Total Source: Calculations based on Socio-Economic Accounts, July 2014 Release. Table 1: Shift-Share Analysis, Developed Countries other developed countries were subject to the same trends. 4 During the same time period, the total share of aggregate imported intermediate inputs increased from 16.6% to 25.9%; this was driven mainly by increasing imported intermediate inputs from developing countries, which increased from 5% to 12.3%. Although the data reveal similar patterns for the nonmanufacturing sector, the trends in the manufacturing sector are more distinctive, especially in the case of increasing intermediate inputs from developing countries. 5 Table 1 provides a shift-share analysis for developed countries from 1995 to In 2007, the value share for the manufacturing sector was 15.56%, but it contributed to 32.09% of the total decline. This finding is consistent with other studies, which find that manufacturing industries have a large impact on the declining trend in labor share (Lawrence, 2015; Elsby et al., 2013). Additionally, most of the total change is driven by changes within sectors. In Table 1, 1.79% of the total decline of 1.86% is explained by changes within sectors. In Table 11, a shift-share analysis that uses 35 industries in the Appendix similarly shows that within changes account for 81.7% of the total change. The results are consistent with other studies that show that the change is driven by declines in intra-industry labor shares rather than by movements in activity towards industries that have lower labor shares (Lawrence, 2015; Elsby et al., 2013; Rodriguez and Jayadev, 2013). This paper introduces offshoring in a model of a heterogeneous firm with two intermediate 4 See Table 14 and 15 in the Appendix. 5 See Figures 8 and 9 in the Appendix for the developing countries trends. 6 The behavior of labor share is countercyclical (Choi and Rios-Rull, 2009; Ríos-Rull and Santaeulàlia- Llopis, 2010). During the recent financial crisis, labor share sharply increased while offshoring markedly decreased in the manufacturing sector. Since this study does not focus on business cycles, all shift-share analyses examine trends prior to the 2008 financial crisis. 3

5 inputs. Unlike the typical setting of the heterogeneous firm model, which employs composite input, the model employs two factors of production, labor and capital, because the focus of the study is the distribution between labor and capital. To generate the different labor shares depending on a firm s offshoring status, the model uses CES technology and it allows different non-neutral technologies to produce the two intermediate inputs. At the firm level, it decomposes firm s revenue into payments to each factor and it aggregates keeping track of firms decisions. In this way, it decomposes the share of income going to labor and capital in the economy. In the empirical section, this study uses the World Input-Output Database (WIOD) to analyze labor share patterns. It uses a country-industry panel from 1996 to 2009, and it decomposes the total intermediate inputs from foreign countries into their places of origin: intermediate inputs imported from developed countries and from developing countries at the country-industry-year level. Briefly summarizing the empirical results, this paper finds that offshoring, especially offshoring to developing countries, negatively affects labor share in the manufacturing industries of developed countries. The paper is organized as follows. Section 2 reviews related literature, section 3 introduces the model, and in section 4 the empirical studies are presented. Section 5 concludes. The Appendix provides supplementary materials, and a separate Additional Appendix includes additional supplementary materials. 2 Literature A common explanation for declining labor share is technical change, which is often attributed to innovations in information and communication technology (ICT). In the literature, the elasticity of substitution between labor and capital, ε, plays an important role in determining labor share. However, researchers are divided in their opinions about whether the elasticity of substitution is below or above unity. When it is less than unity, the declining trend of labor share is associated with labor-augmenting technical change (Acemoglu, 2002). 4

6 Lawrence (2015) claims that rapid labor-augmenting technical change has caused the decline in the labor share in the United States since the 1980s. Since labor-augmenting technical change increases effective labor (despite the increase in the measured capital-labor ratio), it can decrease the labor share. The labor-augmenting technical change is consistent with the empirical evidence that elasticity is less than unity (Antras, 2004; Chirinko, 2008; Oberfield and Raval, 2014). When elasticity is above unity, the declining trend of labor share is associated with an increase in capital-augmenting technical change. Arpaia et al. (2009) argue that a declining pattern in labor share in Europe is governed by a capital-augmenting technical progress that is low-skilled labor saving. 7 In both cases, the direction of technical progress is labor saving, which decreases the relative demand for labor. This paper assumes that the direction of the technical change is exogenous, which requires relatively less labor for advanced technology. In contrast to this paper, which focuses on the relative demand for production factors, some recent studies have focused on supply-side considerations. Identifying elasticity as above unity, proponents of this approach claim that the current trend is caused by capital deepening. Karabarbounis and Neiman (2014), for example, argue that a decrease in the price of investment goods induced firms to shift away from labor and toward capital. This, they claim, increases capital intensity and explains roughly half of the observed decline in labor share. 8 Similarly, Piketty (2014) claims that this trend is caused by an increase in the capital-output ratio by natural law. Focusing on the bargaining position between labor and capital, others attribute declining trends to globalization, which contrasts with this paper s approach. Rodrik (1997) argues that globalization changes the bargaining position of labor and capital because of their relative mobility. Researchers rely on the bargaining model for this approach (Harrison, 2005; Jayadev, 2007; Schneider, 2011). Under an imperfect market, labor and capital engage in 7 In their model, they use different labor skill types. Under capital-skill complementary, the capitalaugmenting technical progress generates a declining labor share. 8 Focusing on long-run trends, they estimate ε = 1.25 on the basis of cross-sectional variation in countries and industries. 5

7 the efficient bargaining over excess profit. Openness, which reduces the bargaining position of labor, leads to the declining labor share. Using country-level panel data, the previous empirical work on this topic suggests that rising trade shares reduce labor share (Stockhammer, 2013; Harrison, 2005; Jayadev, 2007) and that offshoring 9 negatively affects labor share (IMF, 2007). The bargaining power between labor and capital can be changed by labor market institutions. Blanchard and Giavazzi (2003) consider labor market regulation as a determinant of the bargaining power of workers, and they argue that the decrease in the labor share in Europe during the 1980s was caused by a decrease in the bargaining power of workers. Empirical studies support the role of labor market institutions. The usual proxy variables for bargaining power include union density (Stockhammer, 2013), unemployment benefits, and government spending (Harrison, 2005). Finally, this paper is based on firm heterogeneity à la Melitz (2003) and it considers offshoring at the firm level. This modeling framework is based on importer premia from recent empirical studies. Like exporter premia, recent empirical work using manufacturing firm level data has consistently found that importers are more productive than non-importers in Germany (Vogel and Wagner, 2010) and that importers are more productive and more capitalintensive than non-importers in the United States (Bernard et al., 2007), Italy (Castellani et al., 2010), Belgium (Muûls and Pisu, 2009), and Chile (Kasahara and Rodrigue, 2008). 3 Model The model assumes an economy that consists of a single monopolistically competitive industry where heterogeneous firms produce differentiated products by combining two intermediate inputs and decide offshoring for a single intermediate input. To produce each intermediate input, firms use CES technology that employs two factors of production: labor and capi- 9 Offshoring is measured by the imports of intermediate inputs, which are provided in the OECD Input- Output Tables. 6

8 tal. The representative household provides labor and capital and owns all firms. Thus, all payments to labor and capital and all profits go to the household. The model decomposes income sources of the household and studies the effect of offshoring on the share of labor compensation. It presents the discussion from the point of view of developed countries. Firms in developed countries offshore to firms in developing countries. 3.1 Household ( Household preferences across varieties take the standard CES form U = y(ϕ) σ 1 σ 0 ) σ σ 1 dϕ with an elasticity of substitution between varieties, σ > 1. These preferences generate a demand function y(ϕ) = EP σ 1 p(ϕ) σ for every variety, ϕ, where p(ϕ) is the price of each variety, P = ( 0 p(ϕ) 1 σ dϕ ) 1 1 σ is the price index, and E is the aggregate level of spending in the economy. The household inelastically provides homogeneous labor, L, and capital, K, to the economy. 3.2 Firm Production Function Each firm produces a unique variety and faces monopolistic competition. Firms are heterogeneous in productivity, ϕ, which is drawn from the cumulative distribution, G(ϕ), before deciding on production and offshoring of its intermediate input. Each good is produced by combining two intermediate inputs, x 1 and x 2, without additional labor or capital. { x1 y(ϕ) = ϕ min, x } 2, where γ j > 0 γ 1 γ 2 The resulting intermediate input demands are x 1 = γ 1y, x ϕ 2 = γ 2y. Firms use CES technology, which employs two production factors, labor and capital, to produce ϕ intermediate 7

9 inputs. x 1 (ϕ) = x 2 (ϕ) = [α (A l1 l 1 (ϕ)) ε 1 ε [α (A l2 l 2 (ϕ)) ε 1 ε ] + (1 α) (A k1 k 1 (ϕ)) ε 1 ε ε 1 ε + (1 α) (A k2 k 2 (ϕ)) ε 1 ε ] ε ε 1 where, α is a distribution parameter α (0, 1) and A lj and A kj are labor-augmenting and capital-augmenting technology parameters, respectively. It allows different factor-augmenting technologies for producing x 1 and x 2. l j (ϕ) and k j (ϕ) represent the amount of labor and capital employed. A lj l j (ϕ) are the effective labor and A kj k j (ϕ) are effective capital used for the production. ε is an elasticity of substitution between labor and capital in production. If ε < 1, then labor and capital are gross-complements. If ε > 1, then labor and capital are gross-substitutes. The marginal cost and price for the goods are as follows: MC(ϕ) = γ 1W 1 + γ 2 W 2, p(ϕ) = σ γ 1 W 1 + γ 2 W 2 ϕ σ 1 ϕ where, W 1 = ( α ε w 1 ε A ε 1 l 1 ) + (1 α) ε r 1 ε A ε 1 1 ε 1 k 1, W 2 = ( α ε w 1 ε A ε 1 l 2 The resulting cost-minimizing factor demand functions are below: ( α ) ε l 1 = W1 ε γ 1 y w ( 1 α k 1 = W1 ε r ϕ Aε 1 l 1, l 2 = W ε 2 ) ε γ 1 y ϕ Aε 1 k 1, k 2 = W ε 2 ( α ) ε γ 2 y w ( 1 α r ϕ Aε 1 l 2 ) + (1 α) ε r 1 ε A ε 1 1 ε 1 k 2. ) ε γ 2 y ϕ Aε 1 k 2 (1) The firm uses a technology to produce x 2 that is more advanced than the technology used to produce x 1 : i.e., A l1 A l2 and A k1 A k2. This implies that the marginal cost of producing x 1 is higher than that of x 2, W 1 > W 2. Thus, from the firms point of view, producing x 1 is a relatively inefficient part of production, and so firms consider whether or not to offshore x The model allows for different relative-factor augmenting technologies for x 1 and x 2, 10 For the sake of simplicity, I only models the extensive margin of offshoring. 8

10 A k1 A l1 A k 2 A l2. Combined with a magnitude of ε, whether it is greater than or smaller than the unity, the different relative-factor augmenting technologies generate the different labor shares, depending on a firm s offshoring status. As the model shows in the following, a firm s ( ) Ak1 ε 1 ( ) Ak2 ε 1. labor share decreases when it offshores x 1 if A l1 < A l2 In the literature, two approaches explain the declining trends of labor share that accompany technical change: capital-augmenting technical change with ε > 1 and labor-augmenting technical change with ε < 1. In both cases, the direction of technical change is labor saving, which leads to a decrease in the relative demand for labor. These two explanations are ( ) Ak1 ε 1 ( ) Ak2 ε 1, consistent with the condition A l1 < A l2 which this paper takes as a given. The condition holds in two cases. The first case is A k 1 A l1 < A k 2 A l2 given ε > 1. Here labor and capital are gross substitutes and the firm uses relatively more capital-augmenting technologies for x 2 than x 1. Thus, the firm uses more capital per labor to produce x 2 than to produce x 1. The second case is A k 1 A l1 > A k 2 A l2 given ε < 1. In this case, labor and capital are gross complements and the firm uses relatively more labor-augmenting technologies for x 2 than for x 1. Thus, the firm uses less labor per capital to produce x 2 than to produce x 1. From the input demand functions (1), capital intensity for x 1 and x 2 follows: ( ) k = l i ( 1 α α ( 1 α α ) ε ( w r ) ε ( w r ) ε ( Ak1 A l1 ) ε 1 if i = 1 ) ε ( Ak2 A l2 ) ε 1 if i = 2 The condition implies that in both cases the capital intensity for producing x 1 is smaller than that needed for x 2. Thus, in terms of capital intensity, offshoring x 1 can be viewed as firm s offshoring the relatively labor-intensive part of production. 11 Foreign firms in the offshoring destination provide x 1 at price W Thus, if a firm offshores x 1 its marginal cost for x 1 is W 0, which firms take as a given. The analysis is 11 Similarly, Elsby et al. (2013) argue that offshoring of labor-intensive components in the United States supply chains causes the decline in labor share. 12 I assume that firms import x 1 through arm s length and pay W 0, which is given exogenously. 9

11 limited to the case W 0 < W 1 because no firm has an incentive to offshore in the opposite case. Depending on its idiosyncratic productivity, ϕ, a firm decides to produce domestically if its expected profits are high enough to cover its fixed costs of production, f d. Keeping ϕ and taking W 0, the firm also decides whether or not to offshore the inefficient part of production x 1. By offshoring x 1, the firm can reduce the marginal cost γ 1W 1 +γ 2 W 2 > γ 1W 0 +γ 2 W 2 ϕ ϕ because W 0 < W 1. However, as noted by Antras and Helpman (2004), offshoring incurs higher fixed costs than producing domestically, f o > f d. 13 Thus, there is a tradeoff between the lower marginal cost and higher fixed costs. The higher fixed costs of offshoring generate efficient firms to engage in offshoring. The capital intensity of offshoring firms is higher than that of non-offshoring firms because firms offshore the relatively labor-intensive part of production. These are consistent with the importer premia: importers are more productive and capital intensive than non-importers Profit and Cutoff Productivities Firms compete in monopolistic competition markets, and so each firm s profit maximizing price is a constant markup over marginal costs. When deciding whether or not to offshore x 1, the firm compares the total profit under two possible choices, which are described below: Profits if it serves without offshoring. π d (ϕ) = 1 ( ) 1 σ σ (γ 1 W 1 + γ 2 W 2 ) 1 σ EP σ 1 ϕ σ 1 f d (2) σ σ 1 Profits if it serves with offshoring. π o (ϕ) = 1 ( ) 1 σ σ (γ 1 W 1 + γ 2 W 2 ) 1 σ EP σ 1 θ σ 1 ϕ σ 1 f o (3) σ σ 1 where, θ = γ 1W 1 +γ 2 W 2 γ 1 W 0 +γ 2 W 2 > 1. After drawing productivity ϕ, the firm will not produce at all if the expected profit is smaller than the production fixed costs, f d. Thus, the survival cutoff 13 Antras and Helpman (2004) point out that the fixed costs of search, monitoring, and communication are significantly higher in the foreign country. 10

12 π π o π d 0 ϕ σ 1 f d f o (ϕ ) σ 1 (ϕ o ) σ 1 Exit Don t offshore Offshore Figure 3: Equilibrium Offshoring Sorting productivity, ϕ, is pinned down by the zero profit condition, π d (ϕ ) = 0. ϕ = σ γ 1 W 1 + γ 2 W 2 σ 1 P ( ) 1 σf σ 1 E (4) The marginal firm that offshores x 1 is indifferent between offshoring and not offshoring. The additional profit that the least efficient offshoring firm earns should be zero. Thus, the cutoff productivity for offshoring, ϕ o, comes from the condition π d (ϕ o ) = π o (ϕ o ). ϕ o = ( fo ) 1 σ 1 f d 1 ϕ (5) θ σ 1 1 Note that as long as fo f d > θ σ 1, only the most productive firms will offshore. Figure 3 shows the selection into offshoring. Only the most productive firms find it worthwhile to pay the higher fixed costs to benefit from the lower marginal costs associated with offshoring. There is also a free entry condition into the industry. To enter the industry, firms pay a fixed entry cost, f e, and draw a productivity, ϕ, from the cumulative distribution, G(ϕ). Some of these firms draw ϕ < ϕ and exit immediately. Also, firms have a uniform probability 11

13 of a sudden forced exit, δ. In equilibrium, the free entry condition requires that the sunk entry cost equals the present value of expected profits: [1 G(ϕ )] π δ = f e (6) where 1 G(ϕ ) is the probability of survival and π is the per-period average profits. I assume that firms are drawing ϕ from a Pareto distribution G(ϕ) = 1 ϕ κ, in which κ > 1. Imposing the Pareto distribution and using (4) and (5), the average profit is a weighted average of two types of firms, non-offshoring and offshoring. where, ϕ σ 1 d and ϕ σ 1 o to below. 14 π = G(ϕo ) G(ϕ ) π 1 G(ϕ d ( ϕ d ) + 1 G(ϕo ) ) 1 G(ϕ ) π o ( ϕ o ) (7) = ϕ o ϕ σ 1 g(ϕ) dϕ is the average productivity of the non-offshoring firms ϕ G(ϕ o ) G(ϕ ) = ϕ ϕ σ 1 g(ϕ) dϕ is the average productivity of offshoring firms. (7) simplifies ϕ o 1 G(ϕ o ) where, = 1 + (θ σ 1 1) π = f d σ 1 κ σ + 1 (8) ( ) ϕ σ κ 1, ( ) σ κ 1 ( ) o ϕ and ϕ o σ κ 1 ϕ = f σ 1 o f d 1 (θ σ 1 1) κ σ+1 σ 1. The free entry condition (6) determines the cutoff productivity for the marginal surviving firm, and the cutoff productivity for the marginal offshoring firm is determined from (5). ( σ 1 ϕ f d = κ σ + 1 δf e ) 1 κ, ϕ o = ( fo f d 1 θ σ 1 1 ) 1 σ 1 ( σ 1 κ σ + 1 f d δf e 14 See the Appendix for details. I impose the parameter restriction for the average profit to be positive: κ > σ 1. ) 1 κ 12

14 ϕ 0 ϕ o 0 ϕ ϕ 1 ϕ o 1 ϕ Exit Stay non-offshoring Start offshoring Continue offshoring Figure 4: Effect of Falling Fixed and Variable Offshoring Costs Effect of Decreasing Offshoring Costs The decrease in offshoring fixed costs, f o, and variable cost, W 0, increases the survival cutoff productivity, ϕ f o < 0, ϕ W 0 < 0 and it lowers the offshoring cutoff productivity, ϕo f o > 0, ϕo W 0 > As a result, and as is illustrated in Figure 4, the fraction of offshoring firms among surviving firms increases as offshoring costs decrease. 16 Overall, the representative household is made better off by decreasing offshoring costs. Welfare is determined by the inverse of the price index, which can be obtained by substituting the survival cutoff productivity in the zero-profit condition (4) for the marginal firm. P = σ γ 1 W 1 + γ 2 W 2 σ 1 ϕ ( ) 1 σfd σ 1 E Since decreasing offshoring costs increases the survival cutoff productivity, ϕ, it increases welfare. Thus, irrespective of its impact on the distribution of total income to each factor of production, offshoring increases the welfare of the representative household. Nonetheless, in reality, the household does not own the same proportion of labor and capital. If offshoring changes the relative payment to labor and capital, it can make some households worse off. 15 See the Appendix for proofs of all comparative statics. ( 16 The fraction of offshoring firms is 1 G(ϕo ) 1 G(ϕ ) = fo with respect to f o, and W 0. f d 1 ) κ σ 1 ( θ σ 1 1 ) κ σ 1, which is a decreasing function 13

15 3.3 Labor Share A firms revenue less payment to offshoring becomes the household s income because the household owns the firms and provides production factors, labor and capital. In this section, I decompose the income sources of the household and study the effect of offshoring on labor share Decomposition of the Average Revenue In this economy, there are two types of firms, offshoring and non-offshoring. Thus, like the average profit (7), the average revenue is a weighted average of non-offshoring firms average revenue, R d, and offshoring firms average revenue, R o. G(ϕ o ) G(ϕ ) R 1 G(ϕ d ( ϕ d ) + 1 G(ϕo ) ) 1 G(ϕ ) R o ( ϕ o ) = σf dκ κ σ + 1 (9) Each firm s revenue is the sum of payment to labor, capital, offshoring destination, profit, and fixed costs. Keeping track of each component for both types of firm s revenue, the average revenue (9) is decomposed into each component. 17 [ ( (σ 1)f d κ γ1 W1 ε α ε w 1 ε A ε 1 ( ) ) l 1 ϕ o σ κ 1 1 κ σ + 1 γ 1 W 1 + γ 2 W 2 ϕ + γ ] 2W2 ε α ε w 1 ε A ε 1 l 2 γ 1 W 1 + γ 2 W 2 }{{} Average payment to labor [ ( + (σ 1)f dκ γ1 W1 ε (1 α) ε r 1 ε A ε 1 ( ) ) k 1 ϕ o σ κ 1 1 κ σ + 1 γ 1 W 1 + γ 2 W 2 ϕ + γ ] 2W2 ε (1 α) ε r 1 ε A ε 1 k 2 γ 1 W 1 + γ 2 W 2 }{{} Average payment to capital + (σ 1) f ( ) dκ γ 1 W 0 ϕ o σ κ 1 κ σ + 1 θσ γ 1 W 1 + γ 2 W 2 ϕ }{{ } Average payment to offshoring + (σ 1)f d κ σ f d }{{}}{{} Average fixed costs Average profit (10) (11) (12) (13) 17 See the Appendix for details. 14

16 The average labor compensation, (10), is the average value of marginal product of labor; the average capital compensation, (11), is the average value of marginal product of capital. These depend on each firm s technology for producing two intermediate inputs. In this monopolistic competition with fixed costs, surviving firms earn positive profits and pay fixed costs, (13), which also become the household s income. I assume that profits and fixed costs also are compensated to the household in the form of compensation to labor and capital. This decomposition can be divided into two parts: (10)-(12) is σ 1 σ revenue, and (13) is 1 σ fraction of the average fraction of the average revenue. Then, there are two sources of labor income from each part. Therefore, labor share, S L, is a weighted average of two labor shares, S L1 and S L2. S L = λs L1 + (1 λ)s L2 where, λ = σ 1 σ ( 1+ θ σ )( γ 2 W 2 ϕ o ) σ κ 1 1 γ 1 W 1 +γ 2 W 2 ϕ ( 1σ ) ) ( ) θ σ γ 1 W 0 +γ 2 W 2 ϕ o σ κ 1. 1 γ 1 W 1 +γ 2 W 2 ϕ ( 1+ If the goods markets are competitive and if there are no fixed costs, then the average payments to production factors, (10) and (11), exhaust the average revenue after payments are made to the offshoring destination, (12). In this case, the share of labor compensation is defined as S L1. S L1 = wl wl + rk = rk wl (14) where, L = ϕ l(ϕ)dϕ, K = ϕ k(ϕ)dϕ. S L1 depends on the relative price of labor, w r, and the capital intensity of the economy. Under an imperfect market, labor and capital engage in bargaining. S L2 is the share of labor compensation obtained through bargaining over the profit and fixed costs. However, for the sake of simplicity, this model does not include bargaining structure because its focus is the effect that offshoring with different technologies for producing intermediate inputs has on factor compensation. I focus on S L1 and treats S L2 as determined outside of the model by 15

17 labor market institutions. Abstracting from the institutional setting, a change in labor share is explained as a result of changes in underlying production technologies, which is reflected in S L Effect of Offshoring on the Relative Demand for Labor In this economy, the supply of production factors is fixed because the household supplies labor and capital inelastically. ( ) S L = L K K (15) Thus, S L1 is determined by the relative price of labor. The aggregate relative demand for labor is calculated from (10) and (11). ( ) D ( L α = K 1 α ) ε ( w ) ε A ε 1 l 1 + ρ γ 2 r A ε 1 k 1 + ρ γ 2 ( W 2 γ 1 ( W 2 γ 1 ) ε W 1 A ε 1 l 2 ) ε (16) W 1 A ε 1 k 2 ( ( 1+ ϕ o ) σ κ 1(θ ) ϕ where, ρ = σ 1). The equilibrium relative price of labor is pinned down by 1 ( ϕo ϕ )σ κ 1 the market clearing from (15) and (16). Then, using the relative price of labor and (14), S L1 simplifies to below. S L1 = α α ( K L ) ε 1 ε 1 [ ( ) A ε 1 k +ρ γ 2 W2 εa ] 1 ε 1 ε 1 γ 1 W 1 k ( ) 2 A ε 1 l +ρ γ 2 W2 εa ε 1 1 γ 1 W 1 l 2 (17) In the Cobb-Douglas case, ε = 1, S L1 becomes α, which does not vary under any circumstance. If the relative factor-augmenting technologies for the two intermediate goods are the same, A l 1 A k1 = A l 2 A k2 = A l A k, capital intensity for producing x 1 and x 2 is the same and offshoring does not affect labor share. In this case, S L1 simplifies to 1 decreases as ( A k 1+ 1 α α ( K L ) ε 1 ε ( ) ε 1. Thus, S L1 A k ε A l A l ) ε 1 increases. In other words, SL1 decreases when the direction of technical change is labor saving. This technical change explains the global declining trend of labor 16

18 w r ( L K ) S = L K ( w r ( w r ) ) 1 2 A B ( L ) D K 1 ( L ) D K 2 L K Figure 5: Effect of Offshoring on Relative Demand for Labor share. When there are different relative factor-augmenting technologies for the two intermediate goods, offshoring the inefficient part of production, x 1, enhances the technical change. In this economy, there are two types of firms, offshoring and non-offshoring. Here, ρ can be interpreted as a weight for offshoring firms. It is a decreasing function with respect to f o and W 0. As offshoring fixed costs and marginal cost decrease, a greater fraction of firms engage in offshoring (increasing ρ); this occurs in response to both decreasing the offshoring cutoff productivity and increasing the survival cutoff productivity. It reallocates labor and capital away from small, less-efficient firms and into large, more-efficient firms. When resources are reallocated, the relative demand for labor decreases under the labor-saving technical change assumption. Therefore, labor share decreases as more firms engage in offshoring. 18 Figure 5 shows the relative demand and supply for labor depending on the relative factor price. The relative demand curve slopes downward and the relative supply curve is vertical, which reflects the fact that the supply of factors is fixed. The decrease in offshoring costs decreases the relative demand for labor and shifts the relative demand from ( ) L D to ( ) L D. K 1 K 2 With the decrease in the relative demand for labor, the equilibrium shifts from point A to point B. That is, the relative price of labor decreases from ( ) w to ( ) w. The supply of r 1 r 2 18 See Additional Appendix for the simulations of decreasing offshoring costs on labor share. 17

19 Done in developed countries x 1 x 2 Labor-intensive Offshoring Capital-intensive x 0 x 1 Done in developing countries Figure 6: Implication for Developing Countries factors is fixed in this model, which understands that offshoring is a demand shock. If the household endogenously decides on the supply of labor and capital, the relative supply curve slopes upward. In this case, the decrease in the relative demand for labor not only decreases the relative price of labor, it increases capital intensity in the economy, which decreases labor share-just as it does in the case of a fixed relative supply of factors. The decrease in the relative demand for labor is consistent with both a growth in real wages that has lagged behind labor productivity and an observed increase in capital intensity (Fleck et al., 2011) Implication for Developing Countries Until now, I have presented the discussion from the point of view of developed countries. In the developing offshoring destination countries, too, the household provides labor and capital to firms and firms are employing labor and capital. Then, the average payment to offshoring, (12), is also compensated to the household as labor income and capital income in the offshoring destination. In developed countries, x 1 is relatively labor intensive. If the x 1 uses more advanced technology in developing countries, or if the x 1 is relatively capital intensive in developing countries, as illustrated in Figure (6), then offshoring will decrease the relative demand for labor and decrease labor share in developing countries. 18

20 4 Estimation The focus of the empirical study is to assess whether aggregate firm decisions to reallocate part of production to developing countries decrease the relative demand for labor and thereby decrease labor share at the industry level in developed countries. 4.1 Empirical Specifications The estimating specification is motivated by equation (17). The empirical specification is as follows: S Lijt = β 1 + β 2 Offshoring ijt + β 3 Growth ijt + β 4 log (K/L) ijt + µ it + ɛ ijt (18) where i, j, and t index countries, industries, and time, respectively; Offshoring ijt is an offshoring index; µ it is the country-year fixed effects; and ɛ ijt is the error term. This specification assumes that offshoring affects labor share by changing the relative factor price only. In reality, however, offshoring can affect labor share by also changing capital intensity. Allowing both capital intensity and the relative price of labor to vary leads to an alternative specification. S Lijt = β 1 + β 2 Offshoring ijt + β 3 Growth ijt + µ it + ɛ ijt (19) Offshoring is measured as the share of foreign intermediate inputs in total intermediate inputs. It also distinguishes the origin of the intermediate inputs either from developed countries or developing countries. In both specifications, the coefficients on offshoring, β 2, are expected to be negative as firms offshore the relatively labor-intensive parts, particularly in the case of offshoring to developing countries. 19

21 4.2 Data The empirical work in this paper uses the World Input-Output Database (WIOD). The WIOD covers the period from 1995 to 2011 and includes 35 industries-14 manufacturing industries, and 21 non-manufacturing industries-in 40 countries plus the Rest of the World. 19 The WIOD includes the World Input-Output Tables (WIOTs) and the Socio Economic Accounts (SEA). The WIOTs are constructed by combining national input-output tables with bilateral international trade data (Dietzenbacher et al., 2013). The SEA contains annual data ( ) on value added, labor compensation, capital compensation, real fixed capital stock in 1995 prices, and the total hours worked by employees in each country-industry-year. The main source of the data is the EU KLEMS, and it includes additional data for a larger set of countries (Erumban et al., 2012). The SEA uses local currency while the WIOTs uses US dollar per unit of local currency. Thus, SEA variables are converted to current US dollar using the exchange rates used in constructing the WIOTs. 20 In this study, the dependent variable is labor share. For each country-industry-year, the labor share is a ratio of labor compensation to value added. S Lijt = Labor compensation ijt Value added ijt where i, j, and t index countries, industries, and time, respectively. In theory, the value added is decomposed into compensation to labor and capital. In the SEA, compensation to capital is defined as a residual-i.e., value added minus compensation to labor. 21 Thus, the sum of labor and capital compensation equals the value added by the construction. Also, the SEA adjusts self-employed workers income, which resolves the issue of calculating labor 19 The WIOD includes 27 countries of the European Union and 13 other major economies: Australia, Brazil, Canada, China, India, Indonesia, Japan, Mexico, Russia, South Korea, Taiwan, Turkey, and the United States. 20 Exchange rates are from Timmer et al. (2014), who sourced them from IMF Statistics. 21 Since capital income is defined as residual, it can be interpreted in a broad sense: as compensation to physical, intangible, and financial capital (Timmer et al., 2014). 20

22 share that Gollin (2002) raises. 22 The empirical studies focus on manufacturing industries in developed countries because these show the distinctive patterns with offshoring that are noted in the introduction. In developing countries, declining trends are mainly explained by the non-manufacturing industries. Also, many developing countries in the WIOD went through transition periods. Overall, the decline in labor share in developing countries was led mainly by China. 23 Excluding China, two non-manufacturing industries contribute most of the decline in labor share: agriculture and the mining industry. 24 Since the late 1990s, 12 developing countries among 40 countries in the WIOD transitioned from centrally planned economies to market economies. 25 The shift-share analysis in Table 17 of the Appendix shows that from 1995 to 2007, the change of labor share in transition economies was dramatic. In the case of Poland, labor share decreased from to In transition economies, labor share can be mainly affected by the liberalization and privatization process when it is accompanied by legal and institutional reforms. The key independent variable is the proxy variable for offshoring. Following the ideas of Feenstra and Hanson (1999), I measure offshoring as the share of imported intermediate inputs in total purchases of intermediate inputs in each country-industry-year. Feenstra and Hanson (1999) assume that the share of an industry s imports of each input relative to its total demand is the same as the share of economy-wide imports relative to total demand, which is called the proportionality assumption (Feenstra and Jensen, 2012). 26 Constructing the WIOTs, Dietzenbacher et al. (2013) develop an estimation method that determines the share of imports that goes to the end-use categories: intermediate consumption, final consumption, and gross fixed capital formation. Within each end-use category, the allocation 22 For developed countries, the SEA assumes that the compensation per hour of self-employed is equal to that of employees. For developing countries, it uses additional information that differs by country. (Erumban et al., 2012) 23 See Table 9 and 10 in the Appendix. 24 See Table 13 in the Appendix. 25 The classification of the transition economies follows IMF (2000): Bulgaria, China, Czech Republic, Estonia, Hungary, Lithuania, Latvia, Poland, Romania, Russia, Slovak Republic, and Slovenia. 26 This is also called an import comparability assumption. 21

23 is based on the proportionality assumption. In this study, directly from the WIOTs, offshoring is defined as follows: Offshoring ijt = Input abt Input abt Input abt a i b a i,a A b a i,a D b = + Input abt Input abt Input abt a b a b a b }{{}}{{} Offshoring to developed ijt Offshoring to developing ijt (20) where Input abt is the purchase of inputs by country i industry j from country a industry b during year t. The denominator is the total intermediate inputs used, while the numerator is total intermediate inputs from foreign countries for each country-industry-year. The total intermediate inputs from foreign countries are split according to origin: intermediate inputs imported from developed countries (A) and developing countries (D). The sum of offshoring to developed countries and developing countries is equal to the offshoring. The capital intensity is the logarithm of the total hours worked by employees over real fixed capital stock in 1995 prices. 27 The growth is the proportionate change in value indices for value added in each industry-country-year. Since labor share behaves countercyclically, it controls fluctuations. Labor share can be affected by a change in the bargaining position of labor, which is usually proxied by labor market institutions. However, due to the limitations of the data, finding proper proxies to control for the bargaining channel at the country-industry-year level is difficult. Instead, it uses country-year fixed effects and country-industry fixed effects to control for labor market institutions. Table 2 presents summary statistics of the variables included in the statistical analysis. 28 To check the trends of variables the table also includes summary statistics for the selected years 1996 and Table 2 shows the same patterns in aggregate variables found in Figure 27 If available, SEA uses EU KLEMS data for capital stock that has been constructed using the Perpetual Inventory Method. For other countries, SEA uses the ICVAR and Harberger method to produce estimates (Erumban et al., 2012). 28 After eliminating missing information, 1.3% of observations are excluded as outliers. This excludes labor share that does not lie between 0 to To check the trends, the table selects 2007-prior to the financial crises in

24 Year: Year: 1996 Year: 2007 Variable Mean Std. Dev. Mean Std. Dev. Mean Std. Dev. Labor share Capital intensity Offshoring Offshoring to developed Offshoring to developing Growth Observation Source: Calculations based on the World Input-Output Database Table 2: Summary Statistics: Variables in Regressions 2. Between 1996 and 2007 the average labor share declined while the average offshoring in manufacturing industries increased. The increase in the average offshoring was driven mainly by the increase in offshoring to developing countries. Table 2 also shows that average capital intensity increased. 4.3 Results Table 3 reports results from regressions of labor share on offshoring variables from the panel of 21 developed countries and 14 of their manufacturing industries. 30 In all specifications, country-year fixed effects control for country-specific labor market institutions and common trends, which are clustered at the country-industry level to account for potential serial correlation of errors. Additionally, growth controls for countercyclical fluctuations. In all estimations, all coefficients on growth are negative and significant. Column 1 in Table 3, which is based on specification (19), estimates the total effect of offshoring by changing both the relative price of labor and capital intensity. The coefficient on offshoring is negative and significant; it is also large, implying that a one percentage point increase in offshoring is associated with about a percentage point decrease in labor share. With the same specification, columns 2 and 3 in Table 3 decompose offshoring into its origin: offshoring to developed countries and developing countries. Column 4 includes both 30 See Additional Appendix for the same regression results for all countries, for developed and developing countries, and for manufacturing and non-manufacturing industries in developed and developing countries. 23

25 destinations. Exactly as predicted, the results show that offshoring to developing countries is significantly negatively associated with labor share. Columns 5 to 8 in Table 3 replicate the same specifications with country-industry random effects. Consistent with pooled OLS results, the results show that the coefficients on offshoring are negative and significant. Decomposing offshoring by its origin, the results show that offshoring to developing countries is significantly negatively associated with labor share. The magnitudes of coefficients are large still, although they decrease compared to pooled OLS results. With random effect estimations, the results imply that a one percentage point increase in offshoring to developing countries is associated with about a to 0.42 percentage point decrease in labor share. Columns 9 to 12 include the country-industry fixed effects, which only exploit variation within country-industry over time. Estimation results are similar to the random effect estimations, although they have slightly reduced magnitudes. Columns 1 to 12 in Table 4 present the same specifications found in Table 3, except that a control for capital intensity has been added. The results also show that offshoring, especially offshoring to developing countries, is robustly negatively associated with labor share. With random effect estimations, the results imply that a one percentage point increase in offshoring to developing countries is associated with about a to percentage point decrease in labor share. Compared to specifications that do not control for capital intensity, the magnitudes of coefficients decrease. The results imply that offshoring to developing countries not only decreases the relative price of labor, it also increases capital intensity. Table 5 shows that coefficients on offshoring to developing countries are positively associated with capital intensity. 24

26 Table 3: Effect of Offshoring on Labor Share Results 1: OLS, Random Effect, Fixed Effect Estimations Dependent Variable: Labor share Pooled OLS Random Effect Fixed Effect VARIABLES (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) Offshoring *** *** *** (0.0803) (0.0530) (0.0718) Offshoring to developed * (0.114) (0.0985) (0.109) (0.0860) (0.135) (0.117) Offshoring to developing *** *** *** *** *** *** (0.0706) (0.0718) (0.0661) (0.0646) (0.105) (0.104) Growth *** *** *** *** *** *** *** *** *** *** *** *** (0.0335) (0.0369) (0.0339) (0.0339) (0.0225) (0.0212) (0.0224) (0.0228) (0.0233) (0.0223) (0.0233) (0.0237) 25 Constant 0.751*** 0.672*** 0.722*** 0.723*** 0.732*** 0.690*** 0.710*** 0.725*** 0.739*** 0.678*** 0.686*** 0.728*** (0.0392) (0.0386) (0.0357) (0.0371) (0.0385) (0.0395) (0.0363) (0.0379) (0.0231) (0.0296) (0.0111) (0.0267) Observations 3,718 3,718 3,718 3,718 3,718 3,718 3,718 3,718 3,718 3,718 3,718 3,718 R-squared Number of group Country*Year FE Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Clustered robust standard errors are in parentheses. Errors are clustered at the country-industry level. *** p<0.01, ** p<0.05, * p<0.1 Source: Calculations based on the World Input-Output Database

27 Table 4: Effect of Offshoring on Labor Share Results 2: OLS, Random Effect, Fixed Effect Estimations Dependent Variable: Labor share Pooled OLS Random Effect Fixed Effect VARIABLES (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) Offshoring * *** *** (0.0599) (0.0445) (0.0711) Offshoring to developed * (0.0816) (0.0818) (0.0906) (0.0756) (0.134) (0.115) Offshoring to developing * * *** *** *** *** (0.0761) (0.0756) (0.0596) (0.0571) (0.106) (0.105) Capital intensity *** *** *** *** *** *** *** *** (0.0144) (0.0140) (0.0146) (0.0143) (0.0154) (0.0162) (0.0169) (0.0168) (0.0250) (0.0258) (0.0258) (0.0252) 26 Growth *** *** *** *** *** *** *** *** *** *** *** *** (0.0340) (0.0354) (0.0347) (0.0342) (0.0227) (0.0216) (0.0226) (0.0229) (0.0236) (0.0226) (0.0236) (0.0240) Constant 1.272*** 1.302*** 1.245*** 1.255*** 1.021*** 1.039*** 0.981*** 0.997*** 0.829*** 0.767*** 0.776*** 0.818*** (0.0590) (0.0585) (0.0599) (0.0579) (0.0701) (0.0750) (0.0748) (0.0777) (0.131) (0.141) (0.128) (0.136) Observations 3,718 3,718 3,718 3,718 3,718 3,718 3,718 3,718 3,718 3,718 3,718 3,718 R-squared Number of group Country*Year FE Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Clustered robust standard errors are in parentheses. Errors are clustered at the country-industry level. *** p<0.01, ** p<0.05, * p<0.1 Source: Calculations based on the World Input-Output Database