International Capital Movements and Relative Wages: Evidence from U.S

International Economic Studies Vol. 47, No. 1, 2016 pp. 17-36 Received: 08-09-2015 Accepted: 24-05-2016

International Capital Movements and Relative Wages: Evidence from U.S. Manufacturing Industries

* Indro Dasgupta Department of Economics, Southern Methodist University, Dallas, USA Thomas Osang* Department of Economics, Southern Methodist University, Dallas, USA*

Abstract In this paper, we use a multi-sector specific factors model with international capital mobility to examine the effects of globalization on the skill premium in U.S. manufacturing industries. This model allows us to identify two channels through which globalization affects relative wages: effects of international capital flows transmitted through changes in interest rates, and effects of international trade in goods and services transmitted through changes in product prices. In addition, we identify two domestic forces which affect relative wages: variations in labor endowment and technological change. Our results reveal that changes in labor endowments had a negative effect on the skill premium, while the effect of technological progress was mixed. The main factors behind the rise in the skill premium were product price changes (for the full sample period) and international capital flows (during 1982-05).

Keywords: capital mobility, speciﬁc factors, skill premium, globalization, labor endowments, technological change

JEL Classiﬁcation: F16, J31.

* Corresponding Author, Email: [email protected] * We would like to thank seminar participants at Southern Methodist University and Queensland University of Technology for useful comments and suggestions. We also thank Peter Vaneﬀ and Lisa Tucker who provided able research assistance.

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1. Introduction investment is an important factor in The U.S. economy has witnessed a explaining relative wage changes. Eckel [8] significant increase in volatility and formulates a 3x2 trade model with magnitude of international capital flows efficiency wages and demonstrates how since 1980, as shown in Figure 1. In capital movements, and not wage rigidities, addition, while there were moderate net are responsible for an increase in wage outflows of capital prior to 1980, the U.S. inequality3 . Feenstra and Hanson [11], economy experienced a strong net inflow of Taylor and Driffield [34], and Figini and foreign direct investment (FDI)1 between Görg [13], using industry-level data for 1980-90 and then again from 1996 to 2001. Mexico, the UK, and Ireland, respectively, Between 2001 and 2005, net FDI flows find that international capital flows affect have become substantially more volatile the wage premium. Blonigen and Slaughter with large in-and outflows. One of the [4], in contrast, do not find significant interesting implications of this reversal in effects of FDI on U.S. wage inequality. U.S. international capital flows is its impact The goal of this paper is to study the on the relative wages between skilled and impact of capital flows on relative wages in unskilled workers, i.e. the skill premium. the U.S. over the period 1958-2005, while Provided that capital and skilled labor are at the same time taking account of other complementary factors of production2, net factors that potentially affect relative wages capital inflows constitute a positive demand such as international trade in goods and shock for skilled labor causing a rise in the services, total factor productivity (TFP) skill premium. Therefore, the reversal of growth, factor-specific technological international capital flows in the 80s and change, and changes in labor endowments. the second half of the 90s is a potential We formulate a multi-sector specific factors culprit for the rise in the U.S. skill premium (SF) model of a small open economy with that began in the early 80s and peaked perfectly mobile international capital4 . The around 2001 (see Figure 2). specific factor is skilled labor, while both The issue of whether capital flows cause capital and unskilled labor are mobile changes in the skill premium has been across sectors. Exogenous changes in the examined in papers by Feenstra and international interest rate trigger capital 5 Hanson [10], [11], [12], Sachs and Shatz outflows and inflows in this model . The [32], Eckel [8], Blonigen and Slaughter [4], solution to this multi-sector SF models Taylor and Driffield [34] and Figini and yields the Görg [13],[14], among others. Feenstra and Hanson [10] and Sachs and Shatz [32] formulate theoretical models in which they examine the impact of capital outflows from a skilled labor abundant economy like the United States. In both papers the capital 3 outflow occurs in the form of outsourcing De Loo and Ziesmer [7] formulate a specific factors model with international capital mobility. Two forms intermediate goods production to an of globalization are examined: exogenous product unskilled labor abundant economy. Both price changes and exogenous changes in interest papers investigate empirically the rates. However, the model does not classify labor inputs as skilled or unskilled and thus does not relationship between import shares, address the skill premium issue employment levels, and factor intensity and 4 For a discussion of why the SF model is an arrive at similar conclusions: foreign appropriate framework for analyzing the globalization and relative wage issue, see Engerman and Jones [9]. Also note that Kohli [24] contrasts the predictive capability of a SF model with a H-O 1 Throughout this paper the terms FDI and capital model and finds the former better suited to analyze flows are used interchangeably U.S. data. 2 See Griliches [15], amongst others, for empirical 5 In particular, an increase (decrease) in the world evidence supporting the capital-skill interest rate leads to an instantaneous outflow complementarity hypothesis (inflow) of capital from the economy.

International Capital Movements and Relative Wages: Evidence from U.S. Manufacturing Industries 19

Figure 1: U.S. Inflows (+) and Outflows (-) of Net Foreign Direct Investment, 1950-2010. Source: BEA. Capital Inflows: FDI in the U.S.; Capital Outflows: U.S. Direct Investment Abroad (for years prior to 1977, Direct Investment Capital Outflows = Equity & Intercompany Accounts Outflows + Reinvested Earnings of Incorporated Affiliates). Numbers in Billion USD.

Figure 2: Ratio of average non-production labor wage to average production labor wage in U.S. manufacturing industries, 1958-2005

change in the relative wage rate as a premium as predicted by the model and function of changes in international interest compare the predicted with the actual rates as well as changes in product prices, change1 . We then calculate the contribution TFP growth, factor-speciﬁc technological progress, and labor endowment changes. 1 Using estimates of factor-demand The literature on globalization and wage inequality deals primarily with U.S. manufacturing industries, elasticities and data on the U.S. mainly due to the unavailability of disaggregated manufacturing sector from 1958 to 2005, wage data for skilled and unskilled workers in non- we calculate the change in the skill manufacturing industries. As Figure 1 reveals, the manufacturing sector has experienced, by and large,

20 International Economic Studies, Vol. 47, No. 1, 2016 to the predicted change by each of the theoretical model is derived in section 2. In exogenous forces. In addition to the full section 3 and 4 we discuss model sample, we consider four subperiods: 1958- simulation results and data issues, 66, 1967-81, 1982-2000, and 2001-05. respectively. We present our main results in Our main results are as follows. First, section 5. Section 6 concludes. the net capital outflow that U.S. manufacturing industries experienced 2. The Theoretical Model during the period 1958-81 had a depressing Our model is closely related to a class of effect on the skill premium. In contrast, the models based upon the 2x3 SF model net capital inflows that occurred in the derived in Jones [18], which allow for majority of years between 1981 and 2000 international capital mobility (see, for had a positive effect on the skill premium. instance, Thompson [35] and Jones, Neary Second, trade effects working through and Ruane [21]). Our model is similar in product price changes caused an increase in this respect. However, it differs the skill premium for all periods. Third, significantly in that it incorporates the increases in non-production labor multi-sectoral feature of an economy endowments worked towards depressing following Jones [19]. We consider a small the skill premium, as did a fall in open economy which produces m production labor endowment. Fourth, commodities in as many sectors of production labor specific technical change production. There are three factors of increased the skill premium, while non- production in each sector. Two of these production labor specific technical change factors, capital (K) and production labor had the opposite effect on the skill (P), are perfectly mobile between sectors, premium. while the third factor, non-production labor In terms of relative contributions, (NP), is sector specific, i.e., immobile1. technology played the largest role in Production functions are continuous, twice affecting the skill premium, followed by differentiable, quasi-concave and exhibit changes in interest rates and product prices, diminishing returns to the variable factors. which had approximately equal Domestic prices are exogenous and are contributions. Labor endowment changes assumed to be affected by globalization had the least relative impact on skill shocks. Capital is also assumed to be premium changes. perfectly mobile internationally. Its return The finding of this paper that capital is determined in world markets and is movements played a significant role in exogenous. Production sectors are indexed affecting relative wages in the U.S. by j =1, ...., m, and factors of production provides strong empirical support for the are indexed by i = K, NP, P . Aggregate theoretical results of Feenstra and Hanson factor endowments are denoted by Vi. [10], Sachs and Shatz [32], and Eckel [8]. Thus, there are a total of m + 2 factors of In addition, our results reflect findings from production in the economy. Let two distinct strands of the skill premium aKj,aNPj,aPj denote the quantity of the literature. With the labor economics three factors required per unit of output in literature, such as papers by Berman, the jth sector, i.e., aij denote unit input Bound and Griliches [2] and Berman, coefficients. Let pj ,qj represent price and Bound and Machin [3], we share the output of the jth sector and r, wNPj,and wP conclusion that (factor-specific) denote factor prices. Here r and wP denote technological change is likely to be one of the capital rental price2 and production the primary forces which increased the skill premium. Like certain papers from the 1 empirical trade literature, such as Sachs and Here non-production workers are assumed to be skilled, while production workers are Shatz [31], Leamer [28], and Krueger [26], assumed to be unskilled labor. Note that an we concur that product price changes may alternative modeling strategy would have been have strongly contributed to the observed to assume capital to be sector specific as well. increase in the skill premium. We do not pursue this approach as accurate data The paper is organized as follows. The on sector specific capital rental rates are not available. 2 The terms ‘interest rate’, ‘user cost of capital’, and similar net capital flows as the overall economy. ‘capital rental price’ are used interchangeably in this

International Capital Movements and Relative Wages: Evidence from U.S. Manufacturing Industries 21 labor wages, respectively, while wNPj Theorem, which implies that: denotes non-production labor wages in the 휃퐾푗 푐̂퐾𝑗 + 휃푁푃푗 푐̂푁푃𝑗 + 휃푃푗 푐̂푃𝑗 = 0 ∀푗 (9) jth sector. The following set of equations represents the equilibrium conditions for From the factor market clearing this model: equations (1)-(2) we get: 푎 푞 = 푉 ∀ (1) 푁푃푗 푗 푁푃푗 푗 푞̂ = −푐̂ + 휃 푐̂ + ∏ +푉̂ ∀푗 푗 푁푃𝑗 푃푗 푃𝑗 푁푃𝑗 (10) ∑ 푎 푞 = 푉 푁푃푗 푁푃푗 푗 푃 (2) 푗 ∑ λ푝 푞̂ + ∑ λ푝 푐̂ = 푉̂ + ∏ 푝 푗 푗 푗 푝푗 푝 (11) 푗 푗 The above equations are factor market clearing conditions for labor inputs. Notice ̂ where ∏푁푃 = 푏푁푃 and ∏푃 = that a similar condition does not hold for 𝑗 ∑ λ푝 푏̂ represent the reduction in the use capital inputs. With perfect capital 푗 푗 푝푗 mobility, the small open economy facing of production labor across all sectors. Note 푎푖푗푞푗 exogenous capital returns faces an infinitely that λ푖푗 is defined as . Thus, we refer elastic supply curve of capital. Demand 푉푖 to ∏ 푗 in equation (8) as sector-specific conditions determine the amount of capital technological change (TFP) and to ∏ 푖 as employed. Sectoral unit input coefficients factor-specific technological change. Note are variable and are subject to technological that both these terms measure technological change. In particular, changes in these change holding factor prices constant. Re- coefficients can be decomposed as in Jones placing 푞̂ in equation (11) with (10) we [20]1: 푗 ̂ get: 푎̂푖푗 = 푐̂푖푗 − 푏푖푗 ∀푗, 푖. (3) ∑ λ푝 푐푝̂ − ∑ λ푝 푐̂ + ∑ λ푝 (푉̂ 푗 푗 푗 푁푝푗 푗 푁푝푗 푗 푗 푗 (12) Here, 푐̂푖푗 denotes changes in input + ∏ 푁푃 ) = 푉̂ + ∏ 푝 coefficients as a result of changes in 푗 푝 relative factor prices, while 푏̂ denotes 푖푗 From equations (4)-(6) we get: exogenous technological progress (i.e., the 푐̂ = 퐸퐾 푟̂ + 퐸푁푃푤̂ + 퐸푃 푤̂ ∀ reduction in the amount of factor i required 퐾푗 퐾푗 퐾푗 푁푃𝑗 퐾푗 푝 푗 (13) 퐾 푁푃 푃 to produce one unit of output j). Note that 푐̂푃푗 = 퐸푝푗 푟̂ + 퐸푝푗 푤̂푃𝑗 + 퐸푝푗 푤̂푝 ∀푗 (14) 퐾 푁푃 푐푖푗 is a function of returns to sector specific 푐̂ = 퐸 푟̂ + 퐸 푤̂ 푁푃푗 푁푃푗 푁푃푗 푁푃𝑗 factors as well as returns to the mobile 푃 (15) + 퐸 푤̂푁푝 ∀푗 factor: 퐾푗

푐 = 푐 (푟, 푤 , 푤 ) ∀ 푗 (4) 휕푐 퐾푗 퐾푗 푁푃푗 푝 where 퐸퐾 = ( 푖푗 )(푤푘 )for k = K, NP, P 푖푗 푐 = 푐 (푟, 푤 , 푤 ) ∀ 푗 (5) 휕푤푘 푐푖푗 푁푃푗 푁푃푗 푁푃푗 푝 is deﬁned as the elasticity of cij with

푐푃푗 = 푐푃푗 (푟, 푤푁푃푗, 푤푝) ∀ 푗 (6) respect to changes in wk, holding all other 2 factor prices constant . Next, zero-proﬁt conditions are given To solve this model for mobile factor by: prices, substitute equations (14) and (15) in 푝 = 푎 푟 + 푎 푤 + 푎 푤 ∀ 푗 equation (12). This yields: 푗 푘푗 푁푃푗 푁푃푗 푃푗 푝 (7) ∑ λ푝 (퐸퐾 푟̂ + 퐸푁푃푤̂ + 퐸푃 푤̂ ) 푗 푝푗 푝푗 푁푃𝑗 푝푗 푝 Using hat-calculus and denoting factor 푗 − ∑ λ푝 (퐸퐾 푟̂ shares by 휃, Equation (7) can be written as: 푗 푁푝푗 푗 (16) 푁푃 푃 푝̂푗 = 휃퐾 푟̂ + 휃푁푃 푤̂푁푃 + 휃푃 푤̂푝 − ∏ ∀푗 + 퐸 푤̂ + 퐸 푤̂ ) 푗 푗 푖푗 푗 (8) 푁푝푗 푁푃𝑗 푁푝푗 푝 푗 + ∑ λ푝 푉̂∗ = 푉̂∗ 푗 푁푃푗 푝 ̂ 푗 where ∏푗 = ∑푖 휃푖푗푏푖푗 is a measure of TFP in sector j. To derive equation (8) we made use of the Wong-Viner Envelope 2 Note that due to the zero-homogeneity of 푐푖푗, ∑ 퐸퐾 = 0 ∀ ∀ and ∑ 휃 퐸퐾 = 0 ∀푘, 푗. Further, 푘 푖푗 푖 푗 푖 푖푗 푖푗 paper. 휃 by symmetry, 퐸퐾 = 푘푗 퐸푖 ∀푖, 푗. 1 푖푗 푘푗 Here 푋̂ = 푑푋/푋. 휃푖푗

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̂∗ ̂ 푖 1 where 푉푝 = 푉푖 + ∏ 푖. With 휀푖푗 = 퐸푝푗 − 푤̂ = . [푉̂∗ 푝 휀푁푝 푝 푖 1 ∑ λ푝 (휀 − 푗 휃 ) 퐸 Equation (16) can be rewritten as : 푗 푗 푝푗 푝푗 푁푃푗 휃푁푝푗 푟̂ ∑ λ푝 휀 + ∑ λ푝 휀 푤̂ ̂∗ 푗 퐾푗 푗 푁푝푗 푁푃𝑗 − ∑ λ푝푗 푉푁푃푗 푗 푗 푗 휀푁푝 − ∑ λ푝 푗 (푝̂ (21) + 푤̂푝 ∑ λ푝푗휀푝푗 (17) 푗 푗 휃푁푝푗 푗 푗 = 푉̂∗ − ∑ λ푝 푉̂∗ + ∏ ) − 푟̂ ∑ λ푝푗 (휀퐾푗 푝 푗 푁푃푗 푗 푗 푗 휀푁푝 − 푗 휃 )] 휃 푘푗 Equation (17) together with equation (8) 푁푝푗 can be used to solve for 푤̂ and 푉̂∗ . To 푁푃𝑗 푁푃푗 Using this solution in equation (18) we do so, rewrite Equation (8) as: can solve for 푉̂∗ : 1 ̂ 푁푃푗 푤̂푁푝푗 푤̂푁푃𝑗 = (푝푗 + ∏ 푗 − 휃푘푗 푟̂ 휃푁푃푗 (18) 1 = (푝̂ + ∏ −휃 푟̂ ) 휃 푗 푘푗 푗 − 휃푝푗푤푝̂ )∀푗 푁푝푗 푗 휃푝 1 푗 ̂∗ − . 휀 . [푉푝 Using the above in equation (17) we get: 휃푁푝 푁푝푗 푗 ∑푗 λ푝푗(휀푝푗 − − 휃푝 ) 휀 휃푁푝 푗 푁푝푗 푗 푟̂ ∑ λ푝푗휀퐾푗 + ∑ λ푝푗 (푝̂푗 ̂∗ (22) 휃푁푝 − ∑ λ푝푗 푉푁푃푗 푗 푗 푗 푗 휀 + ∏ −푟̂휃 푁푝푗 푘푗 − ∑ λ푝푗 (푝̂푗 + ∏ ) 푗 휃푁푝 푗 푗 푗 휀 − 휃 푤̂) 푁푝푗 푝푗 푝 (19) − 푟̂ ∑ λ푝푗 (휀퐾푗 − 휃푘푗 )] ∀푗 휃푁푝 푗 푗 + 푤̂푝 ∑ λ푝푗휀푝푗 푤̂푁푝푗 − 푤̂푝 푗 1 = (푝̂푗 + ∏ −휃푘푗푟푗̂ ) − (1 ∗ ̂∗ ̂ 휃푁푝푗 푗 = 푉푝 − ∑ λ푝푗 푉푁푃 푗 휃푝 1 푗 푗 ̂∗ + ). 휀 . [푉푝 휃 푁푝푗 푁푝푗 ∑ λ푝 (휀 − − 휃 ) 푗 푗 푝푗 휃 푝푗 That gives us: 푁푝푗 (23) 휀푁푝 − ∑ λ푝 푉̂∗ 푟̂ ∑ λ푝 (휀 − 푗 휃 ) 푗 푁푃푗 푗 퐾푗 푘푗 푗 휃푁푝 푗 푗 휀푁푝 휀 − ∑ λ푝 푗 (푝̂ + ∏ ) 푁푝푗 푗 푗 휃푁푝 푗 + ∑ λ푝푗 (푝̂푗 푗 푗 휃푁푝 휀 푗 푗 푁푝푗 − 푟̂ ∑ λ푝푗 (휀퐾푗 − 휃푘푗)] ∀푗 휃푁푝 + ∏ ) 푗 푗 푗 (20) + 푤̂푝 ∑ λ푝푗(휀푝푗 Before proceeding to the next section, 푗 certain characteristics of the above solution 휀푁푝 − 푗 ) in equation (23) should be considered. 휃 푁푝푗 First, changes in sectoral skill premiums ̂∗ ̂∗ are functions of interest rate changes, = 푉푝 − ∑ λ푝푗 푉푁푃푗 푗 product price changes, changes in labor endowments, and factor-speciﬁc as well as Using equation (20) we can solve for sector-speciﬁc technological change. Second, changes in the skill premium also 푤̂푝: depends on factor intensities (휀) and factor elasticities (λ) in all sectors. Third, without making unreasonable ad hoc assumptions about these intensities and elasticities, it is not possible to determine the sign of the partial derivatives of the sectoral skill premium (푤̂푁푝푗 − 푤̂푝) with respect to the 1 Note that 휀푖푗 is the change in 푉푝푗⁄푉푁푃푗 due to a exogenous variables. change in the factor price of input i.

International Capital Movements and Relative Wages: Evidence from U.S. Manufacturing Industries 23

3. Simulation Results 푞1 In this paper, we are interested in how the −𝜎 = 퐴1 [휇1(훿푝푉푝1) changes in the skill premium (푤̂푁푝푗 − 푤̂푝) −𝜌 (27) respond to changes in interest rates, product + (1 − 휇1){λ1(훿푘퐾1) + (1 1 − prices, TFP growth, factor-specific 𝜎 𝜎 −𝜌 푝 technological change, and changes in labor − λ1)(훿푁푃1푉̅푁푝1) } ] endowments. Since the analytical partial 푞 derivatives of the sectoral skill premium 2 −𝜎 with respect to the exogenous parameters = 퐴2 [휇2(훿푝푉푝1) cannot be signed without strong −𝜌 + (1 − 휇2){λ2(훿푘퐾2) + (1 (28) 1 assumptions, we compute instead a − 𝜎 𝜎 numerical solution for a simplified version −𝜌 푝 − λ2)(훿푁푃2푉̅푁푝2) } ] of the above model. Based on these simulations, it is straightforward to find the sign and magnitude of the skill premium Here A1 and A2 are the sector specific change with respect to the different (neutral) technological change parameters, parameter changes. while 훿 represents factor specific (skill- For the numerical simulations, we biased) technical change. µ and λ denote reduce the number of sectors to two, the share parameters. In this specification denoted by 1 and 2. For the two sectors, the elasticity of substitution between 푉푝 and zero-profit conditions are given by: K is identical to the elasticity of 푝1푞1 = 푟퐾1 + 푤푝푉푝1 + 푤푁푝1푉̅푁푝1 (24) substitution between 푉푝 and 푉푁푝. This is 1 푝2푞2 = 푟퐾2 + 푤푝푉푝2 + 푤푁푝2푉̅푁푝2 (25) given by The elasticity of substitution 1+𝜎 between K and 푉 is given by 1 . Here where p, q denote prices and quantity 푁푝 1+𝜌 respectively; K denotes the endogenously 𝜎, 𝜌 ∈ [−1,∞]. If 𝜎 = 𝜌 = 0 then we have determined quantity of capital; 푉̅NPj a Cobb-Douglas in 3 factors. As these denotes the fixed quantity of sector specific parameters approach -1 we get greater non-production labor; and 푉 denotes the substitutability than in the C-D case. Thus, 푃 for 𝜌>𝜎 we get capital-skill mobile factor. r, wP ,wNPj denote returns to the factors of production. Market clearing complementarity. In both sectors, wages of for the mobile factor is given by: mobile factors equal the value of their ̅ marginal product: 푉푝1 + 푉푝2 = 푉푝 (26) −𝜎 1+𝜎 푝1훿 휇1푞 푤 = 푃 1 (29) 푝 퐴𝜎푉1+𝜎 Output in the two sectors is determined 1 푃1 −𝜎 1+𝜎 via a ‘nested’ CES production function as 푝2훿 휇2푞 푤 = 푃 2 (30) proposed by Krusell et al [23]. The 푝 퐴𝜎푉1+𝜎 advantage of using such a specification is 2 푃2 that it allows for varying elasticity of Finally, in both sectors the marginal substitution between factors of production: product of capital must equal the exogenously determined interest rate:

𝜎 −1 푝 훿−𝜌λ (1 − 휇 )푞1+𝜎{λ (훿 퐾 )−𝜌 + (1 − λ )(훿 푉̅ )−𝜌}𝜌 푟 = 1 푘 1 1 1 1 푘 1 1 푁푃1 푁푝1 (31) 𝜎 1+𝜌 퐴1 퐾1 𝜎 −1 푝 훿−𝜌2(1 − 휇 )푞1+𝜎{λ (훿 퐾 )−𝜌 + (1 − λ )(훿 푉̅ )−𝜌}𝜌 푟 = 2 푘 2 2 2 푘 2 2 푁푃2 푁푝2 (32) 𝜎 1+𝜌 퐴2퐾2

Table 1: Parameter Values ̅ 𝜎 -.33 휇1 .20 푉푝 270 푝1 1 훿푃 1 ̅ 𝜌 .66 λ1 .55 푉푁푝1 100 푝2 1 훿푁푃1 1 ̅ 휇1 .55 λ2 .50 푉푁푝2 100 퐴1 1 훿푁푃2 1 Source: Authors

24 International Economic Studies, Vol. 47, No. 1, 2016

The parameter values used in the simulated sector 2 is 40%. Thus, production labor is used models are given in Table 1. These values most intensively in sector 1, while non- were chosen to mimic the values of relative production labor is used most intensively in prices and quantities for the U.S. sector 2 (Factor intensity is defined as follows: manufacturing industries for average values sector 1 uses factor P intensively and sector 2 over the period 1958-05. For example, the uses factor NP intensively average ratio of production to non-production iffθ_P1⁄(θ_P2>θ_NP1⁄θ_NP2 )). The workers in U.S. manufacturing industries for elasticities of substitution among factors were this period is 2.7, which is the number we use chosen following Johnson [17] such that they in our simulations. The revenue share for reflect capital-skill complementarity. Table 2 production labor in sector 1 is assumed to be presents the simulation results. 55%, while that for non-production labor in

Table 2: Simulation Results ̅ ̅ ̅ Base 푟̅ 푝1 푝2 퐴1 퐴2 훿푘 훿푝 훿푁푃1 훿푁푃2 푉푝 푉푁푝1 푉푁푝2 푘1 315 -7.7 9.0 -0.9 9.0 -0.9 -1.6 3.4 6.9 -3.7 3.4 6.9 -3.7 푘2 339 -7.9 -1.2 9.8 -1.2 9.8 -1.4 0.3 -0.3 9.6 0.3 -0.3 9.6 푤푝 .50 -0.9 10.3 0.7 10.3 0.7 0.8 7.3 2.3 3.0 -2.5 2.3 2.9 푤푁푝1 .55 -3.6 15.3 -1.4 15.3 -1.4 3.6 5.7 4.8 -6.0 5.7 -4.7 -6.0 푤푁푝2 .76 -4.1 -2.0 16.8 -2.0 16.8 4.1 0.5 -0.5 9.3 0.5 -0.5 -0.6 푄1 205 -1.2 2.6 -1.7 12.8 -1.7 1.1 6.7 4.0 -7.0 6.7 4.0 -7.0 푄2 126 -2.4 -2.4 4.9 -2.4 15.4 2.3 0.7 -0.6 9.2 0.7 -0.6 9.2 - - 푉 238 0.2 2.1 -2.7 2.1 -2.7 -0.1 0.7 0.5 10.7 0.5 푝1 10.9 10.9 푉푝2 32.2 -1.1 -15.7 19.8 -15.7 19.8 1.0 -5.0 -3.9 4.7 4.5 -3.9 4.7 푤푁푝 ( )1 1.10 -2.8 4.6 -2.1 4.6 -2.1 2.7 -1.5 2.5 -8.6 8.4 -6.8 -8.6 푤푝 푤푁푝 ( )2 1.52 -3.3 -11.2 16.1 -11.2 16.1 3.2 -6.3 -2.7 6.3 3.1 -2.7 -3.4 푤푝 푤푁푝 ( ) 1.31 -3.1 -4.6 8.4 -4.5 8.4 3.0 -4.3 -0.5 -0.2 5.3 -4.4 -5.7 푤푝 Source: Authors

For the benchmark simulation, we set the increase in the skill premium are: an increase inter-industry capital ratio between sector 1 in the endowment of production labor; an and 2 to .93, which implies an average non- increase in product price of sector 2; TFP production to production wage ratio of 1.31. growth in sector 2; and capital specific This number is close to the actual ratio of 1.61 technological progress. In contrast, the skill (the average ratio for U.S. manufacturing premium falls with production labor specific industries over the sample period). In Table 2, technological progress; non-production labor we present the change in the skill premium specific technological progress; TFP growth in (sectoral as well as average) between non- sector 1; a higher price of good 1; an increase production and production workers for a 10% in interest rates; and larger endowment of non- increase in endowments, product prices, production labor. factor-specific technological change, interest The critical conclusion to be drawn from rates and TFP growth. The forces that cause an these results regards the change in the skill

Economic Impact of Regional Trade Agreements and Economic Co-operation: Econometric Evidence 25 premium due changes in the interest rates. We good) causes a rise in the skill premium, while find that the average skill premium declines by an increase in the price of the unskilled labor less than 10%. Thus, for parameters chosen in intensive good implies a decline in the the benchmark case there is an inverse premium. Therefore, the model predicts relationship between interest rate changes and Stolper-Samuelson type effects of product the skill premium. Recalling that interest rate price changes as well. increases are an indicator for capital outflows, this decline in the skill premium is expected as 4. Data with less capital, the demand for skilled To obtain the equilibrium factor price changes, workers decline. Also note that an increase in we first write out the full system of the price of good 2 (the skilled-labor intensive equilibrium equations as given in (8) and (20):

푝̂ + 훱̂ − 휃 푟̂ 휃 0 . . 0 휃 1 1 푘1 푁푃1 푃1 . 0 . . . . . 푤̂푁푃1 ...... = . . . . 0 . (33) ̂ . 푝̂푚 + 훱푚 − 휃푘푚푟̂ 0 . . 0 휃푁푃푚 휃푃푚 푤̂푁푃푚 푉̂∗ − ∑ λ푝 푉̂∗ − 푟̂ ∑ λ푝 휀 λ푝 휀 . . . λ푝 휀 ∑ λ푝 휀 푃 푗 푁푃푗 푗 퐾푗 1 푁푃1 푚 푁푃푚 푗 푃푗 [ 푤̂푝 ] [ 푗 푗 ] [ 푗 ]

To calculate the factor price changes, we observations for 2005. The λ variables in the need data for the elements of the LHS vector matrix above are functions of factor-demand and the RHS matrix. The data set we use is the elasticities. These elasticities are not directly latest version of the NBER-CES observed and must be estimated. A detailed Manufacturing Database [29]. This database description of how we estimate these contains annual information on all U.S. elasticities is given in Appendix A. Appendix manufacturing industries from 1958 to 2005. B contains a brief description of how we At the 4-digit 1972 SIC level there are 448 construct the remaining variables. Table 3 industries. Due to missing data, we exclude provides descriptive statistics for the key SIC 2384, 2794 and 3292 from our analysis. exogenous variables, and for the actual factor Note that all growth rates in period t are price changes observed in the data. Note that deﬁned as the change between period t + 1 and while some of the statistics are computed by t relative to period t (see Leamer [28] for a pooling over all industries and over the entire similar deﬁnition). Growth rates are thus sample period, others are computed by pooling forward looking. As a result, we lose over industries only.

26 International Economic Studies, Vol. 47, No. 1, 2016

Table 3: Descriptive Statistics variable Mean S.D. Min Max Obs. 푝̂ 푗 -.015 .0515 -.7009 .98 20492 훱 푗 .0064 .0405 -.9321 1.7659 20492 훱̃ 푚 .0065 .0379 -.9262 1.7382 20492 훱 푃 .0357 .0317 -.0397 .112 47 훱 푁푃 .0354 .0464 -.0947 .1453 47 푉̂ 푃 -.0044 .0396 -.1017 .0589 47

푉̂푁푃 .002 .0265 -.065 .0491 47 푊̂ 푃푗 .0478 .056 -.5859 1.4518 20492 푊̂ 푁푃푗 .0543 .1553 -.9250 12.22 20492 푟̂(푀표표푑푦′푠퐵푎푎) .011 .0965 -.1831 .2788 47

Source: Authors

Several issues need to be discussed at this his estimates show that the endowment of point. First, we use the production and non- skilled and unskilled workers grew at a rate of production labor classification from the NBER -.0076 and .0048, respectively. The data set as a proxy for unskilled and skilled corresponding growth rates for skilled and workers. This approximation has been unskilled workers using average criticized on the grounds that production manufacturing employment data are -.0078 worker category may include workers with and .0104, respectively. The substantial co- high education levels or skills, while the group movement between the change in labor of non-production workers may include endowments and the change in employment workers with low education levels or skills. indicates that the approximation error is likely However, we maintain this classification since to be small. Third, capital factor shares are it is a reasonable approximation used widely in computed as 1 minus labor and materials the literature. In addition, results by Kahn and factor shares, i.e., as a residual. This implies Lim [22] show a high correlation between that our definition of capital factor shares cost-shares based on the two classification includes payments to other sector-specific schemes indicating that the two schemes are assets as well and is thus larger than the true close substitutes. Second, due to the lack of capital share. Similarly, since we do not have (manufacturing) sector specific data on labor data on the quantity of these other assets or on endowments, we use growth rates of observed industry-specific depreciation rates and labor employment instead. Kosters [25] (Table consumption of fixed capital, we compute the 1-6) presents estimates for changes in the ex post rental price of capital as value added proportion of the work force from 1973-88 for less total labor compensation divided by the workers with 12 years of education or less, and capital stock ( Errors in the NBER dataset for workers with 16 or more years of resulted in a negative rental price of capital for education. Translated into annual growth rates, a few industries. These values were arbitrarily

Economic Impact of Regional Trade Agreements and Economic Co-operation: Econometric Evidence 27

ﬁxed at an uniform rate of 10%.). Compared to one is upward biased. the true rental price of capital, our computed

Figure 3: Moody’s Baa rate, 1958-200 Source: Economic Report of the President, 2011. Table B-73.

Fourth, the empirical implementation of sample period and a negative average growth equation (33) requires data on international rate of 3.3% during 1982-05. According to the interest rates. An obvious choice, the 1-year international capital flow mechanism outlined London Interbank Offer Rate on U.S. Dollar earlier, these growth rates are consistent with Deposits (LIBOR), is not available for the observed flows for the manufacturing sector, entire sample period. We therefore use a close i.e., net outflows prior to 1982 and mostly net proxy (see Figure 3), the Moody’s Baa inflows in subsequent years. Fifth, our series13, which is also used by Feenstra and theoretical model does not include

Hanson [12]14 . This measure yields a positive intermediate inputs. In the empirical analysis, average annual growth rate of 1.1% over the we account for the impact of intermediate inputs on product prices by deriving a value-

13 Annual percent yield on corporate bonds (Moody's added price change measure. This is done, as Baa: Economic Report of the President, 2011. Table B- in Leamer [28], by subtracting from the vector 73). Note that this is an ex ante measure of the rental of product price changes the inner product of a price of capital. diagonal matrix with material cost-shares on 14 For a small open economy, the domestic interest rate its main diagonal and a vector of growth rates must be equated to the world interest rate. Therefore, of material deﬂators. Sixth, according to changes in the domestic interest rate triggers off capital equation (3), changes in unit input coeﬃcients ows similar to those due to changes in the world interest can be decomposed into changes due to factor rate.

28 International Economic Studies, Vol. 47, No. 1, 2016 price variations (holding technology constant) Rewriting the last equation yields: 푝̂ = 휃 푟̂ + 휃 푤̂ + 휃 푤̂ + 휃 (̂푤 and changes due to technological progress 푗 퐾푗 푗 푁푃푗 푁푃푗 푃푗 푝 푃푗 푝푗 − 푤̂ ) + 휃 (푟̂ − 푟̂) (holding factor prices constant). Since we only 푝푗 퐾푗 푗 (38) observe 푎̂푖푗 in the data, we proceed by − ∏ ∀푗 푗 constructing an estimate for 푐̂푖푗 and then use

̂ (3) to construct a measure of 푏푖푗 Using the Equation (38) is identical to equation (8) estimated factor-demand elasticities (see except for the extra term on the RHS17. Appendix A), we derive an estimate of 푐̂푖푗 15 Following Feenstra and Hanson we add these using the following equations 퐾 푃 two terms to 훱푗 and call the resulting 푐̅̂̅̅̅ = 퐸 푟̂ + 퐸 푤̂ 퐾푗 퐾푗 푗 퐾 푁푃𝑗 ̃ 푁푃 (34) expression eﬀective TFP,훱푗. Thus we have: + 퐸퐾 푤̂푁푝푗 ∀푗 푝̂ = 휃 푟̂ + 휃 푤̂ + 휃 푤̂ − 훱̃ ∀푗 ̅̅̅̅ 퐾 푃 푁푃 푗 퐾푗 푗 푁푃푗 푁푃푗 푃푗 푗 (39) 푐̂푃푗 = 퐸푃 푟푗̂ + 퐸푃 푤̂푃𝑗 + 퐸푃 푤̂푁푝푗 ∀푗 (35) 퐾 푃 ̅̅̅̅̅̅ ̂ 푐̂푁푃푗 = 퐸푁푃푟푗̂ + 퐸푁푃푤̂푁푃𝑗

푁푃 (36) With these caveats in mind, we calculate + 퐸푁푃 푤̂푁푝푗 ∀푗 the predicted skill premium growth rate as the

̅̅̅̅ 16 manufacturing sector average of differences where 푐̂푖푗 is the predicted value of 푐̂푖푗 . between 푤̂푁푃 and 푤̂푃, followed by a 푗 decomposition of the total effect into the Finally, the assumption of perfect mobility changes caused by globalization, endowment, of procij bduction labor (and capital, for our and technological change. To calculate the second model) across sectors is a potential impact of a particular factor, say product price source of error when we apply our model to change, we set all other exogenous variables in the data. This is due to the fact that in the data, the LHS vector of (33), i.e., 푉̂∗ − returns for these two factors of production 푝 ∑ λ푝 푉̂∗ − 푟̂ ∑ λ푝 휀 , 훱̃ , and −휃 푟̂ to vary across sectors. To adjust for this 푗 푗 푁푃푗 푗 푗 퐾푗 푗 퐾푗 empirical fact, we proceed as in Feenstra and zero. Hanson [12] and modify the zero-profit conditions so that all factor returns are indexed 5. Model Predictions and Decomposition by j: Our main results are presented in Table 4. All 푝̂푗 = 휃퐾 푟푗̂ + 휃푃 푤̂푃 + 휃푁푃 푤̂푁푝 푗 푗 푖푗 푗 numbers are averages of annual growth rates. − ∏ ∀푗 (37) Over the sample period from 1958-05 the skill 푗 premium in U.S. manufacturing industries grew at a modest rate of .11% per year. The 15 Note that there are two differences between (13)-(15) skill premium growth rates reported for the and (34)-(36). First, the returns to mobile factors are four subperiods, 1958-66, 1967-81, 1982- industry-specific in equations (34)-(36). Second, the 2000, and 2001-05, correspond to different elasticities are now identical across industries. Both trends in the skill-premium. changes are necessary to be consistent with the estimation described in Appendix B. 16 Note that for estimating elasticities, as well as for 17 We construct wbP as the growth rate of average ̅̅̅ calculating 푐̂푖푗 use a sectoral user-cost of capital measure. manufacturing factor returns to production labor

Economic Impact of Regional Trade Agreements and Economic Co-operation: Econometric Evidence 29

Table 4: Observed and Predicted Average actual skill premium declined. In terms of Annual Skill Premium Growth Rates magnitudes, the model over-predicts for the Years Observed Predicted Correlations entire period (2.8% predicted growth as 1958-05 .0011 .0279 .1017 1958-66 .0049 .0493 .1268 compared to .11% actual growth) as well as 1967-81 -.005 -.0331 .1158 for each of the subperiods. The correlation 1982-00 .0072 .0555 -.1867 coefficients reported in the last column of 2001-05 -.0133 .0777 .5136 Source: Authors Table 4 reveal that the co-movement between the predicted and actual growth rates is fairly Comparing the actual growth rates with the low except for the final subperiod. Figure 4 growth rates predicted by our model, we find depicts the observed and predicted growth that the model correctly predicts the direction rates for the entire period. The difference in of changes for the entire sample period and for magnitude between the volatile predicted three of the four sub-periods. Only for the values and the rather smooth observed skill 2001-05 subperiod does the model predict a premium values is clearly visible from this further rise in the skill premium, while the figure.

Figure 4: Actual and Predicted Skill Premium Growth Rates in U.S. Manufacturing Industries, 1958-2005 Source: Authors Table 5 contains the decomposition of the technological change mirrors that of predicted skill premium growth rates. Global- globalization, while endowment changes, for ization (i.e., product price changes and interest the entire period and for all sub-periods, rate changes) had a positive eﬀect on the skill caused a decline in the skill premium. premium for the entire period as well as for the To better understand the impact of changes periods after 1981. The impact of of these three broad categories on the skill

30 International Economic Studies, Vol. 47, No. 1, 2016 premium, we further decompose each category as well as the entire period. into their constituent parts (see Table 6). The striking result which emerges from this Table 5: Decomposition of the Predicted Skill decomposition is that interest rate changes had Premium Growth Rate a positive effect on the skill premium from Years Globalization Technology Endowments 1958-05 .0368 .0071 -.0159 1982 onward. As mentioned earlier, this is 1958-66 -.0231 .0748 -.0023 exactly the period when capital inflows started 1967-81 -.0048 .0044 -.0327 to become the norm. Globalization working 1982-00 .076 -.0154 -.0051 2001-05 .1413 -.0287 -.0349 through product price changes had a positive Source: Authors effect on the skill premium for all sub-periods

Table 6: Decomposition of Individual Eﬀects Globalization Technology Endowments Years Price Interest rate TFP P specific NP specific P labor NP labor 1958-05 .0436 -.0068 -.0101 .0567 -.0395 -.0072 -.0087 1958-66 .0059 -.0249 .0639 .0651 -.0543 .0303 -.0327 1967-81 .0613 -.0662 -.0232 .0306 -.003 -.012 -.0207 1982-00 .0435 .0325 -.0271 .064 -.0523 -.007 .0018 2001-05 .0718 .0696 -.0473 .1014 -.0829 -.0748 .0399 Source: Authors

Table 7: Contributions by Factor (in %) and Residual Explained Variation: Contribution by Factor Residual Years Price Interest Rate Technology Endowments 1958-05 25.5 27.2 31.2 16.0 49.5 1958-66 23.5 19.5 36.8 20.2 49.5 1967-81 28.5 27.7 29.3 14.5 51.4 1982-00 29.0 28.3 30.9 11.8 47.9 2001-05 40.0 20.4 28.9 10.7 42.8 Source: Authors

As expected, the observed decrease in the technological change had a positive effect on endowment of production workers had a the skill premium for the full sample as well as negative effect on the predicted skill premium during each subperiod, while non-production over the full sample period, as did the increase labor specific technical change lowered the in the number of non-production workers18 . skill premium in all periods. Interestingly, Similar changes in the supply of production except for one subperiod (1958-66), TFP and non-production workers for the various growth always contributed to a decline in the subperiods explain the pattern of skill skill premium. premium changes shown in the last two Table 7 presents the relative contribution to columns of Table 6. Production labor specific the explained variation by each factor as well as the residual (unexplained variation)19.

18 The actual annual growth rates for production and non-production workers for the entire sample period are - 19 Note that the four contribution shares add up to 100. .4% and .2%, respectively. The contribution by each factor i is deﬁned as:

Economic Impact of Regional Trade Agreements and Economic Co-operation: Econometric Evidence 31

While we report shares for price and interest price’ insensitivity result of the Heckscher- rate changes separately, the shares for Ohlin model. Therefore, we are able to provide technology and endowments are reported as an evidence on the relative impact of aggregate over their components. The numbers globalization, technological progress (sector for the residual shares show that for the entire and factor-specific), and labor endowment sample period, as well as most subperiods, changes on movements in the U.S. skill approximately 50% of the observed variation premium. in the skill premium is explained by the model. Several results emerge from our analysis. The explained variation breaks down as First, the net capital outflow that occurred follows. Interest rate and product price during the period 1958-82 had a depressing changes each account for roughly a quarter of effect on the skill premium. In contrast, the net the predicted changes in the skill premium. capital inflows that were prevalent between Technology accounts for 31%, while labor 1981 and 2001 had a positive effect on the endowment changes account for 16%. These skill premium. Second, globalization effects relative contributions do not vary drastically working through product price changes caused over the four sub-periods. However, the an increase in the skill premium for all impact of product price changes appears to periods. Third, increases in non-production increase over time, while that of labor labor endowments worked towards depressing endowment changes seems to decline20. the skill premium, as did the decline in the supply of production workers. Fourth, 6. Summary and Conclusions production labor specific technical change This paper contributes to the globalization and increased the skill premium, while non- wage inequality literature in two ways. First, production labor specific technical change and by assuming that interest rates are determined TFP growth reduced the skill premium. in the world market, we allow for capital to be Finally, in terms of relative contributions, an endogenous variable that is mobile globalization effects, working through changes internationally. Thus, we provide direct in interest rates and product prices, had the empirical evidence on the effects of biggest impact on the skill premium, followed international capital movements on relative by technology, while labor endowment wages. Second, by using a multi-sector changes had the least relative impact on skill specific-factors model which we apply to U.S. premium changes. manufacturing data, we avoid the ‘factor- There are two possible explanations for the large differences in magnitude between the abs(predicted ) 푖 . The residual share is defined as: actual and predicted skill premium growth ∑ 푎푏푠(predicted 푗 rates. First, our model does not take into

abs(actual−predicted) . This gives us the % of account capital market imperfections, abs(actual−predicted)+abs(predicted) impediments to capital mobility, and risk and actual growth rate that is unexplained. uncertainty with respect to foreign direct 20 The results shown in Table 7 are along the lines of investment. This may lead to biased those in Dasgupta and Osang [6]. However, that paper predictions. Second, in some sectors such as does not consider the effects of international capital autos and chemicals, the U.S. may be flows.

32 International Economic Studies, Vol. 47, No. 1, 2016 considered a large economy with potential following model21: market power. For these sectors the user cost 퐿푛푉푖푗 = ∑ 훽푖퐿푛푤푖 + 훾푗퐿푛푄푗 + ϱ푗 (42) of capital is likely to be determined in 푖 domestic markets rather than being set on where ϱ is the error term. As noted in the world markets as assumed in our model. 푗 literature (see Roberts and Skoufias [30]) The analysis presented in this paper lends equation (42) must be estimated in long time- itself to several extensions. The model could differences to avoid the potential errors-in- be easily applied to data for other countries, variables problem. Accordingly, we estimate just as ‘mandated-wage regression’ analysis of (42) using 10-year time differences. We U.S. industries was later applied to wage consider two different specifications. In the inequality issues in countries such as the UK first specification, we use cross-sectional data and Sweden. Another extension would be to and estimate the elasticities for each year from include service sector industries in the 1968-94. In the second specification, we use a empirical analysis, as U.S services sectors panel data approach and estimate the above have witnessed significant capital inflows equation with time and industry dummies. For since the early ’80s as well. both specifications, we impose two

constraints: ∑ 훽 = 0 and 훾 = 1. Since the Appendix A 푖 푖 푗 second specifications yields implausible To calculate the predicted skill premium in results for some own price elasticities, we use equation (33), we need values for 휀푖푗. Since the first specification. Averaging the yearly 휀 = 퐸푖 − 퐸푖 ,we can use equations (3) for 푖푗 푝푗 푁푝푗 estimates from the first specification yields the following values for the demand elasticities 22: 퐸푘. Since 푎̂ = 푉̂ − 푄̂, we can use equation 퐸퐾 퐸퐾 퐸퐾 푖푗 푖푗 푖푗 푗 퐾 푃 푁푃 −.700 . 005 −.091 푝 푃 푃 [ 퐸퐾 퐸푃 퐸푁푃] = [ . 521 −.111 . 554 ] (43) 푁푃 푁푃 푁 . 179 . 107 −.463 (3) and (13)-(15) to write the following: 퐸퐾 퐸푃 퐸푁푃 푉̂ − 푄̂ = 퐸푘 푟̂ + 퐸푝 푤̂ + 퐸푁푃 푤̂ 푖푗 푗 퐾푗 푗 퐾푗 푃 퐾푗 푁푃 ̂ (40) − 푏푖푗 ∀푖 As predicted by theory, all own price elesticities re negative. However, the

Moving the 푄̂푗 term to term to the right, symmetry condition does not hold. We did not ̂ holding technology constant, i.e., 푏푖푗 = 0, and impose this restriction in our elasticity indexing factor returns to labor by sector j, we estimations since it has been noted in the get: 푉̂ = 퐸푘 푟̂ + 퐸푝 푤̂ + 퐸푁푃 푤̂ + 푄̂ ∀푖 21 푖푗 퐾푗 푗 퐾푗 푃푗 퐾푗 푁푃 푗 (41) In the context of international trade and wage inequality, Slaughter [33] has estimated constant-output

푘 factor demand elasticities using the same dataset that we The 퐸푖 on the RHS of this equation are 푗 use. However, he does not report these manufacturing- factor demand elasticities. Following the labor wide elasticity estimates in his paper. demand literature, summarized in Hamermesh 22 Using time averaged instead of yearly estimates entails [16], we estimate these elasticities with the a trade-off. It allows us to use a larger dataset to calculate (27), i.e., we avoid losing the years 1958-67. The cost is that we need to assume that the actual elasticites we are 푘 푘 trying to estimate are time-invariant, i.e., 퐸푖,푡 = 퐸푡 .

Economic Impact of Regional Trade Agreements and Economic Co-operation: Econometric Evidence 33

literature that such restrictions do not 휇푗푃̂: adjustment term for intermediate necessarily improve the eﬃciency of the inputs = product of an m*m matrix with estimates. materials revenue-share 휃Mj on its main

diagonal with the m*1 vector of 푃푀̂푗 Appendix B 푝̂푗: growth rate of PISHIP for industry

Here we describe the construction of the 푗 − 휇푗푝̂ variables used in our analysis.

푤푁푃 : Non-production labor wages = PAY - References PRODW 1. Baldwin, Robert E. and Glen G. Cain,

푉푁푃 : Non-production employment = EMP “Shifts in U.S. Relative Wages: The Role -PRODE of Trade, Technology and Factor 푟: User cost of capital for jth industry = Endowments”, The Review of Economics (VADD-PAY)/CAP and Statistics, 580-595, November 200. r : Nominal interest rate on corporate bonds 2. Berman, Eli, John Bound and Zvi (Moody’s Baa, from ERP, 2011.) Griliches, “Changes in the Demand for

푉̂푃 : Growth rate of total production Skilled Labor within U.S. Manufacturing: employment = growth rate of ∑푗 PRODE Evidence from the Annual Survey of

푉̂푁푃푗 : Growth rate of non-production Manufactures”, Quarterly Journal of employment in jth industry Economics, pp.367-397, May 1994.

λPj: Share of jth industry in total production 3. Berman, Eli, John Bound and Stephen labor force = PRODE/ PRODE Machin, “Implications of Skill-Biased

λNPj: equal to 1 by deﬁnition Technological Change: International

휃Pj : Revenue share of production labor for Evidence”, Quarterly Journal of jth industry = PRODW/VSHIP Economics, pp.1245-1280, November

휃NPj : Revenue share of non-production 1998. labor for jth industry = 푤NP /VSHIP 4. Blonigen, B. and M. Slaughter, “Foreign 휃Mj: Materials revenue-share for jth Aﬃliate Activity and US Skill Upgrading”, industry = MATCOST/VSHIP Review of Economics and Statistics,

휃Kj = 1 − θP푗 − θNP푗 − θM푗 pp.36276, 2001.

푄̂푗: growth rate of real value-added 5. Cline, William R., Trade and Income 푎̂Pj : growth rate of production labor-input Distribution, Institute for International coefficient for industry j =(P RODÊ 푗)-푄̂푗 Economics, Washington D.C., November 푎̂NPj : growth rate of non-production labor- 1997. input coefficient for industry j =(VNPĵ ) - 푄̂푗 6. Dasgupta, Indro. and Thomas Osang, 푎̂Kj : growth rate of capital-input coefficient “Trade, Wages, and Specific Factors”, for industry j =(CAP̂j) - 푄̂푗 Review of International Economics, vol.15

훱푗: Total factor productivity growth in jth no.1, pp.45-61, 2007. ̂ industry =∑푖 Θ푖푗 푏푖푗. 7. De Loo, Ivo and Thomas Ziesmer, 훱푗 : Measure of factor-speciﬁc “Determinants of Sectoral Average Wage technological change for i-th factor = ∑ λ 푏̂ 푗 푖푗 푖푗 Growth Rates in a Speciﬁc Factors Model 푃푀̂푗: growth rate of PIMAT for industry j with International Capital Movements: The

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