Structural Change and the Skill Premium in a Global Economy

Transcription

1 Structural Change and the Sill Premium in a Global Economy Yang Xu Abstract We develop a multi-country general equilibrium model with structural change to investigate the factors affecting the global changes in the sill premium between 1997 and Trade and technological change increase the sill premium by inducing reallocations to sill-intensive sectors. We apply our three-sector framewor to 37 countries, and the model accounts completely for countries trade, production, consumption, and sill premium in terms of different types of fundamental shocs. Technological changes, both sill biased and Hics neutral, account for most of the increases in the sill premium. The effects of Hics-neutral total factor productivity growth act through structural change. Keywords: trade, technological change, structural change, sill premium JEL codes: F16, F62, F63, O14 Over the past 20 years, both developed and developing countries have experienced a rapid pace of globalization. Many of these countries have also experienced large increases in the sill premium, measured by the wage ratio of college graduates to non-college graduates. 1 Figure 1 illustrates that around two thirds of countries experienced rising sill premium from 1997 to 2007, including both advanced economies, such as the US and Italy, and emerging ones, such as China and Brazil. While there has been considerable research on the reasons SOE & WISE, Xiamen University. xuya0005@e.ntu.edu.sg. This paper is originally the first chapter of my dissertation. I am extremely grateful to Nuno Limão for his continual guidance and support through the various stages of this project. I am indebted to Luca David Opromolla and Felipe Saffie for their many helpful comments and suggestions. I am grateful to Eunhee Lee for many in-depth and insightful discussions at the later stage of the project. For their helpful comments, I also than the seminar participants at the trade group meetings and brown bag meetings of the University of Maryland as well as the participants at the 2016 spring Midwest international trade meetings. All errors are my own. 1 See, for example, Goldberg and Pavcni (2007) for evidence of a rising sill premium in developing countries in the 1990s. 1

2 behind the global increase in the sill premium, such as trade and sill-biased technological change, to date, there is no conclusive evidence on the relative importance of different factors. Moreover, most studies on the effects of globalization on the sill premium focus on reallocations within the tradable manufacturing sector. Meanwhile, the global economy has also experienced substantial reallocation of economic activity across broad sectors, that is, structural change. There have been substantial shifts from the agricultural to the manufacturing sector in developing countries, and from the manufacturing to the services sector in developed countries. These structural changes might further increase the sill premium because sill intensity in production is the highest in services and the lowest in agriculture. Thus, we examine the effects of different factors on the sill premium in the presence of structural change. Specifically, we address the following two questions. First, to what extent have recent changes in the fundamental shocs, such as reductions in trade costs and technological change, impacted the sill premium across countries? Second, how are the impacts from these fundamental shocs affected by structural change across developed and developing countries? We address these questions by first developing a multi-sector, multi-country general equilibrium trade model based on Eaton and Kortum (2002) and Caliendo and Parro (2015), augmented with elements of structural change. We divide the economy into three sectors agriculture, manufacturing, and services and all sectors are tradable. The production factors include silled and unsilled labor as well as intermediate inputs from each sector. Structural change is driven by endogenous changes in expenditure shares. For households, structural change is due to nonhomothetic preferences, while for firms, it occurs through changes in aggregate expenditure on intermediate goods. The framewor allows us to perform a structural decomposition exercise to quantify the relative importance of alternative explanations, in the spirit of the accounting approach used in Eaton et al. (2016). Specifically, changes between any two periods can be fully explained by six types of country-specific shocs: (i) changes in the bilateral trade cost between each pair of trading partners in each sector, (ii) changes in each sector s Hics-neutral total factor productivity (TFP), (iii) changes in each sector s sill intensity, (iv) changes in the supply of silled and unsilled labor, (v) changes in trade deficits, and (vi) changes in the model residuals. 2 3 After retrieving these shocs, we conduct counterfactual exercises by feeding in each type of shoc separately into the initial equilibrium to evaluate its contribution to the 2 Trade deficits in our framewor are exogenous transfers between countries because the model is static. 3 The residual shocs include the residuals from the estimation of household expenditure and firm intermediate expenditure functions, as well as the changes in value-added share. 2

3 changes in the sill premium. We apply the quantitative framewor to 37 countries from 1997 to 2007, a period when global trade values increased by more than 50%. We retrieve data on production, factor payments, consumption, and bilateral trade from four versions of the Global Trade Analysis Project (GTAP), corresponding to 1997, 2001, 2004, and In addition, we assemble data on the sill premium from various sources for each sample country. We use these data to retrieve fundamental shocs based on our framewor. First, the model generates a gravity equation that relates bilateral trade flows to bilateral trade costs and sectoral TFP, which we obtain using an approach similar to that of Parro (2013) and Reyes- Heroles (2016). Second, shocs to the supply of silled and unsilled labor are adjusted for consistency with the observed sill premium. Third, we measure sill intensity as the cost share of silled labor in total labor payments. The changes in fundamental shocs replicate the observed production shares, household expenditure shares, trade shares, and the sill premium for 37 countries between 1997 and Moreover, these shocs affect relative sectoral prices and real income, which in turn affect structural change through changes in expenditure shares. By feeding each type of fundamental shoc separately into the model, we quantify its effect on the sill premium. Several results emerge. First, we find that changes in sill intensity are the most important factor that drives the increases in the sill premium. The median effects are 6.1% in Organization for Economic Cooperation and Development (OECD) countries and 4.5% in non-oecd countries. There is much heterogeneity across countries, ranging from -24% to 43%. The reason for the fall in the sill premium is that some countries experienced decreases in sill intensity, or technological change biased toward unsilled labor. Second, we find that changes in trade costs and trade deficits have little effects on the sill premium, except for some countries that have experienced trade liberalization, such as China. However, the result that trade costs and trade deficits have little effects does not imply that international trade is unimportant, because changes in foreign sectoral TFP impact the home economy through trade. If we feed the changes in trade costs, deficits, and foreign sectoral TFP simultaneously into the initial equilibrium, the resulting changes in the sill premium are 7.4% in OECD countries and 10.9% in non-oecd countries. Trade has large effects on the sill premium because productivity growth in foreign countries induces structural change, which in turn increases the relative demand for sill-intensive goods from home through international trade. To investigate the effects of structural change on the sill premium, we compare our 3

4 baseline results with a framewor in which the expenditure shares are constant. 4 We find that the median effects of structural change on the sill premium are % in OECD countries and % in non-oecd countries. Structural change is more important in non- OECD countries than in OECD countries because developing countries have experienced larger increases in sectoral TFP. 5 Our study is related to a large body of literature on the impact of international trade on the sill premium focusing on within-manufacturing reallocations. This body of research includes labor-economics literature, which finds little effects of trade by measuring the changes in factor content of trade (Borjas et al., 1997; Katz and Murphy, 1992; Berman et al., 1994), and recent trade literature, which studies different mechanisms of how trade is sill-biased (e.g., Burstein and Vogel (2016) on technology sill complementarity; Parro (2013) on capital sill complementarity; Verhoogen (2008) on quality upgrading in Mexico; Bustos (2011) on sill upgrading in Argentina). Our wor departs from this literature by quantifying the effects of different fundamental shocs on the sill premium through between-sector reallocations, that is, structural change. Another strand of literature explores the determinants of structural change. The literature finds that non-homothetic preferences, complementarity between sectors, and international trade are important drivers of structural change (Herrendorf et al., 2014). Our contribution is to build a tractable multi-sector multi-country quantitative framewor incorporating all these channels of structural change, which we use to quantify the effects of different shocs on the sill premium. 6 A more closely related study to ours is that of Cravino and Sotelo (2017), who, in parallel wor, build a similar model to quantify the effects of trade-induced structural change on the sill premium. Our wor differs in two important aspects. First, our structural analysis allows us to separately quantify the effects of changes in trade cost and sectoral TFP on the sill premium, while the approach of Cravino and Sotelo (2017) can compute only the effects of trade. Separate quantification is important because sectoral TFP growth is the major driver of structural change, and thus, is the major fundamental shoc governing the effects of structural change on the sill premium. Second, we can study how changes in foreign sectoral TFP are 4 This method implies that there are no endogenous changes in household and aggregate intermediate expenditure shares. 5 In previous studies, changes in sectoral TFP are identified as the major driver of structural change. See, for example, Świeci (2017). 6 We are not the first to quantify the effects of structural change on the sill premium. Buera et al. (2015) build a two-sector closed economy model and show that structural change can explain around 30% of the observed increases in the sill premium in advanced economies. Our wor departs from theirs in that we show that trade increases the sill premium by transmitting foreign structural changes to home countries. 4

5 transmitted across sectors and countries to affect the sill premium in a given country. The rest of the paper is organized as follows. Section 1 presents the observed patterns of sill intensity and structural change. Section 2 builds a quantitative multi-sector multicountry framewor with structural change. Section 3 discusses the strategy to retrieve fundamental one-time shocs and calibrate the model parameters. Section 4 uses the framewor to conduct counterfactual analysis, which investigates the effects of different fundamental shocs on the sill premium. Section 5 concludes. 1 The Facts: Structural Change and Sill Intensity In this section, we present the observed structural change and the changes in sill intensity in our sample countries between 1997 and We measure structural change by sectoral changes in the production share: y value of output in sector =, which is in the spirit of the final consumption expenditure approach total value of output in Herrendorf et al. (2013). 7 We observe from the first three columns of Table 1 that sectoral reallocation occurs from agriculture and manufacturing to services in OECD countries, while the pattern of structural change in non-oecd countries is from agriculture to manufacturing and services. Changes in both household consumption expenditure and firm expenditure on intermediate across sectors influence structural change. Columns 4 9 of Table 1 illustrate that both consumers and firms spend more on services and less on agriculture from 1997 to Moreover, non-oecd countries experience greater sectoral reallocations than OECD countries do. Structural change affects the sill premium because sectors differ in sill intensity. Table 2 presents the data on average sill intensity (β ) in each sector, measured as the ratio of wage payments to silled labor relative to total wage payments. 8 The left panel reveals that the services sector is the most sill intensive while the agriculture sector is the least sill intensive. As the data has shown, resources have been allocated to sill-intensive sectors so structural change might increase the sill premium in all countries. The right panel shows that in OECD countries, the services sector has the largest increase in sill intensity, while all three sectors in non-oecd countries experience increases in sill intensity. The changes 7 Using measures of sectoral changes in employment share or value-added share yields similar results. 8 We do not observe employment share of the silled labor in each sector in the GTAP database. In our quantitative framewor silled and unsilled labor are combined with a Cobb-Douglas technology, and thus, an increase in the wage payment share of silled labor captures sill-biased technological change. 5

6 in sill intensity capture the changes in relative demand for silled labor within each sector. 9 What might be the driving forces behind the observed structural change across countries? Table 3 shows that on average, OECD countries consume more services and less agriculture than non-oecd countries. This finding suggests that nonhomothetic preferences can explain the fact that rich countries consume more services. On the firm side, Table 4 shows that each sector uses own-sector intermediates intensively, which implies that structural change is amplified through input-output linages, because aggregate demand for sector intermediates, e, is an output share weighted average of each sector s expenditure on sector intermediates e = l {A,M,S} yl e l. 2 Framewor The static trade model is based on Eaton and Kortum (2002) and Caliendo and Parro (2015). The world economy has n = 1,..., N countries, each with three tradable sectors: agriculture (A), manufacturing (M), and services (S). Let Ω = {A, M, S} denotes the set of all sectors. Country n is endowed with U n units of unsilled labor, and S n units of silled labor. Output in each sector is a constant elasticity of substitution (CES) aggregate (with σ) of the outputs of a unit continuum of goods (which is different by sector) indexed by j [0, 1]. Country n s efficiency z n(j) at maing good j in sector is the realization of a random variable z n distributed as: ( Fn (z) = Pr(zn z) = exp Tn z θ), (1) drawn independently across each good j in country n. Here, T n reflects the overall production efficiency in country n sector, and the parameter θ is an inverse measure of the dispersion of productivity. Households consume outputs from all sectors with a preference structure of the almost ideal demand system (AIDS). Production of good j in each sector combines the services of each type of labor and intermediates from each of the three sectors. Technology is such that the intermediates from each sector are combined with two labor inputs following a Cobb- Douglas technology with constant returns to scale. Trade in the outputs of the three sectors incurs standard iceberg costs, such that delivering one unit of output from country i to country n requires κ ni 1 units, with κ nn = 1. Taing 9 We do not tae a stand on what mechanisms drive the changes in sill intensity, because our focus is on the effects of between-sector reallocations. 6

7 into account the ad valorem tariff rate τ ni 0, the trade cost from country i to country n is d ni = ( 1 + τ ni) κ ni. 10 A Preferences The preference of household o in country n is of the AIDS structure, as in Fajgelbaum and Khandelwal (2016). The preference is defined by the expenditure share on goods from each sector, h n(o): ( ) h n(o) = α + δ A ln Pn A + δ M ln Pn M + δ S ln Pn S In (o) + b ln P n Ω, where I n (o) is household o s income and P n is the sectoral price level. The overall price level P n is of the translog form: ln P n = Ω α ln Pn + 1 δ l ln Pn ln P l 2 n. Ω l Ω We restrict Ω α = 1, Ω δ l = 0, Ω b = 0 so that the expenditure shares add up to 1. We further restrict l Ω δ l = 0 and δ l = δ l so that the AIDS is well defined. In the AIDS, the substitution patterns between sectors are translog, which is more flexible than the standard CES considered in the structural change literature. Non-zero income elasticity of demand b implies that the AIDS is nonhomothetic. In summary, both changes in relative sectoral prices and real income affect structural change through the changes in household expenditure shares under the AIDS. h n: We aggregate the individual decisions to derive the economy household expenditure share ( )] h n = α + δ A ln Pn A + δ M ln Pn M + δ S ln Pn S Īn + b [T h n + ln P n Ω, (2) where Īn is the average income of consumers in each country, and T h n is the Theil index of inequality. 11 The preferences are the same across countries, but the expenditure shares differ because real income per capita, the Theil index, and the relative sectoral prices vary. In the quantitative exercises we utilize those variations in the data to calibrate the parameters of AIDS. 10 There is no tariff in the services sector, and thus, τ S ni = See Deaton and Muellbauer (1980). 7

8 B Technology In each sector, production of a composite intermediate bundle combines the intermediates from every sector with a Cobb-Douglas technology. The price of the composite intermediate bundle r n can be written as r n = l Ω 1 γ l n (P l n) γl n, (3) where l Ω γl n = 1 for, l Ω. Sector s expenditure share (relative to sector s total intermediate expenditure) on sector l s intermediates is e l n = γ l n (4) for, l Ω. In the data, the constant terms γn l are sector and country specific, and γn > 1, 2 so that structural change is amplified through input-output linages. Competitive input marets imply that a firm producing good j in country n s sector taes wages and the price of intermediate bundles as given, and solves the following costminimization problem: min c n(j) = wnu u n(j) + wns s n(j) + rnm n(j) {u n (j),s n (j),m n (j)} subject to z n(j) [ (u n(j) ) 1 βn ( s n(j) ) ] βn v n ( M n(j) ) 1 v n 1, where u n(j), s n(j), and Mn(j) are the demand for unsilled labor, silled labor, and composite intermediate bundles, respectively, vn is the value-added share, wn u and wn s are the wages paid to unsilled and silled labor, respectively. Competitive output marets imply that the price of good j in country n s sector is p n(j) = min { p ni(j) : i = 1,..., N }, where p ni(j) = c i (j)d ni is the price charged by a firm in country i exporting to country n. C Equilibrium Relationships In this subsection, we derive the equilibrium outcomes of the model that we later apply to the data. 8

9 C.1 Prices and Trade Shares From the firm s cost-minimization problem, the unit cost c n of producing in country n s sector, combining labor and the composite intermediate bundle, is [ ( ) v 1 n ( ) ] [ 1 v 1 n ( ) w c u 1 β n ( ) ] n = n w s β v n n n (r 1 v n vn 1 vn 1 βn β n), (5) n where r n is given by (3). The price level in country n s sector, after combining production costs in each country, is P n = ɛ [ N l=1 T l ( c l d nl) θ ] 1 θ, (6) [ ( )] 1 θ where ɛ = Γ +1 σ 1 σ, and Γ( ) is the gamma function. θ The share of spending in country n s sector that goes to goods imported from country i is π ni = X ni X n = T i ( c i d ni) θ where Φ n = N l=1 T ( ) l c l d θ nl is the multilateral resistance term. Φ n, (7) C.2 Maret Clearing Denote Xn as the value of country n s total spending on sector, and Yn gross production. World goods maret clearing implies that as the value of Y n = N πin X 1 + τin i. (8) i=1 Using expression (2), total spending on goods from sector is the sum of household spending on sector and the use of sector s output as intermediates in sector l: X n = s ni n + l Ω (1 v l n)γ l n Y l n, (9) where I n = wnu u n + wns s n + D n + ( l Ω Xl n 1 ) N πni l i=1 is the total household income 1+τni l in country n, consisting of wage payments wnu u n +wns s n, trade deficits D n, and tariff revenue ( l Ω Xl n 1 ) N πni l i=1. 1+τ l ni 9

10 Clearing in the competitive marets for each type of labor implies that total labor income equals expenditure on each type of labor across sectors: w u nu n = Ω w s ns n = Ω (1 β n)v ny β nv ny n. n, (10) Finally, the sum of gross production, trade deficits, and tariff revenue equals total spending in each country: [ ( Yn + Xn 1 Ω N i=1 π ni 1 + τ ni )] + D n = Ω X n. (11) Because the model is static, trade deficits are exogenous transfers between countries. 12 D Exogenous Variables For the purpose of performing quantitative exercises, we divide exogenous variables of the model into constant parameters Θ and one-time shocs Ψ: Θ = {α, δ l, b, γ l n, θ } and Ψ = {κ ni, τ ni, T n, β n, v n, U n, S n, D n }, for, l Ω, and n, i = 1... N. 13 Equations (2) (11) determine the endogenous variables, which include wages w u n and w s n, prices of intermediate bundle r n, prices P n, trade shares π ni, household expenditure shares h n, aggregate intermediates expenditure shares e n, total spending X n, and output Y n for sectors Ω. Shocs in the framewor affect structural change through their effects on sectoral prices and real income, which in turn affect household expenditure shares according to (2). In addition, sectoral linages amplify structural change owing to intensive usage of own-sector intermediates. 12 When solving the model, we normalize the total world expenditure N n=1 X n = 1. Trade deficits are then regarded as a constant share of total world expenditure that satisfies N n=1 D n = The value of elasticity of substitution σ is irrelevant for quantitative analysis as long as θ > σ 1. 10

11 E Connecting Shocs to the Sill Premium To highlight the structural change channel, we decompose the effects of shoc ν on the sill premium into two parts: d(w s n/w u n) dν = (ws n/w u n) ν h n,e n + Ω (wn/w s n) u dh n h n dν + Ω (wn/w s n) u de n e n dν, where the first term is the direct effect of shoc ν holding the expenditure shares constant, and the second and third terms represent the effects from endogenous changes in expenditure shares. The last two terms can be interpreted as the effects of structural change on the sill premium. 14 Three channels affect the sill premium without influencing expenditure shares. First, shocs to sill intensity β n capture all within-sector reallocations. An increase in β n implies that the sector becomes more sill intensive in production, and therefore, it can be interpreted as sill-biased technological change. 15 Second, shocs to the relative supply of silled labor S n U n capture the supply-side effects of the labor maret. An increase in the relative supply decreases the sill premium. Third, shocs affect between-sector reallocations through comparative advantage in international trade. Trade increases the sill premium in countries that have comparative advantage in sill-intensive sectors, implying that these countries are relatively more productive in these sectors or more sill abundant (large Sn U n ) than are countries without such comparative advantage. Changes in trade costs {κ ni, τ ni}, trade deficits D n, sectoral TFP Tn, and sill abundance Sn L n affect the magnitude of this force. In addition, all shocs affect the sill premium by influencing the expenditure shares. The household expenditure shares are affected by changes in sectoral prices and real income. The firm s aggregate intermediate expenditure shares are driven by changes in output shares owing to intensive usage of own-sector intermediates, as emphasized by Cravino and Sotelo (2017). Lastly, structural change in foreign countries implies an increase in the demand for sill-intensive goods at home through international trade, that is, structural change is transmitted. 14 The changes in expenditure shares do not capture all between-sector reallocations, because international trade implies that sectoral production and consumption might differ. In Appendix D, we show that the effect of between-sector trade on the sill premium is small in OECD countries and negative in non-oecd countries. 15 Because our focus is on between-sector reallocations, we treat β n as exogenous to other types of shocs, implying that we do not allow reductions in trade costs or increases in sectoral TFP to affect sill intensity, as in Burstein and Vogel (2016) and Parro (2013). 11

12 3 Applying the Model to the Data In this section, we calibrate the parameters (Θ) of the model and retrieve the one-time shocs (Ψ). We focus on the period between 1997 and 2007, which encompasses China s World Trade Organization accession. In the spirit of Eaton et al. (2016), the quantification strategy enables fundamental shocs of the model to perfectly explain the observed changes between 1997 and 2007 for 37 countries, so that we can assess the quantitative importance of each type of shoc in explaining the observed changes in the sill premium. A Data To investigate the effects of structural change on the changes in sill premium, the framewor should at least explain the observed changes in those two variables. Data involving the structural change come from the GTAP versions 5 to 8, corresponding to the years 1997, 2001, 2004, and 2007, for 37 countries in addition to a constructed rest of the world. First, we use data on total expenditure X n(t), output Y n (t), and bilateral trade flows X ni(t) to compute production shares y n, trade shares π ni for Ω, and country trade deficits D n (t). 16 Second, we use data on consumption expenditure to calculate consumption expenditure shares h n(t), and input-output tables to compute value-added shares v n(t) as well as intermediate expenditure shares e l n (t) for, l Ω. Third, we use data on silled wage payment share to measure sill intensity β n(t) for Ω. Fourth, we tae total employment L n (t) directly from the Penn World Tables 8.1. We calculate the sill premium as the wage premium for those with college to high school education from various sources. We use data from the EU KLEMS to compute the sill premium for the OECD countries. For Latin American countries, we resort to data from the World Ban and the Socio-Economic Database for Latin America and the Caribbean (SEDLAC). Details are provided in Appendix A. B Quantification Procedure The quantification involves two major steps. First, we estimate trade costs and TFP from the structural gravity equation implied by our framewor. Second, we calibrate the demand parameters Θ d = {α, δ l, b, γ l n } and retrieve the one-time shocs Ψ while solving for the general equilibrium of the model. 16 Specifically, yn = Y n l Ω Y, π n l ni = X ni, and D Xn n = Ω X n Ω Y n. 12

13 B.1 Estimating Trade Costs and TFP In this subsection, we present a method to estimate trade costs and TFP simultaneously from the model-implied gravity equation. The intuition is that bilateral variations in trade flows are informative of the values for trade costs, while the source and destination country fixed effects are informative of the values for TFP. 17 We start from the structural gravity equation (7). By dividing the trade share from country i to country n by country n s own share and taing logs, we obtain ( ) π [ ln ni ( ) ] = ln T πnn i c θ [ ( ) ] i ln Tn c θ n θ ln d ni, (12) where trade cost d ni = ( 1 + τ ni) κ ni incorporates both the tariff τ ni and the iceberg cost κ ni. Since the iceberg cost is not observed, we further parameterize it as κ ni = κ niζni, where κ ni = κ in represents the symmetric part and ζniζ in = 1 the asymmetric part. The advantage of this parameterization is that we can calculate the symmetric part of the iceberg cost by utilizing the trade flows from n to i: ( ) π ln in π ii [ ( ) ] = ln Tn c θ ( ) n ln [T ] i c θ i θ ln d in. (13) Summing the two opposite trade flows (12) and (13), we obtain ( π κ ni = ni π in πii πnn ) 1 2θ [ (1 + τ ni )(1 + τ in) ] 1 2. Rearranging the gravity equation (12) by moving both the tariff ( 1 + τ ni) and symmetric iceberg cost κ ni to the left-hand side, we obtain the following expression: ln [ (π ni πin πnn ) πii 1 2θ ( 1 + τ ni 1 + τ in ) 1 ] 2 [ (T = ln i ) 1 θ c i } {{ } exporter fixed effect ] [ (T ln n ) 1 θ c n } {{ } importer fixed effect ] + ln ζni. (14) }{{} residual We can estimate the econometric version of (14) by ordinary least squares (OLS) for each year-sector given the value of trade elasticity θ : ln [ (π ni πin πnn ) πii 1 2θ ( 1 + τ ni 1 + τ in ) 1 ] 2 = fi Di fnd n, (15) 17 The procedure we employ is similar to that used by Parro (2013) and Reyes-Heroles (2016). 13

14 where Di and Dn are the dummies of the source and destination countries, respectively. By construction, we can identify TFP from either the exporter or importer fixed effects, and the asymmetric part of the iceberg cost from the regression residuals. Moreover, the trade cost and TFP obtained from estimating (15) are orthogonal to each other. For the values of trade elasticity, we choose θ A = 4.44, which is a trade volume-weighted average of the trade elasticity estimates of agriculture and food from Caliendo and Parro (2015). 18 For the trade elasticity of the manufacturing sector, we set the value of θ M so that the trade volume-weighted average of trade elasticity in the goods sector (agriculture and manufacturing) equals 4, which is the estimate from Simonovsa and Waugh (2014). This yields θ M = Finally, since there is no estimate for trade elasticity in the services sector, we set the value to θ S = From expressions (6) and (7), we obtain sectoral prices from estimating (15): where S n = ( T n P n = ) 1 θ c n is country n fixed effect. 20 ɛ S n (π nn) 1 θ, (16) B.2 Retrieval of Shocs From the equilibrium conditions (2) (11) and the values of endogenous variables {yn, ws n, π w ni, P n u n }, we can retrieve the following shocs without nowing the equilibrium wages. 1. We compute trade costs d ni by utilizing expression (6), and applying expression (7) to n i relative to n = i: ( π d ni = ni π ii ) 1 θ Pn Pi. (17) In addition, we obtain the iceberg costs κ ni = d ni τni 18 In Caliendo and Parro (2015), θ(agriculture) = 8.11 and θ(food) = The agricultural sector in our framewor includes both agricultural and food industries in Caliendo and Parro (2015). 19 We perform robustness checs to observe whether our results are affected by different values of θ S. See Subsection C for details. 20 Technically, we can obtain only relative sectoral prices to some base country, and thus, we normalize the US prices in To obtain the US prices in other years, we use data on the US sectoral productivity growth so that the changes in sectoral prices are consistent with the observed TFP growth. See Appendix B for details. 21 An alternative method is to use the bilateral residuals ζni from (15) so that d ni = ( 1 + τni) κ ni ζni. These two methods yield the same trade costs. 14

15 2. We measure the value-added shares v n as the ratio of total labor payments to total production costs from the data. 3. We measure the sill intensity β n as the ratio of payments to the silled labor to total labor payments from the data. 4. We measure the total labor force L n as the total employment in country n from the data. 5. We compute the relative supply of silled labor by dividing the two labor maretclearing conditions (10), given the observed sill premium ws n : wn u S n U n = Ω β nv ny n Ω (1 β n)v ny n ( w u n w s n ). (18) In addition, we obtain S n and U n in levels given the value of total employment L n. We require the values of wages to retrieve sectoral TFP from the country fixed effects. The values of w u n and w s n can be obtained in two steps. First, we compute the equilibrium outputs Yn from expressions (8) and (11) given observed trade shares, tariffs, and deficits. Second, we compute the wages using labor maret-clearing conditions (10) given observed value-added share and sill intensity. We can compute the unit cost c n from expression (5) given equilibrium wages, and retrieve sectoral TFP from expression (7) with n = i: B.3 Calibrating Demand Parameters ( P Tn = n ɛ c n ) θ. (19) We calibrate the demand parameters Θ d = {α, δ l, b, γ l n } by minimizing the distance between the model-implied expenditure shares and the observed ones. To find the AIDS parameters, we first compute the model-implied household expenditure shares h n(t) according to expression (2), and then solve the following problem: {α, δ l, b } = argmin Ω N [ h n(t) h 2 n(t)]. (20) n=1 t 15

16 To find the intermediate expenditure parameters {γ l n }, we first calculate the model-implied intermediates expenditure shares ẽ l n (t) from (4), and then solve the following minimization problem sector by sector: {γ l n } = argmin l Ω N [ e l n (t) ẽ l n (t) ] 2, Ω. (21) n=1 t To ensure that the quantitative framewor replicates the observed structural changes, we match the model-implied household expenditure shares to the observed ones, and impose restrictions such that the model-implied aggregate intermediate expenditure shares are consistent with the observed structural changes. We introduce additional shocs to both the household expenditure and intermediate expenditure to capture the differences between the model-implied and observed shares. On the household side, we define preference shifters as a n(t) = h n(t) h n(t), Ω, n = 1,..., N, (22) so that the model replicates the observed household expenditure shares. On the firm side, we define the input shifters as the solution of the following minimization problem in each year-sector: subject to l= Ω g l n (t) = argmin l Ω N n=1 [ 1 v l n (t) ] [ ẽ l n (t) + g l n (t) ] Y l n(t) = X n(t) h n(t)i n (t) [ e l n (t) ẽ l n (t) g l n (t) ] 2, (23) and l g l n (t) = 0, where the first restriction ensures that the model matches the observed structural changes. 22 The quantification procedure delivers the constant parameters Θ and the one-time shocs Ψ = {κ ni, τ ni, T n, β n, v n, U n, S n, D n, a n, g l n } (including expenditure shifters) of the baseline model. By construction, the solution to the baseline model matches the trade shares π ni, household expenditure shares h n, production shares yn, and sill premium ws n wn u initial (1997) and the end (2007) equilibria. in both the 22 Setting g l n (t) = e l n (t) ẽ l n (t) does not ensure the model matches the observed structural changes. The reason is that the consumption expenditure shares and aggregate intermediate expenditure shares do not add up to production shares, as we do not include factor payments other than labor, such as capital and land. 16

17 C Values of Exogenous Parameters Table 5 presents the calibrated AIDS parameters. First, the values of income elasticities b indicate that goods from the agricultural sector are necessities, while goods from the services sector are luxuries. These calibrated income elasticities are consistent with the structural change literature, which finds services to be a luxury sector. Second, the calibrated price elasticities are small, implying that the substitutability between sectors is close to unity, which is consistent with the price elasticity estimates from the final expenditure approach in Herrendorf et al. (2013). Table 6 reports the cumulative changes in one-time shocs for each country and sector from 1997 to The first three columns of Table 6 summarize the average changes in trade costs. First, reductions in trade costs are larger in non-oecd countries, especially in the manufacturing sector. Second, the services sector also experienced significant reductions in trade costs. Because the services sector has the largest production share in each country, especially in OECD countries, the effects of trade tend to be larger than in trade models treating services as non-tradable. ( ) 1 θ Columns 4 to 6 of Table 6 present the relative changes in average sectoral TFP ˆT M n. Again, productivity growth is much larger in non-oecd countries, especially in the manufacturing sector. As sectoral TFP growth is identified as the most important driver of structural change in the literature, the impacts of structural change on the sill premium are liely to be larger in non-oecd countries than in OECD countries. Columns 7 to 9 of Table 6 show that most of the increases in sill intensity occured in the services sector. As OECD countries have larger production shares in services than non- OECD countries do, the impacts of sill-biased technological change on the sill premium are liely to be more important in OECD countries than in non-oecd countries. Finally, the last column of Table 6 shows the changes in the relative supply of silled labor. On average, the share of silled labor increases, implying a decrease in the sill premium. D External Validation The model replicates the observed trade shares, production shares, consumption shares, and sill premium, and thus, we assess the fit of the model by using external data to verify some shocs in the model. 17

18 Trade Cost We first regress the model trade costs on their determinants commonly used in the literature. 23 These determinants include tariffs, log distance, and dummy variables, such as contiguity (=1 if two countries share a border), common language (=1 if two countries have the same official language), non-reciprocal preferential trade agreements (NRPTAs) (=1 if two countries have a NRPTA), reciprocal preferential trade agreements (RPTAs) (=1 if two countries have a RPTA), and trade agreements (TAs) (=1 if two countries have the same currency or are in the same economic union or free trade agreement). Table 7 presents the regression results for the levels of sectoral trade costs in 1997 and First, all coefficients on tariffs and distance are positive and statistically significant, except for the tariff coefficient on agriculture in Second, all coefficients on contiguity and common language are negative and statistically significant, except for the common language coefficient on services in In summary, the levels of trade costs in our framewor are reasonable, as they correlate well with the common determinants of trade costs. 24 Labor Productivity Second, we compare labor productivity in the model to the observed TFP by country. Figure 2 plots labor productivity in the model against TFP in the data. 25 Labor productivity in each country is an output weighted average sectoral labor productivity. We calculate model sectoral labor productivity as LP n = c n, which incorporates the effects of trade, as emphasized Pn by Finicelli et al. (2013). The plots show that labor productivity in each country correlates well with TFP in both years. Relative Supply of Silled Labor Third, we externally verify the relative supply of the silled labor Sn L n in each country. Figure 3 plots the model-implied Sn L n against the share of populations with incomplete tertiary degrees taen from Barro and Lee (2013). 26 The fit is reasonable with R 2 over 0.2 for both years, but the model over-predicts the relative supply of silled labor for most countries. 23 As almost all country pairs in the sample have bilateral trade flows, there is little problem of zero trade flows. 24 The exception is that some of the coefficients on the trade agreement dummies imply higher trade costs. These results might reflect endogeneity bias, since trade agreements are correlated with bilateral unobserved characteristics (see for e.g., Limão (2016)), which we cannot control for in levels. 25 TFP data are taen from PWT 8.1 as the TFP valued at current purchasing power parity. 26 As data from Barro and Lee (2013) are at 5-year intervals, we compare the model-implied share in 2007 to the data in 2005, and the model-implied share in 1997 to the data in

19 Alternatively, we regress the model-implied relative supply of silled labor on observables, which helps explain cross-country differences in educational attainment. Restuccia and Vandenbrouce (2014) find that variations in TFP and life expectancy explain most of the differences in educational attainment across countries and over time. Therefore, to assess the model fit, we regress the model-implied Sn L n on TFP, life expectancy, and the share of government expenditure on education to GDP. Table 8 presents the regression results. The first observation is that for the model-implied Sn L n, all three observables are positive and the R-squares are more than 0.5 in both years. Moreover, the data measure from Barro and Lee (2013) does not fit well as the model-implied Sn L n, indicating that the model Sn L n the quality of silled labor that is explained by factors outside the model. might reflect 4 Counterfactuals With the one-time shocs that fully account for the observed changes from 1997 to 2007, we can provide insight into the types of shocs that drive the changes in the sill premium in each country. To do so, we consider a scenario in which we apply only one type of shoc to the initial equilibrium, while eeping other types of shocs fixed at their initial levels. Table 9 summarizes the main findings on the percentage changes in the sill premium across countries. 27 We present the results for each type of shoc acting in isolation, and in the final column, we group the value-added shocs and the two demand shifters together as residuals. 28 The first three rows present the median values across the respective group of countries. In general, technological changes increase the sill premium, while labor supply shocs decrease it. First, sill-biased technological change is the most important factor that drives the increases in the sill premium. The median effects are 6.1% in OECD countries and 4.5% in non-oecd countries. The effects of sill-biased technological change are larger in OECD countries because from Table 6, rich countries are services economies that experienced significant increases in sill intensity in the services sector. Moreover, the effects are very heterogeneous across countries, ranging from -24% to 43%. From the left panel of Figure 4, this heterogeneity can be explained by differences in the changes in aggregate sill intensity across countries. 27 Changes in the sill premium are measured in relative terms: SP% = SP(c) SP(97) SP(97) 100%, where SP(c) is the sill premium in the counterfactual scenario. 28 There is no reason for the effects of each shoc to add up to the observed value because there are interactions between different shocs. 19

20 Second, changes in sectoral TFP also contribute to the increases in the sill premium. The median effects are 2.6% in OECD countries and 3.1% in non-oecd countries. The effects from sectoral TFP are larger in non-oecd countries, because from Table 6, non-oecd countries experienced larger increases in TFP. Moreover, the effects from sectoral TFP are positive for all countries, except Thailand and Uruguay, which experienced a decrease in TFP in the services sector. From the right panel of Figure 4, heterogeneous effects from sectoral TFP can be explained by differences in the changes in aggregate TFP across countries. Third, the changes in trade costs and deficits contribute little to the increases in the sill premium, except for China and Luxembourg. However, we cannot conclude that trade is unimportant, because technological change in foreign countries also affects the sill premium at home through trade, which we show in Subsection B. Last, changes in the relative supply of silled labor decrease the sill premium. The median effects are -8.8% in OECD countries and -14.5% in non-oecd countries. The reason for this result is that on average, countries have experienced increases in the relative supply of silled labor, and this effect is larger in non-oecd countries. A Effects of Structural Change We investigate the effects of structural change on the sill premium by comparing the counterfactual results in our baseline to a simplified framewor with fixed expenditure shares. In the fixed expenditure share framewor, both the household expenditure share h n and aggregate intermediate expenditure share e n are fixed. Specifically, the household expenditure share is fixed to its 1997 level h n(1997), which can be rationalized with a Cobb Douglas utility. The intermediate expenditure share is the same across all sectors and is fixed to its 1997 level, e A n = e M n = e S n = e n(1997) for Ω, which can be rationalized with a Cobb Douglas production function over intermediates. Therefore, there are no sectoral reallocations induced by changes in consumption and intermediate expenditure shares. 29 We quantify the fixed expenditure model with the same moments as the baseline, so that it yields the same exogenous variables and one-time shocs. 30 Instead of the preference and input shifters in the baseline, shocs occur directly to the household and aggregate intermedi- 29 In the fixed expenditure model, there is still structural change induced by international trade, which is the net export channel, as in Uy et al. (2013), owing to differences in sectoral TFP and sill abundance across countries. 30 Changes in sectoral TFP are slightly different across the two models because the sectoral linages differ, implying a different unit cost c n(t) under the same values of wages and sectoral prices. Quantitatively, the differences are small. 20

21 ate expenditure shares to capture the respective changes in the baseline. 31 These two shocs with changes in value-added share are counted as residuals in the fixed expenditure model. Table 10 presents the differences in the changes in the sill premium generated by each type of shoc between the baseline and the fixed expenditure model. First, the effects of changes in sectoral TFP on the sill premium are larger by 2.5% for OECD countries and 3.7% for non-oecd countries under the baseline. Second, other types of one-time shocs have similar effects under the two models. The reason is that changes in expenditure shares are driven mainly by changes in sectoral TFP, while other types of shocs have little effect on structural change. 32 The last two columns of Table 10 calculate the effects of structural change on the sill premium. Because both the baseline and fixed expenditure models perfectly explain the observed changes in the sill premium, we calculate the effects of structural change either by comparing the differences in the model-implied sill premium when applying all shocs (except residuals) between the two models or by computing the differences between the two residuals. The median effects of structural change on the sill premium are % in OECD countries and % in non-oecd countries. Structural change has larger effects in non-oecd countries because these countries experienced more sectoral reallocations during the period. B Effects of Trade In previous counterfactuals, we find that the effects of changes in trade costs and deficits on the sill premium are small. However, up to now, we have ignored the effects of changes in sectoral TFP in foreign countries that affect the home country through international trade. We now evaluate the effects of trade by applying shocs to foreign sectoral TFP ( ˆT n), trade costs, and trade deficits for each home country n. Table 11 presents the effects of trade on the sill premium when we incorporate the effects from foreign sectoral TFP. We find large effects from trade, specifically, 7.4% in OECD countries and 10.9% in non-oecd countries. The large effects arise mainly from the changes in foreign sectoral TFP, because such changes induce structural changes in foreign countries, which in turn increase the demand for sill-intensive goods in the home country through international trade. 31 Thus, in the fixed expenditure model, shocs to the consumption expenditure share replicate the observed changes, while shocs to the aggregate intermediate expenditure share those consistent with the observed structural changes. 32 Appendix C presents how different types of shocs affect structural change. 21

22 C Robustness In this section, we chec whether the results are sensitive to the specifications of the production function and values of trade elasticity in the services sector. In all the exercises, we recalibrate the parameters and retrieve the shocs so that the model with alternative specifications replicates the same data as in the baseline. CES Labor Aggregator In the baseline specification, silled labor and unsilled labor are combined with a Cobb Douglas aggregator. In the literature, silled labor and unsilled labor are found to be substitutes. For example, Acemoglu and Autor (2011) estimate that the elasticity of substitution between silled and unsilled labor is 1.6. Since most countries in the sample experienced increases in the sill premium, the effects of increases in sill intensity tend to be attenuated. In the following, we assume that the unit cost in each sector is ( ) ϕ c v n ( ) n = n r 1 v n n, (24) vn 1 vn where ϕ n is the price of the labor bundle derived from a CES aggregator: ϕ n = [ ] (1 ξn)(w n) u 1 ρ + ξn(w n) s 1 ρ 1 1 ρ, (25) where ρ is the elasticity of substitution between silled and unsilled labor. We calibrate ρ by utilizing the equilibrium conditions on relative payments to silled labor: ( ) w s ln n s n wnu u n ( ) ξ = ln n + (1 ρ 1 ξn ) ln ( w s n w u n ). (26) ( ) The left-hand side is the observed sill intensity ln β n, and the right-hand side is the 1 βn model-implied sill premium. We utilize cross-country variations and estimate (26) by OLS when solving the model. 33 The calibrated elasticities are ρ A = 0.86, ρ M = 1.50, and ρ S = 0.94, which are close to unit elasticity. Using the calibrated elasticities, we can retrieve ξ n so 33 We do not use values of ρ from the literature, because most of them are estimated using data on the labor marets in developed countries. 22