SKILLED FACTOR ABUNDANCE AND TRADED GOODS PRICES

Transcription

1 SKILLED FACTOR ABUNDANCE AND TRADED GOODS PRICES Eddy Bekkers Johannes Kepler University Linz Joseph Francois Johannes Kepler University Linz and CEPR London Miriam Manchin University College London ABSTRACT: We develop a monopolistic competition model with nonhomothetic factor input bundles where larger quality goods require relatively more skilled workers. More skill abundant countries export higher quality, higher priced goods. This provides a theoretical underpinning for the empirical findings on the effect of skill abundance on unit values. We extend the core model with several variables from the literature on traded goods prices. The model features a novel mechanism through which trade liberalization affects the skill premium. Using a multicountry dataset on unit values we find a positive significant effect of exporter skill abundance on traded goods prices. Keywords: Traded goods prices, exporter skill abundance, nonhomothetic factor inputs, per unit trade costs, skill premium JEL codes: F2, F4 printdate: August 9, 203 We want to thank Jean Marie Viaene, Felix Lamp and Octavio Fernandez-Amador for useful comments and discussions. All possible errors are ours. Corresponding Address: Department of Economics, Johannes Kepler University, Altenbergerstrasse 69, A4040 Linz, Austria eddy.bekkers@jku.at joseph.francois@jku.at miriammanchin@gmail.com

2 SKILLED FACTOR ABUNDANCE AND TRADED GOODS PRICES ABSTRACT: We develop a monopolistic competition model with nonhomothetic factor input bundles where larger quality goods require relatively more skilled workers. More skill abundant countries export higher quality, higher priced goods. This provides a theoretical underpinning for the empirical findings on the effect of skill abundance on unit values. We extend the core model with several variables from the literature on traded goods prices. The model features a novel mechanism through which trade liberalization affects the skill premium. Using a multicountry dataset on unit values we find a positive significant effect of exporter skill abundance on traded goods prices. Keywords: Traded goods prices, exporter skill abundance, nonhomothetic factor inputs, per unit trade costs, skill premium JEL codes: F2, F4 Introduction In an important paper Schott 2004 found that US import prices within detailed product categories rise in the skill and capital abundance of the exporting country. result provides evidence for within-sector specialization. This The characteristics of goods vary within detailed product categories in a systematic way. More skill-abundant and capital-abundant countries export goods with higher unit values, purportedly goods of higher quality. There is no theoretical work on the effect of factor abundance on traded goods prices. Also, the empirical findings of Schott 2004 have not been tested with other datasets. The substantial literature on both firm level and sectoral traded goods prices has not focused on the effect of skill abundance of exporters, but on the effect of importer characteristics or distance. This paper tries to fill both these gaps by proposing a novel theoretical mechanism based on nonhomothetic factor input bundles and by evaluating the effect of factor abundance using a wider dataset on unit values with multiple importers and exporters. We incorporate nonhomothetic factor input bundles into a monopolistic competition model of trade that includes a role for per unit trade costs and importer and exporter gdp per capita. Manova and Zhang 202, Verhoogen 2008, Kugler and Verhoogen 202, Crozet, et al. 202, Martin 202, Görg, et al. 200, Bastos and Silva 200, Hallak and Sivadasan 200 are examples of studies with firm level prices. Hummels and Skiba 2004, Hummels and Lugovskyy 2009, Baldwin and Harrigan 20, Harrigan, et al. 20 and Bekkers, et al. 202 use average prices at various HS levels.

3 We propose a model of monopolistic competition with homogeneous firms in the spirit of Krugman 980, adding a role for quality. So, preferences are CES including a taste parameter as a measure for quality. We work with a variant of the Krugman model developed by Venables 994 with fixed export costs besides regular fixed costs. This implies separate free entry conditions for each destination market and the possibility that only a subset of firms export. There are two factor inputs, high skilled and low skilled labor, and factor input bundles are non-homothetic. Goods with a higher quality require relatively more skilled labor. Moreover, similar to Baldwin and Harrigan 20 and Feenstra and Romalis 202, the marginal cost parameter rises with quality. This setup gives a straightforward explanation for the relation between exporter skill abundance and traded goods prices in Schott In relatively skill abundant countries the relative wage of skilled workers is lower, implying a lower cost of producing high quality goods. This raises the incentive for firms to produce higher quality goods. And goods of higher quality display higher marginal costs raising the price. We extend the basic framework with three additional elements from the literature on traded goods prices. First, we add per unit trade costs to the model, besides the standard iceberg trade costs. This generates a Washington apples effect as in Hummels and Skiba 2004 and Feenstra and Romalis 202. Goods shipped at larger distance have a higher quality. Second, we define a quality elasticity of marginal costs with respect to quality as in Baldwin and Harrigan 20 and assume that this quality elasticity is a function of a country s productivity. As such, countries with a higher productivity and gdp per capita produce higher quality higher priced goods as in Flam and Helpman 987 and Hummels and Klenow Third, we include a taste for quality parameter on the demand side and following Hallak 2006 this parameter is a function of income per capita. This implies that richer countries demand higher quality goods. After defining equilibrium, we abstract first from the three additional features to derive the effect of relative skill abundance on quality and price analytically in the core model. We then solve the complete model numerically in a two country setting. The parameters are set such that the elasticities of the export price with respect to relative skill abundance and distance are equal to the empirical elasticities of unit values with respect to these variables. Simulations with the complete model show that relative skill abundance has a positive effect on traded goods prices and this finding is robust to a wide variation in the parameters. Model simulations also uncover that the combination of per unit trade costs and a link between quality and skill intensity of production generates an intuitive relationship between trade costs and the skill premium. A reduction in ad 2

4 valorem relative to per unit trade costs enforces the Washington apples effect, raises the quality of exporter s goods and therefore also the demand for skilled workers. This mechanism also implies that tariff liberalization leading to a reduction in ad valorem trade costs will raise the skill premium. Simulations with the model show that the effect is modest: a % reduction in the ratio of ad valorem to per unit trade costs raises the skill premium by about 0.05%. For the empirics we employ a large, multi-country dataset with product level HS6 unit values for the period The empirics confirm the main prediction of our model and the findings in Schott A larger relative skill abundance of the exporting country leads to higher traded goods prices. Based upon our model we also examine the effect of distance and exporter gdp per capita on unit values. We include an importerproduct-time fixed effect to capture the role of importer gdp per capita and variation in the definition of unit values across products. With this fixed effect we can also account for other relevant demand side variables not present in our theoretical model like market size and income inequality. The coefficients on distance and exporter gdp per capita have the expected positive signs. We estimate the same model including nonlinear terms. The results confirm the findings of the log linear model: coefficients have the same size and marginal effects are close to the linear specification. Most theoretical work explaining traded goods prices focuses on demand side characteristics 2, on distance 3 or on firm characteristics. 4 Early work by Falvey 98 is related to our paper. He sets up a specific factors model with mobile labor and sector specific capital and the possibility of quality differentiation. The production of each good requires a fixed amount of labor and an amount of capital rising in the quality of the good. The prediction is that a country with more capital specific to a sector will produce higher quality goods in that sector. Hence, the work by Falvey 98 also relates the quality of goods to factor abundance with a nonhomothetic production function. Our model setup is different in at least three aspects. First, we work with a monopolistic competition model with firms paying fixed costs and using markup pricing, whereas Falvey 98 works with perfect competition. These imperfect competition features seem more realistic to describe the production of quality differentiated goods. Second, in our model quality is set endogenously by firms as a function of relative factor abundance, whereas in Falvey 98 perfectly competitive firms produce a given range of goods of different quality. 2 See for example Flam and Helpman 987, Hallak 2006, Hsieh and Klenow 2007, Hummels and Lugovskyy 2009, Simonovska 200, Alessandria and Kaboski 20 and Bekkers, et al See among others Hummels and Skiba 2004, Baldwin and Harrigan See among others Verhoogen 2008, Kugler and Verhoogen 202, Hallak and Sivadasan 200 3

5 Third, in our model the amount of both high skilled and low skilled labor varies with quality, whereas in Falvey 98 it varies only with capital. More recent related work is Verhoogen 2008 and Kugler and Verhoogen 202. In Verhoogen 2008 heterogeneous firms produce goods of different quality for different destination markets because of a different taste for quality across markets with richer countries having a larger taste for quality. Higher quality goods require relatively more skilled workers, implying that an increased incentive to sell in high income markets raises the relative demand for skilled workers. The increased incentive studied in Verhoogen 2008 is a peso devaluation in Mexico. So, although the model by Verhoogen 2008 features rising demand for skilled workers when higher quality goods are produced like in our model, it does not explore the effect of a country s skill abundance on traded goods prices. Kugler and Verhoogen 202 focus on traded goods prices showing both theoretically and empirically that larger firms sell higher priced goods and use higher priced intermediate inputs. They explain this pattern with the quality complementarity hypothesis: plant productivity and input quality are complementary leading to a higher quality of outputs. Our model instead relates output quality to the demand for skilled relative to unskilled workers instead of differential demand for intermediate inputs. 5 Flam and Helpman 987 and Hummels and Klenow 2005 also model between country differences in the incentive to produce and export goods of different quality. Differences in the ability to produce quality stem from absolute productivity differences between countries, but are not related to factor abundance. The work by Feenstra and Romalis 202 is also related to our paper. These scholars set up a firm heterogeneity model of quality differentiation with per unit trade costs and a demand for quality varying with importer income per capita. Factor abundance on the supply side does not play a role in their model like in our model. Still, many of the parameters estimated in Feenstra and Romalis 202 are identical to parameters in our model and in a robustness check we solve our model with the parameter values from Feenstra and Romalis 202. The size of the elasticities change, but the signs do not. The next section outlines the theoretical model. Section 3 contains the empirical analysis and in section 4 we use the estimated coefficients to calibrate the theoretical model and run simulations. Section 5 concludes. 5 Bekkers 203 proposes a different mechanism to explain the effect of skill abundance on quality and traded goods prices. In a firm heterogeneity model, firms can raise the quality of their goods by investing more in innovation. With factor input bundles in innovation being relatively skill intensive, more skill abundant countries produce higher quality, higher priced goods. 4

6 2 Theoretical Model The modelling setup follows Venables 994, adding endogenous quality, nonhomothetic factor cost bundles and per unit trade costs. We model an economy with two countries indexed by k, l = H, F, R sectors and two factors of production, skilled workers S and unskilled workers U. All workers in the two countries have identical preferences with Cobb Douglas preferences across sectors. We concentrate on one of the sectors and omit a sector subscript. 2. Demand Demand for goods in one of the sectors in country k, Q k, consists of a CES composite of domestic varieties Q kk and foreign varieties Q lk with substitution elasticity ε. Preferences for both domestic and foreign varieties are a CES function over a continuum of varieties ω Ω kk and ω Ω lk with substitution elasticity : 6 Q ε ε kk Q k = Q lk = + Q ε ε ε ε lk α ω ξk q ω dω 2 ω Ω lk q ω and α ω are respectively the quantity and quality of variety ω. ξ k measures the importance of quality for consumers in country k and following Hallak 2006 it is a function of income per capita in country k, i k, according to the following function: ξ k = ξ + µ ln i k 3 Variables with a subscript lk represent flows from country l to country k. Demand for variety ω by all consumers in country k imported from country l is given by: q lk ω = α lk ω ξ k p lk ω P ε lk P ε k I k 4 6 As explained by Venables 994 this setup with an upper Armington nest together with destination specific fixed costs makes it possible that only a subset of firms exports. Without the Armington nest, the four free entry conditions two for each country following from destination specific fixed costs would not be independent and thus not allow for both trading and non-trading firms. 5

7 The price index P k and P lk are defined as: P k = P ε kk P lk = ω Ω lk + P ε ε lk 5 α ω ξk p ω dω I k is total income in country k and the sum of skilled and unskilled labor s income: 6 I k = w ks S k + w ku U k 7 w ks and w ku are respectively the wages of skilled and unskilled workers and S k and U k the number of effective skilled and unskilled workers and are a function of productivity in country k. The effective number of high skilled and low skilled workers, respectively S k and Ũk, are defined as follows with ϕ k a productivity shifter: Income per capita can be defined as: S k = ϕ k Sk 8 U k = ϕ k Ũ k Supply We now turn to the supply side. Like in Krugman i k = w kss k + w ku U k S k + U k firms are identical and can produce with an identical increasing returns technology with a marginal cost a and a fixed cost f. Following Venables 994 firms have to pay market specific fixed costs. 7 So, a firm from country k pays domestic fixed costs to sell in its home market, f kk and additional exporting fixed costs f kl to sell abroad. We can interpret the fixed costs as beachhead costs to enter a market. To export goods firms pay iceberg trade costs τ kl and per unit trade costs t kl. 8 The presence of per unit trade costs reflects the Washington apples effect meaning that exported goods are of higher quality discovered by Alchian and Allen 964 and explored in a trade setting by Hummels and Skiba Marginal costs for sales to a specific destination domestic and exporting are a func- 7 Also Jean 2002 and Melitz 2003 work with fixed export costs. 8 Domestic sales do not face trade costs, so τ kk is equal to and t kk = 0. 6

8 tion of the quality of the sold good in the destination with an elasticity /φ k. φ k is called the quality elasticity in Baldwin and Harrigan 20 and it is a measure for the ability of country k to produce high quality goods. 9 We postulate that more productive workers have a higher ability of producing high quality goods implying that φ k is a function of the productivity parameter ϕ k : by: φ k = ϕ ν k With these ingredients, the total cost function C k of a firm from country k is given C k α kk, α kl, w ks, w ku = l=h,f ϕ α ν k CB αkl, w ks, w ku kl τ kl + t kl q kl + f kl 2 ϕ k CB α kl, w ks, w ku is the cost of input bundles used in production and fixed costs. The cost of input bundles is nonhomothetic and a function of the quality of the good produced in k and sold in destination l, α kl, with higher quality goods requiring relatively more high skilled workers. We use a nonhomothetic CES cost function see for discussion Shimomura 999: 0 CB kl = CB α kl, w ks, w ku = γ α kl w θ ks + γ α kl w θ θ ku 3 γ α kl is the CES-weight in the cost function dependent on quality α kl. So, with our specification costs depend on quality through marginal costs and through the non-homotheticity in skilled and unskilled labor. We work with the following explicit function for γ α kl : γ α kl = α η kl ; η > 0 4 θ is the substitution elasticity between skilled and unskilled labor in the cost of input bundles in 3 not taking into account endogenous quality changes. Each firm produces a unique variety and sets cif the price in the two markets according to the following markup equation: p kl = ϕ ν k CBkl αkl a kl τ kl + t kl 5 ϕ k 9 To be precise, the quality elasticity as defined in Baldwin and Harrigan 20 is equal to φ in our model. 0 The production function corresponding to the cost function CB in equation 3 is given by Y α km, U k, S k = γ α km θ S θ θ k + γ α km θ U θ θ θ θ k. 7

9 Using the pricing rule in equation 5, profit of a firm from country k can be expressed as: π k = l=h,f α ξ l kl [ ϕ ν k CBkl αkl a k τ kl + t kl ϕ k ] P ε kl Pl εi l l=h,f f kl CB kl 6 Taking the first order condition of profit in equation 6 with respect to quality leads to: 0 = p klq kl f kl θ ξ l α kl ηα η kl ϕ ν k ϕ ν k ϕ ν k kl α a k τ kl αkl a k τ kl + t kl w θ ku CB θ kl w θ ks θ ηα η kl w θ ku CB θ kl w θ ks The domestic and exporting market can be seen as separate markets, because there are fixed exporting costs besides regular fixed costs. Entering the domestic market and paying the domestic beachhead cost does not imply that a firm can also export as in Krugman 980. This implies that there are two separate zero profit conditions, one for the domestic market and one for the exporting market: 7 p kl q kl = f kl CB kl 8 Combining the zero profit conditions in equations 8 with the first order conditions in equation 7 leads to: p kl q kl ϕ ν k ξ l α ϕ ν kl a k τ kl k α kl ϕ α ν k kl a k τ kl + t kl θ ηα η kl w θ ku CB θ kl w θ ks = 0 9 The first term between brackets in equation 9 represents the marginal benefit of higher quality as a result of larger sales. The second term represents the direct marginal cost of higher quality and the third term represents the marginal cost of higher quality due to a larger required use of the more expensive skilled labor. The balance of the three terms determines the optimal level of quality. Venables 994 works with one free entry condition for firms selling only in the domestic market and one free entry condition for firms selling in both markets. This is equivalent to our approach with a free entry condition for each market. 8

10 2.3 Equilibrium To define equilibrium in the model, we add the labor market equilibrium conditions for skilled and unskilled workers. Applying Shephard s lemma to the cost function in equation 2 and using the FE in equation 8 gives: S k = U k = l=h,f l=h,f N kl f kl CB θ kl N kl f kl CB θ kl γ α kl w θ ks 20 ϕ k γ α kl w θ ku 2 ϕ k To complete equilibrium characterization, we need to determine the number of domestic and exporting firms in each country, respectively N kk and N kl, for which we use two equations. First, total costs are equal to total factor payments: Second, following Venables l=h,f N kl f kl CB kl ϕ k = w ku U k + w ks S k we combine the free entry condition, the expression for the price index and the markup pricing rule to express the share of exporting firms as follows: Nkk N lk ε f ξ k ε lk αlk = f kk α kk We can now define equilibrium as follows: ϕ α ν l lk a lτ lk + t lk ϕ α ν k kk a kτ kk + t kk CB kl ϕ l CB kl ϕ k ε 23 Definition Equilibrium in the model is defined by a tuple of vectors in both countries k = H, F {α kk, α kl, CB kk, CB kl, w ku, w ks, N kk, N kl, ξ k, i k } and is determined by the following equations in both countries k = H, F :. The FOC for quality in equation 7 to each destination market l 2. The expression for the cost of input bundles in equation 3 to each destination market l 3. Labor market equilibrium for skilled and unskilled workers in equations 20 and 2 9

11 4. The income identity in equation The expression for the share of exporting firms in equation The expression for the quality elasticity with respect to income per capita in equation 3 7. The expression for income per capita in equation The Effect of Skill Abundance In section 4 we solve the model numerically to explore the effect of changes in per unit relative to ad valorem trade costs, gdp per capita and skill abundance on the export price. In this subsection we derive the effect of skill abundance on the export price analytically abstracting from a role for per unit trade costs and gdp per capita in the determination of quality. In particular, we set per unit trade costs t kl at 0, the quality elasticity with respect to income per capita in utility, ξ k, at and the quality elasticity in production, φ k, also at. With these assumptions we can rewrite the FOC for quality α kl in equation 9 as follows: α kl θ ηα η kl w θ ku CB θ kl w θ ks = 0 24 Using the expression for CB kl in equation 3, equation can be rewritten to express the relative wage w ks w ku as a function of quality α kl : wku w ks θ = θ + η αη kl θ θ + η α η kl 25 We can divide the labor market conditions in equations 20-2, using the free entry conditions, α kl q kl +f kl = f kl, and the fact that quality α kl does not vary with destination market without per unit trade costs and a role for exporter and importer gdp per capita, leads to the following expression: S k U k = αη kl α η kl wku w ks θ 26 0

12 Substituting equation 25 into 26 shows that quality α kl is directly related to relative skill abundance S k /U k : S k U k = αη kl α η kl [ θ + η α η kl θ + η α η kl θ ] θ θ 27 and α kl generates the following ex- Log differentiating equation 27 with respect to S k U k pression: Ŝ k U k = η α η α kl + kl θη θ + η α η kl θ α kl 28 Variables with a hat indicate relative changes. Equation 28 implies that the RHS of 27 rises monotonically. 2 Also, it can be easily shown that the RHS of equation 27 rises from 0 to for γ α kl = α η kl [0, ]. So, there is a unique positive equilibrium for α kl and α kl rises monotonically in relative skill abundance S k U k We can easily determine the effect of relative skill abundance on the export price. From equation 5 the export price p kl is determined by the level of quality α kl and the cost of input bundles CB kl. Log differentiating equation 5 gives: p kl = α kl + ĈB kl 29 We start with the effect of relative skill abundance on the export price through the second term CB kl by log differentiating the expression for the cost of input bundles in equation 3 with respect to γ α kl and the relative wage w ks w ku : 3 ĈB = γ α kl γ α kl w ks + γ α kl θ γ α kl w ks w ku θ ŵ ks w ku θ w ku + γ αkl θ w ks w ku w ks w ku θ + γ αkl γ α kl 30 2 Given that w ku w ks in equation 25 is positive the denominator of the second term on the RHS of equation 28 will be positive. 3 We keep the unskilled wage w ku constant, reflecting that we could choose this price as numeraire.

13 We can express w ks w ku as a function of γ α kl by log differentiating equation 25: γ α kl = θ w ks w ku θ w ks w ku θ ŵ ks w ku 3 Substituting the log differentiation in 3 into equation 30 makes immediately clear that ĈB kl = 0. So, the relative change of unit wage costs as a result of a change in the relative wage w ks w ku is zero when taking into account the endogenous reaction in quality. The direct effect of a larger relative skilled wage w ks w ku exactly cancels out against the effect of the reduction in quality γ α kl induced by a larger relative skilled wage. So, the costs of input bundles does not vary with relative wages. Hence, the effect of relative skill abundance on the export price is determined by the first term in equation 29. From equation 28 we know that γ α kl rises in relative skill abundance S k U k. Therefore, we have the following result: Result In the model without per unit trade costs and ξ k = φ k =, export goods from relatively more skill abundant countries have a larger quality and a higher price. The model presented in this section contains a link between skill abundance, quality and market price. In a more skill abundant country, the relative wage of skilled workers is lower. Therefore, the marginal cost of producing higher quality goods falls. As a result firms will offer higher quality goods. The relations are consistent with the empirical findings by Schott A larger relative skill abundance in an exporting country leads to a higher export quality and a higher export price. In section 4 we will explore the effect of skill abundance numerically in the full model with per unit trade costs and a role for gdp per capita on the importer and exporter side. Before turning to the numerics we use a multicountry dataset in the next section to estimate the effect of exporter skill abundance, distance and exporter gdp per capita on traded goods prices. The estimated elasticities are used to calibrate the numerical model. 3 Empirics We now turn to an empirical analysis of the impact of skill abundance on unit values. Based upon Result we explore the effect of skill abundance on traded goods prices of countries. Anticipating the simulation results of the complete model we also include 2

14 exporter income per capita and distance between trading partners in the estimating equations. Also importer income per capita plays a role in the complete model. We control for this variable and other variables reflecting demand side effects like importer market size and importer income inequality by including importer-time-product fixed effects. The product specific fixed effects also serve to account for differences in measurement of unit values across products. Finally, we explore the interaction effect of the product substitution elasticity with exporter skill abundance. 3. Data We proxy traded goods prices with unit values. The data used for unit values come from the BACI database 4 which contains quantity and the value of bilateral imports in 6-digit Harmonized System HS classification. The database is constructed from COMTRADE Commodities Trade Statistics database. We use data for the period between BACI takes advantage of the double information on each trade flow to fill out the matrix of bilateral world trade providing a reconciled value for each flow reported at least by one of the partners. Therefore the missing values in BACI are those concerning trade between non reporting countries. The skill abundance and income per capita data originate from the World Bank s World Development Indicator database. We use GDP per capita as a measure of income per capita. We define skilled labor as workers with tertiary or secondary education, while unskilled labor as having only primary education. Also Schott definition. Data on distance are taken from Clair et al works with this The distance data are calculated following the great circle formula, which uses latitudes and longitudes of the relevant capital cities. Measures for the product substitution elasticity are taken from Broda, et al. 2006, who estimate the substitution elasticities for 73 countries at the HS6 level. 6 found in 5. The list of countries used in the regressions based upon data availability can be The data can be downloaded from dew35/tradeelasticities/tradeelasticities.html 3

15 3.2 Estimating Equations First, we estimate the effect of our explanatory variables in a linear specification: S ln UV klmt = β ln + β 2 ln GDP pc kt + β 3 ln distance kl + ϖ lmt + ε klmt 32 U kt UV klmt indicates unit values of trade from country k to country l in sector m in period t, as a measure for export price p kx. L s L u kt is the relative skill abundance in country k in period t, GDP pc kt is GDP per capita in country k in period t. distance kl is distance between the trading countries. ϖ lmt is the importer-time-sector fixed effect and ε klmt is the error term. To check for nonlinearities we also estimate a second equation including the squares and interaction terms of the explanatory variables: 2 S S ln UV klmt = β ln + β 2 ln GDP pc kt + β 3 ln distance kl + γ ln U kt U kt + γ 2 ln GDP kt 2 + γ 3 ln GDP pc kt 2 + γ 4 ln distance kl 2 + ϖ lmt + ε klmt 33 Finally, we estimate the linear model including interaction terms of skill abundance ln S with measures for the product substitution elasticity per sector and per country U kt in the linear specification. 7 We cannot include the measure itself as we have sectoral fixed effects: S ln UV klmt = β ln U S + δ ln U kt + β 2 ln GDP pc kt + β 3 ln dist kl ln lm + ϖ lmt + ε klmt 34 kt The product substitution elasticity data are country and sector specific. We interact relative skill abundance in exporter country k with the substitution elasticity in importer country l. 7 We also explored the interaction effect with in the nonlinear model and effects were very similar. Results are available upon request. 4

16 3.3 Estimation Results Table presents the results of the three proposed estimating equations. The results confirm the prediction of the theoretical model in Result that higher exporter skill abundance leads to higher export prices. They are also in line with the empirical results of Schott 2004 who found a positive effect of exporter skill abundance on unit values with US importer data. Similar to Schott 2004 we find that GDP per capita of the exporter country has a positive effect on export unit values. The coefficients on GDP per capita are between 0.9 and 0.23, implying that a 0% increase in exporter GDP per capita is associated with an increase in traded goods prices between.9% 2.3%. Our coefficient is somewhat higher than the coefficient in Schott 2004, probably driven by the fact that we have multiple importers. Furthermore, we find that prices increase with distance supporting the Alchian-Allen effect in Hummels and Skiba All quadratic and interaction terms are significant, implying that effects are indeed nonlinear. Nevertheless the marginal effects presented in the third column are very close to the coefficients of the linear specification. The coefficient of the interaction of skill abundance with the product market substitution elasticity column 4 is negative and non-significant. This is in line with the modeling predictions following from the simulations, which displayed a negative but very small effect of on the impact of skill abundance on traded goods prices. 4 Numerical Analysis of the Theoretical Model In this section we numerically solve the 2 country model as defined in Definition to evaluate the robustness of Result on the effect of skill abundance in the complete model and to explore the effect of distance and exporter and importer income per capita. 8 In particular, our goal is to set the parameter values of the model such that the elasticities of the export price with respect to the explanatory variables are identical to the estimated elasticities of the previous section. Like for example in the study of comparative advantage and firm heterogeneity by Bernard, et al. 2007, our aim is not to calibrate the model to multiple country real world data. We motivate the baseline values of the parameters from the literature and from the empirics and set core parameters in our model such that elasticities of the export price with respect to distance and factor abundance are identical to our own empirical estimates. At the end of the section we show that a reduction of ad 8 The GAMS code of the numerical model is available upon request. 5

17 Table : Effect of relative skill abundance, control variables and interactions with substitution elasticities on unit values Dependent variable: ln UV klmt eq 32 eq 33 eq 33 eq 34 marginal effects ln S/U *** 0.59*** *** *** ln GDP pc 0.90*** -0.42*** 0.243*** 0.90*** ln distance 0.932*** 0.79*** 0.90*** 0.932*** ln S/U *** ln GDP pc *** ln distance *** 0.05 ln S/U ln GDP pc *** ln S/U ln distance *** ln GDP pc ln distance 0.84*** ln S/U ln -6.37e e-06 constant *** 0.622*** *** Observations 6,422,493 6,422,493 6,422,493 6,422,493 R-squared Robust standard errors in parentheses *** p<0.0, ** p<0.05, * p<0. Importer-product-time fixed effects are included. 6

18 valorem relative to per unit trade costs leads to an increase in the skill premium. Since tariff liberalization reduces ad valorem relative to per unit trade costs this implies a new mechanism for increasing income inequality as a result of tariff liberalization. We check robustness of the modelling predictions and present two types of robustness checks. The first takes parameter values from Feenstra and Romalis 202 and the second varies the different parameter values one at a time. We evaluate how variations in the parameter values change the elasticities of the export price with respect to skill abundance, distance and exporter gdp per capita and in particular whether these elasticities keep the same sign. We also check the robustness of the effect of a reduction in ad valorem relative to per unit trade costs on the skill premium. Without loss of generality we work with a baseline where the two countries are identical. The model is a monopolistic competition model with two sectors given the Armington specification with domestic and foreign varieties. From Francois and Nelson 2002 we know that a monopolistic competition model with multiple sectors and multiple factors of production generates multiple equilibria. Therefore, we decided to concentrate on the symmetric equilibrium as baseline. When exploring the effect of exporter gdp per capita we will deviate from the symmetric equilibrium. In the simulations we concentrate on the fob price, as our traded goods price data are also using fob prices. The fob price can be expressed as a function of the cif price as follows: 4. Calibration p fob HF = pcif HF t HF 35 τ HF Table 2 displays the used baseline values of the parameters, their description and their source. The Armington substitution elasticity ε and the substitution elasticity between varieties are taken from Feenstra, et al. 202 who come to estimates for the substitution elasticity between domestic and foreign varieties the macro elasticity around and for the substitution elasticity between varieties from different countries the micro elasticity equal to 3.. The substitution elasticity between factor inputs not taking into account quality changes is set at.2, corresponding with the median value across sectors in Hertel, et al µ is taken from Hallak 2006 who estimates a value of 9 The substitution elasticity accounting for quality adjustment is larger than θ. The reason is that an increase in the relative wage of skilled workers reduces the relative demand for skilled workers both directly and indirectly through a reduction in quality and thus a reduction in the shift parameter on 7

19 Table 2: Baseline Values of Parameters Parameter Value Description Source ε. Armington substitution elasticity on product market Feenstra, et al Substitution elasticity between varieties on product market Feenstra, et al. 202 θ.2 Substitution elasticity between skilled and unskilled labor Hertel, et al. 202 ξ Base value of taste for quality parameter Hallak 2006 µ 0.27 Elasticity of taste for quality parameter with respect to income/capita Hallak 2006 f kk Fixed costs of production Bernard, et al f kl Exporting fixed costs Bernard, et al S k U k. Relative skill abundance WDI U k 75 Number of unskilled workers WDI ϕ k 0.82 Productivity WDI d kl 8.77 Distance between countries Clair et al 2004 δ 0.38 Elasticity of ad valorem trade costs Anderson and with respect to distance Van Wincoop 2003 η 2.05 Elasticity of skilled factor intensity with respect to quality Simulations ν 0. Elasticity of quality productivity with respect to productivity Simulations κ.42 Elasticity of per unit trade costs with respect to distance Simulations t 0.05 Per unit relative to ad valorem trade cost shifter Simulations 8

20 = ξ is set at as in Feenstra and Romalis 202 who work with the Hallak-specification in the expenditure function. 20 The fixed trade costs f are set at. Bernard, et al work with an equally arbitrary value of 0. in their simulations, motivating this value with the fact that 0. is 5% of their value for sunk entry costs. Given that we do not have sunk entry costs, we can choose a value of for fixed costs without loss of generality. Following Bernard, et al exporter fixed costs are set equal to domestic fixed costs, so that without per unit and ad valorem trade costs selling at home and abroad would be equally attractive. For the relative skill abundance S we U use the share of college to noncollege graduates in the US in our dataset. The number of unskilled workers U is set equal to the number of noncollege graduates in the US in our dataset. Productivity ϕ k is determined by the average of GDP per capita in the US in our dataset, which is 37 in thousands of dollars. This leads to a ϕ k in the baseline of To fix the skill intensity of prodution and therefore also quality in the baseline, we use a skill premium of.6 log wage skill premium of college to noncollege workers of 0.47 from Acemoglu 2003 implying a skill premium of.6. Both ad valorem and per unit trade costs are written as a function of distance as in the gravity literature: τ kl = d δ kl; t kl = td δ+κ kl 36 For δ, the elasticity of ad valorem trade costs with respect to distance, we use the value for the elasticity of trade flows with respect to distance estimated in Anderson and Van Wincoop They find a value of 0.8 for this elasticity implying a δ of 0.38 given that the elasticity of trade with respect to distance is equal to δ and is set equal to 3. in our model. t is a shift parameter shifting the size of per unit relative to ad valorem trade costs in exporting relative to domestic sales and thus shifting the quality and price premium of exported goods relative to domestic goods. t kl τ kl / t kk τ kk = td κ kl The trade cost shift parameter t is set at This shift parameter determines the difference between domestic and exporting quality and setting it at 0.05 the skilled labor shift parameter γ α kl stays below. Reflecting the Washington apples effect per unit trade relative to ad valorem trade costs rise with distance and thus we expect a positive skilled labor. We calculated the quality adjusted substitution elasticity in our baseline and found a value of Hallak 2006 does not report a value for ξ, since it drops out of his estimating equation. 9

21 value of κ. The determination of κ and t will be discussed below. Distance between countries d kl is from Clair et al 2004 and we set it equal to the average distance between countries in our dataset. This leads to a value of d kl of 8.77 in thousands of kilometres. 2 Next, we come to the determination of the three remaining parameters η, ν and κ. We try to choose values for these parameters such that the elasticities of export price with respect to distance, skill abundance and exporter gdp per capita are equal to the values in our estimations with the other parameters at their baseline values. Setting η, ν and κ equal to respectively 2.05,.42 and 0. we get elasticities of the export price with respect to distance, factor abundance and exporter gdp per capita of respectively 0.9, 0.5 and.00. Therefore, we manage to get the same elasticities as in the empirics for distance and skill abundance. For exporter gdp per capita our elasticity is much larger. We explored a wide range of parameter values to generate lower values for the elasticity with respect to exporter gdp per capita, but this elasticity is very robust and always stays around. 4.2 Simulations with Baseline In this subsection we present simulation results with the baseline parameter values. 22 Figure displays the fob export price as a function of distance and relative skill abundance in the baseline. We see that both variables have a positive effect on the export price and although not visible from the figure the elasticities are equal to the elasticities in the empirics. Exploring the simulation results also leads to the insight that the interaction effect between distance and skill abundance is negative. So, the effect of distance on the export price falls when skill abundance is larger. This is in line with the negative interaction term in the empirics. The left panel of figure 2 shows the fob export price as a function of exporter gdp per capita. The relation is positive and the elasticity is not different from and thus larger than what our empirical estimates indicate. We cannot study interaction effects for this variable with distance and skill abundance, because variations in gdp per capita go along with endogeneity of the productivity parameter ϕ, whereas in the simulations with distance and skill abundance ϕ is fixed. In the right panel of figure 2 we expose the effect of variation in importer gdp per capita on the fob export price indicating a positive effect. This is what we would expect since the importance of quality in the utility function is a function of income per capita in the model. We accounted for this effect in the empirics 2 Domestic ad valorem and per unit trade costs are set equal to and 0, respectively. 22 In all the simulations we checked the SOC defined in Appendix A to be sure that it is satisfied. 20

22 Traded Goods Price Traded Goods Price Traded Goods Price Traded Goods Price, Skill Abundance and Distance Figure : Traded goods price as a function of distance and skill abundance in baseline calibration with an importer fixed effect and can thus not compare the simulated elasticity with an estimated elasticity. Traded Goods Price and Exporter Income per Capita Traded Goods Price and Importer Income per Capita Exporter Income per Capita Importer Income per Capita Figure 2: Traded goods price as a function of exporter and importer income per capita in baseline calibration 4.3 Effect of Tariff Liberalization on Skill Premium In this subsection we study the effect of a change in the ratio of ad valorem to per unit trade costs on the skill premium. A reduction in the ratio of ad valorem to per unit trade costs makes the Washington apples effect stronger. Therefore, firms will raise the quality of exported goods. As a result the demand for skilled labor will rise and therefore the 2

23 Skill Premium ws/wu skill premium. In figure 3 we display the wage ratio of skilled to unskilled workers as a function of the ratio of ad valorem to per unit trade costs, starting from the level of this ratio in the baseline. The skill premium rises as ad valorem trade costs fall relative to per unit trade costs. The elasticity is 0.06 for the baseline level of ad valorem to per unit trade costs, so a reduction in ad valorem relative to per unit trade costs of % raises the skill premium by 0.06%. We can also explore the effect of tariff liberalization on the skill premium. We have to distinguish between tariffs applied on fob prices and tariffs applied on cif prices. The left panel of figure 4 shows the effect of tariff liberalization from a 00% tariff to a 0% tariff with the baseline corresponding with a 00% tariff when tariffs are applied on fob prices. The skill premium rises with tariff liberalization with an elasticity varying between 0.03 and less than The right panel of figure 4 shows the effect of tariff liberalization on the skill premium when tariffs are applied on the cif price. The skill premium also rises in this case with tariff liberalization but the elasticity is much smaller and a factor 0 smaller Skill Premium and Ad Valorem Relative to Per Unit Trade Costs Ad Valorem Relative to Per Unit Trade Costs Figure 3: The skill premium as a function of ad valorem relative to per unit trade costs, τ/t The reason for the difference between tariffs applied on fob and cif prices can be seen 23 The elasticity becomes smaller as the tariff tar declines, because the ad valorem trade costs τ are equal to τ = + tar τ with τ the non-tariff part of ad valorem trade costs. So, the elasticity of τ with respect to tar falls with the level of the tariff, τ = tar tar +tar 22

24 Skill Premium ws/wu Skill Premium ws/wu Skill Premium and Fob-Applied Tariff Rate Fob-Applied Tariff Rate Skill Premium and Cif-Applied Tariff Rate Cif-Applied Tariff Rate Figure 4: The skill premium as a function of the fob-applied tariff rate and the cif-applied tariff rate by rewriting equation 35 for the relation between cif and fob prices in the case of cif applied tariffs and fob applied tariffs: cif-applied tariffs: p cif = + tar p fob τ + t 37 fob-applied fariffs: p cif = p fob + tar τ + t 38 tar is the applied tariff rate. With cif-applied tariffs per unit and ad valorem trade costs are affected equally by tariff liberalization. The only equation affected in the equilibrium equations in Definition is equation 23. The only effect of tariff liberalization is to raise the share of exported varieties. Given that exported goods have a higher quality this composition effect will raise demand for skilled labor and thus the skill premium. But this effect is small in our model. With tariffs applied on the fob price there is a second effect: ad valorem trade cost fall relative to per unit trade costs, as is clear from equation 38. So, there is still a composition effect of tariff liberalization towards exported goods thus implying a higher demand for skilled labor, but there is also a direct effect with fob-applied tariffs through the FOC in equation 7. Firms raise the quality of the exported goods when ad valorem trade costs fall relative to per unit trade costs. 4.4 Robustness Checks In this subsection we discuss the two robustness checks. We start with the Feenstra and Romalis 202 parameter values. Parameters on which Feenstra and Romalis 202 does not contain information are kept at the value of the baseline simulation. Table 3 displays the changed parameter values relative to our baseline in the calibration to 23

25 Table 3: Baseline Values of Parameters Parameter Value Description 6.39 Substitution elasticity betwee varieties on product market µ 0.02 Elasticity of taste for quality parameter wrt income per capita δ 0 Elasticity of ad valorem trade costs wrt distance κ 0.5 Elasticity of per unit trade costs wrt distance Feenstra and Romalis 202. They estimate a of 6.39, a µ of 0.02 and a κ of Ad valorem trade costs τ are not a function of distance, so δ is equal to 0. Since factor abundance plays no role in Feenstra and Romalis 202, there is no estimate of η and we keep it at the baseline level. φ, the quality elasticity, is an estimated parameter in Feenstra and Romalis 202, whereas in our model it is a function of productivity ϕ. Working with the discussed parameter values from Feenstra and Romalis 202, we get a φ equal.93. Feenstra and Romalis 202 estimate a φ equal to Varying other parameters like ν we can get a φ close to 0.63, but this would lead to violation of our second order conditions and therefore we keep the other parameters at their baseline value. 26 Figures 5 displays the effect of distance and skill abundance and exporter and importer gdp per capita on the traded goods price. A larger distance and skill abundance both still raise traded goods prices, but the effect of distance is much smaller, as is clearly visible from figure 5. This is reflected in the elasticity of the traded goods price with respect to distance. we find that an elasticity of 0.04, which is much smaller than in our baseline and in our empirics. The elasticity with respect to skill abundance is somewhat larger than in the baseline and the empirics and equal to The much lower elasticity with respect to distance is driven by a much lower value for κ, the elasticity of per unit relative to ad valorem trade costs with respect to distance. The effect of gdp per capita is almost identical to effect in the baseline calibration. The elasticity with respect to exporter gdp per capita is still equal to. So, we omitted the figure on the effect of gdp per capita and it is available upon request. Finally, we check the robustness on the effect of ad valorem 24 Feenstra and Romalis 202 specify the relation between cif and fob prices as p cif = τ p fob + T with τ ad valorem and T per unit trade costs. τ is not a function of distance in their model and they write T as a function of distance with the function T = δd β. Given that T is equal to t/τ with t our measure for per unit trade costs, we have from equation 36 that our κ and t are equal to respectively β and δ in Feenstra and Romalis 202. Estimates of δ are not reported in Feenstra and Romalis 202, so we keep t at our baseline value. 25 Our φ corresponds with the symbol θ in Feenstra and Romalis In Feenstra and Romalis 202 φ has to be smaller than to satisfy the SOC. Our model is different and contains an effect of quality on skill intensity, implying a different SOC. 24

26 Traded Goods Price relative to per unit trade costs on the skill premium. The elasticity of the skill premium with respect to the ratio of ad valorem to per unit trade costs is 0.05 at the baseline level of trade costs. Traded Goods Price, Skill Abundance and Distance Figure 5: Traded goods price as a function of distance and skill abundance in the Feenstra and Romalis 202 calibration In the second robustness check we vary the values of the parameters ε,, θ, µ, f kl, f kl /f kk, U k, ϕ, δ, η, ν and κ one at a time. Table 4 shows how the elasticity of the traded goods price with respect to skill abundance, distance and exporter gdp per capita varies with the parameter values. The second column shows the minimum and maximum value of the different parameters in the robustness check and for comparison the baseline value. The next three columns show the elasticities corresponding with the maximum and minimum parameter values. The last column shows the elasticity of the skill premium with respect to the ratio of ad valorem to per unit trade costs for the minimum and maximum parameter values. We can make the following six observations on the robustness exercises. First, signs of the three elasticities of the export price with respect to skill abundance, distance and exporter gdp per capita and of the elasticity of the skill premium with respect to the ad valorem to per unit trade cost ratio always stay the same. Second, the level of fixed cost f kl and market size U k have no impact on the elasticities. So, although the level of fixed costs was set somewhat arbitrary this has no impact on the model outcomes. Third, the parameters ε,, f kl /f kk, ϕ, δ, v have a relatively small effect on the elasticities. 25