Trade and Real Wages of the Rich and Poor: Cross-Country Evidence

Transcription

1 Trade and Real Wages of te Ric and Poor: Cross-Country Evidence Zeli He June 207 Abstract Trade liberalization a ects real-wage inequality troug two cannels: te distribution of nominal wages across workers and, if te ric and te poor consume di erent bundles of goods, te distribution of price indices across consumers. I provide a unified framework incorporating bot cannels by allowing for non-omotetic preferences and worker eterogeneity across obs. Because skill-intensive goods are also ig-income elastic in te data, I find an intuitive, previously unexplored, and strong interaction between te two cannels. I parametrize te model for 40 countries using sector-level trade and production data, and find tat trade cost reductions decrease te relative nominal wage of te poor and te relative price index for te poor in all countries. On net, real-wage inequality falls everywere. I would like to tank Donald Davis, Amit Kandelwal, Eric Veroogen, Jonatan Vogel and David Weinstein for teir invaluable advice and support. I also tank Mattieu Bellon, Pablo Fagelbaum, Reka Juasz, Ryan Kim, Antonio Miscio, Ildiko Magyari, Paul Piveteau, Stepen Redding, Lin Tian and oter seminar participants at Columbia University for elpful comments and discussions. All remaining errors are my own. Department of Economics, Columbia University, 022 International A airs Building, 420 West 8t Street, New York, NY z278@columbia.edu.

2 Introduction Trade liberalization may impact an individual s real wage troug er nominal wage and er consumer price index. Te cange in er nominal wage depends on canges in producer prices and te ob in wic se is employed, were te ob of er employment is determined by er caracteristics suc as age, gender and educational attainment. On te oter and, te cange in er consumer price index depends on canges in prices of te basket of goods tat se consumes, were er consumption basket is determined by er nominal wage in addition to prices. A vast maority of te literature focuses on te e ect of trade on te distribution of nominal wages. A small number of studies consider its di erential impact on consumer price indices. In tis paper, I provide a unified framework tat incorporates bot te expenditure cannel, i.e.,cangingconsumerpriceindices,and te income cannel, i.e., canging nominal wages, to measure te distributional e ects of trade in a large cross-section of countries. I build a model combining demand eterogeneity across consumers wit productivity eterogeneity across workers. On te demand side, I use te Almost Ideal Demand System (AIDS) to capture non-omotetic preferences. Tis demand specification allows te consumption baskets of ig-income and low-income individuals to di er so tat price canges resulting from trade liberalization ave a di erential impact on teir consumer price indices. On te supply side, I use an assignment model of te labor market parametrized wit a Frécet distribution to capture eterogeneity of workers across obs. Individuals ave comparative advantage across sectors based on teir age, gender and educational attainment and, terefore, sort into di erent sectors. Consequently, price canges resulting from trade liberalization ave a di erential impact on individuals nominal wages depending on te sectors in wic tey work. In addition, I also allow individuals to di er in teir absolute advantage suc tat labor groups di er in teir average productivity and, terefore, ave di erent nominal wages regardless of individuals sectoral coices. 2 Tis assumption generates a potential link between te skill distribution and te wage distribution and, as a result, a potential correlation between te cange in an individual s nominal wage and te cange in er consumer price index. In isolation, tese two cannels ave well-understood implications. Sutting down te expenditure cannel, I find tat te income cannel benefits te poor more tan te ric in low-income countries and te ric more tan te poor in ig-income countries. Tis I focus on labor earnings, wic are te main source of income for most people. 2 Workers in a labor group sare te same observable caracteristics suc as age, gender and educational attainment.

3 is consistent wit standard factor proportions teory in wic a reduction in trade costs raises te relative nominal wage of te abundant factor in every country, benefiting te unskilled (and poor) workers in skill-scarce countries tat are low income and te skilled (and ric) workers in skill-abundant countries tat are ig income. Sutting down te income cannel, I find tat te expenditure cannel benefits te poor more tan te ric in every country and more so in ig-income countries. Intuitively, lower trade costs increase real incomes and, terefore, decrease te relative demand for and te relative price of low-income elastic goods. Because low-income consumers spend more on tese goods, tey benefit relatively more. Te expenditure cannel benefits te poor relatively more in ig-income countries because tese countries are net importers of low-income elastic goods. Tese two cannels do not work in isolation. Studying eiter cannel in te absence of te oter leads to profoundly biased results qualitatively and quantitatively. Specifically, teir interaction implies tat te income cannel benefits te ric in every country, wic is consistent wit a large body of empirical evidence; see e.g. Goldberg and Pavcnik (2007). Intuitively, wen bot cannels are active, lower trade costs increase real incomes and, terefore, decrease te relative demand for and te relative price of low-income elastic goods as discussed above. 3 Since te poor disproportionately produce unskill-intensive goods, wic are low-income elastic, teir relative nominal wage falls in every country. Tis e ect is absent wen only te income cannel is active. Moreover, te interaction of tese two mecanisms also implies tat te poor s relative benefit from te expenditure cannel is magnified in every country. Intuitively, because nominal wage inequality rises in every country, as ust described, te relative demand for and te relative price of lowincome elastic goods fall even furter, reducing te relative price index for te poor in every country. Tis e ect is absent wen only te expenditure cannel is active because nominal wage inequality is constant in tat case. 4 3 Alternative models can also generate te increase in te skill premium, for example, a close-economy macroeconomic model were tere is a uniform increase in productivity wit non-omotetic preferences. Caron et al. (204) find tat it raises wages of skilled workers significantly, increasing te nominal wage inequality at equilibrium. In tis paper, I focus on te impact of a decrease in trade costs as an explanation. 4 Tere are oter types of gains from trade. For example, te access to more product varieties makes everyone better o. Fagelbaum and Kandelwal (206) find tat low-income consumers spend relatively more on sectors tat are more traded, were ig-income consumers spend relatively more on services, wic are among te least internationally traded sectors. As a result of trade liberalization, tere is a bigger increase in product varieties in te sectors tat ave a low income elasticity, wic benefits te poor even more. On te oter and, Faber and Fally (206) find tat canges in product varieties a ect te price indices of ric and poor ouseolds asymmetrically. More product entry benefits ricer ouseolds sligtly more due to iger estimated love of variety. Consequently, it becomes an empirical 2

4 Iparametrizetemodelforasampleof40countries(27Europeancountriesand3 oter large countries) and 35 sectors using a range of datasets including te World Input- Output Database (WIOD) and te Integrated Public Use Microdata Series, International (IPUMS-I). WIOD provides information on bilateral trade flows and production data. 5 I derive a sectoral non-omotetic gravity equation tat allows me to estimate te elasticity of substitution and te income elasticity of goods as follows. 6 First, I estimate te elasticity of substitution by proecting countries sectoral expenditure sares on trade costs. Second, I estimate te income elasticity of eac good using te following insigt: if ig-income or more unequal countries spend relatively more on a good, ten I infer tat tis good is ig-income elastic. IPUMS-I provides publicly available nationally representative survey data for 82 countries tat are coded and documented consistently across countries and over time. It reports individual-level information including age, gender, educational attainment, labor income and sector of work. Tis ric database enables me to estimate te Frécet dispersion parameter of te witin-group distribution of e ciency units across sectors wic determines te extent of worker reallocation and, tus, te responsiveness of group average wages to canges in sectoral output prices. In addition, I am able to estimate te comparative advantage of di erent labor groups across sectors based on observed worker sorting patterns. Intuitively, if a worker type (relative to anoter worker type) is more likely to sort into a sector (relative to anoter sector), ten I infer tat tey are relatively more productive in tat sector. Using te estimates of group average wages and oter parameters, I can back out te absolute advantage of di erent labor groups. Wit tese parameter estimates, I conduct two counterfactual analyses to quantify te distributional e ects of trade liberalization. To demonstrate ow te model works, I begin wit a simple counterfactual exercise in wic I consider a 5% reduction in all bilateral trade costs. I find tat te average welfare gain across te 40 countries is about.2%, wic is in line wit te previous literature tat abstracts from relative e ects across individuals witin countries. 7 wage distribution, gains decline. question wic factor dominates. Witin eac country, as one moves up te initial nominal Specifically, moving up from one decile to te next 5 One important feature of te WIOD is tat it includes te input-output transactions of a country wit itself. Typically, te domestic market accounts for te large marority of demand for most production. 6 Te sectoral non-omotetic gravity equation based on te AIDS was first dervied in Fagelbaum and Kandelwal (206). However, teir model assumptions imply tat te cange in income is 0 for all consumers. 7 Eaton and Kortum (2002) consider a counterfactual were te 9 OECD countries collectively remove te 5 percent tari on all imports and find tat most countries gain around one percent. 3

5 reduces gains by 0. percentage point: te bottom 0t percentile experiences a real wage gain tat is larger tan te top 0t percentile in every country, and te di erence is 0.8 percentage points in te average country. Tese results igligt tat te distributional e ects of trade liberalization are large compared to its average e ect. I obtain te result tat te poor gain relative to te ric in spite of te fact tat I find te opposite result for nominal wages. In te average country, te bottom 0t percentile see teir nominal wages decrease by 0.2 percentage points relative to te top 0t percentile. Hence, te reduction in te poor s relative price index must fall substantially. In te average country, te bottom 0t percentile see teir consumer price indices decrease by percentage point more tan te top 0t percentile. My framework also allows me to re-examine te impact of a significant increase in U.S. manufacturing imports from Cina on U.S. real-wage inequality wile accounting for bot cannels and teir interaction. 89 Iconsiderauniformreductionintradecosts between te U.S. and Cina tat would yield a $000 per U.S. worker increase in Cinese manufacturing imports. I find tat tis reduction in trade costs decreases te consumer price index for a U.S. representative consumer by 0.85%. An individual wose nominal wage is at te 0t percentile of te initial distribution sees a furter 0.35 percentage point reduction in er consumer price index compared to te representative consumer, wile an individual wose nominal wage is at te 90t percentile sees er consumer price index decrease by 0. percentage point less tan te representative consumer. Tis result arises because Cinese manufacturing goods are low-income elastic and, consequently, teir lower prices benefit more te poor individuals wo spend relatively more on tese goods. Altoug te former sees a bigger decline in er nominal wage (0.3% vs. 0.%) because se s more likely to work in manufacturing sectors tat are in direct competition wit ceaper Cinese imports, tis income e ect is more tan o set by er muc lower consumer price index. Rising Cinese import competition increases te real wage of te poor by 0.43 percentage points more tan tat of te ric in te U.S. Avastbodyofresearcasexaminedteimpactoftradeontedistributionof earnings across workers. Most recently, Galle, et al. (205) develop te notion of riskadusted gains from trade to evaluate te full distribution of welfare canges in one 8 Autor et al. (203), Autor et al. (204) and Acemoglu et al. (206) study te impact of increased Cinese import competition on employment and earnings of U.S. workers by comparing more a ected industries and local labor markets to less a ected ones but ave no implications at te aggregate level. 9 Anoter interesting counterfactual to consider is te Trans-Pacific Partnersip (TPP). I can use my framework to simulate te aggregate and distributional e ects of tis trade agreement for eac of te participating countries. 4

6 measure wic generalizes te specific-factors intuition to a setting wit endogenous labor allocation. Similarly, I focus on canges in relative nominal wages across labor groups tat result from canges in relative demand across sectors driven by international trade. 0 Tere is a small number of studies tat ave considered price indices as a cannel troug wic trade liberalization can a ect inequality. For example, Fagelbaum and Kandelwal (206) develop a metodology to measure te unequal gains from trade troug te expenditure cannel using only aggregate statistics. I extend tis approac to incorporate te di erential impact of trade liberalization on individuals nominal wages. In contrast, Faber (204) exploits barcode level microdata from te Mexican Consumer Price Index and studies te relative price e ect of NAFTA on te di erential cange in te cost of living between ric and poor ouseolds. Faber and Fally (206) use detailed matced U.S. ome and store scanner microdata to explore te implications of firm eterogeneity for ouseold price indices across te income distribution. I complement te existing literature by incorporating bot te expenditure and te income cannels as well as teir interaction in a unified framework to analyze te eterogeneous impact of counterfactual trade socks across individuals in a large set of countries. To my knowledge, tere are only tree case studies tat ave looked at tese two cannels ointly. Porto (2006) studies te distributional e ects of Mercosur, a regional trade agreement among Argentina, Brazil, Paraguay and Uruguay, during te 990s. Nicita (2009) extends Porto s approac by adding a link from trade policy to domestic prices and studies te trade liberalization tat took place in Mexico during te period Marcand (202) allows te tari pass-troug to di er across geograpical regions and studies te trade reforms in India between 988 and Te structure of my model allows me to estimate te e ects for more countries. By looking at a wide 0 See also Adão (205), Burstein, Morales and Vogel (206) and Dix-Carneiro and Kovak (205). I don t incorporate some of te mecanisms tat ave been studied in te literature linking international trade to inequality troug te earnings cannel. For example, Yeaple (2005), Veroogen (2008), Bustos (20), Burstein and Vogel (206) and Bloom, et al. (205) sow tat trade liberalization increases te measured skill bias of tecnology by reallocating resources from less to more skill-intensive firms witin industries and/or inducing firms to increase teir skill intensity. A maor di culty is te lack of a compreensive, matced employer-employee dataset in many countries tat covers te period of rising inequality wic is usually confidential. In addition, tese papers igligt te role of firms because te standard neoclassical teory of trade is inconsistent wit te empirical finding tat nominal wage inequality goes up everywere in response to trade liberalization. I sow tat in a neoclassical setting, non-omotetic preferences allow te model to be fully consistent wit te data. Terefore, it becomes an open question wic mecanism is more important. Atkin et al. (205) draw on a new collection of Mexican microdata to estimate te e ect of foreign supermarket entry on ouseold welfare. Tey do consider bot te price index e ect and te income e ect, but focus only on te gains from retail FDI. 5

7 range of countries, I am able to identify general patterns across countries wit di erent caracteristics. I am also able to conduct model-based counterfactuals of di erent trade socks wic are important for policymakers. In addition, as critiqued in Goldberg and Pavcnik (2007), te predictions of tese studies depend in a crucial way on estimates of te degree of pass-troug from trade policy canges to product prices as well as te wage-price elasticities. Tese are di cult to estimate consistently wit time-series data on wages and prices in a setting wen many oter policies cange contemporaneously wit trade. Te remainder of te paper proceeds as follows. In Section 2, I describe my multisector Armington model of trade wit non-omotetic preferences on te demand side and eterogeneous labor wit comparative advantage across sectors on te supply side. I study tese two cannels and teir interaction analytically in Section 3. Section 4 contains a description of te data, and estimation strategy and results are gatered in Section 5. In Section 6, I discuss my counterfactual results. Section 7 concludes. 2 Te Model 2. Te Environment IstudyaneconomywitN countries indexed by n 2N = {,...,N} and J final good sectors indexed by 2J = {,...J}. Eacgoodisdefinedasasector-countryoforigin pair. Witin any (, n) 2J N, outputisomogeneous, andtemarketisperfectly competitive. In country n, tereisacontinuumofeterogeneousworkersindexedby z 2Z n wit measure L n. Tey are grouped into a finite number of types indexed by 2 witmeasurel n ( )basedonobservablecaracteristics: age,genderandeducation. Iassumetattypesaremutuallyexclusive:Z n ( ) \Z n ( 0 )=;, 8 6= Definition of Welfare Cange Consider ome n country o. Trade liberalization induces a set of infinitesimal canges in log prices, [p (,n),andlogwages,{cw z } z2z. 2 Idefinetelocalwelfarecange (,n)2j N of individual z as te equivalent variation associated wit tis set of canges: 3 2 [ p ln(p (,n) ) is te infinitesimal cange in te log prices and cw ln(w z ) is te infinitesimal cange in te log wages. 3 Please see Appendix 9. for te derivation of te local welfare cange as te equivalent variation. 6

8 bu z = X X n s z [p (,n) (,n) + cw z () Here, s z (,n) is te initial individual expenditure sare on good (, n). An individual s welfare is a ected in two ways. Te first is te cange in er cost of living resulting from te cange in prices wic I refer to as te expenditure e ect. Specifically, it is te price cange applied to te pre-sock expenditure sares. A decrease in prices reduces te cost of living, and terefore increases an individual s welfare. Te second is te cange in er nominal wage wic I refer to as te income e ect. Icanfurterdecomposetelocalwelfarecangeofindividualz into tree components: bu z {z} total e ect = X X s z [p (,n) (,n) + cw {z} z n income e ect {z } expenditure e ect = X X S(,n) [p (,n) + X X s z (,n) S [p (,n) (,n) n n {z } {z } agg. exp. e ect c E + cw z {z} income e ect ind. exp. e ect c z (2) bu z = E c + c z + cw z,tatis,tetotale ectistesumofteaggregateexpendituree ect, ce,teindividualexpendituree ect, c z and te income e ect, cw z. S(,n) is country 0 s aggregate expenditure sare on good (, n). Te aggregate expenditure e ect can be tougt of as te impact of trade liberalization on te cost of living under omotetic preferences were te ratios of goods demanded by consumers depend only on relative prices, not on income or scale. Tis e ect is te same across all individuals witin a country. Onteoterand,teindividualexpendituree ectimpliestatifindividual z spends more on good (, n), ten te price decrease of tat good increases er welfare by a larger amount. 2.3 Non-omotetic Preferences I use te Almost-Ideal Demand System (AIDS) to capture te non-omoteticity in consumer preferences. It gives an arbitrary first-order approximation to any demand system and satisfies te axioms of order, aggregates over consumers witout invoking parallel linear Engel curves, is consistent wit budget constraints, and is simple to estimate. 7

9 Te AIDS allows consumption baskets of ig-income and low-income individuals to di er so tat price canges resulting from trade liberalization ave a di erential impact on teir consumer price indices. It belongs to te family of Log Price-Independent Generalized Prefereces defined by te following indirect utility function: v w z, p = F " /b (p wz ) # (3) a (p ) were F [ ] is a continuous, di erentiable, and strictly increasing function. Te AIDS is te special case tat satisfies: were a p ( a p = exp + X X (,n) ln p (,n)+ n ) X X X X (,n)( 2 0,n 0 ) ln p (,n) ln p ( 0,n 0 ) n 0 n ( 0 ) X X b p = exp (,n) ln p (,n) n is a omotetic price aggregator wic captures te cost of a subsistence basket of consumption goods. is te outlay required for a minimal standard of living wen prices are unity. (,n) is importer s taste for good (, n). (,n)( 0,n 0 ) is te cross elasticity between two goods (, n)and( 0,n 0 ). b p is a non-omotetic price aggregator wic captures te relative price of ig-income elastic goods. Goods for wic (,n) > 0 ave positive income elasticity, wile goods for wic (,n) < 0avenegativeincome elasticity. For AIDS to be a proper demand system, te following parametric restrictions need to be satisfied: 4 X X (,n) = (6) n X X X X n n (4) (5) (,n) = 0 (7) (,n)( 0,n 0 ) = 0 8 ( 0,n 0 ) (8) (,n)( 0,n 0 ) = ( 0,n 0 )(,n) 8 (, n), ( 0,n 0 ) (9) 4 Under tese constraints, te budget sares equations sare te properties of a demand function, tat is, tey are omogeneous of degree 0 in prices and total expenditure, sum of budget sares add up to and tey satisfy te symmetry of te Slutsky matrix. 8

10 Applying Separd s Lemma to te indirect utility function, I can derive te individual expenditure sares as follows: s z (,n) = s (,n) w z, p = (,n) + X X (,n)( 0,n 0 ) ln p wz ( 0,n 0 ) + (,n) ln a (p ) 0 n 0 (0) According to tis equation, if a consumer as relatively low nominal wage, ten se spends relatively more on low-income elastic goods. Under te AIDS, I can describe te market by te beavior of a representative consumer wit te inequality-adusted average nominal wage, w = w e,wicdependsonteaveragenominalwageincountry, " # w,andteteilindex, P E w w ln w w,ameasureofinequalitywitinacountry. It is terefore straigtforward to derive te aggregate expenditure sares in country : S(,n) = s (,n) w, p = (,n) + X X w (,n)( 0,n 0 ) ln p ( 0,n 0 ) + (,n) ln a (p ) 0 n 0 () Similarly, adusted for te price level, a p,ifcountryas iger inequality-adusted average nominal wage, w, eiter because of iger average nominal wage or iger inequality, ten it spends relatively more on ig-income elastic goods. It is convenient to rewrite te individual expenditure e ect under te AIDS as: c z = X = ln X n s z (,n) wz X X w S (,n) n (,n) [ p (,n) {z } b [p (,n) (2) Intuitively, for an individual z wo as lower nominal wage relative to te representative consumer in te country, if te price of a low-income elastic good goes down, se is better o and vice versa. Note tat I do not ave to observe eac individual z s expenditure sare on eac good (, n) in order to compute te cange in er consumer price index. Plugging in te above expression for c z, I can write te local welfare cange of individual z under te AIDS tat corresponds to an infinitesimal cange in prices and 9

11 nominal wages as follows: bu z = E c ln w z bb w + cw z (3) Te global welfare cange of individual z under te AIDS between an initial scenario under trade and a counterfactual scenario can be derived by integrating eac component of te equation above: 5 u trcf z {z } total e ect = E cf E tr {z } agg. exp. e ect wz tr w tr ln(b cf /b tr ) {z } ind. exp. e ect wz cf w tr z {z } income e ect (4) E cf E tr = Y (,n) p,tr S (,n) (,n) (5) p,cf (,n) ln b cf b tr = X X n (,n) ln p,cf (,n) p,tr (,n) (6) Note tat E cf and ln( b cf )arefunctionsoftesetofpricesintetwoscenarios,te Etr b tr aggregate expenditure sares tat are observed in te data and a model parameter, If u trcf z <, individual z is worse o after te cange and vice versa. 2.4 Heterogeneous labor wit comparative advantage across sectors My supply-side specification allows for eterogeneous labor wit comparative advantage across sectors so tat di erent labor types sort into di erent sectors. As a result, price canges resulting from trade liberalization ave a di erential impact on teir nominal wages. (,n). I use an assignment model of te labor market parametrized wit a Frécet distribution. In tis environment, workers wit di erent unobservable caracteristics but identical observable caracteristics may be allocated to di erent sectors in a competitive equilibrium. 6 In particular, an arbitrary worker z of type draws a vector of e ciency 5 Please see Appendix 9.2 for te derivation of te aggregate and individual expenditure e ects between an initial scenario under trade and a counterfactual scenario. 0

12 units across di erent sectors from a multivariate Frécet distribution: 7 G ( (z); ) = Pr[e (z; ) apple (z; ) 8] ( ) X = exp (z; ) ( ) (7) were ( ) > governswitin-typedispersionofe supplies (z; ) e ciencyunits. Workerz inelastically ciencyunitsoflaborifsecoosestoworkinsector. Production requires only one factor, labor. 8920, sector, usingl e ciency units of labor type is: 2 A ( )isteproductivityoftype of type Te production function in country y (l;, ) =A ( )T (, )l (8) workers in country and T (, ) isteproductivity workers wo coose to work in sector. A ( )capturesteabsoluteadvantage of type workers in country. T (, ) capturestecomparativeadvantageoftype n o workers in sector. Consider te partial equilibrium in wic output prices, p (,) 6 I assume tat te labor market is perfectly competitive, tat is, tere is no friction. Dix-Carneiro (204) finds tat workers median costs of switcing sectors range from.4 to 2.7 times individual annual average wages, but tese vary tremendously across individuals wit di erent observable caracteristics. For example, female, less educated, and older workers face substantially iger costs of switcing as a fraction of individual wages. Tis increases te probability of unemployment of te low-skilled, and biases te gains from trade towards te ig-skilled and ig-income. 7 Frécet distributions of productivity socks across factors ave been imposed in te recent closedeconomy models of Lagakos and Waug (203) and Hsie et al. (203) as well as te open economy models of Burstein, Morales and Vogel (204), Costinot, Donaldson and Smit (204), and Fagelbaum and Redding (204). Sector and country caracteristics are assumed to be perfectly observed by te econometrician, but factor caracteristics are not. See Costinot and Vogel (205) for a detailed discussion. 8 For simplicity, I abstract from capital in my production function. Capital may matter for two reasons. First, it may generate comparative advantage across sectors. Tis is very similar to introducing Hicks-neutral capital were capital is more important in some sectors tan oters. Tat would generate tecnological di erences at te country-sector level. Capital reallocation reinforces labor reallocation in response to trade liberalization. Second, capital may be di erentially complementary to di erent types of labor. In tat case, tere is a large number of cross elasticities I need to estimate, wic is callenging. 9 I do not feature complementarity between di erent types of equipment and eterogeneous workers across sectors as in Burstein, Morales and Vogel (206) because I do not ave data to compute te sare of total ours worked by eac labor group tat is spent using di erent equipment types across sectors. 20 My model is static, so I am not taking any stand on te accumulation of skills and capital in response to trade liberalization. I take eac country s endowments of skills and capital as given for now, but it would be great to introduce dynamics to te framework. 2 My model does not feature Ricardian-type country-sector productivity. However, I demonstrate in Appendix 9.3 tat I am not understating te specialization of skill-abundant countries in skill-intensive sectors. 2J,

13 are given. Perfect competition and free entry entail tat te per e ciency unit wage x (, ) ofaworkeroflabortype working in sector in country is: x (, ) =p (,)A ( )T (, ) (9) Worker z 2Z ( )witrealizationoftevectorofe ciencyunits (z) ={ (z; )} 2J needs to coose te sector tat maximizes er labor earnings wic is te product of er draw of e ciency units and per e ciency unit wage: w z =maxw z () = (z; ) x (, ) (20) Te multivariate Frécet distribution implies tat te probability of a type coosing to work in sector in country is: were x ( ) dispersion of e (, ) = i ( ) p (,) A ( )T (, ) p ( 0,) A ( )T (, 0 ) P 0 2J i ( ) worker = x (, ) ( ) x ( ) ( ) (2) P x ( (, ) ) ( ). Wit a iger ( ), wic implies tat tere is less ciency units across sectors, a cange in price or a cange in productivity a ects te factor allocation even more. As a result, te worker sorting pattern is determined by comparative advantage: apple ( 0, 0 ) ( 0,) ( 0 ) / apple (, 0 ) (,) apple ( ) T( = 0, 0 ) T( 0,) / apple T(, 0 ) (22) T (,) If type 0 workers (relative to type workers) ave a comparative advantage in sector 0 (relative to sector ), ten tey are relatively more likely to sort into sector 0,adusted for potentially di erent values of ( )and ( 0 ). For larger ( 0 )(i.e.lessdispersionin e ciency units among type 0 workers), it is even more likely for tem to sort into sector 0,inwicteyaveacomparativeadvantage. Te distribution for w z =max w z () conditionalonz 2Z ( )is: n Pr w z apple w z 2Z ( ) =exp x ( ) ( ) w ( ) o (23) It is also distributed Frécet wit te scale parameter, x ( ), te average per e ciency 2

14 unit wage of labor type across te sectors, along wit te dispersion parameter, ( ). 22 Te average nominal wage, w,andteteilindex, P,incountry can also be expressed in terms of x ( )and ( ): w = X L ( ) ( ) x ( ) (24) L x ( )lnx ( ) ln w (25) = w X L ( ) L ( ) were ( ) ( ) digamma function. ( ) ( ) x ( ) is te gamma function and ( ) ( ) is te 2.5 General Equilibrium In te general equilibrium, output prices, clearing conditions: n o p (,), are determined by te market 2J X y L ( ) (, );, = X (,)D n (,) n 8 2J (26) were y = A ( )T (, ) ( ) (, ) ( ) L ( )istesupplyofsector good by labor type in country. 23 n (,) n is te bilateral trade cost between export country and import country n in sector. D n (,) = Sn (,) wn L n /p n (,) is country n s demand for good (, ), were S n (,) is given in equation () and wn in equation (24). It depends on country n s wage distribution (in particular, w n and n )aswellastevectorof prices tat consumers face in tat country p n (in particular, p n (,) = (,) n p (,)). Since tese output prices enter bot te demand side and te supply side nonlinearly, I apply te Gauss-Jacobi algoritm, an iterative metod, to solve te system of market clearing equations numerically. 24 IalsoappealtoteImplicitFunctionTeoremtosowtat te price equilibrium tat I ave found numerically is locally isolated as a function of te parameters. 25 Tat is, in response to a small perturbation, if tere exists an equilibrium, 22 Burstein, et al. (206) find tat te wage distribution implied by te assumption of Frécet distributions is a good approximation to te observed distribution of individual wages. 23 Please see Appendix 9.4 for te derivation of te total supply. 24 I demonstrate te existence of an equilibrium numerically. 25 Please refer to Appendix 9.5 for a brief discussion of te Gauss-Jacobi Algoritm and te local property of te equilibrium. 3

15 ten te system stays in te neigborood of tat equilibrium. I find no quantitative evidence of multiple equilibria Analytical Results In tis section, I study tese two cannels and teir interaction analytically. I consider a simple case were tere are two countries, two sectors and two labor groups to illustrate te intuition. Setup Suppose tat tere are two countries, =, 2, two sectors, =, 2andtwolaborgroups, =, 2. Te two labor groups di er in teir skill levels, wic allows nominal wages to vary across workers witin a country. I assume tat =isigskilled. Goods produced in eac sector are omogeneous and not di erentiated by country of origin. As aresult,terearetwogoodsintotal, =, 2, wic simplifies te analysis tat follows. Tese two goods, owever, ave di erent income elasticity, wic are > 0and, respectively. 27 Tat is, good is ig-income elastic relative to good 2. Te implied non-omotetic preferences allow price indices to vary across consumers witin a country. Ifurterassumetatgoodismoreskillintensive,basedonteempiricalfindingtat tere is a positive correlation between te skill intensity of a good and its income elasticity. Allowing te two goods to di er in teir skill intensity also leads to comparative advantage of di erent labor groups across sectors, wic is necessary in generating te pattern of trade consistent wit te Heckscer-Olin model. Finally, I assume perfect competition in all markets as before. Demand Suppose tat country s taste for good independently from prices or income, =, and for good 2, 2 =, =, Ifurterassumetattesemi-elasticityofte 26 I ave tried multiple starting points and te system always converges to te same equilibrium. I ave not proven eiter existence or uniqueness analytically. It is a complicated model wit interactions and is not mapped neatly into te class of models considered in Alvarez and Lucas (2007). 27 More precisely, is semi-elasticity since it relates expenditure sares to log of income, but I refer to it as elasticity to save notation. 28 One reason tat 6= 2 or 2 6= 2 2 is because of ome market e ect. However, since I consider te case were bot countries produce bot goods, and tat eac good is omogeneous regardless of country of origin, it is reasonable to assume tat = 2 and 2 =

16 expenditure sare in one good wit respect to te price of anoter, 2 = 2 =,and tat wit respect to its own price, = 22 =. Under tese parametric restrictions, te budget sares equations in te Almost Ideal Demand System sare te properties of a demand function. In addition, I assume tat te outlay required for a minimal standard of living wen prices are unity, = 0, following te literature. Te omotetic price aggregator becomes: ( ) a(p ) = exp ln p +( )lnp 2 + ln p ln p 2 =(p ) (p 2) (p 2) ln p (27) Te non-omotetic price aggregator becomes: b(p ) = exp ( ln p ln p 2 ) = p p 2 (28) Te aggregate expenditure sares in country are: " S = ( + )lnp + " S2 = +( + )lnp # ( ) ln p 2 ln p ln p 2 + ln w (29) # ( ) ln p 2 + ln p ln p 2 ln w (30) Country is endowed wit H ig-skilled workers and L low-skilled workers, and tey are paid wh and w L, respectively. Suppose te two countries are of te same size, tat is, H + L = H 2 + L 2 H = N, butcountryismoreskillabundant, > H2 Te inequality-adusted average nominal wage, w = w e P,were w = N (H w H + L w L ). Terefore, Production ln w = ln w + X =ln w + N " H w H w ln w H w + L w L w ln L w L w Te production side follows closely te Heckscer-Olin model wit Cobb-Douglas production function: L 2. (3) were 0 < 2 < <. y = (H ) (L ),,=, 2 (32) 5

17 A producer in country, sector, solves te following cost minimization problem: min w HH + w LL s.t. y apple (H ) (L ) (33) Tis implies te following equation, under te assumption tat bot countries produce bot goods: L w L = H w H (34) Total supply of good produced by country is, terefore, L p (H ) (L ) = w H H + w L L,combinedwitequation(34),leadto: w L w H. Zero profits, p = (w L ) (w H ) ( ) (35) Autarky Equilibrium Te goods market clearing condition implies tat: S w N/p = L w L w H (36) Substitute p using equation (35), w LL = S w N ( ) (37) Use good 2 as te numeraire, tat is, p 2 =,=, 2, ten equations (29) and (30) become: S = ( + )lnp + ln w (38) S 2 = +( + )lnp ln w (39) In addition, according to equation (35), p = (w L ) (wh ) ( ) Te latter implies tat: and p 2 = (w L ) 2 (w H ) 2 ( 2 ) =. 2 wl = ( 2 ) 2 2 (wh) 2 2 (40) 6

18 Substitute wl using equation (40), 2 ( ) 2 p = ( 2) 2 ( ) Furtermore, equation (37) implies tat: (w H) (4) w LL = S w N ( ) (42) w LL 2 = S 2 w N ( 2 ) (43) wic add up to te following equation: " # wll = w N ( )S +( 2 )S2 (44) Since S = S2,Isimplifyequation(44)furterandobtain: " # wll = w N 2 +( 2 )S (45) Note tat every variable in tis equation is a function of wh and model parameters, and once I solve for wh, I can back out p, wl, L and L 2. Finally, using equation (34), I can back out H and H2 as well. Tese variables caracterize te autarky equilibrium of te two countries. Case : =0 Under tis restriction, te demand system is omotetic. For simplicity, I furter impose tat = 0, tat is, tere is no substitution across goods. As a result, S = and S2 =. SubstitutewL using equation (40), " # ( ( 2 )+( 2 ) wh = " # 2 +( 2 ) L H ) 2 (46) 7

19 Case 2: = 2 = 2 Under tis restriction, equation (40) implies tat wl =.Equation(45)tenimplies 4wH tat: Solve te equation, 4w H Free Trade Equilibrium " = ( 2) H N L N w H + L N w H = 2 r L 4w H # (47) H (48) In te two country example, free trade implies tat te price of eac good is te same in bot countries, tat is, p = p 2 = p and p 2 = p 2 2 = p 2. I consider te case in wic bot countries produce bot goods. Te producer cost minimization problem implies, as in equation (34), tat L w L w H = H.Combinedwitzeroprofits, p = (w L ) (wh ) ( ),,=, 2 (49) Since tecnologies and prices are te same in te two countries, equation (49) implies tat: (wl) (wh) = (wl) 2 (wh) 2 (wl) 2 (wh) 2 = (wl) 2 2 (wh) 2 2 (50) Replace tese two equations in one anoter: wh = w2 H = w H and wl = w2 L = w L.Tat is, factor price equalization (FPE) olds in te free trade equilibrium. From te cost minimization of te producer: Sum up over and use FPE: Use goods market clearing condition: p y = w HH (5) p (y + y 2 ) = w H (H + H 2 ) (52) 8

20 S (H w H + L w L )+S 2 (H 2 w H + L 2 w L ) = p (y + y 2 ) = w H (H + H 2 ) (53) Add up over : # X "S (H w H + L w L )+S 2 (H 2 w H + L 2 w L ) X = w H (H + H 2 ) = w H (H + H 2 ) (54) Since S2 = S and S2 2 = S,equation(54)canberewrittenas: 2 # # (H w H + L w L ) "( 2 )S + 2 +(H 2 w H + L 2 w L ) "( 2 )S = w H (H + H 2 ) (55) were S = ( + )lnp + ln w (56) S 2 = +( + )lnp ln w (57) p = (w L) (w H ) ( ) p 2 = (w L) 2 (w H ) 2 ( 2 ) Use good 2 as te numeraire, tat is, p 2 =,Iobtain: and it follows tat: 2 (58) (59) w L = ( 2 ) 2 2 (w H ) 2 2 (60) 2 ( ) 2 p = ( 2) 2 ( ) (w H ) (6) Note tat every variable in equation (55) is a function of w H and model parameters, and once I solve for w H,Icanbackoutp and w L. Recall tat te capital-labor ratio implies tat: 9

21 L w L ( )w H = H (62) Add tat up for bot goods: w L w H " (L L 2)+ 2 2 L 2 # = H (63) Equation (63) can be rearranged as te following: " # L 2 = ( 2)( ) w H H L 2 w L L (64) wic can be used to solve for L 2 and L, =, 2. Finally, using equation (62), I can back out H and H 2 as well. Tese variables caracterize te free trade equilibrium of te world economy. Case : =0 Under tis restriction, te demand system is omotetic. For simplicity, I furter impose tat = 0, tat is, tere is no substitution across goods. As a result, S = and S2 =. SubstitutewL using equation (60) into equation (55): " # w H = ( ( 2 )+( 2 ) " 2 +( 2 ) # ) H + H 2 2 L + L 2 (65) Case 2: = 2 = 2 Under tis restriction, equation (55) implies tat: 2 (H w H + L w L + H 2 w H + L 2 w L ) = w H (H + H 2 ) (66) Substitute w L = 4w H into te above equation: w H = 2 r L + L 2 H + H 2 (67) 20

22 Compare te two cases in te autarky equilibrium wit te free trade equilibrium, I find tat suppose H L > H2 L 2, 8 < : 8 < : wh aut wh aut wl aut wl aut <wft H >wft H for = for =2 >wft L for = <wft L for =2 (68) wic is consistent wit te prediction based on te Heckscer-Olin model, but inconsistent wit my quantitative result in te next section tat te relative nominal wage of te skilled workers in skill-scarce countries also goes up after trade liberalization. Recall tat te goods market clearing condition in te autarky equilibrium is: ( #) wll = w N 2 +( 2 ) " ( + )lnp + ln w (69) and te goods market clearing condition in te free trade equilibrium is: ( #) w H (H + H 2 ) = (w H H + w L L ) 2 +( 2 ) " ( + )lnp + ln w + ( #) (w H H 2 + w L L 2 ) 2 +( 2 ) " ( + )lnp + ln w 2 (70) Trade liberalization in te form of lower trade costs increases ln w and ln w 2 exogenously. In bot cases, it is only wen 6= 0and 6= 2 tat tis increase leads to a rise in te relative nominal wage of te skilled workers in bot countries according to equations (69) and (70) since > 2. I also solve te two equilibria numerically and find consistent result wit my quantitative exercise for reasonable parameter values. 4 Data For te demand-side estimation, I use mainly te World Input-Output Database (WIOD), wic provides information on bilateral trade flows and production data for 40 countries (27 European countries and 3 oter large countries) and 35 sectors in te economy. It also distinguises between final consumption and intermediate uses. 29 2

23 World Input-Output Table looks like te following: Figure : Scematic Outline of a World Input-Output Table (WIOT) For te supply-side estimation, I use mainly te Integrated Public Use Microdata Series, International (IPUMS-I), wic provides publicly available nationally representative survey data for 82 countries tat are coded and documented consistently across countries and over time. It also provides individual-level data wit labor incomes and worker caracteristics. I divide te workers in IPUMS-I dataset into 8 disoint groups,, by age (5-24, and 50-74), gender (male and female) and educational attainment (ED0-2, less tan primary, primary and lower secondary education; ED3-4, upper secondary and post-secondary non-tertiary education; ED5-8, tertiary education). 5 Parametrization 5. Supply-side Parameters On te supply side, I need to estimate ( ), te worker type specific Frécet dispersion parameter, L ( )/L,tefractionoftype workers in country, A ( ), te productivity of type workers in country and T (, ), te productivity of type workers wo coose to work in sector. To estimate te worker type specific Frécet dispersion parameter ( ), I follow te metodology in Lagakos and Waug (203) and Hsie et al. (203) and matc te moments of te empirical distribution of witin type worker wages. 30 In particular, te mean and te variance of nominal wages witin a labor group satisfy: 29 I do not use te UN Comtrade Database because it does not ave information on te input-output transactions of a country wit itself. 22

24 " # V AR w z z 2Z ( ) " # 2 = E w z z 2Z ( ) 2 ( ) ( ) 2 (7) Irestrictmysampleintefollowingway:Idropworkerswoareyoungertan5years old, are self-employed or work part-time (<30 ours per week), do not report positive labor earnings, or ave missing information on age, sex or education. I also drop te top and bottom % of earners to remove potential outliers, and to minimize te impact of potential cross-country di erences in top-coding procedures. All calculations in my analysis are weigted using te applicable sample weigts. I measure w z as te annual labor earnings; (z; ) capturesbotteoursworkedande ciencyunitsofworkerz wo cooses to work in sector ; ( )reflectsdispersioninbotoursworkedande units of type workers; L ( )isteeadcountoftype workers. ciency I use IPUMS-I to estimate ( )for6countries. 3 Since te estimates of ( )arevery close across te 6 countries for eac labor type,iuseteaverageofteseestimates for all countries and assume tat ( )doesn tcangeovertime. Ibackoutx ( )using E w z z 2Z ( ) = x ( ) ( )forte6countries. Sinceallearningsdatain ( ) IPUMS-I are in local currency units, I use te o cial excange rate (LCU per US$, period average) from te World Bank to convert all values to US$. I also find tat output-side real GDP per capita ave strong explanatory power for x ( ), so I use te predicted values of x ( )forterestoftecountries. 32 Since IPUMS-I does not provide information on L ( )/L for all of te 40 countries, I use te following complementary datasets. First, I use Eurostat, wic provides information on te full-time and part-time employment by age, gender and educational attainment. It includes 27 European countries in WIOD. Second, I use UNdata, wic as information on population 5 years of age and over, also by age, gender and educational attainment, for Russia, Australia, Korea and Cina. Tis dataset comes from UNSD Demograpic Statistics United Nations Statistics Division. Tird, I use National Statistics, Republic of Cina (Taiwan) and finally, Population Statistics of Japan. In order to estimate te sector-level non-omotetic gravity equation, wic I explain 30 As a robustness ceck, I also ointly estimate ( ) and x ( ) for eac labor type using maximum likeliood. 3 Te list of countries can be found in Appendix I get te data on output-side real GDP at cained PPPs (in millions of 2005 U.S.$) and population from te Penn World Tables. 23

25 in detail in te next section, I need to compute te inequality-adusted average nominal wage of eac country, wic requires an estimate of its average nominal wage as well as its Teil index. Table reports my estimates of te average labor earnings and te Teil index for te 40 countries based on equations (24) and (25). I estimate w and P for te years 2005, 2006 and 2007, and ten take te average. Country Teil Avg Labor Earnings Country Teil Avg Labor Earnings Table : Average Labor Earnings and te Teil Index Recall tat te Teil index measures te level of inequality witin a country, wic in my framework is te dispersion in labor incomes. Since my Teil indices are calculated using only te labor earnings of te population aged between 5 and 74, I also use IPUMS- ItoconstructalternativemeasuresofwageGinicoe cientsusingtreedi erentmetods tat are widely used in te literature. Let y i be te labor income of a person indexed in non-decreasing order (y i apple y i+ ), my first two measures of te wage Gini coe cients are calculated as follows: G = 2 P n i= iy P i n P n+ 2 n and G i= y i n 2 = (n n i= iy i P n n ). On te oter i= y i and, Guillermina Jasso and Angus Deaton independently propose te following formula: G 3 = N+ 2 (P n N N(N )µ i= P ix i )wereµ is mean income of te population, P i is te income rank P of person i, witincome,x i,suctattericestpersonreceivesarank 24

26 Teil inde Wage Gini coefficient Figure 2: Wage Gini coe cient calculated using IPUMS-I of and te poorest a rank of N. Tetreemetodsgivemeverysimilarestimatesand Figure 2 demonstrates tat my model-implied Teil indices perform very well against te Jasso and Deaton measure. Teir correlation is significantly positive at I plot in Figure 3 my model-implied Teil indices for all of te 40 countries against te Gini coe cients reported in te World Income Inequality Database tat are computed using all sources of income. Te two measures are still positively correlated and te correlation coe cient is 0.6. In te rigt panel, I exclude te tree potential outliers and te correlation coe cient remains positive and is around Teil index Gini coefficient Teil index Gini coefficient Figure 3: Teil Index 25

27 In Figure 4, I plot my model-implied labor earnings per capita against output-side GDP per capita. My measure of income per capita tracks te data very well. Tese parameter implications provide evidence tat my model assumptions on te supply side do well at matcing te data. Average labor earnings Output-side GDP per capita Figure 4: Average Labor Earnings As discussed above, te worker sorting pattern can be used to parametrize T (, ). I need + J = 52 normalization. I pick =suctatt (, 0 )=8 0. I also pick =suctatt ( 0,)=8 0.TenIaveT ( 0, 0 )= apple ( 0, 0 ) ( 0,=) ( 0 ) / apple ( =, 0 ) ( =,=) 8 0 6=8 0 6=were (, ) =L (, )/L ( )andl (, ) isteeadcountoftype ( =), workers in country tat coose to work in sector. Since tere is no information on L (, ) in Eurostat or UNdata, I use data on te countries tat are available in IPUMS-I to compute T (, ) andtenuseteaverageofteestimatesforalloftecountries. 33 Given te specified normalization, ( 0,) (, ) 0 ) = T ( 0,) ( (72) T (, ) ( ) I plot in Figure 5 tis ratio aggregating te 8 labor groups into tree broad categories based on educational attainment against an estimate of te skill intensity of eac sector wic matces te sare of ours worked in tat sector by workers wit a completed 33 Tis restriction implies, for example, a U.S. and a Cinese female worker wo are 25-year-old and college educated are bot twice as productive in ealt care tan in mining. Because of data limitations, I cannot estimate T (, ) for every country. Tis restriction is reasonable and does well in capturing te systematic relationsip between te di erent labor types and te sectors tat tey sort into. 26

28 tertiary degree in te U.S Te correlation coe cients are -0.4 and respectively. Tese graps illustrate tat workers wit less education are more likely to work in unskillintensive sectors. Tis implies tat a decline in te relative price of goods in unskillintensive sectors decreases te relative nominal wage of unskilled workers. 36 ED vs ED2 ED2 vs ED3 Worker Sorting Worker Sorting Skill Intensity Skill Intensity Figure 5: Worker Sorting To estimate A ( ), te productivity of type workers in country, Itakeafirst-order approximation of te following equation at p =, T =: x ( )= X x (, ) ( ) ( ) ( X = p (,) A ( )T (, ) ( ) ) ( ) 2J ( X = A ( ) p (,) T (, ) ( ) ) ( ) (73) 2J wic gives me: 37 log x ( ) = log A ( ) + log J x () A () ( ) + () J X 2J log T (, ) T (,) (74) 34 ED corresponds to less tan primary, primary and lower secondary education; ED2 corresponds to upper secondary and post-secondary non-tertiary education; ED3 corresponds to tertiary education. 35 I tank Jonatan Vogel for providing me wit tese estimates. 36 In partial equilibrium, canges in wages are proportional to canges in output prices, were te weigt depends on factor allocation in te initial period. An increase in sector s output price raises te relative wage of labor groups tat disproportionately work in sector in te initial trade equilibrium. 37 Please see Appendix 9.7 for te derivation of equation (30). 27