Non-homothetic Preferences, Pattern of Trade and Inequality

Transcription

1 Non-homoheic Preferences, Paern of Trade and Inequaliy Xiaolu Li Nanyang Technological Universiy Yang Tang Nanyang Technological Universiy Absrac This paper explores he disribuional impacs of non-homoheic CES preference srucure and rade liberalizaion. We embed non-homoheic preferences ino a rade model wih monopolisic compeiion. Individuals are heerogeneous in heir human capial endowmen, and counries only differ in he disribuion of human capial. By inroducing elasic labor supply, secoral consumpion demand becomes less responsive o changes in human capial han in he case of exogenous labor supply. We parameerize he model o mimic cerain sylized facs in he real-world counerpar. The quaniaive resuls sugges ha he more alened counry enjoys higher GDP and average living sandards. However, individuals a he boom percenile may be beer off in he less alened counry. The resource disribuion across secors becomes idenical in boh counries when non-homoheic preferences are removed. Trade liberalizaion ends o reduce inequaliy boh wihin and beween counries. Keywords: Non-homoheic Preferences; Trade; Inequaliy JEL Classificaion: F12; F63; O11 lixiaolu.sg@gmail.com angyang@nu.edu.sg 1

2 1 Inroducion A growing body of recen lieraure has aimed o embed non-homoheic CES preferences ino he class of growh and new rade models. 1 Examples include Masuyama [2015] and Comin, Lashkari, and Mesieri [2015]. These sudies focus on examining how changes in preference srucure affec he aggregae performance of he economy and he paern of rade across counries. However, lile aenion has been devoed o how individuals of differen ypes may be influenced. These quesions are poenially imporan if we wish o undersand he role of rade liberalizaion in inequaliy. This paper aemps o address hese quesions. In his paper, we develop a rade model feauring individuals who are heerogeneous in heir human capial endowmen. Counries are all idenical excep in he disribuion of human capial. Non-homoheic preference srucure is inroduced ogeher wih endogenous labor supply decision. Essenially, an individual s uiliy level posiively depends on final consumpion and leisure ime, while final consumpion is an implici non-homoheic CES aggregaor of secoral-level consumpion. A a lower ier, secoral consumpion is a homoheic CES aggregaor of all varieies available in he secor. The producion side of he economy is modeled as monopolisic compeiion. Each firm is he single producer of one variey. Free enry prevails in each secor. The heoreical framework has he following disincive feaures. Firs, by inroducing a radeoff beween labor supply and leisure, income is no longer exogenous. Therefore, insead of convenionally defining an income elasiciy, we focus on he elasiciy of human capial agains secoral consumpion. We show ha human capial elasiciy can be decomposed ino wage elasiciy and elasiciy of human capial agains labor supply, and he laer is proven o be less han one wih reasonable parameerizaion. Therefore, secoral consumpion is less responsive o changes in human capial han in wages. Second, he nonhomoheic preference srucure enables us o rank he elasiciy of human capial agains secoral consumpion over secors. Therefore, individuals wih higher human capial ends o proporionally spend more on he secor wih higher human capial elasiciy. Third, 1 The New rade heory is proposed in Krugman [1980], and developed by Meliz [2003] and Eaon and Korum [2002]. They usually feaure homoheic preferences and monopolisic or perfec compeiion. 2

3 in he case of open economy, we model he wo counries as idenical ones excep for he iniial disribuion of human capial. The more alened counry hus demands more from he secor wih he highes human capial elasiciy. Due o he home marke effec, more varieies will be produced and he secoral price will end o be lower, and hus he more alened counry is more likely o become he ne exporer of he secoral varieies. We calibrae he model ino a closed economy wih even resource disribuion across he secors. In he case of open economy, we le he human capial disribuion in he alened counry firs order sochasically dominae ha in he oher counry. We compare seleced individuals a he same percenile from he human capial disribuion in each counry. The benchmark resuls sugges individuals a he boom percenile in he less alened counry end o obain higher uiliies han hose from he alened counry. The main reason is ha he price level for he secor wih leas human capial elasiciy is lower in less alened counry, as i conains a larger marke demand. Individuals a he boom percenile spend proporionally more on he secor wih lowes human capial elasiciy, and hus are beer off in he less alened counry. To furher evaluae he role of asymmeric human capial disribuion, elasic labor supply, non-homoheic preferences, and rade liberalizaion in deermining oucomes a he aggregae, secoral, and individual level, we run several couner facual exercises. The main findings are as follows: he more alened counry ouperforms he oher one in erms of GDP and average living sandards, due o larger marke size. The less alened counry in urn has a larger rade share, as more varieies are offered by he more alened counry. Resource disribuion becomes idenical in boh counries when eiher asymmeric disribuion or non-homoheic preference srucure is removed. When labor supply becomes exogenous, resource disribuion ends o become more dispersed and inequaliy widens, because he elasiciy of human capial agains labor supply is less han 1 in he benchmark resuls. Trade balance is mainained wihin each secor boh in he case of exogenous labor supply and homoheic preferences. Trade liberalizaion ends o reduce boh wihin and beween counry inequaliy. When price levels become lower, individuals end o increase heir leisure ime, and hus hose wih higher human capial will lose more income given he same magniude of decline in labor supply, which explains he lower inequaliy wihin he counry. The 3

4 shrinkage of beween counry inequaliy mainly occurs because when rade fricion decreases, Counry 1 can expor o a larger marke han Counry 2. In addiion, rade liberalizaion proporionally induces more firm enries ino secors in which Counry 1 is a ne exporer. Our model is buil upon he class of new rade models, such as Krugman [1980], and muliple variaions and exensions of Meliz [2003]. However, hese models ypically assume ha consumers have idenical and homoheic preferences in all counries. As argued in Markusen [2013], such models imply ha aggregae demand only depends on price indexes and aggregae income, and is independen of he disribuion of income. We inroduce nonhomoheic preferences and heerogeneous individuals o an oherwise sandard new rade model. The purpose is o evaluae he disribuional impacs from changes in preference srucure and rade liberalizaion. Our paper is mos closely relaed o Masuyama [2000], Masuyama [2015] and Comin, Lashkari, and Mesieri [2015]. Masuyama [2015] focuses on how non-homoheic preference srucure may affec he rade paern beween wo counries ha differ only in populaion size. Individuals are homogeneous in his paper, and i is purely heoreical; simplificaion assumpions are required o obain more analyical resuls. Comin, Lashkari, and Mesieri [2015] embed non-homoheic preferences ino a muli-secor growh model o generae non-homoheic Engel curves a all levels of developmen.duare and Resuccia [2010] use a model wih non-homoheic preferences o sudy srucural ransformaion, and argue ha non-homoheic preference is one reason for labor reallocaion across secors. Boh households and firms are represenaive in heir work, and he economy is closed and he role of rade liberalizaion is absen. The major conribuion of his paper is hree fold. Firs, his heoreical framework is probably he firs o embed non-homoheic CES preferences and heerogeneous individuals ino a rade model wih monopolisic compeiion. This framework allows us o explore he disribuional impacs of non-homoheic preference srucure and rade liberalizaion. Including leisure ino he uiliy funcion also adds an exra erm o human capial elasiciy, which is hus lower han convenionally defined wage elasiciy. Second, we inroduce a wo-ier uiliy srucure wih endogenous labor supply decision. The efficiency labor supply is hen no longer equal o he populaion size. In addiion, individual heerogeneiy furher inroduces obsacles o analysis, because he marke demand is now an inegraion of indi- 4

5 vidual demands of differen ypes. These issues all grealy complicae he analysis compared wih Masuyama [2015], ye we are sill able o obain mos analyical resuls even under a more general parameer space. Third, we go beyond Masuyama [2015] by providing deailed quaniaive analysis o quanify he role of each conribuing facor in deermining aggregae, secoral, and individual-level oucomes. The findings shed ligh on he role of rade liberalizaion in wihin and beween counry inequaliy. The res of his paper is organized as follows. Secion 2 describes he model seing. We perform quaniaive analysis in Secion 3. Our conclusion is offered in Secion 4. 2 Model The heoreical framework is an exension of Masuyama [2015], wih heerogeneous workers and endogenous labor supply decision. Moreover, we allow more flexible assumpions in he parameerizaion, bu he analyical resuls sill remain racable. We sar by characerizing he opimizaion problem for individuals and firms. We hen define a closed-economy equilibrium and obain some analyical properies. Finally, we open up he economy and examine how he paerns of rade are endogenously deermined wihin he framework. The economy is closed and populaed wih a mass N of workers. Workers are heerogeneous in erm of heir human capial endowmen, which is assumed o follow a cerain disribuion funcion G( ). There are a finie number S > 1 of secors in he economy. 2.1 Preferences and Individual Opimizaion Problem Individual workers obain uiliies from final consumpion as well as leisure. Specifically, he uiliy funcion for a worker wih human capial h akes he following specific form: U(h) = C(h)1 σ 1 σ + θ l(h)1 σ 1 σ, where C(h) denoes he final consumpion and l(h) (0, 1) is he leisure ime, where we normalize he ime endowmen for each worker o be 1. θ > 0 governs he preference of 5

6 leisure agains final consumpion. We follow Masuyama [2015] by assuming ha final consumpion is an implici nonhomoheic CES aggregaor of secor-level consumpion. Specifically, a worker wih human capial h has final consumpion C(h) defined as follows: S s=1 C (h) ɛ(s) C s (h) 1 = 1, (1) where C s (h) denoes secor-level consumpion. When ɛ(s) = 1, he funcional form above can be reduced o sandard homoheic CES preference. We formally characerize he opimizaion problem for a represenaive worker of human capial h as follows: s.. max C s(h),l(h) S s=1 C (h) ɛ(s) C(h) 1 γ 1 γ + θ l(h)1 γ 1 γ C s (h) 1 = 1, S C s (h)p s = E(h) wh(1 l(h)). s=1 The las line describes an individual s budge consrain, and P s is he price level in secor s. w is he exogenous wage rae, and h(1 l(h)) is he efficiency labor supply. We solve he opimizaion problem above in he Appendix A.1. The secoral consumpion can be obained as: C s (h) = E(h)P s P 1 C (h) ɛ() ɛ(s). I is sraighforward o show ha consumpion demand decreases wih secoral price and increases wih expendiure level. By subsiuing C s (h) above ino he expression of implici consumpion in equaion 1, we have E(h) 1 = P 1 C(h) ɛ(). (2) 6

7 Therefore, secoral consumpion can be furher rewrien as C s (h) = E(h) C(h) ɛ(s) Ps. The elasiciy of wage rae agains he secoral level consumpion demand C s (h) can hus be expressed as: ln C s (h) ln w ln C(h) ln E(h) = (ɛ(s) ) + ln w ln w, (3) S =1 P 1 C (h) ɛ() = (ε (s) ) S =1 ɛ() 1 P 1 C (h) ɛ() +. (4) A number of feaures sand ou from our seing. Firs, differen from Masuyama [2015] and ohers, income is no longer exogenous in our model, bu insead depends on he labor supply decision made by he individual. Therefore, i is no suiable o define an income elasiciy in his paper, and insead we define elasiciy of human capial endowmen agains secoral consumpion demand in a laer secion. Second, if we rank secors according o he value of ɛ(s) in ascending order, hen secors of a higher index have a higher value of ɛ. We resric he analysis o he case where 0 < ɛ(s) < and > 1. I is sraighforward o show ha he elasiciy of he wage rae agains secoral-level consumpion increases wih he secor index. Moreover, he firs par of equaion 4 can be shown o be less han 1 in he secor wih he lowes index, and larger han 1 in he secor wih he highes index. Specifically, we have ln C 1 (h) ln w < 1 and ln C S (h) ln w > 1. The implicaion is ha Secor 1 is he leas wage-elasic secor, wih elasiciy less han one, and secor S is he mos wage-elasic secor, wih elasiciy greaer han one. Moreover, in any secor s, wage elasiciy posiively depends on he individual human capial level. Tha is, secoral consumpion is more elasic for individuals wih higher human capial. We can also show ha secoral price elasiciy is independen of individual human capial 7

8 level and equal o : ln C s (h) ln P s =. A a lower ier, secoral consumpion is a homoheic CES aggregaor of all he varieies available in he secor. Specifically, he consumpion level in secor s for an individual wih human capial h, C s (h), can be expressed as: [ C s (h) = c s (v, h) σ 1 σ v Ω s dv ] σ σ 1, where c s (v, h) denoes he consumpion level for variey v wihin secor s for an individual wih human capial h, and σ is he elasiciy of subsiuion among all he varieies in secor s. Condiional on he secoral consumpion demand C s (h) for an individual wih human capial h, he demand for a single variey wihin secor s can hus be obained by solving he following expendiure minimizaion problem: min p s (v)c s (v, h)dv D s(v,h) v Ω s [ s.. c s (v, h) σ 1 σ v Ω s dv ] σ σ 1 = C s (h), where p s (v) is he price level for variey v in secor s. The soluion yields: c s (v, h) = C s (h) v Ω s p s (v) 1 σ dv p s(v) σ 8

9 We define he secoral price index P s as: Producion [ ] 1 P s = p s (v) 1 σ 1 σ dv. v Ω s Producion wihin each secor is characerized as monopolisic compeiion. Each firm is he single producer of a variey. Following Krugman [1980], firms are all idenical wihin each secor. Labor is he only inpu of producion. To produce one uni of variey in secor s requires ψ s uni of labor. Free enry ino each secor is assumed, and φ s labor is required as he enry cos ino secor s. Solving a monopoly firm s profi maximizaion problem by aking he individual worker s demand funcion as given yields: σ p s (v) = wψ s σ 1. Free enry condiion implies ha each individual firm s sales revenue shall equal he sum of producion and enry coss. Tha is: p s (v) D s (v) ψ s D s (v) w = wφ s. D s (v) is he oal demand for variey v, which is he sum of all individual workers demands: D s (v) = N c s (v, h)dg(h). The quaniy being produced for each variey in secor s can be solved from he free-enry 2 The secor-level price level P s is he cos o obain one uni of secoral oupu, which is essenially he soluion o he following expendiure minimizaion problem: min p s (v)c s (v, h)dv v Ω s [ v Ωs ] s.. c s (v, h) σ 1 σ σ 1 σ dv = 1, 9

10 condiion as: D s (v) = (σ 1)φ s ψ s. Toal secoral sales revenue hus equals I s wσφ s, where I s denoes he number of firms in secor s. By equalizing above wih he oal expendiure on goods from secor s, we have: I s wσφ s = N P s C s (h)dg(h). The number of firms in secor s can hus be pinned down from he equaion above. 2.3 Equilibrium in a Closed Economy We resric he analysis o a closed economy and summarize our equilibrium definiion in his subsecion. Definiion Given {φ s, ψ s } and wage rae w, he compeiive equilibrium consiss of a series of prices {p s (v), P s }, consumpion quaniies {C s (h), c s (v, h)}, he number of firms in each secor I s, and he labor supply decision made by each individual l(h), such ha he following condiions hold: 1. Given {p s (v), P s }, each individual worker maximizes his uiliy by choosing C s (h), c s (v, h) and l(h). 2. Given he aggregae demand funcion from individual workers, each monopoly firm chooses he price of he variey o maximize is profi. 3. Free enry condiion holds. In Appendix A.1 solving he individual uiliy maximizaion problem can also yield he expression for leisure choice: [ s l(h) = C(h) (ɛ(s) ) ] C(h)ɛ(s) 1 Ps 1 1 θe(h) γ wh(1 ) (5) 10

11 We furher explore he relaion beween human capial endowmen and labor supply, in addiion o oal expendiure, in he following proposiion. Proposiion 1 In a closed economy, boh leisure choice and expendiure level increase wih human capial endowmen. Moreover, he elasiciy of human capial agains labor supply or oal expendiure is less han 1 when he following condiion holds: Proof See he Appendix. ɛ(s) 2 < γ 1 2 If γ and are high enough, which corresponds o a higher risk aversion coefficien or price elasiciy, hen he above inequaliy is more likely o hold. When γ and are sufficienly large, i can be shown ha boh leisure and income(e(h)) are increasing wih he human capial level. As discussed before, because income is endogenous in our seing, we insead define an elasiciy of human capial endowmen agains secoral consumpion as follows: ln C s (h) ln h = ln C s (h) ln E(h) (6) ln E (h) ln h { } { } S s=1 = (ε (s) ) P s 1 C (h) ɛ(s) S ɛ(s) s=1 P 1 1 s C (h) + 1 l(h) ln l(h). ɛ(s) 1 l(h) ln h }{{}}{{} wage elasiciy elasiciy of human capial agains labor supply (7) We can decompose human capial elasiciy as defined above ino wo pars: wage elasiciy and he elasiciy of human capial agains labor supply. Noe ha when leisure is no included in he uiliy funcion (θ = 0), our expression can be reduced o wage elasiciy. In addiion, when ɛ(s) is no longer secor-specific, he wage elasiciy erm reduces o one and hus he elasiciy of human capial agains labor supply dominaes. From Proposiion 1, we have already proved ha when and γ are sufficienly large, labor elasiciy is wihin he range 0 o 1. Therefore, human capial elasiciy is smaller han wage elasiciy. In addiion, we have shown earlier ha wage elasiciy agains consumpion demand for secor S is larger han 1, which may no longer be rue for human capial elasiciy afer aking ino accoun 11

12 he effecs of endogenous labor supply. This resul implies ha consumpion demand is less responsive o changes in human capial han in wage levels. 2.4 Trade Equilibrium and Paerns of Trade We apply he seing o an open economy wih wo counries, Counry 1 and 2. The wo counries are idenical in every aspec excep for he iniial human capial disribuion. We le he disribuion in Counry 2 firs-order sochasically dominae ha of Counry 1. Therefore, Counry 2 is denoed as a more alened economy, as i comprises more individuals wih higher human capial. Sandard iceberg rade cos assumpion applies. To deliver 1 uni of goods from counry j o i, τ ij > 1 unis of goods need o be shipped. Counry j s demand for a variey produced in secor s of counry i can hus be solved as: D ij s (v) = N j h h Ej (h) C j (h) εj(s) dg (h) Ps j σ p ij s (v) σ. The price for a variey sold o counry j from secor s of counry i is hus: s (v) = τ ij w i ψ i σ s σ 1. p ij Moreover, he free-enry condiion in counry j implies: i [ p ji s (v) q ji s (v) τ ji ψ j sq j s (v) w j ] = w j φ j s. In a closed economy, he wage rae is assumed o be exogenous. In he case of an open economy, he relaive wage beween he wo counries will be pinned down by he rade balance in each counry: w j L j = J i=1 s V s j D ji s (v) p ji s (v) J j=1 s V s j Ds ji (v) p ji s (v) wi L i, j {1, 2} The ne expor value in secor s of counry i is he value of goods sold o counry j minus 12

13 he value of goods purchased from counry j, which can be expressed as NX i s = V i s D ij s (v)p ij s (v) V j s D ji s (v)p ji s (v). (8) We denoe m i s o be he expendiure share on secor s in counry i, and L e i oal efficiency labor supply in counry i. These can be expressed as: o be he E m i i s = s (h) dg i (h) E i Ei (h) dg i (h) = (h) C i (h) ε(s) (Ps) i 1 dg i (h), (9) Ei (h) dg i (h) L e i = N i h(1 l(h))dg i (h). (10) In he Appendix A.3, we show in deail ha he general formula for he ne expor value in counry i can be expressed as: { NXs i = ρl e jw j m i sω ω σ ρ L e i L e j ωσ m j s 1 ρω σ }, (11) where ω = wi w j and ρ = τ 1 σ ij. When here are no secoral differences in he labor requiremen and enry cos, he expression above can be furher reduced o he one in Masuyama [2015]: NXs i = ρle i w i ( m i ω σ ρ s ms) j By evaluaing equaion 11, i is sraighforward o demonsrae ha changes in he following variables can conribue o a higher ne expor value: higher m i s or lower m j s; lower rade cos τ; higher raio in he efficiency labor supply L e i /L e j. Due o he non-homoheic preference srucure, individuals wih higher human capial end o proporionally spend more on secors wih a higher index. Moreover, ogeher wih 13

14 he home marke effecs proposed in Krugman [1980], hese resuls imply ha he more alened counry ends o be a ne exporer of goods from he secor wih higher index. 3 Quaniaive Analysis We quanify he model in his secion. We resric he analysis o a wo-counry seing, where counries are idenical in every aspec excep for he disribuion of he iniial human capial endowmen. The purpose is o examine how non-homoheic preference srucure, he asymmery of human capial disribuion, endogenous labor supply, and rade liberalizaion affec he economy from differen perspecives. A he aggregae level, we focus on he impacs on GDP, income inequaliy as well as erms of rade for boh counries. A he secoral level, we focus on he disribuion of employmen, number of firms, and sales revenue across secors. Finally, a he individual level, we explore how individuals a differen perceniles of human capial disribuion are affeced in erm of heir consumpion, income, uiliies, ec. 3.1 Parameerizaion We calibrae he model ino a closed economy. We le human capial disribuion follow a Pareo disribuion defined over [h, ): G(h) = 1 ( h h )α, where α > 0 governs he skewness of he disribuion. The parameer seing in he case of wo counries only differs from he closed economy in he disribuion of iniial human capial and iceberg rade cos, which will be specified laer in his secion. We le he number of secors be hree. The daa counerpar refers o he agriculure, manufacuring and service secor, respecively. We normalize he populaion size o be 1. γ governs he risk-aversion coefficien, and we follow he lieraure in seing i a 2. σ capures secoral-level price elasiciy. We assume σ is larger han o mimic he fac ha differeniaed goods are closer subsiues wihin each secor han across secors. We le σ equal 6 and equal 4, 14

15 so hey are consisen wih he range commonly used in he lieraure. We normalize he labor requiremen in he manufacuring secor ψ 2 o be 1. Similarly, we also normalize he enry cos in he manufacuring secor φ 2 o be 1. The minimum human capial level (h) is se a 1. The remaining parameers include {ψ 1, ψ 3, φ 1, φ 3, ɛ 1, ɛ 2, ɛ 3, α, θ}. We calibrae hem o simulae a hypoheic economy wih he following disincive feaures. ψ 1 and ψ 3 are he uni labor requiremen for he agriculural and service secors, respecively. We calibrae hem o mach an equal employmen share (1/3) in each secor. φ 1 and φ 3 are he enry coss in erm of labor requiremen in he agriculural and service secors, respecively. Similarly, we calibrae hem o mach an equal fracion (1/3) of firms in each secor. As shown before, ɛ i (i = 1, 2, 3) reflecs he wage elasiciy of secor i. We follow Markusen [2013] o arge a wage elasiciy of 0.65 in he agriculure secor, 1.0 in manufacuring secor, and 1.7 in service secor. Finally, θ conrols he preference for consumpion agains leisure, and is chosen o mach a 1/3 fracion of leisure ime on average among all agens. α is he shape parameer of he Pareo disribuion. We have i mach a raio of 3.2 beween he 90h and 10h percenile of he income disribuion. In he wo-counry case, we firs le he human capial disribuion of Counry 2 firsorder sochasically dominae ha of Counry 1, which implies Counry 2 is a more alened counry. We se he shape parameer (α) in Counry 2 o be 20 percen lower han ha in Counry 1, while keeping he scale parameer (h) he same beween he wo counries. Secondly, we calibrae he iceberg rade cos parameer τ o mach an average 30 percen of rade share. We summarize he calibraed parameer values in Table 1. Given he benchmark parameerizaion, we numerically solve he model. The algorihm involves firs obaining demand a he upper ier: given he wage rae and secoral prices, we solve for secoral consumpion and leisure choice. A he lower ier, given he secoral consumpion, we solve for demand agains each variey. On he producion side, we solve for firm disribuion across secors using free-enry condiions. Finally, marke clearing condiions pin down wages and secoral prices. The benchmark resuls are repored in Table Noe ha he benchmark resuls differ from he calibraion arges in he disribuion of employmen and firm numbers because we now open up he economy. 15

16 Para. Sources/Targes Para. Value ψ 1 employmen share in agriculure secor 0.78 ψ 2 normalizaion 1 ψ 3 employmen share in service secor 1.04 φ 1 number of firm share in agriculure secor 1.45 φ 2 normalizaion 1 φ 3 number of firm share in service secor 0.46 ɛ 1 wage elasiciy in agriculure secor 0.5 ɛ 2 wage elasiciy in manufacure secor 1.25 ɛ 3 income elasiciy in service secor 1.90 α income 90/10 raio 2.02 θ share of leisure ime 0.16 σ elasiciy of subsiuion wihin secors 6 price elasiciy 4 γ risk aversion coefficien 2 Table 1: Benchmark Parameerizaions Noe: We calibrae he secoral labor requiremen and enry fee o mimic an even disribuion of employmen and he number of firms across secors in a closed economy. The elasiciy of subsiuion is chosen o mach he income elasiciy of agriculural, manufacuring, and service goods esimaed in he lieraure. The shape parameer in he less alened counry is calibraed o mimic a income raio a 3.2. The iceberg rade is chosen o mach an average 30 percen of rade share in boh counries. Oher parameers we choose eiher by normalizaion or by following he lieraure. For more deails, see he main ex. In he op panel, we presen he aggregae resuls. Boh GDP and per-capia GDP in Counry 2 are 1.17 imes of hose in Counry 1. The main reason is ha Counry 2 is a more alened counry wih higher human capial sock, and hus he efficiency labor supply is more ample. These feaures push up he oal labor income, which equals o GDP in his seing due o he free enry condiion. As he populaion size is equalized in boh counries, higher GDP necessarily resuls in higher per-capia GDP. If we define he rade share as he fracion of expendiure on impored goods, our resuls sugges ha rade share in Counry 1 is larger han in Counry 2. This difference is mainly driven by he larger marke size of Counry 2. As a resul of he home marke effec, more varieies are produced in Counry 2 han in Counry 1. Individuals in Counry 1 hus spend proporionally more on goods produced in Counry 2. We measure inequaliy using he coefficien of variaion in individual income and consumpion, as well as he income raio. Because human capial disribuion is more dispersed in Counry 2 han Counry 1, i is no surprising o 16

17 GDP Trade Share CV Inc. CV Cons Inc.R. Counry Counry Counry 1 Counry 2 Sec 1 Sec 2 Sec 3 Sec 1 Sec 2 Sec 3 Employmen Expendiure Firm Dis Trade Share Counry 1 Counry 2 Boom Median Top Boom Median Top Uiliy Consumpion Leisure Income Table 2: Benchmark Resuls Noe: In he op panel, we presen benchmark resuls for he aggregae variables including GDP and rade share, as well as inequaliy measures in income and consumpion. In he middle panel, we presen benchmark resuls on secoral disribuion in erms of employmen, expendiure, and firm numbers. We also repor secoral prices and ne expors. In he boom panel, we selec individuals wih human capial in he boom 10, median and op 10 percenile of he disribuion in each counry, and compue heir uiliies, consumpion, leisure, and income levels. For more deail, see he main ex. find ha Counry 2 exhibis larger inequaliy in boh income and consumpion. In he middle panel, we repor he secoral resuls. Employmen share and he fracion of firms in Secor 3 dominae in boh counries. Counry 1 has a higher (lower) employmen share and fracion of firms in Secors 1 and 2 (3), while expendiure share for Secor 3 appears o be he highes in Counry 2. The simulaion resuls are consisen wih our heoreical predicions. Because Secor 3 is he one wih he highes human capial elasiciy, and human capial disribuion in Counry 2 has a hicker righ ail han ha of Counry 1, i would seem ha he demand for varieies produced in Secor 3 is higher in Counry 2 han Counry 1. Due o he home marke effec, Counry 2 should have a larger Secor 3. The second o las row also repors he ne expor value in each secor. Trade balance is mainained wihin each counry bu no wihin each secor. Our resuls sugges ha Counry 1 is a ne exporer of goods produced in Secors 1 and 2, while Counry 2 is a ne exporer of goods 17

18 produced in Secor 3. In he boom panel, we selec individuals wih human capial endowmen in he boom 10 percenile, median and op 10 percenile of he disribuion in each counry. I is ineresing ha individuals a he boom of he disribuion enjoy higher uiliies and consumpion in Counry 1, whereas he paern is reversed a he median and op percenile of he disribuion. 4 These resuls are largely due o he fac ha he price index in Secor 1 is lower in Counry 1 han in Counry 2. Individuals in he boom percenile of he human capial disribuion proporionally spend more on Secor 1 han on oher secors and hus consiue he major demand for goods produced in Secor 1. Counry 1 has more individuals a he lower end of he disribuion, which also explains why Counry 1 has more labor and firms in Secor 1 han Counry 2. Therefore, he secoral price in Secor 1 should be lower in Counry 1. In addiion, because Counry 1 is a major exporer of goods produced in Secor 1, individuals from Counry 2 need o pay he exra iceberg rade cos o impor from Counry 1, which furher lowers heir consumpion level and uiliies. 3.2 Counerfacual Exercises To furher evaluae he role of asymmeric human capial disribuion, endogenous labor supply decision, non-homoheic preferences, and rade in deermining oucomes a aggregae, secoral and individual levels, we perform several couner facual exercises in his subsecion by eiher seing he labor supply o be exogenous, seing preferences o be homoheic, or leing he human capial disribuion in he wo counries be idenical. Symmeric Disribuion If we le human capial disribuion in Counry 2 be idenical o ha of Counry 1, Counry 2 hen becomes less alened han is benchmark counerpar. I is hus no surprising o observe ha GDP in Counry 1 slighly increases, while GDP in Counry 2 declines by 14.3 percen relaive o is benchmark level as shown in Table 3. 4 Since he human capial disribuion are differen in he wo counries, and hus he corresponding human capial levels a each percenile are differen in he wo counries. The human capial level for individual a boom 10 percenile in counry 1 is higher han ha in counry 2. However, he resuls ha individuals a he boom percenile obain higher uiliies han hose in counry 2 sill remain even hough we focus on he individuals wih he lowes human capial, which are he same in he wo counries. 18

19 GDP Trade Share CV Inc. CV Cons Inc.R. Bechmark Counry Counry Symmeric Disribuion Counry Counry Homoheic Preference Counry Counry Exogenous Labor Supply Counry Counry Auarky Counry Counry Table 3: Couner-facual Resuls: aggregae Noe: We compare aggregae resuls from he benchmark economy wih several couner facual economies, including symmeric human capial disribuion, exogenous labor supply, homoheic preferences and an auarky case. For more deails, see he main ex. The rade share in boh counries has declined. When human capial disribuion becomes symmeric, he wo counries are essenially idenical in every aspec. Hence, rade balance is expeced wihin each secor, as is shown in Table 4. Such a rade balance may in urn lower he aggregae rade share. In erm of inequaliy measures, Counry 2 has seen a decline in boh income and consumpion inequaliy as a resul of less dispersed human capial disribuion, while inequaliy measures in Counry 1 remain sable relaive o benchmark levels. In addiion, when here are fewer alened individuals in Counry 2, he non-homoheic preference srucure ensures ha he demand for varieies in Secor 3 declines he mos among he secors in Counry 2. Therefore, Secor 3 in Counry 2 has grealy shrunk as shown in Table 4. Moreover, Table 4 suggess ha he employmen share and he fracion of firms in Secors 1 and 2 have shrunk in Counry 1 and expanded in Counry 2. The expendiure share does no change much in Counry 1, while less is spen in Counry 2 on Secor 3 o 19

20 Counry 1 Counry 2 Secor 1 Secor 2 Secor 3 Secor 1 Secor 2 Secor 3 Bechmark Employmen Expendiure Firm Dis Ne Expor Prices Symmeric Disribuion Employmen Expendiure Firm Dis Ne Expor Prices Homoheic Preference Employmen Expendiure Firm Dis Ne Expor Prices Exogenous Labor Supply Employmen Expendiure Firm Dis Ne Expor Prices Auarky Employmen Expendiure Firm Dis Ne Expor Prices Table 4: Couner-facual Resuls: secor Noe: We compare secoral-level resuls from he benchmark economy wih several couner facual economies, including symmeric human capial disribuion, exogenous labor supply, homoheic preferences and an auarky case. For more deails, see he main ex. compensae for higher expendiure on oher secors. A he individual level, because he wo counries become symmeric, he seleced indi- 20

21 Counry 1 Counry 2 Boom Median Top Boom Median Top Bechmark Uiliy Consumpion Leisure Income Symmeric Disribuion Uiliy Consumpion Leisure Income Homoheic Preference Uiliy Consumpion Leisure Income Exogenous Labor Supply Uiliy Consumpion Leisure Income Auarky Uiliy Consumpion Leisure Income Table 5: Couner-facual Resuls: individual Noe: We compare individual-level resuls from he benchmark economy wih several couner facual economies, including symmeric human capial disribuion, exogenous labor supply, homoheic preferences and an auarky case. For more deails, see he main ex. viduals hus obain he same levels of consumpion, income, and uiliies in each counry. Noe ha i is no a fair comparison beween he benchmark and he couner-economy for seleced individuals in Counry 2; he cuoff human capial levels a each percenile vary when he human capial disribuion changes, so we are no comparing he same individual in boh economies. Therefore, we only focus on resuls for individuals in Counry 1. In 21

22 comparison wih he benchmark economy, uiliies and consumpion levels become lower for all individuals. This resul is due o higher price levels, as shown in Table 4, because of less efficiency labor supply and smaller marke demand. The only excepion sems from he higher income levels for individuals a he median and op-10 percenile of he disribuion compared o he benchmark counerpar, likely because higher price levels induce less leisure and higher nominal wage in he counry. However, despie rising incomes, living sandards sill worsen in he counerfacual economy. Non-homoheic Preferences We examine he role of non-homoheic preferences by looking ino an alernaive economy, where ɛ(s) is idenical across all secors and akes he average value among heir benchmark counerpars. Table 3 suggess ha aggregae saisics such as GDP and rade share do no differ much from he benchmark levels. Under homoheic preferences, human capial elasiciy no longer increases wih he secor index. Therefore, individuals wih higher human capial do no proporionally spend more on goods from secors wih a higher index. As a resul, he disribuion of consumpion become more even and less dependen on he human capial disribuion. A he secoral level, when human capial elasiciy becomes independen from he secor index, he disribuional impacs on secoral consumpion demand are compleely eliminaed. Similar o hose rade models wih homoheic CES preferences and monopolisic compeiion, only aggregae expendiure maers in deermining secoral demand. Because secors are only differen in heir uni labor requiremen and enry cos, and are idenical in boh counries, as a resul, homoheic preference srucure enails an idenical resource disribuion beween he wo counries, as shown in Table 4. In addiion, employmen, number of firms and he expendiure become almos evenly disribued across secors in he couner facual economy. This resul implies ha non-homoheic preference srucure grealy conribues o he dispersion of resource disribuion across secors. Noe ha he ranking in he size of each secor also changes, wih Secor 3 sill being he larges, bu followed by Secor 1 and 2. In all oher couner facual exercises, he ranking remains he same as in he benchmark economy. Trade balance is also mainained wihin each secor. When human capial elasiciy does no depend on he secor index, Counry 2 has larger 22

23 marke demand for each secor, and hus secoral-level prices are all cheaper in Counry 2 han in Counry 1, as shown in Table 4. This resul explains why individuals a he boom percenile of he disribuion from Counry 1 are no longer beer off han hose from Counry 2, as shown in Table 5. Comparing price levels wih heir benchmark counerpars, i can be seen ha price levels become higher in Secor 3 and lower in he remaining secors. This resul again is due o he reducion in he overall demand for Secor 3, because of he shif in preference srucure. As expendiure share does no vary over individual s human capial level 5, he uneven changes in secoral price levels may exer an uneven impac on each individual s leisure choice: individuals a he boom may proporionally spend more on Secor 3 han in he benchmark economy, and so hey need o reduce heir leisure ime o overcome he higher price level in Secor 3. In conras, individuals a he median and op par of he disribuion may manage o increase heir leisure ime and hus may no need o spend as much as in he benchmark case on Secor 3, plus he price levels in Secor 1 and Secor 2 also become cheaper. This argumen is suppored by Table 4. Endogenous Labor Supply We shu down he endogenous labor supply decision by seing θ equal o zero, and hus each individual inelasically supplies one uni of labor. Table 3 suggess ha all aggregae saisics become significanly higher han in he benchmark counerpar. When leisure is no considered, he efficiency labor supply in each counry grealy increases, which resuls in higher GDP. Our heoreical resuls predic ha labor supply decreases wih he human capial level. Tha is, in he benchmark economy, more alened individuals enjoy more leisure ime. In conras, when each individual insead inelasically supplies one uni of labor in he couner-economy, inequaliy in boh income and consumpion will grealy increase. A he secoral level, Secor 3 becomes much larger in erms of employmen, expendiure, and he number of firms in he couner-economy. The resuls are suppored by our expression of human capial elasiciy derived in Equaion (7). In he benchmark economy, he elasiciy of human capial agains leisure choice is beween 5 In he case of CES preferences, he secoral expendiure for any individual becomes: m s = P 1 s p1 23

24 0 and 1, which causes he human capial elasiciy for each secor o be lower han in he case of exogenous labor supply. Moreover, when labor supply is exogenous, he elasiciy of human capial agains consumpion demand equals wage elasiciy, and is proved o be larger han 1 in Secor 3. Therefore, Secor 3 becomes more dominan in resource disribuion. In erms of rade paern, Counry 1 is sill he ne exporer of goods produced from Secors 1 and 2. The rade volume becomes significanly higher han in he benchmark economy due o more efficiency labor supply and hus larger marke sizes. Despie lower price levels in Secors 1 and 2 of Counry 1, individuals a he boom percenile of he disribuion from Counry 1 become worse off han hose in Counry 2, which is differen from he findings in he benchmark economy. This resul occurs because a majoriy of he expendiure share is devoed o Secor 3, whose price level is lower in Counry 2. I may also be parially due o he lack of a rade-off beween leisure and consumpion. In he benchmark resuls, individuals a he boom of he disribuion in Counry 1 are found o enjoy more leisure ime han hose in Counry 2. Auarky In his exercise, we evaluae he role of rade liberalizaion. We le he parameer of iceberg rade cos increase o a sufficienly high value, so ha he rade share in boh counries is close o zero. When rade is no allowed, he number of varieies available in boh counries will significanly drop, and hus he price index increases. Our resuls show ha nominal GDP appears o be higher han in he benchmark case, likely because individuals end o provide more labor in he even of a higher price index. However, his resul does no necessarily imply a higher living sandard, as shown in Table 5. Table 4 suggess more labor is reallocaed from Secor 1 o Secor 3 of Counry 2 when rade fricion decreases. The exacly opposie paern is observed in Counry 1, which suggess Counry 2 becomes more specialized in Secor 3, and Counry 1 more specialized in Secor 1, in he process of rade liberalizaion. To examine he role of rade liberalizaion in wihin and beween counry inequaliy, our resuls in Table 3 sugges ha rade liberalizaion ends o reduce consumpion and income inequaliy wihin each counry. When price levels become lower, individuals wish o increase heir leisure ime, and hus hose wih higher human capial will lose more income given he 24

25 same magniude of decline in labor supply. This resul explains he lower inequaliy wihin he counry. Our resuls in Table 5 also indicae ha rade liberalizaion ends o shrink he gap in living sandards beween he counries. In he auarky case, he relaive uiliies beween he wo counries for individuals a he op 10 percenile of he disribuion is 0.515/( 0.653) = 0.789, and he number becomes and for individuals a he median and boom of he disribuion. In he benchmark economy, hose raios all become closer o 1 a 0.796, and 0.992, respecively. Moreover, a furher look a he uiliy gain for differen individuals suggess he following: from auarky o he benchmark economy, uiliies for individuals a he op 10 percenile of he disribuion increase by 2.6 percen in Counry 2, compared wih 1.75 percen in Counry 1. In conras, uiliies for hose a he boom of he disribuion increase by 2.67 percen in Counry 1, compared wih 2.16 percen in Counry 2. Tha is, he more alened individuals benefi more from saying in Counry 2, and less alened ones benefi more from saying in Counry 1. Moreover, he boom ones benefi proporionally more han alened individuals in boh counries, which may provide furher evidence for he decline of he wihin-counry inequaliy. Two major sources conribue o he shrinking gap beween he counries: 1) Counry 1 gains access o a larger marke in he even of rade liberalizaion han Counry 2;. 2) Counry 1 is a ne exporer of Secors 1 and 2, while Counry 2 is a ne exporer of Secor 3. More han half of he oal expendiure in he economy is sill devoed o Secors 1 and 2. Therefore, rade liberalizaion proporionally induces more firm enries ino Secor 1 of Counry 1 han ino Secor 3 of Counry 2. As a resul, he price index in Secor 1 in Counry 1 should proporionally decrease more. As shown in Table 4 in he benchmark economy, he price level of Secor 3 in Counry 2 is percen of ha in auarky, while he number becomes percen for Secor 1 in Counry 1. Therefore, as he major exporer of Secor 1 and 2, Counry 1 benefis more from rade liberalizaion han Counry 2. 25

26 4 Conclusion In his paper, we have developed a rade model wih monopolisic compeiion, non-homoheic preference srucure, heerogeneous agens, and endogenous labor supply. Individuals differ in heir human capial endowmen, and he wo counries are idenical excep for he disribuion of human capial. We apply he heoreical framework o quaniaively examine how preference srucure, elasic labor supply, asymmery in disribuion and rade liberalizaion affec economic performance a he aggregae, secoral, and individual level. The major findings are as follows: he more alened counry ouperforms he oher in erms of GDP and average living sandards, due o a larger marke size. However, individuals from he boom percenile of he disribuion may be beer off han hose from he more alened counry. The resource disribuion becomes idenical in boh counries when eiher asymmeric disribuion or non-homoheic preferences are removed. When labor supply becomes exogenous, resource disribuion ends o become more dispersed and inequaliy widens. Trade liberalizaion ends o reduce inequaliy wihin and beween counries. References Blackorby, C., and R. R. Russell (1981): The Morishima elasiciy of subsiuion; symmery, consancy, separabiliy, and is relaionship o he Hicks and Allen elasiciies, The Review of Economic Sudies, 48(1), Buera, F. J., and J. P. Kaboski (2009): Can radiional heories of srucural change fi he daa?, Journal of he European Economic Associaion, 7(2-3), Comin, D., D. Lashkari, and M. Mesieri (2015): Srucural Change wih Long-run Income and Price Effecs, Discussion paper. Duare, M., and D. Resuccia (2010): The role of he srucural ransformaion in aggregae produciviy, The Quarerly Journal of Economics, 125(1), Eaon, J., and S. Korum (2002): Technology, geography, and rade, Economerica, 70(5),

27 Krugman, P. (1980): Scale economies, produc differeniaion, and he paern of rade, The American Economic Review, 70(5), Markusen, J. R. (2013): Puing per-capia income back ino rade heory, Journal of Inernaional Economics, 90(2), Masuyama, K. (2000): A ricardian model wih a coninuum of goods under nonhomoheic preferences: Demand complemenariies, income disribuion, and norh-souh rade, Journal of Poliical Economy, 108(6), (2015): The Home Marke Effec and Paerns of Trade Beween Rich and Poor Counries, Discussion paper. Meliz, M. J. (2003): The impac of rade on inra-indusry reallocaions and aggregae indusry produciviy, Economerica, 71(6), A Appendix A.1 Solving he Individual Opimizaion Problem An individual worker of human capial h solves he following opimizaion problem: s. max C (h)1 γ + θ l (h)1 γ 1 γ 1 γ ps C s (h) = wh (1 l (h)) We se up he following Langrange: L = C (h)1 γ 1 γ + θ l [ (h)1 γ 1 γ + λ wh (1 l (h)) ] p s C s (h) Taking firs order condiion wih respec o C s and l gives: C (h) γ C (h) C s (h) = λp s, s θl (h) γ = λ. 27

28 We differeniae C s (h) from he recursive uiliy specificaion, and hus C (h) ɛ() C (h) 1 = 1, C (h) C s (h) = = C (h) ɛ(s) 1 C s (h) 1 ɛ() C (h) ɛ() 2 C (h) 1 (1 ) C (h) ɛ(s) Cs j (h) 1 ɛ() 2 (ɛ () ) C (h) C j (h) 1 The firs order condiions hus become: C (h) γ (1 ) C (h) ɛ(s) C s (h) 1 ɛ() 2 (ɛ () ) C (h) C (h) 1 = θl (h) γ p s, s (12) wh Taking he raio of wo arbirary firs order condiions wih respec o C s and C gives: C (h) ɛ(s) ɛ() ( ) 1 Cs (h) C (h) = p s p ha is, [ ] C (h) C s (h) = ps C (h) ɛ() ɛ(s) p. Subsiuing above ino he budge consrain gives: [ ] ps p C (h) ɛ() ɛ(s) C s (h) = wh (1 l (h)) p Therefore, he secoral-level consumpion can be obained as: C s (h) = wh (1 l (h)) p sc (h) = E(h)P s C s (h) ɛ(s) ɛ() ɛ(s) P 1 C(h). ɛ() p1 28

29 The expression for leisure choice can be obained as: [ ] C (h) l (h) = s [ε (s) ] C (h)ε(s) (P s ) 1 1 γ θc (h) 1 E (h). wh (1 ) A.2 The elasiciy of Human capial agains Secoral-level Consumpion Subsiuing he expression for C s (h) ino he recursive uiliy specificaion leads o: s C (h) ε(s) P 1 s E 1 (C (h) ε(s) ) 1 ( P 1 C (h) ε() ) 1 = 1 As a resul, E (h) 1 P 1 C (h) ε(). (13) Subsiuing he expression of E(h) ino he expression of C s (h) yields: C s (h) = P s E (h) C (h) ε(s) E (h) C (h) ε(s) P = 1 ε() C (h) Ps. (14) From equaion 13, we can furher have: ln C (h) ln E (h) C (h) E (h) = E (h) C (h) = P 1 ε(s) 1 C (h) ε() P 1 C (h) ε(), and from equaion 14 we can have: ln C s (h) ln E(h) ln C(h) ln E(h) = (ɛ(s) ) + ln E(h) ln E(h) = (ε (s) ) P 1 ɛ() P 1 1 C (h) ɛ() C (h) ɛ() + Therefore he elasiciy of human capial agains secoral consumpion can be obained 29