Trade Liberalization and Wealth Inequality

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1 Trade Liberalizaion and Wealh Inequaliy Kani Kuevibulvanich JOB MARKET PAPER This version: November 11, 2016 Laes version is available a hp://jobmarkepaper.kanik.com Absrac Previous sudies of he effec of rade liberalizaion on income inequaliy have yielded conflicing resuls. All of hese sudies have used comparaive saics analysis in seings wihou wealh accumulaion. None have incorporaed he dynamics of wealh accumulaion. This paper examines he dynamic effecs of rade liberalizaion on wealh inequaliy and welfare. I develop a heerogeneous agen model wih an incomplee asse marke, small open economy wih wo producion secors, specific-facor rade model wih cosly-swiching secor-specific labor and perfecly mobile capial across secor and border, and iceberg cos as he rade barrier. Measured by he Gini coefficien of wealh, rade liberalizaion, defined as he eliminaion of rade barrier, iniially increases wealh inequaliy before apering owards a more equiable wealh disribuion in he long run. However, here is a long-run increase in beween-secor wage inequaliy. The counerfacual analysis demonsraes a peak increase in wealh inequaliy of 0.8% a 3 years afer he policy implemenaion, and a 0.6% long-run decrease in he long run. Also, GDP increases by 3.7% in he long run, and households swich o he Non-radable secor. Moreover, a decrease in rade barrier for impored goods leads o an increase in GDP, households swich o he Non-radable secor, and wealh inequaliy also decreases in he long run. I also briefly discuss he welfare and poliico-economic aspecs of rade policies. Comparing he seady saes, rade liberalizaion leads o an average of 3.5% welfare improvemen across all households, as measured by he consumpion equivalen variaion. However, no all households benefi from he rade liberalizaion policy and he associaed ransiion. Keywords: Trade liberalizaion, wealh inequaliy, welfare, heerogeneous-agen model, poliico-economics JEL classificaion numbers: F10, F40, E60 Ph.D. Candidae, Deparmen of Economics, Universiy of Wisconsin-Madison, 1180 Observaory Drive, Madison, WI 53706, USA. kani.kuevibulvanich@wisc.edu, URL: hp:// I am grealy indebed o my advisor, Kenneh D. Wes, for his kind advice and never-ending encouragemen, and my commiee members, Charles Engel and Dean Corbae, for heir guidance and suggesions. I also hank Enghin Aalay, Kamran Bilir, and Rasmus Lenz for heir commens, as well as Ohyun Kwon, Dennis McWeeny, Wisaru Suwanpraser, Seve Pak Yeung Wu, and seminar paricipans a he Universiy of Wisconsin-Madison for commens and discussions. All remaining errors are mine. 1

2 1 Inroducion Wha is he effec of rade liberalizaion on wealh inequaliy in he shor and long run? Many of he exising lieraure do no sufficienly sudy he dynamics of inequaliy as a resul of rade liberalizaion. This is due o he comparaive saics seing or seady saes analysis employed by previous lieraure. None of he sudies have invesigaed he effecs owards households wealh and saving. To answer his quesion, I develop, calibrae and simulae a dynamic general equilibrium macroeconomic model wih he following feaures: (1) a small open economy wih exogenous world ineres rae and prices of Tradable goods, (2) wo secors of producion Home Tradable (TH) and Non-radable (N) secors, (3) hree ypes of consumpion and invesmen goods Home Tradable, Non-radable, and Foreign Tradable goods, (4) infiniely-lived heerogeneous households, (5) incomplee asse markes wih idiosyncraic and uninsurable unemploymen risk, (6) iceberg cos rade barriers incurring on goods raded across borders, (7) perfecly mobile capial across borders and secors, (8) capial accumulaion and a capial marke where households saving or borrowing is aggregaed, and (9) secor-specific labor supply in wo secors of producion wih cosly secor swiching. These feaures provide a rich framework o analyze boh he shor-run and long-run effecs of rade liberalizaion. Trade liberalizaion and inequaliy have been wo of he mos polarizing subjecs in boh economic and poliical discussions. Zhu and Trefler (2005) apply rade and wage daa from he World Trade Daabase o a mixure of comparaive advanage and endowmen-based rade models. They find rising wage inequaliy in boh Norhern and Souhern counries. This is due o he shifs in producion from he leas skill-inensive Norhern o he mos skill-inensive Souhern, decreasing he demand for leas-skilled workers in he Norh and increasing he demand for skilled labor in he Souh. Helpman, Iskhoki and Redding (2010) consruc a heerogeneous firm model wih rade and find ha wage inequaliy is higher in rade equilibrium han in auarky. The iniially closed economy experiences he increases in wage inequaliy, due o dispersion of firm revenue, when open o rade. There are wo opposing forces he falling beween-group wage inequaliy and he rising wihin-group wage inequaliy, boh of which are he resul of reallocaion of resources. A counerfacual analysis by Helpman e al. (2014) using Brazilian daa finds ha exporer saus, in addiion o differences beween firms, raises wage inequaliy by en percen. They also nearly mach he Gini coefficien of wage inequaliy in Brazil. Aruç, Chaudhuri, and McLaren (2010) finds ha welfare improves afer rade liberalizaion. The auhors consruc a macroeconomic-syle model wih uiliy-maximizing households and he mechanism of cosly iner-secorial labor mobiliy. To simulae he rade liberalizaion, specific ariff iniially applied o 2

3 world oupu price of he secor of ineres is removed. They find in he U.S. Curren Populaion Survey daa ha, alhough he impor-compeing secor experiences lower wages afer rade liberalizaion, he welfare gain occurs from he increase in he opion value of swiching ou of he secor in which rade is liberalized. The original work on he poliical economy of inernaional rade was done by Grossman and Helpman (1994). In heir model of saic muli-secor economy, special ineres groups lobby he own-welfare maximizing governmen for rade proecion. Ossa (2014) documens he opimal ariff incenivized by he posiive erms-of-rade effec due o he increase in relaive wages and high-profiabiliy indusries, and he rade war by means of realiaion o he ariff. I is well documened ha income equaliy can be exacerbaed by rade, bu lile is quaniaively known abou is effec on wealh inequaliy. Furhermore, rising wealh inequaliy has been observed in he U.S. daa, as Díaz-Giménez, Glover and Ríos-Rull (2011) noe he seady increase of Gini coefficien of household ne worh over ime. Trade openness and rade liberalizaion migh explain his phenomenon. Though Aruç, Chaudhuri and McLaren (2010) inroduce secor-specific capial used in producion, heir model does no analyze household wealh and saving behavior. The mos recen papers ha sudy rade liberalizaion and inequaliy dynamics are Tang (2015) and Bellon (2016), boh of which are based on enrepreneurs, firms and labor marke dynamics. Through heerogeneous enrepreneurial produciviy, Tang (2015) finds ha while inernaional rade increases aggregae oupu and workers wages, income inequaliy among enrepreneurs rises. Bellon (2016) illusraes he sylized relaionship beween wage inequaliy and rade liberalizaion. Using an even sudy analysis, he finds ha wage inequaliy is dynamically relaed o rade liberalizaion in non-monoonically fashion. Tha is, inequaliy iniially rises for 6 years afer liberalizaion. The overshooing hen apers in he nex 10 years, bu his decline is no enough o offse he iniial increase. The sylized daa are also raionalized wih he dynamic heerogeneous firms and workers screening model wih cosly labor adjusmens. Trade liberalizaion and wealh inequaliy played key roles in he Unied Kingdom s referendum o wihdraw from he European Union. Dhingra e al. (2016) esimae a welfare loss from he pos-brexi rade barriers of around 1.3% 2.6% of he UK s GDP. Once hey ake ino accoun for dynamic effecs, hey find an even larger loss of 6.3 o 9.5 percen, and likely even larger effecs due o he lack of he increase in produciviy and R&D, and verical inegraion associaed wih he EU rade. This paper seeks o address he issue of rade liberalizaion, wealh and inequaliy dynamics in he macroeconomic seings. The primary research quesion is: wha are he dynamic effecs of rade liber- 3

4 alizaion on wealh inequaliy and welfare? The key variables in focus of his paper are Gini coefficien of wealh, and households welfare changes. Unlike prior papers, my model allows for he analysis of a much wider array of aggregae-level macroeconomic variables, such as labor supply, prices, exchange rae, secor wages, GDP, secor producion, capial accumulaion and allocaion, saving, and foreign ownership of asses. Furhermore, his seing also lends he possibiliy of incorporaing he poliico-economics and households preferred policy choices ino he inernaional rade analysis. The model employs feaures from various lieraure in harmonizing micro-founded macroeconomics and inernaional rade heory. Examples include specific facors rade model, iceberg rade cos, openeconomy macroeconomics, he basic heerogeneous households seup as Hugge (1993), and he inuiion of inernaional rade and cosly labor mobiliy by Aruç, Chaudhuri, and McLaren (2010). A brief discussion on poliico-economics is due o Corbae, D Erasmo, and Kuruscu (2009). The soluion algorihm is also similar o Krusell and Smih (1998) as prices of oupus and rade barriers also deermine he aggregae sae variables of wages and capial demand, which are relaed o one anoher due o he marginal producs. The key mechanism driving he wealh inequaliy effec, apar from precauionary saving, is as follows. Lower rade barrier leads o a change in demand and supply of he hree ypes of goods. This causes a change in relaive wages and capial allocaion in each secor, causing household s income and demand for each good o change. Seeing he change in wages, households swich o he secor in which hey earn he highes income. This swich is cosly and mus be financed by asse holdings; hence, he wealh disribuion changes. The secor choices by households also change labor supply; hus, wages, capial allocaion, and prices are furher changed, creaing a feedback mechanism ha can cause even more dramaic changes in he disribuion of wealh. The remainder of his paper is srucured as follows. Secion 2 oulines he model used in he analysis, he dynamic programming problem, and he definiion of equilibrium. Secion 3 firs discusses he soluion algorihm and calibraion. I hen inroduces wo counerfacual experimens rade liberalizaion as he bilaeral eliminaion of rade barriers on boh expored and impored goods, and a unilaeral decrease in rade barriers for he impored good. Secion 4 coninues wih welfare measuremen from he wo experimens in he previous secion. The welfare effec, he poliical economy of rade liberalizaion, and myopic voing are briefly discussed. Finally, Secion 5 concludes. 4

5 2 Model The poin of deparure for he model sars as a wealh-heerogeneous agen model due o incomplee asse marke wih borrowing consrain and uninsurable idiosyncraic employmen risk as inroduced by Hugge (1993). In his model, ime flows discreely and infiniely from = 1,...,. The economy is a small open economy wih producion. The counry in consideraion is an aomisic Home counry and Foreign refers o he res of he world. Capial asses are perfecly mobile across borders and producion secors, aking he exogenous world ineres rae as given. The economy is divided ino wo secors, producing wo ypes of goods Home Tradable and Non-radable goods using capial and secor-specific labor. Households have secor-specific skills, which are cosly o acquire upon swiching secors. Three ypes of goods are demanded for consumpion and invesmen, wih Foreign Tradable good being impored. The exchange rae is defined as he Home price of he Foreign currency. All goods raded across borders are subjec o an iceberg cos of rading. 2.1 Iceberg Cos of Trading, Prices of Tradable Goods and Exchange Rae In his analysis, he price of he Foreign Tradable good has he uni of Foreign currency and is se o one as he numeraire, so ha p TF = 1. Furhermore, due o he assumpion of a small open economy, he price of he Home Tradable good has he uni of Home currency and is also se o one, so ha p TH = 1. To conver he price of he Foreign Tradable good and he value of any ransacion wih Foreign counries o he unis of he Home currency, he exchange rae E is defined as he Home currency price for Foreign currencies. A higher value of E implies a depreciaion of he Home currency. Goods which have been impored or expored are subjec o iceberg-ype cos of rading in he spiri of Samuelson (1954). In paricular, 1 τ TH arrive in he Foreign counries, and 1 τ TF in he Home counry. The rade barrier is said o be prohibiive when τ TH [0, 1] fracion of he Home Tradable goods expored acually [0, 1] fracion of he Foreign Tradable goods impored arrive = 1 and τ TF = 1. Likewise, here 5

6 is no rade barrier when τ TH = 0 and τ TF = 0. This iceberg cos is absorbed by he end users of he good. Tha is, when a Foreign Tradable good is impored ino he Home counry a he Home currency price of E p TF, he price he consumer pays for he Foreign Tradable good in period is E p TF / ( 1 τ TF ). Similarly, when a Home Tradable good priced a p TH is expored, only 1 τ TH of he expored goods are no desroyed; hus, he ne price of he expored Home Tradable good is p TH ( ) 1 τ TH. 2.2 Households Ineremporal Problem There is uni mass of infiniely-lived households ha differ by heir asse holdings, and employmen saus. Households are also differeniaed by heir secor of employmen denoed by ype i {TH, N} in period. Each household is subjec o he idenical and exogenous borrowing consrain for asse holdings a +1 such ha a +1 a. Each household chooses he plan of consumpion {c } =1, asse holdings {a +1} =1, and employmen secors {i +1 } =1 o maximize he expeced discouned sum of lifeime uiliy given by E [ β 1 u (c ) =1 ] Households have consan relaive risk aversion uiliy given by u (c) = c1 σ 1 1 σ where σ measures he degree of risk aversion. In each period, each receives a shock represening heir employmen sae ε {1, u}, where 0 < u < 1, which follows a Markov process wih ransiion funcion Pr(ε +1 ε ). Each household earns ε fracion of wage income in is respecive secor i. When ε = 1, such household is said o be employed and inelasically supplies labor o earn he full secor i wage w i. Oherwise, a household is said o be unemployed and earns uw i unemploymen benefis. Each household pays or earns real ineres on he carried-over asses a borrowed or saved from period 1 a he world real ineres rae r w. In period, a household is said o be 6

7 borrowing if i chooses a +1 < 0 and saving when a +1 > 0. Due o he idiosyncraic unemploymen risk and marke incompleeness, saving is essenial as self-insurance. In he even of household swiching from secor i o secor i in he nex period, such a household mus pay a swiching cos χ i,i. The ineremporal budge consrain of each household is herefore c + a +1 + I {i +1 = i } χ i,i = (1 + r w ) a + w i ε. Finally, he disribuion of households over asses, employmen saes, and secors a ime is Γ (a, ε, i ) Inraemporal Problem Given he opimal consumpion bundle c in period, each household minimizes is expendiure in each period by choosing he opimal combinaion of Home Tradable (TH), Foreign Tradable (TF), and Nonradable (N) goods o consume. The consumpion bundle c is a Cobb-Douglas composie baske wih 1 ν (0, 1) share of Non-radable goods and ν share of Tradable goods. The share of Tradable goods consiss of ψ (0, 1) share of Home Tradable goods and 1 ψ share of Foreign Tradable goods. The prices for he Home Tradable, Foreign Tradable, and Non-radable goods purchased by households are p TH, E p TF / ( 1 τ TF ), and p N, respecively. The inraemporal problem in period is an expendiure minimizaion problem of {c TH min,c TF,c N } [ ( p TH c TH + E p TF / 1 τ TF )] c TF + p N c N subjec o c = [ ( ) ψ ( c TH c TF ) 1 ψ ] ν ( c N ) 1 ν The Cobb-Douglas price index P is defined as P = ( p TH νψ ) νψ [ E p TF / ( 1 τ TF ν (1 ψ) ) ] ν(1 ψ) ( p N ) 1 ν. 1 ν Each household s inraemporal demand funcions for each ype of good are he sandard Cobb-Douglas demand funcions given by p TH c TH = νψp c, [ ( E p TF / 1 τ TF )] c TF = ν (1 ψ) P c, and p N c N = (1 ν) P c. 7

8 The economy-wide aggregae consumpion is defined as C = c dγ (a, ε, i ). Given he disribuion of households Γ and he independence of prices in he aggregaion, he aggregae demand funcions for each ype of good are p TH C TH = νψp C, [ ( E p TF / 1 τ TF )] C TF = ν (1 ψ) P C, and p N C N = (1 ν) P C. 2.3 Firms There are wo secors which produce wo differen ypes of goods in he Home economy Home Tradable goods and Non-radable goods denoed by i {TH, N}, respecively. The Home economy canno produce Foreign Tradable goods. In period, each represenaive firm employs labor wih secor i specific skill and rens homogeneous capial, denoed by L i and Ki, respecively. Each secor uses a Cobb-Douglas consan reurns o scale producion funcion, where α (0, 1) is he capial share and A i is secor oal facor produciviy. The oupu of secor i is herefore Y i = A i ( K i ) α ( L i ) 1 α. The cos of depreciaion is borne enirely by firms. Given he world ineres rae r w, he renal rae on capial is r w + δ. The wage rae for he employed labor in secor i is w i. Each uni of good i is sold a he price pi. Each firm maximizes is nominal profi funcion Π i = p i A i ( K i ) α ( ) 1 α [ ] L i P (r w + δ) K i + w i L i. I can be easily shown ha he capial demand and wage rae of secor i {TH, N} are K i = ( p i P ) 1 1 α ( αa i r w + δ ) 1 1 α L i and w i = ( p i P ) 1 1 α (1 α) A i ( αa i r w + δ ) α 1 α. 8

9 Due o consan reurns o scale, firms profis are zero; hus, households dividends received from he ownership of firms are zero in every period. 2.4 Labor Marke and Swiching Cos A household who receives he employmen shock ε = 1 is employed and inelasically supplies labor in he secor i currenly belongs. Thus, he oal labor supply for secor i {TH, N} consiss of all households wih skill in secor i and employmen saus ε = 1 in period and can be wrien as L i = I {i = i, ε = 1} dγ (a, i, ε ). The employmen saus shock evolves according o he Markov ransiion marix Π = Pr (ε +1 = 1 ε = 1) Pr (ε +1 = u ε = 1) Pr (ε +1 = 1 ε = u) Pr (ε +1 = u ε = u). The mass of Home households is consan a one, which rules ou immigraion and populaion growh. As a resul, he Markov ransiion marix yields a saionary unemploymen rae equal o u. Furhermore, due o he uni mass populaion, he unemploymen rae in period is u = 1 L T L N. A household which currenly belongs o secor i in period and wishes o migrae o secor i = i in period + 1 mus pay he swiching cos χ 0 proporion of he curren wage rae in secor i χ i,i = χw i. This swiching cos can be associaed wih he cos of reraining o acquire new skills required in secor i. Furhermore, i mandaorily faces ε +1 = u. Tha is, such household mus become unemployed and earn he ransfer income equals o uw i +1 in period + 1. This is in line wih he required period of job maching afer reraining. Hence, here are wo sources of swiching cos for he household who wishes o migrae from secor i o i in he nex period (1) he explici swiching cos, and (2) he implici cos of he mandaory period of unemploymen. 9

10 2.5 Capial Marke, Capial Accumulaion and Invesmen Curren asse holdings a are aggregaed over he disribuion of households ino he domesic supply of capial sock. Tha is, K domesic = a dγ (a, i, ε ). In each period, he oal capial demanded in each secors, K TH and K N, is deermined by firms profi maximizaion problem. The capial demand is saisfied by capial supplied domesically and, if insufficienly supplied, by asses borrowed from abroad K f oreign. Boh capial demand and supply are measured in he real uni of composie capial goods. Thus, capial marke clearing requires ha K TH + K N = K domesic + K f oreign. Tha is, if K TH + K N > K domesic, hen K f oreign > 0 here is Foreign porfolio invesmen in he Home counry. Oherwise, he Home counry lends o Foreign counries and owns asses abroad when K f oreign < 0. A he beginning of period, he Home economy is iniially endowed wih he domesic supply of capial sock K domesic and ne foreign capial sock K f oreign 1. Each firm demands capial K i, i {TH, N} according o is profi maximizaion problem. Suppose K TH + K N > K domesic + K f oreign 1, ha is, Home firms demand more capial han i could be supplied, hen Home economy borrows K f oreign K f oreign 1 from abroad. The oal capial sock available in he Home economy is K domesic o each secor i {TH, N} for he producion of goods, Y TH is equal o δ ( K TH + K N ) ( = δ K domesic + K f oreign depreciaion, Foreign-owned asses K f oreign + K f oreign, which is disribued and Y N. Afer producion, depreciaed capial ), which is replaced by invesmen. Afer adjusing for are carried forward o period + 1. Domesic asses, K domesic, are also reurned o households, which may choose o consume, c, or save, a +1. Savings a +1 by Home households a he end of period are aggregaed ino he domesic supply of capial sock, K domesic +1. This imeline for capial formaion and usage across ime periods can be summarized graphically in Figure 2.1. Changes in he level of capial sock in he Home counry can arise from hree sources. Firs, he domesic aggregaion of households opimal asse holdings, a +1, as deermined by households ineremporal problem,yields he domesic supply of capial sock K domesic +1 = a +1 dγ (a, ε, i ) in period + 1, less curren domesic supply of capial sock, K domesic. Second, he foreign ownership of Home asse K f oreign in period, less Foreign-owned asse K f oreign 1 carried over from period 1. Third, he depreciaed domesic 10

11 Period Period Period 1 +1 (Invesmen) + (Depreciaion) + (Invesmen) dγ + dγ Households + Decision:, Figure 2.1: Timeline of Capial Formaion and Accumulaion in Home Counry ( and foreign capial sock, δ K domesic ) + K f oreign = δ ( K TH + K N period. Capial invesmen X in he Home counry a ime is X = [ ] [ K+1 domesic (1 δ) K domesic + (1 + δ) E K f oreign ), used in he producion are replaced in ] E K f oreign 1. Noe ha he domesic capial sock is valued a he domesic price index P, while he Foreign-owned asse is valued a he price and exchange rae of E P, aking ino accoun boh domesic price level and exchange rae. From he invesmen deermined by he capial accumulaion equaion, hree ypes of goods Home Tradable, Foreign Tradable, and Non-radable are required o manufacure he capial good. Assuming ha capial good is manufacured using Cobb-Douglas echnology wih he same composiion of hree ypes of goods as in he consumers inraemporal problem in Secion 2.2.2, he expendiure minimizaion problem is {X TH min,x TF,X N } [ ( p TH X TH + E p TF / 1 τ TF )] X TF + p N X N subjec o X = [ ( ) ψ ( X TH X TF ) 1 ψ ] ν ( X N ) 1 ν. Thus, he inpu demand funcions for he producion of he capial good are p TH X TH = νψp X, [ ( E p TF / 1 τ TF )] X TF = ν (1 ψ) P X, and p N X N = (1 ν) P X. 11

12 This specificaion of invesmen and capial good manufacuring is aken from Bajona and Kehoe (2010). 2.6 Balance of Paymens The Home counry expors he residual supply of he Home Tradable good, which is he oupu of Home Tradable good, less he demand by Home consumers and capial good producion. The quaniy of expored goods is Y TH C TH X TH. I assume ha he expors of he Home Tradable good o Foreign counries are seled in he Home currency. Furhermore, due o he iceberg coss, only 1 τ TH arrive in he Foreign counry. Thus, he expored good is valued a he relaive price p TH proporion of oal expors ( ) 1 τ TH /P. Since he Home counry canno produce Foreign Tradable good, i mus be wholly impored as demanded by consumers and capial good producion. Because he price of he Foreign Tradable good is denominaed in Foreign currency, he impored good is valued a he relaive price of E p TF /P. While he price he consumer pays is E p TF / ( 1 τ TF ), he demand funcion for impors is C TF + X TF. The real ne expors in period are given by NX = ( 1 τ TH ) p TH (Y TH C TH P ) X TH E p TF ( C TF P ) + X TF. Given he consan world ineres rae r w, he exchange rae E, and he definiion of Foreign-owned Home asses K f oreign in Secion 2.5, he ne reurn on invesmen from abroad is r w E K f oreign. Tha is, if asses borrowed from abroad are K f oreign > 0, hen he ne reurn from invesmen abroad is negaive, and vice versa. Thus, combining ne expors and he ne reurn on invesmen abroad, he curren accoun in period is defined by CA = NX r w E K f oreign. Wih he definiion of he Foreign-owned Home asse, he capial and financial accoun is defined as he ne change in foreign ownership of he Home counry asses. The nominal value of Foreign-owned Home asses in period is P E K f oreign. The nominal value of he sock of Foreign-owned Home asses in period 1 is P E K f oreign 1, adjused by he curren price level and exchange rae. The real capial and financial accoun in period is given by KFA = E K f oreign E K f oreign 1. 12

13 In he seady sae, KFA = 0 since K f oreign = K f oreign 1 as prices and he exchange rae remain consan and here is no change in he ne foreign ownership of he Home asses. Thus, CA = 0 in he seady sae as well. Wih boh curren accoun and capial and financial accoun defined, he balance of paymens requires ha CA + KFA = Marke Clearing Condiions Since he Non-radable good mus be produced and consumed wihin he Home counry, he marke for he Non-radable good mus be cleared domesically. The marke clearing condiion for he Non-radable good is Y N = C N + X N. The balance of paymens encapsulaes he relaive prices, Foreign-owned Home asses, and Home demand for Home Tradable good. As described above, he balance of paymens mus be zero so ha CA + KFA = 0. The equilibrium in he labor marke is deermined by he labor demand of each secor i {TH, N} and he employed households inelasic labor supply. The labor marke clearing condiion is L TH + L N = I {ε = 1} dγ (a, ε, i ). The equilibrium in he capial marke is deermined by he capial demand of each secor and he available capial sock from Home households aggregae asse holdings and Foreign-owned asses. Therefore, he capial marke clearing condiion is K TH + K N = a dγ (a, ε, i ) + K f oreign. 13

14 2.8 Naional Income Accouning and he Aggregae Resource Consrain For he purpose of naional income accouning, real GDP can be defined using he oupu produced by each secor, labor swiching cos, and ransfer income as Y = ( p TH ) ( p Y TH N ) + Y N + P P I {i +1 = i } χ i,i dγ (a, ε, i ) + I {ε = u} w i ε dγ (a, ε, i ). Equivalenly, real GDP can also be calculaed using he income approach from wage income, ransfer income, gross reurn on capial, and labor swiching cos as Y = w i ε dγ (a, ε, i ) + (r w + δ) [ ] a dγ (a, ε, i ) + K f oreign + I {i +1 = i } χ i,i dγ (a, ε, i ). Furhermore, real GDP can also be calculaed using he expendiure approach from consumpion, invesmen, ne expors, ransfer income, and labor swiching cos as Y = C + X + NX + I {ε = u} w i ε dγ (a, ε, i ) + I {i +1 = i } χ i,i dγ (a, ε, i ). Thus, he calculaion of real GDP in all hree approaches yields he exacly he same resuls. 2.9 Recursive Formulaion In his subsecion, he model as defined in Secion is ranslaed ino a recursive formulaion Individual Decisions The value funcion for households in he Home Tradable goods secor is given by V i=th (a, ε; Γ, p) = { } max V i=th,i =TH (a, ε; Γ, p), V i=th,i =N (a, ε; Γ, p) i {TH,N} where { [ V i=th,i =TH (a, ε; Γ, p) = max u (c) + βe V i =TH ( a, ε ; Γ, p ) ]} ε c,a subjec o c + a = (1 + r w ) a + w TH ε 14

15 and { V i=th,i =N (a, ε; Γ, p) = max u (c) + βv i =N ( a, ε = u; Γ, p )} c,a subjec o c + a + χ TH,N = (1 + r w ) a + w TH ε χ TH,N = χw N. The value funcion for households in he Non-radable goods secor is given by V i=n (a, ε; Γ, p) = { } max V i=n,i =N (a, ε; Γ, p), V i=n,i =TH (a, ε; Γ, p) i {TH,N} where { [ V i=n,i =N (a, ε; Γ, p) = max u (c) + βe V i =N ( a, ε ; Γ, p ) ]} ε c,a subjec o c + a = (1 + r w ) a + w N ε and { V i=n,i =TH (a, ε; Γ, p) = max u (c) + βv i =TH ( a, ε = u; Γ, p )} c,a subjec o c + a + χ N,TH = (1 + r w ) a + w N ε χ N,TH = χw TH. The households expecaion of employmen opporuniies is governed by he Markov ransiion marix Π = Pr (ε = 1 ε = 1) Pr (ε = u ε = 1) Pr (ε = 1 ε = u) Pr (ε = u ε = u). The soluion o he households problem gives policy funcions for consumpion, asse holdings, and secor choices which are c = c (a, ε, i; Γ, p), a = g (a, ε, i; Γ, p), and i = ι (a, ε, i; Γ, p), respecively. 15

16 2.9.2 Aggregae Variables The economy-wide aggregae consumpion, asse holding, and domesic supply capial sock are C = (K domesic) = K domesic = c (a, ε, i; Γ, p) dγ (a, ε, i) g (a, ε, i; Γ, p) dγ (a, ε, i) adγ (a, ε, i). The households demand for each of he hree ypes of goods is given by p TH C TH = νψpc, [ ( Ep TF / 1 τ TF)] C TF = ν (1 ψ) PC, and p N C N = (1 ν) PC. The price index is P = ( p TH ) νψ [ Ep TF / ( 1 τ TF) ] ν(1 ψ) ( p N νψ ν (1 ψ) 1 ν ) 1 ν. The price of Foreign Tradable goods is aken as he numeraire, and he price of he Home Tradable good is assumed o be consan due o he assumpion of a small open economy. p TF = 1 p TH = 1 Labor supply in each secor and oal labor supply are L TH = L N = L TH + L N = I {i = TH, ε = 1} dγ (a, ε, i) I {i = N, ε = 1} dγ (a, ε, i) I {ε = 1} dγ (a, ε, i). Wage raes and capial demand for secor i {TH, N} are w i = K i = ( p i ) 1 1 α (1 α) A i ( αa i P r w + δ ( p i ) 1 ( 1 α αa i ) 1 α 1 P r w L i. + δ ) α 1 α 16

17 Oupu in secor i {TH, N} is given by Y i = A i ( K i) α ( L i) 1 α. The marke clearing condiion for Non-radable good is Y N = C N + X N. The capial marke clearing condiion is K TH + K TN = adγ (a, ε, i) + K f oreign. The capial accumulaion equaion is X = [ ( K domesic) (1 δ) K domesic] + (1 + δ) EK f oreign EK f oreign 1. The inpu demand funcions for he producion of he capial good are p TH X TH = νψpx, [ ( Ep TF / 1 τ TF)] X TF = ν (1 ψ) PX, and p N X N = (1 ν) PX. Ne expors, he curren accoun, he capial and financial accoun, and he balance of paymens are given by NX = (1 τ TH) [ p TH P CA = NX r w EK f oreign KFA = EK f oreign EK f oreign 1 CA + KFA = 0. ( Y TH C TH X TH)] [ Ep TF (C TF + X TF)] P 2.10 Equilibrium Definiion A saionary compeiive equilibrium given he world ineres rae and rade barriers { r w, τ TH, τ TF} is he lis of value funcions { V i=t, V i=n}, policy funcions {c, a, i }, labor supply and labor demand { L TH, L N}, oupus and GDP { Y TH, Y N, Y }, wages { w TH, w N}, prices and exchange rae { p TH, p TF, p N, E }, capi- 17

18 { al allocaion and capial ownership K TH, K N, K domesic, K f oreign}, ne expors and balance of paymens {NX, CA, KFA}, and saionary disribuion Γ (a, ε, i) such ha 1. Given { r w, τ TH, τ N}, { p N, p TH, p TF, E }, { w TH, w N} and Γ (a, ε, i), he value funcions and policy funcions solve he households problems in secor i = TH, N. 2. Given { τ TH, τ N} and wih p TF = 1 as numeraire and p TH = 1 due o he small open economy assumpion, he price of Non-radable good and he exchange rae { p N, E } clear he markes for he Non-radable and Home Tradable goods and deermines he balance of paymens. 3. Wages clear he compeiive labor marke. The mapping for he saionary disribuion and secor choice deermine he amoun of labor supply in each secor in he following ime period. 4. Capial is aggregaed from households curren asse holdings and Foreign-owned Home asses, and allocaed beween secors according o he world ineres rae. 5. The resource consrain is saisfied, and he balance of paymens is zero. 6. The mapping for he saionary disribuion is he fixed poin of Γ ( a, ε, i ) = I { a, ε, i = i } Pr ( ε ε ) dγ (a, ε, i) + I { a, ε = u, i = i } dγ (a, ε, i). 3 Counerfacual Analysis This secion presens he soluion algorihm and calibraion. Then, I perform counerfacual analyses: firs, a bilaeral rade liberalizaion as defined by he eliminaion of rade barriers in boh direcions, and second, a unilaeral decrease in rade barriers for impored Foreign Tradable goods. 3.1 Algorihm and Calibraion In period = 1, assume ha he economy is iniially in is saionary seady sae wih he exising rade barriers for boh expored Home Tradable and impored Foreign Tradable goods of τ TH = 0.05 and τ TF = 0.05, respecively. Tha is, he ransporaion cos of goods across borders is 5% in boh direcions. The associaed value funcions, policy funcions, and saionary disribuion are obained using value funcion ieraion. This calibraion will be referred o hereafer as he benchmark model. 18

19 In period = 2, he economy faces a surprise announcemen of an alernaive rade policy. In scenario (1), ˆτ TH = ˆτ TF = 0. In scenario (2), ˆτ TF = The algorihm o solve for he ransiion pah and he new seady sae is as follows. 1. Since households complee heir secor swiching afer he curren period and mus ener ino a mandaory period of unemploymen phase afer he swich, he curren labor supply in each secor is predeermined according o he law of moion for he saionary disribuion and he secor choice decisions from he previous period. 2. Wih he labor supply deermined, solve for he value funcions, policy funcions for asse holdings and secor choice, and prices ha clear he labor, capial and goods markes, and saisfy he balance of paymens equaion in each period. 3. Given he secor choice decision and he law of moion for he saionary disribuion, obain he labor supply and disribuion of households across asse levels, employmen saus, and secors in he nex period. 4. Repea for T periods o obain he ransiion pah. The soluion approaches he new seady sae as T becomes large. I use a common parameerizaion from macroeconomics lieraure o se he value of four parameers In paricular, I se he discoun rae β = 0.98, he coefficien of risk aversion σ = 1.5, he world ineres rae r w = 0.02, and he depreciaion rae δ = The Markov ransiion marix is calibraed so ha (1) he saionary unemploymen rae is 6%, and (2) he duraion of unemploymen is wo periods. Thus, Pr (ε = 1 ε = 1) = 0.97, Pr (ε = u ε = u) = 0.5, and u The unemploymen benefi is calibraed o u = 0.5; ha is, unemployed households earn ransfer income equal o half he annual secor-specific wage. The oal facor produciviy for boh secors is se o A T = A N = 1, and he capial income share is α = 0.3. The wages for boh secors are w i 0.04 in he neighborhood of he iniial seady sae. The borrowing consrain is calibraed o a = Thus, households can borrow up o approximaely one period of income. The share of Non-radable goods in he baske of consumpion and invesmen is 1 ν = 0.54, which is common in he exising open-economy macroeconomics lieraure. Therefore, he share of Tradable goods in he baske is ν = I hen assume ha half of he Tradable goods used in consumpion and invesmen are produced domesically and he oher half are impored as Foreign Tradable good; hus, ψ =

20 The parameer χ in he labor swiching cos from Secion 2.4 is he proporion of he curren wage of he secor ino which he household is swiching. In he U.S. daa, he average cos of obaining four years of college educaion is roughly equal o hree years of average college graduae wage income; hus, I calibrae χ = 3. In he following subsecions, I presen he simulaion resuls from boh counerfacual analyses. 3.2 Trade Liberalizaion: Bilaeral Reducion of Trade Barriers Figure display he resuls of he counerfacual experimen when rade barriers for boh exporing Home Tradable and imporing Foreign Tradable goods are decreased from τ TH = τ TF = 0.05 o ˆτ TH = ˆτ TF = 0 in period = 2. The bilaeral eliminaion of rade barriers leads o a movemen of households from he Home Tradable o he Non-radable secor. In Figure 3.2.1, immediaely afer rade liberalizaion, he unemployed households previously in he Home Tradable secor wih sufficien wealh, which accouns for 1.4% of he oal populaion, swich o he Non-radable secor. In he new seady sae, he employed labor supply in he Home Tradable secor (L TH ) and Non-radable secor (L N ) decreases and increases by 1.3%, respecively. The unemploymen rae (u = 1 L TH L N ) iniially rises by 0.7% due o he mandaory unemploymen phase of he migraing households before reurning o he seady sae level u. Figure shows ha he real wage in he Home Tradable secor (w TH ) iniially falls by 3.6% afer rade liberalizaion before rising 4.8% above he iniial seady sae, while he real wage in he Non-radable secor (w N ) rises by 2.6% owards he new seady sae. Wages are equal before rade liberalizaion bu diverge afer he liberalizaion. The wides wage gap occurs immediaely afer rade liberalizaion. In Figure 3.2.3, he price of he Non-radable good (p N ) iniially rises by 6.9% upon rade liberalizaion, hen falls o 1.5% below he iniial seady sae as secor labor supply (L N ) and oupu (Y N ) increase. The Home currency (E) iniially depreciaes by 0.7% immediaely afer rade liberalizaion bu hen appreciaes by 5.5% owards he new seady sae. The effecive price of Foreign Tradable goods wih he exchange rae and rade barrier, as measured by Ep TF / ( 1 τ TF), decreases by 10.2%. Figure shows ha producion in he Home Tradable secor (Y TH ) falls by 1.4% in he new seady sae while he oupu of he Non-radable secor (Y N ) rises by 3.6%. Real GDP (Y) also increases by 3.7% in he seady sae, wih he larges increase immediaely afer rade liberalizaion due o he swiching cos. However, Figure shows ha in he seady sae afer rade liberalizaion, oupu per employed worker in boh he Home Tradable secor (Y TH /L TH ) and Non-radable secor (Y N /L N ) increases by 1.1% 20

21 % 0.48 Labor Supply in Home Tradable Secor (L TH ) Labor Supply in Non-radable Secor (L N ) Unemploymen Rae (%, RHS) 6.2% Labor Supply (L TH, L N ) % Unemploymen Rae % % Time Figure 3.2.1: Labor Supply and Unemploymen Rae Real Wage in Home Tradable Secor (w TH ) Real Wage in Non-radable Secor (w N ) Real Wage Time Figure 3.2.2: Secor Wage 21

22 Price of Home Tradable Good (p TH ) Price of Non-radable Good (p N ) Price of Foreign Tradable Good in Home Counry (Ep TF /(1-τ TF )) Exchange Rae (E, RHS) Prices Exchange Rae Time Figure 3.2.3: Prices and Exchange Rae Secor Oupu Oupu of Home Tradable Secor (Y TH ) Oupu of Non-radable Secor (Y N ) Real GDP (Y, RHS) Real GDP Time Figure 3.2.4: Secor Oupu and Real GDP 22

23 Oupu per Employed Worker Oupu per Employed Worker of Home Tradable Secor (Y TH /L TH ) Oupu per Employed Worker of Non-radable Secor (Y N /L N ) Time Figure 3.2.5: Oupu per Employed Worker Capial Allocaion Capial Allocaed o Home Tradable Secor (K TH ) Capial Allocaed o Non-radable Secor (K N ) Foreign Ownership of Home Asse (K foreign, RHS) Foreign Ownership of Home Asse Time Figure 3.2.6: Capial Allocaion and Foreign Ownership of Home Asses 23

24 Expor Quaniy, Impor Quaniy Ne Expors 0.03 Expor Quaniy (Y TH - C TH - X TH ) Impor Quaniy (C TF + X TF ) Ne Expors (NX = (p TH (1-τ TH )(Y TH - C TH - X TH ) - Ep TF (C TF + X TF ))/P, RHS) Time Figure 3.2.7: Expor Quaniy, Impor Quaniy, and Ne Expors Average Household Wealh (a') Average Household Wealh of Home Tradable Secor Average Household Wealh of Non-radable Secor Economywide Average Household Wealh Time Figure 3.2.8: Average Household Wealh by Secor and Economy-wide 24

25 Average Household Welfare Average Household Welfare of Home Tradable Secor (W TH = V(a,ǫ,i)dΓ(a,ǫ,i = TH)) Average Household Welfare of Non-radable Secor (W N = V(a,ǫ,i)dΓ(a,ǫ,i = N)) Economywide Average Household Welfare (W = V(a,ǫ,i)dΓ(a,ǫ,i)) Time Figure 3.2.9: Average Household Welfare by Secor and Economy-wide Gini Coefficien of Wealh (a') Gini Coefficien of Asse Holding (Wealh, a') Time Figure : Gini Coefficien of Wealh 25

26 and 0.8%, respecively. Figure shows ha capial allocaed o he Home Tradable secor (K TH ) and Non-radable secor (K N ) increases by 1.8% and 5.5%, respecively, and oal capial used in producion (K TH + K N ) increases by 3.7%. Foreign ownership of Home asses (K f oreign ) also increases by 6.2%, indicaing capial inflows. The domesic supply of capial (K domesic ) decreases by 0.6%. Figure shows ha he real value of ne expors (NX) iniially decreases by 64% immediaely afer rade liberalizaion due o he sharp decrease in he expor quaniy (Y TH C TH X TH ), he increase in he impor demand (C TF + X TF ), and he depreciaion of he Home currency. However, he value of ne expors increases by 0.9% in he new seady sae, wih a 2.2% decrease and a 10.8% increase in expor and impor quaniy, respecively. Figure deails he changes o he aggregae household wealh, as measured by he average wealh (a ) held by households in each secor. The average wealh of households in he Home Tradable secor iniially decreases due o he lower real wage in Home Tradable secor and he swiching cos paid by he migraing households. The average household wealh in he Non-radable secor decreases as he migraing households are absorbed ino he secor. The economy-wide oal wealh decreases by 0.5% in he seady sae. Figure shows ha, on average, households in he Home Tradable secor are iniially he losers from he policy; however, households in boh secors evenually gain from rade liberalizaion. The measure of welfare improvemen will be discussed in Secion 4. Figure shows ha he Gini coefficien of wealh, as measured wih asse holdings a, immediaely increases afer rade liberalizaion and hen apers owards a more equiable disribuion of wealh. The peak increase in he Gini coefficien of 0.8% occurs hree periods afer he policy implemenaion. The Gini coefficien reurns o he pre-liberalizaion level in he following weny periods hen slowly decreases o 0.6% below he iniial disribuion. 3.3 A Decrease in Trade Barrier for Impored Foreign Tradable Good Figure display he resuls of he counerfacual experimen when only he rade barrier for imporing Foreign Tradable goods is decreased from τ TF = 0.05 o ˆτ TF = Immediaely afer he policy is implemened, 0.2% of he oal populaion from unemployed households in he Home Tradable secor swiches o he Non-radable secor. Labor supply in he Home Tradable secor (L TH ) and Nonradable secor (L N ) decreases and increases by 0.2%, respecively. The unemploymen rae (u = 1 L TH L N ) iniially rises by 0.1%. The real wage in he Home Tradable secor (w TH ) iniially falls by 3.1% afer 26

27 % % Labor Supply (L TH, L N ) Labor Supply in Home Tradable Secor (L TH ) Labor Supply in Non-radable Secor (L N ) Unemploymen Rae (%, RHS) 5.8% 5.75% 5.7% Unemploymen Rae % Time Figure 3.3.1: Labor Supply and Unemploymen Rae Real Wage Real Wage in Home Tradable Secor (w TH ) Real Wage in Non-radable Secor (w N ) Time Figure 3.3.2: Secor Wage 27

28 Price of Home Tradable Good (p TH ) Price of Non-radable Good (p N ) Price of Foreign Tradable Good in Home Counry (Ep TF /(1-τ TF )) Exchange Rae (E, RHS) Prices Exchange Rae Time Figure 3.3.3: Prices and Exchange Rae Secor Oupu Real GDP Oupu of Home Tradable Good (Y TH ) Oupu of Non-radable Good (Y N ) Real GDP (Y, RHS) Time Figure 3.3.4: Secor Oupu and Real GDP 28

29 0.148 Oupu per Employed Worker Oupu per Employed Worker of Home Tradable Secor (Y TH /L TH ) Oupu per Employed Worker of Non-radable Secor (Y N /L N ) Time Figure 3.3.5: Oupu per Employed Worker Capial Allocaion Capial Allocaed o Home Tradable Secor (K TH ) Capial Allocaed o Non-radable Secor (K N ) Foreign Ownership of Home Asse (K foreign, RHS) Foreign Ownership of Home Asse Time Figure 3.3.6: Capial Allocaion and Foreign Ownership of Home Asses 29

30 Expor Quaniy, Impor Quaniy Ne Expors 0.03 Expor Quaniy (Y TH - C TH - X TH ) Impor Quaniy (C TF + X TF ) Ne Expors (NX = (p TH (1-τ TH )(Y TH -C TH -X TH ) - Ep TF (C TF +X TF ))/P, RHS) Time Figure 3.3.7: Expor Quaniy, Impor Quaniy, and Ne Expors Average Household Wealh (a') Average Household Wealh of Home Tradable Secor Average Household Wealh of Non-radable Secor Economywide Average Household Wealh Time Figure 3.3.8: Average Household Wealh by Secor and Economy-wide 30

31 Average Household Welfare Average Household Welfare of Home Tradable Secor (W TH = V(a,ǫ,i)dΓ(a,ǫ,i = TH)) Average Household Welfare of Non-radable Secor (W N = V(a,ǫ,i)dΓ(a,ǫ,i = N)) Economywide Average Household Welfare (W = V(a,ǫ,i)dΓ(a,ǫ,i)) Time Figure 3.3.9: Average Household Welfare by Secor and Economy-wide Gini Coefficien of Wealh (a') Gini Coefficien of Asse Holding (Wealh, a') Time Figure : Gini Coefficien of Wealh 31

32 he new policy before rising o 2.9% above he iniial seady sae, while he real wage in he Non-radable secor (w N ) rises by 5.1% owards he new seady sae. Similarly, wage inequaliy permanenly occurs and he gap beween he wo secors is larges immediaely afer rade liberalizaion. The price of he Non-radable good (p N ) iniially rises by 5.4%, hen falls o 1.4% above he iniial seady sae as secor oupu (Y N ) increases. The Home currency (E) gradually appreciaes by 9.1% owards he new seady sae. The effecive price of Foreign Tradable goods wih he exchange rae and rade barrier, as measured by Ep TF / ( 1 τ TF), decreases by 11.5%. The oupu in he Home Tradable secor (Y TH ) iniially falls by 1.0% before rising o 0.5% above he iniial level, while he oupu of Non-radable secor (Y N ) seadily increases by 1.9%. Real GDP (Y) also increases by 4.0% in he seady sae. Similarly, oupu per employed worker in boh he Home Tradable secor (Y TH /L TH ) and Non-radable secor (Y N /L N ) increases by 0.9% and 1.5%, respecively. Capial allocaed o he Home Tradable secor (K TH ) and Non-radable secor (K N ) increases by 2.5% and 5.5%, respecively, and oal capial used in producion (K TH + K N ) increases by 4.0%. The Foreign ownership of he Home asses (K f oreign ) also increases by 6.5%, while domesic supply of capial (K domesic ) decreases by 0.2%. The real value of ne expors (NX) iniially decreases by 60% immediaely afer he policy and gradually increases o 7.0% below he iniial policy, while expor and impor quaniy increase by 0.4% and 13.7%, respecively. The average household wealh (a ) in he Home Tradable secor iniially decreases due o he lower real wage in he Home Tradable secor and he swiching cos paid by migraing households. The average household wealh in he Non-radable secor iniially increases due o he higher real wage in he Non-radable secor, bu decreases as he real wage gradually decreases and he migraing households are absorbed ino he secor. The economy-wide oal wealh decreases by 0.2% in he seady sae. Households in he Home Tradable secor are iniially he losers; however, households in boh secors evenually gain from he policy. The policy improves wealh inequaliy as he Gini coefficien of wealh (a ) immediaely decreases. 4 Welfare and Poliical Economy In his secion, I discuss he welfare effecs of he wo alernaive rade policies bilaeral rade liberalizaion ( ˆτ TH = ˆτ TF = 0), and he unilaeral decrease in he rade barrier of he Foreign Tradable good ( ˆτ TF = 0.025). The change in welfare is measured by he consumpion equivalen variaion. Using he resuls from Secion 3, he welfare effecs are evaluaed in wo ways beween he wo seady saes of each policy, and along he 32

33 ransiion pah when each of he rade policies is implemened. An inroducory discussion on he poliical economy of rade policies is also presened. 4.1 Welfare Comparison beween Seady Saes To compare he households welfare beween he wo rade policies a he seady sae, we compare he seady-sae households value funcions from each policy regime. Define λ (a, ε, i) as he consumpion equivalen variaion for a household currenly in secor i wih curren asse level a and employmen saus ε. For each household wih he curren sae variables (a, ε, i), I ask he following quesions: wha percenage of permanen consumpion under he curren rade policy i would be willing o pay in order o achieve he seady-sae uiliy value associaed wih he alernaive rade policy? In oher words, for each household wih he same curren sae variables (a, ε, i), which of he wo seady saes would i prefer and how much would i pay o be a he seady sae under he alernaive policy? If λ (a, ε, i) > 0, such household is willing o pay o move o he seady sae under he alernaive rade policy. Oherwise, household mus be compensaed if λ (a, ε, i) < 0. Le V ( a, ε, i; τ TH, τ TF) = E [ =1 β 1 u (c ) ] and ˆV ( a, ε, i; ˆτ TH, ˆτ TF) = E [ =1 β 1 u (ĉ ) ] be he seadysae value funcions associaed wih he benchmark { τ TH, τ TF} and he alernaive { ˆτ TH, ˆτ TF} rade policies, respecively. The consumpion equivalen variaion can be solved from [ ( ] ˆV a, ε, i; ˆτ TH, ˆτ TF) = E β 1 u ((1 + λ (a, ε, i)) c ) =1 I can be shown ha he consumpion equivalen variaion is λ (a, ε, i) = ˆV ( a, ε, i; ˆτ TH, ˆτ TF) + 1 (1 σ)(1 β) V (a, ε, i; τ TH, τ TF ) + 1 (1 σ)(1 β) 1 1 σ 1 The seady-sae value funcions under he benchmark and he alernaive rade policies are he value funcions a ime = 1 and = T, respecively. Since he economy is iniially in he seady sae under he rade barriers of τ TH = τ TF = 0.05 a ime = 1, and he economy converges o he seady sae under he alernaive rade policy { ˆτ TH, ˆτ TF} as T grows large. The economy-wide welfare gain is calculaed from he average of he consumpion equivalen variaion over he iniial disribuion of households across he sae variables (a, ε, i) a ime = 1. Tha is, he average welfare gain as a resul of moving all households from he curren seady sae under he benchmark policy 33