Internal Geographic, Labor Mobility, and the Distributional Impacts of Trade Online Appendix (Not for Publication)

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1 Intrnal Gographic, Labor Mobility, an th Distributional Impacts of Tra Onlin Appnix (Not for Publication) Jingting Fan Univrsity of Marylan Contnts A Thory Appnix 2 A.1 Driving Equation (8) A.2 Driving Equation (10) A.3 Driving Equation (34) A.4 Proposition B Backgroun Information an Data Appnix 5 B.1 Backgroun Information on th Chins Hukou Systm B.2 Data Sourcs an Sampl Construction B.2.1 Wag B.2.2 Migration B.2.3 Workr Employmnt an Birthplac Distributions in B.2.4 Factor Shars in Equipp Composit Labor B.2.5 Cultural Distanc B.2.6 City-lvl Intrnational Tra Surplus B.2.7 Input-output Linkags for China an th ROW C Estimation an Calibration Appnix 13 C.1 Calibrating ρ C.2 Estimating Migration Cost C.3 Jointly Estimating Tra Cost an Prouctivity C.4 Aitional Information on th Joint Estimation C.5 Paramtrs for th Countrfactual Exprimnts with Diffrnt Intrnal Gographis C.6 Discussion on th Estimat Intr-Provincial Effct an Aitional Robustnss Dpartmnt of Economics, Univrsity of Marylan. arss: fan@con.um.u 1

2 A Thory Appnix A.1 Driving Equation (8) π o, = Pr(v z v gz g o,g, g G) Whr F ( v v 1 o,1 z, v v 2 o,2 z,... v vg o,g = Pr(z g = = 0 0 v v g o,g z, g G, ) Pr(z g F ( z,...) := F z an this raw ominats all othr raws. Us th functional form of F, it follows that v v1 o,1 z, v v g o,g z, g G z )f(z )z v v 2 o,2 z,... v z o, g= vg z, g G o,g v vg o,g z,...)z, is th probability that th raw from rgion is z πo, = xp( ( g G( = = 0 v vg 0 xp( ( g G ( v ( v ) ɛ g G ( v g o,g ) ɛ z ) ɛ ) 1 ρ ) (1 ρ)ɛ ( ( o,g g G vg o,g v g G ( vg ) ɛ o,g z ) ɛ ) 1 ρ ) v v z g ) ɛ ) ρ z ɛ 1 o,g z 2

3 A.2 Driving Equation (10) W first riv th istribution of u o, u o = max G { v z }, F u o (u) : = Prob(u o u) = Prob( v z u, G) = Prob(z u v, G) = F ( u o,1 v 1 = xp( [ G = xp( [ G, u o,2 v 2,..., u v,...) ( u ) ɛ ] 1 ρ ) v ( ) ɛ ] 1 ρ u (1 ρ)ɛ ) v = xp( Φ o 1 ρ u (1 ρ)ɛ ) It can b shown that, G, th cumulativ istribution function of u for workrs moving from o, to, is F u o, (u) = F u o (u) = xp( Φ o 1 ρ u (1 ρ)ɛ ), which is a Frcht istribution with position paramtr Φ o 1 ρ an isprsion paramtr (1 ρ)ɛ. 1 E(u o L o, ) = uf u o (u) = u(xp( [ ( v ) ɛ ] 1 ρ u (1 ρ)ɛ )) G = uɛ (1 ρ)xp( [ ( v ) ɛ ] 1 ρ u (1 ρ)ɛ )[ ( G v ) ɛ ] 1 ρ u (1 ρ)ɛ u G = uɛ (1 ρ)xp( Φ o 1 ρ u (1 ρ)ɛ )Φ o 1 ρ u (1 ρ)ɛ u = ɛ (1 ρ)xp( y)yu (chang of variabl : y = Φ o 1 ρ u (1 ρ)ɛ ) y = ɛ (1 ρ)xp( y)y( Φ o 1 ρ ) 1 (1 ρ)ɛ = xp( y)y 1 1 (1 ρ)ɛ Φ o ɛ y = Φ 1 1 ɛ o Γ(1 ɛ (1 ρ) ) (Dfinition of Gamma function) 1 This is obtain by showing F u o, (u) := Prob(u o, u u o,is th highst) = Prob(u o, u,u o,is highst) u0 F π o, = (z )z π o, = F u o (u). 3

4 A.3 Driving Equation (34) For workrs staying in thir homtown, u o,o = v oz o o,o workrs choosing to stay in o is: = v oz o, hnc th istribution of prouctivity raws for F z o,o (z) : = Pr(z o,o < z) = Pr( u o,o v o = F u o,o (zv o) < z) (using o,o = 1) = xp( [v (1 ρ)ɛ o Φ o 1 ρ ]z (1 ρ)ɛ ), which is also a Frcht istribution. For iffrnt rgions, th prouctivity istribution of stayrs thr hav - iffrnt mans, but thir isprsions will b th sam. Thrfor, I rgrss stayrs log wags on rgional fix ffcts to nt out th iffrnt avrag rgional prouctivity raws an intrprt th xponnts of th rsiuals as ranom raws from a Frcht istribution with isprsion paramtr ɛ (1 ρ). Th cofficint of variations for this istribution is givn by Equation (34). A.4 Proposition 1 Proposition 1 is us in Sction C of this appnix, in stimating migration costs. Proposition 1 Givn migration costs { }, thr xists a uniqu st of {v } (up to normalization), such that th mol-prict numbr of workrs mploy in ach rgion quals that in th ata, i.., L = o G π o, l o is satisfi, whr L is th numbr of workrs working in (ata), l o is th numbr of workrs born in o (ata), an π o, is th mol-prict probability of workrs born in o to mov to. Proof Th proof follows Michals t al. (2011) an Lmma 1, Lmma 2 in Ahlflt t al. (2012), so I only sktch th ky stps hr. Consir Equation (9) in th txt L = πo, l o, o G Whr L an l o ar ata, an π o, = ( v ) ɛ o,. Givn { g G ( v g o,}, lo, an L o,g )ɛ is {v }. Lt v b th vctor (v1, v 2,..., v,...). Dfin WD(v ) (workr ficits) as WD(v ) = L o G π o, l o., th only unknowns in this quation WD is simply th gap btwn th numbr of workrs working in rgion in th ata, an th numbr prict by th mol. WD(v ) is a function of v. To prov Proposition 1 w show th following: 1. WD(v ) is continuous; 2. WD(v ) is homognous of gr zro; 3. G WD (v ) = 0, v R G + 4

5 4. WD(v ) xhibits gross substitut proprty. It is asy to vrify that rquirmnt (1) an (2) ar satisfi. Rquirmnt (3) can b shown to b satisfi by noting that G π o, = 1; rquirmnt (4) can b shown to b satisfi by computing th rivativs irctly. Rquirmnts (1) (2) guarant th xistnc of a solution. Th proof is a constructiv on: by homognous of gr zro, w can normaliz v to th simplx {v R + : v = 1}. Dfin WD + = max{0, WD}, v+wd an f(v) = G + v + txtbfg WD(v), thn f is a continuous function mapping th unit simplx onto itslf. Th xistnc of a solution to v = f(v) thn follows from th Brouwr s fix point thorm. Rquirmnt (3)-(4) thn guarant th uniqunss of th solution, s Ahlflt t al. (2012) for a mor tail xplanation. Th implication of proposition 1 is that, givn migration costs, w can solv Equation (9) for th uniqu st of amnity-ajust ral wags for all locations. B Backgroun Information an Data Appnix B.1 Backgroun Information on th Chins Hukou Systm Th Hukou systm, th history of which ats back to th 1950, is th houshol rgistration systm in China. It was originally stablish to control th rural-urban migration in China (back thn, rsints in citis wr subsiiz with ownwar-istort prics for agricultural proucts, an thr was a strong incntiv for popl to liv in citis). Thr ar two typs of Hukous, on for rural rsints, th othr for urban rsints, in ach city. 2 Bfor 1978, popl wr ti to whr thir Hukous wr an wr not allow to mov to any othr placs without prmission from th authority. As a rsult, thr wr only minimum rural-urban or urban-urban migrant workrs. Although popl ar fr to travl now, th Hukou systm is still important for many aspct of lif, as it is ti to halth car, social insuranc, housing, an ucation, tc. In many aspcts, it acts lik within country visa systm, istorting th fr mobility of labor. 3 B.2 Data Sourcs an Sampl Construction Th primary iniviual- an firm-lvl ata I us ar th following: th 2005 Mini Population Cnsus, th 2000 Population Cnsus, th 2004 Economic Cnsus, an th 2004 Annual Survy of Inustrial Prouction. In aition to ths micro ata sourcs, I also us th 2002 intr-rgional an intr-sctoral input-output tabl, an th ata from national accounts an provincial statistical yarbooks. Th 2005 Mini Population Cnsus covrs 1% of Chins population. It rcors iniviual mographic an mploymnt information. To my knowlg, this is th only ata st that provis iniviual-lvl incom information for th ntir country, so I us it to stimat th avrag incom in ach rgion. I also choos 2005 as th bnchmark yar, as th calibration procur rquirs wag information. Th sampl I us in this papr is a 1% sub-sampl of this ata st. 2 Thrfor an urban Hukou in Bijing is iffrnt from ithr an urban Hukou in Shanghai or a rural Hukou in Bijing 3 S th May 6th, 2010 issu of th magazin Th Economist, availabl at for mor information about th Hukou systm in China. 5

6 Th 2000 Population Cnsus covrs th ntir Chins population. My sampl is its 0.095% sub-sampl. Rsponnts in this sub-sampl fill a longr form than othrs, which asks for information on migration, ucation, occupation, inustry, an housing conitions, but unfortunatly, not for information on incom. Th 2004 Economic Cnsus covrs th univrs of rgistr firms. Th sampl I hav accss to is its manufacturing sub-sampl, with firm-lvl rvnu an mploymnt information. Th 2004 Annual Survy of Inustrial Prouction covrs all stat-own ntrpriss, as wll as privat ntrpriss with annual sals ovr 5 million RMB yuan. Diffrnt from th 2004 Economic Cnsus, this ata st contains tail firm-lvl financial information, rathr than only mploymnt an rvnu information. 4 Th rst of this sction covrs tails in sampl construction. B.2.1 Wag Thr ar two typs of workrs, two typs of local labor markts (rural an urban), an N citis in th conomy, so in total thr ar 4N wags (man wags for skill an unskill workrs in all rgions in th conomy) to stimat. Th ata I us for this purpos is th 2005 mini cnsus. I stimat th following spcification: log(wag,i ) = β 0 + β 1 ag + β 2 ag 2 + β 3 sx + β 4 I Skill I Agricultur + F i + S i F i I Skill + A i F i I Agricultur, whr F i is th rgional fix ffct, F i I Skill is th intraction btwn rgional fix ffct an high-skill ummy, an F i I Agricultur is th intraction btwn rgional fix ffct an a ummy for agricultural sctor. In this spcification, I rstrict th rlativ skill prmium in th agricultural sctor (rlativ to th skill prmium in urban sctor of th sam city) to b th sam across citis (β 4 is not city-spcific). This choic is constrain by th powr of th rgrssion, as in th sampl, in many citis, th rural sctor only mploy a small numbr of high-skill workrs. Th omitt group in th rgrssion is th unskill workr in th urban sctor in Bijing, whos avrag wag is β 0. Avrag wags for othr groups of workrs can b calculat as follows: Tabl B.1: Avrag wag for iffrnt groups Eucation Sctor Rgion Wag Unskill Urban i β 0 + F i Unskill Rural i β 0 + F i + A i Skill Urban i β 0 + F i + S i Skill Rural i β 0 + β 4 + F i + S i + A i Th output of th rgrssions ar prsnt in Tabl (B.2). Th signs an magnitus of cofficints ar rasonabl. Th R 2 of th rgrssion is 0.58, inicating that th rgrssion has a strong xplanatory powr. Figur (B.1) prsnts th istribution of th p-valus for th fix ffcts in th wag rgrssion. Th istribution is havily concntrat aroun zro (th spik in th figurs corrspons to p-valu<0.0005), suggsting that th fix ffcts ar vry prcisly stimat. Figur (B.2) shows th istribution of avrag wag for iffrnt workr groups across rgions. Two pattrns mrg: first, thr is consirabl htrognity across rgions; scon, ovrall, wags ar highr for high-skill workrs an urban workrs. Figurs 2(c) an 2() in th txt cast th stimats for avrag 4 Th 2004 Economic Cnsus also covrs tail financial information, but I o not hav accss to othr variabls. 6

7 Tabl B.2: Wag Rgrssions (1) log wag Ag *** (22.32) Ag squar *** (-22.70) Sx *** (-42.36) Skill agri *** (-16.57) Obsrvations R t statistics in parnthss * p<0.10, ** p<0.05, *** p<0.01 wags of urban low-skill workrs an th avrag urban skill prmia ovr th map of China. Th isprsions in Figur(B.2) show up on th map as th iffrnc both across an within gographic aras. B.2.2 Migration Sinc I us th 2005 mini cnsus to stimat rgional wag an calibrat th mol to th 2005 conomy, ially I woul lik to us this ata st to stimat migration costs, too. Sinc th mol nglcts ynamic choic of iniviuals, th migration cision in th mol shoul b bst intrprt as a lif-tim choic. So th molconsistnt finition of migration is on that is bas on birthplac. Howvr, th 2005 ata os not covr birthplac information, so I us th 2000 cnsus to stimat th long-run migration costs. 5 Th unrlying assumption is that th long-run migration costs o not chang much ovr th prio of It is of cours possibl that som migration rstrictions hav bn lift uring th prio; in that cas, th countrfactual xprimnts in th papr shoul b intrprt as: what ar th wlfar implications of intrnational tra for China in 2005, ha th migration costs stay at th 2000 lvl. Th following ar th procurs I us to construct migration flow: first of all, I rstrict th sampl to thos who alray finish thir schooling, ag btwn 20 an 60 (60 is th official rtirmnt ag for urban mal non-physical-labor workrs in China), I also rop thos who ar currntly not working, unlss th rason for not working is ithr on vacation or on sick lav. I classify a workr as a migrant, if h or sh is not working in hr or his birthplac. I intify th sourc sctor (rural or urban) of a workr with th typ of Hukou (rural or urban) th workr currntly hols, an th stination sctor of a workr by th locality th survy rsponnt. 6 Givn th small proportion of workrs with collg grs in China in 2000, I classify a workr to b high-skill, 5 Th mini cnsus os rport th plac of rsinc in Thrfor on altrnativ is to combin th migration ovr th prio of with th long-trm migration in 2000, to construct th long-trm migration in This is problmatic, as a larg fraction of th workrs that migrat uring might ha bn alray living outsi thir birthplac in 2000, i.., thy ar rpat migrants. Empirical stuis focusing in th U.S. hav ocumnt th phnomna of rpat migrant or rturn migrant (Knnan an Walkr, 2011), an th fact that migrants ar mor likly to rspon to conomic shocks by migrating, than nativ workrs (Cana an Kovak, 2013). In light of th vinc, this approach will oubl count rturn migrants an rpat migrants, ovrstimating th long-trm migration in To th xtnt that som rural Hukou holrs hav switch an urban Hukou in 2000, this classification unrstimat rural-urban migration. Howvr, until rcntly, switching a rural Hukou for an urban on was highly rstrict. 7

8 Figur B.1: Distribution of th P-valu for Fix Effcts Dnsity p_valu_rgion Dnsity skill_p (a) Rgional Fix Effcts (b) Skill*Rgional Fix Effcts Dnsity agril_p (c) Agricultur*Rgional Fix Effcts Figur B.2: Avrag Wags for Diffrnt Workr Groups Dnsity skill_rural Dnsity unskill_rural (a) Rural high-skill workrs (b) Rural low-skill workrs Dnsity skill_urban Dnsity unskill_urban (c) Urban high-skill workrs () Urban low-skill workrs 8

9 if h or sh has rciv mor than nin yars formal ucation, quivalnt to finishing junior high school. 7 From ths procurs, for all workrs in th conomy, I intify thir ucation lvl, sourc provinc, sourc sctor, stination city, an stination sctor. I us this to stimat intr-rgional an intr-sctoral migration costs. B.2.3 Workr Employmnt an Birthplac Distributions in 2005 Rcovring {v } Aftr stimating th paramtrs govrning migration costs, I solv th labor markt claring conitions (Equation 9 in th txt) for on mor tim, to obtain {v } for 2005, th rgional fix ffcts that ar consistnt with mploymnt istribution in For this purpos, I n workrs birthplac an mploymnt istributions in 2005, by workrs lvl of skills. I construct th mploymnt istribution from th 2005 mini cnsus. For som citis, u to th small sampl siz an th small shar of skill workrs, thr ar fw skill workrs sampl. For ths citis, I supplmnt th mploymnt istribution aggrgat up from th micro ata with th publish aggrgat city-lvl statistics on mploymnt from th sam survy. I construct workrs birthplac istribution from th 2000 cnsus. I rstrict th sampl to workrs ag in Th istribution of this sampl will b th istribution for workrs ag in To trmin th skill lvl of workrs for this sampl, if a workr has finish schooling in 2000, I classify his or hr skill lvl bas on th ucation attainmnt irctly; for workrs that ar abov 15, but hav not yt finish schooling, I assum thy ar skill by this ag, a typical Chins ki has rciv 8-9 yars of ucation, so th possibility of (wrongly) classifying a stunt rciving lss than 9 yars ucation as skill is minimiz. Rcovring {T s } Th mploymnt istribution construct abov givs us th numbr of workrs mploy in ach rgion. Onc w hav th stimats for migration costs an rgional amnity-ajust ral wags, w can us Equation (12) in th txt to convrt ths into th mploymnt of ffctiv labor units. Sinc thr ar thr inustris in urban rgions, w still o not know th istribution of mploymnt across inustris in ach urban rgion, which is n for th calibration of prouctivity at city-inustry lvl. 8 I supplmnt th rgional mploymnt information with th shar of mploymnt in inustry K ovr inustry M, construct from th manufacturing sub-sampl of th 2004 conomic cnsus, an us th srvic markt claring conitions to obtain th mploymnt information at th city-inustry lvl. 9 Spcifically, lt E,s h an El,s, s {A, M, K, S}, {U, R} b th sctoral ffctiv labor unit mploymnt, thn rgional labor markt claring conitions ar: E h,a = Eh, El,A = El, R E h,m + Eh,K + Eh,s = Eh, El,M + El,K + El,S = El, U (B.1) Th right sis of ths quations ar alray construct from th ata. Sinc only agricultural inustry is locat in rural rgions, from th abov quation w know labor ffctiv unit mploymnt in th agricultural inustry. 7 Th highr ucation rform start in 1999 in China, which xpan th scal of th highr ucation sctor ramatically. Bfor th rform, th collg amission rat in China was blow 5%; in 1999, th collg amission incras by 40%. Th following yars saw aitional incras. But until 2005, collg grauats constitut only a small proportion of th Chins labor markt. 8 In th main txt, I analyz th intuition bhin th quantification stratgy in th contxt of a linar-rgrssion stup, whr w n th tra flows btwn citis for stimation. Such ata is not availabl, so I us a joint quantification stratgy, iscuss in sction C of this appnix, for which I n mploymnt istribution in ach city-inustry to trmin th corrsponing prouctivity. 9 I o not irctly us th 2005 mini cnsus to construct inustry-lvl mploymnt bcaus u to th limit sampl siz, in som citis, thr ar no or only a small numbr of high-skill mploymnt in th capital an quipmnt inustry. 9

10 From th optimality conitions of intrmiat varity proucrs, givn by Equation (18), th prouction of intrmiat varitis in ach plac can b calculat, an this shoul qual to th total man, D s : D A = Eh,A W h β h γl A D s = Eh,s W h β h γl s = El,A W l β l, R γl A = El,s W l β l, s {M, K, S}, U, γl s (B.2) With {D s : s {A, M, K, S}} w can comput th city-lvl man for inustry final output in th srvic sctor, which must qual D S, D S = CS + CS + +DA γs A + s {M,K,S} D s γa s, U, (B.3) whr C S is th urban srvic consumption in rgion ; inicats th rural rgion in th sam city as urban rgion an C S is th srvic consumption of this rural rgion. C S + CS is trmin irctly by workrs wag an mploymnt istribution. Combin Equations (B.1), (B.2) an (B.3), 10 w hav a linar quation systm, with 4N unknowns: E,A h, Eh,M, Eh,K, Eh,s, an 3N quations (B.3) an th subst of (B.1) for high skill workrs. W combin ths thr quations with on mor ata momnt rgional mploymnt shar in capital an quipmnt (K) vrsus othr manufacturing inustris (M), Eh,K E,M h units in all city-inustry. to solv for mploymnts of ffctiv labor Onc w obtain ths mploymnts, w can also us Equation (B.2) to comput th prouction of intrmiat varitis in ach inustry in all citis. B.2.4 Factor Shars in Equipp Composit Labor W n th shars of paymnts to capital, high-skill workrs, an low-skill workrs in ach rgion, to calibrat th rgion-spcific quipp composit labor prouction functions. I comput th ratios btwn paymnts to highskill workrs ovr low-skill workrs irctly from th stimat wags an th istribution of ffctiv labor units, both of which hav bn construct prviously. I furthr n th ratio btwn th paymnt to capital, an th paymnt to labor, in ach rgion. For th urban rgions, I us th 2004 Survy of Inustrial Prouction. I aggrgat firm-lvl ata to obtain th city-lvl ratio btwn wag bill an xpniturs on capital an quipmnt. Th firm-lvl wag bill is th total salary paymnts ntry in th ata st; th firm-lvl xpniturs on capital an quipmnt is th total capital prciations ntry in th ata st. Th total prciations ntry inclus, in aition to prciations to capital an quipmnt, prciations to proprtis an builings. Thrfor I ajust for this by subtracting th shar of builings among aggrgat tangibl fix capital stock in China in 2004, calculat from th national statistical yarbook. Th man ratio across citis, construct this way, is similar to th corrsponing ratio from th national input-output tabl for th urban sctor. For th rural rgions, sinc I am not awar of any ata sourcs that contain information on capital shar at th rgional lvl, I assum th capital shars ar th sam for all rural rgions an us th national input-output tabl to trmin it. 10 W us Equation (B.2) to liminat E,s l 10

11 B.2.5 Cultural Distanc To proxy for th cultural istanc btwn citis, I construct a cultural similarity inx bas on th compositions of thnic minority groups. I xtract th prfctur-lvl information on th compositions of thnic minoritis from th 1990 cnsus. Migrations was not as prvasiv in 1990 as it was in 2000, an thrfor th thnic compositions largly rflct th cultural root of a city. Using th 1990 cnsus ata hlps us avoi th nognity problm that woul aris, if w us th 2000 cnsus to construct cultural istanc. Thr ar 56 thnic groups in China, with Han thnic bing th ominating on. I xclu it, bcaus th shar of Han population is so larg that incluing it liminats most of th variation in th similarity inx. For ach city, I am lft with a 55 by 1 vctor, ach lmnt of which is th shar of on thnic group in th total local thnic minority population. I thn comput th corrlations btwn th vctors of all city pairs, an us ths as th valus of my cultural similarity inx; th cultural istanc is thn fin as on minus this similarity inx. Figur (B.3) is th nsity istribution of th inx. Th man, mian an stanar viation of th similarity inx ar , , an , rspctivly. Figur B.3: Dnsity Distribution of th Similarity Inx Sourc: Author s calculation bas on th 1990 cnsus B.2.6 City-lvl Intrnational Tra Surplus To incorporat intrnational tra imbalancs into th calibration, I construct a ata st of city-lvl intrnational tra surplus. Each city s tra surplus in 2005 is xtract irctly from th provincial statistical yarbook. I mak two mor ajustmnts. First, Bijing tras a lot with th ROW, but th majority of th tra is on by big companis (spcially thos SOEs) with haquartrs in Bijing. It is plausibl that th tra is actually carri in th subsiiaris of ths companis, spra out ovr th country. Fortunatly, Bijing statistical yarbook rports local tra an total tra sparatly, th latr incluing tra on by SOEs. I assign local tra to Bijing, an th rmaining componnt of total tra to all Chins citis, bas on thir rlativ siz. Th implicit assumption is that th opration of thos SOEs haquartr in Bijing ar istribut across all citis, proportionally to thir siz. Scon, somtims th ata is not wll-bhav. For xampl, for Shaoshan, a city in Guangong Provinc, on of th coastal provincs, th tra surplus is 13 tims of its GDP. My conjctur is that thr ar many tra intrmiaris. I mak th following ajustmnts: I aggrgat city-lvl tra surplus to th provinc lvl, an thn allocat th tra surplus of a provinc to th citis in th provinc, accoring to th GDP of ths citis. Th unrlying assumption is that thos tra intrmiaris mostly work with othr companis in th sam provinc, 11

12 an tra surplus is proportional to siz of conomy within a provinc. To trmin th city-lvl tra surplus in th scal of th mol conomy, I first calculat th aggrgat tra surplus from th ata. I convrt th aggrgat surplus into th scal of th mol an istribut it to all citis, proportionally to ach city s contribution to th aggrgat tra surplus in th ata, construct abov. Ths ar th surplus trms, S, in Equation (33). B.2.7 Input-output Linkags for China an th ROW In th mol, th input-output paramtrs for China ar construct from th 2002 national input-output tabl, which rcors, at th 2-igit inustry lvl, th usags of inputs in th conomy. I aggrgat th ata to four inustris agricultural, capital an quipmnt, othr manufacturing, an srvic, an four inputs inustry final outputs in th agricultural, othr manufacturing, an srvic inustris, as wll as quipp composit labor. Th input shars of th ROW ar assum to b th sam as th mian country in Parro (2013). Sinc th inustry classification is finr in this papr, for valus not irctly availabl in Parro (2013), I us th corrsponing valu from China, scal appropriatly. Th unrlying assumption bhin this imputation that, input-output linkags ar similar across iffrnt countris, ar strongly support by Ions (2013). All rsults in th papr ar robust to changs in th input shars. Tabl (B.3) rport th shars of inputs in ach inustry. Tabl B.3: Input Shars in China an th ROW γ s s Output Inustry: China Input A M K S L A M S γs s Output Inustry: ROW Input A M K S L A M S Nots: This tabl rports th input shars for iffrnt inustris in China an th ROW. Th sourc of th valus for China is th national input-output tabl for 2002; th valus for th ROW ar calculat bas on Parro (2013). L s- tans for th quipp composit labor. 12

13 C Estimation an Calibration Appnix C.1 Calibrating ρ I obtain an iniviual panl ata from China (China Nutrition an Halth Survy), an stimat a Mincr rgrssion with rgional fix ffcts, along with gnr, ucation, ag, an ag squar as control variabls. I thn a iniviual fix ffcts to th spcification. I compar th R 2 of ths two rgrssions an s how much of th variation unxplain in th first Mincr rgrssion is xplain by th iniviual fix ffcts. As it turns out, about 70% of th unxplain variations can b xplain by iniviual fix ffcts. Not that th corrlation paramtr, ρ, maps on-to-on into th xplanatory powr of iniviual fix ffcts in th wag rgrssion. For ach givn valu of ρ, I simulat workrs prouctivity raws from iffrnt locations, thn stimat a rgrssion spcification with only iniviual fix ffcts, an calculat th R 2. I chos th corrlation paramtr so that this R 2 is 70%. This procur trmins a valu of 0.4 for ρ. C.2 Estimating Migration Cost I us nonlinar last squars to stimat th migration cost, in which {β} is trmin by minimizing th iffrnc btwn th mol-prict migration flows an thir ata countrparts. Sinc th ata is at th provincto-city lvl, I aggrgat th prict city-to-city flows to provinc-to-city lvl an tak as th objctiv function th sum of squar of th iffrncs btwn th mol s prictions an th ata. Formally, lt p P inxs a provinc in th st of all provincs, P, an o p inxs a rgion o blonging to provinc p. Rcall that lo is th numbr of workrs born in o, an πo, is th mol-prict probability for workrs to mov from o to, thn loπ o, is th mol-prict flow from o to an o p l oπo, is th aggrgat flow from provinc p to rgion. Lt L p, b th flow from p to in th ata, th stimation problm can b formulat in th following way: min p P, G(log( {β} o p l oπ o, ) log(l p, ))2 To prict th migration flows using th mol, w n to know th rgional amnity-ajust ral wags, v. Bcaus thr ar mor than six hunr rgions (rural an urban sctors in 340 citis), it is infasibl to stimat all {v } an {β} simultanously. I aopt a nst procur, similar in spirit to Brry t al. (1995), as follows: in th innr loop, for ach givn {β}, I solv th migration mol for th amnity-ajust ral wags, {v }, so that th mol-prict total numbr of workrs in ach rgion is th sam as that in ata, that is, o G l oπo, = p P L p,, G. Onc w hav {v }, w can comput th mol-prict migration flows, an valuat th objctiv function for th givn {β}. In th outr loop, I thn sarch ovr th spac of {β} to minimiz th objctiv function. 11 Proposition 1 in Sction A of this appnix nsurs th fasibility of this approach by stablishing th xistnc an uniqunss of th solution to th problm in th innr loop. W us th 2000 migration ata, construct in sction A of this appnix, to stimat {β}. Aftr obtaining th stimats, to nsur th rcovr {v } ar consistnt with th 2005 mploymnt istribution, w solv Equation 11 This nst approach is quivalnt to imposing a constraint that th (mol-prict) total numbrs of workrs migrating to ach plac quals th total numbr of workrs in that plac in th ata, an thrfor is similar in spirit to what is rfrr to as structural gravity stimation in tra litratur. S Fally (2013) for a iscussion of th rlationship btwn this an altrnativ approachs of gravity stimation. (C.4) 13

14 o G l oπ o, = p P L p,, G again, using L an l o from 2005, to obtain th nw {v }. C.3 Jointly Estimating Tra Cost an Prouctivity I trmin intrnational tra costs, omstic tra costs, an rgional prouctivity jointly. As iscuss in th txt, u to th aggrgat natur of th ata, I us nonlinar last squar in stimation, which rquirs solving th mol for th prictions of tra flows. In solving th mol, to nsur th siz an spcialization of th citis in th mol ar consistnt with th ata, I comput th prouction of intrmiat varitis in ach inustris in all citis (tails in Sction B.2.3 of this appnix), an forc th joint stimation algorithm to rspct this istribution of intrmiat varity prouction. Figur (C.4) xplains th joint stimation algorithm. I start with an initial guss for intrnational tra costs, an th paramtrs govrning omstic tra costs, {γ}, with which I comput th tra cost btwn any tra partnrs, {τ o, }. I thn guss a istribution for rgional prouctivity, solv th tra mol for prics an tra shars, an chck if th man for intrmiat varitis prouc by ach rgion quals th supply. 12 If not, I upat th guss for th istribution by incrasing prouctivity in rgions with xcss supply, an cras prouctivity in rgions with xcss man. Th intuition bhin this is that, if a rgion facs xcss man, it mans th intrmiat varitis prouc thr is comptitiv in th intrnational markt. To rstor th markt claring conition for this rgion, I mak th intrmiat varitis prouc in that rgions mor xpnsiv by crasing th prouctivity. 13 Onc th istribution of rgional prouctivity that clar all intrmiat varity markts ar foun, I comput th bilatral tra flows, an valuat th objctiv function (C.5). All P1, P2 X P 1,P 2 [log( ) th mol countrpart] 2, Domstic Sals P 1 (C.5) whr X P 1,P 2 is th xport of goos from provinc P1 to provinc P2 in th ata. In spcifying th objctiv function, sinc th omstic tra ata is at provincial lvl, to bring th mol an th ata togthr, I aggrgat th mol-prict tra flows to provincial lvl. I normaliz th tra flows by aggrgat omstic sals of th sourc provincs, so that th stimats ar not affct by th chang in intrnational tra opnnss btwn 2002 an I sarch ovr th spac of {γ} until th global minimum is rach, aftr which I calibrat intrnational tra costs to match th sctoral opnnss, kping both omstic tra costs an rgional prouctivity fix. I rpat th procss until convrgnc. 12 In th stp whr w solv th tra mol, if w know η h an η s, Equations (17), (25), an (28) in th txt can b viw as a systm of quations with prics bing th only unknowns. Onc w solv ths quations for th prics, w can obtain tra shars. Although η h an η s ar unknown bfor th mol is paramtriz, in sction C.4 of this appnix I show that, conitional on information on th shars of iffrnt factors in th quipp composit labor, η h an η s ar unncssary in solving th mol. Onc th mol is solv, howvr, w can us Equation (29) to back out η h an η s, to b us in policy xprimnts. 13 Th fasibility of this approach rquirs that, for any givn lvl of tra costs, w can fin a st of uniqu T s that clar all intrmiat varity markts in all locations. Ring (2012) provs this is tru in a singl-sctor mol. An arlir vrsion of this papr xtns th proof to a multi-sctor mol with input-output linkags within th sam broa sctor. In th gnral mol hr with flxibl input-output linkags an capital-skill complmntarity, th uniqunss cannot b stablish. But in implmntation, I fin th upat rul always convrg uniformly to on uniqu objct. 14 Th omstic tra ata is from 2002, whras th mploymnt ata us to trmin prouction an consumption is from By normalizing th flows using omstic sals of sourc provincs, I ffctivly us only th omstic tra pattrns in 2002 for stimation. 14

15 Figur C.4: Estimation Algorithm Bgin Intrnational tra cots t A, t M, t K Choos omstic tra cost paramtrs γ Upat rgional prouctivity T A, T M, T K Solv th mol, obtain prict tra flows No Markts clar for intrmiat varitis? Ys Evaluat Objct Function (C.5): viations of prict tra flows from ata No Global Minimum Rach? Ys Calibrat t A, t M, t K to match sctoral opnnss Upat No Sam as t A, t M, t K? Ys Exit 15

16 C.4 Aitional Information on th Joint Estimation In solving th tra mol, w n to comput th prics of traabl goos, for th stimat rgional wags an givn istribution of tchnology {T s}. Computing th prics, howvr, rquirs ηh an ηl (s footnot (12)). To proc with th stimation algorithm, not knowing η h, ηl Capital Shar, I substitut th rlativ factor shars, Skill Shar an, at th rgional lvl, to th lft han si of Equation(28) in th txt, an xprss η h, ηl as Equipp Skill Shar Unskill Shar η h = ( P K ) 1 ρ W h kh Capital Shar Skill Shar + ( P K ) 1 ρ W h kh ( W h ) 1 ρ, η l = W l lkh Equipp Skill Shar Unskill Shar + ( W h ) 1 ρ W l lkh (C.6) I thn substitut Equation (C.6) into (28), an solv th mol without actually knowing η h or ηl. Th ia is that, η h an ηl must b consistnt with th optimal choics of quipp composit labor proucrs, an thrfor whn w vary th prics, w also ajust η h an ηl so that th optimal factor shars ar consistnt with ata. Onc th whol procur is ovr an th mol is solv, w can thn back out η h an ηl from (C.6). Ths ar intrprt as th tru paramtr valus, which I kp fix for all countrfactual xprimnts. C.5 Paramtrs for th Countrfactual Exprimnts with Diffrnt Intrnal Gographis In th countrfactual xprimnts with altrnativ intrnal gographis, rport in Sction 7.2, I ruc th valus of intr-provincial ummis in th tra an migration cost spcifications in China to th U.S. lvl. In this sction I scrib th sourcs an valus of ths paramtrs. Th valu of intr-stat tra costs ar from Crafts an Klin (2014), which stimats U.S. intr-stat tra using th latst ata. Unr iffrnt spcifications, thir stimats for th intr-stat ummy rang btwn 2 to To b consrvativ, I us th uppr boun of thir stimats, This stimat of th intr-stat ummy bunls togthr tra lasticity an tra costs, so I rcovr th intr-stat tra cost by iviing 2.55 by 4, th tra lasticity, arriving at Thrfor in rlvant xprimnts I ruc th intr-provincial tra costs from th bnchmark lvl of 1.1 to Tabl C.4: Gographic Paramtrs in Countrfactual Exprimnts Intr-city (provincial) migration costs Intr-stat tra costs Skill Workrs Unskill Workrs Bnchmark Lvl (1.50) 1.20 (1.56) TC (1.50) 1.20 (1.56) SMC (0.99) 1.20 (1.56) UMC (1.50) 0.99 (0.99) Nots: This tabl rports th valus of th paramtrs that trmin th intrnal frictions, us in th countrfactual xprimnts in Tabl (7). Th first column rports th valus of th intr-provincial ummy in tra cost spcification in iffrnt xprimnts; th scon an thir columns rport th valus of intr-city an intr-provincial ummy in migration cost spcification, with intr-provincial ummy in parnthsis. Othr than th paramtrs rport in this tabl, all paramtrs ar kpt at thir calibrat valus. Th valu of intr-stat migration costs ar from Piyaprom (2014), which stimats migration costs for iffrnt mographic groups in th U.S. Sinc high-skill workrs in Piyaprom (2014) ar collg grauats, 16

17 I focus on th low-skill young mal group, for which th stimat intr-stat migration costs is 99 log points. I apply this valu to th intr-provincial migration cost in China, for both unskill an skill workrs. On furthr complication is that my spcification for migration costs inclu an intr-city ummy, but th stimat valus of th intr-city ummy, for both skill an unskill workrs, ar largr than Thrfor, in countrfactual xprimnts, whn I ruc th migration costs for crtain typ of workrs, I ruc both th intr-city an th intr-provincial ummy to Th paramtr valus in iffrnt cass ar summariz in Tabl (C.4). C.6 Discussion on th Estimat Intr-Provincial Effct an Aitional Robustnss In Sction 6.5.2, I rport my stimats of th omstic tra costs. It is usful to compar my stimats to thos obtain using th U.S. Commoity Flow Survy ata. In th litratur, th comparabl cofficint for stat borr, aftr scal appropriatly by th lasticity of tra, is on th rang of 0.38 (Wolf, 2000) to 0.65 (Crafts an Klin, 2014, using 2007 ata). So my stimat of th stat-borr ffct is about twic as larg as th comparabl stimats for th U.S., rflcting largr barrirs to tra flows at provincial borrs in China. On lsson from th U.S. stat borr litratur is that, th stimats might b rivn up by th wholsal inustry (Hillbrry an Hummls, 2003), an might suffr from th aggrgation bias a lot of tra costs ar actually u to gographic istanc, but might b captur by th stat-borr ummy whn stat-lvl aggrgat ata is us. Whn ths two factors ar takn into account, th stimats shrink (Hillbrry an Hummls, 2008). Thrfor, as iscuss in Sction 6.5.2, on natural concrn is whthr in China, u to th quality, or th lvl of aggrgation, of th ata, th stimats might also misattribut th impacts of gographic istanc to th provincial borrs; an if that is th cas, whthr th rsults from th countrfactual xprimnts ar still vali. Without tail micro-lvl tra flow ata availabl for China, I cannot xamin th bias of th stimats. Insta, I us an aitional xprimnt to show that vn if thr is bias in th stimation, it will not affct main conclusions of th countrfactual xprimnt. Spcifically, I prform a robustnss xrcis, in which I ruc intrprovincial an intr-rgional tra costs to 0.65, th lvl of th U.S. conomy, whil at th sam tim incras th cofficints for th continuous gographic componnts, so that th ovrall omstic tra costs an intrnational tra participation ar similar to thos of th bnchmark conomy. Effctivly, I chang th composition of th omstic tra costs, kping its ovrall lvl sam as bfor. I shut own intrnational tra in this conomy, an comput th wlfar gains from tra, as wll as othr outcom variabls iscuss in th txt. Th rsults, rport in Tabl (C.5), ar vry similar to thos of th bnchmark xprimnt, rport in th first column of Tabl (7). 17

18 Tabl C.5: Countrfactual Exprimnt with an Altrnativ Domstic Tra Cost Structur Panl A: Statistics by Workr Group Man st Urban Skill Urban Unskill Rural Skill Rural Unskill Panl B: Aggrgat Statistics National Avrag 7.47 Tra Opnnss Incras in Inquality 6.7 Contribution-Btwn(%) Contribution-Within (%) Rfrncs Ahlflt, Gabril M, Stphn J Ring, Danil M Sturm, an Nikolaus Wolf, Th Economics of Dnsity: Evinc from th Brlin Wall, CEP Discussion Papr 1154, Brry, Stvn, Jams Lvinsohn, an Aril Paks, Automobil Prics in Markt Equilibrium, Economtrica, 1995, pp Cana, Brian C an Brian K Kovak, Immigrants Equilibrat Local Labor Markts: Evinc from th Grat Rcssion, NBER Working Papr 19272, Crafts, Nicholas an Alxanr Klin, Gography an Intra-national Hom Bias: U.S. Domstic Tra in 1949 an 2007, Journal of Economic Gography, Fally, Thibault, Structural Gravity an Fix Effcts, Working Papr, Univrsity of Colorao-Boulr, Hillbrry, Russll an Davi Hummls, Intranational Hom Bias: Som Explanations, Rviw of Economics an Statistics, 2003, 85 (4), an, Tra Rsponss to Gographic Frictions: A Dcomposition Using Micro-ata, Europan Economic Rviw, 2008, 52 (3), Ions, Charls I, Misallocation, Economic Growth, an Input-Output Economics, in Avancs in Economics an Economtrics: Tnth Worl Congrss, Vol. 2 Cambrig Univrsity Prss 2013, p Knnan, John an Jams R Walkr, Th Effct of Expct Incom on Iniviual Migration Dcisions, Economtrica, 2011, 79 (1), Michals, Guy, Stphn J Ring, an Frinan Rauch, Tchnical Not: An Eaton an Kortum (2002) Mol of Urbanization an Structural Transformation, Mimo, Parro, Frnano, Capital-skill Complmntarity an th Skill Prmium in a Quantitativ Mol of Tra, Amrican Economic Journal: Macroconomics, 2013, 5 (2),

19 Piyaprom, Suphanit, Th Impact of Immigration on Wags, Intrnal Migration an Wlfar, Mimo, Ring, Stphn J., Goos Tra, Factor Mobility an Wlfar, NBER Working Papr 18008, Wolf, Holgr C, Intranational Hom Bias in Tra, Rviw of conomics an statistics, 2000, 82 (4),