Trade, Migration and Productivity: A Quantitative Analysis of China

Transcription

1 Trade, Mgraton and Productvty: A Quanttatve Analyss of Chna Trevor Tombe Uversty of Calgary Xaodong Zhu Uversty of Toronto Frst Verson: January 2014; Ths Verson: June 2015 Abstract We study how msallocaton due to goods- and labour-market frctons affect aggregate productvty n Chna. Combng uque data wth a general equlbrum model of nternal and nternatonal trade, and mgraton across regons and sectors, we quantfy the magtude and consequences of trade and mgraton costs. The costs were hgh n 2000, but declned afterward. The declne accounts for roughly twoffths of aggregate labour productvty growth n Chna between 2000 and Reductons n nternal rather than nternatonal costs are partcularly mportant. Despte the declne, mgraton costs are stll hgh and potental gans from further reform are large. JEL Classfcaton: F1, F4, R1, O4 Keywords: Mgraton; nternal trade; spatal msallocaton; gans from trade; Chna Tombe: Department of Economcs, Uversty of Calgary, 2500 Uversty Drve NW, Calgary, Alberta, T2N1N4. Emal: [email protected]. Zhu: Department of Economcs, Uversty of Toronto, 150 St. George Street, Toronto, Ontaro, M5S3G7. Emal: [email protected]. We thank Andrew Atkeson, Lorenzo Calendo, Kunal Dasgupta, Jonathan Dngel, Jm Harrgan, Chad Jones, Ncholas L, Peter Morrow, Albert Park, Mke Peters, Dego Restucca, Aleh Tsyvnsk, Xaobo Zhang, Fabrzo Zlbott, Yaohu Zhao, and especally Dael Trefler for very helpful comments and suggestons. We have also benefted from comments of varous semnar partcpants at the Bank of Canada, CCER n Pekng Uversty, Chcago Fed, CUHK, Fudan Uversty, George Washngton Uversty, HKUST, IMF, Mchgan State Uversty, Phladelpha Fed, Shangha Uversty of Fnance and Economcs, San Francsco Fed, Uversty of Calgary, Uversty of Toronto, Uversty of Vrga and Yale Uversty, and partcpants n many conferences. Tombe acknowledges fnancal support from the Socal Scence and Humates Research Councl (IG ). A prelmnary verson of ths paper was dstrbuted under the ttle of Trade, Mgraton and Regonal Income Dfferences: Evdence from Chna. Stable lnk to paper:

2 1 Introducton Dfferences n aggregate total factor productvty (TFP) are a key source of large cross-country ncome dfferences (Klenow and Rodrguez-Clare, 1997; Hall and Jones, 1999; Casell, 2005) and msallocaton of nputs can be an mportant reason for low levels of aggregate TFP n poor countres (Banerjee and Duflo, 2005; Restucca and Rogerson, 2008; Hseh and Klenow, 2009; Bartelsman et al., 2013). It s therefore mportant to understand the sources of msallocaton. Indeed, n a revew of the recent lterature on msallocaton, Restucca and Rogerson (2013) state the most persuasve evdence n support of the role of msallocaton wll come from work that follows the drect approach n specfc contexts, especally those n whch we observe changes n some underlyng source of msallocaton and can measure the resultng change n msallocaton and aggregate TFP. In ths paper we provde drect evdence on frctons to labour and goods flows across space and sectors as a source of msallocaton n Chna. We further quantfy the contrbuton of changes n these frctons on Chna s growth between 2000 and It s well known that Chna n the early 2000s had substantal polcy-nduced mgraton costs (Poncet, 2006; Ca et al., 2008) and nternal trade costs (Young, 2000; Poncet, 2005). Snce then, the Chnese government has undertaken polcy reforms and nfrastructure nvestments that reduced both mgraton and trade costs and, at the same tme, the Chnese economy has experenced sgfcant aggregate productvty growth (Zhu, 2012). Chna therefore provdes an excellent case study for evaluatng how much of aggregate productvty growth could be attrbuted to reductons n mgraton and trade costs and the resultng decrease n msallocaton. As a framework for our quanttatve analyss, we develop a two-sector multregon general equlbrum model featurng nternal trade, nternatonal trade, and worker mgraton. Our model bulds on the recent work of Ahlfeldt et al. (2012) and Reddng (2015). Followng Reddng (2015), we ntroduce wthn-country trade and worker moblty nto the Eaton and Kortum (2002) model and explctly model worker locaton choces n the presence of mgraton costs. Our man departure from these papers s that we ntroduce frctons to both between-regon and wthnregon between-sector mgraton. Specfcally, wthn each regon there s an agr- 1

3 cultural and a nonagrcultural sector. Workers are heterogeneous n ther productvty across regons and sectors. Some workers mgrate or swtch sectors despte the costs whle others do not. Even wth these rch and realstc features, the model s stll analytcally tractable and can be easly mplemented for quanttatve analyss. We ft ths model to Chna, mappng t drectly nto data for Chna s provnces and sectors, and the rest of the world. To estmate the level and changes n trade and mgraton costs, we use model-mpled gravty equatons and uque data over tme on trade and mgraton flows. We use the 2002 and 2007 Chna Regonal Input- Output Tables, whch provde the full blateral tradng matrces for all provnces and for a varety of sectors, and the 2000 Populaton Census and 2005 Populaton Survey, whch provde nformaton on mgraton between and wthn provnces. Our estmates show that trade costs were large n In nonagrculture, average nternal and external trade costs were 30% and 20% hgher than the correspondng costs n Canada. In agrculture, the gaps were even larger: average nternal and external trade costs were roughly three tmes hgher than n Canada. Between 2002 and 2007, Chna s trade costs declned sgfcantly: on average, nternal costs fell by between 10-15% and nternatonal costs fell by almost 10% n nonagrculture and nearly 25% n agrculture. Turng to mgraton costs, note that we consder them ongong flow costs rather than sunk costs. Chna has a Hukou household regstraton system that mposes large costs of workng and lvng outsde one s Hukou regstraton regon, prmarly through restrcted access to socal servces and lmted employment rghts. These costs are recurrng and exst as long as mgrants do not have a local Hukou resdence status. An ndcaton of how tghtly mgraton costs bnd s the large regonal ncome dsparty across provnces. In 2000, the rato of the ncome per worker for the 90th and 10th percentle provnces n Chna was 3.2 (the correspondng rato for U.S. states s around 1.5). Wth our model and data, we quantfy the magtude of these costs. Accordng to our estmates for 2000, the average cost of wthn-provnce rural-urban mgraton s around 51% of annual ncome; the costs of between-provnce mgraton are even hgher: 94% of annual ncome for ruralto-rural or urban-to-urban mgraton and 98% for rural-to-urban mgraton. These costs are prohbtve for most workers. For others wth hgh ndvdual productv- 2

4 ty n the destnaton regon and sector, the benefts of mgratng outwegh the hgh costs. Between 2000 and 2005, average wthn-provnce mgraton costs declned around 11% and average between-provnce mgraton costs declned between 1.4% and 6%, much lower than the reductons n trade costs. What are the consequences of these measured changes n trade and mgraton costs? In a seres of quanttatve exercses usng the fully calbrated model, we evaluate how cost changes affect trade flows, mgraton, welfare, productvty, and regonal ncome dfferences. Lower nternatonal trade costs ncreased the stock of both nter-provncal and wthn-provnce mgrants by 4-6%. Lower nternal trade costs results n about 2.3% fewer nter-provncal mgrants and 2.3% more wthn-provnce mgrants. Though mgraton responses are small, aggregate welfare responses are large 10.9% gans from nternal trade cost reductons, 3.1% for external, and 13.8% for both. The large gans from nternal trade cost reductons, relatve to the external reductons, are prmarly because the share of spendng gong to producers outsde one s local regon but wthn Chna s larger than to producers outsde Chna. In terms of regonal ncome dfferences, nternal trade cost reductons lower the varance n (log) real ncomes across provnces by over 7% whle reductons n nternatonal trade costs ncrease the varance by nearly 2%. Trade cost changes may account for very lttle change n mgraton, but mgraton costs account for much more. In response to the measured mgraton cost reductons, the stock of wthn-provnce and between-provnce mgrants ncrease by over 20% and 220%, respectvely. The mgraton cost reductons also ncreased aggregate productvty and welfare by 12.1% and 7.3%, respectvely. Wth these results, we perform a growth accountng exercse to decompose Chna s aggregate labour productvty growth between 2000 and 2005 nto components reflectng nternal trade and mgraton cost reductons, external trade lberalzaton, and all other factors (sectoral productvty or captal accumulaton, for example). Internal trade cost reductons account for one-ffth of Chna s aggregate real GDP per worker growth over the perod. Mgraton cost reductons yeld almost as much. Internatonal trade lberalzaton, however, accounted for only 7% of the growth, whch s n stark contrast to perceptons that Chna s growth s an exportled experence. Overall, reductons n trade and mgraton costs account for close 3

5 to half of Chna s aggregate labour productvty growth from 2000 to Despte the declne n trade and mgraton costs, the scope for further cost reductons beyond those measured s stll large. We fnd movng Chna s nternal trade costs to levels measured n Canada yelds welfare gans of roughly 12%. Gans are even larger f mgraton costs fall to match U.S. mgraton rates, wth real GDP ncreasng nearly 23% and welfare by 15%. 1 In summary, our quanttatve analyss shows that domestc reforms that reduced nternal trade and mgraton costs and the resultng msallocaton accounts for a sgfcant porton of Chna s aggregate productvty growth between 2000 and Further reforms that reduce Chna s costs to developed country levels may lead to equally sgfcant aggregate productvty growth n Chna n the future. In addton to the msallocaton lterature dscussed earler, we contrbute to a growng lterature lnkng nternatonal trade flows wth the spatal dstrbuton of labour and economc actvty wthn countres, such as Cosar and Fajgelbaum (2012); Dx-Carnero and Kovak (2014); Allen and Arkolaks (2014); Bryan and Morten (2015); Reddng (2015) and Calendo et al. (2015). There are also papers nvestgatng nternal trade or mgraton costs separately, such as Morten and Olvera (2014), Bryan and Morten (2015) or Gha et al. (2012), and emprcal nvestgatons of trade s effect on nternal mgraton, such as McCag and Pavck (2012) for Vetnam or Aguayo-Tellez and Muendler (2009) and Herng and Pallacar (2012) for Brazl. There s also a large urban-economcs lterature nvestgatng the role of nternatonal trade n alterng the spatal dstrbuton of frms and factors wthn a country, such as Hanson (1998). Lttle work has been done, however, nvestgatng the case of Chna perhaps the largest and fastest expanson of trade and nternal mgraton ever recorded. Exstng work, such as Ln, Wang and Zhao (2004) or Poncet (2006), typcally abstracts from general equlbrum effects and nvestgates data only pror to Brandt et al. (2013) use a general equlbrum model to quantfy the aggregate productvty loss due to msallocaton of labour and captal across space n Chna, but the sources of msallocaton are not explctly modeled. In contrast, we model trade and mgraton costs as specfc sources of msallocaton. 1 We compare Chna to Canada as Statstcs Canada s nternal trade data s superor to the U.S. For mgraton, we can compare Chna to U.S. mgraton flows. 4

6 2 Chna s Internal Mgraton and Trade To set the stage for our quanttatve analyss, we begn wth a dscusson of the data, the spatal aspects of the Chnese economy and the polcy envronment that affects workers and trade flows n Chna. 2.1 Data We need data on real ncome by provnce and sector, nternal and external trade, and nternal mgraton for our quanttatve analyss. For real ncome, we calculate real GDP per worker usng the offcal statstcs on nomnal GDP and employment, and the rural and urban prce levels provded by Brandt and Holz (2006). For trade, we use regonal nput-output tables for 2002 and Specfcally, L (2010) reports blateral trade flows for all provnces and for a varety of sectors n For changes n trade flows, Zhang and Q (2012) provde the blateral trade flows between eght aggregate regons n both 2002 and For mgraton, we use the 2000 Populaton Census and % Populaton Survey. We summarze some key features of the data here and provde a detaled descrpton n Appendx A. 2.2 Spatal Dstrbuton of Income In Fgure 1a, we dsplay real ncomes n 2000 for each provnce of Chna. There are stark dfferences n real ncome levels across provnces. The rato of average real GDP per worker of the top fve provnces to that of the bottom fve provnces s almost 4:1. In general, the provnces of the coastal regons n the east have substantally hgher levels of real GDP per worker than provnces n the central and western regons. Despte large ncome dfferences there was very lttle mgraton. 2.3 Mgraton Polces and Mgraton Patterns In 1958, the Chnese government formally nsttuted a Hukou regstraton system to control populaton moblty. Chan (2010) provdes a detaled dscusson of the Hukou system; we summarze ts key features. Each Chnese ctzen s assgned a 5

7 Fgure 1: Spatal Dstrbuton of Real Incomes and Mgraton n 2000 (a) Real GDP/Worker, Relatve to Mean (b) Mgrant Share of Total Employment Helongjang Helongjang Inner Mongol Jln Inner Mongol Jln (1.5,3] (1.25,1.5] (1.1,1.25] (1,1.1] (.75,1] (.65,.75] (.55,.65] (.45,.55] [.25,.45] No data Xnjang Tbet Qngha Laong Bejng Tanjn Shanx Hebe Nngxa Shandong Gansu Shaanx Henan Jangsu Anhu Hube Shangha Schuan Zhejang Guzhou Hunan Jangx Yunnan Fujan GuangxGuangdong Hanan (.1,.27] (.075,.1] (.04,.075] (.02,.04] (.01,.02] (.0075,.01] (.005,.0075] [.0025,.005] No data Xnjang Tbet Qngha Laong Bejng Tanjn Shanx Hebe Nngxa Shandong Gansu Shaanx Henan Jangsu Anhu Hube Shangha Schuan Zhejang Guzhou Hunan Jangx Yunnan Fujan GuangxGuangdong Hanan Note: Dsplays choropleths of relatve real ncome levels for each of Chna s provnces and the mgrant share of total employment. Dark reds ndcate both hgh relatve real ncomes and large mgrant shares of employment. Hukou (regstraton status), classfed as agrcultural (rural) or nonagrcultural (urban) n a specfc admstratve ut that s at or lower than the county/cty level. Approvals from local governments are needed for an ndvdual to change the category (agrcultural or non-agrcultural) or locaton of Hukou regstraton, and t s extremely dffcult to obtan such approvals. Before the economc reform started n 1978, workng outsde one s Hukou regstraton locaton/occupaton category was prohbted. Ths prohbton was relaxed n the 1980s, but pror to 2003 workers wthout local Hukou stll had to apply for a temporary resdence permt. Ths was dffcult, so many mgrant workers were wthout a permt and faced the dre consequence of beng arrested and deported by the local authortes. As the demand for mgrant workers n manufacturng, constructon and labour ntensve servce ndustres ncreased, many provnces, especally the coastal provnces, elmnated the requrement of temporary resdence permt for mgrant workers after Ths polcy change helped to ease mgraton but the costs reman hgh. Even wth a temporary resdence permt, mgrant workers wthout local Hukou have very lmted access to local publc servces and face much hgher costs for health care and for ther chldren s educaton. More mportantly, mgrant workers always face these costs as long as they do not have local Hukou. Table 1 presents the total number of nter-provncal and ntra-provncal mgrant workers for 2000 and 2005 and ther shares of total employment. Any worker 6

8 Table 1: Stock of Mgrant Workers n Chna Inter-Provncal Intra-Provncal Total Stock (mllons) Share of Total Employment 4.2% 7.2% 14.3% 17.7% Notes: Mgrants are defned based on ther ther Hukou regstraton locaton. Inter-provncal mgrants are workers regstered n another provnce from where they are employed. Intra-provncal mgrants are workers regstered n the same provnce where they are employed, but are ether non-agrcultural workers holdng agrcultural Hukou or vce-versa. n a provnce other than the provnce of hs/her Hukou s classfed as an nterprovncal mgrant. A worker wthn hs/her Hukou regstraton provnce but n an occupaton other than hs/her Hukou category (agrcultural or non-agrcultural) s classfed as an ntra-provncal mgrant. Most of the ntra-provncal mgrant workers are rural-to-urban mgrants who have agrcultural Hukou but work outsde agrculture. Between 2000 and 2005, the numbers of nter- and ntra-provncal mgrant workers have both ncreased sgfcantly. By 2005, there were 49 mllon workers who moved across provncal boundares and 120 mllon workers who swtched occupatons wthn a provnce. Whle mgraton of ths magtude s unprecedented, as a share of total employment t s less mpressve. Despte large ncome dsparty across provnces, nter-provncal mgrant workers accounted for only 4.2% of total employment n 2000 and 7.2% n There s heterogenety across provnces, of course. Fgure 1b plots for each provnce the mgrant workers share of total employment n Not surprsngly, rcher provnces n coastal regons tend to have hgher mgrant worker shares than poorer nteror provnces. Provnces wth more nter-provncal mgrant workers also tend to have hgher ntra-provncal mgrant workers. We provde more detal n Appendx A. 2.4 Trade Polces Several researchers have documented hgh nternal trade costs n Chna n the 1990s (Young, 2000; Poncet, 2005). It has also been documented that the degree of local market protecton n a provnce was drectly related to the sze of the state sector n that provnce (Ba et al., 2004). Snce 2000, these trade barrers have been reduced 7

9 Table 2: Internal and External Trade Shares of Chna Exporter Total North- Bejng North Central South Central North- South- Other Importer east Tanjn Coast Coast Coast Regon west west Abroad Prov. Year 2002 Northeast Bejng/Tanjn North Coast Central Coast South Coast Central Regon Northwest Southwest Abroad Year 2007 Northeast Bejng/Tanjn North Coast Central Coast South Coast Central Regon Northwest Southwest Abroad Note: Dsplays the share of each mportng regon s total spendng allocated to each source regon. See Appendx A (Trade Shares) for the mappng of provnces to regons. The column Total Other Prov. reports the total spendng share each mportng regon allocated to producers n other provnces of Chna. The dagonal elements (the home share of spendng), the share mported from abroad, and the share mported from other provnces wll together sum to 100%. sgfcantly. Some of the reducton was due to the delberate polcy reforms undertakng by the government. For example, the state councl under then premer Zhu Rongj ssued a drectve n 2001 that prohbts local government from engagng n local market protectons. More mportantly, as a result of varous SOE reforms, the sze of the state sector has declned sgfcantly and consequently lowered local government ncentves to engage n local market protectons. Improved transport nfrastructure and logstcs also helped lower nternal trade cost. 2.5 Internal and External Trade Patters We extract provnce-level trade data, both between provnce pars and nternatonally, from the regonal nput-output tables for 2002 and Table 2 reports the aggregate blateral flows between the eght regons and each other, and the rest of the world (see Appendx A for a lst of provnces by regon). To ease comparsons, we normalze all flows by the mportng regon s total expendtures, resultng n a 8

10 table of expendture shares π = x / N =1 x, where x s the spendng by regon n on goods from regon. In addton to the blateral trade flows, we also report n the last column the share of a regon s expendtures that are spent on goods from all other regons wthn Chna. A useful measure of a regon s trade openness s the fracton of ts expendtures allocated to ts own producers that s, t s home share. The dagonal elements of Table 2 provde these values for each regon. Interor regons of Chna have much hgher home-share than coastal regons. In 2002, the central regon s home share s 0.88 compared to only 0.72 for the south coast and 0.63 for Bejng and Tanjn. Whle regons n Chna generally mport more from abroad than from any partcular regon wthn Chna, the total mports from the rest of Chna are stll hgher than mports from abroad for most of the regons. The Central Coast and South Coast regons are the exceptons. In 2000, ther mports from abroad were sgfcantly hgher than mports from the rest of Chna; they also had substantal nternatonal exports. All trade values reported so far are at the regonal level. For 2002, we also compute trade shares for each ndvdual provnce and for each sector (agrculture and nonagrculture) separately. Consstent wth the regonal data, nteror provnces have hgher home-shares than coastal provnces, and coastal provnces export a larger fracton of producton nternatonally. These provnce and sector level trade data wll play a crucal role n our quanttatve exercses to come. They also provde nformaton crtcal to estmate nternal and external trade costs. We turn now to our quanttatve model. 3 Quanttatve Model In ths secton, we develop a two-sector model of trade and mgraton buldng on Eaton and Kortum (2002), Ahlfeldt et al. (2012) and Reddng (2015). The model features two tradable sectors and multple regons of Chna between whch goods and labour may flow. Our man departure from these papers s that we ntroduce between-regon mgraton frctons and wthn-regon rural-to-urban mgratons. There are N + 1 regons representng Chna s provnces plus the rest of the 9

11 world. Each regon has two sectors: agrculture and nonagrculture, denoted j {ag, na}. Each regon s also endowed wth a fxed factor (land, structures), denoted S j n, that s used for housng and producton. Fnally, there are L j n workers regstered n regon n and sector j. Workers dffer n regon-sector specfc productvty (or effectve uts of labour), and we denote the supply of effectve labour n regon n and sector j as Hn j wth the total supply of effectve labour as H n = Hn ag +Hn na. Workers can mgrate between rural and urban sectors wthn a regon and between provnces wthn Chna, but there s no labour moblty between Chna and the world. 3.1 Worker Preferences Workers derve utlty from fnal goods and resdental housng. We assume that preferences are homothetc so that we can express workers problem n effectve labour terms. The representatve worker n sector j maxmzes the Cobb-Douglas utlty u j n = [ (c j,ag n ) ε ( c j,na n ) ] 1 ε α s j 1 α u n, (1) where cn j,ag, cn j,na and su j n are agrcultural goods, nonagrcultural goods, and housng land per effectve ut of labour. The parameters α and ε respectvely determne the optmal share of total expendtures on goods n general and on agrcultural goods n partcular. Overall, total consumpton of k goods n regon n sector j s cn j,k Hn. j Households are subject to a budget constrant rns j u j n +Pn ag cn j,ag +Pn na cn j,na vn, j where Pn ag, Pn na, and rn j respectvely denote the prce of fnal goods and housng and vn j denotes nomnal ncome per effectve ut of labour. Goods prces do not depend on a worker s sector of employment, as we assume trade costs wthn provnces are zero (for reasons we dscuss shortly). 3.2 Producton, Trade and Prces Agrcultural and nonagrcultural goods are a composte of a contnuum of horzontally dfferentated varetes y j n(ν). A perfectly compettve frm produces good j 10

12 usng the CES technology (ˆ 1 σ/(σ 1) Yn j = yn(ν) dν) j (σ 1)/σ, (2) 0 where σ s the (constant) elastcty of substtuton across varetes. Each varety ν may be sourced from local producers or mported, whchever mmzes costs. The goods Y j n are ether consumed drectly by households or used as ntermedate nputs by producers of y j n(ν). These varetes are produced by perfectly compettve frms usng labour, ntermedate nputs, and land. A frm wth productvty ϕ has the followng producton technology y j n(ϕ) = ϕh j n(ϕ) β j S j Y n (ϕ)η j Q j n(ϕ) 1 β j η j, (3) where β j and η j are sector-specfc nput shares for labour and land. Notce that producers also use ntermedate nputs Q j n(ϕ). As these ntermedate nputs are from sector j s fnal good n regon n, we have Y j n = c j nh n + Q j n, where Q j n s the total ntermedates demanded by all frms supplyng sector j n regon n. Land s used ether n producton or for resdental housng, and therefore s j Y n + s j u n = S j n, where S j n s the total fxed supply of land n regon n for sector j. Productvty dffers across frms and, followng Eaton and Kortum (2002), we assume that ϕ s drawn from a Frechet dstrbuton wth CDF F (ϕ) = e T j ϕ θ. We assume that the dsperson parameter θ s common to all regons and sectors. As n Calendo et al. (2013) and Albrecht and Tombe (forthcomng), ths parameter s the same wthn as between countres. In the calbraton to come, we argue that the exstng wthn-country estmate of θ s close to the between-country estmates. Gven perfectly compettve markets, prces equal margnal costs. A frm n sector j of regon wth productvty ϕ charges a buyer n regon n, p j (ϕ) = r j η j P j 1 β j η j /ϕ, where τ j j 1 s an ceberg trade cost, w are wages per τ j w j β j effectve labour, r j s the prce of land, and P j s the prce for the fnal good, all of them are each sector-specfc. Notce that we suppose trade costs τ j do not depend on the purchasng sector, only the type of good. That s, an agrcultural household faces the same consumer prces as a nonagrcultural household. We make ths sm- 11

13 plfyng assumpton because we only have trade flow data between provnces wthn sectors, not by urban or rural areas wthn provnces. Purchasers n each regon source ndvdual varetes y j n(ν) from the lowest cost locaton. Ths results n expendtures beng allocated across regons accordng to each regon s technology, nput costs, and trade costs. Denote π j the fracton of regon n spendng allocated to sector j goods produced n regon (trade shares). As n Eaton and Kortum (2002), t s straghtforward to show the Frechet dstrbuton of technology mples trade shares are π j = and fnal good prces are P j n = γ ( T j N+1 m=1 T j m [ N+1 m=1 ( Tm j τ j where γ = Γ ( σ ) 1/(1 σ). θ τ j w j β j ( τ j r j η j nmw j β j m nmw j β j m r j η j m ) P j 1 β j η j θ r j η j m ) P j 1 β j η j θ, (4) m ] ) 1/θ P j 1 β j η j θ m, (5) 3.3 Nomnal and Real Incomes Let R j n be the total revenue of ntermedate good producng frms n regon n sector j. Gven Cobb-Douglas producton technologes, total labour ncome s w j nh j n = β j R j n. In addton to labour ncome, all payments to land n a gven regon and sector are rebated to the workers of that regon and sector. Spendng on sector j land s (1 α)vnh j n j + η j Rn, j where vn j s the nomnal ncome per effectve worker. So we have vnh j n j = β j Rn j + (1 α)vnh j n j + η j Rn, j whch mples v j n = β j + η j αβ j w j n. (6) 12

14 To determne real ncome, we must deflate nomnal ncome by the prce of consumpton goods P j n and of housng r j n; that s, V j n = ( P ag ε n P vn j na 1 ε n ) α, (7) j 1 α r n Fnally, land market clearng wll solve for rn. j Specfcally, total spendng on land s (1 α)vnh j n j + η j Rn j and total ncome to land s rns j n. j The two must equal. Ths market clearng condton, combned wth equaton 6 and wnh j n j = β j Rn, j yelds the followng: ( (1 α)β rn j j + η j ) j wn Hn j = αβ j. (8) 3.4 Internal Labour Mgraton Labour s moble wthn Chna, across provnces and sectors, but not nternatonally. Workers are regstered to provnces and assgned ether an agrcultural or a nonagrcultural status. Let m jk denote the share of workers holdng a j {ag,na} regstraton n regon n who moved to regon to work n sector k {ag,na}. Workers face costs to work outsde ther regon-sector of regstraton. We model these costs as proportonal to ncome, where a worker from regon n and sector j loses a fracton 1 µ jk of ther ncome n regon and sector k. These mgraton costs can be consdered a reducton n a mgrant s productvty due to the move. In addton, workers have heterogeneous productvty that vares by regon and sector; ths creates dfferences n worker mgraton ncentves. Formally, workers are endowed wth a vector z k n of productvty for each of the N 2 regon-sectors these are..d. across workers, regons, and sectors. Workers then choose where to lve to maxmze ther real ncome net of mgraton costs µ jk zk V k. Wth ths structure, t s straghtforward to solve for mgraton flows. As z k j s a random varable across the contnuum of ndvduals from (n, j), the law of large numbers ensures the proporton of these workers who mgrate to regon s ( m jk = Pr µ jk zk V k S j n { max µ js m,s nmz s mvm} ) s. 13

15 For a partcular dstrbuton of productvty, ths proporton can be solved explctly. Assume that productvty follow a Frechet dstrbuton wth CDF F z (x) = e (x γ) κ, where κ governs the degree of dsperson across ndvduals. A large κ mples lttle dsperson. The parameter γ = Γ ( 1 κ 1) s a normalzng constant so that the mean of z s one. Here Γ denotes the Gamma functon. Proposton 1 Gven real ncomes for each regon and sector, V k, mgraton costs between all regon-sector pars µ jk, and heterogeneous productvty dstrbuted F z (x), the share of regon n workers from sector j that mgrate to regon and sector k s m jk = ( ) V kµ jk κ ( V j k {ag,na} N m=1 mµ nm jk Proof: All proofs of propostons are gven n Appendx B. ) κ. (9) Wth the mgraton decsons fully characterzed, we can solve for the effectve labour supply n each regon and sector H j n. Proposton 2 The total supply of effectve labour n regon n sector j s H j n = N k {ag,na} =1 ( µ k j n m k j n ) 1/κ m k j n L k. (10) ( ) Moreover, h k j n = µk j n m k j 1/κ n s the average productvty of workers from regon and sector k that work n regon n and sector j, and therefore Hn j = k h k j n mk j L n k. 3.5 General Equlbrum and Welfare Total revenue of frms n each regon and sector equals total sales to buyers n all other locatons; that s, R j n = N+1 π j n X j (11) =1 where X j s total expendtures of regon on sector j goods. Wth regon s total ncome denoted I, where I = v ag H ag 14 + v na H na, (12)

16 spendng on sector j goods by regon s X j = αε j I + (1 η j β j )R j (13) From equaton 6, the two equatons above, and the fact that w j nh j n = β j R j n, we have wnh j n j N+1 = =1 π j n [αε j β j ( k=ag,na ) β k + η k αβ k w k H k + ( 1 η j β j) w j H j ]. (14) Defton 1 An equlbrum s a set of wages {wn}, j rental prces of land {rn}, j goods prces {Pn j }, trade shares {π j j,k }, mgraton shares {m } and effectve labour supples {Hn} j, for all regons n = {1,...,N +1} and sectors j = {ag,na}, such that equatons 4 through 10 and equaton 14 hold. Wth real ncome per effectve worker gven by Vn j and the average uts of effectve labour for workers from (n, j) that work n (, k) defned n Proposton 2, the average real ncome per worker for those workers s h jk. From equaton 9, m jk 1/κ /mnn j j 1/κ therefore h j j nnv j n = h jk = V k µ jk /V j V k V k n. Rewrtng yelds mnn j j 1/κ Vn j = µ jk jk 1/κ m V k and. That s, the average real ncome of workers from (n, j) that reman s the same as the average real ncome (net of mgraton costs) of those that mgrate to (,k). Ths mples that m jk s not only the share of workers that mgrate but also the share of total real ncome (net of mgraton costs) earned by all (n, j)-regstered workers earned by those workng n (,k). 2 It s straghtforward to show the followng. Proposton 3 If worker productvty z s dstrbuted Frechet wth varance parameter κ, and agents are able to mgrate between regons at cost µ jk, then aggregate average real ncome (welfare) s W = N j {ag,na} n=1 λ j nv j n m j 1/κ nn = N j {ag,na} n=1 λ j n h j j nnv j n, 2 Ths property s analogous to the well-known feature of Eaton and Kortum (2002) models, where π j represents both the share of sector j varetes that regon n sources from regon but also the share of regon n s spendng on sector j goods that s allocated to producers n regon. 15

17 where λ j n = L j n/ k {ag,na} N =1 L k s the share regstered n regon. Wth the tal equlbrum now fully characterzed, we move on to express how the model responds to changes n exogenous parameters. 3.6 Counterfactual Relatve Changes To ease our quanttatve analyss and calbraton, we follow Dekle, Eaton and Kortum (2007) and express counterfactual values relatve to tal equlbrum values. That s, let ˆx = x /x, where x s the counterfactual value of x. Gven counterfactual trade shares π j j, equatons 11 and 13 solve counterfactual expendtures X, revenues R j, and ncomes I n. To solve for counterfactual trade shares, note that equatons 4 and 5 mply counterfactual trade shares π j = and relatve prce changes π j ˆT ( j ˆτ j N+1 m=1 π j nm ˆT j m ŵ j β j ( ˆτ j ˆr j η j nmŵ j β j m ) ˆP j 1 β j η j θ ˆr j η j m ) ˆP j 1 β j η j θ, (15) m ˆP n = [ N+1 πnm j ˆT ( m j ˆτ j m=1 nmŵ j β j m ˆr j η j m ] ) 1/θ ˆP j 1 β j η j θ m. (16) From equaton 8 and wth revenue proportonal to labour ncome, we have ˆR n j = ŵnĥ j n j and ˆr n j = ŵnĥ j n. j All together, these expressons gve changes n prces ( ˆP n j ), trade flows ( ˆπ j ), and wages (ŵ n) j per effectve worker as a functon of changes n trade costs ( ˆτ j ), underlyng productvty ( ˆT n j ), and effectve labour (Ĥn). j It remans to solve for counterfactual mgraton flows, whch s straghtforward to do. Frst, the counterfactual real ncome per effectve labour s ˆV j n = ( ˆP ag ε n ŵn j α )α na 1 ε n Ĥn j 1 α ˆP, (17) whch uses equatons 6 and 7 and ˆr j n = ŵ j nĥ j n from equaton 8. 16

18 Gven the change n real ncome per effectve worker, and exogenous changes n mgraton costs ˆµ jk, equaton 9 gves m jk = ( m jk ˆV j ˆµ k j k {ag,na} N m=1 m jk k ) κ ( ) ˆV m j ˆµ nm jk κ, (18) ( ) κ. and therefore ˆm jk = ˆm nn j j ˆV k ˆµ jk / ˆV n j Ths, wth equaton 10, yelds H j n V j n = N k {ag,na} =1 ( m kk ) 1/κ V k m k j n L k. (19) Of course, these mgraton expressons hold only between provnces of Chna. There s no nternatonal mgraton, so Ĥ j N+1 = 1 for both sectors. Ths completely characterzes the model s equlbrum response to exogenous changes n trade costs, mgraton costs, and productvty. There are addtonal outcomes that may be of nterest. Frst, counterfactual employment L n (rather than effectve labour H n) s L n = N =1 m n L0. Second, aggregate welfare changes, from proposton 3, s where ω j n = λnv j n j mnn j 1/κ j N m=1 λ mv j mm j mm j 1/κ Ŵ = j N n=1 ω j n ˆV j n ˆm j 1/κ nn, (20). Fnally, value-added from producton plus total housng servces, each valued at tal equlbrum prces, s real GDP. It s straghtforward to show the aggregate real GDP change s where φ j n = (β j +η j )Rn/α j j N n=1 (β j +η j )Rn/α j Ŷ = (1 + α) + α j N n=1 φ j n ˆR j n/ ˆP j n, (21) s regon n and sector j s share of tal nomnal GDP and the 1 α captures the real value of housng servces. 17

19 3.7 Calbratng the Model Usng the method we descrbed to calculate the mpact of the changes n trade costs, mgraton costs, and the underlyng productvty on the changes n equlbrum prces and quanttes, aggregate GDP and welfare, we only need to know the values of observables, regstered workers L j j, tal GDP Y, tal trade shares π j jk and tal mgraton shares m, rather than the unobserved trade costs, mgraton costs and tal levels of the underlyng productvty. Specfcally, the model takes parameters (α,β j,η j,θ,κ) and tal values (π j,mjk, L j,y j ) as gven. Ths secton descrbes ther calbraton, wth a summary n Table Parameters on Factor Shares The producton functon parameters are the labour and land shares of gross output: β and η. These are the share of gross output net of physcal captal, snce our model abstracts from physcal captal. If producton technologes are Y = ÃH β S η K α Q 1 β η α, then gross output net of physcal captal can be wrtten as Y = AH β S η Q 1 β η, where β = β/(1 α) and η = η/(1 α). So, the values of β and η can be nferred from the value-added share of gross output, β + η + α, and the factor shares of value-added β/( β + η + α), η/( β + η + α), and α/( β + η + α). For value-added s shares of gross output, we calculate them drectly from Chna s Input-Output table, whch turns out to average around 0.59 n agrculture and 0.35 n nonagrculture. For factor shares of value-added, we do not use the Chnese data because: (1) There are sgfcant factor market dstortons n Chna so that reported factor shares do not necessarly equal the correspondng factor elastctes n the producton functon; and (2) there s no separate reportng of spendng on land due to a lack of prvate land ownershp t s mplctly ncluded n the reported spendng on labour n agrculture and reported spendng on captal n non-agrculture. To avod these problems, we nstead use the sector-specfc factor shares of valueadded for the US as reported n Casell and Coleman (2001). Specfcally, they report labour s share of 0.6 n both sectors. Land s share s 0.19 n agrculture and 0.06 n nonagrculture. Captal s share s therefore 0.21 n agrculture and 0.34 n nonagrculture. Based on these, we have β ag = = and smlarly 18

20 Table 3: Calbrated Model Parameters and Ital Values Parameter Set To Descrpton (β ag,β na ) (0.404,0.238) Labour s share of output (η ag,η na ) (0.128,0.024) Land s share of output α 0.87 Non-Housng expendture share θ 4 Elastcty of Trade κ 2.54 Income-Elastcty of Mgraton π j Data Blateral trade shares m j Data Blateral mgraton shares L n j Data Hukou regstratons Notes: Dsplays model parameters, ther targets, and a descrpton. See text for detals. β na = 0.21, η ag = , η na = 0.021, α ag = , and α na = Thus, we have our man parameter values β ag = ( ) = and smlarly β na = 0.238, η ag = 0.128, and η na = To calbrate α, we use consumer expendture data from Chna s most recent Natonal Statstcal Yearbook. The fracton of urban household spendng on housng s 11% and for rural households s 15%. We set α = 0.87, mplyng the housng share of expendtures s 13% Cost-Elastcty of Trade There s a large lterature on the productvty dsperson parameter θ. Ths parameter governs productvty dsperson across frms and, consequently, determnes the senstvty of trade flows to trade costs. Between-countres, there are many estmates of ths elastcty to draw upon. For example, Smonovska and Waugh (2011) use cross-country prce data to estmate θ 4. Parro (2013) estmates θ [4.5,5.2] for manufacturng usng trade and tarff data. Based on ths method, Tombe (2015) estmates θ = 4.1 for agrculture and 4.6 for nonagrculture. Wthn-countres, however, there s lttle evdence to draw upon. Usng frm-level productvty dsperson n the US, Bernard et al. (2003) estmates θ = 3.6. We set θ = 4. 19

21 3.7.3 Income-Elastcty of Aggregate Mgraton Smlar to the cost-elastcty of trade s the ncome-elastcty of aggregate mgraton κ. The elastcty of mgraton s drven by the degree of heterogenety n regonspecfc productvty across workers; gven the Frechet dstrbuton of productvty, the proof of Proposton 3 provdes a means of estmatng κ from ndvdual earngs data. Namely, after mgraton ex-post earngs across ndvduals are dstrbuted Frechet. The log of a Frechet dstrbuton s Gumbel, wth a standard devaton proportonal to κ 1. Specfcally, log real ncomes are dstrbuted Gumbel wth CDF [ ( ) G(x) = e k N =1 µ jk κ ] V k e κx, whch has a standard devaton π/(κ 6). Importantly, the standard devaton of real earngs s ndependent of µ jk and V k. How do we estmate ths standard devaton from data? In the data, we observe nomnal earngs, whch corresponds to µ jk zk vk. The above expresson, however, apples to real earngs. Fortunately, the dfference between the two s dentcal for all sector k workers n regon and therefore var(log(z k V k)) = var(log(zk vk )). Next, µ jk s common to all (n, j)-regstered workers now n sector k of regon ; therefore, var(log(µ jk zk V k jk )) = var(log(µ zk vk )) across those workers. We therefore dentfy the value of κ from the wthn-group nomnal earngs varaton, wth groups defned by regon-sector of regstraton and current regon-sector of employment. From the 2005 Populaton Survey, we fnd an average wthn-group standard devaton of log earngs of 0.50, so κ = Indvdual ncome data s not reported n the 2000 Census Ital Equlbrum Values The total regstrants by provnce and sector ( L j n) are drectly observable n Chna s 2000 Populaton Census (see Appendx A). Total natonal employment for Chna s mllon. Total employment n the rest of the world ( j L j N+1 ) s 2,103 ml- 3 Controllng for wde varety of ndvdual characterstcs (age, gender, educaton, health, etc.) has lttle affect on these results, resultng n κ = In models of occupatonal moblty n the U.S., Hseh et al. (2013) estmate κ = 3.44 and Cortes and Gallpol (2014) fnd κ =

22 lon. Ths s nferred from the Penn World Table as the total non-chna employment for The tal mgraton shares m jk are also calculated drectly from the 2000 Populaton Census. Snce we don t have trade data n 2000, we use the trade shares generated from the 2002 Chna Regonal Intput-Output Tables to approxmate the values of the trade shares π j n We have drect data on real GDP per worker by provnce and sector, denoted (Yn j ) data whch corresponds to the tal equlbrum of HnV j n j n the model. From equatons 9 and 10, we have the followng equatons (Y j n ) data = N k {ag,na} =1 ( m k j n m kk ) 1/κ V k L k, whch are used along wth the N 2 equatons from 9 and 10 n Secton 3.3 to solve for the N + N 2 unknowns (Hn,V j n j, µ jk ). See Appendx A for values. 4 Inferrng Trade and Mgraton Costs In ths secton, we quantfy mgraton costs wthn Chna and trade costs wthn and between Chna s provnces and the world. 4.1 Mgraton Costs Equaton 9 provdes a smple representaton of mgraton decsons through whch we nfer mgraton costs. Usng data on mgraton shares m and our calbrated real ncome per effectve worker V n from the prevous secton, we fnd an average (mgraton-weghted) value of µ jk of Mgraton costs therefore average Of course, mgraton costs dffer for dfferent types of mgraton. We summarze these costs, ther changes, and the tal mgraton flows n Table 4. Overall, mgraton costs are largest for mgrants swtchng both sectors and provnces wth an average tal 1 µ jk of In contrast, to swtch sectors wthn one s home provnce ncurs average mgraton costs of How do these costs change over tme? We report the change n average mgraton costs n the last column Table 4. Overall, mgraton costs declned by almost 21

23 Table 4: Mgraton Rates and Average Costs, by Sector and Provnce Mgrant Share Average Mgraton Costs 1 µ jk of Employment Change Overall % Agrculture to Nonagrculture Mgraton Cost Changes Overall % Wthn Prov % Between Prov % Between Provnces Mgraton Cost Changes Overall % Wthn Ag % Wthn Nonag % Notes: Dsplays average mgraton rates and costs n 2000 and The mgrant share of employment summarzes m jk n Average mgraton costs are weghted by tal mgrants shares. We use tal (year 2000) weghts to average the 2005 costs to ensure the dsplayed change reflects changes n costs and not mgraton patterns. 8% and the average mgrant worker captured a larger share of ther real ncome. Costs to swtch between sectors wthn one s home provnce fell the most, from 0.51 to 0.45, especally compared to the cost of swtchng both sector and provnce, whch fell only from 0.98 to For workers remang wthn ther sector of regstraton, the costs of movng across provnces also fall by nearly 6% for agrcultural workers and nearly 4% for nonagrcultural workers. Overall, the cost of mgratng across provnces fell from 0.97 to Modfed Head-Res Index of Trade Costs We estmate trade costs usng a method developed n Head and Res (2001), generalzed by Novy (2013), and ncreasngly featured n nternatonal trade research. Ths method apples to a broad class of trade models, ncludng the model descrbed n Secton 3. It s straghtforward to show average trade costs between regon n and for sector j goods s ( ) τ j τ j τ j n = πnnπ j j 1/2θ π j π j, (22) n whch s a drect result of equaton 4. Ths method has a number of advantages. Frst, τ j s not affected by trade volumes or by thrd-party effects. For example, f 22

24 regon experences a massve ncrease n trade wth some other regon k, say due to lower trade costs between and k, then regon wll lower ts trade wth regon n by the same proporton as t lowers ts purchases from tself. The estmated trade costs between and n s therefore unaffected. It also apples equally well whether trade balances or not. Unfortunately, these trade cost estmates are symmetrc n the sense that goods movng from to n s as costly as movng goods from n to. Ths matters, as Waugh (2010) demonstrates trade costs systematcally dffer dependng on the drecton of trade. In partcular, he shows that addtonal costs facng exporters s key; that s, τ j = t j t j, where t j are symmetrc costs (t j = t j n ) and t j are costs of exportng. Ths and equaton 22 mply τ j = τ j t j /t n. j Ths way of adjustng the Head-Res ndex of trade costs to ncorporate asymmetres s also found n Tombe (2015). As we have data on π j j, and therefore can estmate τ usng equaton 22, t remans for us to estmate the exporter-specfc trade costs tn. j We closely follow the exstng lterature here, so leave detals to Appendx B. Essentally, we use a standard gravty regresson to nfer asymmetres from fxed effects. Overall, we fnd that poor regons face the hghest exporter-specfc trade costs consstent wth exstng cross-country evdence. Export costs are also largely unchanged from 2002 to See Appendx B for the precse estmates. Combng these export costs wth the Head-Res ndex τ j yelds τ j for 2007 and 2002, and therefore we have our ˆτ j. We dsplay the resultng estmates for the relatve change n trade costs n Table 5. Some notable patterns emerge, though t s mportant to keep n mnd that these trade costs are relatve to wthn-regon trade costs. Wthn Chna, trade costs are largely decreasng, wth trade-weghted change ag n trade costs wthn Chna of ˆτ = 0.87 and ˆτ na = For trade between Chna ag and the world, the average change n costs were ˆτ = 0.77 and ˆτ na = What s behnd the measured reducton n trade costs? Consder solatng the porton of trade costs τ j = t j t j t n j due to geographc dstance between regons usng the regresson ln( τ j ) = δln(d ) + ι j n + η j + ε j, 23

25 Table 5: Relatve Change Blateral Trade Costs Exporter North- Bejng North Central South Central North- South- Importer east Tanjn Coast Coast Coast Regon west west Abroad Change n Trade Costs n Agrculture, ˆτ ag Northeast Bejng/Tanjn North Coast Central Coast South Coast Central Regon Northwest Southwest Abroad Change n Trade Costs n Nonagrculture, ˆτ na Northeast Bejng/Tanjn North Coast Central Coast South Coast Central Regon Northwest Southwest Abroad Note: Dsplays changes n blateral trade cost (relatve to wthn-regon costs) for agrculture and nonagrculture for eght broad regons. The eght regons are classfed as: Northeast (Helongjang, Jln, Laong), North Mucpaltes (Bejng, Tanjn), North Coast (Hebe, Shandong), Central Coast (Jangsu, Shangha, Zhejang), South Coast (Fujan, Guangdong, Hanan), Central (Shanx, Henan, Anhu, Hube, Hunan, Jangx), Northwest (Inner Mongola, Shaanx, Nngxa, Gansu, Qngha, Xnjang), and Southwest (Schuan, Chongqng, Yunnan, Guzhou, Guanx, Tbet). In the smulaton, we apply these changes to the provnces wthn each regon. where d s the geographc dstance between regon n and, and ι j n and η j are m- and tn). j We nclude porter and exporter fxed-effects by sector (to control for t j only regons wthn Chna for ths regresson. The results for 2002, we estmate ˆδ ag = 0.51 and ˆδ na = For 2007, these elastctes fall to 0.40 and 0.36, respectvely. The contrbuton of dstance to trade costs s therefore lower, perhaps due to nfrastructure mprovements wthn Chna. If all other factors reman unchanged, the relatve change n trade costs between regon n and would have been ˆτ ag = d 0.11 and ˆτ na = d 0.02 ag. Overall, ths averages across pars to ˆτ = 0.48 and = Though ths s a rough approxmaton, t suggests nearly all of ˆτ na the change n nonagrcultural trade costs are due to lower costs related to dstance. For agrculture, ths more than accounts for the measured change, suggestng nondstance costs grew larger on average. 24

26 5 Quanttatve Analyss In our quanttatve analyss, we ft the tal equlbrum of our model to the Chnese data n and then quantfy the mpacts on aggregate productvty and welfare of varous changes n trade and mgraton costs. In partcular, we examne how much of Chna s GDP growth between 2000 and 2005 can be accounted for by the measured reducton n trade costs and mgraton costs. 5.1 Gans from Trade and Mgraton But frst, by how much are welfare and productvty n Chna affected by the observed trade and mgraton flows n 2000? Ths s a standard queston n nternatonal trade research. It nvolves comparng the tal equlbrum of our model to a counterfactual of no trade and/or no mgraton. Gans from Internatonal Trade. We start wth the tal equlbrum n 2000 and set the changes n trade costs as follows: ˆτ j = f ether n or s the rest of the world, and ˆτ j = 1 otherwse. Ths wll elmnate all nternatonal trade between each provnce and the rest of the world. The nverse of the change n aggregate welfare and aggregate real GDP are the welfare and productvty gans, respectvely. We fnd welfare gans of 4.7% and productvty gans of 6.9%. Note that these are aggregate gans for Chna as a whole. Productvty gans from nternatonal trade for coastal provnces are sgfcantly hgher: over 26% for Guangdong and 21% for Shangha, for example. Gans from Internal Trade. In ths case, we keep the nternatonal trade costs unchanged from the tal equlbrum but set the nternal trade costs to nfty. The welfare and productvty gans are 18.9% and 16.8%, respectvely. These gans are sgfcantly hgher than the gans from external trade because n the tal equlbrum most provnces mport more from other provnces n Chna than from abroad. Interestngly, the gans from nternal trade for Guangdong and Shangha are 11.5% and 14.9%, respectvely, smaller than ther gans from external trade. Gans from Between-Provnce Mgraton. To quantfy the gans from mgraton 4 There s no regonal nput-output table for 2000 n Chna, so we use trade shares from the 2002 Chna Regonal Input-Output Tables to approxmate trade shares n

27 flows observed n 2000, consder a smlar exercse where we make mgraton prohbtvely costly. Elmnatng between-provnce mgraton entals settng ˆµ jk = 0 f n for all j or k but ˆµ jk = 1 otherwse. The aggregate welfare and productvty gans are 1.1% and 1.9%. Provnces that are popular destnatons for mgrants experence larger gans. In Guangdong, Bejng, and Shangha, for example, productvty gans from nter-provncal mgraton are 11%, 8.4% and 4.3%, respectvely. Gans from Wthn-Provnce Mgraton. Fnally, consder the gans from mgratng between sectors wthn provnces. In ths case, workers may stll swtch sectors but must also move across provnces. No worker wth an agrcultural Hukou, for example, can reman wthn ther provnce of regstraton yet work n the nonagrcultural sector. We fnd these wthn-provnce moves have both welfare and productvty gans of 2.4%. The varaton n gans across provnces s mnor, wth the excepton of Zhejang, whch experences productvty gans of 11.7% from wthnprovnce mgraton. In summary, the Chnese economy n 2000 benefted sgfcantly from nternal trade, less from nternatonal trade and least from nternal mgraton due to the extremely hgh costs of mgraton at that tme. 5.2 Quantfyng the Effect of Measured Costs Changes How mportant were the changes n trade and mgraton costs n Chna that we measured n Secton 4? We report the mpact of these changes below The Effect of Lower Trade Costs From the tal equlbrum n 2000, we solve the changes n equlbrum outcomes by usng ˆτ j from secton 4.2, and hold mgraton costs and productvty fxed ( ˆµ j = ˆT n j = 1 for all n and ). Table 6 dsplays the change n trade and mgraton flows, aggregate productvty and welfare, and varous other outcomes. Changes n trade shares are expendture weghted average changes across all provnces and sectors. Lower nternal trade costs, not surprsngly, lower the amount of nternatonal trade as households and frms reorent ther purchase decsons towards domestc supplers. The share of expendtures allocated to producers n another provnce 26

28 Table 6: Effects of Trade Cost Changes p.p. Change n Share of Mgrant Stock Per-Capta Internal External Ag. Wthn Between Income Aggregate Outcomes Trade Trade Emp. Provnce Provnce Varaton Real GDP Welfare Internal Trade % -2.3% -7.3% 10.3% 10.9% External Trade % 5.6% 1.8% 4.0% 3.1% All Trade % 3.4% -5.0% 14.2% 13.8% Agrcultural Trade Cost Changes Internal % -2.6% 1.5% 0.3% 0.8% External % 5.2% -0.6% 0.3% -0.3% Both Ag % 2.3% 0.8% 0.6% 0.4% Nonagrcultural Trade Cost Changes Internal % 0.1% -8.5% 10.0% 10.1% External % 0.5% 2.6% 3.6% 3.4% All Nonag % 0.2% -5.3% 13.5% 13.4% Notes: Dsplays aggregate response to varous trade cost changes. All use trade cost changes as measured, though set ˆτ j = 1 for certan (n,, j) dependng on the experment. The change n nternal and external trade shares are the expendture weghted average changes n regon s n π j and π j nn. The mgrant stock s the number of workers lvng outsde ther provnce of regstraton. Regonal ncome varaton s the varance of log real ncomes per capta across provnces. typcally ncrease by over 9 percentage ponts whle the share allocated to nternatonal producers falls by almost one percentage pont. Lower external trade costs reveal the opposte pattern. In both cases, home shares fall. In terms of mgraton, mproved nternal trade costs actually resulted n fewer workers lvng outsde ther home provnce. The total stock of mgrants declned by over 2% (equvalent to approxmately 0.5 mllon workers). Intutvely, nternal trade costs declng dsproportonately lower goods prces n poor, nteror regons. Ths ncrease n real ncome means fewer workers, who were lvng n other provnces, were wllng to contnue to do so. On the other hand, a greater fracton of workers swtched sectors wthn ther home provnce. Wth lower nternatonal trade costs, rcher coastal regons dsproportonately beneft, so more workers relocate there n addton to more workers swtchng sectors wthn ther home provnce. Ths mgraton response also matters for the gans from trade cost changes. Settng Ĥn j = ˆm nn j j = 1 n the welfare equaton reveals the mgraton response accounts for roughly 10% of the gans. The change n ncome, goods and land prces, and worker s locaton decson all have mplcatons for aggregate welfare. We report the change n welfare and productvty (aggregate real GDP) n the last columns of Table 6. In response to 27

29 lower nternal trade costs, aggregate welfare dramatcally ncreased by nearly 11%. In contrast, external trade cost reductons resulted n a much smaller gan of only 3.1%. As n our earler analyss, nternal trade costs reductons appear to be sgfcantly more mportant for aggregate outcomes. The dfferental mpacts are not due to any sgfcant dfferences n the magtude of cost reductons. To llustrate ths, we smulate ˆτ j = 0.9 for both nternal and external trade costs separately: welfare ncreases by 7.6% from nternal trade cost reductons but only 2.4% from external trade cost reductons. The man reason for the larger welfare gans from nternal cost reductons s that most provnces allocate a larger fracton of ther spendng to goods from other provnces than from abroad. In whch sectors are trade cost changes most mportant? To answer ths, we also nvestgate the results of changng trade costs n agrculture and nonagrculture separately. In the lower panels of Table 6, gans from nternal cost changes n agrculture are 0.8% whle the gans from external trade cost changes are actually negatve, at -0.3% (largely from loses to agrculture n Shangha and Hanan). Overall, agrcultural trade cost changes over the tme perod we study leads to welfare gans of 0.4%. For nonagrculture, nternal trade costs reductons ncreased aggregate welfare by over 10% and external lberalzaton dd so by 3.4%. Overall, reductons n nternal nonagrcultural trade costs are, by far, the most mportant Lower Mgraton Costs Trade lberalzaton accounts for only lmted amount of mgraton. Not surprsngly, lower mgraton costs lead to substantally more workers lvng outsde ther home provnce-sector. As before, we smulate the effect of lower mgraton cost changes and report the effects n Table 7. The stock of mgrants ncreases dramatcally when ˆµ jk s as measured. The number of nter-provncal mgrants ncreases by over 220% from barely more than 4% of the labour force to over 13%. Ths s equvalent to over 57 mllon workers. Wthn provnces, there are also substantal moves from agrculture to nonagrculture. The stock of workers wth agrcultural Hukou that have nonagrcultural employment wthn ther home provnce ncreases by nearly 22%, from over 13% of the labour force to over 16% (nearly 20 mllon workers). The natonal share 28

30 Table 7: Effects of Varous Mgraton Cost Changes p.p. Change n Share of Mgrant Stock Per-Capta Internal External Ag. Wthn Between Income Aggregate Outcomes Trade Trade Emp. Provnce Provnce Varaton Real GDP Welfare All Changes % 221.9% -31.7% 12.1% 7.3% Agrculture to Nonagrculture Mgraton Cost Changes Overall % 191.2% -33.5% 7.2% 4.9% Wthn Prov % -10.9% 8.6% 3.7% 3.0% Between Prov % 274.4% -37.4% 4.5% 2.7% Between Provnces Mgraton Cost Changes Overall % 312.7% -38.0% 9.3% 5.0% Wthn Ag % 49.7% -2.8% 0.3% 0.2% Wthn Nonag % 63.8% -6.1% 5.7% 2.8% Notes: Dsplays aggregate response to varous mgraton cost changes. All use mgraton cost changes as measured, though set ˆµ k j = 1 for certan (n,, j,k) dependng on the experment. The mgrant stock s the number of workers lvng outsde ther provnce of regstraton. Regonal ncome varaton s the varance of log real ncomes per capta across provnces. of labour n agrculture declnes by over 8 percentage ponts. Clearly, the measured changes n mgraton costs are extremely mportant determnants of worker locaton decsons. The large flows are also benefcal for Chna as a whole; real GDP and welfare rse 12.1% and 7.3%, respectvely. Regons dffer n ther responses, dependng on whether they are a source or a destnaton for mgrants. In Fgure 2 we show varous outcomes for each regon. Coastal provnces, such as Shangha, Tanjn, Bejng, and Guangdong, are the prncple destnatons for nter-provncal mgrants. Shangha s employment ncreases by over 300% n response to our measured change n mgraton costs, though from a relatvely low base compared to the other provnces. In response, real ncomes n provnces to whch mgrants move declne. As these are typcally rcher regons, regonal ncome dfferences dramatcally declne (by nearly a thrd; see Table 7). Whle mgraton flows and real ncomes respond a lot to the changes n mgraton costs, the effect on aggregate trade flows s muted. Internatonal and nternal trade shares ncrease by only 0.2 percentage ponts (so provncal home shares π j nn declne by 0.4 percentage ponts on average). Whle aggregate trade s largely unresponsve, there are substantal dfferences between ndvdual provnces. In Fgure 2 we plot the percentage change n each provnce s trade volumes, both nternally and nternatonally. Itally hgher ncome (coastal) regons see ther trade ncrease sgfcantly whle lower ncome (nteror) regons see decreased volumes. 29

31 Fgure 2: Regonal Effects of Lower Mgraton Costs (a) Employment (b) Real Income Shangha % Change n Labour Force Bejng Tanjn % Change n Real Income Guangdong Bejng Tanjn 50 Guangdong Shangha Ital Real Income, Relatve to Mean Ital Real Income, Relatve to Mean 40 (c) Internatonal Trade 40 (d) Internal Trade 35 Shangha % Change n External Trade Volume (Imports+Exports) Guangdong Bejng Tanjn Shangha % Change n Internal Trade Volume (Imports+Exports) Xnjang Guangdong Bejng Tanjn Ital Real Income, Relatve to Mean Ital Real Income, Relatve to Mean Notes: Dsplays the percentage change n total employment and real ncome per capta by provnce n response to lower mgraton costs. Also dsplays the percentage change n trade volumes, both nternatonally and nternally. All panels aggregate across both agrculture and nonagrculture wthn regons. Fnally, we explore changes n mgraton costs wthn and between provnces and sectors. Wthn-provnce changes (that s, only between agrculture and nonagrculture wthn provnces) ncreased welfare by 3%. Lower costs of mgratng between sectors and provnces ncreased welfare by 2.7%. Changes that facltate the movement of workers between sectors, whether wthn- or between-provnces, are therefore of roughly equal mportance. Between-provnce cost changes wthn sectors are much more mportant for nonagrculture than agrculture. 30

32 Table 8: Effects of Varous Cost Changes, Wth and Wthout Productvty Changes p.p. Change n Share of Mgrant Stock Per-Capta Measured Internal External Ag. Wthn Between Income Aggregate Outcomes Change for Trade Trade Emp. Provnce Provnce Varaton Real GDP Welfare Productvty % -7.5% 12.0% 35.2% 32.8% Margnal Effects (changes relatve to what productvty delvers) Internal Trade % -4.5% -11.1% 9.9% 10.6% External Trade % 2.1% 1.4% 3.1% 2.9% All Trade % 1.0% -9.7% 12.6% 12.8% Mgraton % 151.4% -22.7% 5.9% 4.6% Internal Changes % 141.3% -32.2% 16.5% 15.9% Everythng % 152.0% -32.5% 20.1% 18.7% No Change n Productvty (consstent wth Tables 6 and 7) Internal Trade % -2.3% -7.3% 10.3% 10.9% External Trade % 5.6% 1.8% 4.0% 3.1% All Trade % 3.4% -5.0% 14.2% 13.8% Mgraton % 221.9% -31.7% 12.1% 7.3% Internal Changes % 212.9% -37.9% 23.3% 19.1% Everythng % 230.9% -39.0% 28.0% 22.2% Notes: Dsplays aggregate response to varous cost changes wth and wthout productvty change ˆT j n by regon and sector. Margnal effects reflect the changes relatve to the equlbrum wth only productvty change. The mgrant stock s the number of workers lvng outsde ther provnce of regstraton. Regonal ncome varaton s the varance of log real ncomes per capta across provnces Changes n Underlyng Productvty So far we have held the underlyng productvty T j n constant n our evaluaton of the mpacts of measured changes n trade and mgraton costs. Ths results n counterfactual changes n real GDP per worker and other equlbrum outcomes because there had been changes n the underlyng productvty across provnces and sectors. We calbrate changes n the productvty parameter ˆT j n such that, when mgraton and trade costs declne as measured, the resultng change n real GDP per worker n each provnce-sector matches the change n data between 2000 and In Appendx B, we provde the mpled values by provnce and sector. We now ncorporate the estmated productvty changes ˆT j n n our counterfactual smulatons. We dsplay the results of changng productvty, and the nteracton of ths wth changng trade and mgraton costs, n Table 8. The frst row of ths table s dstnct, and provdes the effect of our calbrated ˆT j n alone. Welfare rses sgfcantly. More nterestngly, trade declnes as a greater fracton of spendng s allocated to Chnese producers. Productvty also lowers the stock of nter-provncal mgrants, wth lttle change n the wthn-provnce between-sector mgraton flow. 31

33 Table 9: Decomposng Chna s Overall Real GDP Growth Relatve to Ital Eq m Mean of All Permutatons Change n Share of Change n Share of Real GDP Growth Real GDP Growth Overall (All Changes) 62.4% 62.4% Productvty Changes 35.2% % 0.56 Internal Trade Cost Changes 10.3% % 0.20 External Trade Cost Changes 4.0% % 0.07 Mgraton Cost Changes 12.1% % 0.18 Of the Mgraton Cost Changes, Between-Provnce, Wthn-Nonag 5.7% % 0.08 Between-Provnce, Wthn-Ag 0.3% % 0.00 Between-Provnce, Ag-Nonag 4.5% % 0.06 Wthn-Provnce, Ag-Nonag 3.7% % 0.04 Notes: Decomposes the change n real GDP nto contrbutons from productvty, nternal trade cost changes, external trade cost changes, and mgraton cost changes. The bottom panel decomposes the change due to mgraton cost changes nto varous dfferent types of mgraton. The relatve to the tal equlbrum columns correspond to Tables 6, 7, and 8. As the change n real GDP from each component depends (slghtly) on the order of smulaton, the last two columns report the average margnal effect of each component across all permutatons of changes. Only the mean of all permutatons contrbutons sum to one. Shares are calculated as log(1 + x)/log(1.624), where x s the contrbuton from each component. The negatve effect on nter-provncal mgraton s due to some convergence n the underlyng non-agrcultural productvty across provnces. We dsplay the margnal effects of trade and mgraton costs change, whch are the change n the varous outcome varables relatve to the equlbrum wth only productvty changes, n the second panel of Table 8. The margnal effects of changng trade costs are smlar to our earler results, but the mpact of changes n mgraton costs are now smaller. The change n the stock of mgrants from lower mgraton costs s substantally lower than our baselne, and much closer to the level actually observed. The ncrease n aggregate welfare s now only 4.6% compared to 7.3% when there s no change n underlyng productvty. Agan, the reason for the lower mpacts of the mgraton cost reductons s that there had been some convergence n the underlyng non-agrcultural productvty across provnces. 5.3 Decomposng Chna s Recent Economc Growth By constructon, when we nclude the measured trade and mgraton costs changes along wth the calbrated productvty changes, the model-mpled growth n real GDP per worker for each provnce and sector matches the actual growth between 32

34 2000 and 2005 n the data. The correspondng growth rate of the aggregate real GDP per worker mpled by the model s over 62%. We can decompose the aggregate growth nto the growth due to changes n underlyng productvty, changes n trade costs and changes n mgraton costs by ncludng these changes nto the model sequentally. However, due to the nteracton between these changes, the decomposton result depends on the order we ntroduce these changes n the smulaton. We smulate all possble sequences of changes and present the average contrbuton of each set of changes n Table 9. Overall, reductons n trade and mgraton frctons account for nearly half of Chna s overall productvty growth between 2000 and 2005, wth reductons n nternal trade and mgraton costs each contrbutes roughly one-ffth. In stark contrast, nternatonal trade cost reductons account for only 7% of the overall growth (3.5% out of the 62.4%). Of the contrbuton from mgraton cost changes, almost half s due to changes n the cost of mgratng between provnces wthn the nonagrcultural sector, wth the remander accounted for by the cost of movng from agrculture to nonagrculture. 5.4 Potental Scope for (and Gans from) Further Reform Our decomposton shows that reductons n trade and mgraton frctons and the resultng reducton n msallocaton of labour had played a major role n Chna s growth between 2000 and How much addtonal scope s there for further reductons n trade and mgraton costs? To answer ths queston requres a comparson country. We choose Canada as a geographcally large developed economy to benchmark trade costs and the Uted States to benchmark mgraton flows. Let s begn wth nternal trade costs. We choose snce Statstcs Canada s nternal trade data s superor to the U.S. commodty-flow survey. In partcular, Albrecht and Tombe (forthcomng) estmate Canada s nternal trade costs separately for a varety of sectors. Reformulatng ther results to be consstent wth our model, we fnd the trade-weghted average agrcultural and nonagrcultural trade costs of 94.9% and 149.1%, respectvely. For Chna, the correspondng average nternal trade cost n 2007 are 288.3% and 167.0%, respectvely. Lowerng Chna s costs to 33

35 Table 10: Potental Gans of Further Trade and Mgraton Lberalzaton Relatve to 2005 Eq m Change n Real GDP Aggregate Welfare Average Internal Trade Costs as n Canada 10.9% 11.8% Between-Provnce Mgraton as n U.S. 22.8% 15.0% Both Changes Together 37.0% 30.5% Notes: Reports the change n real GDP and welfare that result from changng Chna s nternal trade and mgraton costs such that average nternal costs equal Canada s (by sector) or such that the between-provnce mgraton flows match the U.S. Percentage changes are expressed relatve to the 2005 equlbrum. Canada s level would mply ˆτ ag = = and smlarly ˆτna = Note we change nternal trade costs only and hold all else fxed. We smulate these addtonal changes n trade costs relatve to our 2005 counterfactual equlbrum. We report the results n Table 10. We fnd Chna s real GDP and welfare could ncrease by a further 10.9% and 11.8% f average nternal trade costs fell to Canada s level. Next, consder lowerng mgraton costs n Chna such that mgraton flows are on par wth developed economes. For ths exercse, we can use the Uted States, as hgh qualty mgraton data (through the Census) exsts. The share of ndvduals lvng outsde of ther state of brth s roughly one-thrd n the Uted States substantally more than the 9.5% who lve outsde ther Hukou provnce n n Chna n To quantfy the consequences of Chna s relatvely low nter-provncal mgraton rate, we choose a constant change n ˆµ jk for all provnce pars such that the share of workers lvng outsde ther Hukou provnce s one-thrd. We fnd ˆµ jk = 2.51 for all n wll delver ths share (note we do not change mgraton costs wthn provnces between sectors). Ths mples that, to reach the U.S. level of labour moblty, the after-mgraton cost porton of nter-provncal mgrant workers ncome have to be two and half tmes as hgh as the current proporton. The resultng ncrease n real GDP and welfare s 22.8% and 15.0%, respectvely. The scope for and gans from further polcy reform are therefore large. Both changes together delver real GDP gans of 37% and welfare gans of nearly 31%. 34

36 6 Concluson Chna experenced rapd GDP growth between 2000 and There s a wdely held belef that the man reason for ths rapd growth s the external trade lberalzaton assocated wth Chna jong the WTO n Ths resulted n export expanson supported by a large ncrease n the supply of cheap mgrant workers, hense the growth. Internal polcy reforms undertaken by the Chnese government durng the same perod have not receved as much attenton. We fnd these reforms helped reduce the costs of both nternal trade and mgraton. Usng a general equlbrum model featurng nternal trade, nternatonal trade, and worker mgraton across regons and sectors, we quantfy the effect of changes n trade and mgraton costs on Chna s aggregate productvty growth and welfare. We fnd that reductons n nternal trade and mgraton costs account for 38% of the aggregate labour productvty growth n Chna between 2000 and In contrast, reductons n external trade costs account for only 7% of the aggregate labour productvty growth durng the same perod. We also fnd that the nternal reforms helped to reduce regonal ncome dfferences n Chna, whle external trade lberalzaton had the opposte effect. Fnally, despte the reductons, nternal trade and mgraton costs n Chna are stll much hgher than those n developed countres such as Canada and the U.S. Further reforms that lower these costs to developed country levels would yeld substantal ncreases n Chna s aggregate productvty and welfare. Whle our results may lead one to conclude nternatonal lberalzaton matters lttle for aggregate outcomes, we should pont out the contrbuton of trade lberalzaton that we quantfy s the effect of trade-nduced resource reallocaton. We have shown that nternal trade lberalzaton results n a much larger reallocaton effect than external trade lberalzaton does. However, external trade lberalzaton may also contrbute to productvty growth through other channels that we have not studed n ths paper. Two channels that we thnk are partcularly relevant for Chna are FDI and the assocated technology transfers (as n Ramondo and Rodrguez-Clare, 2013) and the nfluence of nternatonal lberalzaton on nternal polcy reforms. We leave the study of these ssues to future research. 35

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41 Appendx Appendx A provdes source and summary nformaton for our man data. Appendx B provdes supplementary materal not ncluded n the man text. Appendx A: Data Sources and Summary Statstcs GDP and Employment by Sector and Provnce We use offcal nomnal GDP and employment data for agrculture (prmary sector) and non-agrculture (secondary and tertary sectors) avalable through varous Chnese Statstcal Yearbooks. We accessed these data through the Uversty of Mchgan s Chna Data Onlne servce (at chnadataonlne.org). Spatal Prces We measure real GDP per worker by provnce and sector by deflatng the offcal nomnal GDP data wth the spatal prce data of Brandt and Holz (2006). We use the common basket prce ndex for rural areas to deflate agrculture s nomnal GDP n each provnce. Smlarly, we use the common basket prce ndex for urban areas to deflate nonagrculture s nomnal GDP. Mgraton Shares Usng Chna s 2000 Populaton Census and % Populaton Survey, we calculate mgraton shares. Specfcally, to measure m jk, we calculate the fracton of all employed workers wth Hukou regstraton n regon n of type j (agrcultural or nonagrcultural Hukou) currently workng n provnce and employed n sector k (agrcultural or nonagrcultural). Current ndustry of employment s classfed usng Chna s GB2002 classfcaton system. We assgn to agrcultural all ndustres wth GB2002 codes Trade Shares We use the regonal Input-Output data of L (2010) to measure the tal equlbrum trade shares π j for The data s dsaggregated by sector, wth agrculture on ts own. We aggregate all other sectors nto nonagrculture. The trade share π j s the fracton of total spendng by regon n on goods n sector j sourced from regon. Total expendture s the sum of fnal use and ntermedates. To measure the change n trade costs between 2002 to 2007, we requre data on changes n trade shares from 2002 to For ths, we use the data of Zhang and Q (2012), whch provdes smlar data as L (2010) but aggregated to ether broad regons. The eght regons are: Northeast (Helongjang, Jln, Laong), North Mucpaltes (Bejng, Tanjn), North Coast (Hebe, Shandong), Central Coast (Jangsu, Shangha, Zhejang), South Coast (Fujan, Guangdong, Hanan), Central (Shanx, Henan, Anhu, Hube, Hunan, Jangx), Northwest (Inner Mongola, Shaanx, Nngxa, Gansu, Qngha, Xnjang), and Southwest (Schuan, Chongqng, Yunnan, Guzhou, Guanx, Tbet). In the followng tables, we report varous summary measures of trade, real ncomes, mgraton, employment, and other metrcs for all provnces and sectors. We further provde the calbrated 40

42 equlbrum values for real ncomes per effectve worker and the number of effectve workers n each provnce and sector. See Secton for detals. Table 12: Selected Regon-Specfc Ital Calbrated Values Hukou Real Income per Effectve Regstratons, L n j Effectve Worker, Vn j Workers, Hn j Provnce Ag Nonag Ag Nonag Ag Nonag Anhu Bejng Chongqng Fujan Gansu Guangdong Guangx Guzhou Hanan Hebe Helongjang Henan Hube Hunan Inner Mongola Jangsu Jangx Jln Laong Nngxa Qngha Shandong Shangha Shaanx Shanx Schuan Tanjn Xnjang Yunnan Zhejang Notes: Lsts the values for the regon-specfc tal values. Some are calbrated whle others are drectly observables from data. See secton 3.7 for detals. 41

43 Table 11: Summary Data for Chna s Provnces, 2000 Inter-Provncal Intra-Provncal Agrculture s Relatve Relatve Home Bas Internatonal Employment Mgrant Share of Mgrant Share of Share of Real Ag. Real Nonag. n Total Export Share of Provnce (mllons) Employment Employment Employment Income Income Trade Producton Anhu Bejng Chongqng Fujan Gansu Guangdong Guangx Guzhou Hanan Hebe Helongjang Henan Hube Hunan Inner Mongola Jangsu Jangx Jln Laong Nngxa Qngha Shandong Shangha Shaanx Shanx Schuan Tanjn Xnjang Yunnan Zhejang Notes: Reports varous provncal characterstcs n Employment and GDP data are from offcal sources, deflated usng spatal prce ndexes. Mgraton data s constructed from the 2000 Populaton Census. See text for detals. The last two columns use 2002 data on trade flows. Home-bas reports total producton for domestc use as a share of total absorpton (calculated as 1/(1+I/D), where I s total mports and D s gross output less total exports). 42

44 Appendx B: Supplementary Materal In ths Appendx, we provde (1) the proofs for all man propostons, (2) detals behnd the model s calbraton that was not provded n the man text, and (3) detals behnd estmatng the Head-Res method of estmatng trade costs adjusted for asymmetres. Proofs of Propostons Our proofs omt sector super-scrpts. Proposton 1: Gven real ncomes for each regon V, mgraton costs between all regonal pars µ j, and heterogeneous productvty dstrbuted F z (x), the share of regon workers that mgrate to regon j s ( ) κ Vj µ j m j = N k=1 (V kµ k ) κ. Proof: The share of people from regon that mgrate to regon j s the probablty that each ndvdual s potental payoff from regon j exceeds that from any other regon. Specfcally, ( ) m j Pr µ j z j V j max {µ kz k V k }. k j Snce Pr(z j x) e ( γx) κ by assumpton of Frechet dstrbuted worker productvty, we have Pr(µ j z j V j x) = Pr(z j x/µ j V j ) = e ( γx/µ jv j ) κ. The dstrbuton of net ncome across workers from n regon j s therefore also Frechet. Smlarly, the dstrbuton of the hghest net real ncome n all other regons s descrbed by Pr ( ) max {µ kz k V k } x k j = Pr (µ k z k V k x), k j = Pr (z k x/µ k V k ), k j = e ( γx/µ kv k ) κ, k j ( = e γx/( k j (µ k V k ) κ ) 1/κ) κ, whch s also Frechet. Returng to the orgnal m j expresson, let X = µ j z j V j and Y = max k j {µ k z k V k }, whch are Frechet dstrbuted wth parameters s X = µ j V j / γ and s Y = ( k j (µ k V k ) κ) 1/κ / γ. By the Law of 43

45 Total Probablty, m j = = ˆ ˆ0 0 = 1 Pr (X Y Y = y) f Y (y)dy, ( ) 1 e (y/s X ) κ κsy κ y 1 κ e (y/s Y ) κ dy, ˆ 0 e (sκ X +sκ Y )y κ κs κ Y y 1 κ dy, Wth a change of varables u = y κ and therefore du = κy κ 1 dy, whch s the result. m j = 1 + = 1 s κ Y ˆ u=0 u= ˆ 0 = 1 sκ Y s κ X + sκ Y e (sκ X +sκ Y )u s κ Xdu, e (sκ X +sκ Y )u du, ( ) κ µ j V j = N k=1 (V kµ k ) κ, Proposton 2: If worker productvty z s dstrbuted Frechet wth varance parameter κ, and agents are able to mgrate between regons at cost µ j, then the expected real ncome net of mgraton costs for workers from regon s V 0 = V m 1/κ, and aggregate average real ncome (welfare) s therefore W = N =1 λ 0 V m 1/κ, where λ 0 = L0 N j=1 L0 j s the share regstered n regon. Proof: A worker from regon has heterogeneous productvty across all potental regons n Chna. These productvty are..d. Frechet(κ, γ 1 ) across all workers and regons wth a mean of 1. Each worker wll resde n the locaton that maxmzes real ncome net of mgraton costs µ j z j V j. The probablty that a gven person s welfare s below x s the probablty that no regon gves utlty above x. The probablty that regon j s payoff for a person from regon s below x s e ( γx/µ j V j) κ. The probablty that they are all below x s the product of ths across all potental regons, F U (x) = N j=1 ( e ( γx/µ j V j) κ = e γx/ [ N j=1(µ j V j) κ] ) 1/κ κ. 44

46 To get our result, note that f X Frechet(κ, γ 1 ) then Pr(X < x) F(x) = e ( γx/s) κ and E [X] = s. So, the utlty of workers from regon after mgraton decsons dstrbuted accordng to F U (x) [ above s Frechet wth E [U ] = N ( ) ] κ 1/κ. j=1 µ j V j As real ncome and welfare are synonymous, V κ N j=1 (µ kv k ) κ and therefore V 0 s the mean across all regons of regstraton, weghted by regstraton populaton shares λ 0 V 0 E [U ]. From proposton 1, m = L 0/ N j=1 L0 j, W = N =1 λ 0V m 1/κ. = V m 1/κ. Aggregate welfare = Proposton 3: The total supply of effectve labour n regon n s H n = N =1 µ n m κ 1 κ n L 0. Moreover, h n = µ n m 1/κ n s the average uts of effectve labour for workers from regon n that work n regon, and therefore H n = N =1 h nm n L 0. Proof: Worker productvty follows a Frechet dstrbuton wth mean 1. The productvty of workers from regon that work n regon j wll follow a dfferent dstrbuton. By the multplcaton rule of probabltes, ( ) Pr z j x µ j V j z j max {µ kv k z k } = Pr [( z j x ) ( µ j V j z j max k j {µ k V k z k } )] k j Pr ( µ j V j z j max k j {µ k V k z k } ). (23) From Proposton 1, the probablty of a worker from to work n regon j (the denomnator of the above) s m j. The numerator s [ (z Pr j x ) ( )] µ j V j z j max {µ kv k z k } k j [ ] = Pr max {µ kv k z k } µ j V j z j µ j V j x. k j We saw n Proposton 1 that X = µ j V j z j and Y = max k j {µ k V k z k } are both Frechet dstrbuted random varables. Denote ther CDFs F(x) and G(y), wth means µ j V j and ( k (µ k V k ) κ) 1/κ, respectvely. To ease notaton, defne B = ( k (µ k V k ) κ) 1/κ. Gven a partcular value for Y, Pr [ y µ j V j z j µ j V j x ] = Pr [ µ j V j z j µ j V j x ] Pr [ µ j V j z j y ], = F ( µ j V j x ) F (y). Hence, by the Law of Total Probablty, [ ] Pr max {µ kv k z k } µ j V j z j µ j V j x k j = ˆ µ j V j z j 0 [ F ( µ j V j x ) F (y) ] dg(y), = G ( µ j V j x ) F ( µ j V j x ) ˆ µ j V j x 0 F(y)dG(y). 45

47 Solve for the frst term, G ( µ j V j x ) F ( µ j V j x ) = e ( = e γ µ j V j x ) κ B e ( γx) κ, ] B κ (µ j V j) κ +1 ( γx) κ [ [ ( γx) κ = e = e ( γx) κ /m j,, ] N k=1 (µ k V k) κ (µ j V j) κ where the last lne follows from equaton 9. Next, to solve the second term, fnd the PDF of Y (dg(y)). Snce G(y) s Frechet wth mean B,, dg(y) = γκ B ( ) γy κ 1 e ( γy/b) κ. B Wth ths, and defng A N k=1 (µ kv k ) κ wth some algebra, we have ˆ µ j V j x 0 F(y)dG(y) = ( ) B κ ( e γ µ j V j x ) κ A. A So, usng these two results, [ ] Pr max {µ kv k z k } µ j V j z j µ j V j x k j = m j e ( γx/(a/µ j V j)) κ. The m j therefore cancels out (recalled equaton 23), and the condtonal dstrbuton of z j s ( ) Pr z j x µ j V j z j max {µ kv k z k } = e ( γx/(a/µ j V j)) κ, k j whch s Frechet wth mean A/µ j V j = m 1/κ j. Fnally, snce all mgrants ncur a mgraton cost modeled as a real resource cost (a tme loss, or a drect productvty reducton), the average uts of effectve labour of mgrants net of the mgraton cost s h n = µ n m 1/κ n and our result follows. 46

48 Calbratng Changes n Underlyng Productvty Fnally, we calbrate the change n sectoral productvty (and captal accumulaton) ˆT n j such that observed real GDP changes match the data. Smulatng only mgraton cost and trade cost reductons results n counterfactual changes n real ncomes (per effectve worker) across provnces. These changes, not surprsngly, do not match what we measure for ˆV n j from data. We compare the model outcomes to data n Fgure 3 (a). In the model, changes n productvty ˆT n j make up the dfference. We calbrate changes n provncal the productvty parameter ˆT n j such that, when mgraton and trade costs declne as measured, the resultng real ncome per effectve worker changes match data. The necessary values for ˆT n j are dsplayed n Fgure 3 (b). Fgure 3: Calbratng Productvty Changes ˆT j n (a) Real Income Changes Per Effectve Worker ˆV j n, when ˆT j n = 1 Agrculture Nonagrculture Model 1 Model Data from Data from (b) Impled Change n ˆT j 1/θ(β j +η j ) n to Match Data 350 Agrculture 350 Nonagrculture Percent Change Percent Change Jangsu Henan Fujan Zhejang Hunan Hube Hanan Guangdong Guangx Helongjang Chongqng Qngha Jangx Hebe Shandong Shangha Schuan Anhu Tanjn Jln Laong Guzhou Shannx Bejng Yunnan Nngxa Shanx Inner Mongola Gansu Xnjang Inner Mongola Shanx Shannx Hebe Jangx Henan Shandong Helongjang Jln Laong Jangsu Schuan Zhejang Gansu Tanjn Xnjang Guangx Nngxa Guangdong Hunan Guzhou Yunnan Bejng Anhu Hube Fujan Chongqng Hanan Shangha Qngha Notes: Compares the model-mpled change n real ncome per effectve worker ˆV j n when underlyng productvty s constant to real ncome changes from data. Both are expressed relatve to the mean. To match data, we requre changes n productvty parameters ˆT j n as dsplayed n the bottom panel. We re-scale wth the exponent 1/θ(β j + η j ), as productvty per effectve worker n autarky s proportonal to T j 1/θ(β j +η j ) n. 47

49 Estmatng Trade Costs We begn wth a standard Head-Res ndex of trade costs. From equaton 22 and our data on trade shares, we estmate τ j. We summarze the average values of ths for varous blateral trade flows between regons of Chna. A value of τ j j = 1 mples zero trade costs and τ = 2 mples trade costs equvalent to a 100% tarff-equvalent trade costs. Overall, we fnd the trade-weghted average trade cost between regons of Chna s 300% n agrculture and 200% n nonagrculture. Care must be taken when nterpretng these values, however, as they reflect trade costs between regons relatve to trade costs wthn each regon after all, we normalze τnn j = 1 for all n and j. To arrve at our preferred estmate of trade costs τ j j, we must augment the Head-Res ndex τ to reflect trade cost asymmetres. As dscussed n the man text, gven an exporter-specfc trade cost t j j, we have τ = τ j t j /t n. j How do we estmate these export costs? Wthn the same class of models for whch the Head-Res estmate holds, a normalzed measure of trade flows s ( ) ( ) ln π j /π nn j = S j S n j θln τ j, where S captures any country-specfc factor affectng compettveness, such as factor prces or productvty. See Head and Mayer (2014) for detals behnd ths and related gravty regressons. If trade costs have only a symmetrc and exporter-specfc component, and f the symmetrc component s well proxed by geographc dstance, then we can estmate t j from ( ) ln π j /π nn j = δ j ln(d ) + ιn j + η j + ε j, (24) where δ j s the dstance-elastcty of trade costs, d s the (populaton-weghted) geographc dstance between regon n and, and ιn j and η j are sector-specfc mporter- and exporter-effects. Dstance between Chna s provnces and the world s the dstance between each regon and all other countres weghted ( by ) total trade between Chna and each other country. As the exporter ( ) effect s ˆη j = S j θln t j and the mporter effect s ˆι n j = Sn, j we nfer export costs as ln ˆt n j = ( ) ˆι n j + ˆη n j /θ. We use the regonal nput-output data descrbed n the prevous secton to estmate ths regresson. We fnd dstance-elastctes n lne wth nternatonal trade results; specfcally, ˆδ ag = 1.33 and ˆδ na = 1.06 for 2007 wth standard errors of 0.38 and 0.22, respectvely. For the 2002 trade data, we fnd ˆδ ag = 1.43 and ˆδ na = 1.04 wth standard errors of 0.41 and Fnally, we dsplay the estmates of ln(ˆt n ) for both 2002 and 2007 n Fgure 4. As the overall level of export costs s undetermned, we express values relatve to the mean across all regons wthn each year. Overall, t s more costly for poor regons to export nonagrcultural goods than rch regons consstent wth nternatonal evdence from Waugh (2010). For agrculture, ths pattern s less clear. There were also very few changes to the rankng across regons n trade cost asymmetres between 2002 and

50 Fgure 4: Asymmetres n Trade Costs: Exporter-Specfc Costs Provnce Specfc Export Cost, Tarff Equvalent % Central Coast Bejng/Tanjn Northeast Agrculture North Coast Southwest Central Regon South Coast Northwest Provnce Specfc Export Cost, Tarff Equvalent % Southwest Central Regon North Coast Nonagrculture Northeast Bejng/Tanjn Central Coast Northwest South Coast Notes: Dsplays the tarff-equvalent (n percentage ponts) regon-specfc export costs. All expressed relatve to the average for the year. A value of 10 mples exportng s 10 percent more costly relatve to the average regon. Table 13: Ital Blateral Trade Costs (Year 2002) Exporter North- Bejng North Central South Central North- South- Importer east Tanjn Coast Coast Coast Regon west west Abroad Trade Costs n Agrculture, τ ag Northeast Bejng/Tanjn North Coast Central Coast South Coast Central Regon Northwest Southwest Abroad Trade Costs n Nonagrculture, τ na Northeast Bejng/Tanjn North Coast Central Coast South Coast Central Regon Northwest Southwest Abroad Note: Dsplays blateral trade cost (relatve to wthn-regon costs) for agrculture and nonagrculture for eght broad regons. The eght regons are classfed as: Northeast (Helongjang, Jln, Laong), North Mucpaltes (Bejng, Tanjn), North Coast (Hebe, Shandong), Central Coast (Jangsu, Shangha, Zhejang), South Coast (Fujan, Guangdong, Hanan), Central (Shanx, Henan, Anhu, Hube, Hunan, Jangx), Northwest (Inner Mongola, Shaanx, Nngxa, Gansu, Qngha, Xnjang), and Southwest (Schuan, Chongqng, Yunnan, Guzhou, Guanx, Tbet). 49