Trade, Migration and Regional Income Differences

Trade, Migration and Regional Income Differences Trevor Tombe Xiaodong Zhu University of Calgary University of Toronto This Version: May 2014 Abstract International trade and the internal movement of goods and people are closely related. To study these interrlationships, we develop a general equilibrium model of internal and external trade with migration, featuring both trade and migration frictions. Importantly, the spatial distribution of income endogenously responds to trade patterns and worker migration choices. With unique data on China s internal and external trade and internal migration flows, we estimate trade and migration frictions; they are high but declined substantially after 2000. Using the model, we quantify the effects of liberalizing trade (international and internal) and relaxing internal migration restrictions on aggregate welfare, internal migration, and regional income differences. External trade liberalization has a large impact on China s trade to GDP ratio, but only modestly increases welfare while increasing regional income differences. In contrast, internal trade liberalization has large welfare gains and reduces regional income differences. While both increase migration flows, migration cost reductions are substantially more important for migration but surprisingly only modestly increase aggregate welfare while substantially decreasing regional income differences. Our results suggest internal liberalization is much more important than external liberalization as a source of aggregate welfare gains and improvements in regional income inequality. JEL Classification: F1, F4, R1, O4 Keywords: Migration; internal trade; gains from trade; China Tombe: Assistant Professor, Department of Economics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N1N4. Email: ttombe@ucalgary.ca. Zhu: Professor, Department of Economics, University of Toronto, 150 St. George Street, Toronto, Ontario, M5S3G7. Email: xzhu@chass.utoronto.ca. We thank Kunal Dasgupta, Nicholas Li, Peter Morrow, Diego Restuccia and especially Daniefl Trefler for very helpful comments and suggestions. We have also benefited from comments of various seminar participants at the Bank of Canada, Chicago Fed, CCER in Peking University, Fudan University, Hong Kong University of Science and Technology, Michigan State University, Shanghai University of Finance and Economics and University of Calgary, and various conference participants at the NBER Chinese Economy Workshop, Canadian Economics Association Annual Meeting, North American Econometric Society Summer Meeting, China Economics Summer Institute, Rocky Mountain Empirical Trade, the Society of Economic Dynamics Annual Meeting, Tsinghua Workshop in Macroeconomics. Tombe acknowledges generous financial support provided by the Social Science and Humanities Research Council (IDG 430-2012-421).

1 Introduction In the past decade, China has become increasingly integrated into the global economy and has experienced the largest internal migration in human history. Since its accession to the WTO, China s trade to GDP ratio more than doubled from 20% in 2001 to 44% in 2011, with only a slight temporary decline during the financial crisis. Internal migration flows also increased over this period. Nearly 118 million people switched counties between 2000 and 2005, and over 40 million switched provinces. This figure is up from 70 million switches between 1995 and 2000, 37 million of whom switched provinces. A less well known but important fact is that The internal movement of goods is also large and should not be neglected in 2002, total inter-provincial flows exceeded international flows by over 13%. If internal trade and migration respond to (and facilitate) international trade, they may also be important determinants of (and transmission mechanisms for) the aggregate gains from trade. The broad link between international trade and inter-provincial migration and trade is not surprising. Perhaps the most well known example in China of coastal manufacturing expansion with migrant workers is the case of Hon Hai Precision Industry (Foxconn). The rapid increase of Foxconn s workforce to assemble popular Apple products is predominantly due recruitment of migrant workers. At the company s facilities in Shenzhen, for example, which assemble iphones and ipods at the Guanlan factory and ipads and Macs at the Longhua factory, migrant workers account for slightly over 99% of total employment. 1 This pattern is by no means unique to Foxconn. Just north of Shenzhen, the city of Dongguan exemplifies China s changing economic environment. The city s total trade (imports plus exports) is nearly five times GDP and it alone accounts for a substantial fraction of global supply of computer and electronics components. Its expansion began from a population of 400,000 in 1978, largely engaged in farming and fishing, to over seven million in 2005. Of these seven million, over 70% are migrant workers (World Bank, 2009). The link between internal and external trade is equally intu- 1 These data on migrant workers by facility are available through the Fair Labor Association, which Apple hired to audit working conditions at Foxconn factories following a string of highly publicized worker suicides. 1

itive, with facilities increasingly being located inland, for example, in the city of Chongqing. In this way, inland assembly and internal trade substitutes for coastal migration. Motivated by these observations, we examine in detail the interrelationships between trade liberalization, internal migration, and internal trade in general and for China s recent experience in particular. To do this, we exploit unique data on the complete matrix of trading relationships between China s provinces and each other and with the world. We link these to recent individual-level census data on internal migration flows. Together these data allow us to explore the consequences for a significant liberalization of China s external trade, through its accession to the WTO. In the next section, we provide estimates that suggest migration was important for coastal manufacturing expansion in China. Industries that expanded employment disproportionately hire migrant workers. Also, industries with the greatest reduction in tariffs levied on their exports by countries abroad (post-wto) also disproportionately hire migrant workers. Additional reforms occurred in this period as well, liberalizing the flow of goods and people between China s provinces. We will examine the relative importance of liberalizations in external goods flows, internal goods flows, and internal migration flows for welfare, income differences, and migration flows. With our detailed internal trade data, along with province-level data on gross output, we estimate internal and external trade costs. Our approach provides an estimate of average trade costs with very little structure. Specifically, we follow Novy (2013) s generalization of the Head and Ries (2001) measure of trade cost. This measure applies to a broad class of trade models, from Eaton and Kortum (2002) to Melitz (2003), and applies to the model structure we develop in this paper as well. We find substantial regional variation in trade costs in 2002. Trade costs for coastal provinces in the South, for example, are less than half the costs faced by provinces in the central region of China. We find regions to which migrants flow are regions with lower trade costs. This approach also allows us to measure the change in trade costs through time. While informative, we cannot quantitatively examine the effect of these costs, or changes in these costs, on welfare or migration. We are also unable to measure migration costs with just this data alone. Additional 2

structure is required. To that end, we develop a general equilibrium model of internal and external trade with costly regional migration. At its core, the model is similar to Redding (2012), who extend Eaton and Kortum (2002) to include within-country trade and migration flows. Our key departure is to incorporate inter-provincial migration frictions, which better reflects the unique Hukou system of household registration in China. Specifically, we model regional labour mobility as Artuc, Chaudhuri and McLaren (2010) model occupational mobility. Workers differ in their taste for each region. Given a common migration cost, only some fraction of workers choose to move from one region to another in response to a given income differential between the regions. The main mechanisms in the model are straightforward. Reductions in international trade costs affect some regions more than others, depending on their propensity to engage in international trade. Labour responds to changes in a region s real income, which depend positively on nominal wages (which increase if demand for a region s exports increase) and negatively on consumer prices (which decline if imports become cheaper) and housing prices (which increase with a region s population). We fit this model to key features of China, which is disaggregated into 30 individual provinces (we exclude Tibet for data availability reasons) and the rest of the world captured as a single external entity. Unique to our approach is the use of China s expanded input-output tables. The model calibration crucially depends on data for the full bilateral trading matrix between all provinces with each other and the world. This data has been exploited in other research, notably Poncet (2005) to estimate internal trade costs, but not to examine the relationship between trade liberalization and internal migration flows. Migration data is compiled using the micro-data from China s Population Census 2000 and 2005. Finally, we exploit price level differences between provinces to estimate real income differences from nominal GDP data by province. With the model, we estimate migration costs (see section 3.5 for details) of 1.5 times annual income in the 1995-2000 period. Between 2000 and 2005, however, we find these costs decline to an average of 1.3 times annual income. With the calibrated model in hand, we simulate its response to various counter- 3

factuals. First, we estimate the overall reduction in international trade costs post- WTO to be approximately twenty percentage points, though this varies across regions. Simulating the measured reduction in international trade costs, we find the overall stock of migrants increase by nearly 2%, most of whom moved towards coastal provinces. Lower internal trade results in a roughly similar magnitude reduction in the migrant stock, as workers move home. Both of these responses are small, though aggregate welfare responses are large 7.4% in the case of internal trade reductions, 2.4% for external Simulating lower migration costs, we find a substantially larger number of workers moved provinces. The stock of migrants increases by over 50% in response to the lower measured migration costs. That being said, aggregate welfare is largely unchanged. Lowering both trade and migration costs together increases welfare by nearly 10% and regional income differences decline by 8.5%. Aggregate trade responds little, though there is spatial variation in the response of trade across provinces. Coastal provinces trade substantially more when migration costs decline, while interior regions trade less. We contributed to a recently growing literature linking international trade flows with the spatial distribution of labour within countries. Redding (2012), in particular, expands the Eaton-Kortum trade model to incorporate within-country regions between which labour can flow. He demonstrates that the welfare gains from trade depend not only on a region s home-bias but also on changes in the distribution of workers. Cosar and Fajgelbaum (2012) focus on firm, instead of worker, location decisions to link international liberalization with increased concentration of economic activity in areas with good market access. We build on the insights of these theoretical papers to examine the effect of China s external trade liberalization on its massive internal labour flows. Uniquely, we incorporate migration frictions in the model to reflect often explicit restrictions on inter-provincial migration in China. Our work is also related to empirical investigations of trade s effect on internal migration for other countries. McCaig and Pavcnik (2012) examine the 2001 US-Vietnam Bilateral Trade Agreement and document substantial worker flows towards internationally integrated industries and provinces, especially for younger workers. Research with individual Brazilian data establishes a positive relation- 4

ship between internal migration flows and employment at foreign owned exporting establishments (Aguayo-Tellez and Muendler, 2009) and measures of a region s market access (Hering and Paillacar, 2012). There is also a large urban-economics literature investigating the role of international trade for altering the spatial distribution of firms and factors within a country (see, for example, Hanson, 1998). Little work has been done, however, investigating the case of China perhaps the largest and fastest expansion of trade and internal migration ever recorded. Existing work for China typically abstracts from general equilibrium effects and investigates data only prior to 2000 (see, for example, Lin, Wang and Zhao, 2004 or Poncet, 2006). Our focus will be on developing a full general equilibrium model to quantitatively examine China s recent trade and migration patterns. Our paper proceeds as follows. Section 2 documents China s internal migration flows, focusing on inter-provincial flows for economic reasons. This section also documents key internal trade relationships and regional differences in international trade exposure. Section 4 outlines and calibrates a modified Eaton-Kortum trade model, based on Redding (2012), that we use in Section 6 to explore various counterfactual experiments relating international trade costs, internal migration frictions, internal trade flows, and inter-provincial migration in China. Section 8 concludes. 2 China s Internal Migration and Trade Prior to presenting anything further, it is helpful to be familiar with the China s geography and the spatial differences in real incomes and migrants. In Figure 1 we display those measures as a choropleth on China s provinces. There are stark differences in real income levels across regions, potentially implying large costs of moving between regions. In this section, we briefly outline first the policy environment within which workers make location decisions. We then document the magnitude of inter-provincial migration flows, the characteristics of migrant workers, and how migrants are distributed across regions and industries in China. We conclude with a broad quantitative measure of inter-provincial labour mobility frictions and how it has changed over time. The latter exercise is a key contribution of this paper. 5

Figure 1: Spatial Distribution of Real Incomes and Migrant Labour in 2005 (a) Real GDP/Worker, Relative to Mean (b) Inter-Provincial Migrant/Employment Ratio Heilongjiang Heilongjiang Inner Mongol Jilin Inner Mongol Jilin Xinjiang Tibet Qinghai Liaoning Beijing Tianjin Shanxi Hebei Ningxia Shandong Gansu Shaanxi Henan Jiangsu Anhui Hubei Shanghai Sichuan Zhejiang Xinjiang Tibet Qinghai Liaoning Beijing Tianjin Shanxi Hebei Ningxia Shandong Gansu Shaanxi Henan Jiangsu Anhui Hubei Shanghai Sichuan Zhejiang (2,3] (1.5,2] (1.35,1.5] (1.2,1.35] (1,1.2] (.8,1] (.65,.8] (.5,.65] [.25,.5] Yunnan Guizhou Hunan Jiangxi Fujian Guangxi Guangdong Hainan (.32,.64] (.16,.32] (.08,.16] (.04,.08] (.02,.04] (.01,.02] (.005,.01] [0,.005] Yunnan Guizhou Hunan Jiangxi Fujian Guangxi Guangdong Hainan Note: Displays choropleths of relative real income levels for each of China s provinces and the migrant share of the labour force. Dark reds indicate both high relative real incomes and large migrant shares of employment. 2.1 Policies China s Hukou registration system impose significant barriers to labour mobility across provinces. Prior to 2003, all provinces in China had regulations that required workers without local Hukou to apply for a temporary residence permit. Due to the difficulty in getting the permit, many migrant workers were without a permit and faced the dire consequence of being arrested and deported by the local authorities. Due to the increasing demand for migrant workers in manufacturing and construction industries, many provinces, especially the coastal provinces, eliminated the requirement of temporary residence permit for migrant workers after 2003. This policy change reduced the migration cost signficantly. However, most migrant workers still do not have access to the health, education and social services that are provided to residents with local Hukou. So the cost to labour mobility was reduced significantly between 2000 and 2005, but barriers remain to be high. To be complete. 2.2 Internal Migration Patterns We provide details behind the construction of migrant flows from the Population Census data in the appendix. Overall, between 2000 and 2005, there were 30.6 mil- 6

lion inter-provincial migrant workers. Net migration flows by province are reported in Table 7. Migrants do not randomly sort across industries, but are predominately concentrated among manufacturing and construction enterprises in eastern provinces. The distribution of employment across industries and years is provided in Table 8. The percentage change is listed in the last column. By far, the largest increases were experienced in the health, education, social services, and transport and trade sectors. Manufacturing and construction, as well as raw material production/mining, also saw large increases. These changes can be decomposed by region, and is displayed in Table 9. The total change in employment, by region and industry, can be compared to the total inter-provincial migrant flow. Table 10 displays this breakdown and the contribution of migrants to overall industry employment growth by region. Eastern manufacturing - by far the largest industry of employment for migrants (and also a tradable sector) - displays an interesting result. There were more migrants flowing into this industry than there was overall employment growth. That is, migration seems to have displaced domestic workers in this industry. While suggestive, it appears that migrants are disproportionately flowing towards regions and industries that are more heavily oriented towards trade. Census data from 2005 can also be used to illustrate these patterns. It is clear in the data that migrants account for a larger share of employment in provinces and industries that export more abroad. We illustrate this pattern in Figure 2. Panel a displays the strong propensity of migrants to move towards provinces that export more abroad, with Shanghai, Guangdong, Tianjin, Zhejian, and Beijing among the top destinations. Panel b displays a similarly strong propensity of migrants to seek employment within industries that export more abroad. This patterns is also true within provinces. Indeed, a regression at the industry-province level of migrants on industry exports (both in logs), controlling for industry employment and a set of province fixed-effects, reveals a strong positive coefficient on exports of 0.07. That is, a 10% increase in exports of an industry in a given province, holding total employment constant, will result in a 0.7% increase in migrants employed. Moving beyond export volumes, we can also link changes in global trade policy 7

towards China to migration patterns across industries. We collect tariff data from TRAINS applied to China s exports by the rest of the world in 2005 and 2000. The change in tariff rates reflects China s ability to increase exports. To measure tariffs against China at the industry level, we take the simple average of effective applied rates across product lines within ISIC Revision 3 categories and aggregate to GB2002 with import volume weights. We plot the change between 2005 and 2000 against each industry s migrant share of employment in panel c of Figure 2. The negative relationship suggests industries that the rest of the world liberalized to a greater extent are industries that disproportionately employ migrant workers. Figure 2: Distribution of Migrants by Province and Industry Export Orientation (a) Provincial Exports (b) Industry Exports (c) External Tariffs Changes Interprovincial Migrants / Employment.005.01.02.04.08.16.32 Shanghai Beijing Guangdong Zhejiang Tianjin Fujian Jiangsu Xinjiang Hainan Inner Mongolia Qinghai Liaoning Ningxia Shanxi Shandong Yunnan Chongqing Hebei Guizhou Jilin Guangxi Jiangxi Hubei Hunan Anhui Sichuan HeilongjiangGansu Henan.02.04.08.16.32 International Exports / Gross Output Interprovincial Migrants / Employment.01.02.04.08.16.32.64 24 40 19 39 30 21 41 18 34 29 42 17 36 35 14 22 37 20 3331 27 11 88 28 1332 15 26 25 44 16 12 14 16 18 20 Log(Industry International Exports) Interprovincial Migrants / Employment.02.04.08.16.32.64 40 24 19 39 41 30 18 21 34 29 42 17 35 36 82 14 22 37 33 31 20 32 13 11 76 90 89 2 1 0 1 2 Percentage Point Change in Average Tariffs on China s Exports 2005 to 2000 Excluded: Shaanxi Industries with total exports in excess of $50m US. Excludes agriculture. Excludes agriculture, beverages, crude oil and fuels, and local gas supply Note: Industries coded as two-digit GB2002 codes. Exports by industry are from UN-COMTRADE, by ISIC Revision 3, linked to GB2002. Tariff data from the TRAINS database, simple average across product lines and import volume weighted across ISIC Rev. 3 to aggregate to GB2002. Figure (c) captures percentage point changes in tariffs applied by the rest of the world on China s exports in 2005 minus those applied in 2000. Industry 15 (drinking products), 25-28 (crude oil, fuel, and chemicals), and 45 (local gas supply) are excluded. 2.3 Characteristics of Inter-Provincial Migrants The strong link suggested above between expanding employment opportunities in export oriented industries and provinces is not surprising given the migrants characteristics. The census directly asks respondents who left their original Hukou registration place the reason for migrating. Table 1 displays key characteristics of interprovincial migrants in China. Those individuals who are living in a location other than their original registration place number 165 million in 2005. Those living in a different province number over 53 million. The change in the total inter-provincial stock of migrants between 2000 and 2005 was 17.2 million. 8

Table 1: Migrant Characteristics (from Census Data) (a) Migrant Stock 1990 2000 2005 Total Migrants 32.7 M 130.6 M 165.4 M Inter-Provincial Migrants 10.5 M 35.8 M 53 M Inter-Provincial Migrant Workers 2 M 28 M 34.7 M (b) Five-Year Migrant Flow (Census 2005) Employed All Inter-Provincial Inter-Provincial Migrants Migrants Migrants Number 117.5 M 40.1 M 30.6 M Reason for Migrating Work 48% 75% 93% Family 27% 19% 4% Education 8% 2% 2% Other 17% 4% 1% Other Characteristics With Children 27% 26% 25% Agricultural Hukou 66% 84% 87% Male 50% 52% 56% Private/Other Company 25% 44% 57% Notes: Magnitude and characteristics of migrants, both as a stock and as a flow. Five year flow the 2005 census. Migrants are defined based on their their Hukou registration location. Private/other company refers to employment at a private or other company not at state, collective, or other enterprise and not self-employed. Looking at the flow directly, we see a different pattern than the change in the total migrant stock. Between 2000 and 2005, nearly 118 million people moved out of their location of registration. Of those, 40.1 million moved across provincial boundaries. Restricting to those migrants who are employed, and who moved within the previous five years, lowers the number to nearly 31 million where over 93% say they moved for work. Other characteristics show that recent migrants are disproportionately those without children, coming from agricultural origins (as indicated by their registration type), working at private companies, and are roughly equally mixed between genders. 9

3 China s Internal and External Trade In addition to labour movements, there are large flows of goods between China s regions and provinces. In this section, we discuss the policies surrounding internal and external trade in China and document the trade data inferred from regional input-output tables. 3.1 The Policies Several people have documented high internal trade barriers in China in the 1990s. See, e.g., Young (2000) and Poncet (2005). Since 2000, these trade barriers have been reduced significantly. Some of the reduction were due to the deliberate policy reforms undertaking by the government in preparation for China s joining WTO. The investment in transportation infrastructure and improvement in logistic technology also contributed to the decline in internal trade cost. To be completed. 3.2 Internal and External Trade Patters We extract province-level trade data, both between province pairs and internationally, from various regional input-output tables for 2002 and 2007. 2 The 2002 tables provide the full bilateral trade flow matrix between provinces as well as each provinces trade with the world. The 2007 tables report the same but for a restricted set of eight regions of China. 3 Measuring changes in trade patterns is therefore restricted to eight regions while initial 2002 trade patterns can be measured for all provinces. We provide further details in the appendix. We report the bilateral flows between the eight regions and each other, and the rest of the world, for 2002 and 2007 in Table 2. To ease comparisons, we normalize 2 We thank Zhi Wang for providing us with this data. 3 The eight regions are classified as: Northeast (Heilongjiang, Jilin, Liaoning), North Municipalities (Beijing, Tianjin), North Coast (Hebei, Shandong), Central Coast (Jiangsu, Shanghai, Zhejiang), South Coast (Fujian, Guangdong, Hainan), Central (Shanxi, Henan, Anhui, Hubei, Hunan, Jiangxi), Northwest (Inner Mongolia, Shaanxi, Ningxia, Gansu, Qinghai, Xinjiang), and Southwest (Sichuan, Chongqing, Yunnan, Guizhou, Guanxi, Tibet). 10

Table 2: Regional Trade Patterns in China Exporter North- Beijing North Central South Central North- South- Importer east Tianjin Coast Coast Coast Region west west Abroad Year 2002 Northeast 0.8789 0.0070 0.0099 0.0083 0.0134 0.0109 0.0077 0.0086 0.0553 Beijing/Tianjin 0.0392 0.6335 0.0936 0.0302 0.0261 0.0333 0.0138 0.0116 0.1188 North Coast 0.0183 0.0332 0.7984 0.0336 0.0176 0.0376 0.0092 0.0084 0.0437 Central Coast 0.0024 0.0016 0.0055 0.8101 0.0146 0.0238 0.0048 0.0046 0.1326 South Coast 0.0049 0.0039 0.0054 0.0262 0.7230 0.0193 0.0038 0.0151 0.1984 Central Region 0.0058 0.0026 0.0113 0.0476 0.0232 0.8777 0.0066 0.0071 0.0182 Northwest 0.0202 0.0077 0.0212 0.0325 0.0451 0.0356 0.7735 0.0378 0.0264 Southwest 0.0088 0.0034 0.0038 0.0182 0.0430 0.0137 0.0091 0.8803 0.0197 Abroad 0.0002 0.0003 0.0003 0.0013 0.0016 0.0001 0.0001 0.0001 0.9960 Year 2007 Northeast 0.7871 0.0196 0.0201 0.0092 0.0271 0.0100 0.0137 0.0093 0.1040 Beijing/Tianjin 0.0376 0.6229 0.1006 0.0151 0.0236 0.0181 0.0207 0.0067 0.1545 North Coast 0.0205 0.0582 0.7679 0.0151 0.0154 0.0371 0.0227 0.0080 0.0550 Central Coast 0.0109 0.0073 0.0141 0.7678 0.0178 0.0484 0.0169 0.0085 0.1082 South Coast 0.0146 0.0086 0.0173 0.0516 0.6848 0.0360 0.0178 0.0284 0.1409 Central Region 0.0173 0.0142 0.0445 0.0485 0.0397 0.7297 0.0293 0.0176 0.0590 Northwest 0.0227 0.0220 0.0477 0.0271 0.0548 0.0356 0.6560 0.0359 0.0983 Southwest 0.0160 0.0116 0.0174 0.0165 0.0836 0.0188 0.0318 0.7378 0.0664 Abroad 0.0004 0.0007 0.0008 0.0037 0.0024 0.0003 0.0004 0.0002 0.9912 Note: Displays the share of each importing region s total spending allocated to each source region. all flows by the importing region s total expenditures, resulting in a table of expenditure shares π ni = x ni / N i=1 x ni. Each row will sum to one across columns. Some regions import substantially more from the rest of the world than they do from the other regions of China. Consider the South Coastal region, where many the Foxconn facilities discussed previously are located. This region imports over 2.5 times as much from abroad than it does from other regions within China. This region also exports substantially more than the rest of China. A useful summary measure of a region s trade openness is the fraction of its expenditures allocated to its own producers that is, it s home share. The diagonal elemebts of Table 2 provide these values for each region. Interior regions of China have much higher home-bias than coastal regions. In 2002, we estimate the central region s home-bias is 0.88 compared to only 0.72 for the south coast and 0.63 for Beijing and Tianjin. All trade values reported so far are at the regional level. For 2002, though not for 2007, we can even compute trade shares for each individual province. These provincial-level trade patterns will play a crucial role in our quantitative exercises to come. We do not report the full matrix of bilateral relationships but list each 11

province s home share in Table 7. Notably, and consistent with the regional data, interior provinces have higher home-bias than coastal provinces. In the second column of the same table, we report the ratio of total international exports to total gross output by province. Again, coastal regions have significantly greater fraction of production oriented towards international exports. These measures, while interesting in their own right, will be key inputs into our later quantitative exercises and, importantly, provide information on the magnitude and patterns of trading costs both internal and external. We turn now to our complete model. 4 Quantitative Model In this section, we develop a model of trade and migration building on Eaton and Kortum (2002). The model features multiple regions of China between which goods and labour may flow. Overall, the model is a departure from Redding (2012) in that we incorporate between-province migration frictions. 4.1 The Trade Structure There are N + 1 regions representing China s provinces plus the rest of the world. Households in each region n derive utility from consuming a final good and residential housing (denoted H Un ) using U in = C α n H 1 α Un. Final goods are produced by a perfectly competitive aggregator firm using a CES technology given by (ˆ 1 σ/(σ 1) Y n = y n ( j) (σ 1)/σ d j), 0 where σ is the (constant) elasticity of substitution between intermediate goods j. Intermediates y n ( j) may be sourced from local producers or imported. 12

Production of individual intermediate goods j is undertaken by firms in perfect competition that use labour, intermediate inputs, and land with the following technology y n ( j) = ϕ n ( j)l n ( j) β H Y n ( j) η q n ( j) 1 β η, where ϕ n ( j) is the firm s TFP, l n ( j) is labour, H Y n ( j) is land inputs, and q n ( j) is intermediate input. This intermediate input comes from the total final goods available in region n; that is, Y n = C n + q, where q is the total intermediates demanded by firms producing in region n. Productivity differs across all firms and is modeled probabilistically, following Eaton and Kortum (2002), where for each region ϕ is distributed according to a Frechet distribution F i (ϕ) = e T iϕ θ, with dispersion parameter θ and location parameter T i. Productivity differences across goods j decrease in θ and increase in T i. A firm with productivity ϕ in region i would charge a purchaser in region n p ni ( j) = τ niw β i rη i P1 β η i, ϕ where τ ni 1 is an iceberg trade cost, w i are wages in region i, r i is the price of land, and P i is their aggregate price index. Given this structure, purchasers in each region opt to source intermediates y n ( j) from the lowest cost location. This results in expenditures being allocated across regions according to each region s technology, input costs, and trade costs. Denote π ni the fraction of region n spending allocated to goods produced in region i. Given the Frechet distribution of technology, ( ) T i τ ni w β θ i rη i P1 β η i π ni = ( ) k=1 N+1 T k τ nk w β θ, (1) k rη k P1 β η k 13

which results in an aggregate price index of [ ] N+1 ( ) 1/θ P n = γ T i τ ni w β θ i rη i P1 β η i, (2) i=1 where γ = Γ ( 1 + 1 σ ) 1/(1 σ). θ It will prove convenient to express this price as P n = (π nn /γt n ) 1/θ w β n rn η Pn 1 β η, where we assume τ nn = 1. This can be further simplified to P n = (π nn /γt n ) 1/θ(β+η) wn β/(β+η) rn η/(β+η). Notice, importantly, that a simple manipulation of equation 1 will result in an expression identical to equation 14. Our model is therefore consistent with our trade cost estimates. 4.2 Internal Labour Migration Labour is mobile only between regions within China, not between any Chinese province and the world and vice-versa. For each worker, there is one (and only one) home (or, in China s case, Hukou) region. It is costless to live within one s home region while a migrant worker with home region i face costs to live in region j i that are a share 1 c i j of income in region j. In addition to real incomes net of migration costs, workers have hetergeneous tastes for each region. That is, one worker may attach significant value from living in some region while another worker may not. Specifically, workers draw at birth a vector {ε i } N i=1 of tastes for each region i {1, N}. Tastes are i.i.d. across workers and regions. Workers then choose where to live to maximize their taste-adjusted real income net of migration costs ε i j c i j V j. 4 With this structure, it is straightforward to solve for migration flows. A worker from region i will migrate to region j if and only if ε i j c i j V j > max k j {ε ikc ik V k }. As tastes are a random variable across the continuum of individuals from region i, 4 This approach closely follows recent work by Artuc, Chaudhuri and McLaren (2010) and Ahlfeldt, Redding, Sturm and Wolf (2012). Morten and Oliveira (2014) use a similar approach, though in a very different context. 14

the law of large numbers ensures the proportion of region i workers who migrate to region j is ( ) m i j = Pr ε i j c i j V j max {ε ikc ik V k }. k j For a particular distribution of tastes, this proportion can be solved explicitly. Assume that tastes follow a Frechet distribution with CDF F ε (x) = e x κ, where κ governs the degree of taste dispersion across individuals. A large κ implies little dispersion. The usefulness of this particular distribution is demonstrated in the following proposition. Proposition 1 Given real incomes for each region V i, migration costs between all regional pairs c i j, and heterogeneous tastes distributed F ε (x), the share of region i workers that migrate to region j is Proof: See appendix. ( ) κ Vj c i j m i j = N k=1 (V kc ik ) κ. (3) Given migration shares from equation 3, the number of workers in each region can be determined conditional on the (exogenous) initial distribution of workers across Hukou regions. Define the number of workers registered in region i as L 0 i. The employment in each region i is L i = N m ji L 0 j. (4) j=1 We conclude this section by highlighting a key detail in how we model migration. We measure flows relative to individual s original Hukou registration province. This presumes that migration costs C i j are defined for an individual with Hukou registration in province i that moves into province j. The costs do not change for this 15

individual after the move migration decisions are always taken relative to the original Hukou registration province not the current province of residence. This implies (1) it is costless for migrants to return to their Hukou province and (2) costs of living outside of the Hukou province are perpetually incurred (not once and for all upon migration). 4.3 Real Income Households in each region are populated by L n agents, who supply labour inelastically and are the equal recipients of all income generated in that region. Total income in region n is then given by v n L n = w n L n + (1 α)v n L n + ηr n, where R n is total revenue from all producing firms in region n. In this expression, v n denotes per-capita income derived from labour income and household and firms spending on land. The expression can be further simplified given the Cobb-Douglas nature of the production technology, which implies a constant fraction β of revenue is spent on labour inputs. Through some additional rearrangement, nominal income in region n is and real income is ( β + η v n = αβ V n = v n P α n r 1 α n ) w n,. (5) To solve for the cost-of-living in region n, and therefore the real income expression, note that land market clearing implies ( (1 α)β + η r n = αβ ) wn L n H n, (6) where H n = H Un + H Y n is the total stock of land in region n. With this expression, and the expression for the goods price index, we can express real incomes as 16

V n (T n /π nn ) η+(1 α)β α θ(β+η) β+η hn, where h n denotes land per capita and the proportionality constant is common across all N + 1 regions. This shows the two key channels for increases in a region s real income: (1) lower home-share π nn and (2) higher land-labour ratio h n. The first follows from heterogeneous productivity of firms within a region. Imports can substitute for low productivity domestic producers. The second channel is influenced by migration flows. Inward migration make land more scarce, and therefore expensive, lowering real incomes. 4.4 Simulating the Counterfactual Equilibrium To ease our quantitative analysis and calibration, we follow Dekle, Eaton and Kortum (2007) and express counterfactual values relative to initial equilibrium values. That is, let ˆx = x /x, where x is the counterfactual value of x. The following system of equations solves for changes in prices ( ˆP n ), wages (ŵ n ), and trade flows ( ˆπ ni ) as a function of changes in trade costs ( ˆτ ni ), underlying productivity ( ˆT n ), and regional employment (ˆL n ): ŵ n ˆL n Y n = π ni = ˆP n = ˆV n = N+1 π inŵ i ˆL i Y i, (7) i=1 ( ) π ni ˆT i ˆτ ni ŵ β+η i ˆP 1 β η i ˆL η θ i k=1 N+1 π nk ˆT ( ) k ˆτ nk ŵ β+η k ˆP 1 β η k ˆL η θ, (8) k [ ] N+1 ( ) 1/θ π nk ˆT k ˆτ nk ŵ β+η k ˆP 1 β η k ˆL η θ k, (9) k=1 ŵ α n ˆP n α 1 α ˆL n, (10) 17

which hold for all regions both within China and abroad. Within China, equilibrium relative changes in each region s employment ˆL n are similarly defined by m in = ˆL n = L 1 n ( ) κ m in ˆV n ĉ in N k=1 m ( ) κ, (11) ik ˆV k ĉ ik N i=1 m inl 0 i, (12) given initial migration shares m i j, employment L n, home regions Li 0, the equilibrium relative change in real incomes ˆV n, and the exogenous relative change in migration costs ĉ i j. For the rest of the world ˆL N+1 = 1, as workers cannot move across national boundaries by assumption. Notice the power of solving equilibrium in this way. We need not estimate initial levels of H n, T n, or even τ ni or c i j. Initial trade and migration shares π i j and m i j contain sufficient information to simulate the model s counterfactual response to various exogenous shocks. We use this to simulate the effect of changes in trade costs ˆτ i j, migration costs ĉ i j, or underlying productivity ˆT i. 4.5 Aggregate Outcomes We measure change in three key aggregate outcomes: average real income, real GDP, and welfare. The first measure captures average real income, without accounting for migration costs or non-pecuniary benefits of living in any given region. The second measure is the change in GDP measured with initial prices. The final measure represents the change in aggregate welfare. We derive in the following three subsections. Proposition 2 Given a measure of real income µ n from data and a simulated change in each region s employment share ˆλ n and real income ˆV n, the counterfactual change in the national average real incomes is ˆV = N ω n ˆV n ˆλn, n=1 18

where the weights are each province s contribution to the initial aggregate real income, ω n = µ n λ n / N n=1 µ nλ n. Proof: See appendix. Similar to the change in average income, though slightly different, is the change in aggregate real GDP, which we derive in the next proposition. Proposition 3 Given a change in each region s wages ŵ n, employment share ˆλ n, and prices ˆP n, along with the goods share of household expenditures α, the change in national real GDP is Ĝ = [ N ω n 1 α + α ŵn ˆλ ] n, n=1 ˆP n where the province s initial GDP share are the weights ω n = w n L n / N n=1 w nl n. Proof: See appendix. The final aggregate outcome we are interested in, and perhaps the most significant, is welfare. Aggregate welfare goes beyond changes in real income, as agents derive utility directly from residing in a particular location through their ε draws and incur costs when living outside their home (Hukou) region. To measure aggregate welfare in our model requires we exploit a number of useful properties of the Gumbel distribution in the following proposition. Proposition 4 If locational preferences ε are drawn from a Frechet distribution with variance parameter κ, and agents are able to migrate between regions facing costs c i j, the relative change in aggregate welfare is Ŵ = N 1 i=1 [ ] 1/κ N 1 ) κ ω i m i j (ĉi j ˆV j, j=1 where the weights ω i are each region s contribution to the initial aggregate welfare.. Proof: See appendix. Before proceeding to these experiments, the model must be calibrated in an empirically reasonable way. It is to the calibration that we now turn. 19

Table 3: Calibrated Model Parameters Parameter Value Target / Description β 0.3 Labour s share of gross output 1 β η 0.6 Intermediate s share of output 1 α 0.13 Housing s share of expenditure θ 4 Elasticity of Trade λ n Region Specific Employment share L i Region Specific National employment Y n Region Specific Initial nominal GDP π ni Pair Specific Bilateral trade shares Notes: Displays model parameters, their targets, and a description. China s employment by province is from the national statistical yearbook. Employment for the world (region N) is from the Penn World Table. Bilateral trade shares between all pairs of China s provinces, and between each province and the rest of the world, is from China s extended Input-Output Tables for 2002. See text for more details. 4.6 Calibrating the Model The model s equilibrium system, defined in equations 7 through 12, solves for changes in prices ( ˆP n ), wages (ŵ n ), regional employment (ˆL n ), trade flows ( ˆπ ni ), and counterfactual migration flows m in as a function of changes in trade costs ˆ d ni and migration costs ĉ ni. The exogenously specified parameters include the preference weight on goods consumption (α), labour s share of output (β), land s share of output (η), and a parameter governing the variance of the productivity distribution (θ). The remaining parameters include a region s initial nominal GDP Y i = w i L i, trade shares π ni, and labour allocations L n. We describe the calibration in detail below and provide a brief summary in Table 3. The household utility and production function parameters (α, β, η) are set such that labour s share of gross output is 20% and intermediate inputs share is 60%. Land and structure s share follows from our constant returns to scale assumption, and thus η = 0.2. The 2002 extended input-output tables of China list total labour compensation, total intermediate input use, and gross output. The ratio of intermediate input use to gross output is 0.6112; we round to 0.6. We assume labour s share is larger than the ratio of labour compensation to gross output (approximately 0.2 in the input-output data) to reflect machinery and human capital used by workers, and set β = 0.3, which implies η = 0.1. Finally, to calibrate α, we use consumer 20

expenditure data from China s most recent National Statistical Yearbook. The fraction of urban household spending on housing is 11.30% and for rural households is 15.47%. As a compromise between these values, we set α = 0.87, implying the housing share of expenditures is 13%. 5 The productivity dispersion parameter θ has received a great deal of attention in the literature. This parameter governs productivity dispersion across firms and, consequently, determines the sensitivity of trade flows to trade costs (higher θ implies lower elasticity). Anderson and van Wincoop (2004) review the literature and argue a value for θ between 5 and 10 is reasonable. For example, Alvarez and Lucas (2007) set θ = 6.67, Eaton and Kortum (2002) set θ = 8.3, Waugh (2010) finds θ = 7.9 for OECD countries. Recently, however, Simonovska and Waugh (2011) find θ = 4.1 when the bias inherent in Eaton and Kortum (2002) s procedure, also used in Waugh (2010), is corrected. In what follows, we adopt this value (θ = 4) but ensure our results are robust to alternative values. Regional employment L n for each of China s provinces and the rest of the world are straightforward. China s statistical yearbook reports employment by province, and we adopt those numbers. The employment share in each province is reported in Table 7. Total national employment for China is then 636.508 million. Total employment in the rest of the world of 2,103 million is inferred from the Penn World Table as the total non-china employment in 2002. Finally, to solve equation 7, we require a value for region n s initial total expenditure, Y n. Given regional data on trade and employment, we find the value of Y i that solve the initial trade balance condition. That is, given data for L n and π ni, find w n that solves w n L n = N+1 π in w i L i. i=1 Let w n be the solution to this system, we define Y n = w i L i. To do this, we use province level data on trade π ni from China s extended 2002 input-output tables. We do not report the entire matrix here, but one can get a sense for the value of π ni for each province by reviewing the regional trade patterns from Section 3. 5 This number is not selected at random between 0.113 and 0.1547. It is also the weight given to housing in the spatial consumer price level data that we will employ later in the paper. 21

5 Inferring Trade and Migration Costs In this section, we quantify the extent of migration costs within China and trade costs within and between China s provinces and the world. 5.1 Migration Costs Recall the expression from equation 3, m i j = ( V j c i j ) κ / ( N k=1 (V k c ik ) κ), governing the flow of workers between China s provinces. This representation of migration decisions is simple yet powerful. Migration flows in data, for example, do respond to what is surely a particularly import component of migration costs: distance to home. In Figure 3(a) we plot a normalized measure of migration ln(m i j /m ii ) against the time required to drive between each province s capital cities. Driving time is a slightly better predictor of migration than great circle distances. Migration flows are clearly smaller between provincial pairs that are far apart. Also, migration flows respond positively to real income differences. In Figure 3(b) we plot the same measure of normalized migration against ln(v j /V i ). 6 Migrants flow towards provinces that have higher real incomes relative to their home province. We can more completely characterize migration costs. With real incomes V and migration shares m from data, assuming a particular value for the dispersion of taste parameter κ is sufficient to infer migration costs. From the above expression for m i j, we have c i j = ( mi j m ii ) 1/κ V i V j. (13) What value of κ should one assume? For the variance of tastes to have a finite variance across individuals, κ > 2 is required. Using exogenous variation in the ability of individuals to move between regions of a country (the collapse of the Berlin Wall), Ahlfeldt et al. (2012) estimate κ [4.8, 6.5]. Using the mid-point of their estimate, we set κ = 5.65 throughout the paper. In the appendix, we explore sensitivity of all results to this parameter and find key results are robust. Based on this value for the income-elasticity of migration, we find migration 6 See appendix for description of how real incomes by province are calculated. 22

Figure 3: Migration Flows, Distances, and Real Income Differences (a) Migration vs. Travel Time (b) Migration vs. Income Differences Log(Normalized Migration mij/mii for 2000) 12 10 8 6 4 2 Log(Normalized Migration mij/mii for 2000) 12 10 8 6 4 2 9 10 11 12 13 Log(Driving Time, Between Capitals) 2 1 0 1 2 Log(Real Income in Destination Relative to Home) Notes: Displays the relationship between normalized migration log(m i j /m ii ) in 2000 and (1) travel time and (2) income differences. Travel time is measured as the driving time between provincial capitals, calculated from the Google Maps API. Income differences in the log ratio of real income in the destination province to real income in the home province. Figure 4: Histogram of Bilateral Migration Costs (a) Migration Cost Parameter c i j in 2000 (b) Relative Changes in c i j 160 120 100 120 80 Frequency 80 Frequency 60 40 40 20 0 0 0.25 0.5 0.75 1 1.25 1.5 Disposable Income Net of Migration Costs, Cij, in 2000 0 0.5 0.75 1 1.25 1.5 1.75 2 2.25 Change in Real Income Net of Migration Costs, Cij Notes: Displays the measure of migration costs captured by the fraction of income remaining after migration costs are paid. We denote this value as c i j in the text. Panel (b) displays the ratio of c i j in 2005 to its year 2000 level. Values for relative changes above one represent reductions in migration costs. 23

Figure 5: Selected Spatial Distributions of Migration Costs (a) Costs of Migrating Into Beijing (b) Costs of Migrating Out of Sichuan Heilongjiang Heilongjiang Inner Mongol Jilin Inner Mongol Jilin Xinjiang Tibet Qinghai Liaoning Beijing Tianjin Shanxi Hebei Ningxia Shandong Gansu Shaanxi Henan Jiangsu Anhui Hubei Shanghai Sichuan Zhejiang Xinjiang Tibet Qinghai Liaoning Beijing Tianjin Shanxi Hebei Ningxia Shandong Gansu Shaanxi Henan Jiangsu Anhui Hubei Shanghai Sichuan Zhejiang Yunnan Guizhou Hunan Jiangxi Fujian Yunnan Guizhou Hunan Jiangxi Fujian Guangxi Guangdong Guangxi Guangdong Hainan Hainan Notes: Displays choropleths of selected migration costs into Beijing (a common destination for migrants) and out of Sichuan (a common source of migrants). The darker the red, the higher the migration cost. Tibet excluded. costs declined for most pairs of provinces in China. We display the histogram of both the initial post-migration cost income share c i j and its relative change ĉ i j in Figure 4. Migration costs are large. In 2000, we estimate that over 71% of income is paid as migration costs, though there are large differences between pairs. In Figure 5, we plot the spatial distribution of migration costs for two example cases: inflows to Beijing and outflows from Sichuan. These choropleths represent the magnitude of trade costs (1 c i j ) in terms of color intensity. In panel (a), it is clear that provinces far from Beijing typically have higher costs to move into Beijing. This is also true for outflows. Panel (b) shows the costs of migrating out of Sichuan is largest for the northeastern regions. These large costs across space prevent workers from arbitraging large differences in real income across regions. More relevant for our quantitative exercises are relative changes in these migration costs. Using the ratio of equation 13 evaluated with 2005 and 2000 data, we infer these changes from real income and migrant flow changes between 2000 and 2005. We display the results in panel (b) of Figure 4. Approximately 62% of pairs experience reductions in costs (ĉ i j > 1), with an average value of ĉ i j = 1.24. Among the 38% of pairs for which migration costs increased, we find an average value of ĉ i j = 0.86. Overall, the typical pair experienced a change in migration costs of ĉ i j = 1.08. That is, the share of income kept by migrants after paying migration costs increased by 8%. In the appendix, we show these estimates for ĉ i j are 24