A Model of Trade with Ricardian Comparative Advantage and Intra-sectoral Firm Heterogeneity

Transcription

1 A Model o Trade with Ricardian Comparative Advantage and Intra-sectoral Firm Heterogeneity Haichao FAN y Edwin.-C. AI z Han QI x January 6, 203 Abstract In this paper, we incorporate Ricardian comparative advantage in a multi-sector version o Melitz s (2003) model to explain how the pattern o international specialization and trade is determined by the interaction o comparative advantage, economies o scale, country sizes and trade barriers. The model is able to capture the existence o inter-industry trade and intra-industry trade in a single uni ed ramework. Trade liberalization can lead to a counter-melitz e ect in the larger country in the sectors where it has the strongest comparative disadvantage yet still produces. In this case, the productivity cuto or survival is lowered while the exporting cuto increases in the ace o trade liberalization. This is because the inter-sectoral resource allocation (IRA) e ect dominates the Melitz e ect in these sectors. Consequently, the larger country can lose rom trade liberalization. This is not a criticism o Melitz s work, but rather a complement o his pathbreaking contribution by pointing out richer possibilities when his model is extended to multi-sector setting. Analyses o data o Chinese manuacturing sectors con rm these hypotheses. Our model can be extended to capture the e ect that, in the comparative advantage sector, it is possible that rms that sell domestically have higher average productivity than rms that do not, as ound by u (200). Keywords: inter-industry trade, intra-industry trade, heterogeneous rms, trade liberalization JE Classi cation codes: F2, F4 We would like to thank participants in seminars in the Paris School o Economics, Graduate Institute in Geneva, ECARES in Brussels, Chinese University o Hong Kong and City University o Hong Kong, as well as conerence participants in Tsinghua University International Trade Workshops in 200 and 20, or helpul comments. The work in this paper has been supported by the Research Grants Council o Hong Kong, China (General Research Funds Project no ). y Fan: Department o Economics, Hong Kong University o Science and Technology, Clear Water Bay, Kowloon, Hong Kong. hxac@ust.hk z ai: Corresponding author. CESio Research Network Fellow. Department o Economics, Hong Kong University o Science and Technology, Clear Water Bay, Kowloon, Hong Kong. Phone: (852) ; Fax: (852) ; elai@ust.hk or edwin.l.lai@gmail.com x Qi: Department o Economics, Hong Kong University o Science and Technology, Clear Water Bay, Kowloon, Hong Kong. ste an@ust.hk 0

2 Introduction How do rms entry, exit, output and exporting decisions respond to trade integration and trade liberalization? Do they respond di erently across sectors? How is trade pattern determined by the interaction between pattern o comparative advantage across sectors and monopolistic competition between rms within the same sector? How are trade pattern and welare a ected by globalization? We try to answer these questions by developing a model o trade with comparative advantage across sectors and intra-sectoral rm heterogeneity. There are by and large two types o international trade: inter-industry trade and intra-industry trade. It is widely recognized that the ormer is driven by comparative advantage and the latter by economies o scale. The most widely used models or capturing comparative advantage are o the Ricardian type (e.g. Dornbusch, Fisher and Samuelson (DFS) 977, Eaton and Kortum 2002) and the Heckscher-Ohlin type. The most notable models used to capture intra-industry trade are probably attributed to Krugman (979, 980). More recently, Melitz (2003) extends Krugman s (980) model to analyze intra-industry trade when there is rm heterogeneity, thus capturing the selection o rms according to productivity and pro t-shiting to rms o higher productivity when a country opens up to trade and trade liberalization. It stimulates much urther work in this direction, notably Chaney (2008), Melitz and Ottaviano (2008), and Arkolakis (200), to name just a ew. In this paper, we incorporate Ricardian comparative advantage into a multi-sector version o Melitz s (2003) model. By doing so, we have a model that explains how comparative advantage, economies o scale and rm selection interact to sort sectors into ones in which only one o the countries produces (where there is inter-industry trade) and ones in which both countries produce (where there is intraindustry trade). A number o testable hypotheses are generated. First, sectors in which one o the countries has strong comparative advantage would be characterized by inter-industry trade, while sectors in which neither country has strong comparative advantage would be characterized by intra-industry trade. Second, or any given country, the raction o rms that export is higher or a sector with stronger comparative advantage. These results are supported by Chinese data. Third, we are able to understand the interaction o the orces attributed to comparative advantage e ect and productivity selection e ect, in the ace o trade liberalization. We nd that we can decompose the total e ect o trade liberalization into those caused by inter-sectoral resource allocation (IRA) e ect and rm selection e ect according to productivity (which we call Melitz e ect). Although, like Melitz (2003), trade integration (switching rom autarky to trade) is always welareimproving, the welare e ect o trade liberalization (reduction o trade barriers) depends on the relative size o the two countries and the degree o asymmetry in trade liberalization between the two countries. In particular, in the case o trade liberalization, we nd that the interaction o the IRA e ect, the Melitz e ect and home market e ect in the comparative disadvantage (two-way trade) sectors can give rise to an e ect that is opposite to what is predicted by Melitz. For lack o a better term, we call this e ect counter-melitz e ect. This is not a criticism o Melitz s work, but rather a complement o his pathbreaking contribution by pointing out richer possibilities when his model is extended to

3 multi-sector setting. Melitz predicts that symmetric trade liberalization leads to an increase in the productivity cuto or survival but a decrease in the exporting productivity cuto, and this gives rise to an increase in the average productivity o the rms that serve the domestic market, leading to an increase in domestic real wage in terms o goods in the sector. The counter-melitz e ect in our model predicts that, in the most comparative disadvantage (two-way trade) sectors, trade liberalization can lead to a decrease in the productivity cuto or survival but an increase in the exporting productivity cuto, and this gives rise to a decrease in the average productivity o the rms that serve the domestic market, leading to domestic real wage reductions in terms o goods in these sectors. This is because the IRA e ect dominates the Melitz e ect in the sectors where the country has the strongest comparative disadvantage and yet still produces. The reason why the country can pro tably produce in the sectors in which it has comparative disadvantage is the existence o increasing returns to scale and home market e ect as explained by Krugman (980). For this reason, the counter-melitz e ect cannot exist in country that is too small. In addition to the country being su ciently large, another contributing actor to the existence o counter-melitz e ect is that the country understakes su ciently drastic asymmetric trade liberalization compared with its trading partners. This is because unilateral reduction o iceberg importing cost in Home always leads to the counter-melitz e ect in all sectors in Home, while unilateral reduction o iceberg importing cost o Foreign always leads to the Melitz e ect in all sectors in Home. Thereore, there exists a counter-melitz e ect in the comparative disadvantage sectors and a Melitz e ect in the comparative advantage sectors, i the country is su ciently large or its trade liberaliation is su ciently asymmetric compared with its trading partners. This implies that or a given country, in the ace o trade liberalization, the raction o exporters and the share o export revenue in total revenue both increase in the comparative advantage sectors but they both decrease in the sectors in which the country has the least comparative advantage yet still produces. The theory is con rmed by testing the hypotheses using Chinese rm-level data. China s liberalization upon its accession to WTO in 200 ts the above conditions very well: It was large, and its trade liberaliztion was very asymmetric. Recently, there has been some discussion o another counter-melitz e ect, which is completely di erent rom ours. u (200) introduces comparative advantage in the one-sector Melitz (2003) model and derives the theoretical outcome that, in the comparative advantage sectors, rms that sell domestically can have higher average productivity than rms that do not. She supports her theory by the nding that in sectors where China had comparative advantage (i.e. labor-intensive sectors), Chinese rms that mainly exported were on average less productive than those that served the domestic market. Does her theoretical and empirical ndings contradict our theory or empirical nding here? The answer is no. First, as ar as theory is concerned, our model can be easily modi ed to yield the same theoretical prediction as u by making a slight change in the assumption about market-entry costs, namely, assuming that a rm needs to incur a market entry cost i it enters a market, be it domestic or oreign. Second, even with this modi cation, all the propositions in our paper remain the same. Most importantly, the model continues to yield our counter-melitz e ect. In addition, the modi ed model throws light on how the peculiar eature o the Chinese exporting sector (namely the existence o a large 2

4 raction o rms engaging in processing trade) can possibly explain u s emprical ndings. The introduction o comparative advantage in a multi-sector Melitz model captures a number o e ects that a one-sector Melitz model without comparative advantage cannot. Moreover, these interesting e ects indeed occur in the real world, as revealed by the empirical evidence o this paper and u s (200). In the recent theoretical literature modeling open economy with heterogeneous rms, papers by Okubo (2009) and Bernard, Redding and Schott (2007) are the closest to ours. ike us, Okubo (2009) also introduces multiple sectors into the Melitz model, thus making it a hybrid o the multiple-sector Ricardian model and the Melitz model. In the two-sector case he analyzes the general equilibrium e ects, allowing the endogenous determination o the relative wage. But the ocus o his paper is quite di erent rom ours, though there are some similarities. He mainly ocuses on changes in population and the e ects on the number o varieties. We mainly ocus on how the strength o comparative advantage o a sector a ects rm selection under trade liberalization. We analyze and obtain closed orm solution o the international pattern o specialization and trade as a unction o trade barriers, relative country size and Ricardian comparative advantage. We decompose the total e ect o trade liberalization into the IRA e ect and Melitz e ect and explain the condition under which one e ect can dominate the other. Most importantly, we identiy the conditions under which there is a counter-melitz e ect (accompanied by lowering o real wage) rom trade liberalization in certain sectors or even the entire economy. We carry out empirical tests o the hypotheses while he does not conduct any empirical tests. Bernard, Redding and Schott (2007) incorporate rm heterogeneity into a two-sector, two-country Heckscher-Ohlin model, and analyze how alling trade costs lead to the reallocation o resources, both within and across industries. Inter-sectoral resource reallocation changes the ex-ante comparative advantage and provides a new source o welare gains rom trade as well as causes redistribution o income across actors. In their paper, trade liberalization raises the productivity cuto or survival and lowers the exporting productivity cuto in both industries, with the e ect being disproportionately larger in the comparative advantage sectors. Thereore, there is no counter-melitz e ect in their paper. One could have captured inter-industry trade and intra-industry trade in a uni ed model without assuming rm heterogeneity. As is ound elsewhere in the literature, the aggregate results remain about the same whether or not rm heterogeneity is assumed. Probably the largest bene t rom incorporating rm heterogeneity is that we are able to use rm level data to conront some o the hypotheses. For example, some propositions contain predictions about the variation in the percentage o rms that export across sectors. Such propositions cannot be derived rom a model with homogeneous rms. The paper is organized as ollows. Section 2 presents the model with heterogeneous rms in the closed economy and examines the properties o the equilibrium. In section 3, we carry out an analysis o the equilibrium in the open economy. We analyze the pattern o specialization and trade and identiy the existence o inter-industry trade as well as intra-industry trade. In section 4, we show the impact For example, Helpman and Krugman (985) integrate the inter-industry trade and intra-industry trade model with homogeneous rms. 3

5 o opening up to trade on the productivity cuto s and welare in each sector. In section 5, we analyze the e ects o trade liberalization, and demonstrate the existence o a counter-melitz e ect in the most comparative disadvantage two-way trade sectors. In section 6, we extend our model by modiying our assumption to allow or the possibility that some rms only export but do not serve the domestic market. Ater modi cation, all previous propositions remain unchanged, but the model now yields predictions consistent with with theoretical and empirical ndings by u (200). In section 7, empirical tests o the main propositions in section 5 are carried out. Section 8 concludes. 2 A Closed-economy Model In this section, we shall describe the eatures o a closed economy, but where necessary we also touch upon some eatures o a two-country model when the closed economy opens up to trade. The closed economy is composed o multiple sectors: a homogenous-good sector, and a continuum o sectors o di erentiated goods. There is only one actor input called labor. The homogeneous good is produced using a constant returns to scale technology. It is reely traded with zero trade costs when the country is opened up to trade. Firms are ree to choose the sectors into which they enter. We assume that in order to produce a di erentiated good, a rm has to pay a sunk cost o entry. Ater entry, a rm decides whether or not to produce according to whether the expected present discounted value o its economic pro t is non-negative ater its rm-speci c productivity has realized. The economic pro t is determined by the ollowing actors. There is a xed cost o production per period, and a constant marginal cost o production. The xed cost o production is the same or all rms but the marginal cost o production o a rm is partly determined by a random draw rom a distribution. Upon payment o the entry cost e, the rm earns the opportunity to make a random draw rom a distribution o rm productivity. The draw will determine the rm-speci c component o the rm s productivity (i.e. reciprocal o the unit labor requirement or production). The above characterizations o the model are basically drawn rom Melitz (2003). Unlike Melitz, there is another actor that a ects the variable cost o production o a rm, which is an exogenously determined sector-speci c technological level. In general, this technological level di ers across sectors in a country as well as di ers across countries within the same sector. The set o sector-speci c technological levels across sectors in both countries determine the pattern o comparative advantage across sectors o each country. There are consumers, each supplying one unit o labor. Cobb-Douglas unction: Preerences are de ned by a nested C k = h R i k 0 c k(j) dj ln U = ln C h + R 0 b k ln C k dk () with R 0 b kdk = and 0 < <, (2) where denotes the share o expenditure on the homogenous good, b k is the share o expenditure on di erentiated good k 2 [0; ]; k is the endogenously determined mass o varieties in di erentiatedgood sector k. The homogeneous good is produced with constant unit labor requirement =A h. The 4

6 price o the homogeneous good is w=a h, where w is the wage, as it is produced and sold under perect competition. For the di erentiated-goods sectors, the exact price index or each sector is denoted by P k, where P k = h R i k 0 p k(j) dj, where > = > where p k (j) denotes the price o variety j in sector k, and denotes the elasticity o substitution between varieties. Cost minimization by rms implies that the gross revenue o rm j in sector k is given by where E = w denotes the total expenditure on all goods. pk (j) r k (j) = b k E (3) The labor productivity o a rm in the di erentiated-good sector k is the product o two terms: one is a rm-speci c, random variable ' k ollowing a Pareto distribution P (; ) = ' k where ' k 2 [; ] and (> ) is the shape parameter o the distribution; 2 the other is A k, which is exogenous and sector-speci c. The labor productivity o a rm is thus equal to A k ' k. Production labor employed by rm j in sector k is a linear unction o output y k (j): l k (j) = + P k y k(j) A k ' k (j) ; where is the xed cost o production per period, and A k ' k (j) is the productivity o rm j in sector k. Thereore, under monopolistic competition in sector k the pro t-maximizing price is given by p k (j) = w A k ' k (j) (4) (3) and (4) imply that the ow o pro t o rm j in sector k is given by k (j) = r k(j) w = b kw P k w A k ' k (j) w I a rm draws too low a productivity, it will exit immediately, as its expected economic pro t is negative. Denote the cuto productivity or a rm to survive in sector k by ' k. We shall call this the productivity cuto or survival. Then, the aggregate (exact) price index in sector k can be rewritten as P k = ( R k [p k (')] g(') ' k G(' k ) d' ) = k p k ( e' k ); where p k (') w A k ', G(') is the c.d.. o the distribution o the rm-speci c component o productivity ' in the sector and g(') is its p.d.. The unction G(') is the same or all sectors. Moreover, p k ( e' k ) = w A k e' k 2 The assumption > ensures that, in equilibrium, the size distribution o rms has a nite mean. 5

7 where e' k can be interpreted as the average productivity in sector k. It can be easily shown that e' k = = " Z ' k ' g(') G(' k ) d' + # 'k (5) The zero cuto pro t (ZCP) condition determines the productivity ' k o the marginal rm that makes zero expected economic pro ts: w = r k (' k ) = b kw k 'k e' k = b kw + k (ZCP) (6) As more rms enter, the cuto productivity increases. This in turn lowers the probability o surviving ater entry. So, when the cuto productivity becomes su ciently high, there will be no more entry. More precisely, the ree entry (FE) condition, which relates the cuto productivity to the entry cost e, is given by e w = p in e k = [ G(' k )] e k (FE) (7) where p in G(' k ) is the ex-ante probability o successul entry; e k k ( e' k ) is the net average pro t o a surviving rm, which is equal to w e'k ' = w k + according to the ZCP condition (6) and equation (5). 3 Solving or the above system o 2 equations, (6) and (7), or 2 unknowns, we can get (' k ) = D ; k = + e + Thereore, the raction o rms that can successully enter, bk D 2 (k) G(' k ), is the same across sectors. However, the actual cuto productivity, A k ' k, still di ers across sectors. From now on, we assume + e, in order to avoid corner solution. emma In the closed economy, the raction o rms that can successully enter is independent o A k. The number o rms in each sector is also independent o A k. Note that emma holds even i and di er across sectors. The intuition or ' k to be independent o A k is that an increase in A k causes a rm s optimal price to decrease, and as a result, the aggregate price or this sector decreases as well. Consequently, each rm s optimal price relative to the sectoral aggregate price is unchanged so that the expected pro t o 3 e k k ( e' k ) = r k( e' k ) w = e'k rk (' ' k k ) w = w e'k = w. The third equality arises ' k + rom the act that e'k ' = r k ( e' k ). The ourth equality stems rom the act that w = r k r k (' k ) k(' k ), which is the ZCP condition (6). The th equality comes rom (5). 6

8 each rm does not change. As a result, the raction o rms that can successully enter is independent o A k. Note that though the increase in A k does not a ect the number o rms in the sector, it improves consumers welare due to the increased output o each rm. 3 An Open-economy Model In this section, we consider a global economy with two countries: Home and Foreign. We attach an asterisk to all the variables pertaining to Foreign. We index sectors such that as the index increases Home s comparative advantage strengthens. In other words, the sector-speci c relative productivity a(k) a k A k A k increases in k 2 [0; ]. Thereore, a 0 (k) > 0. On the demand side, we assume that consumers in both countries have identical tastes: ln U = ln C h + R 0 b k ln C k dk with R and C k = R k 0 c k(i) di + R k 0 c k (j) dj 0 b kdk = On the production side, the labor productivity in the homogeneous good sector are respectively A h and A h in Home and Foreign. In the rest o the paper, we assume that the homogeneous good sector is su ciently large so that the homogeneous good is produced in both countries. 4 We also assume that there is no trade cost associated with the homogeneous good. Thereore ree trade o homogeneous goods implies that the wage ratio is determined by relative labor productivity in the sector, i.e.! w w = A h A, h where w denotes Foreign s wage. Without loss o generality, we assume that A h A = and normalize h by setting w =. Thereore, in equilibrium w = w =. The speci cation on technology in the di erentiated-good sectors is the same as in the closed economy. The assumptions o a reely traded outside good that is produced by all countries, and Pareto distribution o rm productivity in each di erentiated-good sector, greatly simpliy the analysis. 5 The subscript dk pertains to a domestic rm serving the domestic market in sector k, the subscript xk pertains to a domestic rm serving the oreign market in sector k, and the subscript k pertains to sector k regardless o who serves the market. For the di erentiated-good sectors, each rm s pro tmaximizing price in the domestic market is given, as beore, by p dk (j) = A k ' k (j). But Home s exporting rms will set higher prices in Foreign s market due to the existence o an iceberg trade cost, such that (> ) units o goods have to be shipped rom the source in order or one unit to arrive at the destination. Thereore, the optimal export price o a Home-produced good sold in Foreign is given by p xk (j) = A k ' k (j). Similarly, Foreign s rms pricing rules are given by p dk (j) = A k ' k (j) and n 4 The su cient condition is > max ; o. However, this is just a su cient, not necessary, condition. In + + general, we do not need such a strong assumption on, as each country usually both imports and exports di erentiated goods. I trade in di erentiated goods is close to balanced, can be much smaller. 5 In adopting these assumptions, we ollow Chaney (2008), who was probably the rst to make these assumptions to simpliy the analysis. 7

9 p xk (j) = A k ' k (j). Following Melitz (2003), we initially assume that trade costs are symmetrical so that iceberg importing cost o Home is the same as that o Foreign. In addition to the iceberg trade cost, the exporting rm has to bear a xed cost o exporting, x, which is the same or all rms. 3. Firm entry and exit According to the rms pricing rules, the gross revenue and net pro t o rm j in di erentiated sector k rom domestic sales or Home s rms are, respectively: pdk (j) r dk (j) = b k, dk (j) = r dk(j). The expressions or the corresponding variables or Foreign s rms, rdk (j) and dk (j), are de ned analogously. The variables P k and Pk are the aggregate price index in sector k o goods sold in Home and Foreign, respectively. Their expressions are given in equation (8) below. Following the same logic, the gross exporting revenue and net pro t o rm j in sector k or Home s rms are, respectively: r xk (j) = b k pxk (j) Pk, xk (j) = r xk(j) x. The expressions or the corresponding variables or Foreign s rms, rxk (j) and xk (j), are de ned analogously. et ' dk and ' xk denote the rm-speci c productivity cuto s in sector k or domestic sales and exporting respectively or Home s rms; ' dk and ' xk denote the corresponding variables or Foreign. Consequently, the mass o exporting rms rom Home is equal to: xk = G(' xk) G (' dk ) 'dk dk = dk where dk denotes the mass o operating rms in Home. P k ' xk The corresponding expression relating the variables xk and dk or Foreign are de ned analogously. Then, in di erentiated-good sector k, the mass o varieties available to consumers in Home is equal to k = dk + xk and k is de ned analogously. The aggregate price indexes are given by: P k = ( k ) pdk ( e' k ); P k = ( k ) p dk ( e' k ) (8) where e' k and e' k denote the aggregate productivity in di erentiated sector k or goods sold in Home and Foreign, respectively. They are given respectively by: ( e' k ) = k " dk ( e' dk ) + xk ( e' k ) = k h dk ( e' dk ) + xk a k e' xk i # e' xk, (9) a k (0) 8

10 where e' dk ( e' dk ) and e' xk ( e' xk ) denote respectively the aggregate productivity level o all o Home s (Foreign s) operating rms and Home s (Foreign s) exporting rms. 6 The relationships between e' dk and ' dk, between e' dk and ' dk, between e' xk and ' xk, and between e' xk and ' xk, are exactly the same as in the closed economy, namely equation (5). That is, e' sk = + ' sk and e' sk = + ' sk or s = x; d. From the above equations, it is obvious that these aggregate productivity measures as well as aggregate price indexes are unctions o (' dk, ' dk, ' xk, ' xk, dk, dk ). As will be shown below, as long as x is su ciently large, an entering rm will produce only i it can generate positive expected pro t by selling domestically, and export only i it can generate positive expected pro t by selling abroad. 7 Then we have the ollowing our zero cuto pro t conditions r dk (' dk ) = b k (P k A k ' dk ) = () rdk (' dk ) = b k (Pk A k ' dk ) = (2) P r xk (' xk ) = b k k A k' xk = x (3) rxk (' xk ) = b Pk k A k ' xk = x (4) De ne e k and e k as the average pro t ow o a surviving rm in sector k in Home and Foreign respectively. It can be easily shown that 8 G('xk ) e k = dk ( e' dk ) + xk ( e' xk ) = 'dk + x G (' dk ) + ' " # xk e k = dk ( e' dk ) + G(' xk ) G ' xk ( e' xk ) = ' + dk + ' dk x. xk These are analogous to the equation shown in ootnote 3 or the closed economy. The potential entrant will enter i her expected post-entry pro t is above the cost o entry. conditions or Home and Foreign are, respectively Hence, the ree entry (FE) e = [ G (' dk )] e k = ('dk) + x (' + xk) (5) e = [ G (' dk )] e k = (' dk + ) + x (' xk ) (6) 6 The derivation o the above two equations are available rom the corresponding author s homepage at or upon request. 7 The condition is x > max ; g. I this condition is not satis ed, then there exist some sectors in which all rms export (besides serving the domestic market). 8 e dk dk ( e' dk ) = r dk( e' dk ) = e'dk rdk (' ' dk dk ) = e'dk =. The third equality arises ' dk + rom the act that e'dk ' = r dk ( e' dk ). The ourth equality comes rom the act that = r dk r dk (' dk ) dk(' dk ), which is the ZCP condition above. The th equality comes rom equation (5). Furthermore, e xk = x can be derived rom similar + steps as above by replacing the subscript d by x and the variable by x. Finally, note that G(') = '. 9

11 3.2 General equilibrium Assuming that both countries produce in sector k, given the wage ratio A h =A h =, we can solve or (' dk, ' dk, ' xk, ' xk, dk, dk ) rom the our zero cuto pro t conditions and two ree entry conditions () to (6) since the aggregate prices are unctions o these six variables (or details, please reer to Appendix A). The solutions are given below. (' dk ) B B = D B (a k ) B B (' dk ) = D B Bx ' xk = ' xk = Bx (a k ) (7) (8) ' dk a k (9) ak ' dk (20) 2 dk = D 2 (k) 4 B B (a k ) B(a k ) B B 2 dk = D 2 (k) 4 B B(a k ) B B B (a k ) 3 5 (2) 3 5 (22) where B x. The variable B can be interpreted as a summary measure o trade barriers; a k can be interpreted as competitiveness o Home in di erentiated goods sector k. Recall that a 0 k (k) > 0 is assumed. In a one-sector model, Melitz (2003) imposes the condition x > so as to ensure that some rms produce exclusively or their domestic market in both countries. In this paper, we adopt a more stringent condition, x > max ; g, so as to ensure that, in each country, some rms sell exclusively to their domestic market in all sectors. 9 This condition implies that B >. 0 According to equations (2) and (22) Home s rms will exit sector k when dk 0, and Foreign s rms will exit the sector i dk 0. This implies that B B (a k ) B(a k ) < < B B (a k) B(a k ) is needed or both countries to produce positive outputs in sector k, otherwise there will be complete dominance by one country in the sector and one-way trade. Rearranging these inequalities, we can sort the sectors into three types according to Home s strength o comparative advantage. Home will not produce in 9 The proo is straightorward. From Table, we see that ' dk < ' xk, x > B(a k) B B (a k. Similarly, ' ) dk < ' xk, x > B (a k). Equations (2) and (22) imply that B(a k) B B(a k ) B B (a k ) and B (a k) B B(a k or k 2 [k ) ; k 2], where dk 0 and dk 0. Hence x > max ; g is a su cient condition or ' dk < ' xk and ' dk < ' xk or all two-way trade sectors. In addition, Table shows that x the country produces) or all one-way trade sectors. 0 As >, x, and >, it is obvious that B x > max ; g is also a su cient condition or ' dk < ' xk and ' dk < ' xk (whenever > under our condition. 0

12 sector k i k k, where k satis es (a k ) = B + B 2 + ; (23) and Foreign will not produce in sector k i k k 2, where k 2 satis es (a k2 ) = B2 B + (24) + : Thereore, the solutions to (7)-(22) are valid i and only i k 2 (k ; k 2 ). It is clear that k 2 (k ; k 2 ) implies that (a k ) 2 B ; B or any possible GDP ratio =, which ensures that the productivity cuto s will never reach the corner or the sectors in which both countries produce. When k =2 (k ; k 2 ), the number o rms in one o the countries solved rom the system (7)-(22) is negative. In that case, there is no interior solution to some o the equations in the system. This re ects the act that no rms rom that country enters in sector k, which means that the other country completely dominates that sector. Thereore, a di erent set o equations need to be solved or this case. Without loss o generality, we consider the Home-dominated sectors. As there is no competition rom Foreign s rms when Home s rms sell in Foreign, the aggregate price indexes become P k = ( dk ) P k = ( xk) A k e' dk A k e' xk Accordingly, the two zero cuto pro t conditions or Home () and (3) continue to hold. As the ree entry condition (5) or Home s rms continues to hold, solving the diminished system o three equations (), (3), (5) or three unknowns, we have dk = b k + = D 2 (k) xk = b k + = D 2 (k) x x (' dk ) = + D. Furthermore, we can easily obtain (' xk ) = + x D by noting that xk = G(' xk ) G(' dk ) dk. An analogous set o solutions or the Foreign-dominated sectors can be obtained. 2, 3 B2 Because + B( B( +) > holds as long as B >, we always have k < k2. 2 They are: dk = b k = D 2 (k) ; xk = b k + x = D 2 (k) x ; and (' dk) = + D. 3 The uniqueness o the above equilibrium is proved in an appendix posted on the corresponding author s homepage at +) B or upon request.

13 Proposition In sectors k 2 [k 2 ; ], where Home has the strongest comparative advantage, only Home produces, and there is one-way trade. An analogous situation applies to Foreign in sectors k 2 [0; k ]. In sectors k 2 (k ; k 2 ), where neither country has strong comparative advantage, both countries produce, and there is two-way trade. We show the three zones o international specialization in Figure. The upward sloping curve (including the dotted portions) corresponds to equation (2), while the downward sloping curve (including the dotted portions) corresponds to equation (22). The horizontal portion o dk in the diagram corresponds to the equation or dk above when Home dominates sector k completely. The horizontal portion o dk corresponds to the analogous equation or Foreign. Domestic Firm Number * θ dk θ dk 0 Only Foreign produces Only Home produces k Both countries produce k2 k Figure. Three Zones o International Specialization (assumptions: (i) expenditure shares are equal across sectors; (ii) < ). 4 Opening up to Trade In this section, we analyze how opening trade between the two countries impacts the economy o each country, e.g. the productivity cuto s, the mass o producing and exporting rms, as well as welare. Beore proceeding with the analysis, it is helpul to list the solutions to the relevant variables corresponding to the three types o sectors in Table. 2

14 Sector type Foreign-dominated Two-way trade Home-dominated k < k k < k < k 2 k > k 2 (' dk ) B B? D (' xk ) B B? D Bx B (a k ) a k D x (' dk ) (' xk ) D + D B B D x + B (a k ) D +? B (a k ) B B D B (a k ) (a k) B x? B (ak) B B(a k ) dk 0 D 2 (k) xk 0 'dk ' xk dk B B D 2 (k) + D 2 (k) x B(ak) dk D 2 (k) D 2 (k) B B (a k ) 0 B B xk D 2 (k) ' x dk ' xk dk 0 P k [D 2 (k) ] ak B + A k e' ck [D 2 (k) ] A k e' dk [D 2 (k) ] P k [D 2 (k) ] A k e' dk [D 2 (k) ] A k e' dk Table : Solution o the System + bk D = ; D 2 (k) = + e ; (a k ) = B + B 2 + ; A k e' dk [D 2 (k) ] B A k e' ck a k (a k 2 ) = B + B Impacts on productivity cuto s In this subsection, we analyze how trade a ects the productivity cuto s rom two aspects: within sector and across sectors. First, we look at how trade integration changes the cuto s within a certain sector. In this regard, we nd that the impacts o trade integration on productivity cuto s are the same as in Melitz (2003) in all sectors. Then we compare the cuto s across sectors upon trade integration. We add a subscript c to all the parameters pertaining to autarky (c=closed economy). It has been shown in Section 2 that the autarky productivity cuto or survival in Home and Foreign is given by (' ck ) = (' ck ) = + = D e. I both countries produce, then the equilibrium cuto s or survival are given by (7) and (8). As (a k ) 2 B, B, we have ' dk > ' ck and ' dk > ' ck. Recall that i only one country produces, the equilibrium productivity cuto s or survival are given by: (' dk ) = + D > (' ck ) i only Home produces (' dk ) = + D > (' ck ) i only Foreign produces Hence, the least productive rms in all sectors will exit the market ater trade integration. result, resources will be reallocated to the most productive rms. Furthermore, ' dk > ' ck implies that e' dk > e' ck, and ' dk > ' ck implies that e' dk > e' ck. Thereore, the average productivity in any sector k As a 3

15 is higher under trade integration than in autarky. Thus we generalize Melitz s result to a setting where there exist endogenous intra-industry trade and inter-industry trade in a uni ed model. In the closed economy, the cuto s or survival are identical across sectors. However, this is not true any more in the open economy. In the sectors where both countries produce, the equilibrium cuto or survival is an increasing unction o the sectoral comparative advantage. More precisely, as a k increases, ' dk rises but ' dk alls, and, ollowing the ree entry conditions (5) and (6), ' xk alls but ' xk rises. Thus, we have Proposition 2 In sectors where both countries produce, or a given country, a sector with stronger comparative advantage has a higher raction o domestic rms that export and higher raction o revenue derived rom exporting. Moreover, ' xk > ' xk > ' dk > ' dk i Home is more competitive in sector k (a k > ), while ' xk > ' xk > ' dk > ' dk i a k <. This result and Proposition 2 are summarized by Figure 2 below. Figure 2. How productivity cuto s vary across sectors 4.2 Impacts on welare The impact o opening up to trade on welare is the same as predicted by the original one-sector Melitz (2003) model. The analysis is similar and so we relegate the proo to the appendix. In the appendix, it is shown that welare increases ater trade integration in both countries. The ollowing proposition and Figure 3 summarize the analysis above. 4

16 Proposition 3 Welare increase in both countries ater they open up to trade with each other. Figure 3. Welare Impact o Trade Integration (w = w = by assumption and normalization) In the next section, we perorm comparative statics concerning the e ects o trade liberalization. 5 Trade liberalization In Melitz (2003), both Home and Foreign gain rom opening to trade and rom trade liberalization. Here, we show that trade liberalization can lead to welare loss or some sectors, and even or the whole country. We shall analyze symmetric and asymmetric trade liberalization separately. 5. Symmetric Trade iberalization So ar, we have been assuming that bilateral trade barrriers are symmetrical. In other words, i is the iceberg trade cost o exporting rom Home to Foreign, and 2 is the iceberg trade cost o exporting rom Foreign to Home, then = 2 =. In this case, symmetric trade liberalization is interpreted as a reduction o, which lowers B x +. Without loss o generality, we only ocus on the case when =. With a slight abuse o language, the real wage in the sector shall mean the real wage in terms o the aggregate good in the sector. As (35) and (7) show, in the sectors where both countries produce, the real wages in Home and Foreign in terms o good k, =P k and =Pk, just depend on the production cuto ' dk and ' dk respectively. Thus, d(' dk ) db > 0, d(=p k) db > 0 and d(' dk) db > 0, d(=p k ) db > 0. We calculate 5

17 d (' dk ) db = 2B + B 2 (ak ) [B (a k ) ] 2 (25) d (' dk ) db = 2B + B 2 (ak ) B (ak ) 2 (26) which shows that ' dk increases with B (and ' xk decreases with B according to (5) ) i and only i (a k ) < 2B. Moreover, ' +B 2 dk increases with B (and ' xk decreases with B according to (6)) i and only i (a k ) > +B2 2B. Recalling that (a k ) = B( +) and (a B 2 + k 2 ) = B2 + and comparing them with the B( +), above thresholds, we can obtain the ollowing conclusions. (i) When =, k and k 2 exactly coincide with these thresholds, meaning that in the two-way trade sectors, ' dk (as well as real wage in sector k) always decreases with B, and ' xk always increases with B. In other word, Melitz s predictions hold in this case. h (ii) As = increases above one, k decreases, and there exist some two-way trade sectors 2B k 2 k ; i, in which ' +B 2 dk increases with B and ' xk decreases with B. That is, symmetric trade liberalization leads to a decrease in the productivity cuto or survival but an increase in the exporting cuto. Moreover, the real wage in these sectors also all. These are all opposite to the predictions o the original Melitz model. Thus, we call this the counter-melitz e ect. (iii) As = increases above one, k 2 decreases, and so there does not exist any sector in which ' dk increases with B or ' xk decreases with B. Thus, the counter-melitz e ect does not exist in any sector in the smaller country. For a more detailed mathematical analysis o the impacts o symmetric trade liberalization, reer to equations (35) to (37) and to Appendix C. Figure 4 summarizes the e ects graphically. The diagram shows the welare e ects o symmetric trade liberalization. The k and k 2 curves show the pattern o international specialization or any given =. (Recall that = is assumed.) The zone to the let o the k curve corresponds to sectors completely dominated by Foreign. The zone to the right o the k 2 curve corresponds to the sectors completely dominated by Home. The downward sloping k curve indicates that as the relative size o Home becomes larger, it can pro tably produce in more sectors. This shows the home market e ect as explained by Krugman (980) the rms located in the larger country has the advantage o saving the trade costs o serving the larger market, which more than compensates or its cost disadvantage relative to the rms located in the smaller country in the same sector. On the other hand, the downward sloping k 2 curve shows that Foreign, the smaller country, can pro tably produce in ewer sectors as the relative size o Home increases. This reminds us o the result in Markusen and Venables (2000), in which they nd that the larger country can export a good in which it has comparative disadvantage because o home market e ect. As will be shown later, this explains why the counter-melitz e ect can only occur in the larger country under symmetric trade liberalization or trade cost reduction. The gure also shows, or any given value o =, the signs o the real-wage e ect o symmetric trade liberalization on Home and Foreign in di erent sectors. The upper sign inside a rectangle indicates the sign o Home s change in real wage in terms o good k due to an in nitesimal decrease in, and the lower sign indicates the sign o Foreign s change in real wage in terms o good k. For example, or = < B 2, when there is an in nitesimal reduction o B (via reduction in ), Home s real wage 6

18 (i) increases in terms o goods in the Foreign-dominated sectors (the zone to the let o the k curve), (ii) decreases in the two-way trade sectors to the right o the k curve but to the let o the vertical 2B line (a k ) = (this corresponds to the slanted-hatched zone), (iii) increases in the two-way trade +B 2 sectors to the right o the vertical line (a k ) = 2B but to the let o the k +B 2 2 curve (this corresponds to the vertically-hatched zone), and (iv) does not increase or decrease in the Home-dominated sectors (the zone to the right o the k 2 curve). Note that Figure 4 indicates that there is a counter-melitz e ect or Home (the larger country) in the slanted-hatched zone, in the sense that ' dk decreases and ' xk increases in response to symmetric trade liberalization. However, the Melitz e ect dominates in Home in the vertically-hatched zone, in the sense that ' dk increases and ' xk decreases in response to symmetric trade liberalization. These results re ect the algebraic derivation above and in Appendix B. Note that there is no counter-melitz e ect or the smaller country under symmetric trade liberalization. However, this result is going to change under asymmetric trade liberalization, as we shall show in the next section. 7

19 Figure 4. Welare E ects o Symmetric Trade iberalization (in nitesimal reduction o B through a reduction o ). In each region, the upper sign inside the rectangle indicates the welare change o Home and the lower sign indicates the welare change o Foreign. The short horizontal arrows indicate the movement o lines as B alls. 2B B 2 + As B decreases, the curves or k and k 2, as well as the vertical lines corresponding to (a k ) = and (a k ) = B2 + 2B, will all shit, with the directions o shits shown by the small horizontal arrows in Figure 4. For any given =, as (and thereore B) decreases rom a large number, k increases, k 2 rst decreases then increases, (a k ) = 2B B 2 + increases while (a k) = B2 + 2B decreases. Depending on the range o [a 0, a ] and the value o =, it is possible that the k or k 2 curve (or both) may situate outside the range k 2 [0; ] or some or all values o =. For example,i a k < a 0 or a given value o =, then no Foreign-dominated sector exist or that value o =. This is because 8

20 as = gets su ciently large, the home-market e ect in Home gets so strong that Home can compete even in the sector in which it has the weakest comparative advantage, namely sector k = 0. The above discussion and Figure 4 can be summarized by the ollowing lemma and proposition: emma 2 When the two country are o the same size, symmetric trade liberalization improves the real wages in all two-way trade sectors in both countries. Proposition 4 Suppose Home is larger than Foreign. In the sectors where Home has the strongest comparative disadvantage but still produces, there is a counter-melitz e ect in the sense that ' dk decreases while ' xk increases in the ace o symmetric trade liberalization, leading to reduction in real wage in these sectors. Proposition 4 deserves more discussion, as it highlights one o the most important results o this paper. I Home is the larger ncountry, the sectors in which its real wage deceases upon symmetric trade liberalization are de ned by k j (a k ) < (a k ) < (a k2 ) and (a k ) < o. 2B The rst condition indicates that the sector is a two-way trade sector. The second condition indicates that the sector +B 2 is among those in which the larger country has the weakest comparative advantage. The two conditions combined says that, in the sectors where the larger country has the weakest comparative advantage yet still produces, Home s real wage decreases with symmetric trade liberalization. In other words, there is a counter-melitz e ect in these sectors, i.e. ' dk decreases while ' xk increases in the ace o symmetric trade liberalization, leading to a decrease in the average productivity o rms serving the Home market, thus lowering real wage in that sector. We can explain the existence o the counter-melitz e ect by decomposing the total e ect o symmetric trade liberalization into two e ects: the Melitz e ect and the inter-sectoral resource allocation (IRA) e ect. We shall analyze rom the perspective o Home and Home s rms. Note that the number o potential entrants in sector k in Home is given by dk n k = G (' dk ) = dk (' dk ) B = D D 2 (k) B (a k ) B (a k ) (27) and recall 2 dk = D 2 (k) 4 B B (a k ) B(a k ) B B 3 5 (2) (' dk ) B B = D B (a k ) (7) d (' dk ) db = 2B + B 2 (ak ) [B (a k ) ] 2 (25) 9

21 P k = B B B (a k ) P ck (35) When =, and a k =, 8k, our model collapses to the Melitz model with a homogenous-good sector. (27) ) n k = D D 2 (k). With symmetric trade liberalization, the numbers o potential entrants n k and n k will remain unchanged. Note that (7) ) (' dk) B+ = D. Thereore, d(' dk ) db < 0. That is, real wages in all sectors rise with symmetric trade liberalization. As a result, the export revenue o a typical exporting rm will increase as trade cost alls. B This creates pressure or both ' xk and ' xk to decrease. Meanwhile, this will orce the least productive rms in each country to exit, as there are more rms exporting to the domestic market. This creates pressure or both ' dk and ' dk to increase. The increase in average productivity in all sectors lead to increase in real wage in all sectors. This is the Melitz e ect. Next, we allow a k to deviate rom or some k, but keep =. This creates comparative advantage or Home in some sectors and comparative disadvantage or Home in other sectors. Note that (25) holds only i sector k satis es the constraint or two-way trade, given by (a k ) < (a k ) < (a k2 ). Observe that (i) (23) ) (a k ) < (a k ) is equivalent to 2B + B 2 (a k ) < 0; thereore, (25) ) d(' dk ) db < 0 or all two-way trade sectors. In other words, symmetric trade liberalization always increases the real wage in a two-way trade sector. That is, the Melitz e ect dominates in all two-way trade sectors as long as =. (ii) (25) ) d(' dk ) db increases with a k. That is, the dominance o the Melitz e ect in a sector decreases as the comparative advantage o Home diminishes. (iii) (23) ) at k = k, 2B + B 2 (a k ) = 0, implying that d(' dk ) db = 0. That is, the Melitz e ect is completely o set in sector k, the sector in which Home has the least comparative advantage yet still produces. What happens to make d(' dk ) db increase with a k? The e ect comes rom re-allocation o resources (labor) between sectors as B decreases, which we call inter-sectoral resource allocation (IRA) e ect. Symmetric trade liberalization leads to resources in Home (as well in Foreign) being re-allocated away rom the di erentiated-good sectors in which it has comparative disadvantage to ones in which it has comparative advantage (and possibly the homogeneous good sector). Thereore, n k decreases and n k increases in the sectors in which Home has comparative disadvantage. As n k increases, Foreign s market becomes more competitive (as there are more rms in Foreign) and so r xk (') decreases or all '. This creates pressure or an increase in ' xk (i.e. only the more productive Home rms can pro tably export now). As n k decreases, dk also decreases. This leads to the expansion o the sizes o the surviving Home rms. Thus, r dk (') increases or all '. This creates pressure or a decrease in ' dk as some less productive rms which were expected to be unpro table beore can be expected to be pro table now. The variables n k, n k, r xk ('), ' xk, dk, r dk ('), ' dk all move in opposite directions in the sectors in which Home has comparative advantage. In other words, the IRA e ect reinorces the Melitz e ect in the sectors in which Home has comparative advantage but counteracts the Melitz e ect in the sectors in which it has comparative disadvantage. Observations (ii) and (iii) above indicate that the IRA e ect is stronger when Home has weaker comparative advantage in the sector. However, as long as =, the IRA e ect never dominates the Melitz e ect, as each country cannot pro tably produce goods in which it does not have su ciently 20

22 strong comparative advantage. Without any home market e ect, the range o goods produced by Home is limited by its comparative advantage. Thereore, there is still no counter-melitz e ect in any sector. Next, we allow = to increase above one, in addition to a k 6= or some k. Now, because o increasing returns to scale and the home market e ect as explained in Krugman (980), it is possible or the IRA e ect to dominate the Melitz e ect in Home, as Home is now able to pro tably produce goods that it was not able to when =. In other words, because o its large size, Home is now able to pro tably produce goods in which it has comparative disadvantage. In these sectors, d(' dk ) db < 0 the IRA e ect dominates the Melitz e ect, and we have the counter-melitz e ect. However, Foreign, the smaller country, can never have counter-melitz e ect in any sector, because it is not able to pro tably produce any good that it was not able to when =. As the IRA e ects in the comparative advantage sectors are positive, there are gains in real wage in terms o these sectors goods upon symmetric trade liberalization. Can these gains o set the losses in the comparative disadvantage sectors mentioned above? The answer is, it depends on Home s relative size. I Home s relative size is large, and the Foreign-dominated sector is small, then the gains cannot o set the losses. For example, when B = 2, = = 5, = 2 (and thereore a k = 0:756 and a k2 = 0:866); and suppose a 0 = 0:8 (and thereore k < 0, which means that there does not exist any sector in which Foreign completely dominates). Then, Home will unambiguously lose rom symmetric trade liberalization, as it loses in the sectors where k 2 [0; k 2 ], and does not gain or lose in the sectors where k 2 [k 2 ; ] and in the homogeneous good sector. Based on the above analysis, we end this section with the ollowing two propositions: Proposition 5 Consider the sectors in which both countries produce. For a given country, in the ace o symmetric trade liberalization, the raction o exporters increases in the comparative advantage sectors but decreases in the sectors in which the country has the strongest comparative disadvantage, i the country is large compared with the rest o the world. Proposition 6 Consider the sectors in which both countries produce. For a given country, in the ace o symmetric trade liberalization, the raction o revenue derived rom exporting increases in the comparative advantage sectors but decreases in the sectors in which the country has the strongest comparative disadvantage, i the country is large compared with the rest o the world. 5.2 Asymmetric Trade iberalization We have shown that counter-melitz e ect occurs only in the larger country under symmetic trade liberalization. However, we shall show below that it occurs even in the smaller country under asymmetric 2

23 trade liberalization, i the importing cost o the smaller country alls su ciently more than that o the larger country. In the extreme case, unilateral trade liberalization o Home lowers its real wage in all sectors regardless o its relative size. This result is important as we shall use it to test the counter-melitz e ect in China, which underwent asymmetric trade liberalization upon its accession to the WTO. et denote the trade cost o exporting rom Home to Foreign, and 2 denote the trade cost o exporting rom Foreign to Home. In general 6= 2 and thereore B 6= B 2. The detailed derivation is relegated to the Appendix. The ollowing equations are particularly worth noting. (a k ) = B + B B 2 + (23 ) (a k2 ) = B B 2 + (24 ) + B 2 d (' dk ) B2 2 = D db 2 B (a k ) (28a) d (' dk ) db = D B 2 (a k ) [B (a k ) ] 2 (28b) Assumptions: (a) db = db 2 where > 0; and (b) jdb =B j < jdb 2 =B 2 j (which is equivalent to jd = j < jd 2 = 2 j, i.e. the percentage reduction in iceberg importing cost is lower in Foreign than in Home). Note that (a) and (b) imply that B > B 2. Note that a counter-melitz e ect exists in a sector i d(' dk ) db 2 + d(' dk ) db > 0. When =, (28a) and (28b) imply that there is counter-melitz e ect when k = k (the two-way trade sector in which Home has the weakest compararive advantage) i d (' dk ) db 2 + d (' dk) db > 0 at k = k i B + B 2 + B 2 2 (ak ) > 0 () (B B 2 ) (B B 2 ) > 0, which is true according to our assumption. Moreover, d (' dk ) db 2 + d (' dk) db = 0 i B + B 2 + B 2 2 (ak ) = 0 i (a k ) = B + B 2 + B

24 which implies that there is counter-melitz e ect or the sectors satisying Thereore we have 2B B B 2 + = (a k ) < (a k ) < B + B 2 + B2 2. Conclusion : There is counter-melitz e ect in Home even i =, as long as jd = j < jd 2 = 2 j. The intuition or Conclusion is as ollows. We assume = and allow a k to deviate rom or some k. This creates comparative advantage or Home in some sectors and comparative disadvantage or Home in other sectors. Note that (28a) and (28b) hold only i sector k satis es the constraint or two-way trade, given by (a k ) < (a k ) < (a k2 ). Observe that (i) (23 ) ) (a k ) < (a k ) is equivalent to 2B ( + B B 2 ) (a k ) < 0; thereore, (28a) and (28b) ) d(' dk ) db 2 + d(' dk ) db > 0 at k = k i (B B 2 ) (B B 2 ) > 0. In other words, asymmetric trade liberalization (with jd = j < jd 2 = 2 j) lowers the real wage or the two-way trade sectors in which Home has the weakest comparative advantage, 2B i.e. sectors k satisying B B 2 + = (a k ) < (a k ) < B +B 2. That is, the counter-melitz e ect exists +B2 2 even when =, contrary to the case with symmetric trade liberalization. (ii) (28a) and (28b) ) d(' dk ) db 2 + d(' dk ) db decreases with a k. That is, the counter-melitz e ect decreases as the comparative advantage o Home increases. (iii) (23 ) ) at k = k, B + B 2 + B2 2 (ak ) > 0, implying that d(' dk ) db 2 + d(' dk ) db > 0. That is, a counter-melitz e ect exists in sector k, the sector in which Home has the least comparative advantage yet still produces. Moreover, we can use the similar principle 4 to compute that the counter-melitz e ect can occur in the most comparative disadvantage two-way trade sectors in Home as long as > B 2 B. The right hand side is less than one. Thereore, we have Conclusion 2: It is possible or counter-melitz e ect to occur in Home under asymmetric trade liberalization even i Home is smaller than Foreign. We summarize the above conclusions in the ollowing three propositions. Proposition 7 Consider the sectors in which both countries produce. I the percentage decrease in Home s iceberg import cost is more than that o Foreign s, then ' dk decreases while ' xk increases in the sectors in which Home has the strongest comparative disadvantage, leading to reduction in Home s real wage in these sectors, as long as Home is not too small compared with Foreign. Proposition 8 Consider the sectors in which both countries produce. I the percentage decrease in Home s iceberg import cost is more than that o Foreign s, then the raction o exporters increases in 4 Simply solve or rom (a k ) = B +B 2. +B2 2 23

25 Home s comparative advantage sectors but decreases in the sectors in which Home has the strongest comparative disadvantage, as long as Home is not too small compared with Foreign. Proposition 9 Consider the sectors in which both countries produce. I the percentage decrease in Home s iceberg import cost is more than that o Foreign s, then the raction o revenue derived rom exporting increases in Home s comparative advantage sectors but decreases in the sectors in which Home has the strongest comparative disadvantage, as long as Home is not too small compared with Foreign. 6 Can rms that sell domestically be more productive than rms that don t? Recently, there has been some discussion o the existence o another counter-melitz e ect. u (200) shows that, theoretically, in a multi-sector Melitz model, the average productivity o exporters can be lower than that o the rms that serve the domestic market in the comparative advantage sectors. She then supports her theory by the empirical nding that, in the comparative advantage sectors, the exporters in China have a relative lower average productivity compared with the rms that serve the domestic market. This e ect, though also runs counter to Melitz s one-sector result, is completely di erent rom the one explained in the last section. Nonetheless, it is still worth asking whether our model can be made consistent with this e ect. The answer is yes. So ar, we simpli ed our analysis by assuming that x > max ; g so as to exclude the possibility that some rms only export but do not serve the domestic market. Our model can in act be modi ed to accommodate this possibility by relaxing this assumption. First o all, we adopt the assumption that a rm needs to incur a market entry cost i it enters a market, be it domestic or oreign. Now, let and x stand or the xed market-entry cost plus the overhead cost or serving the domestic market and oreign market respectively. 5 In this case, we can relax the assumption x > max ; g (only x > is needed), and all o our propositions still hold. In the appendix, we show that when x is su ciently smaller than, then we can have a situation where the cuto productivity or exporting is lower than the cuto productivity or selling domestically in the comparative advantage sectors. Thus, the average productivity o the rms that export is lower than the average productivity o rms that both export and sell domestically in the comparative advantage sector. The main point is that it is possible that or some sector k, we have ' dk > ' xk. Once we have this outcome, we can have the situation where some rms in the sectors where a country has the strongest comparative advantage may only export; thus in these sectors the rms that only export are less productive than those that also serve the domestic market. This is also consistent with Dan u s nding that in labor-intensive sectors, rms that serve domestic market have higher productivity than exporters, as China has comparative advantage in the labor-intensive industries. 5 This is di erent rom the original assumption in Melitz (2003) as well in this paper so ar. 24

26 Detailed calculation is given in the appendix. We state our result in Proposition 0 I the xed entry cost or exporting is not too high, then in the sectors where a country has the strongest comparative advantage, the rms that do not serve the domestic market can have a lower average productivity than those that do. One major characteristic o the Chinese exporting sector is that a large raction o exporting rms engage in processing trade, and they mostly concentrate in the labor-intensive sectors, which are the comparative advantage sectors o China. Export processing in China is subject to very di erent policy treatment compared to non-processing trade. First, processing activities enjoy avorable taxation. The amount o imported inputs actually used in the making o the nished products or export is exempt rom tari s and import-related taxes. All processed nished products or export are also exempt rom export tari s and value-added tax. Second, the nished products using the tax-exempted materials have to be re-exported, and enterprises are not allowed to sell the tax-exempted materials and parts or nished products in China. The assumption that the xed cost or exporting rms is relatively low compared with the xed cost or rms selling in the domestic market ts the observation that the cost o entry into processing trade in China is relatively low because o government policy. According to Dai, Maitra and Yu (20), In China roughly a th o exporters, accounting or about one-third o total export value, are engaged in processing trade only. These rms are 4% to 30% less productive than non-exporters. They go on to say, Our data shows that processing trade rms pay lower average wages implying that they are more unskilled labor intensive, are relatively less capital intensive, and have low pro tability compared to non-processing ones. Given that processing rms pay lower xed cost (due to government intervention) it makes sense that only the low productivity rms would select into processing trade. These ndings are all consistent with this modi ed version o our model. Thus, our theoretical model can indeed be extended to include both types o non-standard e ects. Next, we move on to some emprical evidence. The empirical evidence or u s (200) e ect has already been o ered by her. In the next section, we present the empirical tests o our two major propositions. 7 Empirical Tests o Propositions 8 and 9 Propositions 8 and 9 in section 5 predict the existence o a counter-melitz e ect: For a su ciently large country, like China, in the sectors where it has the strongest comparative disadvantage but still produces, the raction o rms that export and the share o revenue derived rom exporting will both decrease upon asymmetric trade liberalization such that the percentage reduction o China s trade cost is lower than that o its trading partners. Can we nd any evidence to support the existence o the counter-melitz e ect? This section shows that we indeed nd evidence o such an e ect. China acceded to the WTO in December 200. Since then there was a series o tari reductions or a number o years. It is well-documented that the conditions o WTO accession require China to reduce 25

27 its import barriers with very little corresponding changes in its trade partners import barriers against China. Thereore, this kind o asymmetric trade liberalization (that the percentage reduction in China s iceberg import cost is higher than those o its trading partners) ts the description in Propositions 8 and 9 very well. We should thereore expect the comparative disadvantage sectors o China to exhibit counter-melitz e ect while the comparative advantage sectors to exhibit Melitz e ect. We test the theory at the 4-digit CIC level, using Chinese industrial rm data rom National Bureau o Statistics o China (NBSC), Chinese Customs data rom China s General Administration o Customs and tari data rom the World Trade Organization (WTO). To get a panel o variables, we need to rst tackle the problem caused by a major revision to the Chinese Industry Classi cation (CIC) in the year In order to have a consistent de nition o sectors, we ollow Brandt, Van Biesebroeck & Zhang (202) by adjusting the 4-digit CIC so as to make the same industry classi cation code representing the same industry both beore and ater year Ater adjusting the CIC code or each sector, we aggregate the variables at the 4-digit sector level and obtain a panel o aggregate variables (e.g. mass o rms, mass o rms that export, total revenue, total exporting revenue, etc.) rom the years 200 to 2006, and then calculate the variables we need. 7 In order to test the e ect o trade liberalization, we also need to establish a proper measure o trade cost. As transportation cost is hard to measure and should not vary much in a ew years time, we take the tari rate, which decreased a lot ater China joined the WTO, as the measure o trade cost. It is also noteworthy that the tari rates or di erent sectors are di erent, which is not consistent with the assumption o our model. Fortunately, it turns out that the results and equations o the model will not be qualitatively a ected by the heterogeneity o trade costs across sectors. Thereore, we take into consideration the heterogeneity o tari rates across sectors in calculating which sectors are predicted to exhibit the counter-melitz e ect according to the theory. More explanation is provided below. Following Amiti and Konings (2007), Goldberg, Khandelwal, Pavcnik and Topalova (200) and Ge, ai and Zhu (20), we construct the industry tari rate through aggregating tari s to the 4-digit CIC level. ike the CIC, there was a major reclassi cation in the international HS 6-digit codes in Hence we also construct a mapping o the 6-digit HS coding system rom the pre-2002 to the post-2002 periods. With these matchings in place, we assign each 8-digit HS product to the 6-digit HS code to which it belongs, and then connect this 6-digits HS code with the standardized 4-digit CIC code, or each year. 8 Finally, we calculate the industry tari as the volume-weighted average o all 8-digit HS products which all into the same 4-digit CIC code or each year. To be precise, the industry tari is PGi calculated rom it = g= v PGi gt gt = g= v gt, where gt is the 8-digit HS level tari o an imported good g at year t, v gt is the import value o good g in that year, and G i is the number o 8-digit HS sectors included in CIC sector i. ater, we use these tari data to test our theory. These industry 6 The detail o the matching can be ound at 7 The choice o the years is based on the act that China acceded to World Trade Organization in December 200, which urther integrate the country with the world. Under the WTO commitments, China cut average tari rom 5.4% in 200 to 5.3% in The NBSC provide a concordance table between the 6-digit HS code and the 4-digit Chinese industry code. Source o this table can be ound at: 26

28 tari s are the tari s aced by oreign rms entering the Chinese market. As a robustness check, we use the import value in 2003 (which is the middle year o our sample), v g2003, as the weight or tari calculation or all years and rerun all the tests. The purpose o doing so is to control or the variation o trade value within industry across years during the trade liberalization period so that we can get a clearer picture o the pure e ect o tari reduction. In addition to allowing tari rate to be di erent across sectors, we also allow the elasticity o substitution, and the productivity dispersion level to be di erent across sectors. We urther assume that k is di erent across sectors such that k is i.i.d. with mean. It can be shown that the results listed in Table are qualitatively the same as beore. The only change needed in Table A in the Appendix is to change B to B k (k k ) k x k and B2 to B k ( k ) k x k. It ollows k that Propositions 8 and 9 continue to hold. However, di erent sectors have di erent threshold or a k now: (a k ) < Bk + k B k + k(b k ) 2. In other words, the theory predicts that the counter-melitz e ect will occur in the two-way trade sectors in which the relative productivity index (a k ) is less than (a k ) < Bk + k B k + k(b k ) 2. Furthermore, rom the version o Table A modi ed or di erences in and across sectors, we nd that the raction o rms that export in each sector satis es: xk dk = 'dk ' xk k = B k Bk (a k ) k () xk dk B k 2 = B k B k (a k ) k x B k (a k ) k B k (a k ) k x Thereore,, B k B k (a k ) k B k (a k ) k xk B k 2 < dk, B k B k (a k ) k B k (a k ) k k x < x k x < k, B k + k B k + k B k 2 (a k ) k > 0, d (' dk) db k + k d (' dk ) db k > 0, which is the condition or there to be counter-melitz e ect. Thereore, xk dk B k 2 < k x i there is counter-melitz e ect in sector k. Since we assume that k is i.i.d. with mean, there is more likely to be counter-melitz e ect in a sector k when xk dk B k 2 is smaller. We calculate the variable xk dk B k 2, which we call RATIO, or each o the twenty-nine 2-digit CIC sectors, and rank them. Note that a lower RATIO is assigned a lower rank. A higher RATIO implies that China has stronger comparative advantage in that sector. 9 Table 2 shows the ranking o these 2-digit CIC sectors and the corresponding 9 Based on a nested constant-elasticity-substitution utility unction, Broda and Weinstein (2006) estimate productspeci c elasticities o substitution at the HS 0-digit level. The data is available rom Weinstein s website. We aggregate these numbers up to the HS6 level by taking means, and then use the concordance table rom NBSC to calculate the 27

29 sectoral inormation that determine the RATIO. We choose the eight sectors with the lowest RATIOs to test or the counter-melitz e ect and the eight sectors with the highest RATIOs to test or the Melitz e ect. We run (i) the raction o exporting rms and (ii) the share o exporting revenue, on the tari rate or each sector, while controlling or the year and industry (2-digit CIC level) xed e ects and other relevant variables (including employment, capital-labor ratio, average wage in each 4-digit sector). Amongst these variables, employment stands or the size o the sector, and is used to control or the economies o scales; K/ = capital-labor ratio is used to control or production technique; average wage is used to control or the variable costs and worker skill. The right hand side variables we choose are similar to those o Bernard, Jensen and Schott (2006, Table 4). The results are shown in Tables 3A and 3B. (CA stands or comparative advantage.) <Table 2 about here> From Tables 3A and 3B, we see that all the coe cients or the variable Tari are signi cant in both regressions. Most importantly, the signs are distinctly positive or the eight comparativedisadvantage sectors and distinctly negative or the eight comparative-advantage sectors. In other words, both the raction o exporting rms and the share o exporting revenue decrease (increase) with trade liberalization or the sectors in which China has comparative disadvantage (comparative advantage). Thereore, we conclude that, consistent with our theory, there exists counter-melitz e ect in the sectors where China has the comparative disadvantage but still produces; while the Melitz e ect continues to hold in the sectors in which China has comparative advantage. The coe cients o the other right hand side variables make sense too. For example, higher K/ signi es stronger comparative disadvantage, which lowers exporting ratio and share o export revenue according to our theory. Higher wage signi es higher labor quality, which tends to induce higher propensity to export. Higher employment signi es higher economic scale, which also tends to induce higher propensity to export. elasticity o substitution o each sector as the average o all the 6-digit HS products which all into the standardized 2-digit CIC code. For the Pareto location parameter k, we estimate them using the estimates o k and the theoretical prediction that rm sales ollow a Pareto distribution with shape parameter k k within industry k. We ollow Eaton, Kortum and Kramarz (20) in restricting attention to exporters only and back out the shape parameter o the rm sales distribution rom a regression o the logarithm o the rm sales rank on the logarithm o rm sales. As Axtell (200), we nd that k is close to or each sector. Hence, we have B k k k k and we use k k to approximate B k, where k is the average tari rate in each 2-digit CIC industry and k captures the productivity dispersion level in each 2-digit CIC industry. 28

30 Fraction o exporting rms, year Regressor eight sectors with weakest CA eight sectors with strongest CA Tari (0.25) (0.58) (0.5) (0.065) (0.05) (0.050) log(employment) (0.005) (0.004) log(k/) (0.05) (0.05) log(wage) (0.033) (0.029) Industry xed e ect NA Yes Yes NA Yes Yes Year xed e ect NA Yes Yes NA Yes Yes Observations Note: Signi cant at the % level; Signi cant at the 5% level; Signi cant at the 0% level. Table 3A Share o exporting revenue in total revenue, year Regressor eight sectors with weakest CA eight sectors with strongest CA Tari (0.33) (0.50) (0.39) (0.068) (0.052) (0.049) log(employment) (0.005) (0.004) log(k/) (0.04) (0.05) log(wage) (0.03) (0.028) Industry xed e ect NA Yes Yes NA Yes Yes Year xed e ect NA Yes Yes NA Yes Yes Observations Note: Signi cant at the % level; Signi cant at the 5% level; Signi cant at the 0% level. Table 3B The choice o the eight sectors with the lowest RATIOs to stand or comparative disadvantage sectors and the eight sectors with the highest RATIOs to stand or comparative advantage sectors may sound a bit arbitrary. Thereore, we check the robustness o the results by varying the set o sectors we choose. We run six regressions or each set o sectors we choose: we run (i) the raction o exporting rms and (ii) the share o exporting revenue, on the tari rate or each set o sectors, while controlling or the year and industry (2-digit CIC level) xed e ects and other relevant variables (including employment, capitallabor ratio, average wage in each 4-digit sector). Each regression is the same as the corresponding one shown in Tables 3A and 3B, though the set o sectors used is di erent. The result is shown in Figure 5. 29

31 Figure 5. The horizontal axis in Figure 5 indicates what sectors are included when running the regressions. Note that there is a set o bars on the let and another set o bars on the right. On the let, a number x on the horizontal axis indicates that sectors rom the sector with ranking number to the sector with ranking number x are included in the regressions. Thereore, as x increases, the number o comparative disadvantage sectors included in the regressions increase. On the right, a number x indicates that sectors rom the sector with ranking number x to the sector with ranking number 29 are included in the regression. Thereore, as x decreases, the number o comparative advantage sectors included in the regressions increase. The vertical axis indicates the number o regressions or which the coe cient or the variable Tari is statistically signi cant when the corresponding set o sectors indicated on the horizontal axis is included in the regressions. In the gure, the darkest bars represent the number o coe cients with the right sign (positive or the let group o sectors and negative or the right group o sectors) and signi cant at % level. The second darkest bars represent the number o coe cients with the right sign and signi cant at 5% level (but not signi cant at % level). The lightest bars represent the number o coe cients with the right sign, but not signi cant at 5% level. 20 From the gure, it is clear that the counter-melitz e ect becomes signi cant when we include su ciently large number o 20 For example, a number 9 on the horizontal axis indicates that sectors with rankings through 9 are included in the regressions. Corresponding to that, all six regressions similar to the ones shown in Table 3A and 3B yield positive and signi cant coe cients (at % level) or variable Tari. A number 2 on the horizontal axis indicates that sectors with rankings 2 through 29 are included in the regressions. Corresponding to that, ve o the regressions similar to the ones shown in Table 3A and 3B yield negative and signi cant coe cients (at % level) or Tari, while one regression yields negative and signi cant coe cient at 5% level or Tari. 30

32 sectors with the smallest RATIOs (the gure shows that 4 is a su ciently large number o sectors), and the e ect remains signi cant till we include the 9 sectors with the smallest RATIOs. ikewise, the Melitz e ect becomes signi cant when we include su ciently large number o sectors with the largest RATIOs (the gure shows that 4 is also a su ciently large number o sectors), and the e ect remains signi cant till we include the sectors with the highest RATIOs. The coe cients or the sectors at both ends o the ranking are mostly not very signi cant, probably due to the limited sample size (too ew observations). 2 The coe cients are mostly not very signi cant when the sectors in the middle o the ranking are included. This is consistent with our theory, as they are sectors at the margin, and neither the Melitz e ect nor the counter-melitz e ect dominate. Thus, the total e ect is ambiguous. Table 4 shows the results o the OS regressions when the data o all sectors are pooled together. Year Fraction o exporting rms Share o exporting revenue in total revenue Regressor All sectors All sectors Tari (0.040) (0.04) (0.038) (0.044) (0.044) (0.042) log(employment) (0.002) (0.002) log(k/) (0.007) (0.008) log(wage) (0.03) (0.04) Industry xed e ect NA Yes Yes NA Yes Yes Year xed e ect NA Yes Yes NA Yes Yes Observations Note: Signi cant at the % level; Signi cant at the 5% level; Signi cant at the 0% level. Table 4 In Table 4, most o the coe cients are not statistically signi cant and even the signs o the coe cients are ambiguous. This is consistent with our theory, as some sectors exhibit counter-melitz e ect while others exhibit Melitz e ect, and thereore the total e ect maybe ambiguous and statistically insigni cant. This result contrast with that obtained by Bernard, Jensen & Schott (2006). They use plant level data o the U.S. and run a similar regression o the probability o exporting on change in trade cost. They get negative sign (Melitz e ect) at 0% level o signi cance or that regression. The main reason or the di erence might be that, unlike China, the U.S. does not have many sectors in which it has strong comparative disadvantage but in which it still produces. As a result, ewer plants in the U.S. would show counter-melitz e ect. Thereore, the overall outcome is dominated by the Melitz e ect. Moreover, the coe cient is also not very signi cant statistically as the Melitz e ect is countered by the IRA e ect in some sectors. Robustness o the Result 2 Some 2-digit industries contain ewer than ten 4-digit sectors. Thus the degree o reedom o the regression may be limited i we choose too ew 2-digit industries or testing our propositions. 3

33 For robustness check, we construct the tari or each industry using the import volume in 2003 (which is the middle year o our sample), v g2003, as the weight or tari calculation or all years and report the regression results in Figure 6. As in Figure 5, Figure 6 shows that the counter-melitz e ect becomes signi cant when we include su ciently large number o sectors with the smallest RATIOs, and the e ect remains signi cant until we include the 7 sectors with the smallest RATIOs. ikewise, the Melitz e ect becomes signi cant when we include su ciently large number o sectors with the largest RATIOs, and the e ect remains signi cant until we include the 6 sectors with the highest RATIOs. Thus, these results are also consistent with the predictions o our theory. Furthermore, we report the results o the OS regressions when the data o all sectors are pooled together in Table 5. ike in Table 4, the coe cients in Table 5 are not statistically signi cant either, as the counter-melitz e ect and the Melitz e ect cancel each other when all sectors are pooled together. Figure 6. 32