Multiproduct firms, factor endowment and trade liberalization

Transcription

1 Multiproduct firms, factor endowment and trade liberalization Tuan Anh Luong,1 Shanghai University of Finance and Economics 777 Guoding Road Shanghai , China. Abstract This paper develops a model of multiproduct firms in the presence of different types of labor. I show that an increase in the supply of skilled labor has non-uniform impact on the firm scope: a rise in the number of skilled labor allows the productive firms to add more varieties into their product profile but has the unproductive firms reduce their scope. The market becomes more competitive which generates welfare gains. Under economic integration, countries gain in general but the problem of income distribution arises. When labor are immobile, the model can predict the trade patterns based on the country endowment. The predictions are consistent with Chinese export in JEL classification: F1; F2 Keywords: Multiproduct firms, Skilled labor, Firm heterogeneity, Competition effects I would like to thank Marc Melitz, Esteban Rossi-Hansberg, Stephen Reddings, Oleg Itskhoki, Zhihao Yu, Frederic Robert-Nicoud, Larry Qiu and participants at the seminars of Shanghai University of Finance and Economics, Beijing University of International Business and Economics, the MidWest International Trade Meeting, the North America Econometric Society Meeting, the World Congress for International Economics for helpful comments and suggestions. I am especially grateful for the guidance of my advisors, Gene Grossman and Pinelopi Goldberg. All the remaining errors are my own. 1 Address: Shanghai University of Finance and Economics, 777 Guoding Road Shanghai , China. luong.tuananh@mail.shufe.edu.cn. Tel: Preprint submitted to Elsevier January 16, 2015

2 1. Introduction The emergence of multiproduct firms has been well documented both in advanced and in developing countries. Bernard, Redding and Schott (2010) found that 39 percent of American firms produce more than one product; these firms accounted for 87 percent of output in In Brazil, according to Arkolakis and Muendler (2009), 25 percent of exporters ship more than 10 products at the HS-6 digit level; they accounted for 75 percent of total exports in Not only that multiproduct firms are important in the data, ignoring them can bring some serious biases. For instance, productivity measurement can be biased (De Loecker 2010) which can be corrected if we know how the firm chooses its scope (Bernard, Redding and Schott 2009). A typical paper in this literature analyzes the impact of competition 2 which results in a uniform reaction on the firm s scope. Using a nested CES preference utility function Allanson and Montagna (2005) show that in the long run, a firm s scope is independent of the market size. In Mayer, Melitz and Ottaviano (2014), the firms responded to more intense competition by focusing on a few core products and dropping the peripheral ones. Although this uniform reaction seems to be the consensus in the literature, there are still empirical evidence that point out the non-uniform scope adjustment among firms. For instance, experienced Mexican exporters are reported to introduce new varieties while others have to drop the fringe products when foreign markets become more accessible (Iacovone and Javorcik 2008). Berthou and Fontagne (2013) documented similar phenomenon in France in the aftermath of the eurozone. On the aggregate level, if all firms reacted the same way to the degree of competition, we would expect a change in the average extensive margin. However, that measure seemed to be unchanged in India when trade reforms took place in the late 1990s (Goldberg et al. 2010). Why do firms adjust their scope differently? I propose here a simple extension of the Melitz (2003) framework, yet it is able to give an answer to 2 The competition effects refer to the intensity of the competition in the market. Most papers analyze the competition in the product market, i.e. the market for the final goods. In this paper, competition in the labor market, or the factor market, is also included as we will see later. 2

3 this question. The firm can adjust their scope by trading off the extra profit that new varieties generate with the costs of skilled labor they have to hire. With an increase in the supply of skilled labor, productive firms add new varieties to their product profile. These new varieties cannibalize the other varieties in the market, drive down their profit and induce the less productive firms to reduce their scope. Moreover, the competition for skilled labor does not help the less productive firms in enlarging their product portfolio. Similarly, when globalization takes place, new market opportunities allow the productive firms to introduce new varieties. Again, competition in the factor market makes the less productive firms to reduce their scope. They are on the losing end because their low productivity level, which results in high price and low profit, leaves them vulnerable when the competition intensifies. In this regards, my paper is very closely related to Qiu and Zhou (2013). We both argue that there are some costs related to introducing new varieties. There are, however, some key differences. Because I introduce the microfoundation for this variety-introduction fee, I am able to add another layer for the competition effect: that firms also compete for skilled labor when expanding their scope. Moreover, the reasons that competition is intensified are different. In Qiu and Zhou (2013) new firms enter to the market in response to trade liberalization which makes the market more competitive. Alternatively, the introduction of new varieties in my paper is the reason firms find the market more competitive. Also I argue that a competitive market in general generates welfare gains. The extent of welfare gains, however, depends on the degree of firm heterogeneity and the managerial technology of the country. When firms are heterogeneous, new varieties have a large cost-advantage over the other varieties, resulting in a significant fall in the price index. In addition, when firms can manage their brands effi ciently (for instance through more skilled managers), there will be more new varieties introduced, making consumers better off via their love of variety. A country with advanced managerial skills or high firm heterogeneity can benefit from education or immigration policies that improve the quantity or quality of the national talent endowment. I show here that when two countries engage in free trade, they will form an integrated economy if one types of labor is mobile. Factor price equalization holds in this case as if both types of labor were mobile. Unlike the Heckscher-Ohlin model, I do not need any condition on the factor 3

4 endowment, in particular that they are similar enough, to generate this result. This by-product is made possible due to the monopolistic competition: countries are able to trade as long as their factor endowments are not identical. The firms in both countries have the same number of product lines and produce as intensively. Welfare in general in both countries are enhanced although the issue of income distribution might arise, especially in the country with a smaller supply of talent. Indeed, while unskilled workers are always better off, skilled workers where they are the scarce factors are worse-off if the two countries (in terms of endowment) are different enough and if firm heterogeneity is small. This result is in fact in line with Krugman (1994): the scarce factor lose under globalization if the two countries are dissimilar in their factor endowment and if products are less differentiated. My model has predictions about trade pattern when labor are no longer mobile across countries. I show that the firms in the country with a larger supply of talent have higher scope but produce less intensively. As a result, this country exports the extensive margin and imports the intensive margin: it exports a large number of varieties but in less units than its trading partner. My model also generates an interesting result regarding the welfare: trade liberalization can hurt the whole country. Indeed, although the price indices are reduced, nominal income can be reduced at a faster rate, especially in the country endowed by a smaller pool of talent. This is because pre-integration, the competition in the factor market was low. Labor were then paid handsomely. Post-integration, the firms in this country had to lower their price to survive in a more competitive environment. This resulted in the firms paying less to their employees. Finally, this paper proposes a framework to think about competition policy. Indeed, if countries can not agree on a trade agreement, the competition effect through trade liberalization will not take place. The government, however, can improve the pool of talent which makes the market more competitive. This policy would help the government to select the productive firms 3. These surviving firms are then competitive enough to face openness, which will ease the pressure from the opponents of trade reforms. 3 One might be concerned as why the government does not select the productive firms at the first place. In practice, since the costs, or productivity is not observable, and the firms have an incentive not to truthfully reveal their productivity, it is not obvious for the government to select the effi cient firms. 4

5 The paper is organized as follows: in the next section, I will discuss the case of a closed economy. The case of an open economy will be considered in Section III. Section IV provides the empirical support while Section V concludes. 2. Closed economy I assume the economy is endowed with L unskilled workers and S skilled workers. They have different skills that are used in different positions, as will be clarified later. The factor markets are competitive. I will normalize the wage of unskilled workers to be unity. All these different types of labor are, however, consumers with the same preferences. There are an infinite number of potential firms in a single industry. The firms compete in a monopolistic market. Each of them, if they decide to produce, can choose how many products and how much of each product they want to produce and sell Consumer s preferences and demand The preferences of a representative consumer are given by a C.E.S utility function over a continuum of of goods indexed by ω: U = ω Ω qωdω ρ 1 ρ 0 < ρ < 1. The set Ω represent all the available varieties in the market. These varieties are imperfectly substitutable with the elasticity of substitution σ = 1/ (1 ρ). As shown by Dixit and Stiglitz (1977), this utility function yields the demand for each variety: q ω = ( pω ) 1 1 ρ P R P (1) 5

6 where P is considered as the price index in the industry: ( P = p ρ 1 ρ ω ) 1 ρ ρ dω. (2) 2.2. Supply of multiproduct firms There is a continuum of firms. To enter the industry each firm has to pay a fixed entry cost f e in units of unskilled labor. There is a number of firms, M 1 which is determined endogenously, pay that entry cost. Those firms then draw their productivity from the Pareto distribution: f (ϕ) = kϕ k 0ϕ (k+1). The parameter k indicates the heterogeneity among firms: the lower k is, the more heterogeneous the firms are in their productivity level. After discovering its productivity level, a firm decides whether to stay or exit the industry. If it stays, it has to pay a fixed cost F. Only a subset of the M 1 entrants pays this fixed cost. These producing firms whose number is M 2 choose the scope of their production as well as the intensity of each product line. These two activities require different types of labor. Production is often simpler and repetitive, therefore can be done by unskilled workers. The unit cost of production, in units of unskilled labor, depends on its productivity draw: c (ϕ) = 1 ϕ. Expanding the product lines requires skilled labor. Indeed, managing different brands requires the specific skills. This approach is different from several papers in the literature. In fact, the cannibalization effect can be used to pin down the optimal number of varieties within firms (Dhingra 2013, Feenstra and Ma 2008). One can also use the flexible manufacturing approach. According to this approach, every firm has a product that they can produce the best, and the farther a product is from this core product, the higher the marginal cost it incurs (Eckel and Neary 2010, Mayer, Melitz 6

7 and Ottaviano 2014). My approach is based on the finding of Schoar (2002). She documents that firms experience a drop in total factor productivity when introducing new varieties. As a result, one can assume that there is a scope expansion costs 4. Similar to Qiu and Zhou (2013), I assume that there is diminishing returns to scale in expanding the scope. is 5 : More specifically, to develop n varieties, the demand for skilled labor F m (n) = n m, m > 1. The parameter m represents the managerial "technology" in this country. A low m indicates the firms are more effi cient in managerial use. It also indicates the quality of the managers. The more skilled they are, the lower m is. Hence the problem of choosing the quantity for each brand is as follows: maxpq cq. p With the demand given from (1), we have the pricing strategy which yields the profit per brand: p (θ) = c (ϕ) ρ, (3) π 1 (ϕ) = (1 ρ)p ρ 1 ρ Rc(ϕ) ρ 1 ρ. (4) The firm hires skilled workers to expand its scope and maximizes its 4 There are several ways to explain these costs. A usual argument can be that the firm have to invest in R&D to find new products (Dhingra, 2013). In this paper, I assume they have to recruit managers to coordinate different brands which might be in conflict because of the cannibalization effect. 5 This management cost can also be considered as a type of fixed cost. Here I divide the fixed cost into high level and low level costs. The former consists of administrating and coordinating the many products by the managers or the skilled labor. The latter, which is the conventional fixed cost and here denoted by F, are the "simpler" activities such as advertising, customer service, etc. that can be done by less skilled labor. 7

8 total profit: max nπ 1(ϕ) wn m n This equation yields the following solution: π 1 (ϕ) = wmn m 1 (ϕ) (5) Hence, a firm with productivity level ϕ will supply n (ϕ) varieties and receive a profit, net of variable costs and management costs m 1n (ϕ) π m 1 (ϕ). It is worth to clarify the notations here. Each producing firm pays three different types of cost. First, it pays its workers, then it pays its managers, and finally, it pays its fixed costs. I will use the subscripts 1, 2, 3 to denote the profit of the firms after paying each of the different types of cost. In particular, the total profit of the industry net the variable cost (payment to workers) is given by: Π 1 = M 1 n(ϕ)π 1 (ϕ)kϕ k 0ϕ (k+1) dϕ ϕ The total profit (of the industry) net the variable cost and the management cost is as follows: Π 2 = Π 1 ws. Here S denotes the total supply of skilled labor. Finally, the total net profit (of the industry), after paying the variables costs, the management costs and the fixed cost is given by: Π 3 = Π 2 M 2 F. 8

9 2.3. Equilibrium The marginal firm is, by definition, the one whose profit is only enough to cover the fixed cost F. Denote ϕ its productivity level, it supplies only one variety (i.e n ( ϕ) = 1). In this case, its profit net of variable cost and management cost is m 1π m 1 ( ϕ). We then have the zero-profit cutoff condition to pin down this productivity cut-off: m 1 m π 1( ϕ) = F. (6) Recall that M 1 is the number of entrant and M 2 is the number of producing firms. With the Pareto distribution f (ϕ) = kϕ k 0ϕ (k+1) and the productivity cut-off ϕ, the probability that an entrant is producing is then ( ϕ0 ϕ ) k. This yields a following formula that relates M1 and M 2 : M 2 = ( ) k ϕ0 M 1 (7) ϕ The firms enter the industry as long as the expected profit is still higher than the sunk entry cost f e. This process only stops when the expected profit equals to f e. Given that the real total net profit of the industry is Π 3 and there are M 1 entering the industry, the expected profit of being in the industry is Π 3 M 1.We can write the free entry condition as: f e = Π 3 M 1. (8) The constant markup, a feature of the monopolistic framework, yields a result that the variable cost is proportional to the revenue. As this is true for all firms, it also holds at the aggregate level. As a result, total variable cost in the industry is proportional to the total revenue, or the total profit net of variable cost is proportional to total revenue: Π 1 = (1 ρ) R. (9) 9

10 From (5), if we multiply both side by n (ϕ) and integrate over the universe of firms and note that n (ϕ) m is the demand of skilled labor by the firm with productivity level ϕ we have the talent market clearing condition as: S = Π 1 mw. (10) The market clearing condition for unskilled labor is given by: L = ρr + M 2 F + M 1 f e (11) L is the supply of unskilled labor. The right-hand side of Equation 11 indicates that unskilled labor are demanded for production variable costs (ρr), the fixed cost of production (M 2 F ) and the entry cost (M 1 f e ). Replace M 1 f e = Π 3 = Π 1 ws M 2 F = (1 ρ) R (1 ρ)r M mw 2F we have a formula that links the supply of unskilled labor and the total revenue R: R = L 1 1 ρ. (12) m Then from (10) and (12) I calculate the salaries of the managers: w = (1 ρ) R ms = (1 ρ) L (m 1 + ρ) S. (13) An increase in talent endowment implies lower salaries for the managers. Indeed, a larger talent endowment means more managers, therefore making the talent market more competitive, reducing the price of talent The effect of higher skill endowment Having more managers induces more competition in the good market, as stated by the following proposition: 10

11 Proposition 1. Higher talent endowment makes the competition among firms more intense: the productivity cut-off level is higher. Proof. See the Appendix. The intuition is as follows. Higher talent endowment reduces wage for talent, as in (13). As a result, from (5) we see that firms, especially the productive ones, are able to add more varieties. This has two effects on the unproductive firms. The first effect is on the demand side where the revenues of the unproductive firms shrink due to the arrival of the new varieties with lower prices. This effect is similar to a decrease in the market size. The difference here is that the consequences are not the same for every firm as the least productive firms take the hardest hit because their price is far less an advantage than the others. As a result, their small variety-level profit leaves them vulnerable when the good market becomes more competitive. From the demand function (1) we see that the extent of the change on the whole economy depends on the degree of firm heterogeneity: when the firms are more heterogeneous (low k), the new varieties have a far greater cost advantage over existing varieties, and the impact on the unproductive firms is more severe. The second effect is on the supply side, which is similar to what is described in Melitz (2003) when the firms are allowed to export. We can think of an export variety as a new variety introduced by the more productive firms in my model. They now can expand their production, hence using more labor. The unproductive firms as a consequence now have less labor to produce with. The extent of this effect depends on how many new varieties are introduced into the market, which depends on the management technology of the country, as in (5). When the parameter m is low, the firms are effi cient in managing their brands, and more varieties will be introduced. Both the effects on the demand side (which raises the degree of competition on the good market) and those on the supply side (which intensifies the competition in the factor market) have the same consequence: the unproductive firms have fewer sales. Some of them (the least productive ones) will have to exit the market, as they can not pay the production fixed costs F. As the result, the cutoff productivity level is raised. Since the wage of unskilled workers is chosen to be unity and the relative wage of skilled worker is related to the relative supply of skilled workers (see Equation 13), to discuss the welfare, we need to know how the price index responds to a change in the supply of skilled labor. 11

12 Proposition 2. An increase in the talent endowment lowers the price index, which provides welfare gains for workers. Managers are better off when there is not much talent and are worse off otherwise. Proof. See the Appendix. More competition in the (good and factor) markets implies a lower price index. With the wage taken as the numeraire, the workers benefits from an increase in talent endowment since their purchasing power is higher. The managers, however, may be worse off because their wage is lower than before. Indeed, their welfare depends on how many of them in the market: if there are not many of them then they are better off when there is additional talent; but when there are already many managers in the market, a few more of them means a reduction in their welfare (the proof is given in the appendix). This result is intuitive: if there are many managers in the market, it becomes more diffi cult for the firms to recruit the new managers as they bring little profit to the firms. This lowers the compensation of the current managers, making them worse off. 3. Open economy In this section I consider a world economy of two countries. They are denoted as Home (H) and Foreign (F ). In order to see the impact of skilled labor supply, I assume these two countries are similar in every aspect, except their talent supply. Without loss of generality, the Home country is assumed to have more talent than the Foreign country. As a firm is allowed to operate in both countries, its nationality is defined as the location of its headquarters. The purpose of this section is to consider international integration. If both types of labor are allowed to move freely across borders, this integration brings us to the case of one single, closed economy when only the supplies of labor change. Therefore we only need to consider the case when one of (or both) these two types of labor can not move. Since skilled labor are often older, more experienced with family, I conjecture that their moving costs are higher than those of unskilled workers. Therefore, in my model I assume that unskilled labor are of greater mobility than skilled labor although the alternative case when skilled labor is mobile yields the same result, as is shown in the Appendix. 12

13 3.1. Regional integration with labor mobility In this first case, unskilled labor can move freely across borders. With a competitive labor market, the wages for workers have to be the same across countries, which will be taken as the numeraire. I use the subscripts H and F to distinguish the variables in the Home and in the Foreign country respectively. However, the subscripts will be dropped if there is no confusion. With the trade balance condition, the total revenues of the firms equals the total incomes of the workers and managers in each country: R = L + ws The constant markups and the accounting calculations as we did in the case of a closed economy implies that Equation 12 still holds in this open economy case. In other words, the total revenue of one country is still proportional to its supply of unskilled labor. As a result, the wages of managers in each country are given by: w H = (1 ρ) L H (m 1 + ρ) S H (14) w F = (1 ρ) L F (m 1 + ρ) S F. (15) Lemma 1. Factor price equalization holds in the open economies with only one type of labor is mobile. Proof. By contradiction, assume that the salaries of managers in the Home country are lower than in the Foreign country. Since the wages of workers are the same, the marginal costs of two firms with equal productivity 6, one in each country, are the same. Therefore they have the same sales, and the 6 From now on, I will compare the firms in the Home country with the firms in the Foreign country with the same productivity level. They will be called comparable firms. 13

14 same profit per product. As the salaries of managers in the Home country are lower, the Home firm develops more products than the Foreign firm, i.e. n H (ϕ) > n F (ϕ). This is, however, not a stable equilibrium. In fact, for any firm in the Foreign country, there is at least one firm in the Home country that can use the one additional unit of labor more effi ciently. Given that the marginal cost is 1/ϕ, having an extra worker helps the firm produce ϕ more units of goods. With n (ϕ) symmetric varieties, it means the firm produce more of each variety by an amount of ϕ/n (ϕ). This rise in the intensive margin necessarily implies a fall in the unit price. However, the price effect is not the same across countries. Since n H (ϕ) > n F (ϕ), the increase in the intensive margin is smaller for the Home firm, which leads to a lower fall in its price. As a result, its total revenues are higher than those of the Foreign firm. Consequently, the Home firm can pay more to one additional unit of labor than can the Foreign firm, which results in a movement of labor from the Foreign country to the Home country. This labor movement stops only when we have factor price equalization. With factor price equalization, the two countries form an integrated economy. In particular, the consumers in both countries have the same preferences over the same basket of goods, so there is the common price index P = ϕ H M 1,Hp ρ 1 ρ (ϕ) nh (ϕ) kϕ k 0ϕ (k+1) dϕ + M 1,F p ρ 1 ρ (ϕ) nf (ϕ) kϕ k 0ϕ (k+1) dϕ ϕ F where ϕ H and ϕ F denote the Home and Foreign cutoffs. With this same price index and the same pricing strategy due to the monopolistic competition, two firms with the same productivity level in the Home and Foreign countries will have the same profit net of variable costs: ρ 1 ρ, π 1,H (ϕ) = π 1,F (ϕ). The formula that determines the cut-off level (6) then implies that the 14

15 cutoffs in both countries are the same. As workers are paid equally, if the firms have the same productivity level in both countries, they will have the same marginal cost, or the same unit price as in (3). From the demand function (1), for each brand they develop they have the same sales, the same revenues and the same profit π 1. Since management costs are equal due to factor price equalization, from the optimal scope condition (5) the firms in the Home country have the same number of brands as the comparable ones in the Foreign country. Proposition 3. In both countries, the price index is lower than in autarky. Proof. See the Appendix. This lower price index implies that both countries gain from trade (note that the total revenues are proportional to the number of workers). However, the gains are not distributed equally among consumers. The workers in both countries are the clear winners because the price index, in terms of their wages, decreases. Given that their nominal wage is 1, their real income rises. The welfare effect on managers is, however, less clear-cut. Talent in the Home country is the winner with the largest gains because not only is the price index lower, their salaries also increase since the relative factor endowment favors them in free trade ( L S H < 2L S H +S F ) according to equations 13 and 14. Talent in the Foreign country, however, can find themselves worse-off compared to their situation in autarky. Indeed, their salaries are lower since the relative factor endowment does not favor them in free trade ( L S F > 2L S H +S F ). Therefore, if the decrease in their salaries is more than that of the price index, they are worse-off. This happens when the talent endowments are suffi ciently different as this reduces significantly the salaries of Foreign managers; and when the firms are less heterogeneous, which implies the price index does not decrease much. This result is in line with Krugman (1994) when he shows that the scarce factor (which is talent in our case) loses when the two countries are dissimilar in their factor endowment and when the products are less differentiated. To summarize the above results, we have the following proposition: Proposition 4. With labor mobility, the productivity cutoffs in both countries are the same. The country with the higher talent endowment will see 15

16 an influx of workers from the other country, which imports the management services. The two countries form an integrated world. Almost all consumers are better off, except for the managers in the Foreign country who could be worse off when talent endowments are greatly different and firm heterogeneity is small Free trade with labor immobility We have seen in the previous section that when labor is free to move across borders the two countries form an integrated economy where the wages are at the same level. As a result, the firms in both countries behave the same way: with the same productivity level, they develop the same number of products and sell the same amount of units per product. In this section, neither type of labor is mobile across countries. We will see that the production costs, in particular the salaries of workers and managers are different, which implies that the comparable firms will not produce the same amount of goods. First, I will prove the following result: Lemma 2. If the firms in one country have bigger scope than the comparable firms in the other country, they will produce less intensively. In other words, if n H (ϕ) > n F (ϕ) then we must have q H (ϕ) < q F (ϕ) and vice versa. Proof. Again by contradiction, I assume that the Home firms have higher intensive and extensive margins than the comparable firms in the Foreign country. Since the intensive margin of a Home firm is higher, the demand function 1 implies that its unit price is lower, hence its marginal cost is smaller. Because they (the Home firm and the Foreign firm) have the same productivity level, it means the wage rate for unskilled labor in the Home country is lower. Since the Home firms develop more products than the Foreign firms, we have: n H (ϕ) π 3,H (ϕ) = n H (ϕ) π 2,H (ϕ) F = m 1 m n H (ϕ) π 1,H (ϕ) F > m 1 m n F (ϕ) π 1,F (ϕ) F w o = n F (ϕ) π 3,F (ϕ). 16

17 The zero cutoff profit conditions in the Home country and in the Foreign country are m 1 m π 1,H ( ϕ H ) = F = m 1 π 1,F ( ϕ F ). m w o We then have π 1,H ( ϕ H ) < π 1,F ( ϕ F ) because w o > 1. Hence π 1,F ( ϕ H ) < π 1,H ( ϕ H ) < π 1,F ( ϕ F ), which implies ϕ H < ϕ F.Because the cutoff is lower, and n H (ϕ) π 3,H (ϕ) > n F (ϕ) π 3,F (ϕ), the expected profit in the Home country is higher: ϕ H n H (ϕ)π 3,H(ϕ)ϕ k 0ϕ (k+1) dϕ > ϕ F n F (ϕ)π 3,F (ϕ)ϕ k 0ϕ (k+1) dϕ. The entry cost in the Home country f e is, however, lower than in the Foreign country (because the wages are higher in the Foreign country). We thus have a contradiction. In order to make a more precise and meaningful prediction regarding the scope and the intensive margin in the two countries, we have to know the wage rates in the two countries. First I will show that the relative wage of skilled labor in the Home country is lower (recall that the supply of skilled labor is higher in the Home country). Then I will show that the wage rate of unskilled labor at Home is lower. Lemma 3. In the country with a higher supply of talent (Home) : (i) the relative wage of skilled labor is lower. (ii) the wage of unskilled workers is higher Proof. Since managers are more numerous in the Home country, I can show that the salaries of the Home managers, relative to the wages of the workers, are lower than in the Foreign country. Indeed, with the same argument as in the case of mobile labor (the actual proof can be found in the Appendix), the relative salaries for managers in the Home and Foreign countries are given by: w H = 1 ρ m L/S H m 1 (1 ρ) + ρ (16) m 17

18 w F w o These two formulas yield: = 1 ρ m L/S F m 1 (1 ρ) + ρ (17) m w H < w F w o. To prove the second part of this Lemma, I use the contradiction argument, i.e. let me assume that the wage of unskilled workers in the Home country is lower. This implies that the marginal cost is higher in the Foreign country, and hence the unit price is higher: p F (ϕ) = w o ϕρ > 1 ϕρ = p H (ϕ). The monopolistic demand (1) implies that the sale per product is therefore higher in the Home country. As a result, Home country firms have more profit per brand than those in the Foreign country: π 1,H (ϕ) > π 1,F (ϕ). The number of brands per firm in the Home country is given by n H (ϕ) = ( ) 1 1 π 1,H (ϕ) m 1. (18) w H m Similarly, the number of brands per firm in the Foreign country is n F (ϕ) = ( ) w F o π F 1 m 1 1 (ϕ). (19) w F m Since π 1,H (ϕ) > π 1,F (ϕ) and 1 w H > wo w F then we have n H (ϕ) > n F (ϕ). This is a contradiction, according to Lemma 7, because the Home firms can not develop more products and sell more units per product than the comparable firms in the Foreign country. Lemma 2 and 3 then lead us to the following result: 18

19 Proposition 5. The firms in the country with more talent develop more products but sell less units per product. Proof. According to Lemma 3, the wage rate of unskilled labor in the Home country is higher. Therefore, with the same productivity level, the Home firm has a bigger marginal cost, hence a higher unit price. This results in the Home firm produce less intensively than the comparable firms in the Foreign country. From (16), (17),(18) and (19) we have ( ) m 1 nh (ϕ) = n F (ϕ) 1 w H π 1,H (ϕ) w o w F π 1,F (ϕ) = S H S F (w o ) ρ 1 ρ. The ratio of the extensive margin of two comparable firms in the Home and in the Foreign country does not depend on their productivity. Therefore, either the Home firms have higher extensive margins, or the Foreign firms have higher extensive margins. The second scenario is ruled out by Lemma 2. Therefore the Home firms have higher extensive margins than the Foreign firms. Having a larger supply of talent allows the Home firms to focus on developing more products. Consequently this implies a more competitive environment where only the good firms can survive as we see in the following proposition. Proposition 6. In the country with a larger talent endowment, the competition is fiercer, represented by a higher productivity cut-off. Proof. Since the wages of workers in the Home country are higher, it is clear that π 1,F (ϕ) > π 1,H (ϕ). From (6) we have We can rewrite this as m 1 m π 1,F ( ϕ F ) = w o F < F = m 1 m π 1,H ( ϕ H ). 19

20 π 1,H ( ϕ F ) < π 1,F ( ϕ F ) < π 1,H ( ϕ H ). The formula above implies that the cutoff in the Home country is higher than that in the Foreign country. Note that in the previous case, in which labor is mobile, the cutoffs in both countries post-integration are at the same level. As discussed above, the opportunity to sell abroad allows the more productive firms in both countries to expand their production, both the intensive margin (the market size effect, see equation 4) and the extensive margin (more profit per brand enables the firms to pay for the managers to develop more brands, as in equation 5). Increases in the intensive margin imply more demand for labor, whereas increases in the extensive margin lead to higher demand for talent. These two competition effects also occur in the case of labor mobility. The difference here is that when labor is mobile, the cut-off in the Home country in autarky was higher than that in the Foreign country. As a result, when integration takes place the unproductive firms in the Home country compete with all the other firms, in particular the unproductive firms in the Foreign country, for the same pool of labor. When labor is immobile, however, they only compete with the firms in the Home country who are more productive. Compared to the Foreign country, the high talent endowment enables the more productive firms in the Home country to produce more varieties, and therefore, acquire more labor than the firms with the same productivity level in the Foreign country. Consequently, the unproductive firms in the Home country face more competition than their comparable firms in the Foreign country, which explains why the cut-off in the Home country is higher. The last two propositions show the trade pattern. Since the cut-off level in the Foreign country is lower, this country exports the varieties produced by the unproductive firms, which have high prices. With more talent in the Home country, the productive firms in this country develop more varieties than the comparable firms in the Foreign country. As a result, the Home country exports the varieties with low prices. These varieties use more labor and less talent relatively to the varieties exported by the Home firms. Therefore the factor content of trade is that the Home country exports talent and the Foreign country exports labor. It can be shown (see the Appendix) that the wages of the managers, relative to the wages of the workers, do not change from autarky to free trade 20

21 in both countries. Therefore it is possible that free trade worsen welfare for one of the countries. Indeed, while free trade enhances welfare for the Home country, the Foreign country can be worse off. This is because with less talent, competition in the Foreign country is less fierce than in the Home country (the cut-off is lower). As a result, there are more unproductive firms in the Foreign country. When the Foreign country opens up to trade with the Home country, the Foreign firms have to lower their prices in order to compete with the more productive firms in the Home country. The result is that wages in the Foreign country are lower than in autarky. To illustrate this possibility, I run a numerical case in which I choose L = 1, S H =.1, S F =.09, f e = 10, F = 1, m = 5, γ = 5, ρ =.75. (This ρ was chosen to be consistent with other studies, in particular Broda and Weinstein 2006.) In this case, the price index in the Home country in autarky is 3.34 and the wage of the managers is.53. In the Foreign country, the corresponding values are 3.37 and.59. When the two countries engage in free trade, the price index is Since the wages of workers and salaries of managers in the Home country do not change, they are all better off. However, the wages of workers and managers in the Foreign country are now.30 and.17 respectively. They are all worse off as their wages fall more than the change in the price index. Unlike the previous case, the workers in the Foreign country can not move to the Home country where labor is more needed. In this case, compared to the case with factor mobility, the Home managers and the Foreign workers lose: while the Home managers are no longer the winners with the largest gains in free trade, the Foreign workers now may become the losers. 4. Empirical support 4.1. Data Chinese custom data - To provide the empirical support for the model, I employ the Chinese Custom data in 2004, obtained from China s General Administration of Customs. This dataset provides us with the universe of all Chinese trade transactions by importing and by exporting firm at the HS 8-digit level, covering the universe of all Chinese exports and imports. It records detailed information of each trade transactions, including import 21

22 and export values, quantities, products, source or destination countries, contact information of the firm (e.g., company name, telephone, zip code, contact person), type of enterprises (e.g. state owned, domestic private firms, foreign invested, and joint ventures), and customs regime (e.g."ordinary Trade", Processing and Assembling and Processing with Imported Materials ). The trade data is then aggregated to firm-product-country-year with the product being aggregated to the HS 6-digit level so as to be able to concord it consistently over time because China changed HS 8-digit codes in 2002, and the concordance between the old and new HS 8-digit codes (before and after 2002) is not available. Manufacturing survey - To characterize firms attributes such as TFP and capital intensity, I also use the NBSC firm-level production data from the annual surveys of Chinese manufacturing firms, covering all state-owned enterprises (SOEs), and non-state-owned enterprises with annual sales of at least 5 million RMB (which is approximately 800,000USD). The NBSC database contains detailed firm-level information of manufacturing enterprises in China, such as employment, capital stock, gross output, value added, firm identification (e.g., company name, telephone number, zip code, contact person, etc.), and complete information on the three major accounting statements (i.e., balance sheets, profit & loss accounts, and cash flow statements). 7 Due to misreporting by some firms, we use the following rules to delete the unsatisfactory observations and construct our sample, according to Cai and Liu (2009) and the General Accepted Accounting Principles: (i) the total assets must be higher than the liquid assets; (ii) the total assets must be larger than the total fixed assets; (iii) the total assets must be larger than the net value of the fixed assets; (iv) a firm s identification number cannot be missing and must be unique; and (v) the established time must be valid. The merging procedure - Then I match the firm-product-level trade data from the Chinese Customs Database to the NBSC Database, according to the contact information of manufacturing firms, because there is no consistent coding system of firm identity between these two databases. 8 The matching procedure is done in three steps: (1) by company name, (2) by 7 The firm identification information will be used to match the NBSC database with the customs database. 8 In the NBSC Database, firms are identified by their corporate representative codes and contact information. While in the Customs Database, firms are identified by their 22

23 telephone number and zip code, and (3) by telephone number and contact person name together. Compared with the exporting and importing firms reported by the Customs Database, 9 the matching rate of our sample (in terms of the number of firms) covers 45.3% of exporters and 40.2% of importers, corresponding to 52.4% of total export value and 42% of total import value reported by the Customs Database. 10 Variety counting - To classify the products I rely on the Harmonized System (HS) classification. For example, the code corresponds to "Automatic Typewriters and Word-processing Machines". However, we can count the varieties in different ways. The first way is to count the number of products the firm exports. In this way, "Other Electric Typewriters" (HS-6 code ) is a different variety to "Automatic Typewriters and Wordprocessing Machines" (HS-6 code ). Alternatively, we can count the country-product pair as a distinct variety. In this way, "Automatic Typewriters and Word-processing Machines" exported to the U.S. is counted as a different variety to the same product "Automatic Typewriters and Wordprocessing Machines" exported to Europe, due to different standard system and quality control. I will use both ways of counting for robustness concerns. Table 1 reports the key statistics of our data. In particular Panel A gives us the distribution of firm scope in China in There is clearly a large variation across firms. While single product exporters only accounted for 5% of the sample, half of the sample exported at least 10 products. When we count the country-product pair, the prevalence of multiproduct firms is obviously more pronounced. Only less than 1% of the sample exported 1 product to 1 single country. Panel B presents the statistics of the key variables, including the skilled labor which is defined as the number of college holders in the labor force of the province. corporate custom codes and contact information. These two coding systems are neither consistent, nor transferable with each other. 9 As I merge the Customs Database with the manufacturing firms in the NBSC database, I exclude all intermediary firms or trading companies from the customs database. 10 I do not compare the sample with the NBSC Database because it does not contain any information on firms import status. 23

24 Table 1: Summary Statistics Panel A: Distribution of Firm scope No. of varieties Cumulative Distribution Product Count Country-product Panel B: Key Variables Variables Mean Std. deviation Scope Export value (RMB) 132, ,735 Employment l(tfp) capital-labor ratio skill workers (millions) Note: Chinese data in USD = 8.3 RMB. 24

25 4.2. Empirical specification The theory predicts the non-uniform scope adjustment across firms which is supported by the evidence in Mexico (Iacovone and Javorcik 2008), in India (Goldberg et al., 2010) and in France (Berthou and Fontagne, 2013). Another prediction of the model is that the country with a larger supply of skilled labor export the scope or the extensive margin. This is because the firms in this country in general have a bigger scope. To test this prediction I take each province in China as one pseudo nation and run the reduced form regression: scope fpi = α skill p + γx f + I i + u fpi (20) In this regression, the dependent variable is the scope of a firm f that belongs to industry i (CIC 4-digit) in province p. It is defined as the number of HS-6 digit products that the firm supplies. I control for the firm characteristics such as firm size (measured by its output value), factor intensity, productivity, wage as well as its status (State-owned enterprise). I also include the industry fixed effect to control for all characteristics that are industry-specific. The main independent variable is the skill supply in the province p. My theory predicts that α > 0. As the key independent variable varies at the provincial level, I cluster the standard deviation at the same level. Since the dependent variable is a count data, OLS technique might not be appropriate. Indeed, the scope distribution (Table 1) is skewed to the right. The Poisson distribution is often used to address the count data. However, one condition for using this technique is that the mean and the variance are of the same order. I will use other distribution such as the negative binomial and the gamma distribution for robustness check Result Table 2 reports the main results. In general, large and productive firms supply a high number of varieties, which is consistent with Equation 5. However, our interest lies in the impact of skill supply on the firm scope. In Column 1, we can see a significant positive correlation between the firm 25

26 scope and the supply of skilled labor in the firm s location. In particular, a typical firm adds 2 more varieties if the supply of skilled labor doubles. As the OLS technique might not be appropriate for the count data, in Column 2 I employ the Poisson estimation. The coeffi cient of the skill variable is smaller, but still significantly positive. A condition for the Poisson distribution is that mean and the variance are the same, which is not the case here. In particular, the variance of the scope (188) is larger than the mean (88). This over-dispersion problem results in the Poisson distribution being ill-fit to represent the distribution of scope. To deal with this issue, I rescale the standard errors using the square root of the Pearson chi-square dispersion. Column 3 reports that our skill variable is still significantly positive. An alternative way to deal with the ill-fitness of the Poisson distribution is to use different ones. In the case of over-dispersion as we have here, the negative binomial distribution is often chosen. It allows us to have the variance greater than the mean. In Column 4, we see that the effect of skill labor is smaller in magnitude but still significantly positive. In particular, to increase the scope by 1 variety, the supply of skilled labor has to rise by In Column 5, I use another distribution: the Gamma distribution. There is no significant difference in this specification, regarding the coeffi cient of our interest. [Insert Table 2 here] 4.4. Robustness check As we can count the varieties not by the number of products but by the country-product pair, I replace the scope in Equation 20 by the number of country-product pairs the firm exports. Table 3 reports the results of all specifications discussed above with this new variety counting. As in the benchmark case, the firms located in the province with 10% more skilled labor tend to export 1 more variety than the comparable in the other provinces. In all specifications, the coeffi cients of skill variable are significantly positive. [Insert Table 3 here] 26

27 We can also count the number of products a firm exports to a particular country. More specifically, I run the following regression: scope fpid = α skill p + γx f + I id + u fpi (21) The dependent variable is the scope of firm f in a country d. Instead of controlling the industry fixed effect as in the benchmark case, I include here the country-industry fixed effect. Results are reported in Table 4. One more time they are robust to these specifications. Indeed, the coeffi cients of skill variable are positive in all specifications. They are significantly different from 0 in the rescaled Poisson estimation, as well as when I use the negative binomial and the Gamma distributions. [Insert Table 4 here] 5. Conclusion In this paper I extend the framework in Melitz (2003) to the case of multiproduct firms. This proves to be a new source of competition and a new channel for welfare gains. With more talent available, the more productive firms can develop more products, thus causing two effects. On the supply side, new varieties absorb input resources, leaving the unproductive firms with less input for their production. On the demand side, the introduction of the new varieties reduces the market share of a firm s existing varieties (the cannibalization effect). This competition in the product market is equivalent to a reduction in the market size which sees the market share of existing varieties shrink. A higher survival cut-off is the result of this more competitive market. Moreover, the economy enjoys more new varieties from the productive firms, with lower prices. Welfare is then enhanced across the economy, although talented workers could be worse off if their wages fall more than does the price index. I also show that the effects are more pronounced (the gains are bigger) if the firms are more heterogeneous or management is more effi cient. One way to make management more effi cient is to improve the quality of the managers. Policy makers could use education and immigration policies to 27