Endogenous Market Access Costs and the New Consumers Margin in International Trade Costas Arkolakis University of Minnesota This version: June 2006 [preliminary] Abstract In this paper, I introduce endogenous market access costs in a general equilibrium trade model with heterogeneous firms. These costs, explicitly modeled as marketing expenditures, are endogenous in the sense that the firm chooses to incur increasing amounts in order to reach additional consumers. The endogenous hurdle of reaching the first consumer allows me to determine the number of exporters and their average productivity without assuming fixed costs of exporting. In addition, under a certain parameterization, the model encompasses the case of Melitz (2003) and Chaney (2006) with fixed market access costs. Thus, the model retains the main desirable theoretical predictions of this class of models. I calibrate the model using a set of moments of the French firms provided by Eaton, Kortum and Kramarz (2004) and (2005). I demonstrate the quantitative importance of the model in two different dimensions. First, the model, while remaining highly parsimonious, replicates the shape of the distribution of sales of French exporters to particular markets. More specifically, it predicts the prevalence of French exporters selling small amounts to particular markets. This fact is especially puzzling in the view of the fixed market access cost model that assumes that firms sell to all the consumers of a particular market. Second, the paper introduces the notion of the extensive margin of consumers to a firm s sales. The model predicts that the price elasticity of trade flows with respect to a given tariff change is higher for firms with initially smaller export sales: these firms have lower costs of finding new consumers. I verify this prediction by applying a methodology similar to the one of Kehoe and Ruhl (2003) to the data of the U.S. - Mexico trade liberalization episode. I am grateful to my advisors Timothy Kehoe and Samuel Kortum for their continued guidance and their support. I am also grateful to Cristina Arellano for continuous encourangement and various discussions on the topic. I am indebted to Jonathan Eaton, Samuel Kortum and Francis Kramarz for providing me with statistics from their data. For their suggestions and comments, I also would to like to thank John Dalton, Jonathan Eaton, Thomas Holmes, Christos Ioannou, Erzo G.J. Luttmer, James Schmitz, Ina Simonovska and the members of the Trade and Development and the Trade and IO Workshop at the University of Minnesota. All remaining errors are mine. Contact: Department of Economics, University of Minnesota, 1035 Heller Hall, 271 19th Ave. S., Minneapolis, MN, 55455. Email: arkolaki@econ.umn.edu. 1
1 Introduction Recent empirical research using firm or plant level data has reinforced the view that firms face substantial hurdles to selling in foreign markets. The results of this research suggest a world where national markets are highly fragmented: exporters tend to be the minority, and they usually export only a small fraction of their output. Several theories incorporating different types of trade barriers designed to deter foreign exporters have emerged in response to these observations. Bernard, Eaton, Jensen, and Kortum (2003) assume per unit iceberg trade costs in the tradition of Samuelson. In addition to considering per unit costs, Melitz (2003) and Chaney (2006) assume that firms pay a fixed exporting cost in order to obtain access to a foreign market. 1 Fixed costs of exporting have been interpreted by Melitz (2003) as the marketing costs of informing the consumers about new goods and establishing distribution channels in order to obtain access to the foreign market. Although the empirical evidence testing the existence of these costs is substantial (see Tybout (2001)), empirical evidence on their quantitative magnitude is controversial. Das, Roberts, and Tybout (2005) estimate the value of fixed costs for plants breaking into foreign markets using a sample of Colombian plants for the period 1981-1991. For their sample of firms, they find that fixed costs are substantial and range from $344,000 to $440,000, thus concluding that fixed costs of exporting are substantially high. 2 However, the existence of many small exporters in the French data reported from Eaton, Kortum, and Kramarz (2005) (EKK05) poses doubts on the large fixed costs of exporting. In 1986, 10% of French exporters sold on average only about $1,161 per foreign market. Given this low revenue earned by many firms, the fixed cost of exporting must be trivial for these firmstohavean incentive to export. Finally, the literature is not conclusive in whether costs of breaking into foreign markets are fixed or related to the sales of firms. My work is motivated by the apparently simplistic assumption of fixed costs of exporting that 1 Melitz (2003) pionereed the analysis of fixed costs of trade in a general equilibrium model of trade. However, the idea of fixed costs goes back to Dixit (1989), Baldwin (1989) and Baldwin and Krugman (1989). Also, more recently, Bernard and Jensen (2004b) and Roberts and Tybout (1997a) among others have used empirical models to test the existence of fixed trade costs. Fixed costs of trade refer to one time sunk market entry costs that firms face. In a static model, as the one I consider here, the fixed costs of exporting are the modeling equivalent of one time sunk market entry costs of trade amortized per period. In future work, I plan to consider a dynamic version of the model with sunk costs of trade. 2 The sample includes firms from three industries: leather products, knitted fabrics and basic chemicals. 2
is commonly used in the trade literature: firms, upon paying this fixed cost to export, extend their consumer base to all the consumers in the market. This paper proposes a new approach to the modeling of market access costs of exporting that reconciles theory and empirical evidence. By modeling this cost at the micro-level of the decision of the firm,itassumesthatmarket access costs are per consumer (customer) of a market and not for accessing the whole market per se. These market access costs, interpreted as marketing costs, are endogenous rather than fixed (exogenous) in the sense that paying higher costs allows firms to reach an increasing number of consumers in a country. In this model, firms with relatively low productivity choose to reach only a few consumers and thus export small amounts. Therefore, market access costs of trade are trivial for firmswithsmallsalesbutaresubstantial forfirms with large sales. Despite the fact that I do not assume fixed costs of exporting, the per consumer costs of accessing a market create an endogenous hurdle to exporting. A firm will decide to enter a market if it is productive enough so that the marginal revenue from the first consumer exceeds the marginal cost of accessing her. This allows me to determine the number of the exporters and their average productivity as in Melitz (2003). The model also incorporates the main desirable predictions of the existing trade literature 3 by encapsulating the production structure proposed by Melitz (2003) and Chaney (2006). I adapt their monopolistic competition structure with firms with heterogeneous productivities in a multi-country set up. A contribution of this paper is to incorporate a structure where heterogeneous firms incur a marketing cost per consumer in a model that yet remains highly analytically tractable. I also show that under a certain parameterization my model reduces to the case of Melitz (2003) and Chaney (2006) where firms incur a fixed cost to sell to all consumers in the market. Therefore, the model incorporates in a parsimonious way the existing models of monopolistic competition and, without losing any of their main desirable properties, delivers a series of new theoretical predictions. This modeling adds two new dimensions to the existing trade models. The first is endogenous responses of average sales to market size reported by Eaton, Kortum, and Kramarz (2004) (EKK04): in the French firms data, a clear pattern emerges showing average sales of French 3 See, for example, Bernard, Jensen, and Schott (2003) for a review on the main theoretical predictions of new firm-level models of international trade with heterogeneous firms. The authors also present empirical evidence in support of these predictions. 3
firms to be larger in markets with larger expenditures. The second dimension is the extensive margin of consumers in firms sales. I define the extensive margin of consumers as the number of consumers who actually purchase the firm s good, namely the firm s consumer base. To test my theory, I compare the static and dynamic predictions of the model to the available trade data. To calibrate the model, I use the data on average sales and size of the market and the relation between average sales in a market and number of markets served reported by EKK04 and EKK05. The parameterized model closely matches both relationships. In addition, the parameterized model performs very well in replicating the shape of the distribution of sales of French firms. In conclusion, the model is very successful in replicating the main stylized aggregate data facts on size and location of exports as reported in EKK04 and EKK05. The introduction of endogenous market access costs is of critical importance to deliver these facts endogenously through the mechanisms of the model. Furthermore, I test the dynamic predictions of my theory in the case of a trade liberalization. In line with trade data from the U.S.-Mexico trade liberalization episode, the model with endogenous market access costs predicts that the growth of exports of the least traded goods will be much larger than the growth of exports of goods with already large sales in the importing country. This is in contrast to the existing models of trade that predict constant growth rates for all goods with the price elasticity of export sales depending only on the elasticity of substitution of the good. Related to the last prediction, the model adds a new dimension to the analysis of episodes of trade liberalization neglected by the trade literature. It adds a third margin of response of export sales to the decrease in trade costs, the new consumers margin. This is in addition to the already analyzed new firms margin and the intensive margin per consumer. I show that the consumer base of firms with a small number of consumers increases substantially as a response to even small increases in their marginal revenue per consumer after trade liberalization. The reason is that costs of searching for new consumers increase slowly for these firms compared to the firms that already have a large consumer base. This paper is a continuation of a substantial theoretical literature that has emerged in response to recent empirical literature s use of firm and plant level data in measuring the behavior of exporters along many dimensions (see, for example, Aw, Chung, and Roberts (2000), Bernard 4
and Jensen (1995), Bernard and Jensen (2004a), Clerides, Lach, and Tybout (1998) or Tybout (2001) for a review). This empirical work has shown that exporters are only a small fraction of the firms operating in a country but they tend to be more productive and to sell more domestically. However, in general, export sales constitute only a small part of the total sales of the exporters. These empirical facts about the micro-level characteristics of the production suggest the existence of substantial export costs as EKK04 point out. Detailed firm level data on export location, along with export size, have also been brought to light through the recent work of EKK04 and EKK05. This work added the dimension of export destination to the empirical literature examining international trade at the level of individual producers. EKK04 and EKK05 have reported a series of striking regularities in the data of French exporters. Looking across firms, the size and productivity advantages of exporters extend very similarly into size and productivity advantages of firms that export to more countries and to less popular destinations. Looking across destinations, the number of French sellers to a destination increases with overall French market share with an elasticity close to one, while the number increases with market size with an elasticity of around two-thirds. All their results reinforce the view of a world in which national markets are highly fragmented and in which per unit costs, as well as market access (entry) costs of exporting, play a role in separating them. Motivated by the bulk of empirical data on the existence of trade barriers, substantial empirical work has been devoted to evaluating the importance of the per unit and market access cost of trade. Tariffs on imports and freight costs that constitute the main per unit costs of trade have been studied by Bernard, Jensen, and Schott (2003) among others. The authors report per unit tariff and trade cost for imported goods in the U.S. The per unit costs of trade for U.S. imports add an average of 8.3% to the price of traded goods across industries 4. Estimates for the significance of fixed costs of exporting are reviewed by Tybout (2001), and empirical evidence on the quantitative magnitude of fixed entry costs are provided by Das, Roberts, and Tybout (2005) as indicated above. This paper provides a unified theoretical framework in explaining the behavior of exporters by using both per unit costs and market access costs of trade. In addition, this paper tests the 4 See http://www.som.yale.edu/faculty/pks4/sub_international.htm for detailed data on per unit trade costs and Bernard, Jensen, and Schott (2003) for details. 5
theoretical predictions generated by the model using recently available empirical data on the behavior of exporters. The outline of the rest of the paper is as follows: In the next section I describe the model in detail. I first describe a one country version of the model and explain in which dimensions it differs from existing models of trade. Subsequently, I present the multi-country version of the model. In section 3, I test the predictions of the model. First, I test the predictions of the model for the distribution of sales of firms in relation to export destinations reported by EKK04 and EKK05. Second, I test the predictions of the model in a trade liberalization episode using an analysis similar to Kehoe and Ruhl (2003). Section 4 concludes. 2 Model The model considered here is a monopolistic competition multi-country model of trade that incorporates the production structure of Melitz (2003) and Chaney (2006). Thus, I am able to retain the main desirable theoretical predictions of this class of models. The model, however, departs from the existing literature in the demand structure. In this model, the number of consumers who can buy a firm s good is the result of an optimal decision on the part of the firm. Firms have to pay an increasing cost of reaching additional consumers (customers) and thus will choose the number of consumers of its good in order to maximize profits. Therefore, a subset of consumers may not have access to a particular good. I will start the exposition of the model by describing the one country case. This enables me to lay out the main features of the model and the dimensions in which it differs from existing trade models. I then proceed to analyze the multi-country case. 2.1 One country model 2.1.1 Consumer I assume that there exist a continuum of consumers of mass L. There is a mass J of potential entrants, each one of which can produce a differentiated good. Only a mass M of firms, where 6
M J, chooses to operate. 5 IdenotebyΩ the set of all goods produced by operating firms. 6 Potentially, each consumer has access to a different subset of these goods Ω Ω. 7 In order for the consumer to have access to the good, the firm that produces it must pay an accompanying cost. I will analyze the details concerning this cost when I consider the firm s problem. Labor is inelastically supplied and each consumer has identical symmetric CES preferences over the goods ω Ω she has access to. Each consumer has a labor endowment of 1 and receives payment for her labor w and flows of profits π from the firms. 8 Therefore, each consumer takes as given prices p (ω) of goods ω Ω and picks allocations x (ω) for each good ω to solve 2.1.2 Demand µz 1 max (x (ω)) ρ ρ dω, 0 < ρ < 1 x(ω) ω ΩZ s.t. p (ω) x (ω) dω = w + π ω Ω The maximization problem of a consumer who has access to a set of goods Ω givesrisetothe usual Dixit-Stiglitz demand for each good x (ω) over the set of goods Ω Ω : x (ω) = P 1 σ (p (ω)) σ (w + π), ω Ω, Z P 1 σ (p (ω)) 1 σ dω, σ = 1 ω Ω 1 ρ > 1. Each firm, denoted by ω Ω, chooses n (ω), the probability that a consumer will have access to its good. Therefore, the firm pays an accompanying cost related to the expected number of 5 Alternatively, you can think of J as the mass of differentiated varieties of goods available to firms to produce. 6 There is a one-to-one mapping between firms and goods in the model, meaning that each firm produces a different good. Therefore, the mass of Ω is the mass of the firms operating in the economy. 7 Idonotdefine a consumer specific Ω, since it is not crucial for the characterization of the problem, as I will show below. However, it is true that consumers have access to a potentially different set of goods. 8 I assume that consumers own an equal share from each firm of their country. Therefore, profits of firms of a country are equally distributed among the consumers of the country. This assumption will apply in the multi-country model as well. 7
consumers n (ω) L that have access to its good. I assume for simplicity that the consumer cannot search for new goods to consume. In order for the above integrals to have a meaning, it is necessary to put enough structure on the functions ω. To do this I will re-label the goods as follows. In the model, I assume that firms operating in the economy can have potentially different productivities φ = φ (ω). Productivities are independently distributed across goods, and I denote by µ (φ) the probability density of productivities of firms conditional on operating. A particular distributional form will be specified later on. In addition, all firms with the same productivity φ choosethesameprice for their good p (φ) and the same probability that the consumers will have access to their good n (φ). The probability that a consumer has access to a particular firm s good is independent of the probability of having access to any of the other firms goods. Thus, using the fact that all goods ω enter symmetrically in the CES preferences, the above integrals can now be meaningfully rewritten in terms of the productivities. 9 Using the independence assumptions, I can assume that the Law of Large Numbers holds and the price index P 1 σ observed by each consumer is almost surelythesameandcanbere-writtenastheexpectedpriceindexintermsofproductivities P 1 σ = M Z 0 (p (φ)) 1 σ n (φ) µ (φ) dφ. (1) Denote by η the share of profits out of total income wl + πl. 10 Therefore, ignoring a set of measure zero consumers, the expected demand for a firm with productivity φ is: q (φ) =n (φ) wl (p (φ)) σ = n (φ) Lx (φ) a.s. 11 1 η P 1 σ 9 See Alvarez and Lucas (2005) for an exposition of this approach of re-labeling the goods in terms of productivities in models of heterogeneous firms. 10 In appendix B, I show, for the multi-country version of the model, that the profits are a constant share out of total income equal to η = πl wl+πl = σ 1 θσ,whereθ is a parameter that governs the distribution of firms and will be specified below. The results follow for the one country case trivially. 11 I will discard the almost surely (a.s.) notation for the rest of the analysis. 8
2.1.3 Firm Each operating firm has to perform two distinct procedures to realize profits. The first is to produce the good. This is done using a constant returns to scale production function y (φ) =φl, where l is the amount of labor used for production and φ is the labor productivity of the firm. This first process creates the good that can be used for consumption conditional on a particular consumer having access to it. The second procedure is to pay a cost to make the good available to consumers, or alternatively, to inform the consumers about the existence of the good. This market access cost is described below. Searching for consumers and the market access technology The market access cost that a firm with productivity φ pays is a function of the total number of consumers n (φ) L who have access to the firm s good. The work of Melitz (2003) and Helpman, Melitz, and Yeaple (2004) has formalized the idea of fixed costs of market access in a general equilibrium model with trade. They assume that a firm pays a fixed cost per market in order to establish a distribution and/or servicing network. Upon paying this fixed cost, the firm has access to all the consumers in the market. Melitz (2003) claims that the amount of these costs is fixed and independent of the size of the firm. Even though there is mixed evidence regarding this claim, the claim per se contradicts the observation of many small exporters in the trade data (see EKK05) and the existence of small producers in general. 12 In order to answer the question of the exact role that the costs of establishing a distribution and servicing network play in international trade, I begin by modeling these costs at the microlevel. I consider the costs of a firm which is aiming at establishing this network in order for consumers to obtain access to its good. 13 In the vein of Melitz (2003) and Helpman, Melitz, and Yeaple (2004), this cost could be interpreted as a cost of informing buyers about the firm s product (e.g. advertising). 12 The existence of small producers would require the assumption of trivial fixed costs. In contrast, empirical studies that evaluate fixed costs conclude that these costs are significant (see, for example, Roberts and Tybout (1997a), Bernard and Jensen (2004b)) and substantial (see Das, Roberts, and Tybout (2005)). 13 Alternatively, in a dynamic entry-exit context as the one of Melitz (2003), this cost can be interpreted as a one-time sunk cost of building a distribution network. Given that in my model there is no uncentainty, this cost can be written equivalently as a per period cost amortized by the probability of exit of the firm. 9
I begin by a simple example and then proceed to formalize the more general case. 14 Assume that firms must pay a cost to inform the consumers about the existence of the good. Since the interpretation of the market access technology as an advertisement technology is more straightforward, I will proceed with this description, but the results go through for a general market access technology in an environment where firms search for consumers. Assume that S is the number of advertisement signals sent by a firm. The firm sends advertising signals to the consumers independently without the ability to target any particular consumer. Following the tradition of informative advertising, I assume that the advertisement sent by a firm is essentially a posting that contains information about the existence of the good and the price of the good. 15 Potential consumers of goods do not know which firms charge a particular price and learn about firms and their prices only through signals sent by firms. Finally, denote again by L the number of consumers. Each consumer observes the signal of an advertisement with probability r in a Bernoulli fashion. Therefore, any additional advertisement bears the same probability r to be seen by a consumer. I will make the following assumption: Assumption 1: r = 1 L α,α [0, 1], 0 < 1 < 1. Using the above assumption, the expected number of consumers who see a particular advertisement is 1 L 1 α. If α =0, the expected number of people that see a given ad increases linearly with the size of the population. If α =1, the expected number of people that see an ad stays constant. 16 Empirical evidence presented in Campbell and Hopenhayn (2005) indicates that per consumer advertisement costs decrease when population increases, which suggests that α<1. 17 Thus, the assumption that α<1 is meant to capture the empirical regularity that 14 Costs of obtaining access in a market include a variety of activities related to informing foreign consumers and learning about the foreign market. Establishing distribution channels is an example. As Roberts and Tybout (1997b) report, firms can hire for a fee third parties to handle the distribution, which, reportedly, is very frequently the case. If this market is characterized by free entry and perfect competition, the market access cost formulation can be used as described in this chapter and be interpreted as an external activity without changing any of the results of the model. 15 See Butters (1977), Stegeman (1991) or, more recently, Dinlersoz and Yorukoglu (2006). 16 This would indicate constant returns to scale in the advertising technology. 17 They find that the per consumer cost of reaching a person through an advertisment in newspaper decreases with elasticity 0.4 to the increases in population. 10
in bigger markets a firm can potentially inform more consumers about its good with a given advertisement. The exact value of α will be estimated using trade data. 18 I assume that advertisement signals are untargeted. Since the advertisements arrive in a Bernoulli fashion, the number of advertisements that a consumer observes from each firm follows a binomial distribution with number of trials S and probability of success r. Thus, some consumers see more than one advertisement for a particular good. However, observing the first advertisement is enough for them to consider the particular good in their consumption bundle. Using the binomial distribution, the probability that a consumer has seen none of the advertisements after S ads is (1 1 L α ) S. Therefore, the probability that a consumer sees the advertisement, n, as a function of the number of advertisement signals the firm sends, S, is: n =1 (1 1 L α ) S. (2) As S, L +, a good approximation of (2) is n =1 e 1 L α S.Equivalently,asS, L +, and r = 1 L α, the number of advertisements that a consumer sees from a particular firm follows a Poisson distribution with parameter S 1 L α. 19 Using the Poisson distribution, the probability that a consumer will see no advertisement is exactly e 1 L α S and thus n =1 e 1 L α S. 20 Rearranging (2) and taking natural logarithms on both sides, S = Lα 1 log (1 n). Now, assume that sending each advertisement signal requires 1 units of labor. 2 This gives rise to the following market access cost of reaching any of the consumers from the 18 However, notice that, in models of trade like Melitz (2003) and Chaney (2006), α =0. 19 The Poisson probability distribution arises as the limit of a Binomial probability distribution which corresponds to the case of the discrete number of advertisements and consumers. 20 Alternatively, you can think of the advertisements as flows of mass S 1 L 1 α that are seen randomly by the continuum of consumers. The number of advertisements that corresponds to each consumer follows a Poisson distribution with parameter S 1 L α. 11
population L with probability n in terms of labor requirements: where = 1 2. f (n, L) = Lα log (1 n), α [0, 1] = (3) f (n, L) = Lα 1 log (1 n), L (4) Expression (3) denotes the total cost of reaching nl consumers in terms of labor, while expression (4) represents the market access cost per potential consumer of the firm s good. Since this function is an important part of my theory, I will delve into its properties. properties of this function are: The main f (n, L) n f(0,l) lim n 0 + n L > 0, f2 (n, L) n 2 > 0, (5) = Lα 1 > 0. (6) Expression (5) implies that the marginal cost of reaching a consumer is positive and is increasing in the number of consumers a firm reaches. Expression (5) denotes that the marginal cost of reaching the first consumer is positive. The marginal cost of reaching the first consumer is also decreasing in the size of the population of the country. Equation (6) implies that selling into bigger markets is less costly per consumer reached as long as α<1. Finally, notice that f(n,l) lim =+, which means the cost of reaching all the consumers is infinite for this particular cost function. The above assumptions broadly capture the empirical regularity that n 1 n the reach of advertising is subject to diminishing returns or else the marginal cost of advertisement increases as n increases. 21 In the further analysis, I consider a more general cost function f (n, L) = Lα 1 (1 n) β β. (7) 21 For a more extensive discussion see Sutton (1991) (e.g. p. 51, 100). 12
For β 0, this function is equal to (3). It also inherits all the properties of function (3) described above for β > 1. In figure (1), I draw the cost function for different β s. Notice that, for β<0, the function is bounded n [0, 1]. However, the marginal cost of reaching an extra consumer goes to infinity as n 1 as long as β> 1. Finally, notice that, for β 1, the cost function is concave. This means that the marginal cost of reaching an extra consumer decreases (or is constant in the case of β =1) as the total number of consumers who have access to the good increases. All the cases will be analyzed more thoroughly below in the context of the problem of the firm. Firm s problem The firm faces an increasing cost of reaching additional consumers. However, new consumers bring extra revenue to the firm that increases linearly with the number of consumers reached, n (φ) L. Therefore, using the market access cost function (7) and the production technology specified above, the maximization problem for an individual firm with productivity φ is: π (φ) = wl max n (φ) n(φ),p(φ) 1 η s.t. n (φ) [0, 1] (p (φ)) 1 σ P 1 σ n (φ) wl (p (φ)) σ w w Lα 1 (1 n (φ)) β 1 η P 1 σ φ β Notice that the maximization problem of the firm is similar to the one in Melitz (2003). The difference lies in the fact that in order to reach a certain number of consumers through advertisement the firmhastopayacostwf (n, L) in terms of labor. Notice also that I do not assume any fixed cost of operation, but, as I show below, I can still determine a lower bound threshold productivity of the operating firms in the economy, φ (I consider as operating firms the ones choosing n (φ) > 0 = π (φ) > 0). The first order conditions (FOC) with respect to p (φ) and n (φ) give the optimal decisions of the firm. For the case when β> 1, theoptimaldecisionsofthefirm for p (φ) and n (φ) are 13
determined by the following equations: p (φ) : p (φ) = σ w σ 1 φ, (8) ³ 1 σ σ w w σ 1 φ 1 = wlα 1 1 if φ>φ (1 η) P n (φ) : 1 σ σ {z } (1 n (φ)) {z } (9) marginal revenue per consumer marginal cost per consumer n (φ) =0 otherwise. The LHS of the top of equation (9) represents the marginal revenue from selling to an additional consumer and is independent of the number of consumers reached. Due to the elastic demand, more productive firms can charge lower prices and extract higher marginal revenue per consumer. The RHS of the same equation captures the corresponding marginal cost of selling to an additional consumer. It is increasing as a function of the number of consumers reached. A higher β implies that the cost increases faster as a function of consumers reached. Notice that firms with productivities φ φ choose optimally n (φ) =0. Thus, even though the prices they would charge are finite, consumers do not take in account these goods in their consumption bundle. In order to decide whether to enter a market or not, a firm compares the marginal cost of reaching the first consumer with the marginal revenue received from this consumer. The marginal cost of reaching the first consumer is given by cost of the first ad expected number of people that see the ad = w 1 = (10) L1 α = w Lα 1. This is the expected cost of reaching the first consumer. Alternatively, one can think of it as the derivative of the total market access cost evaluated at n (φ) =0, represented by the RHS of expression (9). Notice that the cost to reach the first consumer falls as the population increases since the denominator in expression (10) increases. This allows firms with lower productivities, which have smaller sales per consumer (see the LHS of (9)), to enter the market. Thus, bigger 14
markets will attract more firms, as the cost of reaching the first consumer is smaller. However, when α>0, the number of firms increases with the population with an elasticity less than one, as I will show more thoroughly in the multi-country case. Figure (2) plots the marginal revenue per consumer w( σ w σ 1 φ ) 1 σ 1 and the marginal cost per (1 η)p 1 σ σ consumer Lα 1 w. The point of intersection corresponds to the solution to equation (9). (1 n(φ)) This gives n (φ) as a function of φ for the case of β > 1. Notice that since the marginal revenue per consumer is higher, the higher the φ, more productive firms find it profitable to pay for searching additional consumers. Also, given the aggregate price level P,thereexistsaφ such that φ φ, n (φ) =0. This arises from the fact that for these φ s very low marginal revenue from the first consumer is not enough to cover the cost of reaching her. However, for β 1, the decision rule is no longer continuous. The following proposition summarizes the above discussion: Proposition 1 a) Assume that β> 1, then i) there exists a threshold φ such that φ φ, n (φ) =0. ii) φ 1 >φ 2 = n (φ 1 ) >n(φ 2 ), φ 1,φ 2 φ b) Assume that β 1, then n (φ) {0, 1} and there exist φ such that φ φ, n (φ) =0, φ >φ, n (φ) =1. Proof. a) Part i) This part is proved formally in appendix A. Also, notice that, by solving (9) with respect to n (φ), forn (φ) > 0, wehave n (φ) =1 1 µ L 1 α ( σ w σ 1 φ ) 1 σ 1 (1 η)p 1 σ σ 1. (11) Observe that n (φ) > 0 only if φ σ 1 > 1 L 1 α σ w 1 σ 1 P σ 1 σ 1 σ 1 η. Thus, define (φ ) σ 1 = 1 L 1 α σ w 1 σ 1 P σ 1 σ 1 σ 1 η (12) 15
such that φ >φ, n (φ) > 0. For φ φ, as shown in appendix A, n (φ) =0. Thisprovespart i) of a). a) Part ii) From equation (9) and the proof of uniqueness in the appendix A, part ii) follows. b) As long as β< 1, the marginal cost of reaching an additional consumer Lα decreasing with respect to n (φ). 1 (1 n(φ)) This means that every consumer brings increasingly more profit to the firm. For the first consumer, this profit can be negative since the cost of reaching the first consumer is always positive. For the last consumer, this profit will always be positive, as the marginal cost is decreasing and goes to zero. Therefore, if the total revenue from selling to all consumers is larger than the total cost of reaching them, then the firm will choose n (φ) =1. If the total cost of reaching all the consumers is larger than the corresponding total revenue from selling to them, then the firm chooses n (φ) =0. Since total profits are strictly increasing in φ, part b) follows. For the case of β> 1, the cost of advertising to get the first consumer creates an endogenous market access cost to enter the market: the productivity of the firm has to be high enough so that the marginal sales per consumer (intensive margin of sales) surpasses the cost of reaching the first consumer. In addition, more productive firms find it profitable to pay the cost to reach is more consumers. However, when β 1, the marginal cost of reaching an extra consumer is constant or decreasing. Therefore, the market access decision of the firm becomes a binary decision. The firms compare total profits from L consumers to total costs of reaching them, and if they find it profitable, they pay the cost to enter the entire market, as is also done in Melitz (2003). 22 2.1.4 Equilibrium Define the cdf and the pdf of the distribution of firms by G (φ) and g (φ) respectively. The probability that a firm is actually operating in the economy is the probability that firm has a productivity draw φ such that φ φ, G (Φ φ ). Thus the mass of operating firms is given by 22 For simplicity, I will assume that the number of potential goods is fixed and equals J. The extension to a context with an unbounded pool of entrants, as in Melitz (2003), is straightforward. 16
JG(Φ φ ). The conditional distribution of firmsisgivenby µ (φ) = g(φ) 1 G(φ ) if φ φ 0 otherwise. (13) I can now summarize the above discussion and define an equilibrium in the closed economy. Given the number of potential entrants J, an equilbrium is the number of firms operating in the economy ˆM; a lower bound threshold productivity ˆφ ;pricesˆp (φ) φ >ˆφ ;awageŵ; a price index ˆP ; an equilibrium distribution of firms conditional on operating ˆµ (φ); a consumption plan for the representative consumer ˆx (φ) and a production plan for each operating firm ŷ (φ), ˆl (φ), ˆn (φ), ˆl m (φ) such that: Given ˆP, ŵ and ˆp (φ), the representative consumer solves her maximization problem by choosing ˆx (φ) for the goods φ she has access to according to x (φ) = ŵl (ˆp (φ)) σ. 1 η ˆP 1 σ ³ Given ˆP, ŵ and the indirect demand function p ŷ (φ), ˆP that comes from solving the representative consumer s utility maximization problem, firm φ φ [b, + ] chooses ŷ (φ), ˆn (φ) to solve ³ π (φ) =max p y (φ), ˆP y (φ) ŵ y (φ) φ 1 (1 n (φ)) β ŵlα β s.t. y (φ) n (φ) L ŵl (ˆp (φ)) σ. 1 η ˆP 1 σ ˆφ =sup{φ : π (φ) =0and φ [b, + )}. ˆl (φ) = ŷ(φ) φ and ˆl m (φ) = Lα 1 (1 ˆn(φ)) β β. The price index satisfies ˆP 1 σ = ˆM R (ˆp (φ)) 1 σ ˆn (φ)ˆµ (φ) dφ. 0 Themassofoperatingfirms ˆM = JG ³Φ ˆφ. The conditional distribution of operating firms ˆµ (φ) is given by (13). 17
The individual goods market clears ˆn (φ) Lˆx (φ) =ŷ (φ), φ [b, + ]. The labor market clears ˆM R + 0 R + ˆl (φ)ˆµ (φ) dφ + ˆM 0 ˆlm (φ)ˆµ (φ) dφ = L. To derive stark predictions from the model, I will make a particular assumption regarding the distribution of the productivities. Similar to Helpman, Melitz, and Yeaple (2004) and Chaney (2006) I assume that productivity of the firms is drawn from a Pareto distribution with shape parameter θ>σ 1, cdfg (Φ φ) =1 bθ, pdf g (φ) =θ bθ and support [b, + ), whereb can φ θ φ θ+1 be interpreted as the level of technology. 23 Thus, we have G (Φ φ )= bθ and the mass of (φ ) θ operating firms is simply given by M = J bθ.finally,µ(φ) = θ(φ ) θ represents the conditional (φ ) θ φ θ+1 density. Substituting the optimal decision rules (8) and (9), as well as the number of entrants M and the conditional density defined above, into the price index (1) (φ ) θ = Jbθ L 1 α 1 1 η σ where the case of β 1 results when taking the limit β 1 +. The above equation, together with Ã! 1 θ σ +1 1, (14) θ (σ 1) β P σ 1 = L1 α 1 η 1 σ w 1 σ (15) 1 σ 1 σ (φ ) σ 1 and the normalization w =1, delivers two equations and two unknowns, φ and P, that determine the equilibrium of the model. 24 2.1.5 Sales Having described the decision rules for p (φ) and n (φ) of firms with different productivities, I can proceed to study the total sales of firms as functions of their productivities. Total sales of a 23 In addition, this assumption about the distribution of productivities will allow the model to match the empirically observed distribution of sales of the firms. See Kortum (1997), Gabaix (1999), Eaton and Kortum (2002) and Eaton, Kortum, and Kramarz (2005) for justifications of using this distribution of productivities. 24 I assume that the parameters are such that φ b = L 1 α 1 σ > J µ 1 θ σ+1 1 θ (σ 1) β. 18
firm with productivity φ are given by n (φ) L {z } extensive margin ³ σ σ 1 1 σ w φ w P 1 σ {z 1 η } intensive margin For the case where β> 1, figure (3) graphs the probability n that a consumer is reached by the firm as a function of its productivity φ. Figure (4) plots the intensive margin of sales as a function of productivity. The total sales are the product of the two. Therefore, total sales in the model with β> 1 (endogenous market access costs case) and in the one with β 1, as in Melitz (2003), look different. Observe that in the economy with endogenous market access costs there exist firms with total sales close to zero,whereas this does not occur in the Melitz (2003) economy. In the economy with endogenous market access costs, low productivity firms not only have small sales per consumer but also sell to a small number of consumers, which could be arbitrarily close to zero as in figure (3). Another thing that is worth noticing about these figures is that high productivity firms choose n (φ) close to one. Thus, the distribution of sales of large firms inherits the Pareto distribution of productivities as in Chaney (2006). The particular pattern has been reported by Axtell (2001) for the distribution of U.S. firms sales. The interaction of the extensive margin of consumers and the intensive margin of sales per consumer can also be observed in these pictures.. Even though the intensive margin of sales increases in φ with an elasticity of (σ 1), the extensive margin of consumers increases much faster in φ for low n (φ). 2.2 Multi-country model The above completes the analysis of the one country model. This section incorporates the mechanism of endogenous market access into a multi-country environment and analyzes the properties of this version of the model. 19
2.2.1 Environment Consumer There exist j =1,..., N countries. Goods are produced using labor. Country j has population of mass L j and there is a mass of J j goods that can be potentially produced from that country. Each household has one unit of labor and earns labor income w j and profit flows π j. The problem of the consumer is the same as before except that the bundle of goods each consumer considers, Ω, contains imported goods as well domestic ones. Therefore, the effective price index for country j will now be Pj 1 σ = X b θ Z + i J i i φ θ (p (φ)) 1 σ n (φ) µ (φ) dφ, 0 where p (φ) is the price that a firm with productivity φ from source country i charges in country j, n (φ) represents the probability that a consumer from country j has access to the good of a firm from country i having productivity φ and µ (φ) is the probability that a firm from country i has productivity φ conditional on selling in j. Finally, firms from source country i that have drawn φ below the productivity threshold φ choose not to sell to country j. The demand for each good from each consumer is given by x j (φ) = (p (φ)) σ (w j + π j ). P 1 σ j Total demand for a firm with productivity φ from source country i selling in country j is given by where η = σ 1 θσ is the profit share.25 n (φ) L jw j (p (φ)) σ 1 η Pj 1 σ, Firm I assume that firms wanting to export must make an irreversible investment in building a distribution/servicing network. Evidence for the exact nature of these startup costs is provided by Keesing (1983) and Roberts and Tybout (1997b). The authors quote a series of startup costs reported from direct interviews of managers of exporting firms. These costs, usually modeled as fixed costs of exporting (see, for example, Melitz (2003) among others), are associated in many 25 In appendix B, I show that the profit share is constant and equal to η = σ 1 θσ. 20
ways to costs of marketing the good to foreign consumers as the data on interviews reported in Roberts and Tybout (1997b) indicate: firms must research the foreign market by identifying and contacting the potential consumers of the good. They must then develop new goods or adapt their products to foreign consumers tastes. Finally, the firms must set up direct or indirect distribution channels to make the good available to the foreign consumers and inform them about the existence of the good. Departing from other trade models, I assume that the cost of building a distribution network is an increasing function of the total number of consumers who have access to it, n (φ) L j. Thus, with a similar reasoning as in the one country case, the total units of advertisement signals used for this investment are S = Lα j 1 (1 n (φ)) β For simplicity, I assume that the parameters β and governing the market access technology are the same for all countries. In addition, I do not model any other uncertainty concerning the export markets. β Foreign labor is oftentimes employed in order to undertake startup investment, and startup costs are oftentimes paid in terms of foreign wages (see Keesing (1983) and Roberts and Tybout (1997b)). For example, creating distribution channels in foreign markets may require hiring foreign labor for advertising purposes. However, there is still substantial evidence of startup labor costs that are paid in terms of the exporters country s wage. I choose to combine this evidence and consider a general case where the startup cost of each firm is denominated both in foreign and domestic wages. I, therefore, make the following assumption: Assumption 2: The production of advertisements requires a bundle of labor services from source country i and destination country j:. S = l γ j l1 γ i, 0 <γ<1. Iwillestimateγ using trade data. Therefore, the total cost of a firm from source country i to reach a consumer from country j with population L j with a probability n (φ) is given by the 21
following expression: 26 w γ L α j w1 γ j i 1 (1 n (φ)) β β. I also assume that there exist per unit export costs modeled in the standard iceberg formulation. This implies that, for a firm operating in country i and selling to country j, τ > 1 units of a good must be shipped in order for one unit of the good to arrive at the export destination. For firms from country i that sell in country i, I assume that τ ii =1. 27 Given the above, each firm makes a different decision on selling to each one of the markets. The problem that a firm with productivity φ from source country i solves when considering whether to sell in market j is π (φ) = max (φ) L jw j (p (φ)) 1 σ n (φ),p (φ) 1 η Pj 1 σ w γ L α j w1 γ j 1 (1 n (φ)) β i β s.t. n (φ) [0, 1] n (φ) w jl j 1 η τ (p (φ)) σ w i φ P 1 σ j Total profits of a particular firm are the summation of the profits from exporting activities in all the j =1,...,N countries (or a subset thereof). The FOCs for the firm in the multi-country model are given by p (φ) : n (φ) : σ w i τ, σ 1 φ 1 n (φ) =1 n (φ) =0 L1 α w 1 γ j j 1 η ( σ σ 1 τ w i φ w 1 γ P i j 1 σ ) 1 σ σ 1 if φ>φ otherwise. 26 Iredefine per unit advertisment cost 1 to incorporate an extra term γγ (1 γ) 1 γ. This term is related to the wage cost of the bundle of labor services. 27 Ifurtherassumeτ iv τ iv τ vj (i, v, j) to exclude the possibility of transportation arbitrage. 22
When compared to the corresponding equations from the one country model, it can be seen that relationships in the multi-country case are adjusted for the per unit cost of trade τ. 2.2.2 Equilibrium analysis The productivity of the firms is drawn from a Pareto distribution with shape parameter θ. However, I allow for the possibility that different countries have different technologies, and thus, the productivity distribution of country i is defined over [b i, + ) i 1,.., N. More technologically advanced countries have higher b i.thecdfisg(φ φ) =1 bθ i, and I assume that θ>σ 1, φ θ which ensures that the distribution has a finite mean. I denote by µ (φ) the probability of a firm from source country i selling in country j and having productivity φ. Of course this probability is conditional on φ φ, whereφ was defined above. Thus, µ (φ) is given by µ (φ) = g(φ) 1 G(φ ) if φ φ 0 otherwise. An equilibrium is defined in a way similar to the one country case. What is different here is that for each country i there exist j =1,..., N cutoffs φ determining the minimum productivity of the firms from country i sellingtocountryj. In addition, trade balance requires that condition (18) below holds (see appendix B), which imposes restrictions on the relative wages of the countries (where λ is the fraction of spending by country j on goods from country i). Using the FOC for the firm, the price index and the labor market clearing condition, I can characterize the equilibrium by the following set of equations: 28 28 See Eaton and Kortum (2005) for an in-depth analysis of the derivation of the labor market equilibrium in models with heterogeneous firms. 23
φ σ 1 = (P j ) θ = 1 L 1 α j w 1 γ j ( σ σ 1 τ w i) 1 σ P 1 η w 1 γ σ j σ 1 i µ µ w i L i = (1 η) L 1 α j w 1 γ j 1 η σ θ θ θ σ+1 θ (σ 1) β NX j=1 λ w j L j 1 η L 1 α j w 1 γ j σ 1 η σ 1 NP i=1 J i b θ i w1 γ i θ σ 1 1 σ σ ³ (τ w i ) 1 σ w 1 γ i θ σ 1 i, j 1,..., N, (16) j 1,..., N, (17) i 1,..., N. (18) Note also that G Φ φ = b θ. The number of firms from source country i selling in (φ ) θ market j is M = J i φ θ. The above expressions allow me to solve for the sales of a firm with productivity φ from source country i selling to country j: 29 q (φ) =L α j w γ j w1 γ i φ b θ i à µ σ 1 µ σ φ φ φ (σ 1) β!,φ φ. (19) Shutting down the endogenous responses to the size of the market by setting α =0and γ =0 and taking β 1 + gives the following: µ σ 1 σ φ q (φ) =w i φ,φ φ. This corresponds to the case of Melitz (2003) and Chaney (2006) with fixed market access costs (having 1 being the corresponding fixed cost of export). Observe that in the Melitz (2003) and Chaney (2006) case, sales for the firms with φ = φ begin from a threshold w i σ andthenincreasewithfirms productivity. In the fixed market access 29 Similarly to the one country case, we have to choose the parameters such that b i min j φ. 24
cost economy, even firms with very low productivities sell to all the consumers. Thus, their sales are nontrivial. This is not in accordance with trade data. EKK05 report that 10% of the French firms selling in a country in 1986 export goods worth on average $1,161 and that the French exports are characterized by many exporters exporting very small amounts. The model with endogenous market access incorporates this stylized fact by combining the extensive margin of consumers with the intensive margin of sales. In this model, firms with low productivity sell small amounts to only a small number of consumers. The result is that for a firm with φ close to φ total sales are close to zero. The two extra dimensions that the endogenous market access costs add, endogenous responses to market size and the extensive margin of consumers, will be of critical importance in matching international trade data, as I show below. 3 Testing the Predictions of the Model By incorporating the production structure proposed by Melitz (2003), the model with endogenous market access costs retains the main theoretical predictions of this class of models. Thus, it can replicate the main facts related to the sales and average productivity of the exporting firms. 30 The model is also able to replicate facts about reallocation of production towards more productive firms due to reduction in costs of trade. 31 In addition, I gauge the ability of the endogenous market access costs model to capture the export behavior of French firms (as reported by EKK04 and EKK05) and predict trade flows in the event of a trade liberalization episode. The model is particularly simple to calibrate. The appropriately parameterized endogenous market access costs model is able to endogenously replicate the responses of average exports of firms to market size as reported in the French data by EKK04. In addition, EKK05 report that the simple monopolistic competition model with fixed costs (as in Melitz (2003) and Chaney (2006)) can very closely match the empirical relationship between average sales in France of 30 Exporters are only a small fraction of the firms, but they tend to be more productive and to sell more on average domestically. In general, export sales constitute only a small part of the total sales of the exporters. 31 See Melitz (2003) and Bernard, Eaton, Jensen, and Kortum (2003). For empirical facts related to reallocation of market shares due to trade, see Bernard and Jensen (2004a) and Pavcnik (2002). 25
French firmsandthenumberofdestinationstheyserve. IusesimilarvaluesasEKK05to calibrate the rest of the parameters in the endogenous market access costs model. Using the parameterized model, I can test the new theoretical predictions that the endogenous market access cost model generates. To verify the first set of predictions related to the distribution of sales of firms,icomparethepredictionsofthemodeltothestaticdataofekk05onthe distribution of sales of French exporters in 1986. I also verify the set of predictions related to trade liberalization using export data from the US-Mexico trade liberalization case. To do the latter, I use the methodology developed by Kehoe and Ruhl (2003). 3.1 Static predictions 3.1.1 Export sales, firm entry and market size The use of the Pareto distribution allows to analytically derive expressions for total export sales of country i to j: T = λ L j w j 1 η, where λ, the fraction of spending by country j on goods from country i, can be written as a function of cost parameters: trade barriers τ, the measure of potential entrants J i, the technology b i,andthewagesw i of the countries. λ = (τ ) θ J i (b i ) θ w (1 γ)(1 σ 1) θ i. NP (τ ) θ J i (b i ) θ w (1 γ) (1 σ 1) θ θ i i=1 θ Alternatively, I can express export sales as the number of exporting firms times average export sales per firm: Ã! T = M L α j w γ σθ 1 j w1 γ i θ (σ 1) 1 θ (σ 1) β {z } average sales per firm. 26
Combining the two expressions above, I obtain: M λ = w1 γ j L 1 α j 1 η µ w 1 γ σθ i 1 1 1 θ (σ 1) θ (σ 1) β. (20) Using the last expression, I can estimate γ and α using trade data reported in EKK04, assuming for simplicity that γ = α. According to the estimation from French data reported by EKK04, the elasticity of the number of exporters divided by French exports market share to the changesinthesizeofthemarketis0.62.thisimpliesthat γ = α =0.38. The model with endogenous market access costs captures in a parsimonious way the stylized fact reported by EKK04: when normalized by French market share, the number of French firms selling in a market increases systematically with market size but with an elasticity less than one. 3.1.2 Sales and export destinations Using the data on French firms, EKK05 report a striking regularity relating the sales of French firmsinfranceandthenumberofmarketstheexportersserve: therelationshipbetweenaverage sales of French firms in France and the minimum number of destinations they serve is approximately linear in logarithms. EKK05 show that the simple monopolistic competition model with fixed market access costs predicts this loglinearity with a slope (σ 1) /θ. The model with endogenous market access costs predicts the same relationship for the left tail of the relationship, since the most productive firms not only sell to the least popular locations but also choose to reach almost all the consumers in France. To characterize the relationship between sales in France and number of destinations French firms serve, I will first construct the distribution of sales and then use this to derive the relationship between average sales in a country and minimum number of destinations that the firms serve. I will derive expressions for the cases of fixed and endogenous market access costs, which can be solved analytically. In doing so, the analysis is similar to the one of EKK05 for the 27
monopolistic competition model with fixed market access costs. Idefine the smallest sales firms from country i selling in country j as x min. Sales of a firm with productivity φ from country i selling in country j are given by equation (19). Notice that in the case of Melitz (2003) and Chaney (2006), namely when β 1 +,the minimum sales in country j that correspond to firms with productivity φ = φ are given by x min =(w j ) 1 γ (L j ) α (w i ) γ σ. However, in the case of endogenous market access, when β> 1, sales for firms with productivity φ = φ are x min =0. The distribution of sales Pr X<x X x min = F (x) isderivedinappendixcandisthe solution to the following equation: x =(w j ) 1 γ (L j ) α (w i ) γ σ ³(1 F (x)) σ 1 θ (1 F (x)) σ 1 θ β, x x min. Notice that we can solve analytically for the case when β 1 and β =0: Ã x β 1: F (x) =1 (w j ) 1 γ (L j ) α (w i) γ σ Ã x β = 0 : F (x) =1 +1 (w j ) 1 γ (L j ) α (w i) γ σ! θ σ 1! θ σ 1, (21). (22) Denote by M (k) the measure of firms from source country i selling in j and that also sell in at least k less popular markets in terms of how many firms from country i sell there than j. In the model, there is a strict hierarchy of destinations depending on the ordering of φ s for different j. Thus,M (k) is decreasing in k. Using the relationships (21) and (22) in the model, the mean sales in market j of firms from i selling also to k less popular destinations are given by (see appendix D) 28
β 1: x (k) β = 0 : x (k) cj = (w j) 1 γ (L j ) α (wc) ³ 1 1 θ γ σ =(w j ) 1 γ (L j ) α (w c ) γ σ cj à M (k) M (0)! 1 θ µ M (k) 1 θ M (0) ³ 1 1 1 θ,, where θ = θ. σ 1 For β 1 and β =0, the model delivers a precise relationship between the average sales in any given market and the number of less popular destinations that firms sell in. 32 Setting j to be France, I compare the results of a model with, first, fixed market access costs and with, second, endogenous market access costs to the empirical counterpart reported by EKK05 for the French data. Figure (6) plots this relationship for various values of the parameter β. The relationship suggest a value of θ =1.5, whichistheslopeoftherelationshipinthedatainthelefttail. All the models deliver the same relationship in the left tail as explained above. The model with endogenous market access costs delivers a better fit to the data for average sales in France and number of less popular destinations served in the right tail: firms selling to only a few destinations are the least productive ones. These firms also choose to reach only a few consumers in France, that is, n (φ) is close to 0. When one accounts for these firms, the average sales in France become much smaller as a function of the number of destination served, which generates the nonlinearity in the right tail of the relationship that is also observed in the French data. The results of the above analysis suggest a β closer to 0 rather than to 1. 3.1.3 Distribution of sales The distribution of sales can be derived analytically for the cases β 1and β =0.Infigure (7), I plot the distribution of sales for β 1 and β =0,1, as well as the distribution of export sales to Portugal from French firms using data from EKK05. In the simple case of the monopolistic 32 I can solve analytically only for β 1 and β =0. The rest of the results are numerically computed. 29
competition model with fixed market access costs, the distribution of sales in any market is given by (21). Figure (7) shows that this relationship is linear in logarithms with a slope of 1/ θ. The distribution of sales for the endogenous market access costs when β =0is given by (22). The endogenous market access cost model matches the distribution very closely while the fixed market access costs model falls short of predicting the nonlinearity that the distribution of sales exhibits. The reason is simply the mechanism illustrated in section 2: firms with lower productivity not only sell less per consumer but also to less consumers as well. Therefore, the decrease in their sales as a function of their productivities is faster than what the simple monopolistic competition model with fixed market access costs and Pareto distribution of productivities would predict. In addition, because of the shape of the market access cost function, the number of consumers reached decreases substantially for the small firms generating the large nonlinearity in the right tail of the distribution, which is also observed in the data. An additional fact emerging from the analysis of figure (7) is that the variance of the distribution of sales is governed by the parameter β. Ahigherβ implies that the cost of reaching new consumers is increasing faster, and, thus, firms with smaller productivities find it profitable to reach less consumers, while more productive firms already selling to most of the consumers choose to change only slightly their consumer base. This increases the gap between large and small firms and generates the larger variance in the distribution of sales observed in the graph. EKK05 report that the distribution of export sales of French firms has higher variance the higher the total exports of French firms to the country. This feature of the data is still puzzling. Even though quantitatively it can be replicated from the endogenous market access costs model by adapting different β s for different markets, the mechanisms of the model do not provide any explanation of why this is the case. Finally, EKK05 report that the French data are characterized by the existence of many small French exporters selling to the foreign markets. The fixed (exogenous) market access costs model by assuming that firms sell to all the consumers of a country falls short in replicating this fact. The endogenous market access cost by allowing for the extensive margin of consumers in the sales of the firm is able to replicate this fact related to the behavior of French exporters. The reason is that exporters with productivities slightly above the threshold φ sell to only a few consumers in country j and, thus, their total sales are trivial. This property of the endogenous market access cost model will prove essential in explaining the 30
pattern of trade flows in the event of a trade liberalization. 3.2 The new consumers margin in international trade Trade liberalization episodes have been characterized by asymmetric increases in trade flows across different goods (Kehoe (2005)). Kehoe and Ruhl (2003) study bilateral trade patterns of countries involved in significant trade liberalizations using detailed data on the value of trade flows by commodity. They find that goods that were traded the least before the liberalization account for a disproportionate share in the trade following the liberalization: the export flows of goods that were accounting for less than 10% of total trade flows may account for as much as 40% of trade flows following a liberalization episode. Existing trade models account for this fact by relying on the introduction of newly traded goods following trade liberalization episodes. The model of endogenous market access costs provides additional insights into the effects of trade liberalization on trade flows. In this model, the rate of growth of the trade flows of the least traded goods that were already traded before the trade liberalization (trade flows>0) is much higher than the growth rates of the most traded goods. This comes in sharp contrast to the predictions of the existing models of trade that build on the Dixit-Stiglitz specification. These models predict that the response of trade flows to international price differences depends only on the elasticity of substitution of the good. In the model with endogenous market access costs, the marginal cost of searching additional consumers is a function of the consumers already reached. This marginal cost increases slowly for firms with a small consumer base preceding the trade liberalization. Therefore, even a small decrease in trade costs that brings about a small increase in the marginal revenue per consumer will make it desirable for firms with a small consumer base to search for many new potential consumers for their goods. The total percentage increase in trade flows of a firm,whichisthesumofthepercentageincreaseintheintensivemarginof sales plus the percentage increase in the new consumers margin, will be substantial for firms with small trade flows preceding the liberalization. 33 33 Diminishing returns to scale in advertising outlays are well established in the economic literature (see Sutton (1991) p. 51,100 and the references quoted there). This convexity that the market access cost exhibits, which in turn generates the assymetric response of firms with different sizes to trade liberalization, could potentially be reproduced through a diminishing returns to scale production func- 31
The following proposition formalizes the above argument: Proposition 2 Assume that all countries are symmetric with τ ii =1 i and τ = τ iυ > 1 j, υ, s.t. j, υ6= i. Define trade liberalization as: τ 0 ii =1 i, andτ 0 i 6= j such that τ >τ 0 1 i 6= j and τ 0 = τ 0 iυ j, υ s.t. j, υ 6= i. Then: The elasticity of trade flows of a firm with respect to τ, i 6= j is higher the lower the productivity φ of the firm for all φ s.t. φ φ. Proof. Normalize w j =1 j =1,...,N. Itcanbeshownthatthenewtariff rate τ 0 i 6= j, given τ 0 ii =1, results in a decrease of φ i 6= j. The exact elasticity depends on the model s parameters and initial level of tariff rates τ i, j. It is, therefore, sufficient to concentrate on the result of a decrease in φ to trade flows q (φ) and interpret this as a trade liberalization. Rewriting (19) and using the normalization w i =1: q (φ) = σ 1 µ L α σ φ j φ {z } µ φ (σ 1) 1,φ φ φ, i6= j. {z } intensive margin of sales extensive margin of sales The objective is to compute the elasticity of trade flows with respect to a change in φ, ζ= ln q (φ). I will show that this elasticity is higher for low initial productivity φ. Notice that: ln φ ζ = (σ 1) = (σ 1) {z } intens. margin el. (σ 1) Ã 1 ³ φ (σ 1) 1 1 φ φ ³ φ φ + σ 1 β +1 (σ 1) ³ φ φ! φ ln φ 1 σ 1 1 {z } new consumers margin elasticity Notice finally that ζ = ζ (φ) and is decreasing in φ and, thus, decreasing in initial export sales. = tion for the one country case. However, the market access technology has diminishing returns to scale per country, an assumption which would be clearly unrealistic for the diminishing returns to scale in production case. 32
Finally, note that as β 1 +, ζ (σ 1). 34 To test the predictions of my model in the case of trade liberalization, I measure the increase in trade flows for the already traded goods following an analysis similar to Kehoe and Ruhl (2003). Using data from the OECD International Trade by Commodity database (see appendix E for details), I divide the traded goods (trade flows>0) in 1990 in 10 categories with equal number of goods. These categories include goods in a decreasing order of tradability: category 1 includes the most traded goods while category 10 the least traded goods. The top of figure (8) graphs the natural logarithm of export sales ratio between 1990 and 1999 for each of these categories. A striking pattern emerges: the percentage increase of trade flows is higher the least tradable the good was in 1990. Even though alternative explanations can be offered for these patterns, such as asymmetric tariff changes or asymmetric entrance of new firms in the least traded goods categories, the model with endogenous market access costs provides a simple and straightforward explanation: sales per consumer increase with the same elasticity for all firms, but the number of new consumers of the goods that were least traded goods increases faster. This is because firms with a small consumer base have smaller search costs of finding new consumers. A last point that is worth noticing is that the contribution to total growth of export sales is still higher for the categories with the most traded goods, as can be seen in the bottom of figure (8). Both the model of endogenous market access costs and fixed market access costs are consistent with this pattern (ζq (φ) is increasing with φ). Kehoe (2005), in an evaluation of models of NAFTA based on the Dixit-Stiglitz specification, arrives to the conclusion that no plausible parametrization can make these models match what actually happened in North America. With the simple inclusion of the extensive margin of consumers in combination with the Dixit-Stiglitz specification, the model of endogenous market access costs has the potential to replicate the main patterns of the increase in trade flows after trade liberalization, while keeping the analysis in an analytically tractable framework. 34 The application of de l Hospital s rule is required for this result. 33
4 Conclusion In this paper, I reconcile theory and empirical findings on fixedcostsofexportswiththesimple incorporation of endogenous market access costs in a model of monopolistic competition. I show that the endogenous market access costs model nests in a parsimonious way the existing models of monopolistic competition with fixed (exogenous) market access costs, while remaining highly analytically tractable. Therefore, the model retains the main desirable properties of the existing models of monopolistic competition. The model with endogenous market access costs has some important departures from the models of monopolistic competition with fixed market access costs. In particular, the endogenous market access model is very successful in matching the stylized facts related to the export behavior of French firms as reported by Eaton, Kortum, and Kramarz (2004) and Eaton, Kortum, and Kramarz (2005). In addition, the paper introduces the notion of the extensive margin of consumers in the sales of the firms. This extension is crucial in the prediction of the growth rate of trade flows in the event of trade liberalization: firms with small export sales have lower costs for finding new consumers, and, thus, their price elasticity of trade flows is higher in the event of trade liberalization. I have shown that the endogenous market access costs model that features the extensive margin of consumers in combination with the Dixit-Stiglitz specification of preferences has the potential to more accurately predict the changing patterns of trade flows after trade liberalization episodes. Future research will quantitatively assess the importance of this addition in improving the predictions of models studying trade liberalization episodes. 34
References Alvarez, F., and R. E. Lucas (2005): General Equilibrium Analysis of the Eaton-Kortum Model of International Trade, NBER Working Paper, 11764. Aw, B. Y., S. Chung, and M. J. Roberts (2000): Productivity and Turnover in the Export Market: Micro Level Evidence from the Republic of Korea Ad Taiwan (China), The World Bank Economic Review, 14(1), 65 90. Axtell, R. L. (2001): Zipf Distribution of U.S. Firm Sizes, Science, 293(5536), 1818 1820. Baldwin, R. (1989): Sunk-Cost Hysteresis, NBER Working Paper, 2911. Baldwin, R., and P. Krugman (1989): Persistent Trade Effects of Large Exchange Rate Shocks, The Quarterly Journal of Economics, 104(4), 635 654. Bernard, A. B., J. Eaton, B. Jensen, and S. Kortum (2003): Plants and Productivity in International Trade, The American Economic Review, 93(4), 1268 1290. Bernard, A. B., and J. B. Jensen (1995): Exporters, Jobs, and Wages in U.S. Manufucturing: 1976-1987, Brooking Papers: Microeconomics, pp. 67 119. (2004a): Exporting and Productivity in the USA, Oxford Review of Economic Policy, 20(3), 343 357. (2004b): Why Some Firms Export, The Review of Economics and Statistics, 86(2), 561 569. Bernard, A. B., J. B. Jensen, and P. K. Schott (2003): Falling Trade Costs, Heterogeneous Firms and Industry Dynamics, NBER Working Paper, 9639. Butters, G. (1977): Equilibrium Distributions of Sales and Advertising Prices, The Review of Economic Studies, 44(3), 465 491. Campbell, J. R., and H. A. Hopenhayn (2005): Market Size Matters, The Journal of Industrial Economics, 1(03), 1 25. 35
Chaney, T. (2006): Distorted Gravity: Heterogeneous Firms, Market Structure and the Geography of International Trade, Working Paper, University of Chicago. Clerides, S. K., S. Lach, and J. R. Tybout (1998): Is Learning by Exporting Important? Micro-Dynamic Evidence from Colombia, Mexico, and Morocco, The Quarterly Journal of Economics, pp. 903 947. Das,S.,M.J.Roberts,and J. R. Tybout (2005): Market Entry Costs, Producer Heterogeneity, and Export Dynamics, NBER Working Paper, 8629. Dinlersoz, E. M., and M. Yorukoglu (2006): Informative Advertising by Heterogeneous Firms, Working Paper, University of Houston. Dixit, A. (1989): Entry and Exit Decisions Under Uncertainty, Journal of Political Economy, 97(3), 630 638. Eaton, J., and S. Kortum (2002): Technology, Geography and Trade, Econometrica, 70(5), 1741 1779. (2005): Technology in the Global Economy: A Framework for Quantitative Analysis. Manuscript, University of Minnesota. Eaton, J., S. Kortum, and F. Kramarz (2004): Dissecting Trade: Firms, Industries, and Export Destinations, The American Economic Review, 94(2), 150 154. (2005): An Anatomy of International Trade: Evidence from French Firms, Working Paper, University of Minnesota. Gabaix, X. (1999): Zipf s Law for Cities: An Explanation, The Quarterly Journal of Economics, 114(3), 739 767. Helpman, E., M. J. Melitz, and S. R. Yeaple (2004): Export Versus FDI with Heterogeneous Firms, The American Economic Review, 94(1), 300 316. Keesing, D. B. (1983): Linking Up to Distant Markets: South to North Exports of Manufactured Consumer Goods, The American Economic Review, 73(2), 338 342. 36
Kehoe, T. J. (2005): An Evaluation of the Performance of Applied General Equilibrium Models of the Impact of NAFTA, in Frontiers in Applied General Equilibrium Modeling, ed. by T. J. Kehoe, T. Srinivasan, and J. Whalley, pp. 341 377. Cambridge University Press, New York. Kehoe, T. J., and K. J. Ruhl (2003): How Important is the New Goods Margin in International Trade, Federal Reserve Bank of Minneapolis, Staff Report, 324. Kortum, S. (1997): Research, Patenting, and Technological Change, Econometrica, 65(6), 1389 1419. Melitz, M. J. (2003): The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity, Econometrica, 71(6), 1695 1725. Pavcnik, N. (2002): Trade Liberalization, Exit, and Productivity Improvements: Evidence from Chilean Plants, TheReviewofEconomicStudies, 69(1), 245 276. Roberts, M. J., and J. R. Tybout (1997a): The Decision to Export in Colombia: An Empirical Model of Entry with Sunk Costs, The American Economic Review, 87(4), 545 564. (1997b): What Makes Exports Boom? The World Bank, Washington, D.C. Stegeman, M. (1991): Advertising in Competitive Markets, The American Economic Review, 81(1), 210 223. Sutton, J. (1991): Sunk Costs and Market Structure. The MIT Press, Cambridge, Massachusetts. Tybout, J. R. (2001): Plant -and Firm- Level Evidence on "New" Trade Theories, NBER Working Paper, 8418. 37
Appendix Appendix A: the maximization problem of the firm The maximization problem of the firm is wl (p (φ)) 1 σ max n (φ) n(φ),p(φ) 1 η P 1 σ n (φ) wl Lp (φ) σ w w Lα 1 (1 n (φ)) β 1 η P 1 σ φ β (23) s.t. n (φ) [0, 1] Assume that β> 1. Notice that the function 1 (1 n(φ)) β inherits an Inada condition when n (φ) 1 since β β 1 (1 n(φ)) lim =+. Therefore, the constraint n (φ) 1 never binds, and I need only n(φ) 1 β consider the restriction n (φ) 0. Rewriting the problem in a Langrangian formulation with the additional constraint that n (φ) 0: L = n (φ) wl (p (φ)) 1 σ 1 η P 1 σ TheFOCsoftheLangrangiangive FOC with respect to p (φ): n (φ) wl p (φ) σ 1 η P 1 σ φ w 1 (1 n (φ)) β wlα β + λn (φ). (1 σ) n (φ) wl (p (φ)) σ 1 η P 1 σ FOC with respect to n (φ) : L p(φ) = 0 = + σn (φ) wl p (φ) σ 1 1 η P 1 σ φ p (φ) = = 0 = (24) σ w σ 1 φ, (25) wl (p (φ)) 1 σ 1 η P 1 σ and λn (φ) =0,λ 0. wl p (φ) σ w 1 η P 1 σ φ wlα L n(φ) = 0 = (26) 1 + λ = 0 (27) (1 n (φ)) 38
Using equation (25), (27) becomes ³ 1 σ σ w σ 1 φ 1 (1 η) P 1 σ σ Lα 1 1 + λ =0. (1 n (φ)) Notice that there exists φ, s.t. φ φ this equation holds only for some λ>0 = n (φ) =0(the constraint n (φ) 0 is binding). However, φ>φ the constraint is not binding and the corresponding n (φ) (0, 1) is actually the solution to the above equation for λ =0. Thus, for φ φ,n(φ) =0. For all φ>φ, condition (28) will determine the optimal n (φ) when β> 1. ³ 1 σ σ w σ 1 φ 1 (1 η) P 1 σ σ {z } marginal revenue per consumer 1 (1 n (φ)) {z } marginal cost per consumer = Lα 1 Now I check the second order conditions and derive sufficient conditions for this problem to have a unique solution for n (φ) [0, 1]. Evaluating the first and second principle submatrices of the Hessian matrix, (28) A = 2 h p 2 2 h n p 2 h p n 2 h n 2, results in the following derivations: notice that φ >φ n (φ) (0, 1) and 2 h p 2 2 h n 2 = σ (1 σ) n (φ) wl (p(φ)) σ 1 +( σ 1) σn (φ) wl p(φ) σ 2 < 0, 1 η P 1 σ 1 η P 1 σ φ =( β 1) w Lα 2 h = 2 h n p p n =(1 σ) wl 1 < 0 only if β> 1, (1 n(φ)) β+2 (p(φ)) σ + σ wl p(φ) σ 1 = 1 η P 1 σ 1 η P 1 σ φ ( σ σ 1 w φ ) σ ( σ σ 1 w φ ) σ 1 =(1 σ) wl + σ wl =0. 1 η P 1 σ 1 η P 1 σ φ Therefore, the principle submatrices satisfy A 1 < 0, A 2 > 0. 39
Since the second order condition holds, the unique pair (n (φ),p(φ)) that solves the equations (25) and (28) is the unique maximum of the firm s optimization problem (given the effective price index P ) φ >φ. Therefore, the above formulation gives n (φ) as the solution of equation (28) φ >φ. For φ φ, n (φ) =0. Finally, p (φ) = σ w. σ 1 φ Appendix B: the share of profits In this appendix, I will show that the share of profits out of total income is constant and equal to η = σ 1 θσ.35 To incorporate the possibility that profit share is not constant, I consider the total income-expenditure of country j, denoted as X j, that consists of labor and profit income. Profits of a firm from source country i selling in country j and having productivity φ are π (φ) = max (p (φ)) 1 σ τ (p (φ)) σ w i (φ) X j n (φ),p (φ) Pj 1 σ n (φ) X j Pj 1 σ φ w γ L α j w1 γ j 1 (1 n (φ)) β i. β s.t. n (φ) [0, 1] FOCs for this problem give p (φ) : p (φ) = σ τ w i σ 1 φ 1 n (φ) =1 n (φ) : L1 α w 1 γ j j ( σ 1 σ 1 η n (φ) =0 τ w i φ w 1 γ P i j 1 σ ) 1 σ σ 1 if φ>φ otherwise. 35 For more details for the case of fixed sunk costs where a similar relationship holds, see Eaton and Kortum (2005). 40
Thus, in order for n (φ) > 0, itmustbethecasethatφ>φ,where (φ ) σ 1 = P σ 1 j = L α j w γ j ( X σ σ 1 τ w i) 1 σ P σ 1 j j w 1 γ σ i 1 L α j w γ j ( X σ σ 1 τ w i) 1 σ (φ ) σ 1 j w 1 γ σ i,. Sales in j for a firm with productivity φ from country i are q (φ) = n (φ) X j (p (φ)) 1 σ q (φ) = L α j w γ j w1 γ i Pj 1 σ σ = µ ³ φ φ σ 1 ³ φ φ (σ 1) β if φ>φ 0 otherwise. Total sales Z + q = M (w j ) 1 γ (L j ) α (w i ) γ σ φσ 1 φ φ σ 1 = M L α j w γ σθ j w1 γ i (θ (σ 1)) (σ 1) à φ σ 1 φ ³ θ (σ 1) β σ 1! β θ θ φ dφ = φ θ+1 Notice that total variable profits from production are q σ = M L α j w γ j w1 γ i = M L α j w γ j w1 γ i à θ 1 θ (σ 1) 1 θ (σ 1) β (σ 1) θ ³ (θ (σ 1)) θ (σ 1) β! =, 41
and labor income from production is (σ 1)q. Total market access costs are σ m = M Z + φ m = M w γ L α j w1 γ j i w γ L α j w1 γ j i 1 (1 n (φ)) β (σ 1) β ³ θ (σ 1) β θ φ θ dφ = φ θ+1 (θ (σ 1)) = q θσ. Total labor income of country i from the bilateral trade relationship with country j equals income from production of goods (using the production function y = φl) and market access costs w L = (σ 1) q σ +(1 γ) q (θ (σ 1)) θσ + γq ji (θ (σ 1)) θσ. Summing over all j and using a) the equality of income and expenditure N P j=1 q = X i, b) the equality of total labor income of country i and total labor income generated in order to P produce and sell the good to all the N countries w i L i = N w L P c) and the trade balance condition N P q = N q ji, we have that where η = σ 1 θσ is the profit share. j=1 j=1 X i = w il i (1 η), Finally, notice that trade balance implies w il i (1 η) = N P j=1 j=1 λ w j L j (1 η). Appendix C: sales distribution I consider the case of sales of firms from country i in market j. I proceed to represent the results as in EKK04 and EKK05 in order to compare the predictions of the model with the data they report. Define by x min the sales for the firm with threshold productivity φ. 42
The objective is to derive the distribution of sales denoted by F (x). Wehavethat Notice the following: x = q (φ) = x = (w j ) 1 γ (L j ) α (w i ) γ σ (φ)σ 1 φ σ 1 Ã (φ) σ 1 φ σ 1! β. (29) Pr X x X x min However, this can also be written as Pr [Φ φ] = Pr Φ φ = b θ (φ) θ = b θ (φ ) θ φ θ. (φ) θ which means I can solve Pr X x X x min =1 Pr X<x X x min =1 F (x), 1 F (x) = φ θ. (30) (φ) θ Replacing (30) into (29) obtains x =(w j ) 1 γ (L j ) α (w i ) γ σ ³(1 F (x)) σ 1 θ (1 F (x)) σ 1 θ β, x x min. Recall that mean sales, as derived in the text, are given by q =(w j ) 1 γ (L j ) α (w i ) γ σ Ã! θ θ +1 σ θ θ (σ 1) β. Therefore, percentile sales over mean sales are x q = ³(1 F (x)) σ 1 θ µ (1 F (x)) σ 1 θ θ θ θ+1 σ θ (σ 1) β β. 43
For β 1 +, I can solve for the distribution of sales analytically à x F (x) =1 (w j ) 1 γ (L j ) α (w i) γ σ! θ σ 1. Therefore, when β 1, the sales distribution is Pareto with coefficient θ σ 1 as in EKK05 and Chaney (2006). However, the interesting cases emerge for β> 1. I can solve for the sales distribution for some cases analytically. For example, when β =0, à x F (x) =1 (w j ) 1 γ (L j ) α (w i) γ σ +1! θ σ 1. Appendix D: sales in a market and number of markets served I will express average sales in one market as a function of the total number of markets served. The purpose is to express the statistics of the model in a form corresponding to their data counterpart reported by EKK04 and EKK05 for French firms. In the model there is strict hierarchy of destinations depending on φ. Ahigherφ implies fewer firms selling in market j. However, this strict ordering is not observed in the data. In fact, as EKK05 report, looking at the top seven destinations, approximately 27% of the firms sell to a string of destinations that satisfies hierarchy. In a more general model, EKK05 match this feature of the data using taste and entry shocks. Here I am only interested in evaluating whether the mechanism of endogenous market access can deliver the main stylized facts observed in the data on exports and sales destinations. The probability that a firm selling in j also sells in k or more less popular markets is M (k) M (0) Using again the strict ordering of relationships, to sell in k markets or more, it must be the 44
case that in market i you sell x or more where x solves 1 F (x) = M (k) M (0) This means that to sell in at least k or more less popular markets sales in j must be at least. x (k) = à (k) M M (0)! σ 1 θ à M (k) M (0)! σ 1 θ β (w j ) 1 γ (L j ) α (w i ) γ σ. When β 1 or β =0, I can derive a precise relationship for the mean sales in market j from firms from country i selling also to k or more less popular destinations. This is accomplished by using the distribution of sales derived in appendix C: β 1: x (k) β = 0 : x (k) cj = (w j) 1 γ (L j ) α (wc) ³ 1 1 θ γ σ =(w j ) 1 γ (L j ) α (w c ) γ σ cj à M (k) M (0)! 1 θ µ M (k) 1 θ M (0) ³ 1 1 1 θ., Appendix E: data description I use data from the OECD International Trade by Commodity database (www.sourceoecd.org) on exports by commodity from Mexico to the US. 36 The data are recorded using the Harmonized System (HS) 1988 revision (rev. 1) at the finest level of detail (6 digit) and include 6873 different commodities. Data on HS rev. 1 are available from 1990-2000. I only include data from 1990 to 1999 (10 years) due to inconsistency of the imports of U.S. from Mexico reported by U.S. and the exports of Mexico to U.S. reported by Mexico, particularly for 2000 (note that the results do not change even if I include data for 2000). Also note that trade flows of the 6-digit level add 36 A similar pattern to the one I report for the Mexico-US case emerges for the Canada-Mexico trade liberalization episode. 45
up to aggregate trade flows from 1990-1995. From 1996, there is an average of 1%-2% of trade flowsthatarenotrecordedinthe6digittradeflows. The reason is that the HS was revised in 1996 (rev. 2) and the data on trade flows from 1996 onward were initially reported according to therev. 2andthentranslatedtotheHS1988(rev. 1). Goods that could not be categorized back in rev. 1 were discarded. Even though some of the trade flows are missing at the 6-digit level, there is no observable persistent inconsistency that could lead to a mistaken interpretation of the data. Grouping the goods I first look at the year 1990. I rank all the goods in terms of export sales. I distinguish between traded goods (trade flows>0) and nontraded goods (trade flows=0). I subsequently look at 1999. For the traded goods in 1990, I distinguish between the ones that are still traded (category 1_1) in 1999 and the ones that stopped being traded in 1999, which I designate as newly nontraded (category 1_0). Finally, I designate as newly traded goods (0_1) the goods that were nontraded in 1990 but are traded in 1999. I group the goods in (1_1) into ten categories, each with an equal number of goods. The categories include goods in a decreasing order of tradability in 1990 (e.g. category 1 contains the 10% most traded goods in 1990 while category 10 contains the 10% least traded ones). At the top of figure (8), I report the ratio of export sales in natural logarithms for each of the ten categories of the goods (1_1) between 1990 and 1999. Finally, in the last column of the top figure, I report a measure of the newly traded goods margin: the ratio of newly traded goods (0_1) to newly nontraded (1_0) exports. In the bottom figure, I report also the contribution of each category of goods to the increase in total export sales. In the last column of the bottom figure, I report the contribution of the difference of flows of newly traded goods (0_1) minus newly nontraded (1_0) exports in the total growth of trade flows. To avoid the possibility of regression to the mean, I also consider taking averages for the trade flows before 1994 and after 1994 for different sub periods instead of just considering the years 1990-1999. There were no substantial differences compared to the previously observed pattern. 46
Figure 1: Total market access cost under different β s Figure 2: Productivity and market access 47
Figure 3: Share of the consumers reached as a function of productivity Figure 4: Firm sales per consumer as a function of productivity 48
Figure 5: Sales per firm as a function of productivity 49
Figure 6: Average sales in France and number of firms selling to k or more markets 50
Figure 7: Distribution of sales under different β s 51
Figure 8: Growth of Mexican exports to U.S. from 1990-1999 by goods categorized by tradability 52