Import Competition and the Endogenous Response of Quality and Markup: Evidence from U.S. Import Data

Transcription

1 Preliminary Draft Import Competition and the Endogenous Response of Quality and Markup: Evidence from U.S. Import Data Hamed Atrianfar August 2018 Abstract I investigate the heterogeneity in response of countries to China s import competition after its accession to WTO. Standard models predict that in a given market, imports from rich countries are less affected by Chinese competition than imports from poor countries. But examining U.S. import data reveals that competition makes rich countries reduce their shipments to the U.S. more than poor countries. I develop a model of Ricardian trade that can rationalize this pattern. Countries are heterogeneous both in physical efficiency and quality capability. Firms can simultaneously adjust on both margins of quality and markup in response to import competition. Estimation results indicate that rich countries are more productive both in physical and quality production. Moreover, and in response to import competition, rich countries mainly upgrade quality while poor countries mainly reduce markup. Counterfactual experiment shows that as U.S. market gets bigger, it benefits from free trade with quality-capable countries more than those who are less capable. JEL: F12, F13, F14, F61, O31, O57. Keywords: Import Competition, Quality Upgrading, Markup reduction. I am grateful to my adviser Jonathan Eaton for his substantial guidance and support and to James Tybout and Stephen Yeaple for fruitful discussions. Department of Economics, Pennsylvania State University, hua129@psu.edu 1

2 1 Introduction How do firms respond to import competition? This is a key question that not only academic community is interested in but also policy makers are concerned about because it has direct consequences on the welfare of consumers. There are two broad but distinct strands in the literature that try to answer this question. The first one considers response on the price margin and argues that import competition leads to firms losing their market and this makes them reduce their markups; the effect which is called pro-competitive effect of trade. This fact not only has been theoretically rationalized with different market structures (see Melitz and Ottaviano (2008) for monopolistic competition and De Blas and Russ (2015) for Bertrand competition), but also verified empirically by many firm-level studies; see e.g. Levinsohn (1993), Krishna and Mitra (1998), Edmond et al. (2015), Brandt et al. (2017), Feenstra and Weinstein (2017), Hsu et al. (2017). The second strand investigates the impact of import competition on innovation activity of firms which in some papers interpreted as improving quality of output. Theoretical models on this margin of response stems from the pioneering work of Aghion et al. (2005) which predicts differential response of competition on the innovation activity based on the position of firm in technology ladder. Frontier firms have more incentive to innovate because they could escape the competition by innovating more ( escape-competition effect ). But the laggard firms would be discouraged to innovate since the competition reduces their post-innovation rent ( Schumpeterian effect ). In the context of international trade, there are bunch of papers which examine the effect of trade shocks either on general innovation activity, technological progress, etc. of firms (see e.g. Bertschek (1995), Bustos (2011), Hombert and Matray (2015), Bloom et al. (2016), Autor et al. (2017), Aghion et al. (2018)) or more specifically on quality upgrading behavior of firms (see e.g. Verhoogen (2008), Amiti and Khandelwal (2013), Fernandes and Paunov (2013), Smeets et al. (2016), Medina (2017)). Although the literature has elaborated on each margins of response to import competition (i.e. price and quality) separately, it lacks a unifying model which can account for both channels simultaneously. Accounting for both margins of adjustment is important because it has bearing both on size and distribution of welfare gain associated with policies related to import competition. Suppose a country has experienced a period of import competition but the average price of goods hasn t fall 2

3 as much as expected. Therefore, we may erroneously conclude that there isn t much benefit associated with import competition. But what happens actually within firms is that they not only cut down their prices but also upgrade output quality which pushes up the price. So there would be two opposite force acting on price which may make the net decrease in the average price negligible, but it doesn t mean that the welfare effect is also negligible, rather it could be relatively large. In terms of distributional effects, it should be noted that although firms can respond to import competition along these two margins (i.e. markup reduction and quality upgrading), each margin would have totally different welfare implication when consumers are heterogeneous in their income. Rich people care more about the quality of their consumption basket while poor people mainly benefit from access to cheaper products. Hence, we need a unifying model which nests both margins of adjustment so that we would be able to gauge the relative importance of each margin and its impact on different income groups. Moreover, these two margins of firm s response are required to explain the observed patterns in data. Using U.S. import data at the most disaggregated level, I document how other exporting countries respond when competition in the U.S. market gets tougher after China joined WTO in Basically, I document that countries have responded differentially to this competition and show that we need to account for quality channel as well as price channel in order to be able to rationalize this heterogeneity in response. Following the identification strategy proposed by Pierce and Schott (2016), I use variation in the gap between MFN and Non-MFN tariff rates across product categories to identify the effect of China s import competition on other exporting countries in the U.S. market. The more gap has been removed, more uncertainty is eliminated for Chinese producers which leads to more sizable entry of China and makes the competition tougher (Handley and Limão (2017)). Results show that increasing tariff gap from 25th percentile of its distribution (0.229) to 75th percentile (0.464) would lead to other exporting countries decrease the price on average by log point. I also let the price response be dependent on the GDP per capita of exporting country as an indicator for the level of its development. Results show that rich countries cut down the price less than poor countries. So far, the results can be explained by the extant theories in the literature in two different ways: (i) China import penetration makes the competition in the U.S. 3

4 market tougher for other exporting countries and consequently leads to firms innovating more in order to escape the imported competition. Rich countries are more efficient in innovation, so they can more easily escape Chinese competition and will be less affected in terms of price, (ii) In the spirit of Holmes and Stevens (2014), Chinese competition is targeting mostly products originated from less developed countries because they used to produce similar standardized goods. Hence, the market for products imported from rich countries would be less hit by Chinese import shock and this makes them less responsive in terms of price. But investigating the amount of quantity that has been shipped to the U.S. from each country reveals a surprising fact: Chinese import competition causes rich countries to reduce their shipment to the U.S. market more than poor countries. This is totally in contrast with the extant theories which emphasizes that rich countries either are less hit by Chinese import competition or can escape it more easily. This paper contributes to the literature by developing a model that can rationalize these empirical regularities by allowing firms to respond on both margins of price and quality. I build a Ricardian model of trade which nests both dimensions of firm s response when it faces an increased volume of import from abroad. In the model, there is a Home country whose consumers buy their consumption basket from firms located all around the world including the Home country. Countries are differential in two aspects: physical efficiency that indicates the amount of output it can make using a bundle of input, and quality capability which shows the ability of the country in producing high-quality products. Firms need to decide both about the price and quality of their outputs when they sell in the market. They engage in a Head-to-Head competition with each other in the sense that the one who can provide the least quality-adjusted price will be the only seller of product in the Home market. Increased import competition can be attained if the Home country lowers trade barrier with one of its partners by cutting down tariff rates, signing free trade agreements, etc. Then the incumbent firms, in order to survive in the market and remain the active seller, adjusts on both margins of price and quality: firms from developed countries with more capability in quality production find it more efficient to mainly upgrade their output quality while firms from less developed countries would react mainly on price margin by cutting down the markup. I estimate the model using U.S. import data in year Using trade share and 4

5 average export price data, I estimates country level technology efficiency and quality capability simultaneously. Results shows that rich countries are not only more efficient in producing physical output, but also more capable in quality production. The model can generate the empirical regularities found in data. It also does a good job in the out-of-sample prediction about how countries respond heterogeneously to the U.S. market competition in year Finally, counterfactuals reveals that if the U.S. market gets bigger, it would benefit from free trade with quality-capable countries like Japan and Germany more than countries providing cheap goods but at low quality. Related Literature. This paper is related to an extensive literature concerning about the effect of import competition on firm performance. There are numerous papers documenting that in response to import competition, firms either reduce their markups (e.g. Brandt et al. (2017) and Feenstra and Weinstein (2017)) or upgrade their quality (e.g. Amiti and Khandelwal (2013) and Medina (2017)). I contribute to this literature by developing a unifying model which can account for both margins of adjustment. Within the narrower part of this literature that focus on the effect of globalization on quality upgrading response of firms, there are three groups of studies who consider different channels through which globalization triggers quality upgrading. First group that includes Fan et al. (2015), Bas and Strauss-Kahn (2015) andfieler et al. (2018), argues that globalization reduces the price of high quality inputs and thus makes it more profitable for firms to produce high quality products. Second group (e.g. Bustos (2011), Antoniades (2015) and Fieler et al. (2018)) focus on the role of economy of scale for quality: international trade enlarges the market where firms can sell their products and hence the expanded revenue justifies fixed cost of quality improvement. Third group (Medina (2017) and Bloom et al. (2018)) relies on factor reallocation within firms: import competition decreases the return of fixed factors that can not be adjusted instantaneously. Therefore, firms re-assign them to produce products differentiated from imported ones in order to escape the competition. My paper, however, propose a new channel for quality improvement: it is neither due to cheaper intermediate nor due to the interaction of fixed cost and market size. Rather, it is due to the direct effect of competition in the output market. In fact, firms engage in a Head-to-Head competition with foreign firms and this type of competition can be considered as a new channel which forces the incumbents to increase the quality 5

6 in order to survive. In this sense, firms are not escaping competition (as they do in the third group) but rather confronting it and this makes them provide high quality products in the same market in which import competition happens rather than directing their sales toward other markets. This paper is also related to the literature on cross country differences in endogenous quality choice. In many papers, The well-known fact that rich countries charge higher prices for their exports is attributed to the quality of their products. The reason why rich countries endogenously produce at higher level of quality is either their proximity to the markets appreciating high quality goods (e.g. Hallak (2006)) which is in known as Linder Hypothesis, or the fact that they are more productive and hence are able to produce high quality goods (e.g. Feenstra and Romalis (2014)). This paper departs from the standard tradition in the literature and differentiate between physical productivity and quality productivity. In this sense it is similar to Hallak and Sivadasan (2013). They consider two types of productivity for firms: process productivity which is the ability of firm in transforming input to physical units of output, and product productivity which is the ability of firm in producing high quality goods. This paper distinguishes these two types of productivity but at the country level. I show that distinguishing between physical and quality productivity is crucial for capturing differential responses of countries to import competition. The remainder of this paper is organized as follows. Section 2 documents some empirical regularities in data showing the heterogeneous response of countries when facing import competition in the U.S. market. Section 3 develops a model of import competition that can generate the empirical regularities. Section 4 discuss a special case of model. Section 5 describes the estimation procedure and Section 6 presents the results. Section 7 performs a counterfactual and Section 8 concludes. 2 Empirical Regularities In this section, I present three empirical facts to show that firms respond to import competition along both margins of markup and quality and this response is heterogeneous across countries. To assess heterogeneous respond of countries to the shock to import competition, 6

7 I use China s accession to WTO as a natural experiment. Although U.S. import from China had to be subject to high tariff rates known as non-mfn or column 2 tariff, but Chinese firms used to export to the U.S. market under MFN or column 1 tariff rates which were lower than non-mfn rates. The reason was that U.S. government was allows by law to grant MFN rates to China on an annual basis. Beginning on 1980 until 2002, U.S. government kept approving low MFN tariff rates for China but this approval had to be renewed every year which was uncertain. This was generating a great deal of uncertainty for Chinese firms to incur sunk cost of entry into the U.S. market because there was always the threat that tariff rates revert back to high non-mfn rates. In 2002 and after China joined WTO, U.S. government granted permanent MFN rates to China. This removed the uncertainty faced by Chinese firm and lead to a huge amount of China s entry to the U.S. market. The gap between MFN and non-mfn rates can be served to indicate the size of competition imported from China after In the sense that more gap has been removed, more uncertainty has been eliminated and therefore more firms would enter the U.S. market. Following Pierce and Schott (2016), I use the cross product variation in the gap between MFN and non-mfn rates to identify differential response of countries to import competition. To be more clear, I fix the U.S. as the destination market where all countries sell their products. Using increased import competition from China after 2002, I examine how other exporting countries would react to this tougher competition. I use the U.S. import data produced by U.S. Census Bureau and prepared by Schott (2008). This data set records the annual value and physical quantity of 10- digit HS product categories that is exported by all the countries in the world to the U.S.. In the following, value, quantity and price (unit value) of product h exported by country c to the U.S. at time t are denoted by v cht, x cht and p cht, respectively. v cht and x cht are directly recorded in the data set but I construct the price data by dividing the value by quantity: p cht = v cht /x cht. The gap between two tariff schedules is defined as Gap g = Non MF NRate g MF NRate g (1) where g stands for 8-digit HS product category. Ad valorem equivalents of MFN and Non-MFN tariff rates are for 1999 and provided by Feenstra et al. (2002). To measure the effect of Chinese competition, I use difference-in-differences (DID) 7

8 specification ln p cht = α 1 D 2002 t Gap g +α 2 log GDP c D 2002 t Gap g +α 3 HI cst +D ch +D ct +ε cht (2) and regress the log of unit value of products exported by all countries except China, ln p cht, on the interaction of gap between MFN and Non-MFN rates associated with group g (where product h lies in) and dummy variable D 2002 t which takes value 1 for t I also include country-product fixed effects (D ch ) to control for various characteristics of product h imported from country c as well as different measurement units. Moreover, country-time fixed effects (D ct ) control for aggregate shocks that hit country c in year t. Table 1 has three columns each includes different sets of explanatory variables. Column 1 is the baseline specification which investigates how Chinese competition affects pricing decision of other exporting countries on average. Column 2 allows for discrepancy in the response of countries by interacting Dt 2002 Gap g with log GDP per capita of exporting country. I use GDP per capita as an indicator for the country s level of development. To make sure that price response happens within firms and is not the result of firms entering or dropping out of U.S. market, I also control for the number of exporting firms by the Herfindahl index. HI cst indicates Herfindahl index of firms located in country c who export products in the 4-digit HS category (denoted by subscript s) to the U.S. at year t. Data for the Herfindahl indices are provided by Feenstra and Weinstein (2017). Column 1 of Table 1 shows that other exporting countries respond to Chinese Competition by cutting down their prices. The coefficient for the difference-indifference term is negative and highly significant showing that on average, countries who used to export in product categories with higher MFN gap, reduced their prices more in response to China s entry to WTO. In other words, average country exporting products that experienced gap removal of (equal to 75th percentile of gap distribution) reduces their prices more by log point (=0.102 ( ) ) than the average country exporting products associated with gap removal (equal to 25th percentile of gap distribution). So I can conclude the first evidence which seems fairly intuitive. Fact 1. All countries respond to China s import competition by reducing export prices. Column 2 of Table 1 allows for heterogeneity in price response of countries by adding the triple difference term log GDP c Dt 2002 Gap g. I use GDP per capita data 8

9 Table 1: Price Regression ln p cht ln p cht ln p cht D 2002 t Gap g (0.009) (0.059) (0.059) log GDP c D 2002 t Gap g HI cst (0.006) (0.006) R (0.021) Observations 1,523,937 1,523,937 1,523,937 Country Product FE yes yes yes Country Year FE yes yes yes Notes: Table indicates the effect of Chinese import competition on the price of products exported by other countries to the U.S. Dependent variable is the log unit value of products imported from all exporting countries except China. Independent variables are interaction of Gap and post-2002 period and triple interaction of Gap, post-2002 period and log of exporting country s GDP per capita. Other control variable is the Herfindahl index which controls for the number of exporting firms at each country, HS4-sector and time. Data span 1992 to Robust standard errors adjusted for clustering at country HS8-product are shown in parentheses below the estimate values. All columns include country HS10-product country year fixed effects. indicates statistical significance at the %99 level. 9

10 for year Coefficient of triple difference term means that if I consider the same movement of going from 25th to 75th percentile of gap distribution, exporting firms from Indonesia reduce their export prices to the U.S. by units more in log term than firms located in Germany. Therefore, I can state the second evidence related to heterogeneity of countries responses. Fact 2. Rich countries respond to China s import competition less than poor countries in terms of price. Notice that column 3 shows that Facts 1 and 2 are still valid after controlling for the number of exporting firms, i.e. they are happening within firm. The facts constructed so far can be explain by the extant theories in the literature in two ways. First, we can borrow from the literature explaining the effect of competition on innovation. In the spirit of Aghion et al. (2005), one might argue that facing increased import from China, incumbent firms try to innovate more to differentiate themselves in the market and hence escape the competition. And since rich countries are more efficient in innovation activities, they can more easily escape imported competition than poor countries. That is why we see they are less impacted in terms of price. Second and using similar argument to Holmes and Stevens (2014), we can rationalize Facts 1 and 2 by assuming that Chinese firms and firms from poor countries are producing similar standardized products while products coming from rich countries are more differentiated. So we can conclude that poor countries are more subject to China s import competition and need to cut down their prices more than rich countries. Surprisingly, these two explanations turn out to be rejected by data. To show this, I run the same regression as 2 but use the quantity of product h exported by country c in year t, x cht, instead of price p cht. Column 1 of Table 2 shows that exporting countries on average don t change quantity volume of their exports in response to China s competition. But this insensitivity is due to averaging over all countries. If we allow for the heterogeneity of response across countries as column 2 does, we see that quantity is significantly impacted by China s competition. Interestingly, estimates indicate that in contrast with Fact 2, rich countries are more responsive to tougher competition. To repeat the same exercise, If I move from 25th to 75th percentile of gap distribution, shipment from German exporting firms to the U.S. is decreased by units more in log term than firms located in Indonesia. This evidence remains valid as column 3 controls for the number of exporting firms 10

11 Table 2: Quantity Regression ln x cht ln x cht ln x cht D 2001 t Gap g (0.021) (0.155) (0.154) log GDP c D 2001 t Gap g HI cst (0.017) (0.016) R (0.044) Observations 1,523,937 1,523,937 1,523,937 Country Product FE yes yes yes Country Year FE yes yes yes Notes: Table indicates the effect of Chinese import competition on the physical quantity of products shipped by other countries to the U.S. Dependent variable is the log quantity of products imported from all exporting countries except China. Independent variables are interaction of Gap and post period and triple interaction of Gap, post-2002 period and log of exporting country s GDP per capita. Other control variable is the Herfindahl index which controls for the number of exporting firms at each country, HS4-sector and time. Data span 1992 to Robust standard errors adjusted for clustering at country HS8-product are shown in parentheses below the estimate values. All columns include country HS10-product country year fixed effects. indicates statistical significance at the %99 level. by adding Herfindahl indices H cst to the regression. Fact 3. Rich countries respond to China s import competition more than poor countries in terms of shipment quantity. This Fact cant not be justified by ones who justified Facts 1 and 2: If rich countries are either less subject to the competition imported from China or can escape it more easily by innovation, then they should also be less affected in terms of quantity. But results in Table 2 reveals the opposite. In order to reconcile this pattern of heterogeneous respond along different dimensions with theory, Section 3 develops a model of import competition within the Ricardian trade framework in which, firms reacts to tougher competition on both margins of price and quality. 11

12 3 The Model There are N countries indexed by i {1,..., N} who can export their products to each other. Consumers, sharing the same utility, consume goods to maximize their utility and provide labor force inealstically to the producers. Producers use labor force which is the only factor of production to make and then sell their products both domestically and in foreign markets. Section 3.1 and 3.2 elaborate on the decision problem faced by consumers and producers, respectively. Section 3.3 explains the market structure and finally section 3.4 solves for the equilibrium. 3.1 Consumers Representative consumer in country n has a utility function which is a CES aggregate of continuum of goods indexed by j [0, 1] : [ U n = ] σ (zj α x j ) σ 1 σ 1 σ dj (3) where z j and x j are the quality and quantity of good j, respectively and α is the relative importance of quality. Optimal consumption of good j in country n is given by: x nj = E n P σ 1 n z α(σ 1) j p σ j (4) where p j is the price of good j, P n is country n s aggregate price index and E n is the total expenditure in country n. The indirect utility u j that consumer in country n gets from good j is obtained by substituting optimal consumption x j back into the utility 3 which would be proportional to: 3.2 Producers u j zα j p j (5) On the production side, I depart from the current standard in the literature and assume two dimensions for the comparative advantage of countries: Countries are 12

13 heterogeneous not only in the technology frontiers for physical production but also in their capability for making high quality goods 1. Following Bernard et al. (2003) (BEJK, henceforth), joint efficiency distribution of best and second best producers in country i obeys bivariate Fréchet distribution: F i (ϕ 1, ϕ 2 ) = [1 + T i (ϕ θ 2 ϕ θ 1 )] exp( T i ϕ θ 2 ) (6) where 0 < ϕ 2 < ϕ 1. T i (> 0) captures the absolute advantage of country i in physical production and θ(> 1) measures the heterogeneity of productivities. Quality can increase the cost of production in two ways: First, firm needs to incorporate more production inputs (here, labor) to produce the same amount of output but at the higher level of quality. So quality raises the marginal cost. Many papers, among which is Feenstra and Romalis (2014), Fan et al. (2017) and Eaton and Fieler (2017), use this approach to account for the role of quality in cost structure. Second, there is a fixed cost associated with quality upgrading which can be interpreted as producing and selling high quality products requires more advanced technology, more product design service, better distribution network, more advertisement and etc. which all make the whole process costlier. Some papers, including Kugler and Verhoogen (2012) and Fieler et al. (2018), consider fixed cost for quality upgrading. This paper uses both ways and makes both marginal and fixed cost, increasing in quality. Therefore, total cost that a typical firm with efficiency ϕ in country i has to incur in order to deliver x units of output with quality level z to country n is given by: C in (x, z; ϕ) = w id in z γ x + w i z β i (7) ϕ where w i is the prevalent wage in country i and d in is ad valorem trade cost showing the amount of output that needs to be shipped from source i in order to deliver one unit to destination n. Comparative advantage of country i in producing high quality goods is reflected in β i. So β i can be interpreted as the capability of country i in upgrading quality. The higher β i, the more costly for firms in country i to make high quality goods. 1 Hallak and Sivadasan (2013) also differentiate between two types of abilities but at the firm level: ability in producing goods at lower marginal cost (process productivity) and ability in producing goods at higher quality (product productivity). 13

14 3.3 Market Structure For each good, there are bunch of producers from all over the world who are perfect substitutes for each other. They engage in a two-dimensional Bertrand competition where they not only choose the price but also the quality levels. At the end, the one who can provide the consumer with the lowest quality-adjusted price, will be the only seller of that good in the market. 3.4 Equilibrium Now I have all the components to characterize the Ricardian trade equilibrium. Since this paper is to focus on import competition effects in a given country, I fix destination country and call it Home country to: 1) analyze export price and quality decision of other exporting countries when serving the Home market and 2) investigate how they would react if the Home market becomes more competitive. Therefore, I can drop destination subscript n while remembering that variable x i should be recognized as variable x when it is sourced from country i and goes to the Home country. For example, d i means the iceberg trade cost of shipping goods from source i to the Home country. To characterize the Bertrand equilibrium, two steps are in order. First, I need to figure out who wins the competition and second, given the identity of winner, I have to derive price and quality at which the winner sells its product. For the first step, notice since producers are perfect substitutes, there will be one active seller for each good in the market and consumer buys that good only from one who can offer the lowest quality-adjusted price or the highest utility as indicated in 5. Therefore, the winner of Bertrand competition is the one providing the highest utility subject to earning non-negative profit. Consider a producer with efficiency ϕ from country i. The highest utility U i (ϕ) that she can deliver to Home s consumers subject to earning non-negative profit, solves the following maximization problem: max z,p s.t. U i (ϕ) = zα p Bz α(σ 1) p 1 σ w id i z γ ϕ Bzσ 1 p σ + w i z β i (8) 14

15 Figure 1: Utility Maximization Problem z π < 0 π > 0 π = 0 p where B = EP σ 1 captures Home s aggregate demand component. The left hand side of the budget constrain is the total revenue of firm and the right hand side is the total cost. Figure 1 illustrates graphical representation of this problem. It shows decision space of firm where quality is on the vertical and price is on the horizontal axis. The objective function is the slope of blue ray which indicates quality divided by price. Iso-profit curves of the firm are shown in red and as we move the curve to the right and down, firm earns higher profit. So as the firm increase utility of consumer by offering higher quality and lower price (i.e. rotating blue ray counter clock wise), its profit decreases. Therefore, maximum utility that firm can afford is attained at the point where the blue ray is tangent to zero-profit curve. Equivalently, analytical solution to this utility-maximization problem is: U i (ϕ) = (λ i B) = A i ϕ [ λ i 1 (σ 1)λ i 1 1 (σ 1)λ i 1 (1 + λ i )w i λ i ] 1+λ i 1 (σ 1)λ 1 i 1 (σ 1)λ d i i ϕ 1 1 (σ 1)λ i (9) where λ i = α γ 1 (σ 1)λ β i and A i = (λ i B) i ((1 + λ i )w i ) 1 λ i 1 (σ 1)λ 1 (σ 1)λ i d i i. Sufficient condition for solution 9 to maximize problem 8 is α > γ and λ i < 1. Note that there σ 1 are two components contributing to U i (ϕ): country-specific components w i, λ i and d i which are collected into A i and firm specific component ϕ. Denoting the highest 15 1

16 and second highest efficiency in country i by ϕ 1i and ϕ 2i, the highest and second highest utility that can be provided to Home by country i would be U 1i = U i (ϕ 1i ) and U 2i = U i (ϕ 2i ), respectively. Since ϕ 1i and ϕ 2i are obeying bivariate Fréchet distribution 6, I can derive the joint distribution of U 1i and U 2i as: G i (u 1, u 2 ) = Pr(U 1i u 1, U 2i u 2 ) = [1 + Φ i (u θ i 2 u θ i 1 )] exp( Φ i u θ i 2 ) (10) where Φ i = T i A θ i i governs the average size of utilities coming from i and θ i = θ(1 λ i (σ 1)) governs its heterogeneity. Denote the highest and second highest utility that can be delivered to Home from all over the world by U 1 and U 2, respectively. Then where Country i U 1 = max i U 1i (11) U 2 = min{u 2i, min i i U 1i} = arg max i U 1i is the winner of Bertrand competition. So having the probabilistic formulation of highest utilities from each source country, I can derive the probability that a given country be the active seller for a particular good. Proposition 1. Probability that a firm from country i be the supplier for a particular good in the Home market is: Proof. See Appendix A.1. π i = Φ i θ i u θi 1 exp( 0 j Φ j u θ j )du (12) In the second step to characterize the Bertrand equilibrium and given the identity of winner (i.e. best producer), I need to determine what price and quality the winner would offer in the market. Suppose that the best producer is monopolist. Then she chooses price p m and quality z m (where m stands for monopolist ) which together provide utility U m = zα m pm to the consumer. Now in the Bertrand competition, the best producer is limited by the second best producer as long as U 2 > U m. In this case, the objective of best producer is to maximize its profit conditional on providing utility which is weakly greater than U 2 in order to remain active seller in the market. This means that it needs to lower the price and raise the quality relative to the monopolist s choice, up to the point that keeps the second best producer out 16

17 Figure 2: Profit Maximization Problem z π 1 = 0 π 1 > 0 π 2 = 0 p of the market. In other words, it solves this profit-maximization problem: max p,z s.t. π 1 (13) z α p U 2 where I subscripted best and second-best producers by 1 and 2, respectively. It can be verified that the monopolistic utility U m is fraction δ = [( σ 1)(1 + λ)] 1+λ 1 λ(σ 1) σ of U1 where sufficient condition λ < 1 for problem 8 implies δ < 1. So if U σ 1 2 > δu 1, then the best producer needs to solve problem 13. Otherwise, it would be a monopolist in the market and decides about its price and quality accordingly. Figure 2 illustrates graphical representation of problem 13. Green and red curves represent iso-profit curves of best and second-best producers, respectively. Blue ray s slope is the maximum utility that second-best firm can deliver subject to earning non-negative profit. This gives the utility that best producer is bounded to provide. So the equilibrium point is where the best producer s iso-profit curve becomes tangent to the blue ray. Equivalently, analytical solution for equilibrium price and quality is: 17

18 [ ] EP σ 1 α β (α γ) 1 1 β p = w 1 (β 1 + α γ) 1 +(α γ) ασ α(β 1 if U (σ 1)(α γ)) 2 > δ 1 U 1 β U 1 +α γ β 2 U 1 (β 1 +α γ) (14) 1 p m if U 2 < δ 1 U 1 [ ] EP σ 1 1 σ β β (α γ) 1 U 1 +α γ 2 β z = w 1 (β 1 + α γ) 1 if U (σ 1)(α γ) 2 > δ 1 U 1 β U 1 (β 1 +α γ) (15) 1 z m if U 2 < δ 1 U 1 Now let s investigate the effect of competition on the equilibrium price and quality. In this model, competition acts through two channels. First channel stems from the Head-to-Head nature of competition that firms are engaged in. This channel implies that the incumbent firm is directly responding to the competition induced by the second best producer. I call it the direct effect and measure its size by U 2. Second channel acts through the aggregate price P in the sense that tougher competition reduces aggregate price and market share of each firm which in turn affects firm s incentives when deciding about price and quality. This is the standard effect of competition in monopolistically competitive markets which I call it the indirect effect. To fix the idea, assume that U.S. is the Home market and consider the comparative statics that China gets access to the WTO. Following this accession, there would be a huge amount of Chinese firms entering into the U.S. market which makes the competition tougher for the incumbents. In the context of model, this translates to: 1) an increase in U 2 because the pool of potential producers expands and consequently the second highest utility that can be delivered out of this pool would be higher than before (direct effect), and 2) a decrease in aggregate price index P (indirect effect). As for the direct effect, incumbent firm now faces a stronger rival and therefore has to provide higher utility to the consumer in order to remain in the market. Inspecting 14 and 15 shows that it would do so by adjusting on both margins of price and quality in response to an increase in competition (i.e. higher U 2 ): It needs to both upgrade quality and reduce the price. But how much of this response is on the price margin and how much of it is on the quality margin, depends on the capability of exporting country in producing high quality goods (i.e. β 1 ). Incumbent firms from developed(less developed) countries have lower(higher) fixed cost 18

19 of upgrading quality, so their main response would be upgrading quality(reducing price). This effect is captured by the elasticity of price and quality with respect to competition. Price elasticity of competition is β 1+(α γ) ασ of competition is σ β 1 +(α γ) β 1 +(α γ) and quality elasticity. As we move from less- to more-developed countries, β decreases and so price(quality) elasticity of competition decreases(increases). This means that incumbent firms from less-developed countries reacts to the competition mainly by cutting down prices and therefore price response is larger for these countries relative to more-developed countries. As for the indirect effect, reduction in aggregate price and market share makes the firm cut down its markup. Moreover, firm would also downgrade its quality because shrinkage in the market share reduces the marginal benefit of providing higher quality. This captures the Schumpeterian effect in which competition discourages innovation (here, quality upgrading). Direct and indirect effect both lead to firm reduce its price but they have opposite impact on quality. Back to the literature of competition and innovation, I have developed a highly tractable and static model that can nest both types of innovation response to competition. Following corollary summarizes aforementioned facts. Corollary 1. Firm responds to Head-to-Head import competition both directly and indirectly. Direct effect acts through the potential rival s threat and makes the firm increase quality and decrease price. More capable firms (with lower β) respond more on the quality margin rather than price margin and vice versa for less capable firms. Indirect effect acts through market share and makes the firm decrease both price and quality. On top of that, my model implies two other properties that have been already verified in the literature. Corollary 2 (Washington Apple Effect). Everything else equal, firms from distant countries ship higher quality goods to the Home markets. This fact first introduced by Alchian and Allen (1964) and then empirically verified by Hummels and Skiba (2004) among others. Washington apple effect is generated by assuming specific trade cost but here, Head-to Head competition helps to generate it without resort to specific trade cost: Firms from more distant countries would charge higher prices (because of incurring more trade cost) which reduces the highest utility they could afford to deliver to the consumer, i.e. U 1. So to remain 19

20 in the market as the active seller, they need to compensate this disadvantage by raising quality which can be readily verified through equation 15 (lower U 1 results in higher z). Corollary 3. Everything else equal, firms ship higher quality goods to larger economies. This corollary comes from the fact that the cost of quality upgrading is paid in the form of fixed cost. So there would be economy of scale in quality provision: If the destination market is larger (in terms of total income), any level of investment in quality upgrading results in more revenue. This would give the firm more incentive to incur the cost and improve quality. This corollary can serve as a driving force of the fact pointed by Manova and Zhang (2012) that Chinese firms who charge higher prices in bigger markets. 4 Special Case Although I showed the main mechanisms working in the model in section 3.4, it is still useful to investigate a simple special case in which I can analytically investigate quality upgrading response of firms to intensified import competition in the Home market. This special case is constructed by setting elasticity of substitution σ to one which means assuming Cobb-Douglas utility function over goods. In this case, average utility that comes from country i would become Φ i = T i A θ i where A i = (λ i B) λ i ((1 + λ i )w i ) 1 λ i d 1 i. Notice that the dispersion of utilities would be identical for all source countries, i.e. θ i = θ, when σ = 1. While this assumption (σ = 1) removes the difference between dispersion of utilities coming from different sources, it makes the model tractable in the sense that I can derive closed form solutions for trade shares and distribution of equilibrium quality. Corollary 4. Under the Cobb-Douglas utility, the equilibrium price and quality that source i provides in the Home market is: [ where p i = E(α γ) w i (β i + α γ) p i = z i = z i ( U2 ] α β i and zi = U 1 p i U 1 α α β i +α γ β 2 U i +α γ 1 ) 1 β i +α γ [ ] 1 E(α γ) β i. w i (β i + α γ) (16) (17) 20

21 Proof. Equations can be derived just by plugging σ = 1 into equations 14 and 15. Notice that in this special case, best producer is always bounded by the second best producer because the utility she delivers as monopolist is zero (by choosing p = and z = 0) which is always less than the second highest utility. Proposition 2. Under the Cobb-Douglas utility, trade share of country i in the Home market is identical to the probability that a firm from country i be the supplier for a particular good in the Home market which is equal to: s i = π i = Φ i Φ (18) where Φ = j Φ j. Proof. See Appendix A.2. Proposition 3. Under the Cobb-Douglas utility, the ratio of second highest to the highest utility for a good sourced from country i is: ( ) U2 Pr x i = x θ, U 1 0 < x < 1 (19) Proof. See Appendix A.3. Now using this Proposition and the expression for equilibrium quality 17, I can make statements about quality distributions. Proposition 4. Under the Cobb-Douglas utility: (i). The quality distribution of products exported by country i to the Home market is: ( ζ H i (ζ) = Pr(z i ζ i) = z i ) θ(βi +α γ) (20) (ii). The quality distribution of all products sold in the Home market is: H(ζ) = Pr(z ζ) = n ( ) θ(βi +α γ) π i ζ z i i=1 (21) Proof. The proof immediately follows combining equilibrium quality 17 and Proposition 3. 21

22 Now let s examine what happens to quality distribution after a shock to import competition. Suppose we reduce the trade cost of country i toward the Home country, d i. First, notice that the conditional quality of all other exporting countries remain unchanged. This becomes clear when inspecting 17: Consider an exporting country j i. Increased import from i, makes the competition tougher for j s firms. So they would react based on two channels. On one hand, tougher competition makes less efficient firms exit the market. Remember that in the context of Bertrand competition, firms are cost minimizers because the quality-adjusted price which totally pins down firm s revenue would be determined by the second best producer. Since efficiency can only reduce the variable cost, more efficient firms tend to minimize the cost by shifting the cost toward the variable part rather than the fixed part. In other words, they charge lower price and sell more in the market while reducing fixed cost by offering lower quality. So the exitors are the ones who used to provide higher quality. But on the other hand, according to the direct effect of competition 2 explained in section 3.4, surviving firms will be induced to upgrade their quality. Therefore, two opposite effect forces act on the quality of goods sourced from j. The functional form of Fréchet distribution leads to these effects cancel out each other exactly, leaving the quality distribution of each country unchanged. This results is similar to unresponsiveness of markups in BEJK when changing trade cost. Having derived analytical form for the quality distribution, I can investigate the effect of intensified import competition on the quality of goods in the Home market. Proposition 5 states this effect. Proposition 5. Consider trade policy that the Home country reduces trade barriers toward country i which induces import competition from country i. Denote the quality distribution of goods in the Home market before and after this trade policy by H 1 (ζ) and H 2 (ζ), respectively. Moreover, denote the distribution function of quality provided by a surviving firm ϕ before and after trade policy by h 1 (ζ ϕ) and h 2 (ζ ϕ), respectively. Then under the Cobb-Douglas utility function: (i). Surviving firm ϕ would stochastically increase its quality, i.e. h 2 (ζ ϕ) h 1 (ζ ϕ). (ii). If country i s quality is stochastically inferior to the average quality in the Home market (i.e H(ζ) H i (ζ)), then the quality distribution of goods will be stochastically downgraded 2 Notice because of Cobb-Douglas utility, price index doesn t appear in 17 so there is no indirect or discouraging effect of competition on quality. 22

23 after country i s import competition, i.e H 1 (ζ) H 2 (ζ). Proof. See Appendix A.4. The intuition for part (i) is straight forward and is explained before. Basically, it is the increased competition effect in the Home market that makes firm ϕ upgrade its quality in order to survive the competition. Part (ii) needs more explanation. Consider a particular good produced by country j i before policy change. If country j remains the source of good after policy change, then its quality wouldn t change. This is because that selection to more efficient firms and quality upgrading of surviving firms cancel out their opposite effects on quality, leaving the quality distribution of country j unchanged (as explained in Proposition 4). But in the case that a firm in country i takes over the incumbent firm from country j after policy change and starts to produce the good, then it would provide it at the lower quality level because country i s endowment on quality production is inferior to the average world s endowment. Then we would expect that the quality of goods become downgraded on average. In a nutshell, if the policy change shifts trade shares toward a country whose quality is below (above) the world s quality, then the quality distribution of goods sold in the Home market will be downgraded (upgraded). 5 Estimation The set of parameters that need to be estimated is: = {{T i } n i=1, {β i } n i=1, α, γ, σ, θ} (22) where T i and β i are technology and quality cost parameters governing the efficiency of country i in physical and quality production, respectively. α is the relative importance of quality in utility function, γ is the elasticity of variable cost with respect to quality, σ is the elasticity of substitution and θ governs the dispersion of physical efficiencies. The estimation strategy focuses on recovering {T i } n i=1 and {β i } n i=1 values while borrowing value of remaining parameters from literature. Specifically, I set γ = 1.64 which is the median value of elasticities estimated by Feenstra and Romalis (2014) 3. I assume an arbitrary value of α = 2 to satisfy the sufficient condition 3 Actually, Feenstra and Romalis (2014) estimated 1/γ for 712 industries using bilateral trade date between all countries during They reported the median value of 1/γ across industries to 23

24 α > γ for maximization of problem 8. Values of σ = 2.25 and θ = 2.74 are taken from the study of Simonovska and Waugh (2014). They jointly estimate σ and θ within BEJK framework using trade shares and price data of thirty largest countries. Data. I use U.S. import data provided by Schott (2008) at the 10-digit HS product category. As described in Section 2, this data set records the U.S. import value and physical quantity of products from all countries in the world. Price data are imputed by dividing import value by quantity. I estimate the model using data for the manufacturing sector in year Each 10-digit HS product h coming from source country c is considered as corresponding to product j in the model. In other words, I assume that for each product j, firms from all over the world compete with each other but at the end of the day, there will be only one firm who supplies this product to the U.S. market. I estimate the model for 50 countries (including rest of the world, ROW) who have the largest shares in the manufacturing sector in the U.S.. See Appendix... for the list of countries. For the price data to be comparable across different product categories, I regress them on the 10-digit HS product fixed effect and use residuals as the variable which corresponds to price variable in the model. Another useful feature of U.S. import data set is that it also records the duty and the cost of all freight, insurance, and other charges (excluding U.S. import duties) incurred in bringing the merchandise from the source country to the United States at the 10-digit HS product category. I use this data and construct ad valorem equivalent trade cost between country i and the U.S. by dividing the sum of duty, freight, insurance, etc. charges paid by country i in the manufacturing sector by the total value of its export to the U.S.. Finally, Data for GDP per capita of countries are taken from World Bank. Estimation Procedure. I match trade share data to identify {T i } n i=1 and match average export value of each country to identify {β i } n i=1. To be more clear, trade share of country i in the U.S. market is given by s i = Φ i u σ θi 1 ( Φ j θ j u θj 1 ) exp( Φ j u θ j )du 0 j j ( Φ j u σ θj 1 )( Φ j θ j u θj 1 ) exp( Φ j u θ j )du j j j 0 (23) In the case of σ = 1 (Cobb-Douglas utility), we get θ j = θ and the above equation be

25 will be simplified to 18. Moreover, using equilibrium price 14, I can write the mean value of log export price conditional on country i being the source as: E(ln p i i source) = α ( ) ( EP σ 1 (α γ) σα ln 1 β i w i (β i + α γ) β i + α γ ( 1 σ(α γ) β i + α γ ) E(ln U 2 i source) ) E(ln U 1 i source) (24) Inspection of equations 23 and 24 shows that the country with more advanced technology (high T ) has more share in the U.S. market, while the country who is more efficient in quality production (i.e. low β) charges higher export price on average. These two equation serve as the basic components to estimate the model. The estimation procedure inspired by Fieler (2011) has two steps. In the first step, I assume some values for {β i } n i=1 and try to find out set of values for {T i } n i=1 to match trade shares s i in data. In other words, I solve set of N non-linear equations 23 to back out N unknown values {T i } n i=1. Call the solution { ˆT i } n i=1. In the second step, I plug { ˆT i } n i=1 into equation 24. This gives me another set of non-linear equations whose unknowns are {β i } n i=1. Therefore, I would match the average export price of each country i, which is data counterpart for E(ln p i i source), to back out {β i } n i=1. Call the solution { ˆβ i } n i=1. Then using { ˆβ i } n i=1, I would go back to step one and repeat this procedure until solutions { ˆT i } n i=1 and { ˆβ i } n i=1 converge. Identification. The intuition for the identification of {T i } n i=1 and {β i } n i=1 is straightforward. Higher value for the physical technology parameter T i makes country i more productive leading to have larger share in the U.S. market. On the other hand, lower value for quality cost β i makes firms in country i to produce high quality product relative to other countries and since quality is costly to produce, they would charge higher price. Therefore, lower β results in higher export prices. 6 Results Figure 3 shows the result of estimation (list of countries used for estimation and detailed estimation results can be found in Appendices B and C, respectively). Each circle in the graph is associated with a country. In the left panel log of technology parameter T is graphed versus log GDP per capita of countries and the right panel graphs log of quality cost parameter β against log GDP per capita. General pattern in Figure 3 indicates a strong relationship between development level of country 25

26 Figure 3: Technology and Quality Cost Parameters and its efficiency in physical and quality production: rich countries are more advanced in technology (higher T ) and more efficient in quality production (lower β). Figure 4 and 5 indicate the goodness of fit. Since the model is exactly identified, it can generates the exact value of trade share and average export prices observed in data as indicated in Figure 4. Moreover, The model does a good job in fitting quality as illustrated in Figure 5. I use the method adopted by Khandelwal (2010) to define the quality: conditional on price, every factor that contributes to market share is regarded as quality. So given the assumed value of σ = 2.25, I can back out quality as demand residual both in data and simulation by using demand equation 4. Then I calculate the average quality provided by firms from each source country and plot it against log GDP per capita. Figure 5 illustrates this plot. It should be noted that the level of quality is not important here because part of it has been picked up by product fixed effects and is not observed in the graph. The key thing here is how 26