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International trade and firm performance Wang, Ruoying 2018

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International Tradeand Firm PerformancebyRuoying WangB.Sc., Tsinghua University, 2011A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Economics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)September 2018c© Ruoying Wang 2018The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled:  International Trade and Firm Performance  submitted by Ruoying Wang  in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Economics  Examining Committee: Matilde Bombardini Supervisor  Hiro Kasahara Supervisory Committee Member  Viktoria Hnatkovska Supervisory Committee Member Brian Copeland University Examiner John Ries University Examiner   Additional Supervisory Committee Members: Paul Beaudry Supervisory Committee Member  Supervisory Committee Member  iiAbstractThis dissertation is a collection of three essays that study the effect of opening to trade, especiallyopening to the import market, on firm performance.The first essay (Chapter 2) explores the link between innovation and import competition inChina, a country that during the period we study (2000-2007) saw both a rapid increase in patentingand a lowering of import barriers due to accession to the WTO. Combining manufacturing firmsurvey data with customs and patent data, we find that import competition encouraged innovation,but only for the most productive firms. These top firms saw an increase in patenting rate of 3.6%for every percentage point drop in import tariffs. The result is quantitatively similar whether weuse a sector-wide tariff on output or a weighted tariff at the firm level as a measure of importcompetition. Consistent with the main finding, top firms also feature increased R&D expendituresand an increase in domestic sales following import liberalization.To analyze the mechanism and welfare implications underlying our empirical findings aboutChina, the second essay (Chapter 3 and 4) builds a model. Firms engage in monopolistic com-petition across varieties and neck-and-neck competition within each variety. An increase in theneck-and-neck competition reduces the expected profit of not innovating, thus encouraging firms toinnovate more to escape the competition. We analyze the efficiency and utility implications usinga simple version of the model in Chapter 4.The third essay (Chapter 5) examines the relationship between Canadian manufacturing firms’import behavior and their performance. The focus is on two aspects of import structure, inputvariety and the dynamics of import relationships. Firms importing more products from a larger setof suppliers tend to be larger, more productive, and more successful in export markets. Not only thenumber, but also the duration of supply relationships matters. Firms maintaining a higher shareof continuous supply relationships also benefit in size and productivity. These results suggest thatthe breadth and depth of the import network are relevant factors for the performance of Canadianmanufacturers.iiiLay SummaryThis dissertation studies two aspects of the importing market: the effect of import competitionon innovation, and the effect of buyer-supplier relationship on importer productivity. Chapter 2studies how the intensified import competition after China’s accession to the WTO affect Chinesemanufacturing firm’s innovation behavior. We found that import competition induced more in-novation from the most productive firms. Chapter 3 builds a model that explains the incentivesbehind firms’ innovation reactions, while Chapter 4 analyzes the efficiency and welfare implica-tions of the model. Chapter 5 studies how the structure of buyer-supplier relationship affect firmperformance. Employing detailed buyer-supplier information for Canadian importers, we find thathigher import variety and deeper relationship with foreign suppliers are beneficial to firms in termsof size, productivity, and performance in the export markets. We propose an empirical method toidentify causality.ivPrefaceThis dissertation is based on two unpublished working papers.Chapter 2, 3 and 4 are based on co-authored work with Matilde Bombardini, and Bingjing Li.I started the project and conducted initial data cleaning and exploration after getting access tothe Chinese patent database. Matilde guided the big picture of the project and the model setup.Bingjing and I conducted model simulations and implemented the various empirical specifications.I performed additional robustness checks and wrote the first draft of the paper.Chapter 5 is based on co-authored work with Matilde Bombardini, Keith Head, and Maria D.Tito. Matilde, Keith and Maria started the project, and I joined later. I contributed to runningempirical specifications in Statistics Canada in Ottawa, and designing the identification strategyof our baseline regression. The views presented in the chapter represent those of the authors anddo not necessarily coincide with those of Statistics Canada. The contents of this chapter have beensubject to vetting and pass the Disclosure Rules and Regulations set forth by Statistics Canada.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Import Competition and Innovation: Evidence from China . . . . . . . . . . . . 32.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Estimation Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Import Competition and Innovation: A Theory . . . . . . . . . . . . . . . . . . . 263.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2 Model setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.3 The escape-competition and rent-destruction effects . . . . . . . . . . . . . . . . . . 333.4 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 Welfare analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.2 A simplified setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.3 Constrained optimum of the social planner . . . . . . . . . . . . . . . . . . . . . . . 404.4 Openness and welfare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41viTable of Contents4.5 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 How the Breadth and Depth of Import Relationships Affect the Performance ofCanadian Manufacturers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.3 Estimation Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68AppendicesA Appendix to Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75A.1 Productivity Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75A.2 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79B Appendix to Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85C Appendix to Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87C.1 Coding Supplier Identifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87C.2 Supplemental Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90viiList of Tables2.1 WTO accession tariff and initial period growth rates . . . . . . . . . . . . . . . . . . 92.2 Patent sample construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3 Patent distribution across sectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4 WTO accession tariff and Lerner Index . . . . . . . . . . . . . . . . . . . . . . . . . 132.5 FDI and output tariff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.6 Summary statistics, firm level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.7 Summary statistics, industry level . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.8 Output tariff and patenting, industry measure . . . . . . . . . . . . . . . . . . . . . . 172.9 Output tariff and patenting, firm measure . . . . . . . . . . . . . . . . . . . . . . . . 192.10 Long term effects and falsification test . . . . . . . . . . . . . . . . . . . . . . . . . . 202.11 Technology core vs. scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.12 Effects on domestic output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.13 Effect on TFP, R&D, capital and labor . . . . . . . . . . . . . . . . . . . . . . . . . 243.1 Parameter values for full model simulation . . . . . . . . . . . . . . . . . . . . . . . . 354.1 Parameter values for welfare simulation . . . . . . . . . . . . . . . . . . . . . . . . . 435.1 Aggregate Statistics by 3-digit industry, 2007 . . . . . . . . . . . . . . . . . . . . . . 515.2 Firm-level statistics on importing, 2007 . . . . . . . . . . . . . . . . . . . . . . . . . 525.3 Top 10 Country Distribution, 2003 and 2007 . . . . . . . . . . . . . . . . . . . . . . 535.4 Import value decomposition by type of relationship . . . . . . . . . . . . . . . . . . 545.5 Firm size and productivity regressions . . . . . . . . . . . . . . . . . . . . . . . . . . 595.6 Summary Statistics for variables used in regressions . . . . . . . . . . . . . . . . . . 605.7 How import relationships affect export performance . . . . . . . . . . . . . . . . . . 635.8 Import Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65A.1 Production function estimation coefficients by sector . . . . . . . . . . . . . . . . . . 77A.2 Correlation between estimated productivity, level . . . . . . . . . . . . . . . . . . . . 78A.3 Output tariff and patenting, interaction with quartiles . . . . . . . . . . . . . . . . . 79A.4 Industry specification controlling for FDI . . . . . . . . . . . . . . . . . . . . . . . . 80A.5 Two-stage control function estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 81A.6 Alternative measures of innovation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82viiiList of TablesA.7 Drop 2-digit sectors, one at a time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83A.8 Firm output tariff and patenting, OLS . . . . . . . . . . . . . . . . . . . . . . . . . . 84C.1 Average Market Share by sector, 2002–2008 . . . . . . . . . . . . . . . . . . . . . . . 90C.2 Summary Statistics from Import Registry . . . . . . . . . . . . . . . . . . . . . . . . 90C.3 Long-difference (2003–2007) estimates . . . . . . . . . . . . . . . . . . . . . . . . . . 91C.4 Sales Regressions by Sector (NAICS 31) . . . . . . . . . . . . . . . . . . . . . . . . . 92C.5 Sales Regressions by Sector (NAICS 32) . . . . . . . . . . . . . . . . . . . . . . . . . 93C.6 Sales Regressions by Sector (NAICS 33) . . . . . . . . . . . . . . . . . . . . . . . . . 94C.7 Log Sales Regressions by Sector (OP) . . . . . . . . . . . . . . . . . . . . . . . . . . 95ixList of Figures2.1 Actually applied tariff and bounded tariff . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Tariff trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 Distribution of tariff changes across industries . . . . . . . . . . . . . . . . . . . . . . 83.1 Production cost distribution for the simulation . . . . . . . . . . . . . . . . . . . . . 363.2 Innovation efforts for different firms . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.3 Percentage change in utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.1 Foreign cost is the same as domestic, θ = 1 . . . . . . . . . . . . . . . . . . . . . . . 444.2 Foreign cost is much lower than domestic, θ = 0 . . . . . . . . . . . . . . . . . . . . . 454.3 Utility ratios uinnov/unoinnov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.4 Eliminating limit pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.1 Distribution of number of products and supplier per products . . . . . . . . . . . . . 535.2 Older relations are less frequent but more valuable . . . . . . . . . . . . . . . . . . . 545.3 Decomposition of imports by length of relationship . . . . . . . . . . . . . . . . . . 55C.1 Relationship age in extended sample ending in June 2008 . . . . . . . . . . . . . . . 91xAcknowledgementsI would like to express my sincere gratitude for the guidance and support I received throughoutmy PhD studies, from the Vancouver School of Economics, and especially from my committeemembers, Professor Matilde Bombardini, Professor Viktoria Hnatkovska, Professor Paul Beaudry,and Professor Hiroyuki Kasahara.I owe particular thanks to my supervisor, Matilde Bombardini, who led me into the field ofInternational Trade, and helped me grow into an empirical economist. Matilde’s unfailing encour-agement has supported me through the most difficult times. I very much appreciate the last yearof my PhD career, working closely with Matilde at Stanford University, which gave me so muchexposure to the academic world outside UBC. I would like to thank Professor Viktoria Hnatkovskaand Professor Amartya Lahiri, from whom I learnt a lot through working as an RA and eventuallyco-authoring the paper on China’s One Child policy and structural change. I feel lucky to co-workwith Maria D. Tito and Bingjing Li, who shared with me their skills and insights. I am also gratefulfor the helpful comments I received from Professor Keith Head, Professor Nancy Gallini, ProfessorTomasz Swiecki, Professor Jesse Perla, and participants at the UBC Trade Study Group.Last but not the least, I would like to thank my parents and my husband. I could not have theluxury of delving into the ivory tower without them standing beside me.xiChapter 1IntroductionThis dissertation is a collection of three essays that study the impact of import liberalization onfirm performance. The first essay examines the effect of import liberalization on Chinese firm’spatenting behavior and discovers a novel non-linear relationship between import competition andfirm innovation. Based on this observation, the second essay formulates a trade model to studywhy import competition can generate heterogenous innovation incentives among firms and examinesthe model’s implications on resource allocation and aggregate welfare. The third essay studies theeffect of the breath and depth of import relationships on firm performance, using the Canadianmanufacturing firm data. In this chapter, we summarize the methodology and main findings ofeach essay but postpone the discussion of literature and contribution to the respective chapters.The first essay of this dissertation (Chapter 2) studies how import liberalization after China’saccession to the World Trade Organization related to its rapid growth in innovation during the post-accession period. We use the mandated drop of import tariff by the WTO as the policy shock toforeign competition and use invention patent applications in China to measure innovation. We findthat import competition encouraged innovation among the most productive firms. The magnitudeof this competition channel is comparable to roughly 10% of the total increase in patenting rateamong these firms during the period 2003-2007. We exploit the variation of tariff changes atthe industry-year level, and control for other possible channels through which trade could affectinnovation, such as access to a larger exporting market and access to better imported intermediateinputs. We conduct a falsification test by regressing the pre-policy patent activity changes during1998-2001 on future import tariff changes during 2001-2005 and find no significant relationshipbetween the two. This result suggests that (1) there is no differential pre-trend in the propensityto innovate related to future tariff changes between more and less productive firms; and (2) firmsdo not respond to expectations in tariff decrease before they see the actual increase in foreigncompetition. In addition to reduced form regressions, we also conduct a two-stage control functionestimation where we use the import tariff as instrument for the import volume. Consistent with theprevious findings, the most productive firms patent more in the face of increased import competitioncaused by the tariff drop.The empirical finding that some firms can innovate more as a result of import competitioncannot be easily explained by standard trade models with heterogeneous firms. Under monopolisticcompetition, the profit difference between improving quality or technology always decreases whenthere is higher import competition (the rent destruction effect of competition). Thus, in suchmodels, import liberalization should have a negative effect on innovation, holding other conditions1Chapter 1. Introductionconstant. On the other hand, there is a separate class of models that can generate a positiveeffect of competition on innovation. For example, Aghion et al. (2001, 2005, 2009) find that inmodels with neck-and-neck competition, innovation helps firms survive and maintain their marketshare. So, when competition intensifies, firms will find it optimal to invest more in innovation.Such incentive is called in that literature the “escape competition effect”. However, these modelsusually eliminate any general equilibrium price effects, which is exactly the reason why trade modelsgenerate a uniformly negative effect. Therefore, it is useful to introduce the escape competitioneffect into an otherwise standard trade model. And this is what we do in Chapter 3.More specifically, in our model, firms engage in monopolistic competition across varieties andneck-and-neck competition within each variety. Therefore, the escape competition effect and therent destruction effect both exist in our model. When import competition intensifies, the positiveescape competition effect dominates the negative rent destruction effect for the more productivefirms. And the rent destruction effect dominates for the less productive ones.In Chapter 4, we further study the welfare implications of the heterogeneous reaction of firms.Using a simplified framework, we find that, relative to a constrained social optimum, the decen-tralized equilibrium always features under-investment, because the consumer gains form innovationare not internalized by firms. The second finding is that, because of under-investment, whetherthere is additional welfare gains from innovation depends on whether the escape competition effectprevails over the rent destruction effect.In Chapter 5, we use transaction-level administrative data from Statistics Canada to studyhow decisions regarding import relations (number of suppliers per good, and the duration of therelationship with the suppliers) affect firm performance. An immediate endogeneity issue is thatthe import relationship decision is itself affected by firm performance. This problem is in spiritvery similar to identifying input elasticities when estimating a production function. Therefore, weborrow from that literature and formulate a control function approach to deal with endogeneity.The key condition for identification is that the import relationship is not uniquely determined bythe unobserved productivity shocks. In this way, the observable productivity shock can be proxiedby the input choices such as capital and material. Armed with the identification strategy, the richdata structure allows us to explore the effect of different features of buyer-supplier relationshipsthat have not been previously explored in the literature. In particular we find that a larger varietyof suppliers and a longer duration of buyer-supplier relationships affect the performance of theCanadian buyers positively.2Chapter 2Import Competition and Innovation:Evidence from China2.1 IntroductionThe link between innovation and prosperity is not only at the heart of a large literature on endoge-nous growth, but also the target of much attention by policymakers. A recent paper by Akcigitet al. (2017) documents a long-run relationship between innovation and growth in the United States.This broad consensus on the value of innovation stands in contrast with the disagreement on whatits main drivers are. We focus on a question that has proven particularly difficult to settle, thatis the link between competition, in particular import competition, and innovation. In fact, despiterecent evidence on the effect of trade on innovation in several developed countries (Aghion et al.,2017; Autor et al., 2017; Bloom et al., 2016), no clear consensus has emerged on whether importcompetition encourages or discourages innovation. This paper contributes to this discussion byanalyzing firm level evidence from China. We ask the following questions: what is the impact ofimport competition on Chinese firm’s capacity to innovate? And what firms are affected the most?China serves as an interesting case to study the relationship between import competition andinnovation because it experienced both a rapid growth in patenting and intensified foreign com-petition after its accession to the WTO in December 2001. From 2001 to 2007, invention patentsfiled in the State Intellectual Property Office (SIPO) of China grew at an average annual rate of25 percent, comparing to 6 percent in the US patent office (USPTO). In 2007, the number of totalpatents filed in SIPO has reached 53 percent that of the USPTO. During this post-WTO period,China experienced large drop in import tariff barriers and other kinds of local protections man-dated by WTO, which significantly increased the presence of foreign competition. The effectivelyapplied tariff dropped by 6.2 percentage points, from 0.166 in 2001 to 0.104 in 2005. The Non-TariffBarriers (NTBs) were quite low during that period1. Total import quadrupled from 243.5 billionUSD in 2001 to 956.1 billion USD in 2007. We exploit the variation in the import tariff decreasesacross industries and over time to identify the shock to import competition on firms. It is worthnoting that, even though China’s first application to the GATT dated to 1986, the schedule of tar-iff changes was not known until September 2001. The negotiation took 18 meetings between 1996and 2001 and was characterized by Vice Minister LONG Yongtu, Head of the Chinese Delegation,1The NTBs used in China during this period (2000-2007) were mainly the anti-dumping duties. Among all HS6products, on average, only 0.17 percent of the products were subject to some form of anti-dumping duties. Thisnumber was 0.74 percent for the US.32.1. Introductionin his Statement on Sep 17, 2001: “The complexity and difficulty of this process are beyond theimagination of almost everybody.” It is unlikely that anybody knew the timing and extent of tariffcuts and much less the impact of those tariff cuts on imports.Our firm level variables come from the Chinese Annual Survey of Manufacturing Firms, whichis matched to the patent and customs data. The matched firms account for over two thirds oftotal patents filed by Chinese enterprise assignees during 2003-2007. We estimate the elasticity offirm patent application on two-period lagged industry output tariff through a Poisson count datamodel, controlling for industry fixed effects and time trends. Output tariff is measured as theaverage import tariff faced by products that the industry (firm) produces. The idea is that, whenthe import tariff decreases, there are more competing foreign goods (final or intermediates) in thedomestic market. Thus, a decrease in the import tariff proxies for an increase in total import ofthe industry. Moreover, we use the WTO accession tariff that was scheduled at the time of China’sWTO entry, instead of using the applied tariff for each year. In this way, we try to minimizethe concern that concurrent tariffs may be affected by industry lobbying that is correlated withproductivity or innovation, our outcome variable.We find that for firms above the 75th percentile in terms of productivity, a one percentage pointdecrease in output tariff could induce about 3.6 percent increase in patenting. This increase is dueto both strengthening firms’ core technology and enlarging the technology scope.There are several challenges in our measurement and identification of the problem at hand.First, we measure innovation with patent applications in SIPO. Of course, patent application isnot the only output of innovation. Many innovative activities such as improvement in managementor business model is not patentable, and firms may prefer to keep some new formula secrecy2.However, survey evidence shows that all outputs of innovation are positively correlated (Hall et al.,2014; Moser, 2013), and comparing to productivity, patenting is a more direct and precise wayof measuring technology progress at the firm level (Griliches, 1990; Nagaoka et al., 2010). There-fore, we use patent application count as our benchmark measure of innovation and maintain theassumption that patent count is a sufficient statistic in measuring firm innovation.Another concern is that the measured increase in patenting is totally driven by the changein the propensity to patent. For example, studies have shown that stronger IP protection dueto entrance into the WTO would boost domestic patent filing, and the patent system may shiftfirms’ innovation effort from unpatentable to patentable products (Qian, 2007; Arora et al., 2015).There definitely exist nation-wide trends in IP protection and propensity to patent in China. Thequestion is whether the propensity to patent due to IP protection has differentially affected sectorsthat experienced different degrees of import liberalization. Because we show, similarly to Brandtet al. (2017), that tariff cuts are unrelated to observable pre-trends like productivity growth, we donot find the conditions for our regressions to pick up this type of spurious correlation. Furthermore,2Hall et al. (2014) reviewed the literature on choice between formal IP and secrecy. They concluded that althoughthe choice is made strategically and is affected by various industry and market characteristics, empirical evidenceshows that secrecy and IP are usually complements. And the choices within formal IP — patent, trademark andcopyrights — are used as complements as well.42.1. Introductionif patenting propensity differentially changes by aggregate sectors, our sector-time dummies willabsorb different trends in industry patenting propensity.Our empirical findings point to an “escape competition” motif for firms in the face of intensifiedcompetition, which is stronger for the top firms. We postpone a detailed theoretical exploration tothe next Chapter. For now, it is helpful to state the intuition, which we borrow from Aghion et al.(2001) and Aghion et al. (2009). Competition introduces two impacts on firm profitability. On theone hand, it increases the probability that the domestic firms be replaced by the foreign competitor.If innovation could help the firm to retain its market, then there is more incentive to innovate whenthere is more foreign competition. On the other hand, the entering of foreign competitors erodesaway markups by firms, thus induces a rent destruction effect, which could reduce the incentive toinnovate. The net effect of competition depends on which force dominates. In the case of China,we find that the escape competition effect dominates the rent destruction effect.Our paper is related to several strands of literature. First, it is related to studies about China’sgains from accessing the WTO. In addition to the usual gains from trade such as selection throughexports, or access to more imported varieties, evidence has shown that accessing the WTO helpedcorrect resource misallocation and accelerated the market reforms that is sometimes difficult toimplement within political constraints (Khandelwal et al., 2013; Lu and Yu, 2015). In a recent andvery related paper, Brandt et al. (2017) studies the effect of lowering import tariffs on industryaverage productivity and mark-up. They find that when import competition intensifies, there isa decrease in output price level and mark-up, and an increase in aggregate productivity. Whileconfirming their findings, we go one step further to study the innovation channel of productivityincrease, among other potential channels such as purchasing new machines.The second strand of literature looks empirically at channels through which trade could impactfirm’s capacity to innovate. Four channels have received most attention. First, trade could encour-age innovation by technology diffusion (Coe and Helpman, 1995; Eaton and Kortum, 1999; Bueraand Oberfield, 2017; MacGarvie, 2006). Second, getting access to bigger markets due to exportliberalization has been found to induce firms to switch to skill intensive technology (Bustos, 2011),increase R&D spending (Aw et al., 2011), and engage in more innovation (Aghion et al., 2017; Limet al., 2017). Thirdly, import liberalization could enable access to better imported inputs, whichhelps to enhance knowledge diffusion (MacGarvie, 2006), complements R&D spending (Bøler et al.,2015), and induces quality upgrading (Fieler et al., 2016). While the positive effects of the afore-mentioned channels are quite unambiguous, the fourth channel which is the focus of this paper— import competition — has received more mixed evidence. Bloom et al. (2016)3 and Teshima(2008) find positive effects of import competition on innovation for European countries and Mexico,3Although Bloom et al. (2016) also find a positive effect of import competition on innovation, the underlyingchannel that they propose is quite specific to the situation of Europe, thus difficult to generalize to the case of China.In particular, they motivate their empirical findings by a model of “trapped factors”: since international competitionusually comes from the less developed countries, openning to trade lowers the opportunity cost for European firms toswitch into more novel products. For China, on the other hand, competition usually comes from the more advancedcountries so that the cost of innovation actually should increase due to competition, caritas paribus. The model wepropose in Chapter 3 captures this feature through the rent-destruction effect.52.2. Datarespectively. Autor et al. (2017), on the other hand, documents a drop in patent production inthe US manufacturing sector in response to the rising Chinese competition. Our empirical analysisprovides evidence on China itself. Our analysis on the heterogeneous effects also suggests that thenet effect of foreign competition depends on the productivity of the firm and whether the firm couldovercome foreign competition through innovating.Our paper is also related to the literature that explores the reasons behind the rapid increasein patenting in China after 2000. The most studied causes are increased investment in R&D (Weiet al., 2017; Hu et al., 2005; Hu and Jefferson, 2009), improvement in Intellectual Property Right(IPR) protection (Ang et al., 2014), ownership reforms, government’s pro-patenting policies, andFDI. Fang et al. (2017) find that privatization of state-owned firms motivates more patenting,especially in prefectures with higher IPR protection. Xie and Zhang (2015) find that rising wageshave propelled labor-intensive sectors to become more innovative, and firms in female-intensiveindustries have exhibited more innovations than those in male-intensive industries. Jiang et al.(2018) study the technology transfer from foreign joint venture partners to the Chinese partners.They find that industries with an increase in foreign JV presence experienced an overall increasein TFP growth. While we focus on the effect of import competition and market structure, we takeinto consideration these other forces through controlling for region and ownership characteristics.The remainder of this chapter is organized as follows: Section 2.2 describes the data andsummary statistics. Section 2.3 shows our empirical framework, and Section 2.4 discusses theempirical results. Section 2.5 concludes.2.2 Data2.2.1 International tradeIndustry levelOur baseline measure of import competition uses the average import tariff China imposes on theproducts of each four-digit industry. The import tariff information is obtained from China’s WTOaccession document, which specifies the tariff targets for each year since 2001 for each six-digit HSproduct. Figure 2.1 plots the actually applied tariff against the bounded tariff for 2001-2005. Asmentioned in the introduction, China’s WTO negotiation ended in September 2001, and then itquickly entered the WTO in December 2001. So for almost all 2001, Chinese imports were notsubject to any WTO restrictions. From Figure 2.1 we can see that, in 2001, only 32% of the 5,085six-digit HS products complied with the WTO bounded tariff. This rate quickly raised to 97.5% in2002 and remained above 97% thereafter. Figure 2.2 shows the average of the WTO accession tariffand the applied tariff during 1997-2007. During this period, the average bounded tariff droppedfrom 0.1372 to 0.1002, and the average applied tariff dropped from 0.1588 to 0.0982.62.2. DataFigure 2.1: Actually applied tariff and bounded tariff0.511.5actual import tariff0 .2 .4 .6 .8bounded import tariff45 degree line20010.2.4.6.8actual import tariff0 .2 .4 .6 .8bounded import tariff45 degree line20020.2.4.6.8actual import tariff0 .2 .4 .6 .8bounded import tariff45 degree line20030.2.4.6actual import tariff0 .2 .4 .6bounded import tariff45 degree line2005Figure 2.2: Tariff trends8101214161820Tariff rate (%)1997 1999 2001 2003 2005 2007Actual BoundedWe map the products into the China Industrial Classification (CIC) system at the four-digitlevel (424 sectors), using the concordance developed in Brandt et al. (2017)4, and take simple4Their concordance is based on the HS-CIC concordance table constructed by the National Bureau of Statistics(NBS).72.2. Dataaverage5 to arrive at the industry level output tariff. Then we take log plus one to arrive at ourmeasure of log output tariff,τoutputst = log(1 +1HsHs∑h=1tariffimportht). (2.1)For product h that is matched to industry s, tariffimportht is the WTO specified import tariff forChina in year t. Hs denotes the total number of six-digit HS products within industry s. Figure2.3 shows that the tariff drop between 2001-2005 varied across industries.We use the accession tariff instead of the actually applied tariff, because the applied tariff maybe subject to the same contemporaneous forces that affect firms’ innovation incentives. Whilethe pre-determined accession tariff is exempt from such endogeneity concerns, we require it to bealso independent from any expectations in future innovation trends. We test such restriction byregressing the change in the accession tariff from 2001 onward on the change in patenting or firmproductivity during 1998-2000. Table 2.1 shows that we cannot reject the hypothesis that theaccession tariff is not correlated with pre-trend in patenting or productivity growth.Figure 2.3: Distribution of tariff changes across industries-0.04average change051015Kernel Density-.25 -.2 -.15 -.1 -.05 0Change in the accession tariff, 2001-20055There is a possible bias with trade volume weighted averages: Trade volume is negatively correlated with tar-iff levels. Taking weighted average will tend to give more weight to the most liberalized product lines and thusunderestimate the change in effective protection and could cause an upward bias in the estimated effect of tradeliberalization.82.2. DataTable 2.1: WTO accession tariff and initial period growth rates(1) (2) (3) (4)τ output2002 − τ output2001 τ output2003 − τ output2001 τ output2004 − τ output2001 τ output2005 − τ output2001Panel A: Initial TFP growthtfp2000-tfp1998 0.001 0.001 -0.001 -0.003(0.005) (0.009) (0.013) (0.015)R2 0.330 0.344 0.373 0.373Obs 424 424 424 424Panel B: Initial patent growthpatent2000-patent1998 -0.000 -0.000 -0.000 -0.000(0.000) (0.000) (0.000) (0.000)R2 0.333 0.349 0.376 0.375Obs 424 424 424 424Note: *** p<0.01, ** p<0.05, * p<0.1Any effect that industry output tariff has on the industry could affect other industries throughthe input-output linkages. If the upstream industries experienced higher competitive pressure, thedownstream firms would likely to get cheaper and higher quality inputs. We capture such effectthrough the change in input tariff. Specifically, we define input tariff asτ inputst = log(1 +∑kνsktariffoutputkt). (2.2)The input share of industry k good used in industry s, υsk, is obtained from China’s 2002 input-output table. The sum of υsk is smaller than 1, and the other shares include non-manufacturinginputs, labor and capital inputs. The effects of these other inputs are subsumed into the errorterm of our specification and is assumed to be independent from our main explanation variable:change in trade induced competition in the manufacturing sector. The input tariff captures anycompetition effects transferred from import liberalization in input industries. This is what Fieleret al. (2016) call the magnifying effect in their quantitative analysis.For the importers, the input tariff calculated in equation (2.2) also captures the direct effectof getting access to cheaper or better foreign inputs. Therefore, we also control for an importerdummy and the interaction between the input tariff and the dummy. A firm is defined as importerafter its initial appearance in the customs importer registry.Another channel through which trade could affect innovation is the market size effect broughtby export liberalization as studied in Aghion et al. (2017) and Lim et al. (2017). We control forsuch effect through export demand shock from other countries, which is defined as:Edemandst =∑h,cXhc,2000Xs,2000logMhct, (2.3)92.2. Datawhere Mhct denotes country c’s import from the world other than China of product h at time t.After taking log, we weigh the country-product demand shocks by the export share of China duringyear 2000. Xhc,2000 denotes China’s export of product h to country c in industry s in year 2000.6Finally, we focus on year 2001-2005 because this is the period that experienced highest tariffchange after the WTO accession for most products and industries.Firm levelIn addition to the industry level measure of trade shocks, we also construct firm level trade shocks.τoutputist = ln(1 +∑hXih,t−1∑h′ Xih′,t−1tariffimportht); (2.4)Edemandist = ln1 +∑h,cXihc,t−1∑h′c′ Xih′c′,t−1logMhct ; (2.5)τ inputist = ln(1 +∑hMih,t−1∑h′Mh′i,t−1tariffimportht). (2.6)where Xiht−1 and Miht−1 denotes firm i’s export and import in product h in the previous year,respectively. To reduce missing values, for firms that import (export) with gap years, we use themost recent year that it had imported (exported) to calculate the weight. The firm level exportdemand shock is constructed from the product-country level export demand faced by China, wherec, again, denotes destination countries.2.2.2 Patent and other firm-level variablesThe firm level sample of our study comes from the Annual Survey of Manufacturing Firms conductedby the National Bureau of Statistics (NBS) of China (Hereafter referred to as the NBS data), 1998-2007. The survey covers all state-owned firms, and private firms with annual sales larger than5 million RMB. It has become a standard data set for studying firm level behavior in China’smanufacturing sector (Brandt et al., 2012; Hsieh and Song, 2015). In addition, we match the NBSdata with the customs data and patent data to get firm level trade and patenting information.We distinguish between processing and non-processing firms. A firm is defined as processing firmif during all years with available customs data (2000-2007), over 90% of its total export is throughprocessing export. Among the firms defined as processing firms, 88% are foreign or HMT owned.On the one hand, processing trade is not subject to any import tariffs, and since most processingfirms are oriented abroad, they are not likely to be subject to domestic competition either. On theother hand, fall in import tariff could affect firm’s choice between ordinary and processing trade6The definition of demand shock in equation (2.3) is consistent with those in Bombardini et al. (2015) and Aghionet al. (2017). An alternative measure is Ealternativest = log(∑h,cXhc,2000Xs,2000Mhct). This measure gives similar results.102.2. Datamode (Brandt and Morrow, 2016), thus indirectly affect firms’ incentive to innovate. To avoid suchcomplication, we drop the processing firms from our NBS sample (account for 12% in terms ofpatents filed during 2003-2007).We measure innovative activity using invention patents applied by firms. There are threecategories of patents in the Chinese system: invention, utility and industrial design. The inventionpatent is equivalent to the utility patent in the US, and is subject to the agreement on Trade-Related Aspects of Intellectual Property Rights (TRIPS), which requires, for example, a search inthe international patent database to determine the novelty of patents during examination. Eachapplication under the invention category needs to go through two rounds of examination for noveltyand non-obviousness, while the other two categories got granted immediately7. It takes on averagetwo to four years from application to patent granting. The length of protection for invention patentsis twenty years, while that for the other two categories is only ten years. For these reasons, wefocus on the invention patent category as innovation outputs.Patent data is obtained from the State Intellectual Property Office (SIPO) of China. It coversall invention patents applied during 1985-2015. We identify whether a patent belongs to an NBSfirm by matching assignee names to the list of NBS firms. Since the NBS data is an unbalancedpanel, there are years during which an NBS firm does not have observation in the NBS data (mostlikely because it is not big enough), but it has observation in the patent data. Table 2.2 shows thetotal patent count and the matched patent count for year 2007. Of all invention patents, 72% wereapplied by firms, among which 39% belonged to firms located in China. The NBS firms cover 62%of all patents applied by Chinese corporates. For comparison, Autor et al. (2017) finds that theshare of US corporate patents applied by Compustat firms in the manufacturing sector is around56% in 1999 and around 50% in 20078. Our percentage is higher than theirs because their firmdataset only includes publicly traded firms, whereas ours cover a larger universe of Chinese firms.Out of the patents belonging to NBS firms, 81% fall in our sample of non-processing firms withnon-missing data. 5,904 firms in our final sample filed for at least one patent in 2007.Autor et al. (2017) emphasized the importance of controlling for different industry trends. Table2.3 shows the evolution of patent distribution and application per firm for 1999, 2003 and 2007. Thesample used is the primary sample without Huawei and ZTE. As with the US, we do see differenttrends among sectors. The share of patent count in chemicals and petroleum declined from 39%in 1999 to 23.8% in 2007; the share of the metal and metal products sector decreased from 12.9%in 1999 to 7.5% in 2007. On the other hand, the computers and electronics sector experiencedincrease in patenting share from 20.3% in 1999 to 34.6% in 2007. The machinery and equipmentsector also experienced an increase, from 9.2% in 1999 to 17.2% in 2007. In terms of applicationper firm, all sectors experienced an increase, with the most notable increase happening for thecomputers and electronics sector. In 2003 and 2007, the top three patenting sectors are chemicals7The granted utility or design patents can be revoked if another party sue the patent holder in the court.8In Autor et al. (2017), the percentage of US corporate patents in Compustat is 72%. Out of these patents, theshare of manufacturing patents is 77.2% and 70% in 1999 and 2007, respectively. That is how we arrive at 56% and50%.112.2. Dataand petroleum, computers and electronics, and machinery and equipment. Together they accountfor over a quarter of manufacturing patent application. Therefore, when controlling for differentialsectoral trends, we control for these three sectors separately.Table 2.2: Patent sample construction# application # patenting firms patent per firmSIPO dataAll assignee 233,271Firm assignee 167,670 29,212 5.74Firm located in China 65,621 13,799 4.76matched to NBS 40,057 7,279 5.50and non-processing 32,348 5,904 5.48NBS data # firmsAll 329,836Non-processing 317,467Note: Statistics for year 2007.Table 2.3: Patent distribution across sectors(1) (2) (3) (4) (5) (6)Patent share No. patents per firmApplication year 1999 2003 2007 1999 2003 2007Chem., Petrol., Rubber 39.0% 35.5% 23.8% 1.79 2.30 3.64Computers, Electronics 20.3% 30.6% 34.6% 2.39 5.35 8.38Metal, Metal Products 12.9% 6.7% 7.5% 2.20 2.72 4.42Machinery, Equipment 9.2% 11.8% 17.2% 1.40 1.74 2.91Food, Tobacco 6.6% 4.4% 4.3% 1.45 1.91 3.85Clay, Stone, Glass 5.0% 3.2% 2.2% 1.20 1.84 2.15Transportation 3.3% 4.2% 6.0% 1.56 2.43 4.35Paper, Print 1.3% 1.6% 1.3% 1.38 1.68 3.16Textile, Apparel, Leather 1.2% 1.3% 2.2% 1.11 1.44 3.01Wood, Furniture 1.1% 0.4% 0.5% 1.29 1.38 2.00Other Manufacturing 0.1% 0.3% 0.2% 1.00 1.39 2.33Notes: The sample used is the primary sample of non-processing NBS firms, dropping Huaweiand ZTE. Industries are ordered by column (1), ranking of patent share in 1999. Columns(1)-(3) show the share out of total patent count for each sector. Columns (4)-(6) shows theaverage number of patent application per patenting firm.2.2.3 Tariff reforms and industry competitionSince our hypothesis is that the WTO accession tariff reduction affects innovation incentives throughchanges in the competition environment, we now examine the industry market structure and itsrelationship with tariffs and productivity.122.2. DataFollowing Aghion et al. (2015), we measure competition through variations of the Lerner Index,which is usually defined as total profit net of financial cost, divided by total revenue or value added.We test three versions of the Lerner Index definition for robustness:Lerner Ist =∑is Profitist −∑is Finance Feeist∑is Value AddedistLerner IIst =∑is Profitist∑is Value AddedistLerner IIIst =∑is Profitist −∑is Finance Feeist∑is Revenueist.The indices are measured at the sector s - year t level, by aggregating up firm level values. Weregress them on the output tariffs,log Lernerst = β0 + βττoutputst + δs + δt + εst. (2.7)Table 2.4 shows the results. Taking column (1) as our baseline, a one percentage point drop intariff is related to 5.6% drop in the Lerner Index, which is 5.6% more competition.Table 2.4: WTO accession tariff and Lerner In-dex(1) (2) (3)Lerner Ist Lerner IIst Lerner IIIstτoutputst 5.624*** 2.990*** 5.149***(1.111) (0.761) (1.132)R2 0.458 0.465 0.509Obs 1848 2016 1848Notes: Time period, 2001-2005. Industry fixed effectsand year fixed effects controlled. *** p<0.01, ** p<0.05,* p<0.1.2.2.4 Tariff reforms and foreign investmentIn addition to self-improvement through research and development, one important channel thatbrings about innovation among firms is technology transfer through FDI. Holmes et al. (2015) andJiang et al. (2018) both find evidence that there is significant technology transfer to China throughthe form of Joint Ventures. We agree that FDI is an important source of technology growth forChina, the identification of our story would not be threatened as long as changes in FDI patternsdo not exactly map changes in industry output tariffs.In Table 2.5 we look at the correlation between industry output tariff changes and the level andshare of foreign equity in the industry. Interestingly, we find that during the post-WTO period,industries that experienced a larger drop in output tariff would see less FDI. This could make sense132.3. Estimation Frameworkif exporting to and investing in China are substitutable ways to selling goods in China. When itis easier to export to China, firms would choose to export rather than to establish joint ventures,possibly to avoid transferring technology to China (Holmes et al., 2015). With the results in Table2.5, our estimates of the effect of import competition on innovation are most likely to be under-estimated if there is any confounding effects coming from the correlated changes in FDI. In Section2.4, we also put the FDI measures as a control for our baseline regressions.Table 2.5: FDI and output tariff(1) (2) (3) (4)Dep. var ln(foreign equity) ln(foreign+HMT equity)τoutputs,t−2 3.428*** 0.672 3.624*** 1.400*(0.628) (1.031) (0.591) (0.830)Year dummy y y y yIndustry dummy y yR2 0.033 0.895 0.037 0.925Obs 2,053 2,051 2,085 2,084(5) (6) (7) (8)Dep. var foreign equity share (foreign + HMT) equity shareτoutputs,t−2 0.380*** -0.180 0.749*** 0.017(0.053) (0.133) (0.074) (0.151)Year dummy y y y yIndustry dummy y yR2 0.044 0.771 0.061 0.849Obs 2,119 2,119 2,119 2,1192.3 Estimation FrameworkIn the empirical analysis, we estimate the effect of tariff reduction on firm’s innovation capacitymeasured by patent application. We assume firms apply for patent at Poisson rate λist, so thatPatist|λist ∼ Poisson (λist), and E (Patist|λist) = λist, where Patist denotes patent applied at timet for firm i in sector s. The Poisson arrival rate is affected by firm and industry characteristics, aswell as changes in market structure.We run the following baseline specification:Patist = exp( β1τoutputs,t−2 × Topis,t−2 + β2τoutputs,t−2 + β3Topis,t−2 (2.8)+EXP CONTROLis,t−2 + IMP CONTROLis,t−2+δs + δSt),where τoutputs,t−2 is the industry import tariff as defined in equation (2.1), EXP CONTROLis,t−2 and142.3. Estimation FrameworkIMP CONTROLis,t−2 control for effects brought by shocks from export demand and the importedinputs,EXP CONTROLis,t−2 = α1Dexporteris,t−2 + α2Edemands,t−2 + α3Edemands,t−2 ×Dexporteris,t−2 (2.9)IMP CONTROLis,t−2 = γ1Dimporteris,t−2 + γ2τinputs,t−2 + γ3τinputs,t−2 ×Dimporteris,t−2 . (2.10)Edemands,t−2 measures the market size effect brought by export tariff changes, as defined by equation(2.3). τ inputis,t−2 is the two period lagged input tariff measure which is defined by equation (2.2). We usetwo-period lagged tariff shocks to take into account that it takes a while for innovative ideas to beturned into patents. Further, we control for industry fixed effect δs at the four-digit level, and sector-year fixed effect δSt to take into account the different sectoral trends. S is a categorical variableon four sectors: chemicals and petroleum, computers and electronics, machinery and equipmentsector, and others .Following Bustos (2011), we divide firms into four groups for any industry-year cell, accordingto two period lagged TFP quartiles. The TFP estimation procedure follows Ackerberg et al. (2015),De Loecker and Warzynski (2012) and Brandt et al. (2017), which is discussed in detail in AppendixA.1. Topis,t−2 is then defined to be a dummy which equals to 1 if the firm is above the 75th percentilein terms of productivity among firms in industry s two periods before. Coefficient −β1 measuresthe differential percentage change in patenting rate for the top firms after the industry output tariffdecreases by 0.01.For firms with product composition information, we could also construct competition, export,and imported input shocks at the firm level, which are defined by equations (2.4)-(2.6). We runthe following firm level specification:λist = exp( β1τoutputis,t−2 × Topis,t−2 + β2τoutputis,t−2 + β3Topis,t−2 (2.11)+αEdemandis,t−2 + γτimportis,t−2 + δs + δSt + δi).Since import tariff declined most during 2001-2005, we restrain our time period of analysis to2001-2005 for the tariff shocks. And since we assume it takes one to two years for patents to comeout, our patent variables cover years 2003-2007.Table 2.6 shows the summary statistics of the firm level variables, for the top and non-top firmsin 2003 and 2007. Table 2.7 shows the mean and correlation among the trade shocks. The outputtariff is negatively correlated with the export demand, and positively correlated with the inputtariff.152.4. Empirical ResultsTable 2.6: Summary statistics, firm level2003 2007Top 25% Non-top Top 25% Non-topFirm performance and inputsPatent per firm 0.06 (1.72) 0.03 (0.48) 0.19 (6.44) 0.07 (1.43)Patent dummy 0.02 (0.13) 0.01 (0.10) 0.03 (0.17) 0.02 (0.14)log TFP 1.10 (0.50) 0.87 (0.47) 1.28 (0.54) 1.06 (0.46)log R&D 0.90 (2.19) 0.73 (1.89) 0.82 (2.28) 0.66 (1.98)log Capital 8.55 (1.80) 8.79 (1.51) 8.59 (1.76) 8.66 (1.48)log Employment 4.86 (1.24) 4.92 (1.19) 4.75 (1.17) 4.72 (1.06)Firm level trade shocksfirm τoutputis,t−2 0.14 (0.07) 0.15 (0.07) 0.10 (0.06) 0.10 (0.06)Exporter dummy 0.42 (0.49) 0.41 (0.49) 0.41 (0.49) 0.41 (0.49)firm Edemandis,t−2 9.94 (2.16) 9.73 (2.24) 10.21 (2.19) 10.12 (2.23)Importer dummy 0.24 (0.43) 0.23 (0.42) 0.25 (0.43) 0.24 (0.43)firm τ inputis,t−2 0.10 (0.05) 0.11 (0.05) 0.07 (0.04) 0.08 (0.04)OwnershipState dummy 0.13 (0.34) 0.20 (0.40) 0.06 (0.23) 0.06 (0.24)Foreign dummy 0.10 (0.30) 0.07 (0.26) 0.12 (0.33) 0.09 (0.29)Note: Standard deviations are shown in parenthesis.Table 2.7: Summary statistics, industry level2001 2005 2001-2005 Correlation in 2005τoutputst 0.134 (0.067) 0.096 (0.049) 0.109 (0.057) 1.000Edemandst 12.273 (1.642) 12.247 (1.892) 12.237 (1.764) -0.290* 1.000τ inputst 0.053 (0.020) 0.038 (0.012) 0.043 (0.016) 0.257* 0.209* 1.000Note: Standard deviations are shown in parenthesis. * p<0.01.2.4 Empirical Results2.4.1 Baseline EstimatesTable 2.8 shows the regression results for specification (2.8). From left to right, we gradually add inexport demand and input tariff controls. All columns control for the four-digit industry fixed effectsand sector-year effects. For firms below the 75th percentile of TFP, the effect of import competitionis almost zero, with big standard errors. Relative to them, the top firms are highly responsive toimport tariff drops. Taking column (4) as our baseline result, after a one percentage point drop inimport tariff, the top firms increase their patent application effort by 3.6 percentage points more,relative to the less productive firms. During the period of 2003-2007, the annual growth rate of theaverage patenting rate among the top firms is 37.5 percentage points. Thus a one percentage pointdrop in import tariff roughly contributes to 10 percent of the growth in top firm innovation.162.4. Empirical ResultsBeing an exporter increases average patent application per firm by 0.9. Increase in exportdemand in general discourages non-exporters to innovate, while it tends to encourage exporters.This result is consistent with what was found for French firms in Aghion et al. (2017).For the effect of accessing imported inputs, importers on average file for one more patent thannon-importers. While change in input tariff has no effect for non-importers, the encouragementeffect of innovation for importers is quite big. The average annual decrease in input tariffs is0.00375, which would predict an increase in patenting rate of 2.7% for the importers.Table 2.8: Output tariff and patenting, industry measure(1) (2) (3) (4)Dep. var: Patent application countsOutput competitionτoutputs,t−2 × Topis,t−2 -3.525** -3.675** -3.418** -3.577**(1.412) (1.428) (1.474) (1.466)τoutputs,t−2 -0.506 -0.161 0.966 1.275(1.643) (1.655) (1.896) (1.883)Topis,t−2 1.210*** 1.234*** 1.177*** 1.209***(0.142) (0.143) (0.147) (0.146)Export controlDexporterist−2 1.278*** 0.909***(0.333) (0.329)Edemands,t−2 0.063*** 0.066***(0.021) (0.021)Edemands,t−2 ×Dexporterist−2 0.026 0.023(0.025) (0.025)Import controlDimporterist−2 1.799*** 0.984***(0.188) (0.168)τ inputis,t−2 -0.336 -4.936(11.268) (10.972)τ inputis,t−2 ×Dimporterist−2 -11.314*** -7.385**(3.848) (3.639)obs 800,292 800,292 800,292 800,292Notes: The Top dummy equals to 1 if the firm is above 75th percentile in industrys at time t−2. All columns control for four-digit CIC industry fixed effects, as wellas four-sector by year fixed effects. The four sectors are: chemicals and petroleum,computers and electronics, machinery and equipment sector, and others. Standarderrors are clustered at the industry-year level. *** p<0.01, ** p<0.05, * p<0.1.In Table A.3 in the appendix, we show the effect of output tariff changes on the four productivityquartiles separately, by interacting the output tariff with the lagged TFP quartile dummies, insteadof only the top dummy. Consistent with what we found in the baseline specification in Table 2.8,firms in the top quartile innovate more when there is a larger drop in output tariff.172.4. Empirical ResultsAs discussed in Section 2.2.4, foreign investment is another potential channel that affect firms’innovation capacity and could be confounded with the import competition channel. We add theindustry level FDI as a further control to our baseline specification in Table A.4 in the appendix.The magnitude and significance of our estimates stay stable and robust.While in Table 2.8, and throughout the main text of this chapter, we are showing the reducedform relationship between firm patenting and import tariff changes, in Appendix A.2 we test theunderlying mechanism that a decrease in import tariffs first causes increase in import competition,leading to innovation reaction among firms. More specifically, in Table A.5, we regress patent countson industry import volume changes that were induced by tariff changes. Instead of an instrumentalvariable procedure, we use the control function approach that is widely used in the literature whendealing with Poisson count data regressions (Aghion et al., 2009; Wooldridge, 2010; Blundell andPowell, 2003). The results show that a drop in industry output tariff τoutput indeed causes increasein imports of the competing goods in that industry, which causes an increase in patent applicationamong top firms.Table 2.9 shows the results for firm level specification (2.11). The coefficients on the heteroge-neous effect of output competition remain stable across columns, and the magnitude is close to theindustry specification in Table 2.8. The export demand elasticity increases relative to the industryspecification. While the imported input effects, on the other hand, becomes not significant in thefirm specification. In Table A.8 in the appendix, we show results for the OLS specification. Thecoefficients are comparable.182.4. Empirical ResultsTable 2.9: Output tariff and patenting, firm measure(1) (2) (3) (4)Dep. var: Patent application countsOutput competitionfirm τoutputis,t−2 × Topis,t−2 -4.791** -4.874** -5.285** -5.295**(2.423) (2.335) (2.659) (2.571)firm τoutputis,t−2 -1.368 -0.586 -0.617 -0.086(1.284) (1.322) (1.453) (1.455)Topis,t−2 1.372*** 1.260*** 1.291*** 1.266***(0.232) (0.226) (0.262) (0.252)Export controlfirm Edemandis,t−2 0.102*** 0.082***(0.021) (0.024)Import controlfirm τ inputis,t−2 1.208 1.381(2.290) (2.322)obs 138,640 132,945 72,500 70,246Notes: Poisson specification. All columns control for four-digit CIC industry fixedeffects, as well as four-sector by year fixed effects. See Table A.8 for an OLS specifi-cation. The Top dummy equals to 1 if the firm is above 75th percentile in industrys at time t−2. Standard errors are clustered at the industry-year level. *** p<0.01,** p<0.05, * p<0.1.In all the specifications so far, we use patent application counts as the measure of innovationoutcome. The granting rate for the patent applications is around 60% during the sample period.To better control for the quality of patent application, in Table A.6, we run the same specificationas in column (4) of Table 2.8 using patent grants (column 1) and citation weighted patent counts(column 2) as our outcome variables. The effect of a one percentage point drop in output tariffremains the same as in our benchmark. One may also be concerned that firms file for multiplepatents under the same technology to better protect itself in case of law suits. Therefore, givingeach application the same weight would possibly overstate the effort to innovate. Furthermore, iffirms become more strategic due to competition, our estimate would be upward biased. We checkfor the specification with patent dummy, instead of patent counts, as our dependent variable. Thecoefficient magnitude is not readily comparable, but the direction and significance of the effectremains. In column (4) and (5) of Table A.6, we use alternative specifications that have been usedin the literature, other than Poisson, and still the direction and significance of the estimated effectremains.In Table 2.10 column (1)-(2), we show the long term regression by running the industry spec-ification on years 2003 and 2007 only. Both columns controlled for ownership, region, year andindustry dummies. Column (2) also includes the export and import controls. The long term effectof a one percentage point decrease in output tariff encourages top firms to increase patent rate by192.4. Empirical Results4.6 percentage points.Table 2.10: Long term effects and falsification testI. 2003-2007 II. 1998-2001 (pre-exposure)Dep. var Patit,(t=2003,2007) Patit,(t=1998,2001)(1) (2) (3) (4) (5) (6)Past output competitionτoutputs,t−2 × Topis,t−2 -4.587*** -4.685*** -3.005* -2.982*(1.534) (1.576) (1.546) (1.622)τoutputs,t−2 -0.029 0.646 -0.333 0.733(2.523) (2.623) (2.323) (2.709)Topis,t−2 1.335*** 1.338*** 1.225*** 1.197***(0.152) (0.156) (0.143) (0.145)Pre-exposure trendsPati,t−6 0.128*** 0.117***(0.015) (0.013)Future output competitionτoutputs,t+4 × Topis,t+4 -1.768 -1.815(2.189) (2.193)τoutputs,t+4 0.099 0.920(2.724) (3.400)Topis,t+4 0.897*** 0.859***(0.193) (0.190)obs 337,029 337,029 141,190 141,190 119,146 119,146Notes: The specifications are Poisson with two years stacked. All columns control for ownership and region dummies,four-digit CIC industry fixed effects, as well as four-sector by year fixed effects. The even columns include the exportand import controls in addition. Standard errors are clustered at the industry-year-top level. *** p<0.01, ** p<0.05,* p<0.1The time period we look at is one where the patent rate in China picked up rapidly. One concernis that the differential patenting behavior between top and other firms and across industries wascaused by an unobservable factor that also determined the tariff measures. Therefore, in columns(3)-(4), we add to columns (1)-(2) firms’ patent applications in the pre-exposure years as additionalcontrol. Indeed, patent application is a rather persistent feature for firms. The coefficient in frontof past patent is highly significant and positive. Since patenting was a rather high-tech activity,we should expect that firms that patent before the WTO accession would continue patenting. Thepoint estimate of the interaction term becomes smaller, with slightly higher standard errors, makingthe estimate less precise. Second, we run a falsification test in columns (5)-(6) by regressing thepre-exposure patent application in 1998 and 2001, on the future tariff rates in 2001 and 2005.The interaction term is weakly negative, and not significant at the 10 percent significance level.Therefore, we do not find evidence that the pre-exposure patenting behavior is related to the WTOaccession tariffs.202.4. Empirical Results2.4.2 Technology deepening v.s. technology scopeNext, we further investigate the dimensions of innovation that are induced by import competition.Specifically, we decompose the total patent count into patents filed in the core technology of a firm,versus the total number of technology classes the firm file patents into. Technology class is definedaccording to the six-digit International Patent Classification (IPC)9. A technology class is definedas the core technology if a firm has accumulated the most patent applications in that class up tothe previous year. The technology scope is the sum of the number of classes a firm files patent ina specific year.Table 2.11 shows the estimation result for the industry specification applying on core technologyand technology scope. Column (1) is repeating column (4) in Table 2.8 as benchmark. The resultssuggest that the top firms react to increase in import competition by both increasing innovation inthe core technology as well as broadening its technology space. The point estimate for the effect onpatent scope (column 2) is smaller than the overall effect (column 1), whereas the point estimatefor the core patent (column 3) is larger than the overall effect. The result remains very similarwhen we only look at firms that have applied for patents before (columns 4-6). Column (7) showsthe effect on the ratio of scope to core. The second row show that on average, firms react more byincreasing their patent in core technology, which is consistent with previous columns. There isn’t adifferential effect for the top firms in terms of the relative magnitude of core and scope innovation.9There are 4944 six digit IPC in 2007. For example, in 2007, Huawei filed patents in 144 technology classes.According to our definition, its core patent class was H04L12, “Data switching networks”. Other technology classesthat it filed patent in are H04L29, “Arrangements, apparatus, circuits or systems”, and H04L1, “Arrangements fordetecting or preventing errors in the information received”, etc.212.4. Empirical ResultsTable 2.11: Technology core vs. scope(1) (2) (3) (4) (5) (6) (7)Sample All Patented before scopecoreDep. var application scope core application scope coreOutput competitionτoutputs,t−2 × Topis,t−2 -3.577** -2.397** -3.968** -3.659*** -2.323** -4.833** -0.472(1.466) (0.974) (1.832) (1.591) (1.092) (2.063) (0.821)τoutputs,t−2 1.275 1.188 1.334 1.247 2.281 0.705 3.654**(1.883) (1.337) (1.564) (2.333) (1.650) (1.917) (1.454)Topis,t−2 1.209*** 0.933*** 1.091*** 1.020*** 0.768*** 0.953*** 0.205***(0.146) (0.090) (0.192) (0.152) (0.088) (0.217) (0.071)Export controlDexporterist−2 0.909*** 1.582*** 0.401 -0.022 0.517* -1.163** 0.287(0.329) (0.252) (0.409) (0.455) (0.308) (0.502) (0.196)Edemands,t−2 0.066*** 0.079*** 0.082*** 0.059* 0.052** 0.056* 0.018(0.021) (0.019) (0.022) (0.030) (0.022) (0.033) (0.018)Edemands,t−2 ×Dexporterist−2 0.023 -0.040** 0.028 0.068** 0.012 0.124*** -0.003(0.025) (0.020) (0.033) (0.034) (0.023) (0.039) (0.016)Import controlDimporterist−2 0.984*** 0.968*** 0.631*** 0.469** 0.174 -0.043 0.172(0.168) (0.163) (0.202) (0.205) (0.176) (0.195) (0.172)τ inputis,t−2 -4.936 -9.983 -6.497 -2.990 -13.008 -4.033 -5.160(10.972) (6.907) (7.036) (12.473) (8.584) (9.981) (8.317)τ inputis,t−2 ×Dimporterist−2 -7.385** -4.063 1.744 -6.094 -0.314 7.254* -4.132(3.639) (3.685) (3.905) (5.047) (4.247) (4.330) (4.427)obs 800,292 800,005 800,005 23,931 23,917 23,917 12,721Notes: All columns control for ownership, region, four-digit CIC industry fixed effects, as well as four-sector by year fixedeffects. Standard errors are clustered at the industry-year level. *** p<0.01, ** p<0.05, * p<0.12.4.3 Effect on firm scale and productivityIn this section, we look at the effect of import liberalization on other firm outcome variables.First, we are interested in whether surviving firms get bigger. Table 2.12 shows the effect of tradeshocks on domestic sales in columns (1)-(3) and domestic market share in columns (4)-(6). Fromcolumns (4) -(6), the domestic market share decreases for all firms following import competition,which is a mechanical result to be expected. From column (3), there is a weak increase in thedomestic output for firms surviving the competition, 0.44 percent increase, after a one percentagepoint drop in output tariff.222.4. Empirical ResultsTable 2.12: Effects on domestic output(1) (2) (3) (4) (5) (6)Dep. var log domestic output Domestic market shareOutput competitionτoutputs,t−2 × Topis,t−2 -0.491** -0.435* -0.031 -0.033(0.243) (0.238) (0.033) (0.036)τoutputs,t−2 -0.177 -0.038 -0.427 0.064** 0.072** 0.036(0.397) (0.398) (0.432) (0.027) (0.032) (0.023)Topis,t−2 0.657*** 0.650*** 0.010 0.010(0.033) (0.032) (0.009) (0.009)Export controlDexporterist−2 0.396*** 0.102(0.118) (0.120)Edemands,t−2 0.008* 0.004(0.005) (0.003)Edemands,t−2 ×Dexporterist−2 -0.037*** -0.009(0.010) (0.011)Import controlDimporterist−2 0.744*** 0.025(0.082) (0.023)τ inputis,t−2 4.853*** 0.694(1.633) (0.496)τ inputis,t−2 ×Dimporterist−2 -7.499*** -1.303(1.745) (0.982)obs 741,978 741,978 741,978 808,123 808,123 808,123Notes: All columns control for four-digit CIC industry fixed effects, aggregate sector by year fixedeffects. Standard errors are clustered at the industry-year level. *** p<0.01, ** p<0.05, * p<0.1In Table 2.13 we look at the effect on productivity, R&D, capital and employment inputs. Theeffect on productivity is quite pronounced. After a one percentage point drop in output tariff, thetop firms see increase in productivity by 0.17 percent. This is consistent with the estimate of 0.19percent in Brandt et al. (2017). In column (2), we estimate the effect of import competition onthe R&D input. Consistent with the result for the patent application, the top firms react moreto import competition and put more effort into research and development in the face of moreliberalized import market. Column (3) and (4) shows that the elasticity of capital and labor onoutput tariff is 1.12 and 0.36, respectively.232.5. ConclusionTable 2.13: Effect on TFP, R&D, capital and labor(1) (2) (3) (4)Dep var TFP ln (R&D) ln (capital) ln (labor)OLS OLS OLS OLSOutput competitionτoutputs,t−2 × Topis,t−2 -0.167*** -1.333*** -1.122*** -0.365**(0.036) (0.226) (0.264) (0.152)τ outputs,t−2 -0.447* 0.276 0.522 -0.462*(0.236) (0.374) (0.364) (0.279)Topis,t−2 0.221*** 0.302*** -0.003 0.051**(0.005) (0.027) (0.036) (0.021)Export controlDexporterist−2 0.043*** 0.140 0.339*** 0.242***(0.015) (0.158) (0.075) (0.046)Edemands,t−2 0.002 -0.000 -0.006 -0.005*(0.002) (0.006) (0.004) (0.003)Edemands,t−2 ×Dexporterist−2 -0.003*** 0.022* 0.009 0.019***(0.001) (0.013) (0.006) (0.004)Import controlDimporterist−2 -0.007* 0.639*** 0.957*** 0.449***(0.004) (0.101) (0.048) (0.024)τ inputis,t−2 -0.822 -0.121 8.180*** 4.130***(0.808) (2.096) (1.270) (1.481)τ inputis,t−2 ×Dimporterist−2 0.180** -4.153 -4.012*** -1.105**(0.080) (2.537) (0.960) (0.473)R2 0.567 0.137 0.228 0.196obs 802598 563144 798414 802598Notes: The Top dummy equals to 1 if the firm is above 75th percentile in industry s attime t− 2. All columns control for four-digit CIC industry fixed effects, as well as four-sector by year fixed effects. The four sectors are: chemicals and petroleum, computers andelectronics, machinery and equipment sector, and others. Standard errors are clusteredat the industry-year level. *** p<0.01, ** p<0.05, * p<0.12.5 ConclusionThe China Miracle has been a manufacturing success. But after over forty years of rapid growthwith cheap labor, imitation, and institutional reforms, China’s manufacturing sector has arrivedat a crossroad where further growth depends much on indigenous innovation. In this chapter,we study the impact of change in competition environment brought about by foreign importson Chinese firm’s innovation capacity, measured by patent application. Using a newly combineddata set that covers the universe of medium to large manufacturing firms, and more than 60% ofcorporate innovators, we find that the increase in import competition following China’s accessionto the WTO during 2001-2005 induced more productive firms to innovate more.242.5. ConclusionOur finding adds to the debate on the effect of international competition on innovation. Fora developing country like China, opening to international competition served as a stimulatingmechanism for the top firms to invest in research to improve products and processes. In the meantime, a less productive firm may find it not as attractive to innovate. Whether the aggregate effectis positive or negative depends on the extent of technology spillover and other effects we do notconsider in this work. We believe this is a fruitful future research path to pursue.25Chapter 3Import Competition and Innovation:A Theory3.1 IntroductionIn Chapter 2, we showed empirical evidence that the effect of import competition on firm’s incentivesto innovate is heterogeneous in the case of China. Across the 4-digit industries, a 1 percentage pointdrop in import tariff induces a 3.6 percent increase in patenting rate for the top 25% most productivefirms. We also showed that the effect of competition on innovation of initially less productive firmsis not significantly different from zero.In this Chapter, we propose a model of international trade with endogenous innovation toillustrate the mechanisms behind the heterogeneous response of R&D and innovation to tradeliberalization. More specifically, we build on the trade model with firm heterogeneity as proposedin Melitz and Ottaviano (2008) and introduce two modifications. The first one is the ability toinnovate, subject to a convex cost, and the second one is neck-and-neck competition betweendomestic and foreign firms within each variety of differentiated goods. We show that importcompetition brings about a negative “rent-destruction” effect and a positive “escape-competition”effect. The net effect of import competition depends on the dominating force. We study the welfareimplications in Chapter 4.The escape-competition effect induced by the neck-and-neck competition is a common featureto several papers by Aghion et al. (2001, 2005, 2009)10. However, these models usually have zerocross-price elasticity, which reduces the negative effect of rent destruction introduced by morecompetition. Such rent-destruction effect is important in any trade models with monopolisticcompetition. In addition, in these papers, the change in the competition environment is usuallygoverned by exogenous parameters that are difficult to map to a variable empirically. Our modelcontributes to studying the escape-competition and the rent-destruction effects in a unified model,where the competition environment can be easily summarized by an empirical variable — theimport tariffs.Our model also contributes to introducing within sector oligopoly competition into a typicaltrade model. Looking at narrow product niches, we usually see several big players strategicallycompeting, instead of hundreds of ignorable small players. Therefore, by introducing the neck-and-neck competition, we not only could introduce the missing escape-competition effect, but also could10See also the IO literature surveyed in Gilbert (2006).263.1. Introductionpush the model closer to reality.Our theory is also related to the literature on trade and innovation in a heterogeneous firmframework, although it is worth noting that the vast majority of these papers feature increasedmarket size as the incentive for further innovation. A key contribution that features this mechanismis the one by Atkeson and Burstein (2010). Their main result is that as variable trade costs decline,any increase in average productivity due to additional process innovation is compensated (in specialcases exactly) by reduced entry and therefore lower product variety. The mechanism in that paper isdue to the fact that a shock to the export market initially increases expected profits. But to satisfythe free entry condition, expected profits have to decline. This happens because as firms becomemore productive by investing more, the average firm is more productive and expands, demandingmore labor. This puts pressure on wages, thus further decreasing average profits for the otherfirms that enter the market. Perla et al. (2015) also generate dynamic gains from trade in a modelwhere firms invest to learn from existing firms in the market. Due to Melitz-type selection, tradeopening improves the pool of firms that other firms can learn from. In their setting welfare risesbecause growth increases due to costly imitation, but, similarly to Atkeson and Burstein (2010),their welfare gains are reduced by decreased entry. Other papers in this literature are Rivera-Batizand Romer (1991) and Hsieh et al. (2018), Grossman and Helpman (1991).Four contemporary papers that are related to the mechanism described in this paper are Fielerand Harrison (2018), Aghion et al. (2017), Akcigit et al. (2017) and Lim et al. (2017). Fielerand Harrison (2018) and Lim et al. (2017) share some common features that are different from ourmodel. They work with a constant elasticity of substitution utility function which features differentnests. As firms innovate they can escape to another nest, where they face lower competition. Thedifference between these two papers is the source of increased competition. In Fieler and Harrison(2018), the rise in competition comes form foreign firms entering the domestic (Chinese in theircase) market, whereas in Lim et al. (2017) the increase in competition is a consequence of the risingdomestic entry due to export opportunities. The model is closest to Aghion et al. (2017) and Akcigitet al. (2017). Aghion et al. (2017) also builds on the framework of Melitz and Ottaviano (2008),but focuses on the effect of exporting on innovation for French firms. They find a negative effectof competition coming from the price index effect which would discourage innovation among firmsaway from the technology frontier. In Akcigit et al. (2017), importing happens in sectors where thehome firm is lagging behind, and therefore, only firms at the middle-lower part of the productivitydistribution react to import competition. In contrast, in our model, foreign competition can bepresent along the whole productivity distribution, and we let the data tell us which firms areaffected the most.The remainder of this chapter is organized as follows: Section 3.2 lays out a baseline model withfirm heterogeneity. Section 3.3 analyses the escape-competition and the rent-reduction channelsthrough the lens of the model. Section 3.4 shows simulation results of the model. And Section 3.5concludes.273.2. Model setup3.2 Model setupIn this section, we present a model of import competition in which firms from two countries,Home (H) and Foreign (F ), compete in the domestic (Home) market. There is a finite number ofvarieties and firms compete in a Bertrand fashion when they produce the same variety. Moreover,after entering the market, firms have a chance to further invest in cost-reducing innovation. Themodel asks for a fixed number of varieties of goods. Fixing the number of varieties enables “neck-and-neck” competition (Aghion et al., 2005, 2009; Akcigit et al., 2017). If the number of potentialvarieties is unlimited, then two firms will never enter the market in the same variety. For a givenproductivity draw it is weakly more profitable to enter a variety not previously produced. As willbe shown in section 3.3, the presence of the “neck-and-neck” state will drive the positive reactionof some firm’s innovation to the increased foreign competition.3.2.1 Consumer preferencesConsumers enjoy utility from consumption of a homogeneous good, denoted by qc0, and a massNe of potential varieties of the differentiated good, each denoted by qci . The utility is a quadraticaggregator of the goods, as in Ottaviano et al. (2002) and Melitz and Ottaviano (2008):U = qc0 + αN∑i=1qcidi−12γN∑i=1(qci )2 di− 12η[N∑i=1qcidi]2. (3.1)where N ≤ Ne is the number of differentiated goods being produced. Parameter α measures therelative importance of the differentiated good over the numeraire. The parameter η also governsthe cross-price elasticity of demand. The parameter γ governs the own-elasticity of demand amongthe differentiated varieties.Consumers choose quantities qc0, qci to maximize utility subject to the budget constraint∫i∈Ω piqcidi =Ec, where Ec is the total income of an individual, given by the wage w and a share of profits whenpositive.We make the common simplifying assumptions that the homogeneous good is the numeraire,freely traded, produced and consumed in positive quantities in each country and that its productionis one-to-one with labor, implying that the wage w is equal to 1. The inverse demand for eachdifferentiated good i is given by the following equation:pi = α− γqci − ηQc,and the total demand for each variety isqi = Lqci =αLηN + γ− Lγpi +ηNLγ (ηN + γ)p¯ ∀i = 1, ..., N (3.2)Variable N is the number of active varieties, i.e. those for which the following inequality is satisfied:283.2. Model setuppi ≤ α ≡ pmaxiwhere pmaxi represents the choke price at which demand for a variety is driven to 0.Each consumer earns a equal share of the profits from the firms in the economy. The indirectutility can thus be written in terms of firm profit and the mean and variance of prices.U = 1 + Π +121η + γN(α− p)2 + 12Nγσ2p (3.3)where σ2p ≡ 1N∫i (pi − p¯)2 di is the variance of price. Π denotes the total profits earned by thefirm. Utility increases when firms are more profitable, when average price drops, or when there isa higher dispersion in price.3.2.2 Production and Market StructureWithin each variety, there are two potential producers, one in Home and one in Foreign and theyengage in Bertrand competition. Each of them draws their initial productivity from a country-specific cost distribution Gn (c), where n ∈ {H,F}, and c denotes the production cost. We assumeBertrand competition within each variety, so that only the firm with the lowest cost draw entersthe market and becomes the incumbent for that variety. The incumbent can then further chooseits innovation effort and decrease production costs by a fixed step size δ with some probabilityproportional to its innovation effort.Foreign firms can sell in the domestic market subject to an iceberg transport cost τ > 1. Sincewe are interested in the effect of unilaterally decreasing the transport cost τ , we make the simplifyingassumption that Home exports are in terms of the homogeneous good only. This is inconsequentialin this partial equilibrium setting and thus allows us to more clearly isolate the effect of increasedimport competition from other potential innovation incentives coming from the export market.Similar to Akcigit et al. (2017), we assume that firms incur a small cost ε → 0 to set theprice. Therefore, only the firm with the highest productivity for each variety will set the price andproduce. In this way, we sacrifice the more realistic limit pricing setting (Bernard et al., 2003)for analytical simplicity. In reality, there is no barriers to setting a lower price; therefore, thebest firm could not charge a price that is higher than the cost of the second-best firm. To makethe model easier to illustrate and simulate, we keep the simplifying assumption that the best firmcould still charge the monopoly price. While it doesn’t hurt our analysis in this chapter, this isnot an innocuous assumption for welfare analysis, as will become clear in Chapter 4. We keep thesimplification for now and would return to limit pricing in Chapter 4.In this setup the presence of foreign firms generates an increase in the probability that thedomestic producer will exit the market. This is the key force that drives additional innovation. Ifinnovation can make the domestic producer more productive than foreign firms, then more foreign293.2. Model setupcompetition will induce domestic firms to innovate more.11Labor is the only factor of production. Given marginal cost ci for the firm operating in varietyi, the firm’s static problem is to maximize profits pi (·):maxpipi(ci) = (pi − ci) qisubject to the demand function equation (3.2).Although there is a potential number of Ne varieties, some may not be produced in equilibriumif all firms draw a cost of production that is too high. We denote by cD the highest cost a firmcan draw that will still allow it to make non-negative profits. Then, the cutoff cost, price, quantity,profit and revenue expression for both the Home production of the differentiated good, as well asthe imported Foreign goods are:cD =αγηN + γ+ηNηN + γp; (3.4)p (c) =12(cD + c) ; p∗ (c∗) =12(cD + c∗τ) (3.5)q (c) =L2γ(cD − c) ; q∗ (c∗) = L2γ(cD − c∗τ) (3.6)pi (c) =L4γ(cD − c)2 ; pi∗ (c∗) = L4γ(cD − c∗τ)2 (3.7)r (c) =L4γ((cD)2 − c2); r∗ (c∗) =L4γ((cD)2 − (c∗τ)2)(3.8)where the foreign variables are indicated by a star.3.2.3 Innovation decisionAfter entering the market, domestic incumbent firms can invest in R&D to lower their costs toδc where 0 < δ < 1.12 A common way to model this problem is to have the firm choosing theprobability I of a successful innovation by paying a cost that is increasing and convex in thisprobability. This cost takes the form of I(c)22φ . The innovation decision will have a key componentgiven by the probability of survival. A domestic firm with cost c will survive with probability1 − GF(cτ)if it fails to innovate and with probability 1 − GF(δcτ)if it succeeds, where GF (.) isthe CDF of foreign cost c∗.Therefore the optimization problem for the domestic firm starting with production cost c consists11There is also an additional effect of foreign firms operating through the average price, but as we will discuss later,this is not sufficient to generate a competition-induced increase in innovation. In Chapter 4, introducing limit pricingwill mean foreign firms have the additional effect of lowering the price the domestic firm can charge.12We abstract from the innovation response of domestic firms.303.2. Model setupin maximizing the function V (c):maxI(c)V (c) = I (c)(1−GF(δcτ))pi (δc) + (1− I (c))(1−GF( cτ))pi (c) (3.9)− 12φI (c)2 .The solution to (3.9) gives the following innovation policy function:I (c) =φ (p˜i (δc)− p˜i (c)) if c ≤ cDφp˜i (δc) if cD < c ≤ cDδ (3.10)wherep˜i (c) =L4γ(1−GF( cτ))(cD − c)2 .and the function p˜i (δc) represents expected profits when the firm succeeds in reducing its cost toδc.3.2.4 Firm entry and exitWe assume that in each of the Ne differentiated good varieties, there is only one domestic firm thattakes a production cost draw from the domestic talent (entrepreneur skill) distribution GH (c).They can choose not to produce if their cost realization is too low, thus exiting the market. Thissetup corresponds to the short-run equilibrium in Melitz and Ottaviano (2008), in which there isno free entry and incumbent firms can earn positive profits.An alternative setup is to allow for a pool of entrants who can take the productivity draw byincurring a fixed entry cost. This could generate a domestic incumbent distribution that is relatedto the number of firms taking the productivity draw. Although potentially consequential, we leavethe analysis of this free-entry condition to future research.3.2.5 Endogenous technology distribution and the price indexWe now derive the endogenous distribution of firm costs, taking into account the innovation de-cisions. This also allows us to derive the price index. Let F (c) denote the ex-post cumulativedistribution after the realization of incumbent’s innovation investments. The relation betweenGH (c) and F (c) is given by the following equation:F (c) = GH (c) +∫ cδcI(c′)dGH(c′)(3.11)The PDF of the post-innovation cost distribution is given by the following equation:313.2. Model setupdF (c) = (1− I (c)) dGH (c) + I( cδ)dGH( cδ)(3.12)The number of varieties consumed by the Home consumers in equilibrium is given by:N = Ne[F (cD) + (1− F (cD))GF(cDτ)]. (3.13)which depends on the exogenous number of potential varieties Ne in both countries. The first partshows the number of varieties that can be produced by the home firm (although it could be a foreignfirm that is producing it by crowding out the home firm). The second part shows the number ofvarieties that is produced by foreign firms only because the domestic producer’s cost is too high.The joint distribution of the minimum of the domestic and foreign cost can be then calculatedas follows:H (c) ≡ Pr (min (cH , cF ) < c) (3.14)= 1− (1− F (c))(1−GF( cτ))Having obtained the final cost distribution, we can now write down the average price for thedomestic economy.The price index is simply given by:p =∫ cD0 (c+ cD) dH (c)H (cD)(3.15)3.2.6 Market clearingFinally, we need to make sure that the resource constraint is not violated and that after exporting,the remaining homogeneous good for domestic consumption is non-negative. More specifically, weneed to impose that:q0 = L−R−R∗ ≥ 0 (3.16)whereR =∫ cHD0(1−GF( cτ))((cD)2 − c2)dF (c)R∗ =∫ cFD0(1− F (c∗))((cD)2 − (c∗)2)dGF (c∗)Since domestic wage is 1, R is equal to the labor costs employed in entry, producing the differentiatedgoods, and innovating. R∗ is the total expenditure on the foreign differentiated good, so to maintaintrade balance, Home needs to export to Foreign the corresponding value in terms of homogeneousgood. Therefore R∗ is equal to the labor used in producing the exported homogeneous good.323.3. The escape-competition and rent-destruction effects3.2.7 Solving the model: AlgorithmThere are two sets of endogenous variables in the model: the domestic cutoff cost, cD, and theinnovation policy function I (c). We can solve the model iteratively following the steps below:1. Guess a value of the cutoff cost, c0D.2. Solve for the innovation function using equation (3.10). Then we can obtain the ex-postdomestic price distribution F (c). Domestic variety N , and the average cost p¯ can be solvedusing equation (3.13) and (3.15). We then update the cutoff cost to c1D according to equation(3.4).3. We repeat step 2 until cD converges.3.3 The escape-competition and rent-destruction effectsIn this section, we analyze the two opposing effects that determine how innovation reacts to com-petition, namely, the escape-competition effect and the rent-destruction effect. Then, we showsimulation results under different production cost distributions.We can rewrite the innovation function equation (3.10) as:I (c) =[GF( cτ)−GF(δcτ)]pi1 +[1−GF( cτ)](pi1 − pi0) (3.17)where pi1 ≡ L4γ (cD − δc)2 denotes the profit if the firm succeeds in innovating, while pi0 ≡ L4γ (cD − c)2denotes the profit if the firm does not succeed. In order to illustrate the effects of foreign compe-tition on domestic innovation we differentiate the innovation function with respect to the icebergcost τ ,dI (c)dτ=∂[GF(cτ)−GF ( δcτ )]∂τpi1 (3.18)+∂[1−GF(cτ)]∂τ(pi1 − pi0)+[GF( cτ)−GF(δcτ)]∂pi1∂τ+[1−GF( cτ)] ∂ (pi1 − pi0)∂τ.The first line of the equation above shows the “escape-competition” effect: when the foreignfirm’s production cost, after adjusting for the iceberg cost, lies in the region [δc, c], the domestic firmcan only survive if it succeeded in innovating. Higher competition would thus increase innovationin this case.The second and third line show the rent-reduction effect. When foreigners enter in the region(cτ ,+∞), the firm can survive without innovation. So, the gains from innovation comes from theusual profit gain. Since the probability of foreign firms entering in this region decreases as trade333.4. Simulationcosts drop, competition reduces the expected innovation gains, and thus serves as a source of “rent-reduction”. The other source of rent-reduction effect comes from the change in pi1 and pi0. Ingeneral, when foreign competition intensifies, the cutoff cost cD decreases, making profits shrink.This would in turn induce firms to innovate less. Whether the net effect of competition is positiveor negative depends on whether the escape-competition or the rent-reduction effect dominates.It is worth discussing here whether our assumption of the monopoly pricing made in Section3.2.2 affect the escape competition effect more or less relative to the limit pricing market structureassumption that we will make in Chapter 4. When there is limit pricing, no matter the domesticfirm innovates or not, there will be four possible cases for the final price of a good. In the fist case,the foreign cost is significantly lower than the domestic one. Then the foreign firm could charge adesired mark-up. In the second case, the foreign cost is lower than domestic but not low enoughso that the foreigner has to do limit pricing and charge the domestic firm’s cost. In the thirdcase, the foreign firm has slightly higher cost than the domestic firm and the domestic firm has todo limit pricing. And in the fourth case, the foreign firm is so lagged behind that the domesticfirm could still charge the monopoly price. Since neither the domestic nor the foreign firms couldalways charge the monopoly price, the magnitude of both the escape competition effect and therent reduction effect should decrease. Whether one decreases more than the other depends on thedistribution of foreign firms. More specifically, it depends on how the four cases compose for eachdomestic firm, and how that compare to equation (3.18).3.4 SimulationThis model has no analytical solution, so we now use a numerical simulation to show: i) how inno-vation reacts to decreases in the import transport cost τ and how that varies across the distributionof production costs, and ii) how welfare changes. We assume the production cost is distributedWeibull for both foreign and domestic firms. Table 3.1 shows the parameter values used in thissimulation.343.4. SimulationTable 3.1: Parameter values for full model simulationParameter Description ValueDemandα Demand shifter 1.5γ Elasticity of substitution 6η Cross-price elasticity 13TechnologyλH , λF Scale parameter for the Weibull distribution 0.3kH , kF Shape parameter 3δ Cost reduction if innovated successfully 0.8φ Innovation cost coefficient 1L Domestic labor supply 100Ne Number of the differentiated varieties 20Iceberg costτ0 Initial iceberg cost 1.5τ1 Iceberg cost after liberalization 1.1We assume that the iceberg cost of importing goods drops from 1.5 to 1.1. Figure 3.1 shows theproduction cost distribution for domestic and foreign producers before and after trade liberalization.We can see that the yellow line (representing foreign cost after liberalization) lies above the redline (representing foreign cost before liberalization) when the effective cost is below about 0.6. Theescape-competition effect, corresponding to the first line of equation (3.18), is positive for thesefirms.Figure 3.2 shows the innovation level as function of the production cost draws of the domesticproducers. The blue line shows before liberalization, and the orange line shows the schedule afterliberalization. The model can generate a behavior consistent with what we find in China during theWTO accession. Firms with lower production costs increase their innovation efforts after importcompetition intensifies while other, less productive firms do not increase their investment.353.4. SimulationFigure 3.1: Production cost distribution for the simulation0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Effective cost of production00.511.522.533.54Probability densityHomeForeign, =1.5Foreign, low =1.1Figure 3.2: Innovation efforts for different firms0 0.2 0.4 0.6 0.8 1Initial production cost00.10.20.30.40.50.60.70.8Innovation rate = 1.5 = 1.1Finally, we are interested in how the heterogeneous reaction in innovation affects aggregatewelfare, which is then compared to the case without innovation as a benchmark. In addition tothe two cases where τ0 = 1.5 and τ1 = 1.1, we also add some intermediate points to illustrate thetransition. Figure 3.3 shows the simulated results. The solid blue line shows, for the case withinnovation, the percentage change in utility relative to the initial state where τ0 = 1.5. The dashedorange line shows how utility changes when innovation is allowed. At first it may appear unintuitive363.5. Conclusionthat the two curves are upward sloping, meaning that as trade is liberalized, utility declines. Infact, this phenomenon is not uncommon in other trade models. For example, both Ossa (2011) andMelitz and Ottaviano (2008) find that unilateral trade liberalization is welfare reducing in modelswhere free entry delivers the Metzler Paradox, whereby import tariff decreases cause the domesticprice index to increase. In Section 4.4 in the next chapter, we give more intuition about why thishappens by analyzing the different sources of welfare change in a simpler version of the model.Regardless of whether the baseline trade model delivers negative gains from trade, the relevantresult for our context is that utility declines more slowly in the presence of endogenous investmentcompared to the case of no investment, hence pointing to a potential new source of gains fromtrade. The reason for these additional gains from trade is the topic of next chapter, but essentiallyrelies on the presence of under-investment in the decentralized equilibrium of the model.Figure 3.3: Percentage change in utility1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5Import iceberg cost -4-3.5-3-2.5-2-1.5-1-0.50Change in utility relative to  = 1.5 (%)with innovationwithout3.5 ConclusionIn this chapter, we built a model to help us analyze the heterogeneous effects of import competitionon innovation among firms. We emphasize two opposing channels through which trade liberalizationaffects innovation: the escape-competition channel, and the rent-destruction channel, in the spiritof Aghion et al. (2001) and Aghion et al. (2009). We find that the positive escape-competitioneffect can dominate the negative rent-destruction effect for the most productive firms. Thus, themodel rationalizes the empirical findings, shown in Chapter 2, that Chinese high productivity firmsincreased innovation as they faced tariff cuts in the period 2001-2005.37Chapter 4Welfare analysis4.1 IntroductionIn this chapter, we analyze a simplified setup in order to more clearly highlight the mechanismbehind the welfare consequences of competition-induced innovation. More specifically, we eliminateone of the two sources of competition present in the general model, i.e. the one coming from averageprice variations. Therefore, the only source of competition in this simplified setup is the foreignfirm producing an identical product and competing directly with the corresponding home firm.The goal of this chapter is to compare welfare changes in the presence of competition-inducedinnovation to the standard gains from trade present in a benchmark model without endogenousinnovation. The chapter has three main findings. First, we find that, relative to a constrained socialoptimum, the decentralized equilibrium always features under-investment. This is because, as willbecome clear later in the chapter, the domestic social planner is not affected by the business-stealingaimed at foreign firms. The second finding is that, because of under-investment, whether there areadditional welfare gains from innovation depends on whether innovation increases after competitionincreases. As we saw in the previous chapter, this happens if the escape-competition effect prevailsover the rent-destruction effect. The third finding is that the simplifying assumption we made inthe previous chapter, which eliminates limit pricing, has important welfare implications. Undersuch assumption, the benchmark model without endogenous innovation entails negative gains fromtrade. On the contrary, under limit pricing, trade is always welfare enhancing in the benchmarkcase of no endogenous innovation. This observation explains why in the model by Akcigit et al.(2017) welfare increases upon the imposition of higher import tariffs.4.2 A simplified setupIn the last chapter, we assumed that there is a distribution of domestic and foreign productivities,which, together with the iceberg cost, determine the probability of foreign entry. In this chapter, weshow that the welfare analysis is simplified if, instead of considering the entire foreign and domesticproductivity distribution, we only consider two variables, e and θ, which we now describe. First,the reduction of transport cost can be viewed as a simple increase in the probability of foreignfirm entry, denoted by e, as further explained below. Second, there are two relevant cases forwelfare, one in which there is no escape-competition effect and one in which such effect is strongenough to overcome the rent-destruction effect. Whether we are in one or the other case depends384.2. A simplified setupon the productivity of the foreign firm relative to the domestic firm. We assume therefore a simpledistribution of foreign productivity described as follows. Domestic firm production cost is c. Foreignfirm production cost is:c∗ =c∗1 = c Prob θc∗0  c Prob 1− θwhere θ ∈ [0, 1] is the probability that the foreign firm is close enough in productivity to thedomestic firm that the Home firm can survive if it innovates. Moreover 1 − θ is the probabilitythat the Foreign firm is too productive relative to the domestic firm and therefore it will take overthe domestic market whether the domestic firm innovates or not. We present the welfare analysisin terms of the two variables e and θ under the further four simplifying assumptions.Assumption 1 There is no competition among differentiated varieties η = 0.Assumption 2 The innovation step 1δ is large enough so that if the foreign firm is of type c∗1, thedomestic firm can charge the monopoly price after innovating. α+δc2 < c.Assumption 3 The foreign firm of type c∗0 can always charge the monopoly price:α+c∗02 < δc.Assumption 4 When foreign and domestic firms are equally productive, the foreign firm produces.The first assumption implies that the cutoff cost cD is α. Thus, this assumption helps eliminate theendogenous market price change induced by the change in cD, which simplifies the profit, innovation,and thus utility expressions. Without the endogenous price change, the rent destruction effect couldbecome smaller, as the third line of equation (3.17) disappears. Since this effect is a market effectand thus same across firms, it does not affect the relative behavior among firms, nor should it affectthe qualitative comparison between the decentralized and constrained social optimal utilities thatwe would discuss later.The second and third assumptions simplifies pricing, so that even if we allow for limit pricing, theonly situation where limit pricing could happen is when the foreign firm enters at c∗1. Assumption4 breaks the tie.It is easy to draw a relationship between the more general setup in the previous chapter andthis simplified case. The domestic firm’s optimizing problem is the following:maxIeθIpi1 + [Ipi1 + (1− I)pi0] (1− e)− 12φI2 (4.1)where pi1 again denotes the profit after innovating, and pi0 denotes the profit without innovation.The innovation schedule, denoted by the superscript d for decentralized optimum, can be solved asfollows:Idφ= (1− e) (pi1 − pi0) + eθpi1 (4.2)In comparison with equation (3.17) in Chapter 3, (1− e) corresponds to [1−GF ( cτ )], i.e. theprobability that the foreign firm does not enter the domestic market. This term governs the rent-394.3. Constrained optimum of the social plannerdestruction effect. The term eθ corresponds to[GF(cτ)−GF ( δcτ )], i.e. the probability that theforeign firm enters and that it is close enough to the domestic firm that it can be kept at bay if thedomestic firm innovates. This term therefore governs the escape-competition effect.We take a step back to look at the implication of our pricing rule on firms’ innovation incentive,as we did in Section 3.3. Due to our assumption on the production costs and innovation step size,the profit under innovation for domestic firms, pi1, is the same for the limit pricing and monopolypricing cases. The only difference is pi0, the profit of domestic firms when there is no foreign entry.This term would be higher under monopoly pricing assumption. Therefore, the rent reduction effectis expected to be higher, and the overall innovation incentive would be smaller when the marketstructure is assumed as in the previous chapter.4.3 Constrained optimum of the social plannerThe first goal of this chapter is to investigate whether the decentralized equilibrium features exces-sive or sub-optimal innovation. We therefore derive the socially optimal innovation schedule givenfirms’ price and quantity choices. In this sense, this is a constrained optimum, because the socialplanner is still deciding how much to invest given the private choice of firms in terms of quantityand prices. The social planner problem is the following:maxIu = qc0 + αEq −12γEq2 (4.3)s.t. 1 = qc0 + Eld (4.4)whereEq = e (θ (Iqm (δc) + (1− I) ql (c)) + (1− θ) qm (c∗0)) + (1− e) (Iqm (δc) + (1− I) qm (c))Eq2 = e(θ(Iq2m (δc) + (1− I) q2l (c))+ (1− θ) q2m (c∗0))+ (1− e) (Iq2m (δc) + (1− I) q2m (c))Eld = e (θ (Iδc+ (1− I) c) + (1− θ) pm (c∗0)) + (1− e) (Iδc+ (1− I) c) +12φI2Eld denotes expected labor demand for producing the differentiated good and the exported homoge-neous good; qm (c) =α−c2 denotes quantity under monopoly pricing; and ql (c) = α− c denotes thequantity under limit pricing. If we substitute the homogeneous good quantity using the resourceconstraint (4.4), utility (4.3) can be written asuinnov = 1− 12φI2 + IW1 + (1− I)W0 (4.5)whereW1 = e [θ (pi1 + CSm (δc)) + (1− θ) CSm (c∗0)] + (1− e) [pi1 + CSm (δc)]W0 = e [θCSl (c) + (1− θ) CSm (c∗0)] + (1− e) [pi0 + CSm (c)]404.4. Openness and welfareCSa (c) =12 (α− pa (c)) qa (c) denotes the consumer surplus. When the customers are charged amarkup, a = m. When the customers are charged at cost (the firm has to do limit pricing) a = l.Denote the constrained optimal solution by the superscript co, the innovation function is asfollows:Icoφ= eθpi1 + (1− e) (pi1 − pi0) (4.6)+e [θ (CSm (δc)− CSl (c))] + (1− e) (CSm (δc)− CSm (c))The first line is exactly equal to the decentralized innovation in equation (4.2) and represents theadditional profit derived from innovation. If there is entry, the additional profit is pi1. If thereis no entry the additional profit is (pi1 − pi0). The second line is the consumer surplus created byinnovation, which is not internalized by the firm when it is making a private innovation investmentdecision. Under Assumption 2, α+δc2 < c, it is easy to show that CSm (δc) > CSl (c) and thereforethe consumer surplus part, the second line of equation (4.6), is always positive.Lemma 1. The decentralized equilibrium always features under-investment: Id < Ioc.4.4 Openness and welfareIn this section we investigate how utility is affected by an increase in openness, represented here byan increase in the probability of foreign entry,e. The goal of this section is to show that opennesswill provide additional utility gains when the innovation response to trade is positive, i.e. whenthe escape-competition effect dominates.First, it is helpful to have a benchmark utility where there is no change in innovation as aresult of increased openness. It is still important to have some initial investments in order to startfrom the same average productivity level in the Home country. Therefore, setting innovation to theinitial decentralized optimal level Id0 , we can rewrite the utility function as follows:unoinnov = 1− 12φ(Id0)2+ Id0W1 +(1− Id0)W0. (4.7)We can then take the total differential of utility with respect to e at the initial decentralizedoptimum for both the case of endogenous innovation and the case of no innovation:dunoinnovde=∂u(Id0)∂e(4.8)duinnovde=∂u(Id0)∂e+∂u∂Id∂Id∂e(4.9)We are interested in the sign of the two derivatives dunoinnovde andduinnovde , and in whether the gainsfrom trade are larger under endogenous innovation, i.e. dunoinnovde ≷duinnovde .414.4. Openness and welfareLemma 2. When openness increases, the utility without innovation is increasing. That is, for ∀θ,dunoinnovde > 0.Appendix B provides the proof of the lemma. The intuition is that, foreign entry either enablesthe consumers to consume a better product (when c∗ = c∗0) or consume the same quality productat a lower price (when c∗ = c). There will be losses to the domestic firms. But since there is lessdistortion in the aggregate economy, utility will increase.The market structure that requires limit pricing is crucial here. When we make the assumptionthat allows for monopoly pricing, as we did in Chapter 3, and in Akcigit et al. (2017), welfare candecrease as e increases, because the consumer gains are dominated by the producer losses. Take theextreme case where all foreigners come in at the same production cost as the domestic firm (θ = 1).As foreign entry increases, consumers face the same prices since domestic firms are replaced byforeign firms, but both are charging monopoly prices. The only relevant change is a transfer ofdomestic profits to the foreigners (Assumption 4), which reduces domestic welfare.This observation is consistent with Ossa (2011) (CES demand) and Melitz and Ottaviano (2008)(Linear demand). Both models feature the monopolistic competition market structure in the dif-ferentiated good sectors and a perfect competitive homogeneous sector to balance trade. Bothmodels find that a unilateral import liberalization would cause welfare losses for the liberalizingcountry. The intuition is exactly as discussed above. As phrased by Ossa (2011), there are twoeffects after a unilateral import tariff drop. First, there is a production relocation effect. Domesticconsumers shift expenditure toward the foreign goods that are cheaper now. This is exactly theloss to domestic producers in our model. Second, there is an import price effect that increasesconsumer surplus because they now can consume at a lower price. In Ossa (2011) as well as in ourmodel with the price setting assumption, the negative production relocation effect dominates13.Next, we study whether the utility increases faster with innovation relative to the benchmark.It suffices to investigate whether ∂Id∂e is positive, because under Lemma 1, there is always under-investment, i.e. ∂u∂Id> 0. From equation (4.2), we can take derivative of innovation with respect toentry rate e,∂Id∂e= − (pi1 − pi0) + θpi1The first part of the partial derivative is the negative rent reduction effect, and the second part isthe positive escape-competition effect. We can see that, the escape-competition effect decreases asmore foreign firms come in with very low production cost, thus there is nowhere to escape for thedomestic firms. Therefore, there is a cutoff condition for θ that determines whether the gains fromtrade are larger under endogenous innovation. We summarize in the following lemma.13Demidova (2017) finds another way of changing the relative magnitude of the relocation effect and the priceeffect. She shows that when the homogeneous sector is eliminated and wages are allowed to adjust, one obtains themore intuitive prediction that trade is welfare enhancing.424.5. SimulationLemma 3. dunoinnovde ≥ duinnovde iff θ ≥ θˆ whereθˆ ≡ pi1 − pi0pi1. (4.10)That is, when the escape-competition effect dominates the rent-destruction effect, there wouldbe an additional utility gain under import liberalization.4.5 SimulationIn this section, we simulate the cases studied to provide a graphical representation of the resultsobtained above. Table 4.1 shows the parameter values used.Table 4.1: Parameter values for welfare simulationParameter Description ValueDemandα Demand shifter 2γ Elasticity of substitution 3Technologyc Home firm production cost 1.64c∗0 Production cost of foreign good producers 0.29δ Cost reduction if innovated successfully 0.7φ Innovation cost coefficient 10In Figure 4.1, we show the decentralized innovation and the utilities as the entry rate e increasesfrom 0.1 to 0.3, when the foreign firm is of the same productivity as the home firm, i.e. θ = 1and c∗ = c with probability 1. The quadratic curves on the left panel shows utility as a functionof innovation I. The circles denote the decentralized choices of innovation Id, and the diamondsdenote the constrained optimal choices Ioc, for e = 0.1 and e = 0.3. We can see that the circlesalways lie to the left of the diamonds, which is consistent with under investment.On the right panel, we show utility as function of e. The solid line shows utility with endogenousinnovation. The dashed line shows the benchmark utility setting innovation to the level chosen whene = 0.1. Since this case features a strong escape-competition effect, innovation increases as foreignentry increases, and there is an additional positive gain from innovation.434.5. SimulationFigure 4.1: Foreign cost is the same as domestic, θ = 10.4 0.5 0.6 0.7 0.8 0.9 1Innovation1.0381.0391.041.0411.0421.0431.0441.045UtilityI(eL) I(eH)low eLhigh eH0.1 0.15 0.2 0.25 0.3Entry1.04161.04181.0421.04221.04241.04261.0428Utilityw/ innovw/o innovNote: The circles on both panels indicate the decentralized innovation decisionsand the resulting utility levels. On the left panel, the diamond symbol marks theconstrained optimum level of innovation.Figure 4.2 shows the case when the foreign firm’s cost is much lower than the domestic firms,i.e. θ = 0 and c∗ = c∗0 with probability 1. In this case, there is only a rent-destruction effect wheninnovation is endogenous. Therefore, as shown on the left panel, as e increases, the decentralizedinnovation effort decreases. And on the right panel, the benchmark utility slopes more steeply thanthe utility with innovation, indicating a negative gain from endogenous innovation response.Figure 4.3 shows the ratio of aggregate utilities uinnovunoinnovfor different compositions of foreignfirms. The red line shows a composition where most of the foreign competitors are close to thedomestic firms in productivity (θ = 0.9). In this case, θ is above the cutoff θˆ defined in equation(4.10) and parameterized in Table 4.1. The escape-competition effect dominates, and the ratioof the utility with innovation to the benchmark utility is always above 1. The blue line shows acomposition where most of the foreign competitors are much more productive than the domesticfirms (θ = 0.3). In this case, the rent-destruction effect dominates, though its magnitude decreasesas e increase. In fact, when e = 1, the rent-destruction effect goes to zero. Therefore, the blue linefirst decreases below 1 then increases to above 1.444.5. SimulationFigure 4.2: Foreign cost is much lower than domestic, θ = 00 0.2 0.4 0.6 0.8 1Innovation1.051.061.071.081.091.11.111.121.131.141.15UtilityI(eL)I(eHlow eLhigh eH0.1 0.15 0.2 0.25 0.3Entry1.071.081.091.11.111.121.131.14Utilityw/ innovw/o innovNote: The circles on both panels indicate the decentralized innovation decisionsand the resulting utility levels. On the left panel, the diamond symbol marks theconstrained optimum level of innovation.Figure 4.3: Utility ratios uinnov/unoinnov0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Entry0.99911.0011.0021.0031.0041.0051.006Utility Ratio = 0.3 = 0.9Finally, we simulate a case with the assumption that firms need to incur a cost ε to set the price,like in Akcigit et al. (2017), bringing back monopoly pricing. In Figure 4.4, we replicate Figure 4.1where all foreign firms are of the same productivity as the domestic ones, with the assumption thateliminates limit pricing. As discussed under Lemma 2, the benchmark utility decreases with tradeliberalization. See the dashed line on the right panel.Since in this case, the escape-competition effect dominates the rent-destruction effect (becauseθ > θˆ), according to Lemma 3, innovation could contribute to a slower decrease in the aggregateutility.454.5. SimulationFigure 4.4: Eliminating limit pricing0 0.2 0.4 0.6 0.8 1Innovation0.990.99511.0051.011.015Utilitylow ehigh e0 0.2 0.4 0.6 0.8 1Entry1.00951.011.01051.0111.01151.012Utilityw/ innovw/o innovNote: The circles on both panels indicate the decentralized innovation decisionsand the resulting utility levels. On the left panel, the diamond symbol marks theconstrained optimum level of innovation.46Chapter 5How the Breadth and Depth ofImport Relationships Affect thePerformance of CanadianManufacturers5.1 IntroductionSo far in this dissertation, we have looked at the effects induced by changes in import tariff. In thisChapter, we look at another factor that is important to trade — the supplier-buyer relationship.Specifically, we study how the variety of import relationships and the average duration of therelationships affect the performance of Canadian manufacturing importers.The love of variety forms the basis for the gains from trade in all trade models based on theArmington (1969) assumption or on Dixit-Stiglitz monopolistic competition. It therefore under-pins work based on Melitz (2003) and most computable general equilibrium evaluations of tradeliberalizations. While the existing evidence focuses on the empirical relevance of the love-of-varietyfor final goods, there is remarkably little evidence on its implications for intermediate and capitalgoods purchased by firms, which constitute the bulk of trade.14,15 With inputs acquired by firms, werely on the Ethier (1982) theoretical demonstration that the love-of-variety idea can be extended toproduction functions. Ethier (1982) adopts a parallel version of the Dixit-Stiglitz utility function asan objective for the firm; in this framework, additional inputs increase output in proportion to thetotal number of products acquired for production. In this chapter, our two proxies for breadth arethe number of 10-digit products a manufacturing firm imports and the number of supplying firmsper imported product. We estimate the elasticities of productivity with respect to both variables.A complementary view on how import relationships shape firm performance comes from themanagement literature. In particular, Uzzi (1996) applied Karl Polanyi’s idea of embeddedness toproduction networks. He argues that “buyer-supplier networks operate in an embedded logic ofexchange that promotes economic performance through inter-firm resource pooling, cooperation,and coordinated adaptation[...]” (Uzzi (1996), p. 675). Using data on New York-based apparel14The groundbreaking work by Broda and Weinstein, 2006 has been the first to structurally estimate the impactof increased variety for welfare. For a recent literature review, see Feenstra (2010).15Miroudot et al. (2009) document that trade in intermediates and capital goods accounted for about 70% of thetotal Canadian imports in 2006.475.1. Introductionfirms, he finds that a firm that systematically interacts with a network of suppliers enjoys betteroutcomes in terms of survival and productivity relative to firms that keep all their transactions atarm’s length and do not engage in long-term relationships.16 Inspired by Uzzi, we use the shareof continuous suppliers over the total number of suppliers as our principal measure of relationshipdepth. It is expected to increase productivity and other performance measures.Analogously to Kasahara and Rodrigue (2008), we adopt the control function approach of Levin-sohn and Petrin (2003) to account for unobserved productivity shocks at the firm level. We furtherassume that importing decisions are dictated by the presence of fixed costs that are heterogeneousacross firms and not perfectly correlated with productivity, so that the effect of importing decisionscan be identified. By controlling for intermediate inputs, we also control for the cost reducingchannel that a broader variety of inputs could have for importers. Therefore, we try our best tomeasure the love-of-variety channel using our breadth variables.Our results show that the number of imported products and the number of suppliers per productincrease the size of Canadian importing manufacturers with elasticities of 0.15 and 0.12, respectively.The breadth effects drop to 0.03 and 0.02 after controlling for inputs and including a control functionto account for unobserved productivity. We also quantitatively explore how important continuousrelationships are to the performance of importing firms. We document that older relationshipsare more valuable and increase firm size and productivity. An importer that went from usingall new suppliers to retaining all the prior year suppliers could increase its productivity by 2.4%.The importance of ongoing relationships is also reflected in our analysis of the size and value oftransactions between an importing firm and its long-term partners: both the quantity imported,and the associated unit value are larger. However, after controlling for inputs, the ongoing use of thesame suppliers does not have any statistically significant effects on performance in foreign markets.Finally, we analyze the influences of the suppliers’ country of origin by including as explanatoryvariables the share of suppliers from China and the United States. Greater reliance on Chinesesuppliers is associated with smaller firm size and has a negative impact on exporting performance;its effect, however, is measured imprecisely, and it is not always significant at the 5% level.This chapter contributes to the large empirical literature documenting productivity differencesacross firms differing in their import choices. Data from the United States, Belgium, Italy, Hungary,Colombia, and Chile reveal that importers are bigger in terms of employment, shipments, valueadded, and TFP if compared with non-importing firms.17 In fact, firm heterogeneity in importingbehavior has important implications for the measurement of the gains from trade, especially whenlarge firms import proportionally more of their inputs.18Our paper also relates to recent work that has emphasized the two-sided nature of trade rela-16Uzzi (1997) and Uzzi (1999) extend these ideas.17See Bernard et al. (2007) for the United States; Halpern et al. (2015) for Hungary; Muuˆls and Pisu (2009)for Belgium; Castellani et al. (2010) for Italy; Kugler and Verhoogen (2009) for Colombia; Kasahara and Rodrigue(2008) and Kasahara and Lapham (2013) for Chile. Episodes of trade liberalizations provide additional evidenceon the productivity gains from importing; see, for example, Amiti and Konings (2007), Goldberg et al. (2009), andTopalova and Khandelwal (2011).18See Blaum et al. (2017) and Ramanarayanan (2017).485.2. Datationships. Several contributions have analyzed the buyer-supplier margin using export and importtransaction data. Bernard et al. (2017) and Carballo et al. (2013) describe the behaviour of Norwe-gian and South American (Costa Rica, Uruguay and Peru) exporters. More recently, other contri-butions have focused on the formation of buyer-supplier relationships. Eaton et al. (2015) calibratea search-and-matching model to match the trade patterns between U.S. buyers and Colombianexporters. Monarch (2014) quantifies the magnitude of frictions between U.S. buyers and Chinesesuppliers in finding new partners. Kamal and Sundaram (2016) identify the existence of importer-specific spillovers in the decision of Bangladeshi manufacturers to sell to U.S. importers. Dragusanu(2014) analyzes the matching between buyers and suppliers in a model of sequential production.A closely related contribution is the paper by Lu et al. (2016), who build a model to analyzethe switching behaviour of Colombian importers. Consistent with our findings, they document thatColombian firms importing more products from a larger set of suppliers tend to be larger. Whiletheir approach combines productivity and scale effects, our contribution, instead, tries to identifythe productivity effects of different dimensions of importing using the control function approach.The question of the importance of supplier networks for productivity is also the focus in a paperby Bernard et al. (2017), where the authors find a positive effect on productivity and on the numberof domestic supplier connections after the opening of high-speed train lines in Japan. Our elasticityestimates, however, are not comparable to theirs because they focus on the reduced form effects ina difference-in-difference strategy; in fact, their identification relies on differences in performancebetween input intensive firms and labor-intensive firms located close to a new train station relativeto firms in locations without a new station, before and after the high-speed train expansion. Ourelasticities, instead, are informative of the productivity effects associated with an exogenous changein the breadth and depth variables.The rest of the chapter is organized as follows. We describe the data in section 5.2; we analyzethe main features of the data in subsection 5.2.1. We present our empirical strategy in section 5.3.The results are shown in section 5.4. Section 5.5 concludes.5.2 DataThe data for our project comes from three sources: The Import Registry, the Annual Survey ofManufactures (ASM)-T2LEAP, and the Export Registry.The import registry collects transaction data using Form B3 from the Canadian Border ServiceAgency. Canadian importers are required to fill information on the vendor’s name and address,the country of export, the product (HS10 code), the imported value and quantity. Identifiers werecreated for each supplier from the vendor’s name and address.19 Transaction records with consistentsuppliers’ identifiers are available from August 2002 to June 2008.20The raw data identifiers are the transaction number, the line number (a particular item in atransaction, often corresponding to a deeper level of disaggregation than a HS10 code), and the19See Appendix C.1 for a summary on the methodology.20Import records at the product-, origin-, and firm-level are available since 1993.495.2. Datadate (month-year). We aggregate the data across transactions to the firm-supplier-HS10-countryof origin-year level. The initial dataset contains about 5.5 million observations (corresponding tothe firm-supplier-HS10-origin-year combination).In order to construct firm-level measures of performance, we merge the import customs withfirm-level information drawn from the Annual Survey of Manufactures (ASM). The ASM is a sur-vey covering the universe of manufacturing establishments. It includes data on shipments, industryclassification (5-digit NAICS codes), employment, salaries and wages, cost of materials, and expen-diture on electricity. We enrich the ASM dataset by adding information on assets and investmentextracted from the T2-LEAP database. T2-LEAP links two administrative data sources, the Lon-gitudinal Employment Analysis Program (LEAP) and the Corporate Tax Statistical Universal File(T2SUF). Those two sources include all firms that either register a payroll deduction account withthe Canada Revenue Agency (CRA) or file a T2 tax return with the CRA. The capital/investmentdata reported in T2-LEAP encompass manufacturing and non-manufacturing activities of each firm;we therefore allocate capital/investment to the individual manufacturing establishments using theshare of the establishment revenues in manufacturing over the total firm sales.We merge the import registry with firm-level characteristics and we collapse the information onimport choices at the firm-year level. This creates our final dataset with 93,386 observations (herean observation is a firm-year combination).Export-related information on Canadian firms comes from the Canadian Export Customs. Thecustom data include export records at firm-, product (HS8 code)-, and destination-level for theuniverse of exporters located in Canada.5.2.1 Import Network Characteristics: Breadth and DepthThis subsection explores the main features of the Canadian import registry. We focus our discussionon cross-sectional and dynamic characteristics of the importers’ distribution. Table 5.1 summarizesthe main cross-sectional aggregates by sector in 2007.Columns (1)–(2) describe the intensive import margin: column (1) shows the total import valuefor each sector, while column (2) reports the share of imports out of total manufacturing sales.Although chemical and oil imports are the largest industries in terms of value, other sectors–namely,Computing, Apparel, and Transportation Equipment–are relatively more dependent on foreignproducts. Some sectors, such as Beverages & Tobacco and Apparel, display import shares thatare larger than our estimates of the share of materials in production (see tables C.4 to C.6). Thisfinding may be due to carry-along trade, the fact that firms tend to import both intermediate inputsand final consumption goods.21Columns (3)–(7) focus on the extensive import margin: they show the number of countries,products (HS10 codes), Canadian buyers, foreign suppliers and buyer-supplier relationships. Eachsector imports a large number of products (from 9% of all HS10 codes in Leather to 46% inMachinery) from a large number of countries (the median sector imports from 81 countries). The21See Bernard et al. (2017) for a detailed theoretical and empirical analysis of carry-along trade.505.2. Datalarge scope of the imported products raises concerns on secondary wholesale activities. While wefocus on firms in the manufacturing sectors, this classification requires that the majority of firmrevenues comes from manufacturing activities; thus, we cannot exclude that those firms may includeplants whose industry code is in wholesale or in other non-manufacturing sectors. A similar caveatapplies to firm-level statistics (see column (4) in table 5.2). In the empirical analysis, we rely onfirm fixed effect to capture time-invariant differences in activity classifications across firms. Lookingacross columns (5)–(7), we note that the number of relationships is mainly driven by the numberof suppliers. This fact suggests that Canadian firms tend to adopt a multi-sourcing strategy, asmicro-level statistics will confirm.Table 5.1: Aggregate Statistics by 3-digit industry, 2007(1) (2) (3) (4) (5) (6) (7)Industry Imp. Value1 Imp. Share Countries Products Firms Suppliers RelationsFood 7.90 0.09 115 6067 1396 18684 29624Bev. & Tob. 2.01 0.34 71 2422 145 3641 4619Text. Mills 0.61 0.58 55 2332 197 3251 4197Text. Prod 0.55 0.55 55 2717 301 3947 4760Apparel 1.18 0.67 80 3326 723 10217 14549Leather 0.13 0.62 48 1518 146 1801 2190Wood 1.99 0.11 72 3750 1052 11462 16401Paper 3.75 0.22 74 3580 383 8989 12997Printing 0.78 0.18 54 3077 941 6971 9875Petrol 18.22 0.19 57 2392 86 3153 3840Chemical 18.82 0.57 104 7345 948 22158 33878Plastics 7.21 0.43 83 5964 1218 19204 28477Mineral 2.23 0.25 72 4307 713 8361 11598Metals 11.85 0.33 90 3756 325 8839 11436Met. Prod 5.54 0.31 89 6987 2980 28155 40804Machinery 11.23 0.48 118 7760 2436 40088 61318Computing 9.84 0.80 115 5309 1008 30605 47549Electrical 4.13 0.65 89 4385 588 13630 17644Tran. Eq. 74.75 0.63 123 7143 1029 40726 65539Furniture 3.27 0.29 87 5377 1104 12704 17651Miscel. 3.68 0.63 102 6542 1648 17713 21608n/a 0.16 1.32 62 4316 2065 5883 6594Total Mfg 189.83 0.62 194 16721 21432 233718 4671481 Values in millions.Notes: Aggregate import statistics by sector. The last row reports the totals for all manufacturing.Table 5.2 takes a closer look at the importing behavior of firms, with a focus on 2007. The firsttwo columns report the firm-level average import value and import share across sectors, confirmingthe patterns shown in columns (1)-(2) of Table 5.1. Oil companies are the biggest importers,although their share of imports out of total sales is small compared with firms in other industries.515.2. DataColumns (3)-(5) focus on the extensive margin. The quasi-median firm sources its inputs from 2countries and imports multiple products from a large set of suppliers.22 This evidence confirms astrong multi-sourcing nature of the Canadian import relationships.23Table 5.2: Firm-level statistics on importing, 2007(1) (2) (3) (4) (5) (6)IndustryImport Import Sources2 Products2 Supps2 Avgvalue2 share /firm /firm /firm ageFood 366.57 0.09 2 12 9 1.4Bev. & Tob. 296.02 0.13 2 12 10 1.2Text. Mills 484.16 0.39 3 13 11 1.5Text. Prod 212.10 0.33 2 13 10 1.6Apparel 299.75 0.38 4 17 12 1.3Leather 165.65 0.36 3 11 9 1.7Wood 170.38 0.07 1 7 5 1.5Paper 638.63 0.21 1 11 10 1.7Printing 82.53 0.06 1 7 6 1.3Petrol 5140.36 0.14 2 41 25 1.6Chemical 518.09 0.24 2 20 14 1.5Plastics 344.65 0.17 2 14 11 1.6Mineral 189.25 0.13 2 12 8 1.7Metals 800.08 0.20 2 14 14 1.6Met. Prod 162.28 0.11 1 10 7 1.6Machinery 257.82 0.18 2 15 11 1.6Computing 384.29 0.33 3 23 16 1.4Electrical 363.42 0.31 3 16 14 1.5Tran. Eq. 547.98 0.24 2 25 17 1.7Furniture 137.99 0.10 2 11 8 1.5Miscel. 125.33 0.21 2 9 8 1.5n/a 19.32 - 1 3 3 1.91 Values in thousands of dollars of imports per firm.2 Quasi-medians: means of 10–11 observations around the median.The firm-level statistics in table 5.2 hide a large degree of heterogeneity across suppliers, prod-ucts, and countries. Figure 5.1 offers more details on the distributions of products (top panel) andsuppliers per product (bottom panel). The modal firm imports one product from one supplier;however, while the product distribution is right-skewed, the distribution of log-suppliers per prod-uct is slightly negatively-skewed. Therefore, across sectors the median supplier-per-product ratiois smaller than 1 (in log-scale smaller than zero), suggesting that searching for a supplier might bemore costly than searching for a product.22Quasi-median are calculated as the average of 10/11 observations around the true median. This procedure isrequired to maintain data confidentiality.23Blum et al. (2010) find that Chilean manufacturers import 11.9 HS8 products from 3.2 countries, roughly con-sistent with our findings.525.2. DataFigure 5.1: Distribution of number of products and supplier per products(a) Products imported (top coded at 100) (b) Log suppliers per product importedWe highlight the geographical distribution of the import network in table 5.3. This table showsthe top 10 country of origin for suppliers in 2003 and 2007. The United States is the top sourceof foreign suppliers in both 2003 and 2007. However, the share of U.S. suppliers decreased from75% to 69% over the five-year period, with the bulk of the change absorbed by a larger presenceof Chinese suppliers. China had already reached the top 2 position in 2003 but consolidated itsmargin over Germany by 2007. The rest of the distribution remained almost unchanged between2003 and 2007; only India and Mexico swapped their positions in the ranking.Table 5.3: Top 10 Country Distribution, 2003 and 20072003 2007Country Share of Suppliers Country Share of SuppliersUS 74.80% US 68.53%China 2.99% China 7.32%Germany 2.68% Germany 3.05%Italy 2.41% Italy 2.42%Great Britain 2.17% Great Britain 2.07%Hong Kong 1.68% Hong Kong 1.98%Taiwan 1.29% Taiwan 1.51%France 1.28% France 1.36%India 0.77% Mexico 0.94%Mexico 0.76% India 0.93%Moving back to the firm-level analysis, we emphasize a dynamic dimension of the import networkin the last column of table 5.2, the average age across supplier relationships for a given firm. Martinet al. (2017) suggests that the longer duration of buyer-supplier transactions might be explainedby the specificity of the relationship, due to the cost of switching to new suppliers. In our data, weset “Age” equal to 0 if a firm starts importing from a particular supplier in a given year and has535.2. Datanever imported from the same supplier before; the “Age” variable is equal to 1 if the relationshipwith the supplier existed in the previous year and so on. In the data we used to build table 5.2,the longest relationships are of age 5. Column (6) reveals that, after a relationship is established,firms tend to keep their suppliers for additional 1.5 years; if we include the initial year in which therelationship is formed, the average duration of buyer-supplier relationships totals 2.5 years.Figure 5.2: Older relations are less frequent but more valuableFigure 5.2 explores two characteristics of import relationships along the age dimension; inparticular, we look at the number of relationships and the value share over the age distributionof buyer-supplier relationships. Figure 5.2 plots the shares for 2007, where the oldest observedrelationship is 5 years. In the appendix, figure C.1 extends our results to the partial year of 2008.24Both graphs reveal that older relationships tend to be much less common but much more valuable.Relationships of 5 or more years account for only 10% of the total number of relationships butcapture 40% of Canadian firms’ total imports. Monarch and Schmidt-Eisenlohr (2016) documenta similar finding for U.S. import relationships.Table 5.4: Import value decomposition bytype of relationshipyear Continuous New Discontinuous2003 18.88 24.88 56.242004 14.59 24.19 61.222005 15.56 22.83 61.612006 16.97 20.52 62.522007 12.50 31.95 55.55Table 5.4 looks further into the dynamic import margin. While we rely on the age distribution inour cross-sectional analysis in figures 5.2 and C.1, extending such concept over time would be ardu-24The results are robust across 2007 and 2008; 2007 is our preferred year as the Custom Registry data for 2008 areavailable only through June.545.2. Dataous due to changes in the composition of the different age groups over time. Thus, table 5.4 developsa time-series concept of import dynamics by decomposing the imported value across continuous,new, and discontinuous relationships, where relationships are defined at the supplier-product level.A relationship is considered to be “continuous” if a firm imported the same product from the samesupplier at least the year before. A relationship is considered “new” if the firm imports a productfrom a supplier for the first time in a given year (either the firm has never imported the productfrom that supplier or it has never imported any product from that supplier). We classify all otherrelationships as “discontinuous”. In each year, around one quarter of total imports comes from newsuppliers, more than half from discontinuous, and less than 20% from continuous relationships.Figure 5.3: Decomposition of imports by length of relationship0204060802003 2004 2005 2006 2007yearImport Share ContinuousNew DiscontinuousImport Share from the US01232003 2004 2005 2006 2007yearImport Share ContinuousNew DiscontinuousImport Share from China(a) United States (b) ChinaFigure 5.3 applies a similar decomposition to the import shares for the top 2 Canadian partnersover 2003 to 2007; the y-axis in both panels indicates the percent of total imports. Overall,the U.S. import share decreased from around 80% in 2003 to 70% in 2007; the Chinese importshare, instead, more than doubled over the same period, raising to 2.9% in 2007 from 1% in2003. Decomposing the import values by type of relationship reveals different patterns in the twocountries. While continuous suppliers account for one quarter of the total value imported from theUnited States, continuous relationships with Chinese suppliers represent a much smaller fraction(around one tenth), with a contribution slowly growing over time. A second point of contrast liesin the contribution of new and discontinuous suppliers: while discontinuous suppliers dominate inU.S.-Canada trade, new Chinese suppliers seem to be as important as discontinuous ones. Thisfact suggests that Canadian importers tend to experiment more in the Chinese market.We will now proceed with our investigation of the impact of the breadth and depth of importrelationships on firm performance.555.3. Estimation Framework5.3 Estimation FrameworkIn this section, we lay out a simple estimation framework that clearly identifies the conditionsunder which we can measure the effect of decisions related to the breadth and depth of importrelationships. The primary challenge we face is to disentangle the effect of import decisions fromthat of underlying and unobserved firm productivity. The timing is similar to the one adoptedby Kasahara and Rodrigue (2008), which in turn modifies the standard assumptions in Olley andPakes (1996) and Levinsohn and Petrin (2003) (henceforth, referred to as OP/LP).Establishment i starts each period t with a stock of capital Kit and productivity ωit. It sub-sequently chooses all variable inputs of production (labor, materials, electricity) and decides nextperiod’s capital Ki,t+1. At this point the firm also makes all decisions relating to importing, likethe number of products to be imported and from how many suppliers, which we summarize hereby dit and discuss in detail later. The production function in logs is as follows:yit = β0 + βddit + βllit + βeeit + βmmit + βkkit + βaAgeit + ωit + δst + αi + εit (5.1)where yit, kit, lit, eit, mit are the logarithm of, respectively, the value of output, capital, labor,electricity and material costs; Ageit is the age dummy of firm i and year t; δst is a sector-timedummy, αi is the firm fixed effect and εit is an unexpected shock to firm output after all input andimport decisions have been made.The coefficient of interest throughout this chapter is βd which measures the effect of importingdecisions on output—holding firm productivity and all other inputs constant. The main challengethat we face in identifying βd is the endogeneity of importing decisions, which virtually any modelwould link to the unobserved productivity shock ωit. To address this issue, we adopt the controlfunction approach in OP/LP. The specific assumption in Levinsohn and Petrin (2003) is thatmaterial input choices are a function of capital, age of the firm, and productivity shock ωit. Wecan therefore write:mit = f(kit,Ageit, ωit) (5.2)and, under standard monotonicity assumptions, we can invert the function to find ωit:ωit = f−1(kit,mit,Ageit). (5.3)We can then substitute equation (5.3) into (5.1) and collect all terms for kit, Ageit and mit intothe function ϕ(·) to obtainyit = β0 + βddit + βllit + βeeit + ϕ(kit,mit,Ageit) + δst + αi + εit, (5.4)565.3. Estimation Frameworkwhere ϕ() is a second-degree polynomial in capital, age and materials:ϕ (kit,mit,Ageit) = β1kit + β2mit + β3Ageit + β4k2it + β5m2it+ β6Age2it + β7kitmit + β8mitAgeit + β9Ageitkit,and all the β’s are 3-digit industry specific parameters.The OP/LP procedure would then entail a second stage to estimate the capital, material, andage coefficients, but we omit discussion of this portion of the estimation because we are not directlyinterested in these parameters. The second stage coefficients are industry-specific, so we only reportthem in the industry-specific regressions shown in Appendix C.2.As our coefficient of interest is βd, we now discuss under which conditions this coefficient canbe identified. The key condition for identification is that dit is not uniquely determined by theproductivity shock ωit. Take the case, for example, in which dit represents the number of suppliersfrom which the firm imports. Those suppliers could be firms with which firm i already interactedin the past. Alternatively, firm i may choose to establish new relationships with suppliers it nevercollaborated with. We assume that these decisions entail a fixed cost that may depend on thenumber of relationships and whether those relationships are established or new but does not dependon the quantity imported. Furthermore, we assume these fixed costs are heterogeneous across firmsand not perfectly correlated with the firm’s productivity ωit. This type of assumption has becomecommonplace in the literature that explores various outcomes associated with the export status(see, for example, Helpman et al., 2016) and is typically justified by the fact that, controlling forproductivity, various outcomes such as firm-level wages are still correlated with the firm exportstatus. In our context, it is plausible to assume that a firm’s TFP does not uniquely determine itsfixed cost of establishing and maintaining relationships, a cost which could depend, for example,on the skills of the accounting, purchasing and legal departments of the company. Moreover, thosecosts could also depend on the history of past relationships, a factor that varies from firm to firm.The assumption of fixed cost heterogeneity breaks the perfect collinearity that would otherwisearise between all variable inputs and the importing decisions. In this sense, our assumption ad-dresses the concern raised by Ackerberg et al. (2015) (ACF) in the context of production functionestimation.25 To reiterate the point, if we did not make the assumption that heterogeneous fixedcosts affected importing decisions, then our coefficient of interest could not be estimated becauseof the functional dependence problem pointed out by ACF: once we control for all variable inputchoices, there would be no independent variation left in the choice of dit to estimate βd. It isworth emphasizing that it does not matter for identification whether the fixed costs of importingare positively or negatively correlated with productivity shock ωit as long as the correlation is notperfect. If material purchases are all made after this productivity shock, then the control functionapproach will account for ωit and βd will identify the causal effect of importing on output.25ACF point out that in the OP/LP framework in the absence of further productivity shocks, labour and othervariable inputs are perfectly collinear because they are all determined by ωit. This problem prevents the identificationof the labour elasticity.575.4. ResultsLet us now turn to the different components of dit, a variable that so far has stood in for allimporting decisions. In particular, we are going to focus on three sets of variables (for summarystatistics see Section 5.2.1):• Breadthit: in this category we include two variables. The first one is ln Productsit whichrepresents the variety of imported inputs a firm decides to access. The second variable is theratio of suppliers to products, ln Supp/Prod, which measures the number of different suppliersfrom whom firm i decides to import a given variety.• Depthit: we adopt one variable, the share of continuous relationships, Continuousit to identifythe depth of the import network.• Originit: the variables US Shareit and CN Shareit measures the degree to which imports byfirm i come from the top two source countries, i.e. the United States and China.To summarize, writing our preferred specification (5.4) in explicit form:yit = β0 + βd1Breadthit + βd2Depthit + βd3Originit + Input Controlsist + δst + αi + εit (5.5)where Input Controlsist ≡ βs,llit + βs,eeit + ϕs,t(kit,mit,Ageit). Notice that the coefficients in theInput Controlsist function are sector s specific to allow the production function to differ acrosssectors (3-digit NAICS codes in the regressions). Our coefficients of interest are (βd1, βd2, βd3).Ethier (1982) suggests that β1 > 0 if the number of HS10 codes and the ratio of suppliers to productsinduce productivity gains from breaking-up production into multiple stages; a similar mechanismapplies to products imported from different countries of origin (βd3 > 0) if those products areimperfect substitutes. Finally, we expect βd2 > 0, that is the share of continuous suppliers to bepositively correlated with firm productivity; a positive correlation emerges in Uzzi (1996), whichargues that firms within a network benefit from continuing partnerships with their suppliers. We’llexplore the source of productivity gains in continuous relationships in more details in section 5.4.3.Our causal interpretation of the results relies on the ability of the input control function, sector-timeand firm dummies to capture all factors other than productivity shocks that may simultaneouslyaffect firm importing decisions and sales.5.4 ResultsTable 5.5 shows the results for specification (5.5). Columns (1)–(4) report the coefficients of interestfrom a restricted version of this specification that excludes the Input Controls. The final column(5) includes Input Controls. The number of imported products and the number of suppliers perproduct increase firm size with elasticities of 0.15 and 0.12, respectively. The import breadthelasticities drop to 0.03 and 0.02 after controlling for inputs and including the control function.Having continuous relationship with suppliers has also a positive effect on firm productivity; thecoefficient on the share of continuous suppliers is positive and significant across all specifications.585.4. ResultsThe origin of suppliers shows a somewhat unexpected effect on firm sales. While the share ofU.S. suppliers has no significant impact on the dependent variable, the share of Chinese suppliersshows a negative and significant coefficient that persists in column (5). One possible explanation torationalize the negative effect of Chinese suppliers is that firms sourcing from China are aware thattheir initial supplier draws are likely to be poor, but they expect to find better matches throughsearch and continued experience.Table 5.5: Firm size and productivity regressions(1) (2) (3) (4) (5)Dependent variable: ln Salesln Products 0.154a 0.154a 0.153a 0.153a 0.030a(0.005) (0.005) (0.005) (0.005) (0.003)ln SuppProd 0.122a 0.122a 0.121a 0.121a 0.023a(0.007) (0.007) (0.007) (0.007) (0.003)Continuous 0.037a 0.038a 0.040a 0.040a 0.024a(0.008) (0.008) (0.008) (0.008) (0.004)US share 0.015 -0.001 0.003(0.012) (0.012) (0.006)China share -0.207a -0.207a -0.051c(0.044) (0.045) (0.024)Input Controls∗ n n n n yFirm Fixed Effects y y y y ySector-Year FEs y y y y yObs. 93,386 93,386 93,386 93,386 93,386R2 0.036 0.036 0.037 0.037 0.717ln Products: log number of imported products (HS10).ln SuppProd : log number of foreign suppliers per imported products.Continuous: share of suppliers from which the buyer purchasedfor at least the previous year.US Share: number of U.S. suppliers divided by total foreign sup-pliers.CN Share: number of Chinese suppliers divided by total foreignsuppliers.* Input Controls include employment, electricity, and quadratic incapital, materials and age. All controls are also interacted with3-digit NAICS code dummies.Notes: Firm FE regression, years 2002–2008. A sector represents a3-digit NAICS code. Robust standard errors, clustered at the firmlevel, in parentheses. Significance thresholds are 0.1% (a), 1% (b),5% (c). The last column implements our preferred specificationwith input controls as shown in equation (5.5).The smaller elasticities in column (5) are just what we would expect from a more complete595.4. Resultsmodel of the firm’s behavior. Suppose an increase in breadth variables lead to 1% productivityimprovement. Holding factor prices constant, this should lead to an η− 1 percent expansion in thevalue of sales (pq) of the firm, where η is the local (absolute) price elasticity of demand. The lnProducts coefficients in columns (4) and (5) are consistent with firm own-elasticities of about six(η − 1 ≈ 0.15/0.03) whereas the corresponding supplier per product elasticities imply η ≈ 7. Bothseem on the high side of the values found in the literature but not unreasonably so. In a recentpaper, Antra`s et al. (2017) report a lower trade elasticity (around 5); their estimate, however, isbased on a model that features only the extensive margin of importing at the country level. Thus,with additional (within-country) margins of adjustment at the product and at the supplier level, itis reasonable to expect higher elasticity estimates than in Antra`s et al. (2017). 26Table 5.6: Summary Statistics for variables used in regressionsMean Std DeviationExplanatory variablesln Products (no. of HS10 imported) 2.18 1.44ln SuppProd (suppliers per product) -0.21 0.57Continuous share 0.15 0.09US share 0.73 0.23CN share 0.16 0.32Dependent variablesln Sales 14.93 1.67Productivity (Levinsohn-Petrin residuals) 5.37 1.31ln Exports 13.11 2.71Export Status 0.62 0.49ln Number of Destinations 0.72 0.79ln Exported Products 1.37 1.07How big are the breadth and depth effects we have estimated in Table 5.5? Perhaps the mostnatural thought experiment for the breadth effects is to double the number of products or suppliersper product. This would lead to a 20.03 =2.1% increase in productivity for doubling productswhereas doubling suppliers per product would yield a 1.6% productivity boost. These effects seemsomewhat modest. Raising the Continuous share from 0 to 100% would lead to a 2.4% productivityimprovement. These hypothetical shocks may not be considered realistic. Another popular way toquantify results is to express them in terms of standard deviations of the explanatory variables.Using Table 5.6 to obtain the standard deviations, we see that a one-standard-deviation increasein ln Products implies a productivity gain by 2.6% of a standard deviation (sd); a one-standard-deviation increase in the number of suppliers, keeping the product margin constant, improvesproductivity by 0.8% of a sd. Continuous relationship are also associated with small productivity26When disentangling the “micro” elasticity of substitution among alternative suppliers from the “macro” elasticityof substitution between domestic and foreign suppliers, Feenstra et al. (2017) find that micro elasticity estimates tendsto be larger than macro estimates.605.4. Resultsgains: a one-standard-deviation increase in Continuous raises firm productivity by 0.1% of a sd.The coefficient on the share of Chinese suppliers implies, instead, a sizable negative effect onproductivity: a one-standard-deviation increase in the share of Chinese suppliers is associated witha 1% of a sd drop in productivity.The effects that we document are smaller than the firm-level productivity gains documentedby Amiti and Konings (2007) and Topalova and Khandelwal (2011) (12% in the case of Indonesia,4.8% for India for a 10% reduction in input tariffs); however, while the estimates in those papersreveal the aggregate effect on productivity, our estimates aim at identifying specific channels forthe realization of those gains.5.4.1 Robustness and sectoral estimatesThe additional results in section C.2 show that the panel fixed effects results are mainly robustwhen we instead estimate the regressions in long differences. Table C.3 considers the variationin sales between 2003 and 2007. One notable difference is that the we no longer obtain negativeeffects of the Chinese share on productivity (after controlling for the U.S. share and inputs). Whileinput variety and dynamic variables remain positive and significant with similar magnitudes tothose documented in Table 5.5, the negative sign on the share of Chinese suppliers fades in thespecification with the full set of controls (column (5)).Tables C.4–C.6 and C.7 in Appendix C.2 show the results when we estimate the productivityspecification (5) for each sector. The first three tables show Levinsohn-Petrin estimates of thebreadth, depth, and country-of-origin effects along with the four factor input elasticities. Theseregressions include the second-stage coefficients for regressions based on the same identifying as-sumption as presented in Table 5.5. Table C.7, instead, uses the Olley-Pakes approach in whichinvestment is part of the control function. This approach requires us to drop firms with zero invest-ment which accounts for the sample attrition. Levinsohn and Petrin (2003) motivate their methodin part by warning that such attrition could be non-random. In general, we do not detect system-atic differences. Often the coefficients are very similar, but the higher standard errors in OP leadto less statistically significant results. For example, Transport Equipment has a typical productbreath elasticity of 0.029 in the LP specification with a standard error of 0.011 (Table C.6). In theOP version, shown in Table C.7, the coefficient is 0.027 with a standard error of 0.015. Overallthe LP and OP results both support the near ubiquity of productivity gains from importing morevariety.Importing more products has a positive impact on productivity across all industries; the coeffi-cient is significant in most cases. The product import margin seems to be particularly relevant inindustries using larger share of differentiated inputs (e.g., Computing, Transportation Equipmentand Machinery). Conditioning on the number of imported products, the supplier margin is alsoassociated with a significant productivity increase in about one third of all sectors. The productiv-ity effect of additional suppliers seems to be particularly relevant in Metals and Metallic Products,and across other industries making larger use of homogeneous inputs.615.4. ResultsContinuous relationships with suppliers tend to have a positive impact on productivity acrossall sectors; the effect is significant only in Computing, Paper, Apparels, Metallic Products andChemicals. As for the countries of origin, the share of U.S. suppliers does not display any effect onproductivity; the sign of the coefficient on US Share varies across sectors although the variable isnever significant. The share of Chinese suppliers, instead, tend to be associated with lower produc-tivity in sectors with larger Chinese penetration (Apparel and Other Manufacturing Activities);however, firms in Textiles and Petrol that have more Chinese suppliers tend to have bigger sales,controlling for input usage.The input elasticities reported in Tables C.4-C.6 and C.7 are in line with the estimates byHalpern et al. (2015). In particular, they find that the capital share in production is around 0.04,which is equal to our average capital share estimate across sectors. Moreover, while their labourelasticity estimate (0.2) is in line with our results, their share of materials (0.75) appear significantlylarger than ours. We believe that this difference may be due to the fact that we separately controlfor electricity.5.4.2 Impact of import relationships on export performanceTable 5.7 investigates how the characteristics of the import network affect export performance.Past research has shown that the majority of firms do not export and, among the exporters, themodal firm exports a single product to a single destination.27 In standard models of heterogeneousfirms, more productive firms can cover fixed costs associated with exporting. Thus, to the extentthat our breadth and depth variables trigger productivity gains, we expect them to raise exportperformance. We consider 4 measures of export performance: total exports (columns 1 and 2), thenumber of products (HS8 codes) exported (columns 3 and 4), whether a firm exports to any country(5 and 6), and the number of export destinations (7 and 8). We set the number of destinationsequal to 1 for non-exporters (this can be thought of as home as the first destination). The even-numbered columns adopt a specification similar to column (5) of Table 5.5, where we add controlsfor inputs and age and the LP quadratic function.We find that firms importing more products from more suppliers are more likely to be exporters,export more, and sell more products to more destinations. The imported product and supplierelasticities imply similar magnitudes for the effects on performance. Considering the coefficienton ln Products, a one-standard-deviation increase in the number of imported products increasesexports by 15% of a sd, raises the number of exported products by 14% of a sd, increase the numberof export destination by 7% of a sd and increases the probability of exporting by 3 percentage points.27See Bernard et al. (2007) for the United States and Mayer and Ottaviano (2007) for some European countries.625.4. ResultsTable 5.7: How import relationships affect export performance(1) (2) (3) (4) (5) (6) (7) (8)ln Exports ln Exp. Products Export Status ln Destinationsln Products 0.253a 0.298a 0.110a 0.105a 0.026a 0.024a 0.069a 0.038a(0.016) (0.020) (0.007) (0.009) (0.003) (0.003) (0.003) (0.004)ln SuppProd 0.265a 0.260a 0.082a 0.070a 0.029a 0.026a 0.061a 0.040a(0.025) (0.025) (0.011) (0.011) (0.004) (0.005) (0.006) (0.006)Continuous -0.207a 0.050 0.063a 0.006 -0.017b -0.012 0.079a -0.011(0.036) (0.041) (0.015) (0.017) (0.006) (0.007) (0.007) (0.007)US share 0.100c 0.057 -0.033 -0.014 0.006 0.006 -0.029b -0.015(0.050) (0.048) (0.022) (0.021) (0.009) (0.009) (0.011) (0.011)CN share -0.701a -0.381c -0.268a -0.280a -0.043 -0.024 -0.045 -0.066c(0.199) (0.189) (0.068) (0.069) (0.033) (0.033) (0.031) (0.031)Input Controls∗ n y n y n y n yFirm FE y y y y y y y ySector-Year y y y y y y y yObs. 44,939 44,939 44,939 44,939 67,184 67,184 67,184 67,184R2 0.017 0.091 0.012 0.052 0.003 0.032 0.012 0.059ln Products: log number of imported products (HS10).ln SuppProd : log number of foreign suppliers per imported products.Continuous: share of suppliers from which the buyer purchased for at least the previousyear.US Share: number of U.S. suppliers divided by total foreign suppliers.CN Share: number of Chinese suppliers divided by total foreign suppliers.* Input Controls include employment, electricity, and quadratic in capital, materials and age.All controls are also interacted with 3-digit NAICS code dummies.Notes: Firm FE regression, years 2002–2008. A sector represents a 3-digit NAICS code.Robust standard errors, clustered at the firm level, in parentheses. Significance thresholds are0.1% (a), 1% (b), 5% (c). The even-numbered columns implement our preferred specificationwith input controls as shown in equation (5.5).Neither the share of continuous relationships nor the U.S. import share has a robust effect onexport outcomes. We find that Chinese suppliers tend to have a negative impact on export perfor-mance. Having more Chinese suppliers is associated with lower exports, fewer exported products,and fewer destinations; the coefficient on the likelihood of becoming an exporter is negative but notsignificant. The surprisingly negative effect of relationship with Chinese suppliers on total exportsare quite big. Consider a firm that goes from 0% Chinese suppliers to 100% Chinese suppliers. Thecolumn 1 coefficient of −0.7 implies that its exports will fall by half (exp(−0.7) = 0.496). This is,of course, a radical and unrealistic change but even looking at one standard deviation changes, wefind big effects from increased usage of Chinese suppliers. A one-standard-deviation larger shareof Chinese suppliers reduces exports by 4.5% of a sd, lowers the number of exported products by8.4% of a sd and the number of export destination by 2.7% of a sd.635.4. Results5.4.3 The Dynamics of Import RelationshipsWhat is the source of the productivity gains arising in continuous relationships? A possible expla-nation is that the buyers and suppliers in continuous relationships tend to exchange products bettertailored to the production process of the buyer. In order to provide support to this mechanism, weestimate a specification relating the type of relationship to import outcomes,Import Outcomeijpt = β0 + β1 · Relationship Typeijpt +Dpt + εijpt (5.6)The dependent variable is either the import value, the quantity imported, or the unit value in thetransaction of product p between firm i and supplier j at time t. Relationship Typeijpt includes con-tinuous, new, and discontinuous relationships. We also consider how unique relationships—supplier-product combinations that are linked to a unique buyer—are related to import outcomes. It is pos-sible that when a Canadian firm is the only buyer of a foreign product, it is because that producthas been customized for that firm and that such customization might be reflected in the price paidfor the imported product. The excluded category covers buyer-supplier-product relationships thatare discontinuous and not unique. The specification also includes HS2 dummies, unit of measuredummies, as well as 3-digit NAICS-year dummies.Whether we rely on Uzzi’s idea of embeddedness or on a model with search and matching, weexpect similar predictions. In fact, following Uzzi (1996), a firm embedded in a production networkwould have longer-lasting relationships and better-customized products. Similarly, in a frameworkin which searching for a trade partner is costly and agents’ learn about their partner’s productivityover time, better matches tend to last longer and generate larger surplus, which translates intolarger pay-offs for all participants in the relationships. In particular, we expect that firms incontinuous relationships tend to import larger values, not only because of bigger quantities, butalso because they pay higher unit values.645.4. ResultsTable 5.8: Import Relationships(1) (2) (3) (4) (5) (6) (7) (8)ln Import Value ln Imp. Val. ln Imp. Quant. ln Unit ValueContinuous 1.121a 0.116a 0.317a 0.039a 1.107a 0.079a -0.002 0.017a(0.028) (0.005) (0.013) (0.004) (0.031) (0.006) (0.016) (0.004)New -0.229a -0.159a 0.008 -0.038a -0.325a -0.180a 0.102a 0.010c(0.030) (0.005) (0.016) (0.004) (0.031) (0.007) (0.017) (0.005)Unique -0.409a 0.093a -0.149a 0.027a -0.397a 0.076a -0.034c 0.007(0.023) (0.005) (0.011) (0.004) (0.029) (0.006) (0.014) (0.004)ln Quantity n n y y n n n nRel. FE n y n y n y n ySector×Year y y y y y y y yObservations 5.5mn 5.5mn 3mn 3mn 3mn 3mn 3mn 3mnR2 0.164 0.144 0.677 0.668 0.343 0.107 0.505 0.012Continuous: dummy equal to one if a firm imported the same product from the samesupplier at t− 1.New : dummy equal to one if a firm imports a product from a supplier for the first time.Unique: dummy equal to one if a supplier sells a product only to one firm at t.Notes: The odd-numbered columns report pooled OLS regressions, while the even-numbered columns report relationship (defined as firm-product-supplier dummies) fixed-effect regressions. In all columns, we also control for log sales, log export, HS2 productdummies, and dummies for the unit of measurement. A sector stands for a 3-digit NAICScode. Robust standard errors, clustered at the firm level, in parentheses. Significancethresholds are 0.1% (a), 1% (b), 5% (c).Table 5.8 reports the OLS and Relationship FE regression results for specification (5.6).28 Allspecifications control for the characteristics of the Canadian firm in its output market, i.e. the logof total sales and the log of total exports, so that we can compare firms with equal sales that adoptdifferent strategies regarding the duration or exclusivity of their relationships. Firms in continuousrelationships import larger values than in discontinuous connections; the effect on value comesboth from larger quantities and higher unit values (columns (3)-(4) and (8)). New relationships,instead, involve lower import values; this outcome seems to be primarily a quantity rather thana price effect. Evidently, buyers are reluctant to place large orders from firms they have no priorexperience with.Finally, let us consider the behavior of unique supplier-product combinations. Exploiting boththe cross-sectional and time variation, unique relationships seem to be associated with lower importvalues, resulting both from lower quantities and lower unit values; however, suppliers becoming theunique provider of a certain good (columns (2), (4), (6) and (8)) export larger values, largerquantities and sell their products at a higher unit value (the coefficient on Unique in column (8) ispositive but not significant). We believe that our dummy for unique relationships captures attempts28We include Dpij fixed effects in the even numbered columns of table 5.8.655.5. Conclusionof buyers to find the best inputs compatible with their production process.5.5 ConclusionIn this chapter, we have explored the productivity effects of the breadth and depth of firms’ importrelationships. With the caveat that our identification strategy relies on the control function ap-proach to partial out unobserved productivity shocks, we find significant and economically relevantbreadth effects. Both the number of varieties imported and the number of suppliers per variety raiseproductivity. These results support the theoretical foundation in Ethier (1982) and are consistentwith a wider literature in which we see that reductions in the costs of imported inputs (via tariffcuts or changes in transport access) lead to productivity improvements. These results on breadthhave many other counterparts in the literature on gains from variety in final consumer goods.We also find novel and promising effects of import relationship depth. The share of continuousimporting relationships the firm is engaged also appears to raise firm performance. In addition, wefind that firms engaged in continuous import relationships with the same suppliers systematicallyfeature transactions that are larger and, to a lesser extent, have higher value. We are not aware ofany model that can fully explain these findings, but we hypothesize that it could be the result of asearch and matching process whereby only the most successful matches survive. Only a firm’s bestsupplier relationships carry on and because they are better matches, they take up a larger share ofthe firm’s total imports. We have only laid out a possible theoretical interpretation of these novelresults, but we are optimistic that they could help a better understanding of where the productivitygains of importing come from. They come not only from wider variety of inputs, but also from adeeper pool of suppliers in which the firm can find an ideal partner.Our results point to several important policy implications. First, import tariff reductions onintermediate inputs are likely to help Canadian productivity and boost the performance of Canadianfirms in international markets. This is consistent with evidence from less developed countries butwas not previously known for a country like Canada with a well-developed manufacturing sector.Secondly, since the United States provides the majority of the suppliers used by Canadian firms,it would be helpful to shrink the fixed costs of adding and maintaining suppliers. It is not obvioushow to achieve that but travel and visa facilitation are probably valuable. There may also be gainsfrom harmonization of technical standards. The most general policy implication of all is that evenif trade policy makers are focused on export markets, they should not neglect that Canadian firms’success in selling abroad is very much predicated upon their ability to use a broad and deep rosterof foreign suppliers.66Chapter 6ConclusionIn this dissertation, we study the impact of two important aspects of the importing market on firmperformance: import competition and the buyer-supplier relationship.In studying the effect of import competition on firm performance (Chapters 2-4), we founda robust empirical relationship for China during the period around the WTO accession, that anincrease in import competition would raise innovation among the most productive firms. Whilethe effect is not significantly different from zero for the less productive firms. We develop a modelwith monopolistic competition as in Melitz and Ottaviano (2008) across varieties, and neck-and-neck competition within varieties. The model stresses the two opposing forces that drive firm’sinnovation incentives when there is a change in import competition: the escape-competition effectand the rent-reduction effect. When competition increases, the positive escape-competition effectdominates for the more productive firms. In the aggregate economy, if the escape-competitioneffect dominates overall, there will be an additional gains from trade under a unilateral tradeliberalization.Our empirical study is among the first that focus on the relationship between import competitionand innovation in the context of a developing country. Our model is the first to combine the neck-and-neck competition in a classic trade framework. It aims to isolate the competition channel fromtechnology diffusion or the market size effect, and suggest that, a unilateral trade liberalization maybe harmful to domestic innovation if the home firms are too lagged behind and competition wouldonly bring about rent destruction. In the case of China, it seems at least for the more productivefirms, they were well equipped with the potential to improve when China entered the WTO in2001. The next step in our study is to calibrate the model to the Chinese data and calculate themodel-implied welfare changes.In Chapter 5, we explore how the structures of import relationships could affect the performanceof Canadian importers. Under the control-function identification strategy, we find that the breadthand depth of firms’ import relationships have significant and economically relevant effects on firmperformance. Firms grow bigger and more productive if they import a wider variety of products,source from more suppliers in each product, and was able to find relationship that could last longer.In the past twenty years, the trade literature has focused much on the gains from exporting orsymmetric trade liberalization. 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China Economic Journal 8 (2),122–142.74Appendix AAppendix to Chapter 2A.1 Productivity EstimationIn this section, we describe our production function estimation procedure and report the estimatedcoefficients.We assume that the final output of a firm is produced by labor, capital, and intermediatematerial input following a Cobb-Douglass production function.yt = β0 + βllt + βkkt + βmmt + ωt + εt (A.1)where yt, lt, kt and mt denote the log gross output, labor, capital and material inputs, respectively.We deal with the classical endogeneity problem, that the unobserved productivity ω is correlatedwith inputs, following the two-step control function procedure in Levinsohn and Petrin (2003) andAckerberg et al. (2015). Incur the usual assumptions of the control function approach as statedin Ackerberg et al. (2015): (i) productivity shocks ωit are First Order Markov, (ii) both labor andcapital are quasi-fixed, (iii) firm’s investment or intermediate input decisions are only determinedby one unobservable that is ωit, and (iv) the decision function is invertible. We can re-write theproduction function:The first stage involves regressing the log gross output on the same set of fourth order polyno-mials as in the value added specification, where the higher orders are already transformed into theChebyshev polynomials.yt = φt(kt, lt,mt, it) + εt (A.2)yt = δ0 +4∑i=04−i∑j=04−i−j∑r=04−i−j−r∑z=0δijkitmjt lrt invzt + εt (A.3)In the first stage, for all approaches, we estimate φˆit as a fourth order polynomial in k˜it, l˜it, m˜it, ˜invit,where invit denotes log investment, and x˜ =x−µxσxdenotes the normalized variables. To ensureorthogonality of the polynomial basis, we also apply the Chebyshev polynomial transformation29.29The Chebyshev polynomial transformation T (·) acts as follows:T0(x) = 1T1(x) = xTn+1(x) = 2xTn(x) − Tn−1(x).75A.1. Productivity EstimationIn the second stage, the law of motion for productivity is approximated by an AR(1) process:ωˆt = ρ0 + ρ1ωt−1 + ηt (A.4)Substitute into the production function,φˆt = βllt + βkkt + βmmt + ρ0 + ρ1(φˆt−1 − βllit − βkkt−1 − βmmt−1) + ηt (A.5)We use the NLS method to estimate the second stage equation, which is equivalent to thefollowing moment condition:Elt − ρ1lt−1kt − ρ1kt−1mt − ρ1mt−1φˆt−1 − βllit − βkkt−1 − βmmt−11× ηt = 0 (A.6)Table A.1 shows the estimation results. Columns(1)-(3) shows the coefficient estimates. Theoutput elasticity of intermediate good is averaged around 0.81, being as high as 0.91 in the Chemicalindustry (code 28) and as low as 0.68 in the furniture manufacturing industry (code 21). Column(4) shows the estimate of the auto regressive coefficient for the productivity shock process. Theaverage estimate is 0.66. Out of the 29 industries, 18 industries have the auto regressive coefficientabove 0.6. The electric equipment and machinery industry (code 39) has the lowest persistenceparameter (0.28) which implies the firms are more subject to transitory shocks. Column (5) showsthe returns to scale. With the gross output production function specification, the return to scaleestimate is quite reasonable, being very close to 1. Column (6) shows the correlation between theestimated TFP from the ACF approach and a simple OLS regression within each two digit sector.The average sectoral correlation is 0.98. The aggregate correlation is 0.86.Alternatively, we can also formulate the production function using value-added output, or usingthe translog specification30.30The production function for the value-added output isvt = β0 + βllt + βkkt + ωt + εtAnd the production function for the translog specification isyt = β0 + βllt + βkkt + βmmt + βll l˜2t + βkkk˜2t + βmmm˜2t + βlk l˜tk˜t + βlml˜tm˜t + βkmk˜tm˜t + βlkm l˜tk˜tm˜t + ωt + εt76A.1. Productivity EstimationTable A.1: Production function estimation coefficients by sector(1) (2) (3) (4) (5) (6) (7)code industry name l k m ρ1 rts corr no. obs13 Food Processing 0.09 0.09 0.80 0.61 0.99 0.97 32,40714 Food Production 0.07 0.08 0.90 0.67 1.05 0.97 13,98015 Beverage Production 0.09 0.13 0.83 0.78 1.05 0.93 9,70516 Tobacco Industry 0.06 0.14 0.81 0.78 1.01 0.93 1,06317 Textile Industry 0.07 0.06 0.84 0.58 0.98 0.98 51,96118 Garment and Other Fiber Products 0.12 0.08 0.76 0.66 0.96 0.98 28,54919 Leather, Furs, Down & Related Products 0.10 0.06 0.81 0.49 0.98 0.99 13,99120 Timber and Bamboo Processing 0.14 0.10 0.75 0.81 0.98 0.96 10,48921 Furniture Manufacturing 0.15 0.08 0.68 0.89 0.91 0.91 6,39522 Papermaking and Paper Products 0.08 0.08 0.79 0.79 0.95 0.93 19,29823 Printing & Record Medium Reproduction 0.12 0.20 0.80 0.79 1.12 0.88 13,21024 Cultural, Educational & Sports Goods 0.12 0.06 0.79 0.48 0.97 0.99 8,41525 Petroleum refining and Coking 0.03 0.05 0.86 0.80 0.94 0.99 5,41226 Raw Chemical materials/Products 0.05 0.06 0.87 0.45 0.97 1.00 46,22427 Medical and Pharmaceutical Products 0.10 0.12 0.78 0.64 1.00 0.96 15,15228 Chemical Fiber 0.03 0.03 0.91 0.71 0.97 0.99 2,98929 Rubber Products 0.10 0.11 0.74 0.61 0.96 0.94 7,27430 Plastic Products 0.12 0.11 0.71 0.70 0.95 0.94 28,04531 Nonmetal Mineral Products 0.09 0.09 0.78 0.86 0.95 0.90 52,20232 Ferrous Metal Mining and Dressing 0.05 0.04 0.88 0.59 0.97 0.99 13,49233 Nonferrous Metal Mining and Dressing 0.08 0.04 0.82 0.87 0.94 0.97 10,54334 Metal Products 0.07 0.07 0.84 0.36 0.97 0.99 31,06835 Ordinary Machinery 0.05 0.07 0.87 0.52 0.98 0.99 46,17236 Special Purposes Equipment 0.03 0.08 0.88 0.56 0.99 0.98 23,44037 Transport Equipment 0.08 0.10 0.84 0.56 1.02 0.98 30,13439 Electric Equipment and Machinery 0.06 0.06 0.87 0.28 0.99 1.00 37,23140 Electronic and Telecommunications 0.13 0.10 0.76 0.80 0.99 0.96 20,96041 Instruments, Cultural act Machinery 0.09 0.08 0.80 0.87 0.96 0.96 8,60742 Other Manufacturing 0.08 0.04 0.85 0.57 0.98 0.99 10,993Columns(1)-(3) shows the coefficient estimates for the Cobb-Douglas gross output productionfunction estimation using the ACF method. Column (4) shows the estimate of the autoregressivecoefficient for the productivity shock process. Column (5) shows the returns to scale. Column(6) shows the correlation between the estimated TFP from the ACF approach and a simple OLSregression within each two digit sector. The overall correlation is 0.86.Table A.2 shows the correlation between our baseline estimation and the two alternative speci-fications. The correlation between the gross output (GO) and translog (TL) production function isquite high. The average correlation within the 29 two-digit industries is 0.83, while this average cor-relation is 0.66 between the GO and VA approaches, and 0.54 between the TL and VA approaches.The main reason that the VA approach has lower correlation with the other two approaches couldbe that the output measure is log value added, which is different from the gross output in the other77A.1. Productivity Estimationtwo methods.Table A.2: Correlation between estimated productivity, level(1) (2) (3) (4)code industry name GO vs. TL GO vs. VA TL vs. VA obs13 Food Processing 0.87 0.67 0.49 118,85214 Food Production 0.95 0.45 0.27 47,43415 Beverage Production 0.84 0.61 0.45 32,97416 Tobacco Industry 0.94 0.72 0.53 2,45917 Textile Industry 0.81 0.66 0.39 163,45918 Garment and Other Fiber Products 0.80 0.74 0.49 92,56019 Leather, Furs, Down and Related Products 0.78 0.69 0.43 45,91620 Timber and Bamboo Processing 0.91 0.75 0.61 42,22421 Furniture Manufacturing 0.79 0.83 0.70 22,32622 Paper making and Paper Products 0.81 0.77 0.57 57,82523 Printing & Record Medium Reproduction 0.89 0.56 0.41 40,34824 Cultural, Educational & Sports Goods 0.76 0.70 0.46 25,27425 Petroleum refining and Coking 0.90 0.54 0.32 17,41026 Raw Chemical materials/Products 0.85 0.56 0.28 140,67927 Medical and Pharmaceutical Products 0.83 0.73 0.56 40,57428 Chemical Fiber 0.80 0.62 0.24 9,79829 Rubber Products 0.56 0.76 0.56 22,97030 Plastic Products 0.81 0.77 0.60 89,49131 Nonmetal Mineral Products 0.86 0.78 0.62 169,01932 Ferrous Metal Mining and Dressing 0.85 0.56 0.27 46,65033 Nonferrous Metal Mining and Dressing 0.92 0.56 0.35 35,02734 Metal Products 0.69 0.61 0.36 103,63235 Ordinary Machinery 0.78 0.59 0.35 146,18136 Special Purposes Equipment 0.85 0.61 0.37 80,20537 Transport Equipment 0.84 0.61 0.38 92,06039 Electric Equipment and Machinery 0.78 0.52 0.25 113,06440 Electronic and Telecommunications 0.83 0.72 0.52 61,85241 Instruments, Cultural act Machinery 0.85 0.70 0.51 26,54842 Other Manufacturing 0.89 0.62 0.32 37,732minimum 0.56 0.45 0.24maximum 0.95 0.83 0.70mean 0.83 0.66 0.44aggregate correlation 0.77 0.37 0.2878A.2. RobustnessA.2 RobustnessTable A.3: Output tariff and patenting, interaction with quartiles(1) (2) (3) (4)Dep. var: Patent application countsOutput competitionτoutputs,t−2 × Top Quartileis,t−2 -4.027** -3.366* -2.414 -2.827*(2.018) (1.996) (2.239) (1.452)τoutputs,t−2 × 3rd Quartileis,t−2 -0.825 -0.304 0.659 0.234(1.854) (1.860) (2.058) (1.272)τoutputs,t−2 × 2nd Quartileis,t−2 0.452 1.175 1.997 1.678*(1.646) (1.647) (1.988) (0.964)τoutputs,t−2 × Bottom Quartileis,t−2 -1.376 -0.306 0.079 0.002(1.795) (1.808) (1.942) (1.602)Export controlDexporterist−2 1.278*** 0.909***(0.333) (0.329)Edemands,t−2 0.063*** 0.066***(0.021) (0.021)Edemands,t−2 ×Dexporterist−2 0.026 0.023(0.025) (0.025)Import controlDimporterist−2 1.799*** 0.984***(0.188) (0.168)τ inputis,t−2 -0.336 -4.936(11.268) (10.972)τ inputis,t−2 ×Dimporterist−2 -11.314*** -7.385**(3.848) (3.639)obs 800,292 800,292 800,292 800,292Notes: The Top dummy equals to 1 if the firm is above the 75th percentile productivity inindustry s at time t − 2. All columns control for four-digit CIC industry fixed effects, as wellas four-sector by year fixed effects. The four sectors are: chemicals and petroleum, computersand electronics, machinery and equipment sector, and others. Standard errors are clustered atthe industry-year level. *** p<0.01, ** p<0.05, * p<0.1.79A.2. RobustnessTable A.4: Industry specification controlling for FDI(1) (2) (3)Dep. var: Patent application countsFDI variable ln(foreign equity) ln(foreign HMT equity) foreign equity shareOutput competitionτoutputs,t−2 × Topis,t−2 -3.521** -3.549** -3.542**(1.477) (1.466) (1.464)τoutputs,t−2 2.904 2.367 1.709(1.946) (1.929) (1.936)Topis,t−2 1.207*** 1.208*** 1.206***(0.147) (0.147) (0.147)FDI controlFDIs,t−2 -0.093* -0.065 0.247(0.049) (0.049) (0.340)obs 797,958 799,335 800,276Notes: The Top dummy equals to 1 if the firm is above the 75th percentile productivity in industry s at timet − 2. All columns control for four-digit CIC industry fixed effects, as well as four-sector by year fixed effects.The four sectors are: chemicals and petroleum, computers and electronics, machinery and equipment sector,and others. Standard errors are clustered at the industry-year level. *** p<0.01, ** p<0.05, * p<0.1.80A.2. RobustnessTable A.5: Two-stage control function estimation(1) (2) (3) (4) (5) (6)Dep. var: Patent application countsSpecification OLS CF OLS CF OLS CFOutput competitionlnMoutputs,t−2 × Topis,t−2 0.102** 0.121*** 0.107*** 0.126*** 0.104** 0.112**(0.040) (0.045) (0.039) (0.045) (0.042) (0.047)lnMoutputs,t−2 0.023 0.476 0.035 0.443 0.018 0.219(0.025) (0.322) (0.028) (0.318) (0.025) (0.370)Topis,t−2 0.768*** 0.750*** 0.787*** 0.770*** 0.740*** 0.749***(0.088) (0.090) (0.087) (0.089) (0.088) (0.090)Export controlDexporterist−2 1.586*** 1.588***(0.102) (0.102)lnXexps,t−2 -0.184*** 0.034(0.046) (0.066)lnXexports,t−2 ×Dexporterist−2 0.206*** 0.217***(0.041) (0.044)Import controlDimporterist−2 1.756*** 1.731***(0.250) (0.251)lnM inputis,t−2 -4.439 0.392(11.949) (14.453)lnM inputis,t−2 ×Dimporterist−2 -11.713** -11.607**(5.161) (5.202)First StageEndogenous var. lnMoutputs,t−2 lnXexports,t−2 lnMinputs,t−2Instruments τ outputs,t−2 -5.544*** τexports,t−2 0.406*** τinputs,t−2 -12.975***(1.641) (0.021) (2.299)obs 802,410 802,410 802,410 802,410 802,410 792,963The even columns show results using the control function approach (CF). It is a two-stage procedure. The Firststage regresses the endogenous variables on the respective instruments. The second stage regresses patent countson the endogenous variables, controlling for the error terms from the first stage.The Top dummy equals to 1 if the firm is above 75 percentile in industry s at time t− 2.All columns control for four-digit CIC industry fixed effects, as well as four-sector by year fixed effects. The foursectors are: chemicals and petroleum, computers and electronics, machinery and equipment sector, and others.Standard errors are clustered at the industry-year level. *** p<0.01, ** p<0.05, * p<0.181A.2. RobustnessTable A.6: Alternative measures of innovation(1) (2) (3) (4) (5)Dep var Granted Citation Patent Patentapplication weighted dummy count ln (Pat+ 1)Poisson Poisson OLS OLS OLSOutput competitionτ outputs,t−2 × Topis,t−2 -2.750* -2.836** -0.057*** -0.917*** -0.096***(1.483) (1.303) (0.008) (0.229) (0.014)τ outputs,t−2 2.732 -0.454 -0.019 -0.002 -0.020(2.370) (2.094) (0.015) (0.167) (0.021)Topis,t−2 1.126*** 1.048*** 0.012*** 0.165*** 0.019***(0.142) (0.122) (0.001) (0.032) (0.002)Export controlDexporterist−2 0.928*** 0.875*** 0.042*** 0.293*** 0.055***(0.159) (0.141) (0.003) (0.047) (0.004)Edemands,t−2 1.477** 1.001 0.015** 0.238*** 0.029***(0.626) (0.639) (0.007) (0.071) (0.009)Edemands,t−2 ×Dexporterist−2 -0.227 -1.143 -0.275*** -2.063*** -0.374***(1.954) (1.679) (0.025) (0.373) (0.035)Import controlDimporterist−2 1.599*** 1.415*** 0.049*** 0.273*** 0.063***(0.284) (0.240) (0.004) (0.047) (0.005)τ inputis,t−2 -0.114 0.120 0.240*** 0.569 0.257***(19.535) (13.923) (0.046) (0.459) (0.062)τ inputis,t−2 ×Dimporterist−2 -16.220** -11.554** -0.556*** -3.599*** -0.739***(6.997) (5.686) (0.077) (0.911) (0.105)R2 0.038 0.008 0.037obs 762,640 770,316 770,978 770,978 770,978Notes: The Top dummy equals to 1 if the firm is above 75 percentile in industry s at time t− 2. Allcolumns control for four-digit CIC industry fixed effects, as well as four-sector by year fixed effects.The four sectors are: chemicals and petroleum, computers and electronics, machinery and equipmentsector, and others. Standard errors are clustered at the industry-year level. *** p<0.01, ** p<0.05,* p<0.182A.2. RobustnessTable A.7: Drop 2-digit sectors, one at a time(1) (2) (3) (4) (5)Dep. var: Patent application countsSector Dropped Food Drinks Tobacco Textile Furniturefirm τ outputs,t−2 × Topis,t−2 -2.417* -2.653* -2.943** -2.919** -2.890**(1.415) (1.416) (1.412) (1.387) (1.362)firm τ outputs,t−2 -1.095 -0.723 0.377 1.183 -0.465(2.071) (2.218) (2.231) (2.025) (1.965)Topis,t−2 1.099*** 1.104*** 1.117*** 1.112*** 1.116***(0.133) (0.133) (0.132) (0.131) (0.131)obs 738657 790877 803282 681173 778623Sector Dropped Paper Chemical Stone Metal Machineryfirm τ outputs,t−2 × Topis,t−2 -2.852** -3.217** -2.874** -2.656* -3.151**(1.377) (1.400) (1.383) (1.428) (1.334)firm τ outputs,t−2 0.117 -1.629 -0.466 -0.102 -0.272(2.062) (2.051) (1.999) (1.939) (2.077)Topis,t−2 1.108*** 1.212*** 1.120*** 1.038*** 1.226***(0.133) (0.150) (0.131) (0.140) (0.134)obs 752471 665091 732278 724141 692330Sector Dropped Transportation Computers Otherfirm τ outputs,t−2 × Topis,t−2 -2.083 -4.202*** -2.884**(1.585) (1.181) (1.371)firm τ outputs,t−2 -1.360 -0.687 -0.372(2.112) (1.656) (1.960)Topis,t−2 1.097*** 0.985*** 1.114***(0.142) (0.128) (0.131)obs 764506 731702 791453Notes: The Top dummy equals to 1 if the firm is above 75 percentile in industry s at time t−2. All columns includethe export and import controls, the four-digit CIC industry fixed effects, as well as four-sector by year fixed effects.The four sectors are: chemicals and petroleum, computers and electronics, machinery and equipment sector, andothers. Standard errors are clustered at the industry-year level. *** p<0.01, ** p<0.05, * p<0.1.83A.2. RobustnessTable A.8: Firm output tariff and patenting, OLS(1) (2) (3) (4)Dep. var: Patent application countsOutput competitionfirm τ outputs,t−2 × Topis,t−2 -3.276*** -3.381*** -4.851*** -5.049***(0.922) (0.953) (1.557) (1.605)firm τ outputs,t−2 0.027 0.084 0.180 0.294(0.248) (0.265) (0.445) (0.475)Topis,t−2 0.573*** 0.586*** 0.828*** 0.852***(0.139) (0.143) (0.224) (0.230)Export controlfirm τ exportis,t−2 0.024*** 0.036***(0.006) (0.011)Import controlfirmτ inputis,t−2 0.320 0.338(0.598) (0.612)R2 0.017 0.018 0.019 0.020obs 141,823 136,031 75,460 73,139Notes: OLS regression instead of Poisson. The Top dummy equals to 1 if the firm isabove 75 percentile in industry s at time t− 2. All columns control for four-digit CICindustry fixed effects, as well as four-sector by year fixed effects. Standard errors areclustered at the industry-year level. *** p<0.01, ** p<0.05, * p<0.184Appendix BAppendix to Chapter 4Proof of Lemma 2. The partial derivative of utility with respect to foreign entry rate e at giveninnovation I is∂u∂e= I [θ (pi1 + CSm (δc)) + (1− θ) CSm (c∗0)− pi (δc)− CSm (δc)]+ (1− I) [θCSl (c) + (1− θ) CSm (c∗0)− pi (c)− CSm (c)]= I (1− θ) ∆1 + (1− I) ∆0where∆1 ≡ CSm (c∗0)− CSm (δc)− pi (δc)∆0 ≡ θCSl (c) + (1− θ) CSm (c∗0)− CSm (c)− pi (c)CSm (c) =(α− c)28CSl (c) =(α− c)22pi (c) =(α− c)24The expression for firm profits pi (·) incurs Assumption 2 and 4, which ensure that as long as thefirm is producing, it could obtain the monopoly profit.To prove that ∂u∂e > 0, it suffices to show that ∆1 > 0 and ∆0 > 0.For the proportion of Home firms that succeeded in innovating, the marginal gain from foreignentry for consumers, CSm (c∗0) − CSm (δc), is always larger than the marginal loss in profits forHome firms. To show this, from Assumption 3,2α+ c∗0 < α+ 2δc⇒2α− 2δc < α− c∗0⇒4 (α− δc)2 < (α− c∗0)2⇒18[(α− c∗0)2 − 3 (α− δc)2]> 0⇒∆1 = CSm (c∗0)− CSm (δc)− pi (δc) > 0 (B.1)Next, we show that for the proportion of Home firms that did not innovate, the marginal gain for85Appendix B. Appendix to Chapter 4consumers is also larger than the marginal loss of producers due to foreign entry.CSl (c)− CSm (c)− pi (c)=(α− c)28> 0CSm (c∗0)− CSm (c)− pi (c)>CSm (c∗0)− CSm (δc)− pi (δc) > 0where the last line comes from equation (B.1). Therefore,∆0 > 0.86Appendix CAppendix to Chapter 5C.1 Coding Supplier IdentifiersTransaction records are collected from Form B3 of the Canadian Border Service Agency. Importersare required to report the vendors’ name on the form among the other information. The vendor’sname is transformed into a consistent identifier according to a procedure articulated into 3 steps.31The first step creates the basic vendor identifier according to the following stages:1. Remove stop words, like ltd, corp, inc etc.; we will refer to the output of this stage as thestandard name.2. Remove punctuation but leave spaces into the vendor’s name; this generates the clean name.3. Replace French characters with English characters.4. Remove other irrelevant words not integrated in the vendor’s name, e.g. and, the, of, a, etc.5. Remove vowels from the name.6. Assign the basic vendor identifier.The second stage of the procedure tries to propagate identifiers across records likely to representthe same firm:• Generate a second identifier using the first two words of the clean name, if the first two wordsare not blank and standard name contains at least 6 characters. Firms whose name has thesame first and second words are assigned the same identifier.• Construct a third identifier based on the clean name, if the first non-blank word does notcontain more than 16 characters.• Generate a fourth identifier based on the first 3 words from the vendor’s name.• Construct a fifth identifier based on the ZIP code and the first three words of the vendor’sname.• Generate a sixth identifier attributed to vendors exporting to the same Canadian firm thesame product and with the same first word.31The matching algorithm was developed by Statistics Canada employees, inspired by the SIMILE project proce-dure.87C.1. Coding Supplier IdentifiersThe second identifier is selected as the preferred identifier; if such identifier could not be created,the third identifier would be used and so on. Finally, the third stage constructs a measure tocharacterize the quality of the identifiers. The quality is measured over 9 levels:32• Level 0 is assigned if the vendor’s name and its address are consistent across observationscarrying the same identifier.• Level 1 is assigned if the clean name and the address are consistent across observationscarrying the same identifier.• Level 2 is assigned if the vendor’s name is consistent across observations carrying the sameidentifier.• Level 3 is assigned if the clean vendor’s name is consistent across observations carrying thesame identifier.• Level 4 is assigned if the distance between the vendor’s and the clean name normalized bytheir length is less than 10, the first word and the address match across observations carryingthe same identifier.• Level 5 is assigned if the normalized distance between the names is less than 6, the basicidentifier and the first word match across observations carrying the same identifier.• Level 6 is assigned if the normalized distance between the names is less than 6, the Cana-dian Business Number and the HS10 product-code imported from the vendor match acrossobservations carrying the same identifier.• Level 7 is assigned if the normalized distance between the names is less than 3.• Level 8 is assigned if the normalized distance between the names is less than 10.Let us work through an example. Consider three fictional vendor’s names• Great Oranges and Nuts, Corporation• Great Oranges and Ne´wton• Great OrangesFollowing the first steps of the algorithm, we would be able to generate the basic identifiers1. Remove Corp./ Corporations• Great Oranges and Nuts,• Great Oranges and Ne´wton32The presence of a match quality indicator is very important as it allows to run robustness checks over groups ofdifferent match quality.88C.1. Coding Supplier Identifiers• Great Oranges2. Remove Punctuation• Great Oranges and Nuts• Great Oranges and Ne´wton• Great Oranges3. Remove French Characters• Great Oranges and Nuts• Great Oranges and Newton• Great Oranges4. Remove stop words• Great Oranges Nuts• Great Oranges Newton• Great Oranges5. Remove Vowels• Grt Orngs Nts• Grt Orngs Nwtn• Grt Orngs6. Assign the vendor basic identifier• 123• 456• 789Following the second step of the procedure, preferred identifiers are based on the matching the firsttwo words of the clean vendor’s name.• 123• 456• 123In the third step firms with equal identifiers from the second step are assigned a measure of thequality of the match. In our example, the two firms with identifier 123 have a match quality of 4if the address is the same. In case the two observations do not share the same address, the matchquality would be 8.89C.2. Supplemental Empirical ResultsC.2 Supplemental Empirical ResultsTable C.1: Average Market Share by sector, 2002–2008NAICS Industry Domestic Mkt Share311 Food 20.91%312 Bev. & Tob. 1.80%313 Text. Mills 0.44%314 Text. Prod. 0.32%315 Apparel 0.64%316 Leather 0.07%321 Wood 4.00%322 Paper 4.91%323 Printing 1.41%324 Petrol 9.42%325 Chemical 7.02%326 Plastics 3.83%327 Mineral 1.88%331 Metals 6.82%332 Met. Prod. 4.06%333 Machinery 4.12%334 Computing 2.90%335 Electrical 1.54%336 Trans. Eq. 21.30%337 Furniture 1.54%339 Miscel. 1.01%Table C.2: Summary Statistics from Import RegistryVariable Mean Std Deviationln Import Value 8.07 2.80ln Unit Value 3.41 2.55Continuous (Indicator) 0.30 0.46Unique 0.78 0.42New 0.65 0.4890C.2. Supplemental Empirical ResultsFigure C.1: Relationship age in extended sample ending in June 2008Table C.3: Long-difference (2003–2007) estimates(1) (2) (3) (4) (5)Variable ln Salesln Products 0.278a 0.280a 0.278a 0.279a 0.046a(0.013) (0.013) (0.013) (0.013) (0.007)ln SuppProd 0.175a 0.174a 0.174a 0.173a 0.025b(0.018) (0.018) (0.018) (0.018) (0.008)Continuous 0.141a 0.151a 0.148a 0.154a 0.028c(0.025) (0.026) (0.025) (0.026) (0.014)US share 0.089b 0.067 0.032(0.033) (0.035) (0.018)CN share -0.280c -0.220 0.043(0.132) (0.138) (0.053)Input Controls n n n n yFirm Effects y y y y ySector Effects y y y y yObs. 28,769 28,769 28,769 28,769 28,769R2 0.085 0.086 0.086 0.087 0.787ln Products: log number of imported products (HS10).ln Supp/Prod: log number of suppliers per imported products.Continuous: share of suppliers from which the buyer pur-chased for at least the previous year.US Share: share of U.S. suppliers.CN Share: share of Chinese suppliers.Notes: Long-difference regressions, years 2003 and 2007. Thelast column implements the first stage of a specification a` laLevinsohn and Petrin (2003); see equation (5.4).91C.2. Supplemental Empirical ResultsTable C.4: Sales Regressions by Sector (NAICS 31)ln SalesVariable Food Bev. Text. M Text. P App. Leath.ln Products 0.017c 0.010 0.052b 0.027 0.035a 0.028(0.007) (0.034) (0.016) (0.015) (0.011) (0.024)ln SuppProd 0.028b 0.002 -0.006 0.025 0.026 -0.020(0.009) (0.041) (0.025) (0.020) (0.014) (0.032)Continuous 0.023 -0.068 0.072 0.032 0.066c -0.042(0.014) (0.090) (0.038) (0.028) (0.026) (0.044)US share -0.005 -0.053 0.071 -0.000 0.023 0.018(0.015) (0.077) (0.038) (0.036) (0.027) (0.058)CN share -0.019 -0.058 0.275c -0.118 -0.092c 0.070(0.081) (0.331) (0.122) (0.066) (0.042) (0.215)Log Empl 0.161a 0.151a 0.300a 0.254a 0.297a 0.178a(0.008) (0.040) (0.020) (0.017) (0.014) (0.024)Log Elect 0.120a 0.239a 0.074a 0.064a 0.081a 0.038c(0.007) (0.034) (0.013) (0.013) (0.012) (0.017)Log K 0.052 -0.015 0.068 0.084 -0.059 0.116a(0.020) (0.090) (0.032) (0.047) (0.031) (0.034)Log Mat 0.561a 0.265a 0.443a 0.379a 0.509a 0.492a(0.043) (0.049) (0.034) (0.035) (0.024) (0.039)Obs. 6,462 572 1,156 1,699 3,887 709R2 0.737 0.643 0.769 0.668 0.714 0.729ln Products: log number of imported products (HS10).ln Supp/Prod: log number of suppliers per imported products.Continuous: share of suppliers from which the buyer purchased for atleast the previous year.US Share: share of U.S. suppliers.CN Share: share of Chinese suppliers.Notes: Firm FE regression, years 2002–2008. Sector represents 3-digit NAICS. Robust standard errors, clustered at the firm level, inparenthesis. Significance thresholds are 0.1% (a), 1% (b), 5% (c). Eachcolumn implements a two-stage Levinsohn-Petrin specification.92C.2. Supplemental Empirical ResultsTable C.5: Sales Regressions by Sector (NAICS 32)ln SalesVariable Wood Paper Print. Oil Chem. Plast. Min.ln Products 0.027a 0.033b 0.026a 0.032 0.059a 0.015c 0.018(0.007) (0.010) (0.006) (0.030) (0.011) (0.006) (0.011)ln SuppProd 0.009 0.046b 0.011 0.106c 0.040c 0.008 0.016(0.009) (0.014) (0.009) (0.051) (0.018) (0.009) (0.015)Continuous 0.003 0.050c 0.010 0.043 0.062c 0.014 0.011(0.013) (0.023) (0.013) (0.081) (0.026) (0.013) (0.021)US share 0.006 -0.018 -0.014 0.016 0.020 -0.027 0.024(0.020) (0.027) (0.016) (0.105) (0.032) (0.015) (0.029)CN share -0.046 -0.000 -0.064 4.436c -0.024 -0.031 0.153(0.066) (0.201) (0.062) (1.974) (0.120) (0.051) (0.079)Log Empl 0.258a 0.228a 0.358a 0.104a 0.213a 0.294a 0.333a(0.010) (0.012) (0.012) (0.026) (0.011) (0.009) (0.013)Log Elect 0.120a 0.095a 0.143a 0.017 0.093a 0.117a 0.097a(0.007) (0.007) (0.010) (0.021) (0.007) (0.006) (0.007)Log K 0.031 0.017 0.028 0.105a 0.024 0.021 0.019(0.033) (0.010) (0.023) (0.041) (0.060) (0.017) (0.016)Log Mat 0.557a 0.595a 0.416a 0.577a 0.338a 0.507a 0.522a(0.024) (0.016) (0.031) (0.033) (0.044) (0.016) (0.026)Obs. 4,719 1,914 4,178 353 4,654 6,276 3,381R2 0.817 0.892 0.769 0.716 0.612 0.797 0.775ln Products: log number of imported products (HS10).ln Supp/Prod: log number of suppliers per imported products.Continuous: share of suppliers from which the buyer purchased for at leastthe previous year.US Share: share of U.S. suppliers.CN Share: share of Chinese suppliers.Notes: Firm FE regression, years 2002–2008. Sector represents 3-digit NAICS.Robust standard errors, clustered at the firm level, in parenthesis. Significancethresholds are 0.1% (a), 1% (b), 5% (c). Each column implements a two-stageLevinsohn-Petrin specification.93C.2. Supplemental Empirical ResultsTable C.6: Sales Regressions by Sector (NAICS 33)ln SalesVariable Met. Met. P. Mach. Comp. Elect. Tr. Eq. Furn. Misc.ln Products 0.073a 0.024a 0.018b 0.098a 0.007 0.029c 0.020b 0.036a(0.016) (0.005) (0.006) (0.015) (0.013) (0.011) (0.006) (0.007)ln SuppProd 0.086a 0.025a 0.015 0.035 0.012 0.039c 0.003 0.030b(0.025) (0.007) (0.008) (0.020) (0.018) (0.016) (0.009) (0.009)Continuous 0.044 0.021c 0.011 0.090c 0.033 0.043 -0.007 0.028c(0.034) (0.009) (0.013) (0.039) (0.029) (0.026) (0.013) (0.014)US share 0.061 0.003 0.014 -0.026 0.005 0.006 0.005 0.000(0.041) (0.013) (0.016) (0.039) (0.032) (0.039) (0.016) (0.018)CN share -0.095 -0.011 0.108 -0.056 -0.147 -0.047 -0.037 -0.136b(0.148) (0.046) (0.075) (0.208) (0.087) (0.140) (0.036) (0.052)Log Empl 0.305a 0.313a 0.313a 0.314a 0.249a 0.238a 0.294a 0.287a(0.017) (0.006) (0.007) (0.015) (0.013) (0.014) (0.012) (0.010)Log Elect 0.068a 0.100a 0.094a 0.121a 0.096a 0.140a 0.104a 0.105a(0.014) (0.005) (0.006) (0.011) (0.010) (0.012) (0.009) (0.007)Log K 0.022 0.053a 0.056a 0.099a 0.027 0.060 0.021 0.024(0.030) (0.016) (0.016) (0.041) (0.026) (0.040) (0.020) (0.022)Log Mat 0.438a 0.467a 0.469a 0.265a 0.458a 0.499a 0.569a 0.454a(0.039) (0.017) (0.016) (0.023) (0.024) (0.027) (0.032) (0.020)Obs. 1,428 14,363 12,026 5,110 2,903 4,852 5,232 7,512R2 0.754 0.708 0.717 0.567 0.732 0.716 0.772 0.683ln Products: log number of imported products (HS10).ln Supp/Prod: log number of suppliers per imported products.Continuous: share of suppliers from which the buyer purchased for at least the previousyear.US Share: share of U.S. suppliers.CN Share: share of Chinese suppliers.Notes: Firm FE regression, years 2002–2008. Sector represents 3-digit NAICS. Robuststandard errors, clustered at the firm level, in parenthesis. Significance thresholds are0.1% (a), 1% (b), 5% (c). Each column implements a two-stage Levinsohn-Petrin speci-fication.94C.2. Supplemental Empirical ResultsTable C.7: Log Sales Regressions by Sector (OP)Variable Food Bev. Text. M Text. P App. Leath.ln Products 0.030b 0.013 0.061c 0.043c 0.015 0.011(0.009) (0.038) (0.026) (0.018) (0.012) (0.029)ln SuppProd 0.038b 0.009 0.020 0.027 -0.009 -0.032(0.012) (0.036) (0.032) (0.024) (0.016) (0.032)Log Empl 0.188a 0.157b 0.335a 0.267a 0.306a 0.146a(0.018) (0.056) (0.050) (0.027) (0.020) (0.039)Log Elect 0.099a 0.240a 0.042 0.094b 0.045b 0.043c(0.014) (0.050) (0.022) (0.029) (0.017) (0.020)Log Mat 0.511a 0.286a 0.335a 0.414a 0.464a 0.501a(0.045) (0.057) (0.077) (0.037) (0.023) (0.057)Obs. 6069 530 998 1504 3174 598R2 0.714 0.605 0.688 0.663 0.685 0.692Wood Paper Print. Oil Chem. Plast. Min.ln Products 0.026a 0.032c 0.026a 0.037 0.072b 0.008 0.013(0.008) (0.016) (0.010) (0.066) (0.026) (0.010) (0.015)ln SuppProd 0.003 0.031 0.018 0.090 0.046 0.009 0.017(0.009) (0.014) (0.009) (0.051) (0.018) (0.009) (0.015)Log Empl 0.257a 0.194a 0.357a 0.113c 0.239a 0.293a 0.317a(0.017) (0.021) (0.021) (0.048) (0.018) (0.021) (0.024)Log Elect 0.111a 0.094a 0.135a 0.004 0.102a 0.118a 0.099a(0.014) (0.025) (0.017) (0.026) (0.014) (0.013) (0.013)Log Mat 0.544a 0.623a 0.349a 0.559a 0.346a 0.500a 0.489a(0.028) (0.047) (0.033) (0.046) (0.041) (0.026) (0.032)Obs. 4359 1758 3810 327 4310 5836 3102R2 0.801 0.868 0.759 0.682 0.518 0.792 0.754Met. Met. P. Mach. Comp. Elect. Tr. Eq. Furn. Misc.ln Products 0.066b 0.019a 0.018c 0.076a 0.008 0.027 0.024b 0.026b(0.021) (0.005) (0.009) (0.020) (0.018) (0.015) (0.008) (0.009)ln SuppProd 0.080c 0.017c 0.014 0.009 0.003 0.023 0.001 0.033b(0.033) (0.007) (0.011) (0.026) (0.020) (0.017) (0.011) (0.010)Log Empl 0.309a 0.308a 0.315a 0.333a 0.249a 0.248a 0.296a 0.291a(0.028) (0.012) (0.014) (0.024) (0.022) (0.021) (0.027) (0.018)Log Elect 0.073a 0.090a 0.085a 0.110a 0.092a 0.126a 0.090a 0.086a(0.020) (0.009) (0.011) (0.017) (0.014) (0.020) (0.017) (0.011)Log Mat 0.401a 0.426a 0.440a 0.278a 0.481a 0.443a 0.498a 0.405a(0.035) (0.012) (0.015) (0.023) (0.028) (0.034) (0.036) (0.018)Obs. 1,332 13,321 10,961 4,606 2,592 4,460 4,686 6,594R2 0.743 0.683 0.703 0.554 0.739 0.671 0.720 0.653All regressions have firm and year fixed effects, Robust standard errors, clustered at thefirm level, in parenthesis. Significance thresholds are 0.1% (a), 1% (b), 5% (c). Eachcolumn shows the first stage results from an Olley-Pakes specification.95

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