Innovation and Trade Policy in a Globalized World

K.7 Innovation and Trade Policy in a Globalized World Akcigit, Ufuk, Sina T. Ates, and Giammario Impullitti Please cite paper as: Akcigit, Ufuk, Sina T. Ates, and Giammario Impullitti (2018). Innovation and Trade Policy in a Globalized World. International Finance Discussion Papers 1230. https://doi.org/10.17016/IFDP.2018.1230 International Finance Discussion Papers Board of Governors of the Federal Reserve System Number 1230 June 2018

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 1230 June 2018 Innovation and Trade Policy in a Globalized World Ufuk Akcigit Sina T. Ates Giammario Impullitti NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from Social Science Research Network electronic library at www.ssrn.com.

Innovation and Trade Policy in a Globalized World † ∗ Ufuk Akcigit Sina T. Ates University of Chicago, NBER, CEPR Federal Reserve Board Giammario Impullitti University of Nottingham June 14, 2018 Abstract HowdoimporttariffsandR&Dsubsidieshelpdomesticfirmscompeteglobally? Howdo these policies affect aggregate growth and economic welfare? To answer these questions, we buildadynamicgeneralequilibriumgrowthmodelwherefirminnovationendogenouslydeterminesthedynamicsoftechnology,marketleadership,andtradeflows,inaworldwithtwo large open economies at different stages of development. Firms’ R&D decisions are driven by (i) the defensive innovation motive, (ii) the expansionary innovation motive, and (iii) technologyspillovers. Thetheoreticalinvestigationillustratesthat,statically,globalization(definedas reducedtradebarriers)hasambiguouseffectsonwelfare,while,dynamically,intensifiedglobalizationboostsdomesticinnovationthroughinducedinternationalcompetition. Accounting for transitional dynamics, we use our model for policy evaluation and compute optimal policies over different time horizons. The model suggests that the introduction of the Research and Experimentation Tax Credit in 1981 proves to be an effective policy response to foreign competition, generating substantial welfare gains in the long run. A counterfactual exercise showsthatincreasingtariffsasanalternativepolicyresponseimprovesdomesticwelfareonly whenthepolicymakercaresabouttheveryshortrun,andonlywhenintroducedunilaterally. Tariffsgeneratelargewelfarelossesinthemediumandlongrun,orwhenthereisretaliation by the foreign economy. Protectionist measures generate large dynamic losses by distorting the impact of openness on innovation incentives and productivity growth. Finally, our model predicts that a more globalized world entails less government intervention, thanks to innovation-stimulatingeffectsofintensifiedinternationalcompetition. Keywords: Economic growth, short- and long-run gains from globalization, foreign technologicalcatching-up,innovationpolicy,tradepolicy,competition. JELClassifications: F13,F43,F60,O40. ∗We thank seminar and conference participants at Harvard University, Princeton University, Stanford University, Duke University, the NBER Summer Institute “International Trade & Investment” and “Macroeconomics and Productivity” groups, the University of Maryland, the University of Pennsylvania, the University of Nottingham, the UniversityofZurich,theUniversityofMunich,theFederalReserveBoard,theBankofItaly,theInternationalMonetaryFund,theInternationalAtlanticEconomicSociety,ASSAMeetings2018,theItalianTradeStudyGroup,CREST Paris, SKEMA, the SED Conference, and the CompNet Conference. We also thank Daniel J. Wilson for sharing and helping with his data. Akcigit gratefully acknowledges the National Science Foundation, the Alfred P. Sloan Foundation, and the Ewing Marion Kauffman Foundation for financial support. The views in this paper are solely the responsibilitiesoftheauthorsandshouldnotbeinterpretedasreflectingtheviewoftheBoardofGovernorsofthe FederalReserveSystemorofanyotherpersonassociatedwiththeFederalReserveSystem. †E-mailaddresses: uakcigit@uchicago.edu,sina.t.ates@frb.gov,Giammario.Impullitti@nottingham.ac.uk.

nnovation and rade olicy in a lobalized orld I T P G W 1 Introduction SincethepastU.S.presidentialrace,aheateddebatecenteredonthepositionoftheUnitedStates in its trade relationships. President Donald J. Trump’s speeches focused, among other issues, on the United States losing its security and competitiveness to other major economic players in the world. A favored, and widely discussed, policy suggestion was raising barriers to international trade. Finally, on March 9, 2018, the United States imposed tariffs on certain imports. Only three weeksaftertheimplementationofU.S.tariffs, onApril2, Chinaretaliatedbyimposingtariffson various U.S. products. Interestingly, similar concerns were raised three decades ago, during the 1970s and early 1980s, following the U.S. exposure to a remarkable convergence by advanced countries such as Japan, Germany and France, in terms of technology and productivity (see Figure 1). This generatedextremeconcernamongU.S.policycircles,mostnotablytheRonaldReaganadministration. As opposed to the recent focus on protectionist measures, the Reagan government, among other policies,introducedaresearchanddevelopment(R&D)taxcreditschemein1981forthefirsttime in U.S. history. To shed light on this recurring debate on how to tackle international technology competition, this paper evaluates alternative trade and innovation policies, focusing on strategic interactionsbetweenfirms. Weprovideanewsetofempiricalfactsthatmotivatetheconstruction ofanewdynamicgeneralequilibriumtheoryofinternationaltechnologycompetition, whichwe then employ to perform quantitative policy analysis. 8 Japan 6 Italy France Germany 4 Canada UK 2 US gnirutcafunaM ni htworG ytivitcudorP robaL ).gva 08−6791 ,% ni ,ruoh/tuptuo( −2 2 6 10 Growth in Patenting (Patent Applications in the U.S., in %, 1976−80 avg.) Figure1: ConvergencebetweentheUnitedStatesanditspeers Notes: The figure shows the relationship between growth of average labor productivity in the manufacturing sector and growth inthenumberofpatentapplicationsfortheUnitedStatesanditsmajortradingpartnersbetween1976and1980. Weobtaindata onpatentapplicationsintheUnitedStatesfromtheUSPTOandoninternationalproductivitycomparisonsfromCapdevielleand Alvarez(1981). 1

nnovation and rade olicy in a lobalized orld I T P G W As illustrated in Figure 1, the United States performed poorly relative to its advanced peers intermsoflaborproductivityandinnovationinthesecondhalfofthe1970s. Theaveragegrowth in output-per-hours-worked in manufacturing was the lowest in the United States. Moreover, innovation by these foreign competitors, proxied by new patent applications registered in the United States by the residents of these foreign countries, expanded substantially except for the United Kingdom. The figure also reveals that the largest growth rates in patent applications have been recorded by those countries whose labor productivity growth in manufacturing most outpaced the United States. Strikingly, patent applications by U.S. residents actually declined in absolute terms during the same period. United States Patent and Trademark Office (USPTO) data reveal that the ratio of foreign patents to total patents doubled between 1975 and 1985.1 While the United States held 70 percent of the patent applications in 1975, 10 later years this share declined to around 55 percent.2 .7 Introduction of Federal R&D Tax Credit (ERTA) 17 AZ 16 MO AZ NJ MO 13 RI NJ .65 NH NH RI U.S. Patent 11 11 CT CT CT Share 10 MA MA MA MA MA 9 IL IL IL IL IL IL 8 OR OR OR OR OR OR OR KS KS KS KS KS KS KS KS 6 ND ND ND ND ND ND ND ND .6 5 CA CA CA CA CA CA CA CA CA R&D Intensity WV WV WV WV WV WV WV WV WV WV 3 WI WI WI WI WI WI WI WI WI WI IA IA IA IA IA IA IA IA IA IA IA 1 1 1 IN IN IN IN IN IN IN IN IN IN IN MN MN MN MN MN MN MN MN MN MN MN MN MN MN .55 US Share in Total Patents .04 .035 .03 .025 .02 selaS/D&R 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 Year Figure2: R&DandinnovationintensityoftheU.S.firms Notes:ThefigureshowstheevolutionofaggregateR&Dintensity(definedastheratiooftotalR&Dspendingovertotalsales)ofthe publicU.S.firmslistedintheCompustatdatabase,andtheshareofpatentsregisteredbyU.S.residentsintotalpatentsregistered intheUSPTOdatabasefrom1975to1995. Theratiosarecalculatedannually. ThebarsshowthetotalnumberofU.S.stateswitha provisionofR&Dtaxcredits,alongwiththeirnames,foreveryyearsincethefirstadoptionofsuchameasurein1982. Unlike the debate today, concerns over U.S. competitiveness in those years led to the introductionofasetofdemand-andsupply-sidepoliciesexplicitlytargetingincentivesforinnovation. One of those was the introduction of the R&D tax credits at the federal level for the first time in 1SeeFigureA.1inAppendixA.1. Thissectiongivesafurtheraccountoftheempiricalfindingsoninternational technologicalcompetitionandtherelevantpoliciesduringtheperiodofinterest. 2Similartrendsarefoundincountries’shareofglobalR&Datthesectorallevel[seeImpullitti(2010)]. 2

nnovation and rade olicy in a lobalized orld I T P G W 1981, immediately followed by individual states’ actions. Upon these policy changes, aggregate R&D intensity of U.S. public firms showed a dramatic increase, indicated by the blue line in Figure2. Withanexpecteddelay, theannualshareofpatentsregisteredbyU.S.residentsintotal patent applications increased as well, as denoted by the orange line in the same figure.3 Starting in 1982 with Minnesota, several states followed suit by introducing state-level R&D tax credits (Figure 2). In contrast, there was no significant action in R&D policies for the other major countries (Figure 3).4 Motivated by these facts, this paper provides a new quantitative investigation of the effects of R&D subsidies in an open economy, comparing them with the effects of raising tradebarriersasaresponsetorisingforeigntechnologycompetition. Thispolicycomparisonalso provides new theoretical insights and quantitative perspectives on the gains from globalization. .25 Introduction of R&D tax credit (ERTA) .2 Changing the base calculation .15 .1 .05 0 etaR ydisbuS D&R lanoitaN/laredeF 1980 1985 1990 1995 Year US UK JAP ITA FRA GER Figure3: EffectiveR&Dtaxcreditratesacrosscountries Notes:ThefiguredepictseffectiveR&DsubsidyratesintheUnitedStatesanditsmajortradingpartnersfrom1979to1995(unavailableforCanada). A sensible quantitative analysis of the economic processes presented above necessitates an open-economy framework where economic growth is shaped by the interplay of innovation and international technological competition. The appropriate framework also needs to recognize the strategic interaction between large firms, because global R&D races and international trade are dominated by such firms, whose choices affect market aggregates and give rise to strategic marketpower. Theaircraftindustryisanexampleofatechnology-intensivesectordominatedbytwo 3InformationonsalesandR&DexpendituresofU.S.publicfirmsareobtainedfromtheCompustatdatabase. 4Following Impullitti (2010), R&D subsidies are calculated using corporate tax data from Bloom et al. (2002), whotakeintoaccountdifferenttaxandcreditsystems. Thesubsidiesreflectkeyfeaturesofthetaxsystemaimedat reducingthecostofR&D,particularlydepreciationallowancesandtaxcreditsforR&Dexpenditures. Thisstructure isresponsibleforthepositivevalueofoursubsidymeasureinitially. Formoredetails,seeImpullitti(2010). 3

nnovation and rade olicy in a lobalized orld I T P G W firms,AirbusandtheBoeingCompany,whichcompetestrategicallyforglobalmarketleadership [Irwin and Pavcnik (2004), Baldwin and Krugman (1988)]. The top one percent of trading U.S. firms account for about 80 percent of total U.S. trade, enabling them, through their large market shares, toimpactmarketprices[Bernardetal.(2017), Hottmanetal. (2016)]. Hence, thestrategic interaction between internationally competing firms is crucial when building a model to analyze our facts; and gaining new insights on trade and innovation policies. Moreover, as our facts are intrinsically dynamic, a careful policy evaluation needs to take into account the changes along the transition path. With these key points in mind, we build a new two-country dynamic endogenous growth model where innovation determines the dynamics of technology and global market leadership. Our framework builds on the step-by-step innovation models of Schumpeterian creative destruction,whichallowforstrategicinteractionamongcompetitors. Inbothcountries,final-goodfirms produce output by combining a fixed factor and a set of intermediate goods, sourced from domestic and foreign producers. In each intermediate sector, a home and a foreign firm compete for globalmarket sharesand investin R&Dto improvethe qualityof theirproduct. Endogenous entry by a fringe of domestic and foreign firms creates an additional source of competitive pressure on both leaders and followers in each product line. International markets are characterized bytradecostsandinternationaldiffusionofideasintheformofknowledgespillovers. Atheoretical investigation of this setting shows that, statically, openness to trade benefits the fixed factor in the final-good production via higher-quality intermediate-good imports. This translates into higher productivity in domestic final-good production. By contrast, the aggregate effect on business owners, which operates through a combination of larger market size for some businesses and loss of markets to foreign rivals for others, is ambiguous. More importantly, trade openness impacts the economies’ dynamics by affecting firms’ motives for innovation. The open-economy dimension of our model redefines firms’ incentives to innovate that are typical of the standard step-by-step models. The key driver of innovation in the closed-economy step-by-step framework is the escape-competition effect, in which the leader firm has an incentive to move away from the follower in order to escape competition. One of the novel implications of our open-economy model is that two such effects arise in a similar spirit. The main difference in an open economy is that vertical competition within each product line assumes an international dimension, as competing firms are from different countries. In each line, firms from both countries compete to serve the domestic and foreign market. Innovation generates a ranking of the product lines based on the quality/productivity difference between the home firm and the foreign firm. As in models of trade with firm heterogeneity [e.g., Melitz (2003)], trade costs generate quality cutoffs that partition the product space into exporting and non-exporting firms. But, in contrast to these models, where competition takes place horizontally between firms producing different goods and where firms are ranked based on their absolute productivity level, the ranking and, consequently, the cutoffs in our model are pinned down by firms’ productivity 4

nnovation and rade olicy in a lobalized orld I T P G W relative to their foreign competitors. When the quality of domestic intermediate goods in country c is too inferior relative to its foreign counterpart, final-good producers in country c decide to source their intermediate goods from abroad, which determines country c’s import cutoff on relative quality. Likewise, if the relative quality of the domestic producer in country c is above a certain threshold, the foreign final-good producers decide to import from the intermediategood producer in country c, which specifies the export cutoff on the relative quality for country c. Hence, the open-economy structure leads to two cutoffs, around which strategic competition between firms becomes stiffer. The key feature of these two cutoffs is that innovation efforts intensify around them due to increased competition. Just below the import cutoff, domestic firms exert additional effort to gain their leadership in the home market; hence, we name it the defensive R&D effort. Likewise, when a domestic firm is just below the export cutoff, it exerts additional effort to improve its lead and conquer the foreign market. We call this effort the expansionary R&D effort. These two new effects generate a double-peaked R&D effort distribution over the relative quality space that, remarkably, is also supported in the USPTO patent data. From a policy point of view, the distinction between defensive and expansionary R&D is crucial, as they generate different responses to alternative industrial policies. Another important feature of our model is the endogenous entry of new firms. In both the domestic and foreign economies, new entrants try to replace incumbents. The entry rate is state-dependent in that there will be more domestic entry into those sectors where the domestic incumbents maintain a larger lead over their foreign rivals. This is another prediction of the model for which we find empirical support in the patent data. We observe more patents coming from new entrants in patent classes where U.S. incumbents have a larger fraction of the patents. Weparameterizethemodeltomatchkeytrade,innovation,andgrowthfactsinthelate1970s and reproduce the evolution of global leadership in those years, with the United States initially representing the technological frontier in most sectors, while a set of European countries plus Japanleadsinafew. Thetransitionaldynamicsofthemodelreproducestheconvergenceintechnological leadership observed in the patent data during the 1970s and early 1980s. We validate ourmodel’smechanismwithout-of-sampletestsconcerningthelinkbetweeninnovativeactivity andtechnologicalleadership,andtheelasticityoffirm-levelR&Dspendingtopolicychanges. In particular, we lay out striking similarities between the model and the data as to the innovation patterns of firms at different technological positions vis-à-vis their foreign competitors. Furthermore, simulating the calibrated model beyond the calibration period, we examine the dynamics offoreigntechnologicalconvergence—amodeofglobalizationthathasnotbeenwidelyexplored in the literature—in the absence of policy interventions. In particular, we demonstrate the significant deterioration in the positions of U.S. firms in international technological competition that would have arisen in the absence of any policy intervention. 5

nnovation and rade olicy in a lobalized orld I T P G W In regards to policy evaluation, we first analyze welfare implications of protectionism—i.e., raising import tariffs unilaterally. The welfare implications of this policy change depend on the time horizon over which the policy is evaluated. A rise in tariffs generates short-run gains, as it tames international business stealing caused by foreign catching-up, keeping business profits at home. Thesegainsmorethancompensateforthenegativeeffectonaggregateproductivityofreplacing better-quality imported goods with inferior domestic counterparts. Over the first decade after a 50 percent (4 percentage points) increase in tariffs, there are gains of up to 0.2 percent of consumption. However, protective measures reduce incentives for domestic firms to invest in defensive innovation, because they weaken domestic firms’ exposure to foreign competitive pressures. As time goes by, this force dominates, leading to substantial drops in welfare in the long run. It operates through the key sources of gains from trade in this economy. First, declining defensive innovative effort limits the ability of the economy to make up for the foregone productivitythatwouldotherwisebeenhancedbythehigh-qualityimports. Second,itdepresses the gains from additional profits generated by protected businesses, reducing the growth in that income relative to baseline. Weaker foreign competition, caused by protectionism and the ensuing reduction in defensive innovative activity, also shape the optimal trade policy in our model: Lower tariffs are preferred when the welfare impact is evaluated over a longer time horizon. As an alternative policy option to protectionism, we feed the model an increase in R&D subsidies similar to the U.S. move in the early 1980s and assess its welfare properties over a period of intensifying foreign competition. The effective average U.S. R&D subsidy increases from about 5 percent in the 1970s to approximately 19 percent in the post-1981 period. This subsidy increase generates non-negligible gains in the model in both the short and long run. Over the three decades following the subsidy increase, the consumption-equivalent welfare is approximately0.9percenthigher,withthisgaindrivenbybothbusinessstealingandinnovation. Reducing the cost of innovation, subsidies stimulate both entrant and incumbent firms’ R&D in the United States, thereby accelerating productivity growth and allowing U.S. firms to obtain market leadership. We also show that the optimal subsidy level for the same horizon is much higher than the observed change, as the growth-stimulating impact of subsidies, which becomes stronger over time, calls for higher subsidies over longer horizons. In fact, the observed increase in subsidies is an optimal response when only a horizon shorter than 10 years is considered. Next, we analyze the optimal policy design when both tariff and R&D subsidy options are available to the policymaker. A key result is that the direction of the trade policy component crucially depends on the assumption about the response of the trade partners. When the policymaker creates the policy under the assumption that unilateral changes are possible, the optimal policy favors protectionist trade measures combined with aggressive R&D subsidies. The reason is that protectionist policies protect domestic profits, yet lower the innovation incentives. Hence, aggressive R&D subsidies are needed to make up for the reduced innovation efforts. However, if the trade partners retaliate, the optimal trade policy reverses and calls for a regime as liberal as 6

nnovation and rade olicy in a lobalized orld I T P G W possible. The risk of losing the export market plays the key role in this reversal. Last but not least, our analysis shows that less policy intervention is needed as the world becomes more globalized through reduced trade costs. This interesting result is due to the fact thatlowertradecostsintensifycompetitionintheglobalmarketplace. Morecompetitivemarkets induce more innovation, both defensive and expansionary. In other words, as globalization takes place, markets take care of the innovation incentives and eliminate the need for policy intervention. Wecloseourpaperwithafinalexercisethatshedsnewlightontherecentdebateconcerning theeffectofrisingimportcompetitiononfirm-levelandaggregateinnovativeactivityinexposed sectors. For instance, Autor et al. (2016) find a negative relationship focusing on the United States, whereas Bloom etal. (2016)findapositiveeffect fortheEuropeanexperience. Inasimple experiment using our model, we show how this relationship may transpire in both directions dependingonthesectoralcompositionoffirms’initialtechnologicalpositionrelativetotheirforeign competitors. Thus, our model provides a rationale that reconciles seemingly contradictory findings in previous empirical work. Takingstock,foreigntechnologicalcatching-uphastakenitstollonthetechnologicalleadership of U.S. firms and led to significant losses in their profits through business stealing. Increasing R&D subsidies during periods of accelerating foreign competition proves to be an effective response to foreign competition, while raising trade barriers generates only small welfare gains in the short run at the expense of substantial losses in the long run. The key message of our analysis is that when a country experiences fiercer foreign technological competition, R&D subsidies help national firms compete without giving up gains from trade. Finally, optimal trade policy design crucially depends on the possibility of foreign retaliation, in which case the threat of losing export markets calls for a more liberal trade regime. Literature Review This paper is related to several lines of research in the literature. The endogenous technical change framework that we use as the backbone of our economy is a model of growth through step-by-stepinnovationasinAghionetal.(2001,2005)andthelatestdevelopmentsbyAcemoglu and Akcigit (2012).5 These closed-economy models are solved in steady state, also abstracting from free entry. We propose the first open-economy version of this class of models, introduce free entry, solve for its transition path, and provide a quantitative exploration of the gains from globalization and the role of innovation subsidies in open economies. 5Building on another strand of growth models pioneered by Romer (1990), Grossman and Helpman (1990) use anexpandingvarietymodeltoanalyzetheroleofinternationaltradeandtradepoliciesindeterminingthelong-run growth. The adoption of a step-by-step framework instead enables us to study explicitly the strategic interaction betweenfirmsanditsimplicationforinnovationandtradepatterns. 7

nnovation and rade olicy in a lobalized orld I T P G W On modeling the trade side, our setting draws similarities to the theoretical literature that analyzes the impact of trade exposure on (industry-level) aggregate productivity in models with heterogeneous firm productivities, pioneered by Melitz (2003).6 Also, our structural general equilibrium framework incorporates several forces, such as competition and market size, whose impact on firm innovation is highlighted by recent empirical work that focuses on the nexus of innovation and trade [see Muendler (2004), Bustos (2011), Iacovone et al. (2011), Autor et al. (2016), Chen and Steinwender (2016), and, in particular, Bloom et al. (2016) and Aghion et al. (2017), among others].7 It also encompasses technology transfer alongside firm innovation as sources of productivity growth, in line with the empirical findings of Cameron et al. (2005). We contribute to this literature by formalizing and quantifying a new theory of endogenous firm decisions and openness to trade. Building on the seminal contributions of Rivera-Batiz and Romer (1991) and Grossman and Helpman (1991b), our analysis emphasizes the role of firms’ innovation decisions in shaping policy-induced aggregate dynamics and, thus, makes contact with a growing literature on dynamic gains from trade.8 A recent line of research began to tackle the hard task of quantifying these dynamic gains. Perla et al. (2015), Buera and Oberfield (2016), and Sampson (2016), among others, introduce knowledge diffusion into frontier trade models with heterogeneous firms and showthatthegainsfromtradeincreasesubstantiallycomparedtothestaticcounterpartsofthose models. Impullitti and Licandro (2017) study gains from trade in a model of innovation-driven productivitygrowthwithfirmheterogeneityandvariablemarkups. Focusingonthesteadystate, they find that accounting for firms’ innovation responses doubles the gains from trade obtained from the static competition and selection channels present in the model. Analyzing various extensions of the canonical Melitz (2003) framework, Burstein and Melitz (2013) discuss the effects of trade liberalization on firm dynamics. In parallel to our findings, they highlight how firms’ innovationresponsesdeterminetransitionaldynamicsinducedbytradeliberalization. Ourwork contributes to this literature by emphasizing the role of strategic interaction between firms in shapingtheirinnovationresponsesand,thereby,thedynamicgainsfromtrade. Wealsoexamine 6Inthefashionofthesemodels,firmswithheterogeneousproductivitiesselectthemarketstoserveinourmodel. Conversely,opennesstotrademayaffecttheinput-sourcingdecisionsoffirms. Forananalysisofthiseffectinasetup ofheterogeneousfirms,seeAntràsandHelpman(2004). 7 While Bloom et al. (2016) show the positive effect of Chinese import penetration on the technical change in 12 European countries, Aghion et al. (2017) examine the differential impact of market size and competition effects on innovation decisions of exporting French firms with heterogeneous initial productivity levels. They find that the marketsizeeffectisthedominantforceforfirmsthathavehigherproductivityattimesofincreaseddemand. Ona relatednote,Mayeretal.(2014)andMayeretal.(2016)lookattheproductrangeandmixofmulti-productfirmsas anothersourceofwithin-firmproductivityvariations. Theydocumentthepositiveeffectofincreasedexportmarket competitiononfirmproductivitythroughadjustmentsinthesemargins. 8In this regard, our attempt advances the literature in the direction pointed out by Burstein and Melitz (2013). In their recent chapter, the authors stress the need for more research on dynamic gains from trade, as opposed to extensively studied static ones, and on the implications of firm and technology dynamics as a potential source. Similarly, Costinot and Rodríguez-Clare (2018) mention that dynamic models could potentially yield substantially larger gains from openness to trade, in contrast to static models [see Costinot and Rodríguez-Clare (2014) for an extensivesurvey],thereforerepresentinganimportantchallengeforfutureresearch. 8

nnovation and rade olicy in a lobalized orld I T P G W these gains quantitatively along the transition path, thanks to our framework, which is capable of following the endogenous evolution of competition and innovation patterns in a tractable fashion. Last but not least, endogenous productivity growth and transitional dynamics provide further channels through which trade liberalization and policy may affect aggregate welfare, in addition to those considered by Atkeson and Burstein (2010) and Arkolakis et al. (2012).9 Finally, industrial policies in open economies have been studied by a large body of work.10 Spencer and Brander (1983) and Eaton and Grossman (1986) explore theoretically the strategic motive to use tariffs and subsidies (to production and innovation) to protect the rents and the market shares of domestic firms in an imperfectly competitive global economy.11 In a theoretical small open-economy framework of endogenous growth, Grossman and Helpman (1991a) study the implications of R&D subsidies and industrial policies for optimal long-run growth and welfare. Morerecently, Grossman andLai (2004) analyzestrategicintellectualproperty rightspolicy in a multi-country endogenous growth model. Ossa (2015) sets up a quantitative economic geography model to study production subsidy competition between U.S. states. In the spirit of our work, Impullitti (2010) uses a multi-country version of the standard Schumpeterian growth model to assess the welfare properties of R&D subsidies in an open economy, although his work isconfinedtothesteadystate.12 Incontrasttothesestudies,adistinctfeatureofourmodelisthe link between different modes of foreign competition and innovation at the firm level. We show that in this setting, different policies affect different types of innovations: For instance, unilateral protectionismdistortsincentivesfordefensiveR&D,whereasretaliationbytradepartnersdistorts incentives for expansionary R&D. This relationship, and the resulting dynamic gains from trade and transitional dynamics, are central to the design of optimal trade and innovation policy. Differentiating between the short and long run, we demonstrate the crucial dependence of policy implications on the horizon considered along the transition. Finally, a recent line of research has explored optimal trade policies in modern intra-industry trade models with firm heterogeneity and in Ricardian frameworks [e.g., Demidova and Rodríguez-Clare (2009), Costinot et al. (2015), and Costinot et al. (2016)].13 We complement this work studying optimal trade policy in a dynamic economy with innovation-driven productivity growth and out of steady-state dynamics. Therestofthepaperisorganizedasfollows. Section2introducesthetheoreticalframework, 9Considering a simple model of sequential production in intermediate goods, Melitz and Redding (2014) also point to trade-induced changes in domestic productivity as a source of departure from the findings of Arkolakis et al. (2012), which state that welfare gains from trade in a group of standard models can be derived from a few aggregate-levelsufficientstatisticsand,accordingly,shouldbefairlymodest. AlessandriaandChoi(2014)emphasize thesignificanceofaccountingfortransitioninthisregard. 10Institutionalchallengesinapplyingappropriateindustrialpoliciesarebeyondthescopeofthispaper. Interested readerscanseeRodrik(2004)foranextensivediscussion. 11SeeLeahyandNeary(1997)andHaalandandKind(2008)forrecentcontributions. 12ThepaperalsorelatestotherecentquantitativeanalysisofR&Dsubsidiesinaclosedeconomy. SeeAcemoglu etal.(2017)andAkcigitetal.(2016a,b). 13 Analyzing trade policies over the business cycle, the recent work by Barattieri et al. (2018) explores the recessionaryeffectsofprotectionisminaDSGEframework. 9

nnovation and rade olicy in a lobalized orld I T P G W followedbySection3withanalyticalresults. Section4outlinesthecalibrationprocedureandprovides out-of-sample tests. Section 5 discusses policy implications and optimal policies. Section 6 discusses the model’s implications in regards to import competition and domestic innovation. Section 7 presents sensitivity and robustness analysis. Section 8 concludes. 2 Model We present a model of international technological competition in which firms from two countries,indexedbyc A,B ,competeovertheownershipofintermediate-goodproduction. Each ∈ { } country has access to the same final-good production technology. There is a continuum of intermediate goods indexed by j [0,1] used in final-good production. The final good is used ∈ for consumption, production of intermediate goods, and innovation. There is free trade in final goodsectorsandnotradeinassets. Lackoftradeinassetsrulesoutinternationalborrowingand lending and enables the two countries to grow at different rates during the transition. In each production line of intermediate goods there are two active firms—one from each country—engaging in price competition to obtain a monopoly of production. Trade of intermediate goods is costly due to a combination of iceberg costs and tariffs. The firm that produces the variety of better quality after adjusting for the trade cost holds a price advantage. Firms innovate by investing resources to improve the quality of their product in the spirit of step-bystep models. If the quality difference between the products of two firms is large enough, then the firm with the leading technology can cover the trade cost and export to the foreign country. Because innovation success is a random process, the global economy features a distribution of firmssupplyingproductsofheterogeneousquality. Inadditiontotradeinintermediateandfinal goods, there is a second channel of interdependency linking the countries: trade in ideas. The exchange of ideas consists of technology diffusion through international knowledge spillovers. Inadditiontoincumbentfirms,thereisanoutsidepoolofentrantfirms. Thesefirmsengage in research activity to obtain a successful innovation that enables them to replace the domestic incumbent in a particular product line. Introducing the entry margin allows the model to distinguish the effects of domestic and foreign competition. Understanding these distinct forces becomes particularly important once we use our model for policy evaluation. Finally,ourmaingoalistoinvestigatethequantitativepolicyimplicationsofourmodel. For interested readers, we provide a brief theoretical discussion of a simplified version of the model in Section 3 and present analytical expressions and results of the main static and dynamic forces in Appendix C. 10

nnovation and rade olicy in a lobalized orld I T P G W 2.1 Preferences Consider the following economy in continuous time. Both countries admit a representative household with the following CRRA utility: U = (cid:90) ∞ exp( ρ(s t)) C c 1 s− ψ − 1 ds, (1) t − − 1 ψ t − whereC representsconsumptionattime t incountry c, ψ isthecurvatureparameteroftheutilct ity function, and ρ > 0 is the discount rate. The budget constraint of a representative household in country c at time t is r A +L w = P C +A˙ +G , (2) ct ct c ct ct ct ct ct where r is the return to asset holdings of the household, L is the fixed factor (could be labor ct c or land) supplied inelastically in country c, w is the fixed factor income, P is the price of the ct ct consumptiongoodincountryc,andG isthelump-sumtaxes/transfers. Householdsincountry ct c ownallthefirmsinthecountry; therefore,theassetmarketclearingconditionrequiresthatthe asset holdings have to be equal to the sum of firm values (cid:90) 1 A = V˜ +V dj, ct cjt cjt 0 where tilde “˜” denotes values pertaining to entrant firms. We assume full home bias in asset holding, an assumption that is robustly supported by the empirical evidence in the 1980s and 1990s.14 2.2 Technology and Market Structure 2.2.1 Final Good The final good, which is to be used for consumption, R&D expenditure, and as an input in the intermediate-good production, is produced in perfectly competitive markets in both countries according to the following technology: Y ct = 1 L c β β (cid:90) 1 (cid:18) q A 1 − β jt βk Ajt +q B 1 − β jt βk Bjt (cid:19)1 − β dj. (3) 0 − Here, k referstotheintermediategood j [0,1], q isthequalityof k ,and β istheshareoffixed j j j ∈ factor in total output. Intermediate goods can be obtained from any country, whereas the fixed 14Forinstance,in1989,92percentoftheU.S.stockmarketwasheldbyU.S.residents. Japan,theU.K.,France,and Germanyshowsimilarpatterns, at96percent, 92percent89percent, and79percent, respectively. Asimilarpicture canbeobserveduntiltheearly2000s,whenthehomebiasstartedtodecline[see,forexample,CoeurdacierandRey (2013)]. 11

nnovation and rade olicy in a lobalized orld I T P G W factor L isassumedtobeimmobileacrosscountries. Wenormalizethesupplyofthefixedfactor c L = 1 in both countries to reduce notation. c Firms in both countries may potentially produce each variety j. In the absence of trade frictions they are perfect substitutes in the final-good production, once adjusted for their qualities. Asaresult,final-goodproducerswillchoosetobuytheirinputsfromthefirmthatoffersahigher quality of the same variety. When trade costs exist, final-good producers buy the intermediate good of higher quality, once the prices are adjusted to reflect the trade costs. Final good producers in both countries have access to the same technology, which will allow us to focus on the heterogeneity of the intermediate-good sector. Both countries produce the same identical final good, which, under the assumption of frictionless trade in final goods, implies that the price of thefinaloutputinbothcountrieswillbethesame.15 Wenormalizethatpricetobethenumeraire without any loss of generality. 2.2.2 Intermediate Goods and Innovation Incumbents. In each product line j, two incumbent firms—one from each country—compete for the market leadership à la Bertrand. Each of these firms has the same marginal cost of production, η, yet they differ in terms of their output quality, q . We say that country A is the cj leaderinindustry jifq > q andthefollowerifq < q .Firmsareinaneck-and-neckposition Ajt Bjt Ajt Bjt when q = q . The quality q improves through successive innovations in A or spillovers Ajt Bjt Ajt from B (detailed later). When there is an improvement in country c specific to product line j during an interval of time ∆ t, the quality increases proportionally such that q cj(t+∆t) = λntq cjt , where λ > 1 and n N is a random variable, which will be specified below. We assume that t ∈ initially q = 1, j [0,1]. cj0 ∀ ∈ Let us denote by N = (cid:82)t n ds the number of quality jumps up to time t. Hence, the quality t 0 s of a firm at time t is q = λNcjt. The relative state of a firm with respect to its foreign competitor cjt is called the technology gap between two countries (in the particular product line) and can be summarized by a single integer m N such that Ajt ∈ q Ajt = λNAjt = λNAjt− NBjt λmAjt. q Bjt λNBjt ≡ As we shall see, m is a sufficient statistic for describing line-specific values, and we will therecjt fore drop the subscript j when a line-specific value is denoted by m. We assume that there is a relatively large but exogenously given limit in the technology gap, m¯, such that the gap between two firms is m m¯,...,0,...,m¯ . ct ∈ {− } 15Freeingintermediate-gooddemandandprofitsfromrelativefinal-goodpricemovements,frictionlesstradeinfinalgoodsprovidessignificantcomputationaltractabilitytoouralreadyintricatestructure,withendogenousforwardlookinginnovationdecisionssolvedovertransitionwhilealsokeepingtrackoftheendogenousgapdistribution. 12

entry qB=λ3qA qB=λ3qA 2 2 2 2 entry qB=λqA qB=λqA 1 1 1 1 qA=qA qA=qA 1 2 1 2 line1 line2 line4 line5 nnovation and rade olicy in a lobalized orld I T P G W Firms invest in R&D in order to obtain market leadership through improving the quality of their products. Let Rx and x denote the amount of R&D investment and the resulting Poisson cj cj arrival rate of innovation by country c in j, respectively. The production function of innovations takes the following form: x = (cid:16) γ R c x jt (cid:17) γ 1 c . Note that q in the denominator captures the fact cjt cαcqcjt cjt that a quality is more costly to improve if it is more advanced. This production function implies the following convex cost for generating an arrival rate x : cjt Rx (cid:0) x ,q (cid:1) = q α c x γc. (4) cjt cjt cjt γ cjt c Entrants. Everyperiod,anewentrepreneurineachproductlineandfromeachcountryinvests in innovation to enter the market. If an entrepreneur succeeds in her attempt, the entrant firm replaces the domestic incumbent; otherwise, the firm disappears. The innovation technology for (cid:18) (cid:19) 1 R˜x γ˜c entrants is, x˜ = γ˜ cjt , which implies the following convex cost function: cjt cα˜cqcjt R˜x (cid:0) x˜ ,q (cid:1) = q α˜ c x γ˜c. (5) cjt cjt cjt γ˜ cjt c Figure 4 demonstrates the evolution of leadership in intermediate product lines as a result of incumbent innovation, entry, and exit. quality, q quality, q A B entry entry exit exit product product line1 line2 line3 line4 line5 line, j line1 line2 line3 line4 line5 line, j a)Productlines b)Entry,exit,andleadership Figure4: Evolutionofproductlines Notes:PanelAexhibitsthepositionsofcompetingincumbentfirmswithheterogeneousqualitygapsinasetofproductlines.Firms fromcountry B(designatedbybluesquares)aretechnologicalleadersinthefirsttwolines,firmsfromcountry A(redcircle)are leadersinthenexttwolines,andfirmsareinneck-and-neckpositioninthelastline. PanelBillustratestheeffectsofinnovationby incumbentsandentrantsandtheresultingdynamicofentry,exit,andtechnologicalleadership.Emptysquaresorcirclesdenotethe previouspositionoffirmsthatinnovateorexit. In the left panel, five product lines with heterogeneous technology gaps are shown. In the 13

nnovation and rade olicy in a lobalized orld I T P G W first two lines, firms from country B (designated by a square) lead, and in the next two lines, firms from country A (designated by a circle) lead. In the last line, firms are in neck-and-neck position. The right panel exhibits how these positions evolve. Country A seizes technological leadership in the first two lines in two different ways. In line 1, an entrant from A enters with a large enough quality improvement, moving ahead of the previous leader, who is from B, and also driving the previous domestic incumbent out of business. In line 2, the incumbent from A generates an innovation with a step size that is larger than the existing gap, which enables it to surpass the previous leader. While there is no change in line 3, firms become neck-and-neck in line 4 as a result of a successful innovation by the incumbent from B. In line 5, an entrant innovationfrom Bbreakstheneck-and-neckcompetitionandbringsthetechnologicalleadership to B, while also forcing the country’s previous incumbent to exit. Lastly, notice that changes in technological leadership may not result in business stealing when trade costs exist. Consider line 2, where country B’s final-good producers initially buy domestic inputs from the technologically superior domestic intermediate producer. Even if technologicalleadershipchangeshandsinthisline,country B’sfinalgoodproducersmaystillprefer buyingdomesticintermediateinputsinsteadofimportingthebetter-qualityforeigninputiftrade costs make it unprofitable despite the quality advantage of country A’s firm. Innovations and Step Size. Each innovation improves the relative position of the firm in the technological competition. Conditional on innovation, the new position at which the firm will end up is determined randomly by a certain probability mass distribution F ( ).16 Because the m · maximumnumberofgapsiscappedbym¯,thereisadifferentnumberofpotentialgapsthateach firm may reach depending on its current position in the technological competition. For instance, if a firm is leading by 10 gaps, with a single innovation it can potentially open up the advantage to 11,...,m¯ ,whereasforaneck-and-neckfirm,aninnovationcanhelpitreach 1,...,m¯ .Hence, { } { } the probability mass function that determines the new position, F ( ), is a function of m. m · In order to keep the model parsimonious, we assume there exists a fixed given distribution F( ), and we derive F ( ) from this distribution in the following way. First, we define the m · · benchmark distribution over positions larger than m¯, the most laggard position, as depicted in − Figure 5a. We assume that it has the following functional form: F(n) c 0 (n+m¯)− φ n m¯ +1,...,m¯ . (6) ≡ ∀ ∈ {− } Thisparametricstructureisdefinedbyonlytwoparameters: acurvatureparameter φ > 0; anda shifter c that ensures ∑ F(n) = 1. It implies a decaying probability in the new position n. This 0 n decay translates into a decay in the probability of an innovation generating larger technological jumps. 16Conversely,eachinnovationcomeswithanassociatedstepsizethatisrandomlygeneratedbysomeprobability massfunction. 14

A F m (n) ∀ n ∈ [m+1,m¯] A m¯ +1 m m+1 m¯ m¯ +1 m¯ − − nnovation and rade olicy in a lobalized orld I T P G W F F A F(n) = c0 (n+m¯) − φ = F m¯ (n) F m (n) ∀ n ∈ [m+1,m¯] − A gapsize gapsize m¯ +1 m¯ m¯ +1 m m+1 m¯ − − a)Benchmark b)Atpositionm Figure5: Probabilitymassfunctionfornewposition Notes: PanelAillustratesthefunctionF(),definedinequation(6),whichweusetogeneratetheposition-dependentdistributions · ofinnovationsize.Thus,itdescribesalsotheprobabilitydistributionoverpotentialpositions,whereaninnovationcantakethemost laggardincumbent,denotedbyF m¯ ( · ).Similarly,PanelBillustratesF m ( · )foragenericpositionm. The highest gap size a firm can reach is m¯. Therefore, the step size distribution specific to the firm’s position, F ( ), is defined over positions n m+1,...,m¯ and is derived as follows: m · ∈ { } (cid:40) F(m+1)+ (m) for n = m+1 F (n) = A . (7) m F(s) for n m+2,...,m¯ ∈ { } As demonstrated in Figure 5b, (m) ∑m F(s) is an additional probability of improving A ≡ s= − m¯+1 the current quality only one more step, on top of what F( ) would imply for that event, which · is given by F(m+1). This specification for position-specific distributions implies that as firms becometechnologicallymoreadvancedrelativetotheircompetitors,itisrelativelyhardertoopen up the gap more than one step at a time. Moreover, their derivation comes at no additional cost in terms of parameters thanks to the additive nature of . Finally, notice that F (n) = F(n). m¯ A − An explanation for this particular way of modeling innovation step sizes is in order. In thepreviousclosed-economystep-by-stepmodels, eachinnovationimprovestheexistingquality of the follower either by a single step or by making the follower catch up with the leader no matter how big the initial gap is. The former is dubbed “slow catch-up regime,” while the latter is dubbed “quick catch-up regime” in Acemoglu and Akcigit (2012). A slow catch-up regime would imply a slow process of convergence in leadership shares in contrast to what is observed in the data, and yet the quick catch-up regime would have the opposite effect. Therefore, by incorporating F(n), we generalize the modeling of firms’ catching up and equip the model with enough flexibility to replicate the convergence process observed in the data.17 17Notethatthisspecificationconvergestothestandardstep-by-stepmodelasφ ∞. → 15

nnovation and rade olicy in a lobalized orld I T P G W The treatment of (m) in the derivation of position-specific distributions serves the same A purpose. Analternativecouldassumeequaldistributionofthetruncatedprobabilitymass (m) A acrosspotentialpositions m+1,...,m¯ . Thisalternativewouldimplyarelativelyfatterrighttail { } in F (n) and, thus, a higher chance of climbing up the position ladder. However, this structure m would favor the United States, most of whose firms are technological leaders in their products, as opposed to the foreign countries, whose firms are lagging in most product lines. Even though a laggard firm can close the gap by multiple steps, a leading firm in this alternative setup could easily open up the gap again. It happens because for a leading firm, equal allocation of (m) A across the few better positions the firm may reach entails a higher chance of reaching better positions quickly again (as compared to the current specification where the probability of onestep improvements is disproportionately higher at larger leads). Because of this advantage of the leading firms, the model, once initiated at the empirical distribution, would have a strong force working against the shift in the leadership distribution toward smaller gaps, as the empirical distribution strongly favors the United States in the early years of the sample period. This feature would contrast with the convergence process in the data. By contrast, our current structure with innovations of heterogeneous step sizes helps the model generate the correct speed of convergence as in the data, while the distributional assumptions capture the idea of “advantage of backwardness” as in Gerschenkron (1962), as relatively more laggard firms are in a more advantageous position to receive multiple-step innovations. ∆ During a small time interval t 0, the resulting law of motion for the quality level of an → incumbent from A that operates in product line j can be summarized as follows. For m > m¯ − the law of motion becomes (cid:40) λnq with probability (cid:0) x +x˜ (cid:1) F (n)∆ t+o(∆ t) for n m+1,...,m¯ Ajt Ajt Ajt m q Aj(t+∆t) = q with probability 1 (cid:0) x +x˜ (cid:1) F (n)∆ t+o(∆ t) ∈ { } , Ajt Ajt Ajt m − and for m = m¯ the law of motion follows −     λnq Ajt with probability (cid:0) x Ajt +x˜ Ajt (cid:1) F − m¯ (n)∆ t+o(∆ t) for n ∈ {− m¯ +1,...,2m¯ } q Aj(t+∆t) = q Ajt with probability 1 (cid:0) x Ajt +x˜ Ajt (cid:1) F m¯ (n)∆ t+o(∆ t) ,  − −   λq with probability (cid:0) x +x˜ (cid:1) F (n)∆ t+o(∆ t) Ajt Bjt Bjt m where o(∆ t) denotes the second-order terms. Considerthequalitylevelsassociatedwiththeincumbentfirmsfromcountry A.Inaproduct line where the firm from A is in position m, the quality improves when either the domestic incumbent or entrant innovates. Moreover, the quality in a product line where the firm from A is inthe highest possiblelag m¯ improves notonly with innovationsby the domesticincumbent − andentrant,butalsowithinnovationsbytheforeignincumbentorentrant,reflectingknowledge spillovers. The assumption of a maximum number of gaps and the resulting spillovers imply 16

nnovation and rade olicy in a lobalized orld I T P G W thatinindustrieswherethismaximumisreached,anadditionalinnovationbytheleader,despite improving its quality, cannot widen the gap further. The underlying economic intuition is that when the leader at gap m¯ innovates, the technology at gap m¯ +1 becomes freely available to − the follower in this product line. Because in this economy the leader and the follower belong to different countries by construction, this knowledge spillover implies a technology flow across country borders. Thisspillover helps ourmodel economy generate cross-countryconvergence in innovation, technology, and income. 2.3 Equilibrium In this section, we solve for the Markov Perfect Equilibrium of the model where the strategies are functions of the payoff relevant state variable m. We start with the static equilibrium. Then we build up the value functions for the intermediate producers and entrants and derive their closed form solutions along with the R&D decisions. These variables help us characterize the evolution of the world economy over time. Henceforth, we will drop the time index t unless it causes confusion and denote export-related variables by an asterisk. 2.3.1 Households We start with the maximization problem of the household. The Euler equation of the household problem determines the interest rate in the economy as: r = g ψ+ρ. ct ct 2.3.2 Final and Intermediate Good Production Next, we turn to the maximization problem of the final good producer in country c A,B . ∈ { } Using the production function (3), the final-good producers generate the following demand for the fixed factor L and intermediate good j [0,1]: c ∈ β (cid:90) 1 β 1 β 1 β w ct = 1 β L c− q jt k jt − dj (8) 0 − p cjt = L c β q c β jt (cid:18) q A 1 − β jt βk Ajt +q B 1 − β jt βk Bjt (cid:19) − β . (9) Now we consider the intermediate-good producers’ problem. In our open-economy setting, producers can sell their goods both domestically and internationally. However, as trade is subject to iceberg costs, the producer faces different demand schedules on domestically sold and exported goods. Therefore, the producer earns different levels of profits on these goods depending on the destination country. Let us start with the case of domestic business. Intermediate 17

nnovation and rade olicy in a lobalized orld I T P G W firms produce using the final good as input with a constant marginal cost η.18 Then, the profit maximization problem of the monopolist in product line j becomes19 (cid:110) (cid:111) (cid:0) (cid:1) β β 1 β π q jt = m kjt≥ ax 0 L c q jt k jt − − ηk jt ∀ j ∈ [0,1]. The optimal quantity and price for intermediate variety j follow from the first order conditions: (cid:20) (cid:21)1 1 β β η k = − q and p = , (10) jt jt j η 1 β − with L set to 1. The realized price is a constant markup over the marginal cost and is indepenc dent of the individual product quality. Thus, the profit earned by selling an intermediate good domestically is (cid:0) (cid:1) π q = πq , jt jt β 1 1 β where π η −β (1 β) −β β. Notice that in deriving profits, we assumed that the monopolist is ≡ − able to charge the unconstrained monopoly price. Assumption 1 introduced below ensures that the leaders are able to act as unconstrained monopolists. The problem when selling abroad is different due to trade costs. In line with the trade literature, we assume that in order to export one unit of an intermediate good, the exporting firm needs to ship 1+κ units of that good (κ 0). Moreover, a firm in country A exporting ≥ to country B pays τB units of flat-rate excise import tariffs.20 This means that when the firm considers meeting the foreign demand, it will take into account that its marginal cost will be (cid:0) (cid:1) 1+κ+τB η. Giventhetradecosts,onlythefirmwiththehighercost-adjustedqualitywillfind it profitable to sell in the other country. Hence, the firm from country A exports intermediate good j to country B if and only if q Ajt q . 1 β ≥ Bjt (1+κ+τB) −β In this Bertrand competition setting, the existence of a competitor with inferior quality—by definition, located in the foreign country—could potentially push the leader to limit pricing. To simplify the analysis we make the following assumption: 18Thestructurewiththefinalgoodbeingtheonlyinputtointermediate-goodproductionhelpsthecomputation of the model substantially, as the intermediate production and export decisions become independent of fixed factor prices. AppendixEpresentsaversionofthemodelwherethefixedfactorisaninputtointermediate-goodproduction inaparticularway,providingabenchmarktostudythedetrimentaleffectofforeigncatch-upandtheresultingloss ofintermediateproductiononthecompensationofthefixedfactor. 19The monopolist’s maximization problem assumes the equilibrium property that a final-good producer buys an intermediateinputfromonefirmonly. Therefore,themonopolistproducer’sdemandk isgivenbyequation(9)with j theamountsuppliedbytheotherfirmk settozero(seeAssumption1). j 20Inthebaselinemodel,weassumeth − atthegovernmentburnsoutthetariffrevenue,thusmakingtariffstooperate similartoicebergcosts. InSection7.5,werelaxthisassumptionasarobustnessexperiment. 18

nnovation and rade olicy in a lobalized orld I T P G W Assumption 1 In every product line, incumbents enter a two-stage game where each incumbent pays an arbitrarily small fee ε > 0 in the first stage in order to bid prices in the second stage. Assumption 1 ensures that only the incumbent with the highest cost-adjusted quality pays thefeeandisthereforeabletosetthemonopolypriceinthesecondstage. Underthisassumption, similar derivations as in the case of domestic sales lead to the following optimal quantity of exports and associated profits: (cid:16) (cid:17) (cid:20) (cid:21)1 1+κ+τc(cid:48) η 1 β β (cid:0) (cid:1) k∗cjt = (1+κ − +τc(cid:48))η L c(cid:48) q cjt and p∗cj = 1 β ⇒ π c∗ q jt = π c∗L c(cid:48) q cjt , (11) − with c ∈ { A,B } , c (cid:54) = c (cid:48) , and π c∗ = (cid:16)(cid:16) 1+κ+τc(cid:48) (cid:17) η (cid:17)β −β 1 (1 − β) 1 −β β β. Figure 6 summarizes the effect of positive trade costs on the technology frontier of two competing countries. quality, q A1 A1 A2 Afirms,whensoldathome A1’ A2’Afirms,whensoldabroad A1’ B1 B1’ B2 B2’ A2 A2’ product 0 1 line, j Export Domesticsaleonly Import Figure6: Effectoficebergcostonqualityandtradeflows Notes:Thefigureexhibitsthetechnologyfrontiers,definedastheproductqualitiesofincumbentfirmsoverallproductlines,oftwo countriesinanexampleeconomy(shownbythesolidlines).Whenexporting,theeffectivetechnologyfrontiers(givenbythedashed lines)arelowerthantheactualonesbecausetheexportersneedtoincurtradecosts. Without loss of generality, Figure 6 illustrates a special case where the quality frontiers of the two economies align perfectly in a descending order of qualities across sectors. The solid lines define the quality frontier of the domestic intermediate producers, where A and B denote thehomeandtheforeigncountry,respectively. Thedashedlinesshowthelevelofthesequalities when adjusted by trade costs. Firms of the home country can export a product as long as the cost-adjusted quality, denoted by the dashed line A , is higher than the domestic quality of (cid:48) 19

nnovation and rade olicy in a lobalized orld I T P G W that product available in the foreign country, denoted by the solid B line. When the reverse occurs, the home country imports the higher-quality product. Otherwise, firms serve only their domestic markets. Two intersections of dashed and solid lines determine two cutoffs that define three regions of product lines according to their position in trade. Next, we define these cutoffs analytically. We denote by m the smallest gap by which a leader from country c A,B needs to ∗c ∈ { } lead its follower in order to be able to export its good. Due to trade costs, it is possible that an intermediate-good producer has a higher-quality product compared to its foreign competitor (e.g.,q > q ),butincost-adjustedtermsthequalityofitsgoodislowerthantheforeigncounterc c(cid:48) part such that the firm cannot export (q / (cid:16) 1+κ+τc(cid:48) (cid:17)1 −β β < q ). To secure a quality advantage c c(cid:48) evenaftertradecostsareaccountedfor,thetechnologygapbetweenaleaderanditsfollowerhas to reach the threshold (cid:40) (cid:41) m∗c ≡ argm m in m ∈ [0,m¯] : λm ≥ (cid:16) 1+κ+τc(cid:48) (cid:17)1 −β β . (12) Nowwedefinethequalityindexofsectorswherefirmsfromcountrycareinstatem.Denote the measure of product lines where firms from c are m-steps ahead by µ . Then the aggregate cm quality across these product lines is given by (cid:90) Q q I dj. cmt ≡ cjt { j ∈ µcm} Using the equilibrium conditions derived previously, total output is given as Y = ∑ m¯ (cid:20) 1 − β (cid:21)1 −β β Q cmt + −∑ m∗c(cid:48) (cid:20) 1 − β (cid:21)1 −β β Q c(cid:48)mt . (13) ct η 1 β (1+κ+τc)η 1 β m= − m∗c(cid:48) +1 − m= − m¯ − The first sum denotes the contribution of domestic intermediate goods. The second sum, which is across product lines where foreign exporters lead domestic firms by at least m gaps, denotes ∗c(cid:48) the contribution of imported goods. Finally, the fixed factor price is w = βY , which follows ct ct from the first order condition of the final-good producer given by equation (8). We complete the description of equilibrium properties of goods’ production with their implications for trade flows. The final good is freely traded and it absorbs possible imbalances in intermediate-goods trade. Hence, trade in this economy is balanced, and the relative price driving the adjustment is the relative price of the fixed factor w /w . A B 20

nnovation and rade olicy in a lobalized orld I T P G W 2.3.3 Firm Values and Innovation This subsection presents equilibrium firm values and innovation decisions.21 Incumbent Firms. We can write the value function for country A’s incumbents:22 (cid:26) (cid:16) (cid:17) (cid:16) (cid:17) (x )γA r V (q ) V˙ (q ) =max Π m;τA,τB q 1 sA α Amt q At Amt t − Amt t xAmt t − − A γ A t m¯ (cid:104) (cid:16) (cid:17) (cid:105) +x Amt ∑ F m (n t ) V Ant λ(nt− m) q t − V Amt (q t ) nt =m+1 +x˜ [0 V (q )] Amt − Amt t (cid:41) (cid:16) (cid:17) m¯ (cid:104) (cid:105) ∑ + x +x˜ F (n ) V (q ) V (q ) , (14) B( − m)t B( − m)t nt = − m+1 − m t A( − nt) t − Amt t where Π(cid:0) m;τA,τB (cid:1) is defined as  (cid:16) (cid:17)  πL A +π ∗L B if m ≥ m∗A Π m;τA,τB =  π 0 L A i i f f m m ∗A ≤ > − m m∗B > − m∗B . Notethatprofitleveldependsonforeigntariffsbecauseprofitsfromexports,derivedinequation (11), are affected by it. Also, domestic tariffs affect profits protecting some firms. The first line on the right-hand side denotes the operating profits net of R&D costs, where sA is the R&D subsidy. Profits are linear in product quality, creating an incentive for innovation even for firms at the largest lead. As is evident from the definition of Π(cid:0) m;τA,τB (cid:1) , capturing the domestic market or expanding into foreign markets adds to profits, thereby intensifying the incentives to innovate. Expansion of markets through exports reflects the market-size effect. The second line denotes the expected gains from innovation. This expectation is over potential new positions. The exact position is determined probabilistically by the step size of innovation. For firmsthatareclosetotheirrivalsand,thus,feelthecompetitionatitsmostintense,theinnovation effortreflectsadominantincentivefortaking overthecompetitorinordertogainmarketpower. This is an escape-competition effect typical of step-by-step innovation models. A distinguishing feature of our model, however, is that this force emerges at two distinct positions instead of a single one as is typical of closed-economy versions. The first case is when a laggard firm is one-stepbehindshortofbeatingtheforeignexporterandgainingaccesstodomesticproduction. Thisleadstoanintenseinnovationactivitybythelaggardfirm,whichwelabelasdefensiveR&D. Second, a similar intensification happens when a domestic producer is one step short of gaining access to export markets, in which case expansionary R&D is observed. We further discuss this 21Inequilibrium,misasufficientstatisticforfirmvalue. Lemma1attheendofthissubsectionverifiesthisresult. Accordingly,wereplacesubscript jwithmunlessotherwisenecessary. 22TheproblemforincumbentfirmsfromcountryBisdefinedreciprocally. 21

nnovation and rade olicy in a lobalized orld I T P G W extensionoftheescape-competitioneffectacrossmultiplestagesofcompetition—inparticular,over domestic and foreign markets—in Section 4.2 by confronting the model with the data. The last two lines on the right hand side capture the creative destruction by domestic and foreign competitors. The third line reveals that entry by domestic firms forces the incumbent to exit with probability one, as by construction every product line is forced to have one firm from each country. This domestic business-stealing effect reduces the value of an incumbent firm and therefore its incentive to innovate. Moreover, in an open economy, there is an additional channel through business stealing. The last line explains the changes as a result of innovation in the foreign country. Any innovation there, regardless of the source being an entrant or an incumbent,deterioratesthepositionandthevalueofthedomesticincumbent;andthesizeofthe deterioration is again determined probabilistically by F ( ).23 We label this additional channel m − · as the international business-stealing effect.24 Thefirms’problemsarecharacterizedbyaninfinite-dimensionalspaceofintermediate-good qualities. The following lemma renders the firm environment independent of the current quality of their products, reducing the state space to finite dimensions and allowing for numerical tractability. Lemma 1 ThevaluefunctionsarelinearinqualitysuchthatV (q) = qv form m¯,...,m¯ where cm cm ∈ {− }      Π(cid:0) m;τA,τB (cid:1) − (cid:0) 1 (cid:104)− sA (cid:1) α A (xA γ m A t )γA (cid:105)         +x Amt ∑m n ¯ t =m+1 F m (n t ) λ(nt− m)v Ant − v Amt    r v v˙ = max . At Amt − Amt xAmt    (cid:16) (cid:17) +x˜ Amt [0 − v Amt ] (cid:104) (cid:105)        + x B( − m)t +x˜ B( − m)t ∑m n ¯ t = − m+1 F − m (n t ) v A( − nt) − v Amt     This ensures that the innovation decision of the firm does not depend on j once controlled for m. Proof. See Appendix B.1. The first order conditions of the problems defined above yield the following equilibrium R&D decisions for an incumbent in state m:  (cid:104) (cid:110) (cid:111)(cid:105) 1 x =    αc (1 1 − sc) ∑m n ¯ =m+1 F m (n) λ(nt− m)v cnt − v cmt γc − 1 if m < m¯ . (15) cmt  (cid:104) (cid:105) 1   αc (1 1 − sc) (λ − 1)v cm¯t γc − 1 if m = m¯ 23Thedistributionfunctionislabeledwiththesubscript mbecauseitisassociatedwiththecompetitor’sposition. − Note that there is no threat of exit posed by the foreign entrant, as that entrant replaces the incumbent of its own country. 24We define the value functions for the two boundary cases where the incumbent is m¯-steps ahead (behind) in AppendixB.2. Asdiscussedthere,theinternationalknowledgespillovermanifestsitselfinthevaluefunctionofm¯-stepbehindincumbent. 22

nnovation and rade olicy in a lobalized orld I T P G W Entrants. Recall that entry is directed at individual product lines and a successful entrant improves on the active domestic incumbent’s technology. The problem of an entrant that aims at a product line where the current domestic incumbent is m > 0 (m < 0) steps ahead (behind) is as follows: (cid:40) (cid:41) V˜ cmt (q t ) = max α˜ c (x˜ cmt )γ˜c q t +x˜ cmt ∑ m¯ F m (n t )V cnt (cid:16) λ(nt− m) q t (cid:17) . (16) x˜cmt −γ˜ c nt =m+1 Again, F ( ) denotes the probability distribution of potential step sizes, from which a random m · step will realize conditional on having an innovation. An entrant who fails to innovate exits the economy. Solving this problem leads to the following equilibrium value of the entrant firm: (cid:18) (cid:19) 1 V˜ (q ) = 1 α˜ (x˜ )γ˜c q > 0, cmt t c cmt t − γ˜ c which is independent of the production line’s index j and is determined by the current gap size. The equilibrium innovation rates for entrants become  (cid:2) (cid:3) 1 x˜ cmt =  (cid:104) λv cm¯t · α˜ −c 1 γ˜c − 1 (cid:105) 1 if m = m¯ . (17)  α˜ −c 1∑m n ¯ =m+1 F m (n)λ(nt− m)v cnt γ˜c − 1 if m < m¯ Closingthemodel,aggregateconsumptionisderivedfromthebudgetconstraintinequation (2). Aggregate R&D spending R is derived combining equations (4), (5), (15), and (17): ct m¯ (cid:16) (cid:17) R = ∑ α x γc +α˜ x˜ γ˜c Q , (18) ct c cst c cst cst s= m¯ − and total intermediate-production input K is determined by equations (10)-(11): ct K = ∑ m¯ (cid:16) 1+κ+τc(cid:48) (cid:17) η (cid:20) 1 − β (cid:21) β 1 Q + m¯ ∑− 1 η (cid:20) 1 − β (cid:21) β 1 Q . (19) ct s=m∗c (1+κ+τc(cid:48))η cst s= − m∗c(cid:48) +1 η cst The government spending reads as m¯ G = sc ∑ α x γcQ , (20) ct c cst cst s= m¯ − implyingthatthetotalexpenditureonsubsidiesisfundedbythetotallump-sumtaxescollected. Noticethattariffsdonotgeneraterevenueinthebaselinemodel(Section7.5relaxesthisassumption). We leave the analytical discussion of the evolution of the aggregate quantities such as µ cmt and Q , which summarize the dynamics of the model, to Appendix B.3. Now we define the cmt equilibrium. 23

nnovation and rade olicy in a lobalized orld I T P G W Definition 1 (Equilibrium) Let the world economy consist of two countries c A,B . A Markov ∈ { } Perfect Equilibrium is an allocation t [0,∞) { r ct ,w ct ,p j ,k jt ,k∗jt ,x cjt ,x˜ cjt ,Y ct ,C ct ,R ct ,K ct ,G ct ,L c , { µ cmt ,Q cmt }m ∈{− m¯,...,m¯ }}c ∈ ∈{ A,B } ,j ∈ [0,1] such that (i) the sequence of prices and quantities p ,k ,k satisfy equations (10)-(11) and maximize the j jt ∗jt operating profits of the incumbent firm in the intermediate-good product line j; (ii) the R&D decisions (cid:8) (cid:9) x ,x˜ are defined in equations (15) and (17), and R is given in equation (18); (iii) supply of fixed cjt cjt ct factor L isequaltotheprofit-maximizingdemandbythefinal-goodproducersdefinedbyequation(8);(iv) c Y is as given in equation (13); (v) C is as derived from equation (2); (vi) K is given in equation (19); ct ct ct (vii) fixed factor compensation w clear the labor markets at every t; (viii) interest rates r satisfies the ct ct households’ Euler equation; (ix) government has a balanced budget at all times in line with equation (20); (x) and µ ,Q are consistent with optimal R&D decisions. { cmt cmt }m ∈{− m¯,...,m¯ } 2.4 Welfare Aggregate welfare in economy c over horizon T calculated at time t is given by 0 Wc = (cid:90) t0 +T exp( ρ(s t)) C c 1 s− ψ − 1 ds. t0 − − 1 ψ t0 − In the quantitative section, we will report the welfare differences between a counterfactual and the baseline economy in consumption equivalent terms using the following relationship: (cid:90) t0 +T exp( ρ(s t )) (C c n s ew)1 − ψ − 1 ds = (cid:90) t0 +T exp( ρ(s t )) (cid:0) (1+ς)C c b s ase (cid:1)1 − ψ − 1 ds. 0 0 − − 1 ψ − − 1 ψ t0 − t0 − If a policy change at time t yields a new income sequence Cnew between t and t +T satisfying 0 ct 0 0 the above relationship, we say that the policy change results in ς% variation in consumptionequivalent welfare over horizon T. This means that the representative consumer in the baseline economywouldneedtoreceiveς%additionalincomeateachpointintimebetweent andt +T 0 0 in order to obtain the level of welfare it would have in the counterfactual scenario. 3 Analytical Results in a Simplified Model and Taking Stock Beforeproceedingtothequantitativeinvestigationofthemodel,wefinditworthwhiletodiscuss some of the key economic forces of our model in more detail.25 We split the discussion into two parts: static and dynamic. Even though it is not possible to express the equilibrium objects in a 25WereferthereaderwhoisinterestedinquantitativeanalysistoSection4. 24

nnovation and rade olicy in a lobalized orld I T P G W fully analytical form in transition, we make significant progress in that direction by focusing on a slightly simplified version here.26 We start with the discussion of static forces. 3.1 Static Effects of Openness In this subsection, we will abstract from iceberg costs and we will consider two extreme economies: open economy (i.e., no tariffs) versus autarky (i.e, prohibitive tariffs). We can solve for the static equilibrium for these two alternative economies and show that income of the fixed factor is always bigger in an open economy—i.e., wautarky < wopen. This result is intuitive. In a worldwithopeneconomies,moreproductiveintermediate-goodproducersselltothefinal-good producers in both countries. This selection channel facilitates the transfer of better-quality intermediate goods across countries, increasing the productivity of the fixed factor utilized in the productionofdomesticfinaloutput. Therefore,thischannel,labeledasdirecttransferoftechnology in Keller (2004), leads to a higher fixed factor income in both countries. However,theimpactofopennessonprofitsisnotobvious. Incontrasttothestateofautarky, theopeneconomyallowsrelativelymoreproductivefirmstoselltoalargermarketbyproviding the opportunity to export. Yet, at the firm level the selection channel implies that less productive domestic firms lose their profits to foreign competitors, which they would earn otherwise in autarky, causing a decline in aggregate profit income. As a result, the net effect of openness on total profits remains ambiguous. Proposition 1 summarizes these findings. Proposition 1 In the environment without iceberg trade costs described above: A) Opening the economy to international trade increases the income of the fixed factor, i.e., wautarky < wopen. However, the total change in profits of the domestic business owners is ambiguous and (cid:82)1Πautarky ≶ dependsontheinitialcompositionofthetechnologygapsbetweentwocountries,i.e., dj 0 j ∑m¯ µ Πopen . m= m¯ m m − B) The static effect of unilateral trade policy liberalization (reduction in tariffs) on aggregate income is shaped by the loss of profits to foreign exporters and the gain in fixed factor income and, therefore, has an ambiguous direction. Proof. See Appendix C. For instance, in an extreme case where a country is lagging in all sectors by a very small margin, opening to trade from autarky may decrease national income initially, as the small productivity gain from transferring slightly better technology may not compensate for the loss of profits in all sectors. 26ForathoroughdiscussionofsimilarchannelsinthecontextofabasicSchumpeteriancreativedestructionmodel, seeChapter15inAghionandHowitt(2009). 25

nnovation and rade olicy in a lobalized orld I T P G W 3.2 Dynamic Effects of Openness and Escape Competition In order to emphasize the dynamic strategic interaction between intermediate producers introducedbyforeigncompetition,wefocusonaspecialcaseofourmodel. Inparticular,weconsider a standard step-by-step open-economy setting with two symmetric countries that abstracts from firm entry, features quick catch-up by followers, and minimizes the incentives for quality improvements. First, we take α˜ ∞ implying zero entry in both countries. Second, innovations c → improve a leader’s position by a single step—i.e. F (n = m+1) = 1, m 0. Third, we set m ∀ ≥ F (n = 0) = 1, m < 0, to allow any innovating follower to reach neck-and-neck position. m ∀ Fourth, we assume that λ = 1+ε where ε is arbitrarily close to zero, implying that quality improvements from innovations are minuscule.27 The following proposition argues that, in this environment, firms in neck-and-neck position have the highest innovation intensity. Proposition 2 The above assumptions imply that 1. the innovation intensity becomes the highest at neck-and-neck position; 2. the followers innovate at the same intensity and strictly less than the neck-and-neck firms; 3. the leaders do not innovate. Formally, x > x = x > x = x = 0 for m > 0. 0 m m¯ m¯ m − − Proof. See Appendix C. Proposition 2 formalizes the fact that the positive effect of foreign competitive pressures on innovationincentivesbecomesthestrongestwhenfirmscompeteagainstrivalsproducinggoods of similar quality. This effect is analogous to the one in closed-economy step-by-step models— namely, the “escape-competition” effect—but it gains an international aspect in the context of a small open economy. Moreover, notice that in our general model, the international structure modifies the escape-competition effect in more subtle ways than merely shifting the origin of the competitivepressurefromdomestictoforeign. Infact,theintensificationofinnovationasaresult ofinternationalcompetitionarisesattwopointsinourgeneralizedmodelinsteadofonebecause of trade costs. Firms have an incentive to escape competition for two similar yet distinct reasons: tocapturedomesticprofits(defensiveR&D);andtocaptureexportmarkets(expansionaryR&D). In Section 4, we proceed with the full-fledged model, removing simplifying features introduced in this subsection for the sake of analytical investigation. 27Therefore,innovationincentivesaredrivenbybusiness-stealingandescape-competitioneffects. 26

nnovation and rade olicy in a lobalized orld I T P G W 4 Quantitative Analysis In this section, we study the quantitative implications of our theoretical framework. After calibrating the model, we first discuss its performance in terms of out-of-sample predictions. Then, we focus on the implications of R&D subsidies and tariff policies for technological competition. We evaluate alternative scenarios including the simultaneous use of both policy measures and tariff retaliation by trade partners in terms of their welfare consequences. We start our exploration with the calibration of our model. 4.1 Calibration When mapping our two-country model to the data, we envision a world that consists of the United States and a foreign country, which is a weighted combination of the six countries employed in the empirical section: Canada, France, Germany, Italy, Japan, and the U.K.28 The weights associated with each country, listed in Table 1, reflect the count of patents registered in the United States by the residents of a specific country in the initial year of the sample (1975) as a fraction of all foreign patents registered in the United States in that year.29 In the remainder of this section, country A will represent the United States and country B the foreign country. Table1: Patentweightsofcountries Canada France Germany Italy Japan U.K. 6.2% 11.7% 30.0% 3.8% 33.1% 14.6% As Figure 3 shows, there is a significant break in the R&D policy before and after 1981. Moreover, as shown in Figures A.1 in Appendix A.1, there is a strong convergence in the relative shares of domestic and foreign patents registered in the United States prior to 1981, which also holds true for the share of sectors led by domestic and foreign firms. A key objective of our calibration strategy is to reproduce this convergence in order to conduct our policy evaluation exercises in an environment that mimics the intensification of the foreign technological competition faced by U.S. firms in those years. Therefore, we match the model to a set of moments that we obtain from the data that span 1975 to 1981. Then, we impose the changes in R&D policy observed in the data to the calibrated model and analyze their implications for the post-1981 period (1981 to 2016).30 28Thesearethemostinnovation-intensivecountriescompetingwiththeUnitedStates,measuredbytheirshareof patentapplicationsintheUSPTOpatentdata. 29Weightsmaynotsumto1becauseofrounding. 30 We focusour analysison the periodbefore 1995for several reasons. First, we wantto avoidthe run-up tothe U.S. dot-com bubble and the crisis that followed in the early 2000s. Second, we isolate our period from heightened 27

nnovation and rade olicy in a lobalized orld I T P G W In the calibrated model, we try to keep the least amount of heterogeneity across countries, otherthansubsidylevels,inordertofocussolelyontheeffectofpolicydifferences. Thetwolarge openeconomiessharesymmetrictechnologiesexceptthescaleparametersofR&Dcostfunctions and the imposed R&D subsidies. These assumptions leave us with the following 16 structural parameters to be determined: (cid:110) (cid:111) θ α ,α ,α˜ ,α˜ ,γ,γ˜,ρ,ψ,β,κ,η,λ,φ,τ ,sA ,sB . ≡ A B A B 75 − 81 75 − 81 75 − 81 Some of these parameters are calibrated externally and the remaining are calibrated internally. We start with the external calibration. 4.1.1 External Calibration We take the CRRA parameter of the utility function ψ = 2, a standard value in the macroeconomics literature. We set the time discount parameter ρ = 1%. These preference parameters imply a 2.8 percent interest rate in the balanced growth path and an average rate of 1.8 percent between 1975 and 1981 for the United States. We set β = 0.5, which leads to a roughly 65 percent share of fixed factor income in U.S. GDP in the balanced growth path, with η set equal to 1 β.31 We assume R&D cost functions to have a quadratic shape such that γ = γ˜ = 2, which is − the common estimate in the empirical R&D literature (see Acemoglu et al. (2017) for a thorough discussion). The left panel of Table 2 lists these values. Table2: Listofparametervalues PanelA:Externallycalibrated PanelB:Internallycalibrated Parameter Value Description Parameter Value Description ψ 2 Elasticityofsubstitution α 0.64 R&Dscale,incumbentsUS A γ,γ˜ 2 R&Dcostcurvature α 1.14 R&Dscale,incumbentsFN B ρ 1% Rateoftimepreference α˜ 44.6 R&Dscale,entrantsUS A β 0.6 Factorincomeshare α˜ 8.77 R&Dscale,entrantsFN B sA 5.3% R&DsubsidyUS,75-81 φ 1.35 CurvatureofF(n) 75 81 − sB 3.8% R&DsubsidyFN,75-81 λ 1.49% Innovationstepsize 75 81 − κ 11.4% Icebergtradecost τ 8% Tariffrate 75 81 − A crucial set of parameters is the R&D subsidy rates. The numbers we use are those calcompetitionexertedbyChina. Althoughvaluableinitself,thiswouldintroduceasecondperiodofexogenousvariationtoouranalysis,makingitmorecomplicatedfornoapparentbenefit. Finally,ourtheoreticalassumptionofhome biasisbettersuitedforthisrelativelyearlierperiodoffinancialglobalization. 31Byincomeapproach,GDPisequaltothesumofprofitsandwagesearned. 28

nnovation and rade olicy in a lobalized orld I T P G W culated in Impullitti (2010), which lack only Canada.32 These data go back to 1979. Given that the rates in the sample countries do not markedly fluctuate before the mid-1980s, we assume the values before 1979 to be the same as in 1979. For the calibration part, the subsidy rates for both countries are 1975-1981 averages, which are again weighted for the foreign countries. When we simulate the model for the post-1981 period, we will recalculate the subsidy rates to match the averages across 1982 to 1995. We also recalculate the weights of foreign countries the same way, but use 1981 patent counts. 4.1.2 Internal Calibration and Identification We have eight remaining parameters: α ,α ,α˜ ,α˜ ,λ,φ,κ,τ . One of these, φ, determines A B A B 75 81 { − } the shape of the generic step-size distribution. In order to calibrate them, we use seven data points and the distribution of firms across technology gaps that we derive using USPTO patent data. We start with the discussion of the seven moments, summarized in Table 3, that are not directly related to the gap distribution. Again, moments pertaining to the foreign country are weighted averages of the values for individual countries. The first two moments are the average growth rates of total factor productivity (TFP) in both countries, calculated using TFP series in Coe et al. (2009). The next two moments are aggregatenon-defenseR&DexpenditureasapercentageofGDP,whichweobtainfromtheMain Science and Technology Indicators (MSTI) database of the OECD.33 As a fifth target, we include the birth rate of new establishments for the United States computed using the BDS database.34 The sixth moment is the ratio of U.S. manufacturing exports to GDP, which we derive using World Bank data. The final moment is the average U.S. tariff rate, which we obtain from U.S. International Trade Commission. These moments allow us to determine seven parameters as follows. Aggregate R&D shares discipline the scale parameters of the incumbent R&D cost functions α ,α . The scale parameter of the entrant R&D cost function for country A (α˜ ) is A B A { } determinedbytheU.S.establishmentbirthrate. Then, TFPgrowthratespindownthebasicstep size λ and the entrant R&D cost for country B (α˜ ). The U.S. export-to-GDP ratio determines B the iceberg cost κ, as κ sets m , the minimum gap a firm needs to open up in order to export, ∗ given λ. Finally, average U.S. tariff revenue during the calibration period determines the tariff rate, which we take to be common for both countries. Thelastparametertobeinternallycalibratedisφ,whichcontrolsthecurvatureofthegeneric probabilityfunctionovertechnologygaps,F(n).Asmanifestedbyequations(A.1),thisfunction, 32WeaddressthisissuebyrecalculatingthepatentweightsafterdroppingCanada. 33 Non-defenseR&DspendingdatadonotincludeJapan. However,ScienceandEngineeringIndicatorsreportsof theNationalScienceFoundation, basedonMSTIdata, provideestimatesofthisvariableforJapan, whichweuseto amendourcalculationswiththeOECDdata. Also,MSTIdatastartin1981,whichiswhyweusetheinitialvaluesof thisvariable. 34Wepreferentrybyestablishmentsinsteadoffirmsbecausewhileinthedatafirmsenteratdifferentsizes,inour modeleveryfirmoperatesinoneproductline. 29

nnovation and rade olicy in a lobalized orld I T P G W by forming the basis of position-specific F (n), becomes an integral determinant of the model m dynamics that govern the evolution of firms’ measure across technology gaps (µ ’s). We make cm use of this relationship to discipline the shape of F(n). To this end, we first derive the empirical distribution of sectors across technology gaps using the information on patents provided by the USPTO data. This procedure, illustrated in Figure 7, provides us with the data counterpart of firms’ measure across technology gaps (gap distribution) in the model. PatentClasses A01B A61K B02C · · · · · · · · · · · · · · E21B F04B srotces+004 sessalc+004 #USpatents Tech. gaps/bins #total 1 0.50 m=m¯ =16 0.02 · 0.46 · · · 0.54 · m=1 0.51 m=0 0.48 m= 1 0.45 − · · · · 0.98 0.03 · m= m¯ = 16 0.53 0 − − Figure7: MappingUSPTOpatentdatatothemodel Notes:ThefigureillustrateshowpatentclassesintheUSPTOdataareassignedtoequallysizedbinsonaunitmeasureaccordingto theshareofpatentsownedbyU.S.residents,obtaininganempiricaldistributionoftechnologygaps. Westartwithsortingsectorsinagivenyearaccordingtothefractionofpatentsineachsector that are registered by U.S.-based entities in that year.35 Then, we divide this unit interval into 33 equally spaced bins, each of which corresponding to a range of approximately 3 percent. For instance,sectorswithafractionofU.S.patentsbetween0and3percentwouldfallintom = 16, − sectors with a fraction between 4 and 6 percent would fall into m = 15, and so on. Sectors in − the data correspond to product lines in our model and, thus, the measure of sectors across bins (normalized to sum to 1) corresponds in our model to µ ’s for country A across 33 gap levels m from m¯ = 16 to m¯ = 16.36 Figure 8a shows the distribution in the data for years 1975 (circled − − 35ThetotalmassofpatentsinagivenyearconsistsofpatentsbyregistrantsfromtheUnitedStatesandtheother sixforeigncountriesthatweusedthroughoutthepaper. Fortherobustnessofourresultstoamethodwheresectoral countrysharesarecalculatedbasedoncumulativepatentcountsoveranumberofyears,seeSection7.4. 36 We chose the maximum gap to allow for a realistic catch-up process for laggard firms while having enough observationsineachbinoftheempiricaldistribution. 30

nnovation and rade olicy in a lobalized orld I T P G W black line) and 1981 (solid blue line).37 It reveals that, initially, a substantial mass of U.S. firms are technological leaders, with the mean gap being close to seven; however, subsequently, their distribution has shifted leftward, with the mean gap falling to around four in 1981. This shift translates into a larger mass of U.S. firms in relatively smaller gap sizes and, therefore, signifies a strong foreign technological catch-up. The calibration of φ aims to match the dynamics of this catch-up process that occurred between 1975 and 1981, as described in the discussion of the model fit below. 0.09 0.08 Data = Model US, 1975 0.08 Data US, 1981 0.07 Model US, 1981 0.07 0.06 0.06 0.05 0.05 0.04 0.04 0.03 0.03 0.02 0.02 0.01 0.01 0 0 -20 -15 -10 -5 0 5 10 15 20 -20 -15 -10 -5 0 5 10 15 20 Technological gaps btw. domestic and foreign firms a)Technologicalgapdistribution: dataandcalibration 1891 ni noitubirtsid SU ?=0:4#?^ ?=0:8#?^ ?^=1.37,calibrated ?=1:2#?^ Technological gaps btw. domestic and foreign firms b)Identificationofφ Figure8: Gapdistributionafterpolicychanges Notes: PanelAdepictsthreetechnologygapdistributionsanddemonstratesthemodel’sperformance(positivevaluesonthehorizontalaxisdenoteU.S.technologicalleadership). Thedottedsolidlineistheempiricaldistributionin1975,whichalsodefinesthe initialdistributionforthemodelsimulationinthecalibration. Thesolidbluelineistheempiricaldistributionin1981anddefines thetargetdistributionofthesimulation.Thedashedredlineisthemodel-generateddistributionin1981,simulatedatthecalibrated parameters. PanelBillustratestheeffectofφ(thecurvatureparameterofthestep-sizedistributionfunction)onthesimulatedgap distribution, the variation in which enables the identification of φ. It exhibits various model-generated distributions in 1981 that resultfromsimulationswithvaryinglevelsofφasotherparametersbeingheldattheircalibratedvalues. Inordertoobtainthemodelcounterpartsofourdatatargets,wesimulatethetwoeconomies between 1975 and 1981, initializing the model at the empirical gap distribution in 1975. Initially, we normalize the quality of U.S. intermediate goods to one—i.e., q = 1 j.38 We solve Aj1975 ∀ the transition path of the model over 1975 to 1981 as described below. We derive the model counterparts of the seven moments presented in Table 3 by taking averages of the simulated series over the relevant period. We also compute the evolution of the gap distribution in the modelusingequations(A.1)definedinAppendixB.3andtrytohittheempiricalgapdistribution in 1981 as the terminal point of the economy in transition. 37Distributionsaresmoothedusingakerneldensityfunctionwithabandwidthof1.8. 38The quality levels of firms from B are initialized accordingly with respect to their position in technological competition. Mathematically,thisnormalizationimpliesthatifinproductlinejthefirmfrom Aisatpositionm,then q Bj1975 =λ− m, m ∈{− m¯,...,m¯ } . 31

nnovation and rade olicy in a lobalized orld I T P G W Solution Algorithm and Model Fit. In order to solve the model, we first discretize it. The solution algorithm assumes that the economy starts in 1975 and transitions to the balanced growth path in T periods, where each period is divided into (∆ t)− 1 = 25 sub-periods. The algorithm is an iterative backward solution method. The main procedure of the algorithm consists of solving for the balanced growth path and then deriving the values over the transition period going backward from the balanced growth path. A brief description is as follows:39 1. Let M be the set of data moments and Mm be the model counterpart. Define R(M Mm) − as the objective function that calculates a weighted sum of the difference between data and model moments. 2. Guess a set of values for the internally calibrated parameters θ . guess 3. Calculatethebalancedgrowthpath,wheretimederivativesarezerobydefinition. Compute theinnovationrates,theimpliedgrowthrates,andfinallytheinterestratescompatiblewith balanced growth. 4. Next calculate the equilibrium over the transition. Guess a time path for interest rates with the terminal values being set to balanced-growth levels at every iteration. Solve for firmvaluesandinnovationratesbackwardintimestartingfromthebalancedgrowthpath. Using the resulting sequences, simulate forward the income path and its growth rate. Use the Euler equation to derive the implied interest rates and compare them to the series fed initially. 5. Once step 4 converges, use the final interest rate series to compute the aggregate variables and the model counterparts of the data moments. (cid:0) (cid:0) (cid:1)(cid:1) 6. Minimize R M Mm θ using a minimization routine. We use the sum of squared guess − errors as the objective function.40 The targeted moments and the model performance in matching these moments are summarized in Table 3 and Figure 8a. Along the transition, the catching-up country exhibits higher R&D-to-GDP ratios growing fasterthantheleadingcountry. Themodelcapturesthesedifferencesbetweenthetwoeconomies observed in the data quite successfully. The entry rate and the export shares are also well fitted. Finally,thepositionofthedashedredlinerelativetothesolidblueoneinFigure8aindicatesthe strong performance of the model in matching the 1981 distribution of technology gaps. In the model, the forces of cross-country convergence that enable the reproduction of the catch-up observed in the data are chiefly governed by the curvature of the step-size distribution φ. Figure 8b illustrates how different values of φ lead to various shapes of technology gap 39AdetailedexplanationofthestepsispresentedinAppendixD.1. 40Themomentsthatpertaintothegapdistributionareweightedbythetargetednumberofbinsinordertomake thetotalweightofthedistribution-relatedmomentsthesameastheothertargets. 32

nnovation and rade olicy in a lobalized orld I T P G W Table3: Modelfit Moment Estimate Target Source TFP Growth U.S. 0.47% 0.55% Coe et al. (2009) 1975-81 TFP Growth FN 1.98% 1.73% Coe et al. (2009) 1975-81 R&D/GDP U.S. 1.65% 1.75% OECD 1981 R&D/GDP FN 1.90% 1.96% OECD 1981 Entry Rate U.S. 9.98% 10.0% BDS 1977-81 Export Share U.S. 7.06% 7.00% WB 1975-81 Tariff revenue U.S. 5.70% 7.70% U.S. ITC 1975-81 distribution. Each line in the figure represents a distribution that emerges in 1981 once the model is simulated between 1975 and 1981 at the calibrated parameter values except φ, which takesadifferent valueineachiteration. Lowervalues of φ meanaflatter probabilitydistribution F(n) over step sizes (or, equivalently, positions ahead), allowing technologically laggard firms to catch up more quickly. Therefore, a low value of φ would imply a larger leftward shift in the initial gap distribution of U.S. firms. The position of the solid blue line in Figure 8b relative to the circled black line, which represents the calibration result, illustrates this case. The converse happens for larger values of φ, as demonstrated by the relative position of the yellow dashed line, which is generated by a value that is 20 percent higher than the calibrated one. The distribution across new positions, F(n), is the engine of convergence, with the international knowledge spillover keeping laggard firms from the foreign country in the global innovation race. Importantly, an innovation can generate an improvement of multiple steps for laggard firms, whereas the number of potential steps to improve becomes smaller as a firm opens up the technologicalgapwithitsfollower. InGerschenkron(1962)’sterms,thisstructurecreatesan“advantage of backwardness” for followers—i.e., laggard firms have an advantage in the number of steps they can improve with each innovation, while far-ahead leaders cannot open further their lead quickly. Thus, foreign firms catch up with domestic firms along the transition, generating a cross-country technological convergence. This convergence in our economy echoes that in the Solowmodelwithakeydifference: InSolowconvergenceisdrivenbydecreasingreturnsincapital accumulation, in our economy knowledge spillovers and an “advantage of backwardness” drive the convergence. The internally calibrated parameters resulting from this procedure are listed in the right panelofTable2. Thecombinationofthetradecostsandthestepsizeimpliesm = 12—i.e.,afirm ∗ needs to lead by at least 12 technological gaps to export. The level of φ generates a considerable chance of improving multiple steps with a single innovation for laggard firms. For example, the probability that an innovation by the most laggard firm brings a multi-step improvement is 60 33

nnovation and rade olicy in a lobalized orld I T P G W percent.41 4.2 Validation of the Model Before discussing the properties and the policy implications of the calibrated model, we present four out-of-sample tests to assess the quantitative plausibility of the integral mechanism of our model, in light of empirical relationships not used in the calibration process. Validation Exercise I: Incumbent Innovation vs. Leadership Figure 9 compares the relationship between innovation efforts of incumbent firms and their technological position relative to their competitors in the model and in the data. Figure 9a displays incumbents’ innovation intensity as a function of the technology gap. Figure 9b shows average patenting intensity of U.S. firms in the USPTO data, measured by patent applications perfirm, acrosssectorsrankedaccordingtotheirshareofpatentsregisteredbyU.S.residents, as described in Section 4.1.2.42 In Figure 9a, we observe two spikes at m = 12 and m 1 = 11 ∗ ∗ − − − that are related to cutoffs defined in equation (12). The left one emerges because of the defensive R&D effort, as the firm increases its innovation to improve its position and capture domestic production. Similarly, the right peak emerges because of the expansionary R&D effort of firms that sell domestically. They increase their innovation efforts massively when closer to the export cutoff, as a new innovation right before that threshold enables the domestic firm to expand into the export market. Interestingly, we observe a similar shape with two peaks also in the data, as illustrated in Figure 9b. Again, the peaks emerge in sectors where U.S. firms hold a strong technological advantage, or disadvantage, as measured by the sectoral share of total patents registered by U.S. residents. The remarkable performance of the model in capturing the innovation intensity observed in the data provides further evidence for our model’s ability to mimic firms’ innovation behavior. The jump in innovation in the proximity of the export cutoff is consistent with a large body ofevidenceshowingthatfirmsinnovateinordertoentertheexportmarket. UsingChileanplantlevel data, López (2009) finds that productivity and investment increase before plants begin to export. Aw et al. (2011), using Taiwanese plant-level data, estimate a dynamic structural model 41Conversely,theprobabilitythatthemostlaggardfirmreceivesasingle-stepinnovationis40percent. 42We create the empirical measure of average innovation intensity across technology gaps as follows. First, we calculatethetotalnumberofdomesticpatentapplicationsanduniquedomesticownersofthosepatentsforeachpair oftechnologyclassandyear. Next,weranktheseclass-yearpairsaccordingtotheshareofdomesticapplicationsin total applications and assign them to technology bins as in Figure 7. Then, in each bin, we sum the total domestic patents and unique domestic assignees across class-year pairs. The ratio of those is the average patenting intensity perassigneeinagivenbin,whichproxiesforinnovationintensityinourmodel. Theexerciseconsidersapplications between1975and1995,alongspanoftime,asthecomparisonistothebalancegrowthpathinthemodel. Togenerate thefigure,wealsodroppatentsassignedtotheassigneeid“0”,asmostoftheotherassigneevalueshavemorethan sixdigits. FigureA.6inAppendixD.2showsthatincludingthosepatentsleadstosharperspikesinthedata. 34

nnovation and rade olicy in a lobalized orld I T P G W 1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 -15 -10 -5 0 5 10 15 Gaps (m) troffe noitavonnI Incumbent innovation US Defensive innovation Expansionary innovation a)Model: Incumbentinnovationintensity .gva ,mrif rep noitacilppa tnetaP 5.3 3 5.2 2 5.1 1 −15 −10 −5 0 5 10 15 Gaps b)Data: PatentingintensityofU.S.incumbents Figure9: Incumbentinnovationeffortandleadership Notes: PanelAshowstheinnovationintensityofU.S.incumbentfirmsinthebalancegrowthpathofcalibratedeconomy. PanelB showstheaveragenumberofpatentsappliedforbytheU.S.firmsintheUSPTOdataacrosstechnologygaps(thecreationofthe technology gaps is illustrated in Figure 7). The hollow markers designate actual data points, and the line is fit using smoothing splines. of the decisions of firms to innovate and to enter the export market. They find that these two decisions are highly correlated—i.e., firms entering the export market are more likely to also speeduptheirinvestmentinR&D.LileevaandTrefler(2010)findthatCanadianplantsthatwere inducedbytheU.S.tariffcutstostartexporting(i)increasedtheirlaborproductivity,(ii)engaged in more product innovation, and (ii) had higher adoption rates for advanced manufacturing technologies. Validation Exercise II: Tariff Reduction and Shift in Innovation Intensity As another validation test, we present a case study on the link between trade barriers and firms’ innovation efforts. Our model implies that because of intensified competition around trade thresholds, which are determined by trade costs, firms increase their innovation efforts in these regions. One way to detect this relationship in the data is to focus on firms’ innovation behavior in a specific sector and its evolution over time with respect to changes in trade barriers in that sector. To perform such an analysis, we map USPTO patent data to Standard International Trade Classification (SITC) industries (revision 2) and concentrate on the manufacturing sector, which makes up about half of patenting activity, over a period with substantial reductions in tariff rates.43 Data on tariffs are available from the World Integrated Trade Solution (WITS) database of the World Bank. Studying tariff reductions in a specific sector instead of a cross-industry comparison allows us to proceed without resorting to using a reliable estimate 43WeobtaincrosswalksformappingUSPTOdatatoSITCindustrylevelfromLybbertandZolas(2014). 35

nnovation and rade olicy in a lobalized orld I T P G W of industry-specific trade costs—known to be notoriously difficult to obtain [Anderson and van Wincoop (2004), Hummels and Lugovskyy (2006)]—as long as non-tariff barriers are not rising over time. 6 5 4 3 Tariff reduction phase 2 Tariff rate on US imports (dashed) 3.5 3 2.5 2 1.5 1 )dilos( stropxe SU no etar ffiraT 1989 1994 1999 2004 Years a)Tariffratesovertime .gva ,mrif rep noitacilppa tnetaP 6 4 2 0 Pre−1993 Post−1998 −15 −10 −5 0 5 10 15 Technological gaps btw. domestic and foreign firms b)Incumbentinnovationbefore1993andafter1998 Figure10: Tariffsandincumbents’innovationintensityacrosstechnologygapsinmanufacturing Notes: PanelAshowsthereductionintheaverageeffectivetariffratesappliedtoU.S.importsandexportsofmanufacturedgoods followingtheUruguayroundoftheGATT.TariffratesappliedbyortogoodsofindividualcountriesareobtainedfromWITSand areweightedbythepatentingintensityofthetradepartnersintheUSPTOdata.PanelBshowsthechangeintheinnovationintensity ofincumbentU.S.patenteesinthemanufacturingsectoracrosstechnologygaps. Thehollowmarkersdesignateactualdatapoints (circlesfortheearlierperiodandtrianglesforthelater),andthelinesarefitusingsmoothingsplines. Figure 10a shows the decline in the tariff rates to which U.S. manufacturing imports and exports were subject over the 1990s.44 On average, both barriers were 2 percent lower between 1997 and 2004 than between 1989 and 1993, in part as a result of the Uruguay round of the General Agreement on Tariffs and Trade completed in 1994 and other bilateral trade agreements. In parallel, Figure 10b depicts the innovation intensity of incumbent patentees in the U.S. manufacturing sector with respect to their technological position relative to foreign competitors, again before and after the mid-1990s.45 Noticeably, incumbent-innovation intensity in the manufacturing sector exhibits a double-peaked profile in line with our findings for the complete set of patents in the USPTO data. Moreover, we observe that the period of tariff reductions coincides 44The tariff data on WITS go back to 1989. The United States is one of the few countries that reports tariffs on importsreliablyacrosstimeandtradepartners. Weusethesamesampleoftradepartnersasintheoriginalanalysis (Canada,Germany,France,Italy,Japan,andtheU.K.)andweighttheaverageeffectivetarifftomanufacturingimports fromeachofthembytheirpatentshareintheUSPTOdatain1988. Similarreductionsintariffsareobservedwhen accounting for larger groups of countries as well. Tariffs on U.S. manufacturing exports are more limited, reported onlybyCanadaandJapan. WeusetheJapaneseseries,asJapanconstitutesabouthalfofforeignpatentsregisteredin theUnitedStatesbythelate1980s. Finally,weusethebroadsectorgroupingformanufacturinginWITSdata,which compriseschapters6(manufacturedproducts)and8(miscellaneousmanufacturedarticles)oftheSITCclassification (excludingnon-ferrousmetalswiththecode68). 45WeconstructedtheinnovationintensityofincumbentsinthemanufacturingsectorovertechnologygapsfollowingsimilarstepstothosedescribedinSection4.1.2,exceptthatweusedSITCsubindustriesinsteadofpatentclasses astheunitofanalysis. TobeinlinewiththeWITSdata,weusedthesamespecificationofthemanufacturingsector, whichconsistsofSITCchapters6and8. 36

nnovation and rade olicy in a lobalized orld I T P G W withaninwardshiftofpeaksinincumbents’innovationintensityprofileacrosstechnologygaps. This observation mirrors the predictions of our model: Lower bilateral trade barriers imply that firmswithalessertechnologyadvantageovertheircompetitorsstartexporting,makingthecompetition for markets stiffer at smaller technology gaps and thereby resulting in peaks closer to (purely technological) neck-and-neck position (which occurs at zero). We will come back to this discussion in Figure 20a of Section 5.7, when we discuss the effect of bilateral changes in trade costs. Validation Exercise III: Entrant Innovation vs. Leadership Entryisanothersourceofbusinessstealinginthemodel. However,incontrasttoincumbents,entrants are not subject to immediate competitive pressures from the other country’s firms. Therefore, the shape of entrants’ R&D effort profile, demonstrated in Figure 11a, reflects mainly the market size effect around the two cutoffs and not a direct effect of foreign competition. 0.11 0.105 0.1 0.095 0.09 0.085 -15 -10 -5 0 5 10 15 Gaps (m) etar lavirra nossioP Entrant innovation US a)Entrantinnovationintensityinmodel rotces yb etar yrtne tnetaP 6. 5. 4. 3. −15 −10 −5 0 5 10 15 Gaps b)PatentingintensityofU.S.entrantsindata Figure11: Entrantinnovationeffortandleadership Notes: Panel A shows the innovation intensity of U.S. entrant firms in the balance growth path of calibrated economy. Panel B showstheaverageentryrateofpatentsappliedforbytheU.S.firmsthatappearinasectorintheUSPTOdataforthefirsttime acrosstechnologygaps(forthecreationofthetechnologygaps,seeFigure7). Numberofpatentsbynewpatenteesisweightedby thenumberofallpatentsregisteredbyU.S.residents. Thefittedlineshowspredictedvaluesfromaweightedlinearregressionof averageentryrateonbinsweightedbythenumberofsector-yearobservationsineachbin. Because entry to the highest gaps implies access to export markets, it is more profitable, leading to a higher entry effort aimed at these positions. Figure 11b shows that this is indeed the case in the USPTO patent data, where we again classified sectors into bins according to the technological lead, as in Figure 9b. The solid black line in the figure depicts the flow of new patents (normalized by the number all U.S. patents in that sector-year observation to eliminate sectoral differences in patenting intensity) registered by U.S. residents that appear for the first 37

nnovation and rade olicy in a lobalized orld I T P G W timeinasector,averagedoutacrosssector-yearobservationsbetween1975and1995ineachbin.46 The dashed line shows the density-weighted regression line for 33 technology gaps. We observe that the entry intensity is higher for sectors where existing U.S. firms have larger technological leads over their foreign competitors. Validation Exercise IV: Credit Elasticity of R&D The ultimate source of growth in our model is innovation. Therefore, when analyzing the effect of policies on aggregate outcomes, a correct measurement of the responsiveness of innovative activity to policy changes is of utmost importance. In order to evaluate our estimated model’s implications in that regard, we now investigate the empirical elasticity of innovative activity to R&D credits and compare it with its model counterpart. In order to measure the credit-elasticity of innovation, we exploit the state-level variation in the dates when credit policies came into action and conduct a simple firm level regression analysis using the Compustat database. The regression specification is as follows: lnY = β +β lnSC +β lnY +ψ +ψ +u , (21) jst 0 1 st 2 jst 1 j t t − where ψ and ψ represent firm and year dummies, respectively, and u is the error term. SC is j t t st the tax credit level in state s where firm j operates. For the dependent variable Y we use both R&D and patent counts. We utilize two different specifications for this regression that differ in the inclusion of the lagged value of the dependent variable. The results are summarized in Table 4. All versions (represented by columns of the table) reveal the positive effect of state level R&D tax credits on the firms’ innovative activities. This effect is also robust to the existence of lagged values of the dependent variable in the regression. The first column of Table 4 shows that, on average, the elasticity of R&D spending with respect to changes in R&D credit is 3.15. To ensure the quantitative validity of firms’ response to policy changes in our model, we derive the model counterpart of the same statistic. We first compute the log-difference in R&D expenditure for incumbent firms of country A in each position m right before and after the subsidy change from sA to sA . Following the same 75 81 81 95 − − steps used to create empirical variables, the average elasticity of R&D spending to subsidy is given by (cid:16) (cid:17) (cid:90) 1 dlog α A (cid:0) x γ A c j1981 q j1 (cid:1) 981 dj = ∑ (cid:0) dlog (cid:0) α A x (cid:1) γ A c m1981 Q (cid:0) Am1981 (cid:1) (cid:1). 0 dlog 1+s 1 A 981 m log 1+s 8 A 1 95 − log 1+s 7 A 5 81 − − This model statistic has a value of 2.27 in contrast to 3.15 in the data. It implies that in the model, an increase in R&D subsidy induces a solid response of R&D expenditure, in line with 46ObservationsofthesamesectoroverdifferentyearsaretreatedasseparateentriesinFigure11b. 38

nnovation and rade olicy in a lobalized orld I T P G W its empirical counterpart, although its strength is somewhat weaker than in the data. Note that the empirical economy-wide elasticity is likely to be lower than state-level elasticity due to reallocation of resources across states; therefore, it is also reassuring to see that our simulated macro elasticity is below the state-level empirical estimate. Table4: TheeffectofR&Dtaxcreditoninnovation(excl. federalcredits) ln(R&D ) ln(R&D ) ln(Patents ) ln(Patents ) t t t t Dep. Var.: (1) (2) (3) (4) 3.153 0.524 2.948 1.203 ln(State credit ) t (10.92) (2.12) (10.93) (4.28) ∗∗∗ ∗∗ ∗∗∗ ∗∗∗ - 0.631 - ln(R&D ) t − 1 - (106.67) ∗∗∗ - - - - - 0.499 ln(Patent ) t 1 − - - - (72.83) ∗∗∗ YearDummy Yes Yes Yes Yes FirmDummy Yes Yes Yes Yes Notes: ThetableliststheresultsobtainedfromdifferentOLSspecificationsthatillustratetheeffectof(U.S.state-level)taxcredits onU.S.firms’innovation. t-statisticsareprovidedinparentheses. ∗∗∗, ∗∗,and∗ denotesignificanceat1percent,5percent,and10 percent,respectively. 5 Policy Evaluation In this section, we first demonstrate the foreign catch-up process that the United States would experience in absence of policies. Then we perform a quantitative investigation of various policy alternatives and assess their welfare implications. We discuss the design of optimal policies considering different horizons for policy and accounting for the transition period. We start the discussion with protectionist measures. Then, we continue with R&D policies, analyzing both the observed post-1981 R&D subsidy changes and the optimal subsidy levels. We also consider thedesignofoptimaljointpolicyandconcludewithadiscussionofhowretaliationfordomestic trade policies by trade partners can alter the structure of optimal policies. 5.1 Technological Convergence and Foreign Catching-Up Foreign technological catch-up is a key implication of the model. Improvements in a country’s trade partners’ technology is a mode of globalization that has received less attention in the literature than the reduction of trade and offshoring barriers. To explore this relationship in our model, we focus on how foreign technological catch-up manifests itself in the technological advantage of the leading country, which again represents the United States. In particular, Figure 39

nnovation and rade olicy in a lobalized orld I T P G W 12 shows the evolution of the average technological lead that U.S. firms would have over their foreign competitors in the absence of any policy intervention. 6 5 4 3 2 1 1975 1980 1985 1990 1995 2000 2005 Years smrif .S.U fo pag ygolonhcet naeM Figure12: AveragetechnologyleadoftheU.S.firms,nopolicyintervention Notes:ThefigureexhibitstheevolutionoftheaveragetechnologyleadthattheU.S.firmshaveovertheirforeigncompetitorsacross yearsalongthetransitionofthecalibratedeconomy. The dramatic decline is the symptom of a strong international business-stealing effect, whereby foreign firms progressively capture leadership in more and more markets, and profits that were previously collected by the U.S. firms are now going into the pockets of foreign firms. This negative income effect of the international business-stealing effect suggests that the foreign technologicalconvergence indeed hurt theU.S. economy. Now weturn to theanalysis of industrial policies that could potentially help the economy tackle foreign technological catch-up. 5.2 A Unilateral Increase in Import Tariffs In this subsection, we explore the implications of a unilateral increase in tariffs and discuss optimal tariff policy. Figure 13a shows the consumption-equivalent welfare gains/losses for the representative household generated by a 50 percent rise in tariffs τUS in 1981 (equivalent to a 4-percentage-point change). Compared to the path in a counterfactual economy that does not experience any policy intervention, protectionism seems to pay off in the short run, where small gainsaregeneratedfromtheincreaseinhomeprofits. However, overtime, thegainsdeclineand turn negative after two decades. Digging deeper, unilaterally higher trade barriers initially generate a small increase in profit income by protecting some sectors from import penetration and shifting market ownership toward home firms. Recall, though, that the measure of relatively most laggard firms that can benefit from trade protection is relatively small for the United States, as indicated by the left tail of the dashed line in Figure 8a. Therefore, the initial gain from laggard firms recapturing 40

nnovation and rade olicy in a lobalized orld I T P G W 0.25 0.2 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 5 10 15 20 25 30 35 40 45 50 Time Periods egatnecreP 1.2 with protection 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 -15 -10 -5 0 5 10 15 Gaps (m) a)Consumptionequivalentwelfare troffe noitavonnI Incumbent innovation US Protectionism b)Innovationresponsetoprotectionism Figure13: Welfareeffectsofprotectionism: unilateral50percent(4ppts)increaseintariffs Notes: Thefigureillustratestheeffectsofaunilateral50percentincreaseinU.S.tariffs(protectionistU.S.policywithoutretaliatory response).PanelAshowsthewelfarechangeinconsumptionequivalenttermsoverdifferenttimehorizons.PanelBshowstheshift intheinnovation-effortprofileofU.S.incumbentfirmsovertechnologygaps. production in the domestic market is limited. Moreover, the replacement of foreign exporters by the laggard home firms means that the high-quality foreign products are foregone and replaced by inferior domestic alternatives. This foregone intermediate-good quality leads to substantial welfare losses. Even though the combined welfare effect is slightly positive over the short run, it turns significantly negative over time. As time passes, the factor that governs variations in welfare is the decline in competitive pressuresondomesticfirms, whichleadstoadropintheirinnovativeactivity. Figure13b shows that innovation efforts by most of the laggard U.S. firms decrease substantially. Because the protectionist policy shifts the threshold for losing the domestic market to a foreign competitor furthertotheleft,morefirmsmovefurtherfromsuchanimmediatethreat. Thisweakerdefensive innovation motive leads to a compression of innovation efforts by these firms, making it harder to compensate for the loss of imported frontier technology. Moreover, most U.S. firms, being either exporters or solid domestic producers that are technologically close to or ahead of their competitors, do not benefit from higher domestic tariffs. As shown in Figure 13b, innovation decisions of this large group of firms barely change, implying that they do not contribute any additional boost to profit income or factor productivity in response to the policy move.47 All in all, the short-run gains from profits are subdued over time by the loss of foreign technology, while weaker defensive innovation incentive leads to less domestic innovation and, thus, to a slower growth of productivity and profit income. 47Evidently, the time path of the average technology lead of the U.S. firms is lower than the one in the “nointervention”casedepictedinFigure12(seeFigureA.5ainAppendixD.2). 41

nnovation and rade olicy in a lobalized orld I T P G W 5.3 Optimal Unilateral Tariffs The negative relationship between the aggregate innovation effort and protection plays also an important role for the design of optimal tariff policy. As shown in Figure 14a, the optimal tariff policy, where the United States unilaterally sets the tariffs on goods imported to the United States,effectivelyclosestheborderstoimports,whentherelevanthorizonoverwhichthepolicymaker calculates the welfare is very short, such as a decade. However, the optimal level of tariffs decreases as the relevant horizon becomes longer and suggests a more liberal tariff regime with respecttothecalibratedeconomywhenthehorizonconsideredextendsbeyondtwodecades. As Figure 14b demonstrates, the reason is the damping effect of higher tariff rates on domestic aggregateinnovation. Thisdynamicnegativeeffectdominatesstaticgainsovertimeand,therefore, implies lower tariffs for optimal policy when longer time horizons are considered. 18 16 14 12 10 8 6 4 2 0 10 20 30 40 50 Horizon in years % ni etar ffirat lamitpO 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Tariff rate a)Optimaltariffpolicyovertimehorizons ytisnetni noitavonni egarevA 0.33 Aggregate innovation 0.325 0.32 0.315 0.31 0.305 0.3 0.295 b)Averageinnovationoveropenness Figure14: Optimaltariffpolicyandinnovationoveropenness Notes: PanelAshowstheoptimalunilateraltariffpolicyfortheUnitedStatesovervariouspolicyhorizons. Horizontaldashedline denotes the calibrated tariff level. Panel B shows the negative effect of unilaterally higher U.S. tariff rates on average innovation intensityofbothentrantandincumbentU.S.firms. 5.4 Introduction of R&D Subsidies Policy intervention in the early 1980s to improve the competitiveness of U.S. companies pushed up the level of R&D subsidies significantly from an average of 5.1 percent in the pre-1981 period to an average of 19.2 percent in the subsequent period. The subsidy level in the foreign country remained fairly constant, with 3.8 percent and 4.1 percent in the respective periods. Figure 15 shows the effect of the subsidy to incumbents’ R&D spending on the post-1981 distribution of technology gaps. 42

nnovation and rade olicy in a lobalized orld I T P G W 0.09 0.07 Data = Model US, 1975 Model US, no change, 1995 0.08 Model US, 1981 Model US, subsidy, 1995 Model US, no change, 1995 0.06 Model US, optimal sub., 1995 0.07 0.05 0.06 0.05 0.04 0.04 0.03 0.03 0.02 0.02 0.01 0.01 0 0 -20 -15 -10 -5 0 5 10 15 20 -20 -15 -10 -5 0 5 10 15 20 Gaps (m) Gaps (m) Figure15: Gapdistributionafterpolicychanges Notes:PanelAexhibitsthetechnologygapdistributionsinthecalibratedmodelatthreepointsintime:initiallyin1975(dottedsolid line,thesameasinthedata),in1981(solidblueline),andin1995(dashedredline)assumingtherewasnopolicychange. Positive valuesonthehorizontalaxisdenoteU.S.technologicalleadership. PanelBexhibitstheresultinggapdistributionsin1995under threedifferentscenarios:undernopolicychange(dashedredline,thesameasinPanelA),undertheactualR&Dpoliciesafter1981 (solidblueline),andunderthemodel-impliedoptimalR&Dpolicyrateforthehorizonbetween1981and1995(dottedsolidline). In the left panel, the model gap distribution in 1981 is the solid blue line, which is closely calibrated to data in 1981 (not shown). In the benchmark economy with no policy intervention, thetransitionafter1981resultsinalargeleftwardshift,leadingtothereddashedlinedistribution by1995onbothpanels. Bycontrast,inthealternativeeconomy,wheresubsidieswereintroduced in1981,theresultingdistributionin1995becomesthesolidbluelineintherightpanel. Theeffect of higher subsidies is a small shift to the right relative to the no-intervention benchmark case represented by dashed lines. This positive shift would have been drastic had the optimal level of R&D subsidy been introduced in 1981 (circled solid line). We will discuss optimal subsidies in the next subsection. Table5: ObservedR&DSubsidy: 1981-1995 Welfare gains Subsidy rate 1981-2016 Observed R&D Subsidy 19.2% 0.87% Now we examine the welfare properties of the R&D subsidy intervention. We compute the welfare difference for a 35-year horizon from 1981 until the present (2016). The result is reported inTable5. WefindthattheU.S.subsidyincreasegeneratesa0.9percentconsumptiongainevery yearoveraspanof35years. Decomposingtheoverallwelfarechangeintovariationsinindividual sources of income (not shown), we find that these gains are driven by an increase in innovation by U.S. firms, which in turn leads to faster growth in both U.S. factor productivity and profit 43

nnovation and rade olicy in a lobalized orld I T P G W income. As illustrated in Figure 16a, the underlying economic mechanism is straightforward: By reducing the cost of R&D, subsidies stimulate innovation in U.S. incumbent firms, thereby accelerating productivity growth and allowing U.S. firms to obtain market leadership, and the related profits, in a large share of sectors in the economy. The gains from these channels more than offset the resources devoted to the higher aggregate R&D spending.48 1.2 1 0.8 0.6 0.4 0.2 -15 -10 -5 0 5 10 15 Gaps (m) troffe noitavonnI 1.2 Incumbent innovation US R&D subsidy 1 0.8 0.6 0.4 0.2 0 5 10 15 20 25 30 35 40 45 50 Time Periods a)Changeininnovationbyincumbents egatnecreP with R&D subsidy b)Consumptionequivalentwelfare Figure16: Consumptionequivalentwelfare Notes: ThefigureillustratestheeffectsofaunilateralR&D-subsidyincreaseintheUnitedStates(replicatingactualpolicychanges). PanelAshowstheshiftintheinnovation-effortprofileofU.S.incumbentfirmsovertechnologygaps. PanelBshowsthewelfare changeinconsumptionequivalenttermsoverdifferenttimehorizons. In Figure 16b, we show the evolution of welfare gains over time generated by the increase in U.S. subsidies. The figure shows that in the short run of less than about 7 years, the subsidy change leads to a welfare loss, which rapidly turns to gains as years go by. This early loss is due to a subsidy-induced shift of resources from consumption to innovation. Over time, the profitshiftingand,evenmoreimportantly,theincreaseinlaborproductivitygeneratedbyhigher domestic innovation offset the losses, leading to sizable gains. 5.5 Optimal R&D Subsidies Next we compute the optimal R&D subsidies for the home country and compare them with the U.S. subsidy observed in the data in the post-1981 period (reported in Table 5). Precisely, we compute the subsidy rate that maximizes the present discounted value of welfare in a 35-year horizon from 1981 to 2016 and calculate the welfare gains from the optimal subsidy with respect to the benchmark scenario, where the U.S. subsidy does not change in 1981. We also compare 48FigureA.5bdemonstratesthepositiveeffectofhighersubsidiesonthetimepathofaveragetechnologyleadof theU.S.firms,resultinginasignificantlyhigherpaththantheoneinthe“no-intervention”caseinFigure12. 44

nnovation and rade olicy in a lobalized orld I T P G W these welfare gains under optimal subsidy with those obtained under the observed post-1981 subsidy. Table 6 reports the results for the optimal policy. Table6: OptimalU.S.R&DSubsidy: 1981-2016 Welfare gains Subsidy rate 1981-2016 Optimal R&D Subsidy 66% 5.49% The comparison of Table 5 to Table 6 indicates that although U.S. policymakers went in the right direction by increasing the subsidy rate in response to accelerating foreign catching-up in the1980s,theydidnotgofarenough. Accordingtoourmodel,thesubsidyrateshouldhavebeen about 66 percent, more than three times higher than the observed one. This high subsidy would have increased welfare by a striking 5.5 percent every year in the 35-year period considered. In fact, the observed post-1981 subsidy is only optimal for a time horizon of about 8 years. In our model, the optimal subsidy is determined by a rich set of externalities typical of Schumpeterian growth models, albeit with some novel twists.49 First, future innovations build on the stock of current innovations, but current innovators do not take into account that their activity will benefit future innovators. This effect, known as the intertemporalspillovereffect, leads tounderinvestmentinR&DandprovidesareasontosubsidizeR&D.Second,entrantinnovation destroys domestic incumbents’ business, exerting a negative externality on domestic incumbent innovation. This effect, known as the business-stealing effect, leads to overinvestment in R&D and rationalizes a tax on R&D. In addition, the international aspect of our model generates a third externality that misses in standard closed-economy models of Schumpeterian creative destruction. Throughcatchinguporleapfrogging,alaggarddomesticfirmcanstealtheforeignleader’s business (or part of it). This effect, which we label as the international business-stealing effect, can encourage or discourage innovation, depending on the technology gap between the competing firms. Finally,ourmodelalsofeaturesinternationaltechnologyspillovers,whichisanothersourceof inefficiencyinR&D.Hence,theopen-economydimensionofourmodelintroducesadditionalinteresting channels on top of the classic strategic trade and industrial policy literature [e.g., Eaton and Grossman (1986)]. By increasing innovation, R&D subsidies help domestic firms compete in the global market, thereby shifting profits from foreign firms to national ones and increasing national income. Figure 17a shows optimal subsidy levels for several horizons. Evidently, optimal subsidy level increases with the length of the policy horizon, because a longer horizon allows larger gains from policy-induced growth to materialize. Intuitively, optimal R&D subsidies are trading 49Closed-form expressions defining these externalities in standard versions of the quality-ladder model can be foundinGrossmanandHelpman(1991c)andSegerstrom(1998). 45

nnovation and rade olicy in a lobalized orld I T P G W 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 10 20 30 40 50 Horizon in years etar ydisbus lamitpO 0.78 0.76 0.74 0.72 0.7 0.68 0.66 0.64 0.62 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Change in openness (trade cost) a)Overdifferenthorizons etar ydisbus lamitpO More Global Less Global b)Overopenness(overthefixedhorizonof35years) Figure17: OptimalU.S.R&Dsubsidy,overdifferenthorizonsandlevelsofopenness Notes: PanelAexhibitstheprofileoftheoptimalR&DpolicyfortheUnitedStatesovervariouspolicyhorizons. PanelBexhibits optimal R&D policy rate for the United States over a fixed horizon of 35 years subject to varying degrees of globalization. Zero meansthecalibratedleveloftariffsforbothcountries,andnegativenumbersmeanamoreglobalworld. off the current reduction in consumption with future gains in growth rates. The longer the horizon, the larger the realized gain from the increased growth rate of aggregate consumption. AnotherinterestingresultisshowninFigure17b,whereweplotthelevelofoptimalsubsidy for afixed 35-year horizonin economies with varyingdegrees of openness. Itis evident that in a more open world with smaller trade costs, the level of optimal R&D subsidy is lower, implying thatalessaggressivepolicyisappropriate. Thisresultisagaindrivenbytheinnovation-boosting effect of foreign competition, which intensifies defensive and expansionary R&D motives. 5.6 Joint Policy Analysis: Optimal Innovation and Trade Policy Having analyzed the implications of individual policy options, we now focus on the optimal joint policy in which the United States could use both R&D subsidy and one-sided tariff policy in tandem. Figure 18 plots the optimal R&D subsidy under this scenario over different horizons with a solid blue line, and the optimal tariff rate with a dashed blue line. The figure reveals thattheoptimalsubsidylevelsareclosetotheonesfoundwhenR&Dsubsidieswereconsidered in isolation (Figure 17a), being only slightly higher in some horizons.50 However, we find that 50Although the close levels of R&D subsidies in single and joint policy exercises may appear to be indicative of a weak interaction between trade and R&D policies, Figure A.7 in Appendix D.2 demonstrates that this is not the case. The figure shows optimal R&D subsidy levels over policy horizons for three different values of unilateral importtariffs. ThefigurerevealsthattheoptimalR&D-policyprofilebecomeslowerwhenthetarifflevelisreduced unilaterally. ThereasonisthatlargereductionsintariffschangetheincentivesofasignificantshareofU.S.firms. In fact,increasedcompetitioninducesabiggershareofU.S.firmstoincreasetheirinnovationeffort,reducingtheneed 46

nnovation and rade olicy in a lobalized orld I T P G W the policymaker optimally chooses a strongly protectionist measure over any horizon with a constant 16 percent tariff rate, effectively closing the borders to any import penetration. This is in stark contrast with Figure 14a, which shows that optimal tariffs decline with longer horizons, when considered in isolation. The reason is that, being allowed to set subsidy levels freely, the home country, while protecting profits of its firms, can incentivize them to innovate at higher rates, compensating for the loss of innovative efforts as a result of lower competitive pressure that protectionism causes. Therefore, allowing the economy to adjust both margins freely, the joint policy alternative leads to a highly protectionist regime. However, it is crucial to note that when considering optimal policies, we assumed away any reaction from the foreign country and focused only on one-sided tariff policies. Next, we delve into the implications of such foreign response. 0.7 0.65 0.6 0.55 0.5 0.45 0.4 10 15 20 25 30 35 40 45 50 Horizon in years )dilos( ydisbus D&R lamitpO 0.2 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.1 )dehsad( etar ffirat lamitpO Figure18: Optimaljointpolicywithunilateraltariffchanges Notes:Thefigurecompareshorizon-dependentoptimaljointpolicyundertheassumptionofnoforeignretaliation. 5.7 Effect of Foreign Retaliation and Optimal Joint Policy Revisited Until now, we analyzed the trade policy in a unilateral fashion: The home country could set its tariff rates freely, without facing a response from the foreign country. Although this analysis serves as a helpful benchmark, such unilateral moves would be unlikely in reality. The natural question is, what would be the effect of foreign retaliation on the design of trade policy?51 To answer this question, we analyze our policy alternatives under the assumption that any change foraggressiveR&Dsubsidies. 51The introduction of the Smoot-Hawley Tariff Act in the United States during the early stages of the Great Depressionprovidesanexampleofhowtheunilateralintroductionoftradepoliciescouldtriggerretaliatoryresponses fromtradepartners,potentiallyharmingthedomesticeconomy. 47

nnovation and rade olicy in a lobalized orld I T P G W in tariffs imposed by the home country is perfectly matched by the foreign one. Figure 19 shows the optimal joint policy in this modified setting with bilateral tariff changes (circled black lines), in juxtaposition with the results obtained in the benchmark setting (blue lines). 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 10 15 20 25 30 35 40 45 50 Horizon in years )dilos( ydisbus D&R lamitpO 0.3 0.25 0.2 0.15 0.1 0.05 0 )dehsad( etar ffirat lamitpO Unilateral Bilateral Figure19: Optimaljointpolicyinunilateralandbilateraltariffchanges Notes:Thefigurecompareshorizon-dependentoptimaljointpolicyincaseof(trade-policy)retaliationtothatinthebaseline. While there are no significant qualitative differences in the optimal R&D subsidy levels, thereisacompletereversalinthetradepolicy. Now,theoptimalpolicyliberalizestheeconomy’s traderegimeasmuchaspossible,removingtariffsirrespectiveofthelengthofthepolicyhorizon underconsideration. Thisresultarisesbecauseinthissetting,protectionistpolicieslimitnotonly themarketforimportstothehomecountry,butalsoexportsfromthehomecountry,becausethe tariffchangesarereplicatedbytheforeigntradepartner. Theeffectsofretaliatorytariffincreases on the U.S. incumbents are demonstrated in Figure 20a. As opposed to Figure 13b, the cutoff for exports increases, making them accessible to only a small group of firms. Moreover, a reduction ininnovativeactivity—drivenbysimilarreasonsexplainedintheanalysisofunilateralpolicies— occursnowforawiderrangeoffirms. Consequently,asillustratedinFigure20b,retaliatorytariff measures lead to a substantial welfare loss in the United States, which is rising over time (about 2.4% over a 50-year horizon). Conversely, liberal policies expand the export market of the home country and stimulate innovation for a large set of firms via a more intense expansionary R&D motive. Given that most U.S. incumbents are in technologically leading positions, the optimal trade policy under the assumption of retaliation favors these firms by opening up their markets toexport, attheexpenseofafewmorelaggardfirmslosingtheirmarketstoforeignimporters.52 52Asimilarreversalhappenswhentradepolicyisanalyzedinisolationsubjecttothethreatofforeignretaliation, withfullliberalizationbeingpreferredevenwhentheshortesthorizonsareconcerned. 48

nnovation and rade olicy in a lobalized orld I T P G W 1.2 1 0.8 0.6 0.4 0.2 -15 -10 -5 0 5 10 15 Technological gap btw. domestic and foreign firms troffe noitavonnI Incumbent innovation US Protectionism -1 -1.2 -1.4 -1.6 -1.8 -2 -2.2 5 10 15 20 25 30 35 40 45 50 Time Periods a)Innovationresponsetoprotectionism egatnecreP Protection b)Consumptionequivalentwelfare Figure20: Innovationandwelfareincaseofretaliation,4percentagepointbilateralincreaseintariffs Notes: Thefigureillustratestheeffectsofabilateral4-percentage-pointtariffsincrease. PanelAshowstheshiftintheinnovationeffortprofileofU.S.incumbentfirmsovertechnologygaps.PanelBshowsthewelfarechangeinconsumptionequivalenttermsover differenttimehorizons. 6 Foreign Competition and Domestic Innovation A recent strand of papers in the empirical trade and firm dynamics literature has drawn notable attentionthankstotheirimportant,andseeminglycontradictory,contributionstoaheatedtopic: the effect of foreign competition on domestic firms and industries and, in particular, their innovative activity. Bloom et al. (2016) argue that Chinese import competition induced innovative activity in exposed domestic sectors in Europe [see also Coelli et al. (2016), Gorodnichenko et al. (2010), and Iacovone (2012)], whereas Autor et al. (2016) argue the opposite, using data on U.S. firms and sectors [see also Hashmi (2013) and Hombert and Matray (2015)], and yet a third set of papers including Aghion et al. (2017) find ambiguous results. Inthissection,weshowthatourframeworkcanhelpreconciletheseseeminglycontradictory observations in the literature. In particular, we present an exercise on rising import competition andillustratethatitseffectonaggregateinnovationcruciallydependsonthesectoralcomposition of domestic firms in terms of their technological competence relative to the foreign competitors. As a result, import competition has a non-monotonic impact on aggregate innovation, given the innovation profile in Figure 9a. Our exercise considers six different economies: Three of them in a relatively laggard initial condition—i.e., in most sectors, their firms are distant followers—and three relatively frontier ones. To generate intensifying import competition in our model, we consider the removal of tar- 49

nnovation and rade olicy in a lobalized orld I T P G W iffs. Asisevidentfromtheearlierdiscussionofunilateralprotectionistpolicies,thischangeshifts the defensive-R&D cutoff inwards, creating heterogeneous effects on firm innovation: Firms that fall further behind the defensive-R&D cutoff decrease their innovation effort, while firms that become closer to the cutoff intensify theirs. The overall effect at the aggregate level depends on the distribution of sectors across relative technological positions in foreign competition. Figure 21aillustratesthispoint,displayingthreeeconomiesthataredistinguishedbytheirtechnological gap distribution across domestic firms’ positions. The values in the figure show the percentage changeintheindustry-levelinnovationrateinresponsetolowertariffs. Intheeconomywiththe largest mass of the relatively most laggard sectors, the effect is negative, while it becomes positive as the technological gap distribution shifts to the right. The reason is that the economy with the least negatively skewed distribution includes relatively more firms that happen to be around the new defensive-R&D cutoff, feeling the more intense threat of losing markets and therefore exerting more innovative effort. However, it is not correct to draw the conclusion that relatively more advanced economies benefit from intensifying foreign competition, as we discuss next. Figure 21b compares three economies where most firms are leaders in global technological competition. We observe that while the economy denoted by the solid blue line experiences a small rise in overall innovative activity in response to stiffer foreign competition, the relatively less advanced economy (red dashed line) experiences a considerably larger increase. The result hinges again on the share of firms in each economy that increase their innovative activity the most with intensifying competition. Finally, the economy denoted by black dots experiences a decline in overall innovation, proving that even an advanced economy—like the countries of interest in most studies referenced above—may suffer from more intense foreign competition. 0.25 0.25 -2.81% 0.2 0.2 0.48% 0.15 0.15 0.1 0.1 -0.19% 4.07% 0.05 0.05 6.07% -0.79% 0 0 -20 -15 -10 -5 0 5 10 15 20 -20 -15 -10 -5 0 5 10 15 20 Technological gaps btw. domestic and foreign firms Technological gaps btw. domestic and foreign firms a)Threerelativelylaggardsectors b)Threerelativelyadvancedsectors Figure21: Effectoftradeliberalizationonaggregateinnovation Notes: Thefigurecontraststhechangeinaggregateinnovationcausedbytradeliberalizationinvarioussectorsdefinedbydifferent initialtechnologicalgapdistributions.Specifiedvaluesshowpercentagechangeinaggregateinnovationineachsector. 50

nnovation and rade olicy in a lobalized orld I T P G W Althoughminusculeinabsoluteterms,therelativelylargermassofrelativelymostlaggardfirms drives this implication, because these firms, now with their chances of capturing a market being diminished, decrease their innovation efforts in response to the more foreign competition. In sum, our analysis indicates that the impact of trade liberalization might have a positive or negative impact on the liberalizing economy’s aggregate innovation level depending on the initialrelativetechnologygapbetweenthecompetingcountries. Moreover,evenarelativelyvery advanced economy might experience a reduction in aggregate innovation, if it has an enough number of sectors that are getting discouraged by foreign competition. 7 Sensitivity and Robustness In this section, we provide various robustness checks for our main results. 7.1 Lower Maximum Technology Gap m¯ Our first exercise considers the robustness of the baseline results to the value of the maximum technology gap that can separate two incumbent firms. In our baseline, this value is set to m¯ = 16. Asarobustnesscheck,wecalculatetheempiricalgapdistributionbysettingm¯ = 10and recalibrate our model accordingly. When a unilateral increase in U.S. tariffs is considered, we observeasimilarshiftinincumbentinnovationasinFigure13b. PanelAofTable7comparesthe resulting consumption-equivalent changes to the baseline experiment for various horizons. The results resonate with the baseline values, except with a slightly larger welfare cost over the long run. Furthermore, profiles of optimal unilateral R&D and tariff policies over different horizons, summarized in Panel B and Panel C, respectively, are very similar to those found in the baseline calibration. Hence, we conclude that our original findings are robust to the values of m¯. 7.2 Dropping the U.K. As illustrated in Figure 1, the U.K. has a similar productivity and innovation performance to the United States in the late 1970s, in stark contrast with the other advanced competitors of the United States. Conjecturing that idiosyncratic factors may have negatively separated the performanceoftheU.K.fromitspeers,werecalibrateourmodelusingdatathatexcludetheU.K. Forthisexercise,were-weightourtargetsusingdataontheremainingfiveforeigncountriesand re-compute the empirical gap distribution. Figure A.8a in Appendix D.2 shows that the shift in the initial distribution caused by dropping the U.K. is minuscule, which is also the case with the othertargets. Consequently,theparametervaluesobtainedbythisalternativecalibration,aswell as the quantitative results, barely differ from the baseline; hence, we do not repeat them here. 51

nnovation and rade olicy in a lobalized orld I T P G W Table7: Policyexperiment (m¯ =10) resultsandcomparisontothebaselineresults PanelA Welfarefor50%tariffincrease Horizoninyears 10 20 30 40 50 Baseline 0.17% 0.04% 0.07% 0.16% 0.24% − − − m¯ =10 0.20% 0.04% 0.11% 0.26% 0.39% − − − PanelB Optimalsubsidylevels Horizoninyears 10 20 30 40 50 Baseline 34% 54% 64% 68% 70% m¯ =10 34% 56% 68% 70% 72% PanelC Optimalunilateraltarifflevels Horizoninyears 10 20 30 40 50 Baseline 18% 12% 0% 0% 0% m¯ =10 16% 12% 0% 0% 0% 7.3 Quality-adjusted Patents In this exercise, we test the robustness of our analysis to the use of citation-weighted patent counts when forming moments from the data, as well as the empirical technology gap distribution. Using citation-weightedpatents implies about a4-percent higher share for Japan among all countries in 1975 at the expense of Germany, the share of which declines by the same amount. As illustrated in Figure A.8b in Appendix D.2, this reshuffling leads to only minimal changes in the empirical technology gap distribution, which also holds true for other moments. As a result, thecalibrationoutputisverysimilartobaseline,asonewouldexpect,whenusingthealternative measure. Therefore, we skip the rest of the results generated by this alternative calibration. 7.4 Gap Distribution Based on Cumulative Patent Count Inourbaselinecalibration,wematchtheshiftintheempiricalgapdistributionfrom1975to1981, where we generate the distributions using patent counts in individual years.53 In this exercise, we test the robustness of our results to computing the empirical gap distributions based on the cumulativepatentcountsstartingfrom1965. Doingso,wemeasuretheevolutionoftechnological leadershipbasedonthecumulativepatentstock. Inparticular,whenwecomputetheU.S.patent share in a sector in a certain year, as in Figure 7, we use the patents registered in that sector between 1965 and the particular year of interest. For example, to generate the empirical gap distribution in 1975, we rank sectors using information from patents registered between 1965 and 1975 instead of 1975 alone. As can be expected, the shift in the empirical gap distribution is 53One reason for starting in 1975 is that in the raw USPTO data, the number of patents that are assigned to a technologyclassismuchsmallerbeforethemid-1970scomparedtosubsequentyears. 52

nnovation and rade olicy in a lobalized orld I T P G W less pronounced in this method, because the country shares of patent stocks vary more slowly. Therefore, in Figure A.9a in Appendix D.2, the distribution in 1981 is to the right of the baseline one. However, this limited change does not lead to substantial differences in our calibration. Indeed, as shown in Table 8, the optimal unilateral tariff policy looks quite similar to the one in the baseline economy. Hence, we conclude that our results are immune to the alternative empirical computation method of distributional targets.54 Table8: Cumulativepatentsandtheoptimalunilateraltariffs Horizoninyears 10 20 30 40 50 Baseline 18% 12% 0% 0% 0% Cumulativepatents 28% 20% 2% 0% 0% 7.5 Tariff Revenue as a Lump-sum Transfer In the baseline exercises, tariffs operate similar to iceberg costs without generating any revenue forthegovernment. Inthisexercise,weexploretheimplicationsofatariffpolicy,whoserevenue is shared by the households via lump-sum subsidies. Then, net government spending becomes G ct = sc∑m s ¯ = − m¯ α c x c γ s c t Q cst − τc∑− m= m∗c − (cid:48) m¯ (cid:104) (1+ 1 κ − + β τc)η (cid:105)1 −β β Q 1 − c(cid:48)m β t in a modified version of equation (20), accounting for tariff revenue. The profile of the optimal unilateral tariff policy, summarized in Table 9, mirrors what we found in our baseline setting in that liberalization is optimal for a far-sighted policymaker. However, complete removal of tariffs becomes optimal at a longer horizon than in the baseline. This result should be expected because in this case, tariff reduction comes at a cost to households, decreasing the amount of lump-sum subsidies generated by the tariff revenue. Nevertheless, the main message that protectionist policies are only optimal for policymakers that have relatively shorter horizons remains intact in this alternative setting. Table9: Optimalunilateraltariffsandcomparisontothebaselineresults Horizoninyears 10 20 30 40 50 Baseline 18% 12% 0% 0% 0% Tariffwithrevenue 14% 10% 4% 0% 0% 54AsshowninFigureA.9binAppendixD.2, thecalibrationtothealternativedistributionsalsoperformswellin matchingthelimitedshift,resultinginamodel-generatedgapdistributionin1981thatliestotherightoftheonein thebaselinecalibration. Thiscomparisonrevealsthatthesimilarityofpolicyimplicationsinbothcalibrationsisnot drivenbyaspuriouslystrongerforceofforeignconvergenceemerginginthealternativecalibrationthanimpliedby therelativelylimitedshiftintheempiricaldistributions. 53

nnovation and rade olicy in a lobalized orld I T P G W 7.6 Lower Discount Rate ρ In the baseline calibration, we fixed the discount rate of the households to 1 percent. In order to test the sensitivity of our results to this parameter, we also ran an alternative calibration, setting the discount rate to 0.5 percent. Our calibration outcome barely changes in this exercise suggesting thatour analysis is robustto varying degrees ofthe discount rate. Becausethe effects are negligible, we do not present the results here. 7.7 Modeling Labor in the Intermediate Goods Sector Acentralconcerninthedebateongainsfromtradeisthepotentialharmthatimportpenetration can cause to domestic workers by stealing the market of the domestic firms [Autor et al. (2013)]. In our baseline model, the fixed factor, which is used in the final-good sector, benefits from trade liberalization thanks to the higher labor productivity, which is brought about by betterquality imports replacing inferior domestic counterparts. As a robustness exercise, we modify the baseline model introducing labor in order to allow trade to have an adverse impact on labor. Inthisversion,laborisutilizedintheproductionofintermediategoods;therefore,foreigncatchup leads to a wage loss as a byproduct of business stealing. We re-estimate this new version and compare its key policy implications with the ones of the baseline model. For the sake of brevity, we present the details and the results in Appendix E. Our key baseline results go through in this version as well, except that unilateral tariff policies appear to increase economic welfare for longer horizons. However, the threat of retaliation works just as in our baseline framework, inducing the policymaker to optimally choose to remove tariffs across all horizons. 8 Conclusion Inthispaper,weshedlightonarecurringdebateaboutthecompetitivenessofU.S.firmsrelative to their foreign competitors, and how to improve their position. Motivated by a set of novel facts on advanced foreign countries catching up to the United States during the 1970s and 1980s, we build an open-economy general equilibrium framework of endogenous growth and trade to evaluate the effectiveness of innovation and trade policies in improving the competitiveness of U.S. firms. Firm innovation decisions in our model are motivated by defensive and expansionary innovation motives, as well as domestic and international business-stealing effects. While knowledge spillovers and decreasing returns to knowledge accumulation lead to cross-country convergence, productivity differences drive trade flows. While realistically mimicking an extensivesetofempiricalrelationships,ourmachineryisstilltractableenoughtoallowfortheanalysis of transitional dynamics, which proves to be crucial for policy evaluation. 54

nnovation and rade olicy in a lobalized orld I T P G W Our theoretical and quantitative analysis obtains several key results. Theoretically we show that in the static sense, increased openness benefits the fixed factor in final production by raising its compensation via higher-quality intermediate imports, while the impact on business owners is ambiguous, because larger export demand and loss of markets to better foreign rivals exert opposing forces. In the dynamic sense, increased openness, and thus foreign competition, encourages more domestic innovation through stronger incentives for defensive and expansionary R&D. Quantitatively, we first show that foreign technological catching-up hurts U.S. welfare by stealing away business and profits of U.S. firms. Second, we assess that the introduction of R&D subsidies in the United States was a viable response to restore the technological competitiveness of U.S. firms, with a notable welfare contribution in the medium term. Moreover, our model implies that the optimal subsidy is increasing over time horizons and decreasing in openness. The latter is an intriguing result, which owes again to the dynamic innovation-stimulating effect of foreign competition on domestic firms. Finally, we consider a counterfactual protectionist responsetoforeigncatching-up. Wefindthat,inthecontextofourmodel,increasingtradebarriers for imports unilaterally increases U.S. economic welfare only in the short run, chiefly through import substitution, which shifts profits from foreign firms to domestic ones. However, failing to incentivize U.S. firms to accelerate technological improvement, the protectionist policy cannot compensate for the loss of high-quality imports and leads to substantial welfare losses in the medium to long run. Therefore, protectionist policies in our model, despite helping businesses to retain profits in the short run, make consumers worse off over the longer term. Moreover, these short-term gains evaporate ones retaliatory responses by trade partners are considered. Motivated by the micro-level evidence, our new dynamic model with its rich competition structureprovidesausefulframeworkforfutureresearchontheeffectoftradeopennessonfirm dynamics. First, an intriguing question in this agenda is the impact of foreign direct investment on innovation incentives in the receiving country. Second, in regards to innovation policy, our framework can be used to analyze quantitatively the optimal policy design on intellectual propertyrightsinopeneconomies. Finally,theframeworkcanshednewlightonthedesignofoptimal corporate tax policies in open economies, accounting for their broader dynamic implications on firms’ innovation decisions. These are some exciting avenues for future research. References Acemoglu, Daron and Ufuk Akcigit, “Intellectual Property Rights Policy, Competition and Innovation,” Journal of the European Economic Association, 2012, 10 (1), 1–42. , , Harun Alp, Nicholas Bloom, and William R. Kerr, “Innovation, Reallocation and Growth,” 2017. National Bureau of Economic Research Working Paper 18993. Aghion, Philippe and Peter Howitt, The Economics of Growth, MIT Press, 2009. 55

nnovation and rade olicy in a lobalized orld I T P G W , Antonin Bergeaud, Mathieu Lequien, and Marc Melitz, “The Impact of Exports on Innovation: Theory and Evidence,” 2017. Manuscript. , Christopher Harris, Peter Howitt, and John Vickers, “Competition, Imitation and Growth with Step-by-step Innovation,” Review of Economic Studies, 2001, 68 (3), 467–492. , Nicholas Bloom, Richard Blundell, Rachel Griffith, and Peter Howitt, “Competition and Innovation: AnInverted-URelationship,” QuarterlyJournalofEconomics, 2005, 120(2), 701–728. Akcigit, Ufuk and William R. Kerr, “Growth through Heterogeneous Innovations,” Journal of Political Economy, 2017. , Douglas Hanley, and Nicolas Serrano-Velarde, “Back to Basics: Basic Research Spillovers, Innovation Policy and Growth,” 2016. Centre for Economic Policy Research Discussion Paper 11707. , , and Stefanie Stantcheva, “Optimal Taxation and R&D Policies,” 2016. National Bureau of Economic Research Working Paper 22908. Alessandria, George and Horag Choi, “Establishment Heterogeneity, Exporter Dynamics, and the Effects of Trade Liberalization,” Journal of International Economics, 2014, 94 (2), 207–223. Anderson,JamesE.andEricvanWincoop,“TradeCosts,”JournalofEconomicLiterature,2004,42 (3), 691–751. Antràs, Pol and Elhanan Helpman, “Global Sourcing,” JournalofPoliticalEconomy, 2004, 112 (3), 552–580. Arkolakis, Costas, Arnaud Costinot, and Andrés Rodríguez-Clare, “New Trade Models, Same Old Gains?,” American Economic Review, February 2012, 102 (1), 94–130. Atkeson,AndrewandArielT.Burstein,“Innovation,FirmDynamics,andInternationalTrade,” Journal of Political Economy, 2010, 118 (3), 433–484. Autor, David, David Dorn, Gordon H. Hanson, Gary Pisano, and Pian Shu, “Foreign Competition and Domestic Innovation: Evidence from U.S. Patents,” 2016. National Bureau of Economic Research 22879. Autor, David H., David Dorn, and Gordon H. Hanson, “The China Syndrome: Local Labor MarketEffectsofImportCompetitionintheUnitedStates,”AmericanEconomicReview,October 2013, 103 (6), 2121–2168. Aw,BeeYan,MarkJ.Roberts,andDanielYiXu,“R&DInvestment,Exporting,andProductivity Dynamics,” American Economic Review, 2011, 101 (4), 1312–1344. Baldwin,RichardandPaulKrugman,“IndustrialPolicyandInternationalCompetitioninWidebodied Jet Aircraft,” in Richard Baldwin, ed., Trade Policy Issues and Empirical Analysis, University of Chicago Press, 1988, pp. 45–78. Barattieri, Alessandro, Matteo Cacciatore, and Fabio Ghironi, “Protectionism and the Business Cycle,” 2018. National Bureau of Economic Research 24353. Bernard, Andrew B., J. Bradford Jensen, Stephen J. Redding, and Peter K. Schott, “Global Firms,” Journal of Economic Literature, 2017. forthcoming. 56

nnovation and rade olicy in a lobalized orld I T P G W Bloom, Nicholas, Mirko Draca, and John Van Reenen, “Trade Induced Technical Change? The Impact of Chinese Imports on Innovation, IT and Productivity,” Review of Economic Studies, 2016, 83 (1), 87–117. , Rachel Griffith, and John Van Reenen, “Do R&D Tax Credits Work? Evidence from A Panel of Countries 1979–1997,” Journal of Public Economics, 2002, 85 (1), 1–31. Buera, Francisco J. and Ezra Oberfield, “The Global Diffusion of Ideas,” 2016. National Bureau of Economic Research 21844. Burstein, Ariel and Marc J. Melitz, “Trade Liberalization and Firm Dynamics,” in Daron Acemoglu, Eddie Dekel, and Manuel Arellano, eds., Advances in Economics and Econometrics Tenth World Congress. Applied Economics, Vol. 2, 2013, pp. 283–328. Bustos, Paula, “Trade Liberalization, Exports, and Technology Upgrading: Evidence on the Impact of MERCOSUR on Argentinian Firms,” American Economic Review, 2011, 101 (1), 304–340. Cameron, Gavin, James Proudman, and Stephen Redding, “Technological Convergence, R&D, Trade and Productivity Growth,” European Economic Review, 2005, 49 (3), 775–807. Capdevielle,PatriciaandDonatoAlvarez,“InternationalComparisonsofTrendsinProductivity and Labor Costs,” Monthly Lab. Rev., 1981, 104, 14–20. Chen, Cheng and Claudia Steinwender, “Import Competition, Heterogeneous Preferences of Managers, and Productivity,” 2016. Harvard Business School Working Paper. Coe, David T., Elhanan Helpman, and Alexander W. Hoffmaister, “International R&D Spillovers and Institutions,” European Economic Review, 2009, 53 (7), 723–741. Coelli, Federica, Andreas Moxnes, and Karen Helene Ulltveit-Moe, “Better, Faster, Stronger: Global Innovation and Trade Liberalization,” 2016. National Bureau of Economic Research 22647. Coeurdacier, Nicolas and Helene Rey, “Home Bias in Open Economy Financial Macroeconomics,” Journal of Economic Literature, 2013, 51 (1), 63–115. Costinot, Arnaud and Andrés Rodríguez-Clare, Trade Theory with Numbers: Quantifying the Consequences of Globalization, Vol. 4 of Handbook of International Economics, Elsevier, and ,“TheUSGainsfromTrade: ValuationUsingtheDemandforForeignFactorServices,” 2018. National Bureau of Economic Research 24407. , Andrés Rodríguez-Clare, and Iván Werning, “Micro to Macro: Optimal Trade Policy with Firm Heterogeneity,” 2016. National Bureau of Economic Research 21989. ,DaveDonaldson,JonathanVogel,andIvánWerning,“ComparativeAdvantageandOptimal Trade Policy,” Quarterly Journal of Economics, 2015, 130 (2), 659–702. Demidova, Svetlana and Andrés Rodríguez-Clare, “Trade Policy Under Firm-level Heterogeneity in a Small Economy,” Journal of International Economics, June 2009, 78 (1), 100–112. Eaton, Jonathan and Gene M. Grossman, “Optimal Trade and Industrial Policy under Oligopoly,” Quarterly Journal of Economics, 1986, 101 (2), 383–406. 57

nnovation and rade olicy in a lobalized orld I T P G W Gerschenkron, Alexander, Economic Backwards in Historical Perspective: A Book of Essays, Belknap Press of Harvard University Press, 1962. Gorodnichenko, Yuriy, Jan Svejnar, and Katherine Terrell, “Globalization and Innovation in Emerging Markets,” American Economic Journal: Macroeconomics, April 2010, 2 (2), 194–226. Grossman, Gene M. and Edwin L.-C. Lai, “International Protection of Intellectual Property,” American Economic Review, 2004, 94 (5), 1635–1653. and Elhanan Helpman, “Comparative Advantage and Long-run Growth,” AmericanEconomic Review, 1990, 80 (4), 796–815. and , “Growth and Welfare in a Small Open Economy,” in E. Helpman and A. Razin, eds., International Trade and Trade Policy, Cambridge, Mass.: MIT Press, 1991, chapter 8, pp. 141–163. and , Innovation and Growth In the Global Economy, MIT press, 1991. and , “Quality Ladders in the Theory of Growth,” Review of Economic Studies, 1991, 58 (1), 43–61. Haaland, Jan I. and Hans Jarle Kind, “R&D Policies, Trade and Process Innovation,” Journal of International Economics, 2008, 74 (1), 170–187. Hall, Bronwyn H., Adam B. Jaffe, and Manuel Trajtenberg, “The NBER Patent Citation Data File: Lessons, Insights and Methodological Tools,” 2001. National Bureau of Economic Research 8498. Hashmi, AamirRafique, “CompetitionandInnovation: TheInverted-URelationshipRevisited,” Review of Economics and Statistics, 2013, 95 (5), 1653–1668. Hombert, Johan and Adrien Matray, “Can Innovation Help US Manufacturing Firms Escape Import Competition from China?,” 2015. CEPR Discussion Papers 10666. Hottman, Colin J., Stephen J. Redding, and David E. Weinstein, “Quantifying the Sources of Firm Heterogeneity,” Quarterly Journal of Economics, 2016, 131 (3), 1291–1364. Hummels, David and Volodymyr Lugovskyy, “Are Matched Partner Trade Statistics a Usable Measure of Transportation Costs?,” Review of International Economics, 2006, 14 (1), 69–86. Iacovone,Leonardo,“TheBetterYouAretheStrongerItMakesYou: EvidenceontheAsymmetric Impact of Liberalization,” Journal of Development Economics, 2012, 99 (2), 474–485. , Wolfgang Keller, and Ferdinand Rauch, “Innovation Responses to Import Competition,” 2011. Mimeo, Princeton University. Impullitti, Giammario, “International CompetitionandUS R&DSubsidies: A QuantitativeWelfare Analysis,” International Economic Review, 2010, 51 (4), 1127–1158. and Omar Licandro, “Trade, Firm Selection, and Innovation: The Competition Channel,” Economic Journal, 2017. Irwin, Douglas A. and Nina Pavcnik, “Airbus versus Boeing Revisited: International Competition in the Aircraft Market,” Journal of International Economics, 2004, 64 (2), 223–245. Keller, Wolfgang, “International Technology Diffusion,” Journal of Economic Literature, 2004, 42 (3), 752–782. 58

nnovation and rade olicy in a lobalized orld I T P G W Leahy, Dermot and J. Peter Neary, “Public Policy towards R&D in Oligopolistic Industries,” American Economic Review, 1997, 87 (4), 642–662. Lileeva, Alla and Daniel Trefler, “Improved Access to Foreign Markets Raises Plant-level Productivity for Some Plants,” Quarterly Journal of Economics, 2010, 125 (3), 1051–1099. López, Ricardo A., “Do Firms Increase Productivity in Order to Become Exporters?,” Oxford Bulletin of Economics and Statistics, 2009, 71 (5), 621–642. Lybbert,TravisandNikolasZolas,“GettingPatentsandEconomicDatatoSpeaktoEachOther: An “Algorithmic Links with Probabilities” Approach for Joint Analyses of Patenting and Economic Activity,” Research Policy, 2014, 43 (3), 530–542. Mayer, Thierry, Marc J. Melitz, and Gianmarco I.P. Ottaviano, “Product Mix and Firm Productivity Responses to Trade Competition,” 2016. National Bureau of Economic Research 22433. , Marc Melitz, and Gianmarco I.P. Ottaviano, “Market Size, Competition, and the Product Mix of Exporters,” American Economic Review, 2014, 104 (2), 495–536. Melitz, Marc, “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity,” Econometrica, 2003, 71, 1695–1725. Melitz, Marc J. and Stephen J. Redding, “Missing Gains from Trade?,” American Economic Review, 2014, 104 (5), 317–321. Muendler, Marc-Andreas, “Trade, Technology, and Productivity: A Study of Brazilian Manufacturers, 1986-1998,” 2004. CESifo Working Paper Series 1148. Ossa,Ralph,“AQuantitativeAnalysisofSubsidyCompetitionintheUS,”2015. NationalBureau of Economic Research Working Paper 20975. Perla, Jesse, Christopher Tonetti, and Michael E. Waugh, “Equilibrium Technology Diffusion, Trade, and Growth,” 2015. National Bureau of Economic Research Working Paper 20881. Rivera-Batiz, Luis A. and Paul M. Romer, “Economic Integration and Endogenous Growth,” Quarterly Journal of Economics, 1991, 106 (2), 531–555. Rodrik, Dani, “Industrial Policy for the Twenty-first Century,” 2004. CEPR Discussion Paper 4767. Romer,PaulM.,“EndogenousTechnologicalChange,”JournalofPoliticalEconomy,1990,98,S71– S102. Sampson, Thomas, “Dynamic Selection: An Idea Flows Theory of Entry, Trade, and Growth,” Quarterly Journal of Economics, 2016, 131 (1), 315–380. Segerstrom, Paul S., “Endogenous Growth without Scale Effects,” American Economic Review, 1998, 88, 1290–1310. Spencer, Barbara J. and James A. Brander, “International R&D Rivalry and Industrial Strategy,” Review of Economic Studies, 1983, 50 (4), 707–722. Wilson, Daniel J., “Beggar Thy Neighbor? The In-state, Out-of-state, and Aggregate Effects of R&D Tax Credits,” Review of Economics and Statistics, 2009, 91 (2), 431–436. 59

nnovation and rade olicy in a lobalized orld I T P G W Appendices A Additional Empirical Material A.1 Empirical Facts Thissectionpresentsempiricalregularitiesinglobaltechnologicalcompetitionanddescribesthe technological convergence between the United States and other major economies. An account of federal- and state-level R&D tax credit policies follows. The section concludes with suggestive evidence on the positive effect of R&D tax credits on firm-level performance. Fact 1: Technological Convergence ThereisastrikingchangeintherelativepositionofforeigncountriesrelativetotheUnitedStates intheworldwidetechnologicalcompetitionoverthecourseof1970suntilthemid-1980s. Atboth aggregate and sectoral level, we observe a clear pattern of catching-up, which we measure using patent and citation counts. .5 .4 .3 .2 erahS 1965 1975 1985 1995 Application Year Foreign Share, patents Foreign Share, citations FigureA.1: Shareofforeignpatents: 1965-1995 Using USPTO data on patent counts, Figure A.1 shows the yearly change in the proportion ofpatentsregisteredintheUnitedStatesbyforeignentities(solidline).55 Italsodepictsthesame ratio for the citations received by those patents (dashed line). Both lines display an obvious, increasing trend, which means that the growth in the number of foreign-based patents is higher 55Thedistinctionbetweendomesticandforeignpatentsisbygeographiclocationofregistry. Formoredetail,see Halletal.(2001). 60

nnovation and rade olicy in a lobalized orld I T P G W thanthegrowthinU.S.-basedones. Interestingly,theconvergenceprocesscomestoahaltaround the mid-1980s, and we observe a reversal of the trend. 80000 60000 40000 20000 yrtnuoc yb stnetaP 1965 1975 1985 1995 Application Year US patents Foreign Patents FigureA.2: PatentCounts Fact 2: R&D Tax Incentives Concerns about the strength of the U.S. industries and their ability to compete in a fast-moving globaleconomyincreaseddramaticallyinthelate1970s. Thekeydiscussionsfocusedonwhether the new technologies arising from federally funded R&D were being fully and effectively exploitedforthebenefitofthenationaleconomy,whethertherewerebarriersslowingdownprivate firms in creating and commercializing innovations and new technologies, and whether publicprivatecollaborationinresearchandinnovationcouldhelptheU.S.economyinfacingthesenew challenges. Several new policy measures were introduced in those years, with particular attention to avoiding unduly substitution of government for private firms in activities that the latter cannaturallyperformbetter. Theseactionsincludedseveralprogramstofacilitatethetransferof the outcome of the federal R&D to private businesses (e.g., the National Cooperative Research Actof1984,andtheTechnologyTransferActof1986),policiestostrengthenintellectualproperty rightssuchastheBayh-DoleAct(1980),andinparticulartaxincentivestoinnovationthatstarted with the Research and Experimentation Tax Credit (R&E) in 1981. TheR&ETaxCreditintroduceda25percenttaxdeductionontheincreaseinR&Dspending overtheaverageofthepastthreeyears. In1985thestatutoryratewasreducedto20percent,and in 1990 the base for eligibility was defined as the average of the 1984–88 R&D to sales ratio (with a maximum of 16 percent) times current sales. The U.S. competitors in high-tech industries— Japan and the large European economies—introduced, or already had in place tax incentives for innovation. Using corporate tax data, Bloom et al. (2002) estimate the R&D subsidy produced by tax policies in the United States, Japan, and key European countries. The data take into account the different tax and tax credit systems used in each country and measure the reduction in the cost of $1 of R&D investment produced by the tax system. Figure 3 of the main text shows the R&D tax subsidy for the set of countries we are interested in. 61

nnovation and rade olicy in a lobalized orld I T P G W Thevariationsacrosscountriesaremainlyduetothepresenceandeffectivenessofaspecific tax credit for R&D. The sudden increase in U.S. subsidies, for instance, takes place with the introductionoftheR&ETaxCreditin1981andwiththerevisionofthebasedefiningincremental R&D in 1990. We can see that in 1980 the reduction in innovation cost attributable to the tax system was about 5 percent; it jumps to about 15 percent in 1981, and further increases to more than 25 percent in 1990. In Japan there is a fixed tax credit of limited effectiveness for the period considered. In the rest of the countries there are no special tax provisions or credits given on R&Dexpenditures,andthepositiveandfairlyconstantsubsidyratesareproducedbytaxcredits common to all assets. In1982startingwithMinnesota,U.S.statesalsointroducedtaxsubsidiesforR&D.InFigure A.3 we report the evolution of the average rate of U.S. state tax credits together with the number of states offering a tax credit each year, using tax credit data of Wilson (2009). The simple average of effective tax credits across states offering a credit was about 6 percent in 1995, nearly one-fourthofthefederalone,andthenumberofstatesfollowingsuchapolicyroseto32. Figure A.3alsoshowstheaverageR&Dcreditlevelweightedbythestate-levelpatentproduction,whose evolution over time is parallel to the simple average.56 .08 .06 .04 .02 0 Effetive Credit Rate, avg. across states (Lines) 30 20 10 0 )sraB( tiderC xaT htiw setatS fo rebmuN 1980 1985 1990 1995 2000 Year Patent−wtd. avg. Simple average Source: Authors’ calculations, USPTO, Wilson (2009) FigureA.3: U.S.state-levelR&Dtaxcredit 56Asopposedtothesimpleaverage,theweightedaveragemultipliesthestate-leveleffectivecreditbythefraction oftotalU.S.-basedpatentsregisteredinthatstate. 62

nnovation and rade olicy in a lobalized orld I T P G W B Additional Derivations B.1 Proofs Lemma 1 We confirm this lemma by guess-and-verify method. Conjecture the following form: V = qv . Substituting this expression into equation (14), we get: cmt mt (cid:16) (cid:17) (x )γ A r v q v˙ q = max Π(m)q 1 sA α Amt q At Amt Amt A − xAmt − − γ A (cid:34) (cid:35) m¯ +x Amt ∑ F m (n t )v Ant λ(nt− m) q v Amt q − nt =m+1 +x˜ [0 v q] Amt Amt − (cid:16) (cid:17) m¯ (cid:104) (cid:105) ∑ + x +x˜ F (n ) v q v q . B( − m)t B( − m)t − m t A( − nt) − Amt nt = − m+1 Dividing all sides by q, we obtain the desired result. B.2 Value Functions for Boundary Gaps To complete the exposition of incumbents’ problem we present the two boundary cases where the incumbent is m¯-steps ahead (behind):57 (cid:26) (cid:16) (cid:17) (x )γ A r At V Am¯t (q) V˙ Am¯t (q) = max (πL A +π ∗L B )q 1 sA α A Am¯t q − xAm¯t − − γ A +x [V (λq) V (q)]+x˜ [0 V (q)] Am¯t Am¯t Am¯t Am¯t Am¯t − − (cid:41) (cid:16) (cid:17) m¯ (cid:104) (cid:105) ∑ + x +x˜ F (n ) V (q) V (q) , B( − m¯)t B( − m¯)t − m¯ t A( − n)t − Am¯t nt = − m¯+1 and  (cid:16) (cid:17)γ A   (cid:16) (cid:17) x A( m¯)t r V (q) V˙ (q) = max 1 sA α − q At A( − m¯)t − A( − m¯)t X A( m¯)t  − − A γ A − m¯ (cid:104) (cid:16) (cid:17) (cid:105) +x ∑ F (n ) V λ(nt +m¯) q V (q) A( − m¯)t − m¯ t Ant − A( − m¯)t n (cid:104) t = − m¯+1 (cid:105) +x˜ 0 V (q) A( − m¯)t − A( − m¯)t (cid:27) (cid:104) (cid:105) +(x +x˜ ) V (λq) V (q) . Bm¯t Bm¯t A( − m¯)t − A( − m¯)t 57Thesevaluefunctionsassumethatm¯-stepaheadleadercapturesboththedomesticandtheforeignmarket—i.e., thequalityadvantageatthelargestgapisenoughtocoverthetradecosts. 63

nnovation and rade olicy in a lobalized orld I T P G W The last term in the value function of m¯-step-behind incumbent captures the knowledge spillovers. When a leader at the maximum gap m¯ innovates, the follower in this sector automatically sees its technology jump by a measure λ. Together with the market-size, escapecompetition, and business-stealing effects described above, the international knowledge spillover is the last key feature driving innovation in our framework. In each period this spillover keeps laggard firms in the innovation race, preventing them from falling too far behind. Because the innovation technology is the same for all firms, laggards always have a chance to catch up. B.3 Aggregation and the Distribution of Leadership Thegrowthrateofthiseconomyisdeterminedbythechangesinaggregatequality/productivity across intermediate goods, Q . In order to analyze the evolution of aggregate quality and cmt breakingitdownintoitsvarioussourcesweneedtoconsiderallpossiblescenariosofinnovation outcomes and keep track of the resulting changes in quality levels across product lines at each gap size. Changes in Q are characterized by the following expressions:58 Amt m 1 m¯ (cid:16) (cid:17) Q˙ Amt = s= ∑− m¯ F s (m)(x Ast +x˜ Ast )λm − sQ Ast + s= ∑ m+1 F − s ( − m) x B( − s)t +x˜ B( − s)t Q Ast (cid:104) − (cid:105) x +x +x˜ +x˜ Q − Amt B( − m)t Amt B( − m)t Amt (cid:104) (cid:105) m¯ 1 Q˙ Am¯t = (x Am¯t +x˜ Am¯t )(λ − 1) − x B( − m¯)t− x˜ B( − m¯)t Q Am¯t + s= ∑− m¯ F s (m¯)(x Ast +x˜ Ast )λm¯ − sQ Ast − (cid:104) (cid:105) m¯ 1 Q˙ = (x +x˜ )(λ 1) x x˜ Q + ∑− F (m¯)(x +x˜ )Q . A( − m¯)t Bm¯t Bm¯t − − A( − m¯)t− A( − m¯)t A( − m¯)t s= m¯ s Bst Bst A( − s)t − The first equation is the generic expression that describes the change in the aggregate quality of intermediate goods produced by firms from country c at position m. The first sum captures the addition of new incumbents improving to gap m. An innovation with step size λm s by − a domestic incumbent or entrant at position s < m happens with probability F (m), and it s implies that the domestic incumbent in that product line will reach gap m. The second sum captures the addition of product lines, where the position of the domestic incumbent worsens to mfromabetterone. Animprovementbyforeignincumbentsorentrantsfromposition s < m − − to m, which occurs with probability F ( m), hits the domestic incumbent in that product s − − − line enjoying the position s > m and brings it down to gap m. The third component in the equationcapturesthefactthatanyinnovationinaproductlinewherethedomesticincumbentis atpositionmcausesachangeinitspositionand,thus,anegativechangeintheaggregatequality index across product lines of position m. The other two equations describe the boundary cases. In case of m¯, notice that innovation by the domestic incumbent or entrants does not change the gap between the domestic incumbent and the foreign follower due to spillover effects, but raises 58TheevolutionofthevariablesforcountryBisgivenreciprocally. 64

nnovation and rade olicy in a lobalized orld I T P G W the average quality by the step size. Reciprocally, any innovation by the foreign incumbent or entrant improves the quality of the good that the most laggard domestic incumbents produce because of spillover effects. The laws of motion that determine the measure of product lines where the incumbent from country c is at position m are described by (cid:16) (cid:17) µ˙ Am¯t = µ˙ B( − m¯)t = ∑m s ¯ =− − 1 m¯ F s (m¯)(x Ast +x˜ Ast )µ Ast − µ Am¯t x B( − m¯)t +x˜ B( − m¯)t (cid:16) (cid:17) ∑m¯ F ( m) x +x˜ µ s=m+1 − s − B( − s)t B( − s)t Ast µ˙ Amt = µ˙ B( m)t = +∑m s=− 1 m¯ F s (m)(x Ast +x˜ Ast )µ Ast − (cid:104) − (cid:105) x +x +x˜ +x˜ µ − Amt B( − m)t Amt B( − m)t Amt (cid:16) (cid:17) µ˙ A( − m¯)t = µ˙ Bm¯t = ∑m s ¯ =− − 1 m¯ F s (m¯)(x Bst +x˜ Bst )µ A( − s)t− µ A( − m¯)t x A( − m¯)t +x˜ A( − m¯)t . (A.1) The drivers of the dynamics are the same as in the case of aggregate quality indices, except that step sizes are not relevant in determining the changes in µ. Notice that the change in the measure of position-m product lines in a country corresponds to the change in the measure of position-( m) product lines in the other country. Moreover, because there is a unit measure − of intermediate product lines we have ∑ µ = 1. Therefore, information on 2m¯ 1 measures m cm − is enough to describe the distribution of product lines according to the technological gap size between the two active incumbents from each country. C Simplified Model and Analytical Results This appendix details the discussion in Section 3 and presents proofs of the propositions. C.1 Static Effects of Openness At the aggregate level, the static effects of openness on the income and welfare of consumers stem from three main channels, with two of them having a positive direction and one having a negative direction. To show this, we consider a closed economy and analyze the effects of it opening up. In autarky, the total output in country c is (cid:20) 1 β (cid:21)1 −β β (cid:90) 1 (cid:90) 1 Y c C = − η (1 − β)− 1 q cj dj ≡ ϕ q cj dj, 0 0 which is produced using only domestic intermediates. Likewise, the fixed factor and profit incomes are (cid:90) 1 wC = βYC and ΠC = π q dj = β(1 β)Y . c c c cj − c 0 65

nnovation and rade olicy in a lobalized orld I T P G W The gross national income, sum of profits and fixed factor income, is given by (cid:90) 1 NIC = β(1 β)YC+βYC = (2 β)βϕ q dj. c − c c − cj 0 When this economy opens to trade (subject only to tariffs) the same expressions become (cid:20) 1 β (cid:21)1 −β β (cid:20)(cid:90) 1 (cid:90) 1 (cid:21) Y c O = − η (1 − β)− 1 0 I qcj >qˆ c(cid:48)j q cj dj+ 0 I qcj <qˆ c(cid:48)j qˆ c(cid:48)j dj (cid:90) 1 (cid:20) 1 β (cid:21) = Y c C+ϕ 0 I qcj <qˆ c(cid:48)j (1+τ)− −β q c(cid:48)j − q cj dj, 1 β where we define qˆ q/(1+τ) −β , abstracting from iceberg costs for now. Similarly, ≡ (cid:90) 1 (cid:90) 1 wO c = βY c O and ΠO c = π 0 I qcj >qˆ c(cid:48)j q cj dj+π ∗ 0 I qˆ cj >q c(cid:48)j q cj dj, with gross income given by (cid:90) 1 (cid:90) 1 NI c O = π 0 I qcj >qˆ c(cid:48)j q cj dj+π ∗ 0 I qˆ cj >q c(cid:48)j q cj +βY c O. (A.2) Thus, the comparison between incomes in autarky and the open economy boils down to the comparison of (cid:90) 1 (cid:90) 1 1 β (cid:90) 1 0 q cj dj and 0 I qcj >qˆ c(cid:48)j q cj dj+(1+τ)− −β 0 I qˆ cj >q c(cid:48)j q cj dj, determining the profit component, and to the comparison of (cid:90) 1 (cid:90) 1 1 β (cid:90) 1 0 q cj dj and 0 I qcj >qˆ c(cid:48)j q cj dj+(1+τ)− −β 0 I qcj <qˆ c(cid:48)j q c(cid:48)j dj, determining fixed factor income. Figure A.4 illustrates these comparisons. As in Figure 6, solid lines determine the domestic technology frontier, whereas dashed lines show the iceberg costadjusted levels of these frontiers that emerge when engaging in trade. The left panel shows the product lines and the associated qualities that determine aggregate profit income for the home country in an open world. The right panel shows the technology frontier that determines the productivity of the domestic fixed factor. First, compared to the state of autarky, the open economy allows relatively more productive firms to sell to a larger market by providing the opportunity to export. This positive effect of market size on aggregate income is evident from the first component in equation (A.2), as profits of leading firms increase proportionally by π . This increase corresponds to the upward expan- ∗ sion of the red line in Figure A.4a, determined by the additional income from exporting. Note that the effective quality when exporting is reduced by trade costs. The second static effect of openness works through the selection of more productive intermediate-good producers due to increasedcompetitionexertedbyforeigncompetitors. Thisselectionchannelfacilitatesthetrans- 66

quality profits q πq US1+US1’ US1 US2USfirms,whensoldathome US1’ US2’USfirms,whensoldabroad USfirms,actualwages USfirms,actualprofits product product line, j line, j nnovation and rade olicy in a lobalized orld I T P G W profits quality πq US1+US1’ q US1 US2USfirms,whensoldathome US1’ US2’USfirms,whensoldabroad USfirms,actualprofits USfirms,actualwages US1 US1 US1’ US1’ FN1 FN1 FN1’ FN2 FN1’ FN2 FN2’ FN2’ US2 US2 US2’ US2’ product product 0 1 line, j 0 1 line, j a)Effectonprofits b)Effectonwages FigureA.4: Staticeffectsofopenness Notes: PanelAillustratestheprofitsgeneratedbytheU.S.incumbentsinanexampleeconomy. Inautarky,profitsaregivenbythe solidlineUS1-US1’,whereasinanopeneconomy,profitsaregivenbythethickredlinestartingat(US1+US1’).Whentheeconomy isopen,exportersearnthesumofprofitsfromsellingbothdomestically,basedontheiractualproductquality(solidlineUS1-US2), andabroad,basedontheirtrade-cost-adjustedquality(dashedlineUS1’-US2’).Firmsthatcannotexportandsellonlydomestically generateprofitsbasedontheiractualproductquality. IncumbentsinsectorswheretheU.S.importsthespecificgoodhavezero profits. PanelBillustratestherelevantqualityfrontierthatdeterminesthelaborproductivityand,thus,thedomesticwagepaidin thefinal-goodsector. Inautarky,therelevantfrontierisgivenbytheproductqualitiesofalldomesticfirms(US1-US1’). Inanopen economy,therelevantqualityfrontier(thickredlineUS1-FN2)istheupperenvelopeofproductqualitiesavailableinbothcountries, takingintoaccountthequalityofimportedintermediategoods. fer of better-quality intermediate goods across countries, increasing the productivity of the fixed factor utilized in the production of domestic final output. Figure A.4b illustrates this selection mechanism,whichindicatesthatthefixedfactorproductivityisafunctionoftheupperenvelope of product qualities available in the international market. Therefore, this channel, labeled as directtransferoftechnologyinKeller(2004),leadstoahigherfixedfactorincomeinbothcountries.59 However, the selection channel implies at the firm level that less productive domestic firms lose theprofitstoforeigncompetitors,whichtheywouldearnotherwiseinautarky,resultinginadeclineofaggregateprofitincome. AsillustratedinFigureA.4a,someproductlinesfailtogenerate profits, as they are substituted by imports. Next we present the proof of Proposition 1.60 59Noticethaticebergcostspreventthetradeofsomebetter-qualityforeigngoodsavailableinthemarket. 60Additionally, scale effects arise in a setting where competing countries are of different sizes. For a discussion, seeChapter15inAghionandHowitt(2009). 67

nnovation and rade olicy in a lobalized orld I T P G W Proposition 1 The effect of opening up on wage income is given by ∆ w = βφ ∆ , where ∆ is w w defined as the following difference: (cid:90) 1 1 β (cid:90) 1(cid:104) (cid:105) (cid:90) 1 ∆ w ≡ 0 I qcj >qˆ c(cid:48)j q cj dj+(1+τ)− −β 0 1 − I qcj >qˆ c(cid:48)j q c(cid:48)j dj − 0 q cj dj (cid:90) 1 (cid:0) (cid:1) = 0 I qcj <qˆ c(cid:48)j qˆ c(cid:48)j − q cj dj > 0. The transfer of better technology affects this component positively. The total effect on profits given by ∆Π = π ∆ Π, where ∆ w is defined as the following difference: (cid:90) 1 1 β (cid:90) 1 (cid:90) 1 ∆ Π ≡ 0 I qcj >qˆ c(cid:48)j q cj dj+(1+τ)− −β 0 I qˆ cj >q c(cid:48)j q cj dj − 0 q cj dj (cid:90) 1 (cid:90) 1 = 0 I qˆ cj >q c(cid:48)j qˆ cj dj − 0 I qcj <qˆ c(cid:48)j q cj dj ≶ 0. The first component is the gain from exports, and the second component is the loss of profits from firms that are laggard in international competition. The direction of the difference depends on the measure of leading firms in country c as well as on the difference between the average quality of country c’s leading and laggard firms. Therefore, the combined effect on national income, which reads as ∆ w+∆Π = βϕ ∆ w +π ∆ Π, is ambiguous. Inthecaseofunilateraltariffreduction,domesticexportersarenotaffected,astheunilateral tariff reduction only affects the cutoff for imports. Therefore, its effect is determined by the loss of domestic profits and the gains from technology transfer driven by the higher import volume. C.2 Dynamic Effects of Openness and Escape Competition AsexplainedinSection2.3.3,marketsizeandselectionchannelsaffectnotonlytheaggregatevalues, but also firm decisions, introducing a dynamic force. Furthermore, two important dynamic channels whose impact are completely absent in a static comparison are defensive and expansionaryR&Dmotives,theincentiveoffirmsproducinggoodsofsimilar(adjusted)qualitiestoescape foreign competition and gain market dominance. To focus on these strategic interactions, consider the simplified environment described in Section 3.2 and abstract from trade frictions. In 68

nnovation and rade olicy in a lobalized orld I T P G W this environment firm values can be written as x2 rv m¯ = − m¯ +x m¯ [v 0 v m¯ ] − − 2 − − − x2 rv m = − m +x m [v 0 v m ]+x m [v m 1 v m ] − − 2 − − − − − − − x2 rv = 0 +x [v v ]+x [v v ] 0 0 1 0 0 1 0 − 2 − − − x2 rv = 2π m +x [v v ]+x [v v ] m m m+1 m m 0 m − 2 − − − x2 rv = 2π m¯ +x [v v ]+x [v v ] m¯ m¯ m¯ m¯ m¯ 0 m¯ − 2 − − − with m 1,...,m¯ 1 .61 The following proposition argues that, in this environment, firms in ∈ { − } neck-and-neck position have the highest innovation intensity. Proposition 2 First, note that v = v and v = v satisfy the set of equation for m > 0. m m¯ m m¯ − − This implies that we have three distinct firm values and innovation rates, and that x = x = 0. m¯ m Now we show x > 0, x > 0 and x > x = x . 0 m¯ 0 m m¯ − − − 1. v > v : Assume not such that v v = v . Then [v v ] 0, and x = 0. This m¯ 0 0 m¯ 1 1 0 0 ≥ − ≤ implies v = 0 v = v . But v = 0 would mean rv = 2π x v and thus v > 0, a 0 m¯ 1 0 m¯ m¯ m¯ m¯ ≥ − − contradiction. Therefore x > 0. 0 2. v > v : Assume not such that v v . Then x = 0 implying that v = 0 v . 0 m¯ m¯ 0 m¯ m¯ 0 − − ≥ − − ≥ This is possible only if x = 0. But since v > v as shown above, x > 0, a contradiction. 0 m¯ 0 0 Therefore x > 0. m¯ − 3. [v v ] > [v v ]: Assume not such that [v v ] [v v ].This means v < 0 m¯ 0 0 m¯ 0 m¯ m¯ 0 0 − − − − − ≥ − unless x = 0. If v < 0, it is a contradiction by step 2. If x = 0 meaning that v = 0 it is 0 0 0 0 a contradiction by step 1. Therefore [v v ] > [v v ] and x > x = x > x = m¯ 0 0 m¯ 0 m m¯ m¯ − − − − − x = 0. m D Quantitative Appendix D.1 Solution Algorithm 1. Let M be the set of data moments and Mm be the model counterpart. Define R(M Mm) − as the function that calculates a weighted sum of the difference between data and model moments. 2. Guess a set of values for the internally calibrated parameters θ . guess 61Lemma 1 applies also in this environment. For the sake of the argument, we assume that neck-and-neck firms havezeroprofits. Wealsodropcountryidentifiersthankstosymmetry. 69

nnovation and rade olicy in a lobalized orld I T P G W 3. Calculate the balanced growth path (BGP), where time derivatives are zero by definition. Start iteration h = 0 with the guess (cid:8) rA,rB (cid:9)h=0 . T T (a) At iteration h, take (cid:8) rA,rB (cid:9)h given and solve incumbent firm values jointly for both T T countries by backward iteration. i. Guess { v AmT+∆t ,v BmT+∆t }m m¯,..,m¯ . Assuming these to be the true BGP values ∈{− } compute innovation rates x ,x˜ ,x ,x˜ . Notice that these { AmT AmT BmT BmT }m m¯,..,m¯ ∈{− } are innovation rates at one period before, as innovation is a forward looking decision and thus depends on the next period value in discrete time. ii. Compute v ,v using the value function equations. By the definition of { AmT BmT }m BGP, values at T+∆ t and T should be the same. iii. Check if max v cmT+∆t v cmT < ε. m,c (cid:107) − (cid:107) If not met, set { v cmT+∆t }m = { v cmT }m and repeat. (b) Take the BGP innovation rates and set Q = 1 m. Iterate forward on aggregate Am0 ∀ quality indices Q using the transition equations until growth rates of the implied cmt income processes for both countries stabilize. Call these (cid:8) gA,gB (cid:9)h . T T (c) Check if (cid:8) rA,rB (cid:9)h and (cid:8) gA,gB (cid:9)h meet the Euler equation. If not, set (cid:8) rA,rB (cid:9)h+1 to T T T T T T interest rates implied by the Euler equation with (cid:8) gA,gB (cid:9)h and repeat until conver- T T gence. 4. Next calculate the equilibrium over the transition. Start iteration h = 0 by guessing a time path for interest rates (cid:8) rA,rB (cid:9)h=0 . The terminal values are set to the BGP at t t t= 1975,...,1975+T { } every iteration. h (a) At iteration h, given the terminal (BGP) values v ,v compute the im- { AmT BmT }m i n p n a l g i l ed i t n h t i e e n r n e (cid:8) o s v r t A a r t , a i r o t B e n (cid:9) s h r (cid:8) a r te T A s ,r { T B (cid:9) x A h , mT c − o ∆ m t , u p x˜ n u A t t m i e l T − { t ∆ v t A , m x = T B − m ∆ T 1 − t , 9 ∆ v 7 t B 5 , m x˜ T B t − m o ∆ T t − o } ∆ b m h t t } . a m h i I n . ter T t a h h t e e e n b , im a g c p i k v l w i e e n a d rd t s e s e r r m u ie s i s - t t t= 1975,...,1975+T 0 { } x ,x˜ ,x ,x˜ h . { Amt Amt Bmt Bmt }mt= 1975,...,1975+T { } (b) Set Q = 1 m. Using the implied innovation rates, compute Q for t = Am0 cmt ∀ 1975,...,1975+T by forward iteration and back up the implied income processes. { } (c) Compute income growth rates (cid:8) gA,gB (cid:9)h . Using period-by-period Euler equations, t t t check if (cid:13) (cid:13) (cid:13) rc h ρ(cid:13) max(cid:13) gc h { t} − (cid:13) < ε. m,c,t (cid:13) (cid:13) { t} − ψ (cid:13) (cid:13) for 1975,...,1975+T 1 . If not, set (cid:8) rA,rB (cid:9)h+1 to interest rates im- { − } t t t= 1975,...,1975+T 1 plied by the Euler equation with (cid:8) gA,gB (cid:9)h { a − nd } repeat until convert t t= 1975,...,1975+T 1 { − } 70

nnovation and rade olicy in a lobalized orld I T P G W gence. (cid:8) (cid:9) 5. Once step 4 converges, use the final interest rates rA,rB to compute the t t t= 1975,...,1975+T { } aggregate variables and the model counterparts of the data moments. (cid:0) (cid:0) (cid:1)(cid:1) 6. Minimize R M Mm θ using an optimization routine. guess − D.2 Additional Figures Figure A.5 demonstrates the effect of tariff and R&D policies on the model-implied time path of average technological lead of U.S. firms over their competitors. Increasing unilateral protection leads to a relatively lower path, while higher subsidies result in a uniformly higher path relative to the one in the case of no policy intervention. 3.5 3 2.5 2 1.5 1 1985 1990 1995 2000 2005 Years smrif .S.U fo pag ygolonhcet naeM No intervention Protectionism 3.5 3 2.5 2 1.5 1 1985 1990 1995 2000 2005 Years a)4percentagepointtariffhike smrif .S.U fo pag ygolonhcet naeM No intervention Higher subsidy b)ActualR&Dpolicy FigureA.5: AveragetechnologyleadoftheU.S.firms,afterpolicyintervention Figure A.6 replicates 9b incorporating patents with assignee id “0” in the analysis. The inclusion of these patents lead to sharper peaks. Figure A.7 shows optimal R&D policies over policy horizons fixing unilateral import tariffs at various levels. It illustrates the interaction between optimal R&D subsidies and the level of tariffs in the model. In a more liberal regime, more firms face stiffer competition, damping the need for aggressive R&D subsidies. 71

nnovation and rade olicy in a lobalized orld I T P G W .gva ,mrif rep noitacilppa tnetaP 6 5 4 3 2 1 −15 −10 −5 0 5 10 15 Technological gaps btw. domestic and foreign firms FigureA.6: PatentingintensityinUSPTOdata,includingassigneeid“0” 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 10 15 20 25 30 35 40 45 50 Horizon etar ydisbus lamitpO Benchmark 8 ppt reduction 16 ppt reduction FigureA.7: OptimalR&Dsubsidyoverpolicyhorizonsfordifferentlevelsofunilateraltariffpolicy FigureA.8displaysthealternativeempiricalinitialtechnologicalgapdistributionsemployed in sensitivity analysis in Sections 7.2 and 7.3. Solid blue lines represent the distribution used in the baseline analysis. Figure A.9a compares empirical initial technological gap distributions used in the baseline analysis (dashed red line) and in the alternative calibration specified in Section 7.4 (solid blue line). Figure A.9b displays the model-generated distribution in 1981 (circled blue line), in juxtaposition with its empirical counterpart (solid black line) and the baseline calibration result (dashed red line). The 1981 distribution generated by the alternative calibration is noticeably to 72

nnovation and rade olicy in a lobalized orld I T P G W 0.09 0.09 Data US, 1975 Data US, 1975 0.08 Data US, 1975, no UK 0.08 Data US, 1975, citation 0.07 0.07 0.06 0.06 0.05 0.05 0.04 0.04 0.03 0.03 0.02 0.02 0.01 0.01 0 0 -20 -15 -10 -5 0 5 10 15 20 -20 -15 -10 -5 0 5 10 15 20 Gaps (m) Gaps (m) a)DroppingtheU.K. b)Citation-weightedpatents FigureA.8: Alternativeinitialtechnologicalgapdistribution Notes: Thefigurecontrastsalternativeinitialtechnologicalgapdistributions(reddashedlines)withthebaseline(solidbluelines). PanelAdepictstheversionomittingtheU.K.,whilepanelBshowstheversionbasedoncitation-weightedpatents. the right of the baseline one, in line with a smaller shift in the empirical counterparts, albeit a tad larger than that. 0.09 0.09 Data, 1981, cumul. Data US, 1981, cumul. 0.08 Data, 1981, baseline 0.08 Model US, 1981, cumul. Model US, 1981, baseline 0.07 0.07 0.06 0.06 0.05 0.05 0.04 0.04 0.03 0.03 0.02 0.02 0.01 0.01 0 0 -20 -15 -10 -5 0 5 10 15 20 -20 -15 -10 -5 0 5 10 15 20 Technological gaps btw. domestic and foreign firms Technological gaps btw. domestic and foreign firms a)Baselineandalternative1981distributions(data) b)Calibrated1981distributions FigureA.9: Calibrationandcomparisontobaselinewiththealternativeempiricalgapdistribution Notes: PanelAcontrastsempirical1981technologicalgapdistributionsinthealternativemethod(solidblueline)andthebaseline (reddashedline).PanelBcontrastsmodel-generated1981technologicalgapdistributions. 73

nnovation and rade olicy in a lobalized orld I T P G W E Robustness with Labor in the Intermediate-Good Sector Following Akcigit and Kerr (2017), assume that final goods are produced by combining a fixed factor (again normalized to 1 for both countries), while intermediate goods are produced using labor: q¯ k = ct h . jt jt η Here, q¯ denotes the economy-wide labor productivity in intermediate-good production, which ct is common across all sectors. Equilibrium profits from domestic sales and exports become π (cid:0) q jt (cid:1) = (cid:20) 1 − η β w q¯ c h t (cid:21)1 −β β βq jt and π ∗ (cid:0) q jt (cid:1) = (cid:20) (1 1 + − κ β )ηw q¯ c h t (cid:21)1 −β β βq cjt , ct ct where wh denotes wages of workers in intermediate-good production. ct We assume that there is a unit measure of workers h supplied inelastically. The market (cid:82)1 clearing condition for labor reads as H = h dj. Solving for the wage from the labor market c 0 cjt condition, we obtain  β w q¯ c c h t t = χq¯− ct β  (cid:124) Q c D t +Q c X t + (cid:123) ( (cid:122) 1+κ) β −β 1 Q c X (cid:125) t   , denote Q¯ ct where χ (1 β)/η1 β. The superscripts D and X refer to sales in domestic and export − ≡ − markets, respectively. Thus, Q¯ can be interpreted as the average quality of sales of all active ct domesticfirms,adjustedfortradecoststhatexportedgoodsaresubjectto. Inthespecialcasewe are considering—i.e., q¯ = Q¯ —we have w = χQ¯ . ct ct ct ct Calibration We recalibrate this model following similar steps as in the baseline version. External parameters share the baseline values. We also kept the tariff rate at the calibrated baseline value, which generates about a 7% tariff revenue in equilibrium (again burned out). Internally calibrated parameters are presented in Table A.1. As summarized in Table A.2, this model also performs well in matching the data targets, except some overestimation of R&D-to-GDP ratio and the growth rate of the United States.62 62Earningsthataccruetothefixedfactorandlaborcombinedmakesupabout75percentoftheaggregateincome duringthecalibrationperiod. 74

nnovation and rade olicy in a lobalized orld I T P G W TableA.1: Internallycalibratedparameters R&D scale R&D scale Step size Iceberg F(n) α α α˜ α˜ λ κ φ A B A B 0.20 0.85 61.1 10.5 0.78% 1.78% 1.15 TableA.2: Modelfit Moment Estimate Target Source TFP Growth U.S. 1.08% 0.55% Coe et al. (2009) 1975-81 TFP Growth FN 1.50% 1.73% Coe et al. (2009) 1975-81 R&D/GDP U.S. 2.15% 1.75% OECD 1981 R&D/GDP FN 2.05% 1.96% OECD 1981 Entry Rate U.S. 10% 10% BDS 1977-81 Export Share U.S. 5.84% 7% WB 1975-81 Policy Implications IntermsofR&Dsubsidies,TableA.3revealsthatsubsidiesleadtolargerwelfaregainscompared tothebaselinemodel. Thisisanintuitiveresultbecauseinthissetting,theaccelerationindomestic innovation increases the productivity of labor in intermediate-good production, in addition to the effects present in the baseline model. This mechanism also leads to a higher level of optimal R&D subsidy. Figure A.10a confirms that this result holds true across all horizons. Also, it implies that the policy function for optimal R&D subsidy over different horizons is qualitatively similar to what has been found in the baseline setting. TableA.3: ObservedandoptimalU.S.R&Dsubsidy: 1981-2016 Welfare gains Subsidy rate 1981-2016 Observed R&D subsidy 19.2% 2.73% Optimal R&D subsidy 76% 21.9% Next, we analyze the effects of protectionist policies. Figure A.11 presents the consumptionequivalent welfare change and the change in optimal innovation effort of incumbent firms following a unilateral 3-percentage-point increase in U.S. tariffs. First, Figure A.11a demonstrates the decline in innovation efforts of laggard U.S. firms, again due to less foreign competition caused by higher protection. Similar to the baseline experiment, protection leads to the loss of better-quality imports, and domestic innovation is not enough to compensate for this loss. How- 75

nnovation and rade olicy in a lobalized orld I T P G W 10 20 30 40 50 Horizon in years etar ydisbus lamitpO 0.78 0.76 0.74 0.72 0.7 0.68 0.66 0.64 0.62 10 20 30 40 50 Horizon in years a)Overdifferenthorizons % ni etar ffirat lamitpO 16 14 12 10 8 6 4 2 0 b)Optimaltariffpolicy FigureA.10: OptimalU.S.R&Dsubsidy,overdifferenthorizonsandlevelsofopenness ever, insharpcontrasttothebaseline, theprotectionistpolicyleadstowelfaregainsoveralltime horizons in this modified setting, as shown in Figure A.11b. The reason is that now protectionist policies prohibit not only business stealing, but also “wage stealing”—i.e., the decline in wages duetothelossofdomesticactivitytoforeignimporters. Thismechanismstrengthensthepositive effect of protectionist policies. Therefore, as depicted in Figure A.10b, the optimal tariff policy is aconstant11percent, whichessentiallyimpliesfullprotectionfromimportsatallhorizons. This boundary result is very different than its baseline counterpart, which calls for a declining tariff profileoverlongertimehorizons. Thisdifferenceisagaindrivenbytheprotectiveeffectoftariffs on domestic wage income. -15 -10 -5 0 5 10 15 Technological gaps btw. domestic and foreign firms troffe noitavonnI Incumbent innovation US Reduced tariffs 2.5 2 1.5 1 0.5 5 10 15 20 25 30 35 40 45 50 Time Periods a)Consumptionequivalentwelfare egatnecreP 0.235 Protection 0.23 0.225 0.22 0.215 0.21 0.205 0.2 0.195 0.19 0.185 b)Innovationresponseofincumbents FigureA.11: Welfareeffectsofprotectionism: unilateral3-percentage-pointincreaseintariffs 76

nnovation and rade olicy in a lobalized orld I T P G W Finally,FigureA.12showstheoptimaljointpolicyresponse,incaseofbilateraltariffchanges. As in the baseline model, the reversal of the trade policy emerges when the foreign country retaliates. This result implies that the gains from wider export markets for the home firms dominate the additional negative effect of import penetration on domestic wages. 0.85 0.8 0.75 0.7 0.65 10 15 20 25 30 35 40 45 50 Horizon in years )dilos( ydisbus D&R lamitpO 0.1 0.08 0.06 0.04 0.02 0 )dehsad( etar ffirat lamitpO FigureA.12: Optimaljointpolicyinbilateraltariffchange Notes:Thefigurecompareshorizon-dependentoptimaljointpolicyincaseof(trade-policy)retaliationtothatinthebaseline. 77