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Board of Governors of the Federal Reserve SystemInternational Finance Discussion PapersNumber 1304October 2020Technology, Geography, and Trade over Time: The Dynamic Effects ofChanging Trade PolicyCarter MixPlease cite this paper as:Mix, Carter (2020). “Technology, Geography, and Trade over Time: The Dynamic Effects ofChanging Trade Policy,” International Finance Discussion Papers 1304. Washington: Boardof Governors of the Federal Reserve System, https://doi.org/10.17016/IFDP.2020.1304.NOTE: International Finance Discussion Papers (IFDPs) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors anddo not indicate concurrence by other members of the research staff or the Board of Governors. Referencesin publications to the International Finance Discussion Papers Series (other than acknowledgement) shouldbe cleared with the author(s) to protect the tentative character of these papers. Recent IFDPs are availableon the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from theSocial Science Research Network electronic library at www.ssrn.com.

Technology, Geography, and Trade over Time: The DynamicEffects of Changing Trade PolicyCarter Mix Abstract: I study the dynamic effects of changes in trade policy in a multi-country modelwith firms that make durable and destination-specific investments in exporting capacity.Using Mexican exporter-level data, I show that incumbent exporters to minor trade partnersaccount for a smaller share of bilateral exports than do incumbent exporters to major tradepartners, indicating a systematic difference in the persistence of the export decision acrossdestinations. The model is calibrated to capture the positive relationship between exportingpersistence and export volume, and predicts that trade liberalizations with minor exportdestinations deliver higher bilateral export growth than liberalizations with major exportdestinations. Panel analysis on bilateral exports after free trade agreements is consistentwith these predictions, confirming that the model is a useful tool for explaining exportbehavior. Furthermore, I find that heterogeneity in export churning across destinations is akey driver of aggregate dynamics and welfare gains from changes in trade policy.Keywords: trade policy, heterogeneous firms, export participationJEL classifications: F12, F13, F6. I am very grateful to my advisor, George Alessandria, for his guidance. I thank Will Johnson andFernando Parro for excellent discussions of the paper. I also thank Yan Bai, Mark Bils, Lorenzo Caliendo,Jonathan Eaton, Doireann Fitzgerald, Narayana Kocherlakota, Logan Lewis, Dan Lu, Ricardo Reyes-Heroles,and Daniel Xu as well as audiences at Claremont McKenna College, the Federal Reserve Bank of Dallas,the Federal Reserve Board, Midwest Macro UGA, the Penn State New Faces in International EconomicsConference, the Philadelphia Fed Trade Conference, the University of Western Ontario, and the VirtualInternational Trade and Macro Seminar for helpful comments. I’m also grateful to Andrea Garcia, whoprovided excellent research assistance. The views expressed in this paper are solely the responsibility of theauthors and should not be interpreted as reflecting the views of the Board of Governors or of any otherperson associated with the Federal Reserve System.

1IntroductionInternational export markets exhibit little churning: in any given year, only a small fractionof exporters to a destination are new to the market, and those new exporters account foran even smaller fraction of export value. Low export churning is consistent with firmsmaking durable investments in market access and has been a key factor in two-countrymodels to explain the gradual response of trade to changes in trade policy and to evaluatedynamics in other aggregate variables (see, for example, Alessandria and Choi (2014)). Themacroeconomic effects of destination-specific export churning in a multi-country setting haveyet to be analyzed quantitatively. To perform such analysis, we must understand how exportchurning varies across destinations. In this paper, I use Mexican exporter-level data todocument that heterogeneity in export churning across destinations is systematic: there isless churning in countries to which Mexico exports more.To explain this phenomenon and to explore its effect on short-run and long-run dynamics, I develop a general equilibrum multi-country model with heterogeneous firms that makedurable destination-specific investments in exporting capacity. The model captures existingfacts about the importance of incumbent firms as well as the new fact regarding variationin churning across destinations. In addition, the model features endogenous capital accumulation, an internationally-traded noncontingent bond, free entry of firms in the domesticmarket, and capital-intensive trade, all important features for quantitative analysis. Although the model has many state variables, it remains quite tractable. As such, it is a toolthat can be widely implemented to study the macroeconomic effects of trade policy overtime.In the model, all firms draw destination-specific fixed costs that must be paid in orderto begin or continue exporting. A firm will export if the expected gain in firm value exceedspayment of the fixed cost, leading to an endogenous cutoff rule: firms that draw a fixed costbelow the cutoff will export while firms that draw a fixed cost above the cutoff will not. Thedecision to export is dynamic since exporters and nonexporters to a destination draw theirfixed costs from different distributions. In calibration, current exporters draw lower fixedcosts than nonexporters on average, so choosing to export also makes a firm more likely to1

export in the next period, leading to the low churning we see in the data. Churning in alldestinations is low, but it is higher in destinations where incumbents are more likely to drawa fixed cost above the threshold and stop exporting. Therefore, the cutoff thresholds for eachdestination and the shape of the fixed cost distributions determine the relationship betweenexport churning and export volume.Many multi-country models feature immediate adjustments in trade after changes intrade policy. The sunk nature of investments in exporting capacity in my model causes firmsto enter or leave foreign markets slowly so that exports adjust gradually, as documented inthe empirical literature. Because of the variation in export churning across destinations, themodel predicts that bilateral export responses vary after changes in policy. Minor exportdestinations have more churning, so the adjustment in the extensive margin of trade is bothfaster and larger. In a simulated global liberalization, the calibrated model predicts thatbilateral exports to minor export partners grow faster in the first 10 years and exhibit higherlong-run growth than exports to major export partners.I use bilateral trade and free trade agreement data to test these predictions. The dataresemble that of Baier and Bergstrand (2007), but the estimation includes an interaction termthat accounts for whether the free trade agreement partner is a major export destination.The results confirm that after a free trade agreement, exports to minor export partners growmore both in the short run and in the long run. Wald tests on both results yield significanceat the 1% level. I conclude that the model captures export behavior better than existingmulti-country models, which predict similar export responses to all destinations.The model has important implications for welfare and aggregate dynamics after a liberalization in trade. I recalibrate initial tariffs to roughly match tariffs in the data as of 2014and simulate a global liberalization that eliminates them. Regions like East Asia or Chinathat depend heavily on trade and have high initial tariffs on incoming or outgoing goodsexperience the largest welfare gains, generally around 2 percent. Countries like the U.S.,Canada, or Mexico that are either more closed or have low initial tariffs have smaller welfaregains, around 0.5 percent. Because countries take time to accumulate capital and increasetrade, the gains from trade are backloaded. In the short run, countries with larger gainsborrow against future income from countries with smaller gains. After the liberalization, the2

U.S. is predicted to increase its net foreign asset (NFA) position by about 6 percent of GDPin the long run while China is expected to decrease its NFA position by 9.5 percent of GDP.The heterogeneity in churning across destinations and the dynamic exporting decisionare key drivers of aggregate dynamics and welfare gains. A model calibrated to match allthe same moments but with uniform churning across destinations delivers smaller welfaregains and a slower and smaller trade response. A static exporter model yields similar welfaregains as the benchmark model, but the sources and timing of the gains in the two modelsare very different. The model’s ability to explain trade dynamics and their effects on otheraggregate variables makes it a useful tool to analyze the short-run and long-run effects ofchanges in trade policy.1.1Related literatureThe model relates to three branches in the literature: static trade, dynamic trade, andinternational real business cycles (IRBC). The static trade literature embodies the prevailingmodus operandi for studying the aggregate effects of trade policy in a multi-country setting.A seminal paper is Eaton and Kortum (2002) (EK), which introduces a static model of tradein which real-world asymmetries in size and trade flows can easily be modeled and illustrateshow this heterogeneity matters for the effects of trade policy. Since then, several variationsof the model have been developed to explore heterogeneity in the gains from trade acrosssectors, workers, regions, etc. Analysis of policy in these models is performed by consideringtwo equilibria under different policy regimes, with no notion of time or a transition of theeconomy.1The IRBC literature studies aggregate fluctuations in an open economy. IRBC modelsgenerally include dynamic elements from the macroeconomics literature such as capital ortrade in assets. Backus et al. (1992) introduce capital and financial markets between countries into an otherwise Armington-type model and find that the model can capture severalempirical regularities in the data. Several papers incorporate IRBC dynamics into an EK1See, for example, Caliendo and Parro (2015). Extensions of the EK framework have also been used tostudy other types of dynamics such as labor market dynamics, which are not addressed in this paper. Papersinclude Caliendo et al. (2019) and Dix-Carneiro (2014).3

model. Alvarez (2017), Eaton et al. (2016), and Ravikumar et al. (2019) show that endogenous capital accumulation generates larger gains from trade than a purely static model.Eaton et al. (2016), Fitzgerald (2012), Ravikumar et al. (2019), and Reyes-Heroles (2016)incorporate financial markets into an EK model. All these papers abstract from heterogeneous firms and firm dynamics and predict a static trade response to changes in trade policythat is similar for all destinations, leading to different aggregate dynamics than are predictedby the model in this paper.The dynamic trade literature includes both empirical and quantitative studies on theeffects of trade policy and trade costs on trade over time. Empirical work by Baier andBergstrand (2007) and Jung (2012) argue that the increases in trade from trade agreementsare large but take several years to materialize. Das et al. (2007) find evidence that firmspay large “sunk costs” to produce in foreign markets which generate exporter hysteresis asin a series of papers by Baldwin, Dixit, and Krugman. Furthermore, recent work by McCallum (2015), Monarch and Schmidt-Eisenlohr (2017), and Morales et al. (2019) impliesthat sunk costs are not global but destination-specific. Ghironi and Melitz (2005) and Ghironi and Melitz (2007) consider the importance of firm dynamics for aggregate outcomesin a two-country model of trade where export entry costs are static. Alessandria and Choi(2007) add a global sunk cost into a two-country Melitz-type (Melitz (2003)) general equilibrium heterogeneous firm model of trade to generate a dynamic trade elasticity. Alessandriaand Choi (2014) use the same sunk cost and show that a dynamic trade elasticity changesthe macroeconomic effects of trade policy. The models with dynamic trade elasticities aregenerally confined to only two symmetric countries, ignoring the impact of cross-sectionalheterogeneity and making analysis of many multilateral trade policies impossible. An important exception is Steinberg (2019) who introduces a three country model of exporting toanalyze the impact of Brexit and trade uncertainty on the UK. The focus of my model isinstead the importance of firm-level churning across destinations on aggregate outcomes.4

2Micro Data - Destination-level export churningI use data on Mexican exporters from 2000 to 2009 from the World Bank Exporter DynamicsDatabase (see Fernandes et al. (2016)). The data includes the destination-specific exportvalues for all exporters in Mexico from 2000 to 2009. Using these data, I confirm thatexporting is persistent at the destination level. I also document that persistence variessystematically across destinations. Destinations to which Mexico exports more exhibit morepersistent exporting by incumbents. In other words, there is less export churning with closertrade partners. These two facts are the basis of the calibration in the model.2.1Exporting is persistent at the destination levelConsider two measures of the importance of incumbent exporters in a destination. Theincumbent exporter share for destination d in year t incndt is the share of exporters to d inyear t that are incumbents (current exporters to d that also exported to d in year t 1). Theincumbent export share incxdt is the share of exports to d in year t sent by the incumbentexporters.The average incumbent share across all Mexican destinations is obtained by taking anexport-weighted average of the destination–year incumbent share across all countries andyears.2 On average, 59 percent of exporters to a destination were incumbents from 2001 to2009. Unless the fraction of Mexican firms exporting to a single destination is close to 59percent, which is unlikely, the incumbent exporter share tells us that current exporters to adestination are more likely than nonexporters to export to the same destination next year,meaning that the export decision is persistent.The incumbent export share is much higher than the incumbent exporter shares, averaging 96 percent over all years and destinations. The higher incumbent export share isconsistent with empirical work such as Ruhl and Willis (2017) that show exporters take timeto grow in foreign markets so incumbents export more than new exporters. The incumbentexport share tells us that in any given year, the contribution of new exporters to changes in2I remove destinations that receive fewer than 1 million U.S. dollars’ worth of exports from Mexico inany given year. All results in this section are robust to including these firms in the analysis.5

total exports is small. In the quantitative literature, the contribution of new exporters tototal exports is a key moment to explain aggregate trade responses (see Alessandria et al.(2018)).2.2Exporter persistence across destinationsWe now know that average export churning is low at the destination level. But does exportchurning vary systematically across destinations? The scatter plots in Figure 1 show theincumbent shares for each destination export-weighted over all years relative to the averagelogged exports to that destination over the same years. The positive relationship betweenpersistence and export volume for both measures is apparent.To show the relationship more generally, I regress the destination–year incumbent shareson logged bilateral exportsincdt ln exdt εdt .Table 1 reports the regression results in columns 1 and 5. A 100 log point increase in exportsincreases the incumbent exporter share by 1.2 percentage points and the incumbent exportshare by 3.8 percentage points. Taking a destination from the 25th percentile of total exportsto the 75th percentile is predicted to increase the incumbent exporter share from 49.8 percentto 53.5 percent and the incumbent export share from 75 percent to 86.7 percent.The positive relationship between incumbent shares and export volume is robust to including year fixed effects as seen in columns 2 and 6. The incumbent export share alsoresponds to changes in exports within a destination across time as evidenced by the positiveand significant coefficient in the regression with destination and year fixed effects in column7. Increasing exports to a destination by 10 log points from one year to the next increasesthe incumbent export share by roughly 0.3 percentage points on average.The results are also robust to excluding the smallest exporters in any destination. Onemight think that the high churning in minor export partners is because some small firmsexport there by chance for one year, never expecting to continue exporting. To addressthis issue, I only count a firm as an exporter to a destination if it exports more than somethreshold value. I use thresholds of 1,000, 10,000, 100,000, and 1,000,000. In all cases,6

the relationship between persistence and export volume is positive and significant. In fact,as the threshold grows, the coefficients of the regression grow as well (results for a thresholdof 100,000 with no fixed effects are shown in Table 1).The Exporter Dynamics Database (EDD) includes summary statistics on destinationspecific export markets for several countries. I chose Mexico as the main country for analysisbecause it is the most-developed country in the database for which exporter-level data isavailable to perform my own calculations. However, the results presented in this section areconfirmed in a large panel using the summary statistics of all countries in the EDD, whichincludes other developed countries such as Belgium, Chile, Denmark, Germany, Portugal,South Africa, Spain, Sweden, and Turkey, and many less developed countries. Results fromthe panel data can be found in Appendix C.The high persistence in destination-specific exporting and the positive relationship between persistence and export volume will be key features to capture in the model.3ModelNow we turn to the details of the model. The model has I regions and each region comprisesJi 1 identical countries. By having multiple identical countries within a region, themodel can account for average policy changes and reliance on trade for countries in a regionwithout modeling each country explicitly. These factors matter for borrowing and lendingincentives after trade policy changes because they influence the expected path of outputand consumption. I denote country variables such as consumption with a hat Ĉi and regionvariables without a hat Ci . Because countries are identical, we have Ĉi Ci /Ji . I ignorethe hats for prices as identical countries have identical prices for all commodities.3.1ConsumersA representative consumer in each country i chooses consumption Ĉi , labor L̂i , investment inphysical capital X̂i , and holdings of a risk-free bond B̂i0 to maximize welfare. The recursive7

value function of country i’s consumer isi1 σ1 h µ ˆĈi (L̄i L̂i )1 µ βV C (K̂i0 , B̂i0 , S 0 )01 σĈi ,L̂i ,X̂i ,B̂isubject to a budget constraint and the law of accumulation for capitalV C (K̂i , B̂i , S) maxPCi Ĉi PXi X̂i QB̂i0 Wi L̂i Ri K̂i B̂i φJi 0 ˆ 2(B̂i B̄i ) Π̂i T̂i2K̂i0 X̂i (1 δ)K̂iˆ is the population; P and P are the prices of thewhere S is the

October 2020 Technology, Geography, and Trade over Time: The Dynamic E ects of Changing Trade Policy Carter Mix Please cite this paper as: Mix, Carter (2020). \Technology, Geography, and Trade over Time: The Dynamic E ects of Changing Trade Policy," Intern