Finance and Economics Discussion SeriesFederal Reserve Board,Washington,D.C.ISSN 1936-2854 (Print)ISSN 2767-3898 (Online)Demand Uncertainty,Selection,and TradeErick Sager,Olga A.Timoshenko2024-042Please cite this paper as:Sager,Erick,and Olga A.Timoshenko (2024)."Demand Uncertainty,Selection,and Trade,"Finance and Economics Discussion Series 2024-042.Washington:Board of Governors of theFederal Reserve System,https://doi.org/10.17016/FEDS.2024.042.NOTE:Staff working papers in the Finance and Economics Discussion Series (FEDS)are preliminarymaterials circulated to stimulate discussion and critical comment.The analysis and conclusions set forthare those of the authors and do not indicate concurrence by other members of the research staff or theBoard of Governors.References in publications to the Finance and Economics Discussion Series (other thanacknowledgement)should be cleared with the author(s)to protect the tentative character of these papers.Demand Uncertainty,Selection,and TradeOlga A.TimoshenkoFederal Reserve BoardTemple UniversityMay16,2024AbstractThis paper examines the role of uncertainty on elasticities of trade flows with re-spect to variable trade costs in a canonical model of trade with monopolistic compe-tition and heterogeneous firms.We identify two channels through which uncertaintyimpacts trade:through export participation thresholds (the selection effect)and thedistribution of shocks governing export selection (the dispersion effect).While theselection effect dampens trade elasticities under uncertainty,the dispersion effect isambiguous.We develop a methodology for using customs firm-level data to quantifytrade elasticities under uncertainty,and the magnitude of each of the two channelsthrough which uncertainty impacts trade.We find that uncertainty amplifies tradeelasticities,on average,indicating that the dispersion effect of idiosyncratic firm-levelshocks dominates -though the effect is heterogeneous across industries.The overallmagnitude of the endogenous selection mechanism on trade elasticities is small,indi-cating that the main drivers of trade in this class of trade models are overwhelminglyincumbent firms.Keywords:Demand uncertainty,firm size distribution,extensive margin,selection,trade elasticities.welfare.JEL:F12,F13.*We thank Arevik Gnutzmann-Mkrtchyan,Mina Kim,Logan Lewis,Martin Lopez-Daneri,Andre Kur-mann,Peter Morrow,Nuno Limao,Moritz Ritter,Andres Rodrigues-Clare,Ina Simonovska,Ben Williams,and Yoto Yotov,as well as seminar participants at Drexel,the George Mason University,the Universityof Maryland,Temple University,Bank of Canada,Asian Meeting of the Econometric Society in East andSoutheast Asia 2023,Canadian Economic Associations Meetings 2018,BEROC International EconomicsConference 2018,Southern Economic Association 88th Annual Meetings 2018,Washington Area Interna-tional Trade Symposium 2018,1st Mid-Atlantic Trade Workshop 2017,and Midwest International TradeMeeting 2017 for valuable comments and discussions.The views expressed herein are those of the authorsand not necessarily those of the Federal Reserve Board of Governors or the Federal Reserve System.Thework was supported in part by the facilities and staff of the George Washington University Colonial OneHigh Performance Computing Initiative.The paper previously circulated under the title "Uncertainty andTrade Elasticities".First version:March 2017.2001 C Street NW,Washington DC,20551,United States.E-mail:erick.r.sager@frb.govCorresponding author,Temple University,Department of Economics,1115 Polett Walk,Philadelphia,PA 19122,United States.E-mail:olga.timoshenko@temple.edu1 IntroductionWhen variable trade costs vary,not only do existing exporters change the size of their ship-ments abroad,but also the set of exporters varies through entry and exit.Participationdecisions for exporters-that is,entry into export markets and the subsequent decision ofhow intensively to produce and ship goods to foreign destinations -is a conceptually andquantitatively important dimension of trade,and factors affecting these decisions can playa central role in determining the social value of trade for an economy.However,the bench-mark framework for measuring the gains from trade considers a special set of circumstancessurrounding potential exporters'decisions:firms have complete information about the de-mand for their products in all foreign markets.While this benchmark has elucidated centralmechanisms that drive the gains from trade,particularly the role of selection,less is knownabout the role of selection in the empirically more relevant case under which firms face someamount of uncertainty about how profitable their venture into foreign markets will be.In this paper,we introduce uncertainty about firm-level idiosyncratic demand in foreignmarkets into a canonical model of trade a la Melitz (2003),and derive predictions of themodel for the partial elasticity of trade with respect to variable trade costs.We show thatregardless of whether firms face uncertainty or not,the partial trade elasticity admits thesame functional form-it equals the firm-level trade elasticity (the intensive margin)scaledby the effect of endogenous selection (the extensive margin).We demonstrate that whileuncertainty has no impact on the intensive margin,these different assumptions about firm-level information do have an ambiguous effect on the endogenous selection component of thepartial trade elasticity through their effect on export selection thresholds and distributionsof the export selection shocks.We therefore identify two distinct channels through which uncertainty impacts partialtrade elasticities:the selection and the dispersion effects.First,demand uncertainty intro-duces a wedge between entry thresholds in the two information environments that capturesfirms'expectations about the unexpected component of idiosyncratic demand shocks.Werefer to this effect as the selection effect of uncertainty.Second,demand uncertainty intro-duces a wedge between the export selection shocks in the two information environments thatcaptures realizations of the unexpected component of idiosyncratic demand shocks.We referto this effect as the dispersion effect of uncertainty.These two distinct channels stem fromthe fact that the information environment has a direct impact on the type of idiosyncraticshocks firms take into account when making export decisions.Under complete informa-tion,the decisions are based on realizations of productivity and demand shocks,while underuncertainty firms make their decisions based on productivity and only partial informationabout demand,namely idiosyncratic expectations about demand shocks.1Using the properties of the model,we show that the selection effect of uncertainty damp-ens the partial trade elasticity relative to a complete information environment,while thedispersion effect is ambiguous.We therefore proceed by using the theoretical model with de-mand uncertainty to derive an empirical methodology that quantifies trade elasticities,andto disentangle the selection and dispersion effects of uncertainty.Our empirical methodologyis based on the model's prediction that export quantity depends on export election shocks,a combination of ex-ante productivity shocks and expectations about demand,while exportsales depend on export selection shocks and a realization of an unanticipated component ofdemand shocks.This property of the model allows us to simultaneously use export quantityand sales data to recover export selection shocks and the dispersion of the unanticipatedcomponent of demand shocks.We apply the methodology to Brazilian firm-level export data for the period between1997 and 2000.We find that relative to the complete information environment,uncertaintyreduces trade elasticities by an average of 8%due to the selection effect,holding all elseconstant.While the dispersion effect is theoretically ambiguous,we find that in aboutninety seven percent of observations the dispersion effect amplifies trade elasticities but doesso by a small amount,holding all else constant.Overall,we find that uncertainty amplifies trade elasticities in about eighty percent ofobservations,but does so by a small amount.Moreover,the effect is heterogeneous acrossproducts,with larger amplification concentrated among more substitutable products.Uncer-tainty dampens trade elasticities in twenty percent of observations,and the dampening effectis concentrated among products with low elasticities of substitution across varieties.Theseresults indicate that the dispersion of export selection shocks is the dominant mechanismthrough which uncertainty impacts trade elasticities among substitutable products,whilethe selection effect of uncertainty plays a larger role in adjustments to trade costs amonginelastic products.Finally,in the model with uncertainty the endogenous selection effect increases trade elas-ticities by an average of 2%relative to a benchmark with no endogenous selection indicatingthat incumbent firms are the main drivers of trade adjustments in this class of models.This paper is related to several strands of the literature on international trade.First,the benchmark model is based on Melitz(2003)and is further developed in many influentialpapers,such as Chaney (2008),Bernard,Redding,and Schott (2010),Arkolakis,Costinot,and Rodriguez-Clare (2012),Melitz and Redding (2015).A growing branch of the literaturehas demonstrated that models incorporating uncertainty along the lines of Jovanovic (1982)are well suited to match salient patterns of empirically observed firm behavior such as firmgrowth as a function of age and size (Arkolakis,Papageorgiou,and Timoshenko (2018)),firm2product switching behavior (Timoshenko (2015b)),and firm input and output pricing be-havior (Bastos,Dias,and Timoshenko (2018)).Although models that follow the benchmarkhave focused on decomposing and measuring trade elasticities,the normative implications ofmodels that incorporate uncertainty,particularly for measurements of trade elasticities arenot yet well understood.1In terms of decomposing trade elasticities,this paper shows that selection into exporting(and hence the extensive margin of trade elasticity),depends on the information structurefaced by firms.Previous work has shown that the partial elasticity of trade with respectto variable trade costs can be decomposed into an intensive and an extensive margin ofadjustment components (Chaney (2008)),and that the extensive margin adjustment cru-cially depends on the distributional assumptions with respect to the sources of firm-levelheterogeneity (Melitz and Redding (2015)).Sager and Timoshenko (2019)characterize aflexible distribution that well describes firm-level heterogeneity and find the extensive mar-gin trade elasticity to be small.With respect to trade elasticity measurement,this paper usesa structural model with alternative assumptions about information and specifies firm-leveldata requirements necessary for identification.Existing work focuses on full informationbenchmarks that estimate trade elasticities using aggregate trade flows and prices data(seeEaton and Kortum (2002)and Simonovska and Waugh (2014))or trade flows and tariff data(Caliendo and Parro (2015)).2This paper relates to several related papers on information asymmetries in trade.Themost closely related papers to this one are Timoshenko (2015a)and Dickstein and Morales(2018).Both study information asymmetries in trade by using data and theory to inferinformation available to firms when making export participation decisions.Notably,thosepapers focus on firm-level outcomes,while this paper's focus is macroeconomic in scopeand therefore complementary to this previous work.Specifically,this paper uses insightsabout export participation decisions from these previous papers to understand the aggregateimplications of imperfect information on changes in trade flows due to changes in variabletrade costs.Accordingly,this paper makes assumptions that are customized to computingtrade elasticities (such as estimating heterogeneity in shocks that lead to sales and quan-tity outcomes)but does not focus on other assumptions that can characterize the extensivemargin of trade (such as heterogeneity in fixed costs of exporting).Despite the difference infocus,this paper's model captures the firm-level relationships found in the previous litera-1A notable exception is Arkolakis,Papageorgiou,and Timoshenko (2018),who characterize constrainedefficiency of a model in which firms learn about demand but do not engage in international trade.2This literature further finds elasticities estimated from aggregate trade flows are smaller than those estimated from disaggregated industry-level data (Imbs and Mejean (2015)),and that there is substantialheterogeneity in bilateral trade elasticities due to heterogeneity in countries'industrial production (Imbsand Mejean (2017)).3ture (Timoshenko (2015a)finds that past continuous export history predicts current exportchoice,and Dickstein and Morales (2018)finds that firm-level sales and industry averagespredict exporting for large firms but not for small firms)because firms in our model thathave positive ex ante information about productivity levels are more likely to be large andexport.Finally,this paper relates to other recent work on trade policy uncertainty.Handleyand Limao (2015)find that trade policy uncertainty lowers entry into foreign markets byreducing the value of the export participation threshold,while we find the opposite result.The distinction arises from differences in the timing of when information is revealed to firmsand the option value of waiting such timing may produce.In our framework,uncertaintyis revealed after entry and production decisions have been made.Therefore,waiting has noimpact on a firm's decision relevant information.In contrast,in Handley and Limao (2015)firms first observe a realization of tariff policy and then make their decisions.Handley andLimao (2015)framework therefore features the option value of waiting.Firms can conditiontheir entry decisions on a realization of a shock and only enter when the realization of ashock is high enough,a mechanism absent from our framework.Baley,Veldkamp,andWaugh (2020)develop a model in which firms export more when there is greater uncertaintyabout the terms of trade in bilateral trade relationships,which can also be thought of astrade policy uncertainty,yet the welfare effects are ambiguous and depend on preferences.3The rest of the paper is organized as follows.Section 2 presents the theoretical framework.Section 3 characterizes the effect of uncertainty on trade elasticities.Section 4 details ourempirical methodology for quantifying trade elasticites in an environment with uncertainty.Section 5 describes our data and presents elasticity estimation results.Section 6 performsa counterfactual analysis of trade elasticities in an environment with complete information.Section 7 concludes.All proofs,derivations,and robustness checks are relegated to theAppendix.43There are other papers that consider the effects of information on trade.Bergin and Lin(2012)show thatthe entry of new varieties increases at the time of the announcement of the future implementation of theEuropean Monetary Union,suggesting that changes in the information available to firms have immediateconsequences for firms'decisions;Lewis (2014)studies the effect of exchange rate uncertainty on trade;Allen (2014)shows that information frictions help to explain price variation across locations;Fillat andGaretto (2015)show that aggregate demand fluctuations can explain variation in stock market returnsbetween multinational and non-multinational firms.4Appendix A provides a detailed description of the model with uncertainty and complete information.Ap-pendix B derives properties of the endogenous selection component of the partial trade elasticity.AppendixC details the steps of the counterfactual analysis.Appendix D presents robustness results accounting forthe measurement error in the quantity data.2 Theoretical FrameworkThis section outlines our main theoretical framework which will serve as the structural bench-mark for quantifying trade elasticities in a model with uncertainty.We consider an economicenvironment in which heterogeneous firms export products to monopolistically competitivemarkets.This environment is similar to that in Melitz (2003)with an added dimensionof demand uncertainty according to Jovanovic (1982)as adapted to a heterogeneous firmsframework by Arkolakis et al.(2018).We assume exogenous entry as in Chaney (2008).52.1 DemandThere are N countries and K sectors in each country.Each country is indexed by j and eachsector is indexed by k.Each country is populated by a mass of Li identical consumers.Each consumer withincountry j owns an equal share of domestic firms and is endowed with a unit of labor that isinelastically supplied to the labor market.The preferences of a representative consumer incountry j are represented by a nested constant elasticity of substitution utility function(1)where ijk is the set of varieties in sector k consumed in country j originating from countryi,cijk(w)is the consumption of variety w e Sijk,ek is the elasticity of substitution acrossvarieties within sector,)is the demand shock for variety and is theCobb-Douglas utility parameter for goods in sector such that1.Cost minimization yields a standard expression for the optimal demand for variety w evarieties from sector k,and Pi is the aggregate price index in country j in sector k.62.2SupplyEach variety w Eiik is supplied by a monopolistically competitive firm f that has access toa linear production technology that transforms labor into output,g=exp(za)e.Upon entry,5All derivations are relegated to Appendix A.6The assumed Cobb-Douglas utility specification over consumption bundles across sectors implies Yik=Yj,where Y;is aggregate income in country j.5a firm f selling from country i to country j in sector k is endowed with an idiosyncraticlabor productivity level and a set of idiosyncratic destination-sector specific demandshocks,Each demand and supply shocks pair (is drawn from ajoint distribution to be characterized later.Firms from country i selling output in sector k to country j face fixed costs,fiik,andvariable 'iceberg'trade costs,Tjk.Fixed and variable costs are denominated in units oflabor,and w;denotes the wage rate in country j.Each firm can potentially supply one variety of a product from each sector.Firms decidewhich markets to export to (the extensive margin decision)and how much to export to eachof the chosen markets (the intensive margin decision).Without loss of generality,we assumethat firms choose a quantity to export.Prices are the result of market clearing given theexported quantity of the variety,and then export sales are realized along with prices.2.3 Information StructureWe consider an environment with complete information and an environment with uncertainty.In the environment with complete information,firms observe all idiosyncratic shocksbefore making decisions.Namely,firms observe their supply,and demand,,shocksbefore deciding where to export and how much to export.Denote the firm's decision relevantbelow,is given by(3)In the environment with uncertainty,firms do not observe all idiosyncratic shocks beforemaking export decisions.The timing of the information and firm's decisions follows Arkolakiset al.(2018)and is as follows.1.First,firms observe their supply side shocks,,and form expectations about demandshocks,E(2.Next,firms decide whether and where to export,and how much to export to the chosendestinations.3.Production takes place and all the quantities are shipped;prices clear in destinationmarkets.7The idiosyncratic demand shocks are realized by consumers,but are a payoff relevant state for the firms.Thus,when firms enter,they draw their realization of the idiosyncratic demand of consumers that determinestheir sales.Following Foster,Haltiwanger,and Syverson (2008),who document that idiosyncratic firm-leveldemand shocks,rather than productivity,account for a greater variation of sales across firms,we focus onthe demand shocks that are firm specific.64.Lastly,firms observe their sales and infer their demand shocks,from the realizedobservations of prices and sales.Denote the firm's decision relevant export selection shock in the environment with uncer-tainty byAs we demonstrate below,is given by(4)Observe from equations (3)and (4),that export decision in the environment with un-certainty are based on partial information about the realization of demand shocks.Thisdifference leads to different implications regarding the magnitude of the partial trade elas-ticities with respect to variable trade costs across information environments,and providesnovel insights into which data are suited to structurally identify the partial trade elasticitiesin the environment with uncertainty.2.4 Model Validation2.4.1 Timing AssumptionThe timing assumption in the environment with uncertainty implies that firms first produceand deliver goods,and receive payments for those goods after delivery.Such post-shipmentpayment method,commonly referred to as exporter finance in the trade finance literature,is the most widespread method of financing export transactions.The IMF (2009)reportsthat globally exporter finance accounts for 42 percent of export transactions.In the contextof Latin America in particular,Ahn (2015)finds that exporter finance accounts for 80 to 90percent of the value of import transactions in Colombia and Chile.While we do not attemptto contribute to the trade finance literature nor do we model export payment methods,itsit reassuring that the timing of payments implied by the model in this paper is consistentwith empirical evidence on export finance.In the context of the trade literature,the timing assumption in the environment withuncertainty follows Jovanovic (1982)as adapted to a heterogeneous firms framework by Arko-lakis et al.(2018).The framework of Arkolakis et al.(2018)(due to the timing assumptionin particular)has been shown to be able to predict within firm and exporter behavior suchas gradual growth over time and declining with age survival rates (Timoshenko,2015a;Ruhland Willis,2017),age and size dependence of firm growth rates Arkolakis et al.(2018),andwithin firm price dynamics (Bastos et al.,2018).In the context of this literature,the goal ofthis paper is to explore trade elasticities properties of a demand process and uncertainty thathas also been shown to deliver properties of firm behavior that are consistent with empiricalevidence.72.4.2 Uncertainty in DemandOur choice to model uncertainty in demand stems from three recent strands of research.First,the literature on firm growth has robustly rejected the notion that firms operate at optimalscale immediately upon entry.For instance,Ruhl and Willis (2017)find that a new exporter'sexport sales grow slowly following entry in firm-level Colombian manufacturing data,takingan average of four years to catch up to the (unconditional)average exporter.Learning modelsdeliver this feature of the data,both theoretically and quantitatively.For example,Bermanet al.(2019)find that the learning process generates the empirically observed decline infirms'sales growth,exit rates,and the variance of sales growth within a cohort conditionalon survival in its market.Moreover,Fitzgerald et al.(2023)find that learning about demandexplains the declining exits over time and the observed quantity and price dynamics in theirIrish export data.Second,the canonical model in which firms choose to export based on productivity hasbeen shown to be counterfactual.In particular,in contrast to the canonical model's pre-diction that the smallest exporter should be larger than the largest non-exporter,Eatonet al.(2011)and Armenter and Koren (2015)find that exporters and non-exporters are notstrictly sorted in this way:there is a significant number of exporters that are smaller thannon-exporters and non-exporters that are larger than exporters.Hence,Armenter and Koren(2015)conclude that size-independent variation is needed to match the observed frequencyand size of exporters.In this paper's model,ex post realizations of demand generate suchsize-independent variation.Finally,recent empirical evidence has shown that demand shocks explain a large fractionof the variation in firm sales.For example,Hottman et al.(2016)have shown that variationin firms'product appeal explains between a half to two-thirds of the variance in firm sales.Eaton et al.(2011)and Munch and Nguyen(2014)use French and Danish data,respectively,to estimate that firm-destination idiosyncratic shocks account for almost half of variation insales.Finally,Foster et al.(2016)find that differences in demand,not productivity,explainsize differences between new and incumbent plants.2.5Environment with Complete InformationIn the complete information environment,a firm f's problem selling from country i to countryj in sector k consists of maximizing profitWiTijk(5)8