Volatile Rates, Fragile Growth: Global Financial Risk and Productivity Dynamics

Board of Governors of the Federal Reserve System International Finance Discussion Papers ISSN 1073-2500 (Print) ISSN 2767-4509 (Online) Number 1434 March 2026 Volatile Rates, Fragile Growth: Global Financial Risk and Productivity Dynamics Nils Gornemann, Eugenio Rojas, Felipe Saffie Please cite this paper as: Gornemann, Nils, Eugenio Rojas, Felipe Saffie (2026). “Volatile Rates, Fragile Growth: Global Financial Risk and Productivity Dynamics,” International Finance Discussion Papers 1434. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/IFDP.2026.1434. 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 and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the International Finance Discussion Papers Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at www.ssrn.com.

Volatile Rates, Fragile Growth: Global Financial Risk and Productivity Dynamics* NILS GORNEMANN † EUGENIO ROJAS ‡ FELIPE SAFFIE § FederalReserveBoard UniversityofFlorida UniversityofVirginia&NBER March6,2026 Abstract Doesglobalfinancialriskaffectlong-rungrowth? Usingapanelstate-spacemodelforemergingandadvancedsmallopeneconomies, wemeasuretheeffectsofU.S.monetarypolicyuncertainty shocks. A one-standard-deviation shock lowers the level of the stochastic trend in emerging markets by at least 25 basis points after three years, with little effect in advanced economies. A small open economy model with growth through innovation and occasionally binding borrowing constraints explains this heterogeneity: higher interest-rate volatility depresses valuations, tightens collateral constraints, and slows innovation in equilibrium. A novel interaction between the occasionally binding constraint and stochastic volatility is key forourresults. Keywords: Endogenous Growth, Stochastic Interest Rate Volatility, Financial Frictions, Long- TermProductivityTrends,GlobalFinancialRiskCycle JELClassifications: F32,F41,G15,O16 *Theviewsinthispaperaresolelytheresponsibilityoftheauthorsandshouldnotbeinterpretedasreflectingthe viewsoftheBoardofGovernorsoftheFederalReserveSystemoranyotherpersonassociatedwiththeFederalReserve System.AnearlierversionofthispaperwaspreparedforandfirstpresentedatthePhiladelphiaFederalReserve–PIER– IERConferenceinhonorofHalCole. WethankPhilippeAghion,Andre´sBlanco,DaniloCascaldi-Garcia,V.V.Chari, NicolasCoeurdacier,HalCole,LucaDedola,EliasDinopoulos,JeremyGreenwood,JonathanHeathcote,PeterKaradi, NarayanaKocherlakota,JulianKozlowski,AlanLedesma(discussant),NelsLind,EnriqueMendoza,PabloOttonello, DiegoPerez,RicardoReyes-Heroles,JuanRubio-Ram´ırez,DavidSappington,Ce´sarSosa-Padilla,Mart´ınUribe,Vivian Yue, and seminar participants at 2022 CEF, 2022 SEA, 2023 SED, 2024 CEMLA, 2024 EEA-ESEM, 2024 International MacroFinanceWorkshopatJacksonHole,2024NASM,2024RIDGEDecemberForum,2024SpringMidwestMacro, 2025 Fall Midwest Macro, 2025 Gator Macro Workshop, 2025 LAEF-HKU, 2025 SED, UAI, and VII Santiago Macro Workshop; aswellasatBinghamtonUniversity,theChicagoFed,theECB,EmoryUniversity,theIMF,LSE,Oxford, SciencesPo,theUniversityofNottingham,andtheUniversityofOklahomafortheirvaluablecomments.Allremaining errorsareourown. †BoardofGovernorsoftheFederalReserveSystem.Email:nilsgornemann@gmail.com. ‡DepartmentofEconomics,UniversityofFlorida.Email:erojasbarros@ufl.edu. §DardenBusinessSchool,UniversityofVirginiaandNBER.Email:SaffieF@darden.virginia.edu.

1 Introduction Emerging markets are vulnerable to shifts in global financial conditions. When perceived global economicriskincreases–signaledbyrisingmeasuresliketheVIXorwideningcreditspreads–capitalflowstoemergingeconomiesreversesharply,exchangeratesdepreciate,andoutputcontracts (Rey, 2015; Miranda-Agrippino and Rey, 2020). This sensitivity to global financial volatility is a defining feature of emerging market business cycles. These economies also exhibit substantially greater volatility in their trend growth than advanced economies (Aguiar and Gopinath, 2007). Arethesetwofactsconnected? Doesglobalfinancialriskaffectnotonlyshortrunfluctuationsbut alsothetrajectoryoflongrunproductivitygrowth? Thispaperprovidesevidencethatitdoes. Weestimateapanelstatespacemodelfortwogroupsofsmallopeneconomies,emergingmarketsandadvancedeconomies,from1993to2019. Themodeldeliversestimatesofthetimevarying growthrateofcountryspecifictrendsinGDP,consumption,andinvestment,whiledecomposing eachtrendintotwocomponents,onedrivenbyglobalfinancialuncertaintyandonecapturingall othersourcesoftrendvariation. Ourbaselinemeasureofglobalfinancialriskisaninnovationto U.S.monetarypolicyuncertainty,identifiedasinHustedetal.(2020). WefindthatshockstoU.S. interestrateuncertaintygeneratepersistentdeclinesintheestimatedstochastictrendofeconomic activityinemergingmarketeconomies,withnocomparableeffectinadvancedeconomies. Anincreaseinperceiveduncertaintybyonestandarddeviationlowerstheleveloftheestimatedtrend inemergingmarketsbyatleast25basispointsafterthreeyearswithnoresultingmakeupgrowth later in time. The result is robust across multiple measures of global financial uncertainty and remains when conditioning on U.S. macroeconomic and credit conditions. Advanced economies exhibitasignificantlysmallerresponse. Toexplainthesedifferentresponses,wedevelopasmallopeneconomymodelwiththreekey ingredients, endogenous productivity growth through innovation and firm entry, occasionally bindingcollateralconstraintswithfirmvalueascollateral,andstochasticvolatilityinworldinterest rates. The mechanism operates through firms’ investment into productivity enhancing innovations. Households own firms and can borrow internationally, but only up to a fraction of the presentvalueoftheirfirms’futureprofits. Wheninterestratevolatilityrises,theexpectedpresent valueoftheseprofitsfalls,bothbecausehouseholdsdiscountthefuturemoreheavilyandbecause 2

large adverse interest rate shocks, which become more likely during high volatility periods, triggersharpcontractionswhenborrowingconstraintsbind. Lowerfirmvaluesreduceinnovationby incumbentsandentrybynewfirms,depressingproductivitygrowth.1 Crucially, the mechanism is asymmetric and relies on occasionally binding borrowing constraints. A large positive interest rate shock forces households to deleverage when the collateral constraint binds, sharply reducing consumption and raising the marginal utility of wealth. This amplifiesthedeclineinfirmvaluationsthroughaFisheriandeflationchannel,fallingassetvalues tighten borrowing conditions endogenously, creating a feedback loop between financial conditionsandrealactivity. Incontrast,whentheconstraintbecomesslack,relaxingitfurtherhaslittle effect. As a result, an equally large negative interest rate shock provides limited stimulus. This asymmetry implies that, even holding fixed the average level of the world interest rate, higher volatilitylowerscollateralvalueanddepressesinnovation,withstrongereffectsineconomiesthat entertheconstrainedregionmoreoften. Inthequantitativeexercise,wealsoallowtheborrowing ratefacedbythemodeleconomytoco-movewithuncertainty,inlinewithpreviouswork,tobring the model closer to the data. We show, however, that the asymmetry generated by occasionally bindingconstraintsiskeyforreproducingtheempiricalpatterns. CalibratedtoMexico,themodelreplicatesthedifferentialresponseofemergingandadvanced economies without targeting it. In the quantitative analysis, emerging and advanced economies sharethesametechnology,preferences,andexposuretotheworldinterestrateandvolatilityprocesses. They differ only in financial development parameters governing the pledgeability and the pricing of external borrowing. Three counterfactual experiments isolate the sources of the asymmetry. First, eliminating interest rate volatility reduces the coefficient of variation of trend growthintheemerging marketcalibrationbyabout30percent while havingnegligibleeffectsin theadvancedeconomycalibration. Second,adjustingonlyfinancialdevelopmentparameters,the fraction of firm value that can be collateralized and the sensitivity of borrowing costs to volatility,substantiallynarrowsthegapintrendvolatilitybetweenemergingandadvancedeconomies. Third, differences in pledgeability account for roughly 60 percent of emerging markets’ excess trend volatility, with the remaining share reflecting higher and more volatility sensitive risk pre- 1OuremphasisonfirmvaluesisconsistentwiththecrosscountryevidenceinLakdawalaetal.(2021). Theyshow thatrisingU.S.monetarypolicyuncertaintypredictsdecliningassetvaluationsabroad,especiallyinemergingmarket economies. 3

mia. The model also matches observed patterns in the cross sectional distribution of growth rates. During periods of elevated U.S. interest rate volatility, the average trend growth falls in emerging markets and its dispersion across these countries rises sharply. Advanced economies exhibit stable, low dispersion throughout. When we simulate many economies facing common global financial shocks but idiosyncratic productivity draws, the model reproduces this pattern. Dispersion in trend growth spikes during high volatility periods in our emerging market model, as nonlinear amplification varies with countries’ idiosyncratic states, but remains largely flat in the advancedeconomyversion. Ourfindingsunderscorethecentralroleoffinancialdevelopmentinshapingthelong-runconsequencesofglobalfinancialrisk. Volatilityinglobalfinancialconditionsisalargelyunavoidable featureoftheworldeconomy. Ourresultsshowthatthewaythisvolatilityinteractswithdomestic financial frictions determines whether it generates just temporary business cycle fluctuations or leaves permanent scars on productivity. Strengthening financial systems, through stronger legal enforcement, deeper financial markets, and more robust institutions, is, therefore, central to ensuringthatperiodsoffinancialturbulencedonottranslateintopersistentstagnation,especially foremergingmarkets. RelatedLiterature. Ourcontributionintersectsthreeresearchareas. First,volatilityshocksinopeneconomies. Classicopeneconomymodels(Mendoza,1991;Neumeyer and Perri, 2005; Uribe and Yue, 2006) studied how fluctuations in world interest rate levels affect emerging markets, often through working capital constraints or exogenous correlation with productivity. More recent work examines second-moment shocks directly. Ferna´ndez-Villaverde etal.(2011)demonstratethatincreasinginterestratevolatilityproducesquantitativelynoticeable effects on the level of activity through precautionary savings. Carrie`re-Swallow and Ce´spedes (2013) show uncertainty shocks generate larger output contractions in emerging than advanced economies. Bhattaraietal.(2020),Reyes-HerolesandTenorio(2020),andRochetal.(2025)extend this evidence to U.S. policy uncertainty and financial channels. Gruss and Mertens (2009) and Johri et al. (2022) emphasize volatility’s role in Sudden Stops. Our empirical contribution shows second-moment shocks affect not just short-run output but also the trend component of growth. We measure this using multiple uncertainty proxies, including the VIX, macroeconomic uncer- 4

tainty(Juradoetal.,2015),andstochasticvolatilityinTreasuryyields,andfindrobustevidenceof persistenttrendeffectsinemergingmarkets. Ourtheoreticalcontributionexplainsthisthrougha mechanismlinkingvolatilitytofirmvaluationandinnovation. Second, the global financial cycle. Rey (2015) argues global risk drives capital flows and underminesmonetaryautonomy. Miranda-AgrippinoandRey(2020)showU.S.monetarypolicyshocks propagateworldwide,whileCharietal.(2022)documentdifferentialeffectsacrossfinancialinstitutions. Zhou(2024)andGerdingetal.(2014)highlightheterogeneityininvestortypesandcapital market structure as source of heterogeneous effects. We isolate a distinct channel: internal financialfrictionsamplifyvolatility’simpactonfirminvestmentandproductivity,soidenticalexternal shocksgeneratedivergentoutcomes. Third, productivity trends and endogenous growth. Aguiar and Gopinath (2007) argue that a defining feature of emerging market cycles is large variation in trend growth—so that much of cyclical volatility reflects shocks to the trend rather than transitory deviations around a stable trend. Cerra and Saxena (2008) document that crisis events, which are more frequent in emergingmarketeconomies,arefollowedbyhighlypersistentoutputlossesratherthanfullrecoveries, consistent with long-lived level effects. Garcia-Cicco et al. (2010) push the interpretation toward finance: whenthemodelisdisciplinedwithlongsamples,addingfinancialfrictionsandcountrypremium shocks markedly improves fit and assigns a smaller role to nonstationary productivity shocks.2 Boz et al. (2011) provide a complementary information-based view, emphasizing learningaboutthetrend-cycledecomposition. Webridgetheseviews: stationaryglobalfinancialshocks, especially changes in risk (second moments), can generate persistent movements in trend activity throughfinancialamplificationandendogenousproductivity. Abroaderlessonisthatwhenproductivityisendogenous,business-cycleshockscanspillinto lower-frequency movements in activity; Comin and Gertler (2006) formalize this medium-run propagation through endogenous productivity dynamics, while Queralto (2020) offers an early application of their model to emerging market crisis. Our model builds on the dynamic version of Klette and Kortum (2004) developed by Ates and Saffie (2021) and embeds it in a collateralconstraint Sudden Stop framework in the spirit of Mendoza (2010). Closest in spirit, Benguria etal.(2022)studyhowSuddenStopsreshapefirm/productdynamics(includingexportmargins) 2ChangandFerna´ndez(2013)findsimilarconclusionsusingquarterlydataandBayesianestimation. 5

and thereby generate persistent output and productivity losses, through a trade and reallocation mechanism distinct from our collateral-based innovation channel. Gornemann et al. (2025) developtheroleofR&D-drivenproductivitydynamicsforrealexchangerates,emphasizingtechnology diffusion rather than our collateral-based innovation channel. Benigno et al. (2025) show that secular interest rate declines slow growth through misallocation. We add to this literature by focusing on the role of second-moment shocks in generating effects on the trend of activity in smallopeneconomies.3 Section2presentstheempiricalevidence. Section3developsthemodel. Section4presentsthe quantitativeanalysis. Section5concludes. 2 Empirical Evidence: Volatility and Persistent Output Losses ThissectionprovidesempiricalevidencethatU.S.interestrateuncertaintyhaspermanenteffects on economic performance across countries. Using a multivariate panel time-series framework, weestimatetheimpactofmonetarypolicyuncertaintyshocksonthestochastictrendcomponents of GDP, consumption, and investment growth for both emerging and advanced economies. We find a clear pattern: uncertainty shocks systematically reduce the stochastic trend in emerging markets, while advanced economies are much less affected. This divergence is consistent with a volatility-drivenpropagationmechanismthatisstrongerinfinanciallyconstrainedenvironments. 2.1 Intuitionfortheapproach In principle, to capture long-lasting effects of uncertainty shocks on economic activity, it would beenoughtoregressGDPgrowthonmanylagsoftheshocksandcumulatethecoefficients,asin a local projection. We augment this approach with two restrictions that strengthen inference on low-frequencycomponents. First, consistent with both exogenous and endogenous growth models, we assume that GDP, 3Inclosedeconomies,MoranandQueralto(2018),GargaandSingh(2021),andJorda`etal.(2024)provideevidence thatmonetarypolicyshocksgeneratepersistentoutputeffectsasfirmsadjustinnovation. 6

consumption,andinvestmentincountry jshareacommonstochastictrendlevel, (cid:32) (cid:33) t ∑ A = exp aˆ , j,t j,s s=−∞ where aˆ denotes the time-varying trend growth rate.4 As a result, the growth rates of log GDP j,s ( ∆y ),logconsumption( ∆c ),andloginvestment( ∆i )canbewrittenas j,t j,t j,t         ∆y α ∆y˜ 1 j,t j j,t                   ∆c j,t   =   α j   +  ∆c˜ j,t   +  1  aˆ j,t .         ∆i α ∆i˜ 1 j,t j j,t Here α is the country-specific average growth rate. The terms ∆y˜ , ∆c˜ , and ∆i˜ are stationary j j,t j,t j,t components capturing the cycle, while aˆ captures permanent, common movement in the levels j,t ofthethreeseriesthatwelabelthestochastictrendgrowthrate. Second,wemodelthetrendgrowthrateasthesumof(i)aresidualpersistentcomponentand (ii)adistributed-lageffectofglobaluncertaintyshocks: aˆ = a + ∑ nσ η σMU, j,t j,t s t−s s=0 where σMU denotes the monetary policy uncertainty shock at time t, and a captures all other t j,t movementsintrendgrowth. The{η }areadirectestimateoftheimpulseresponseofthegrowth s rate of the trend to a monetary policy uncertainty shock. The cumulative sum ∑t η , therefore, s=0 s measures the effect of an uncertainty increase t periods ago on the level of the stochastic trend in logs. 2.2 Dataandproxiesforinterestrateuncertainty We compile quarterly macroeconomic data from 1993Q1 to 2019Q4 for two country groups. The emergingmarketsampleincludesArgentina,Brazil,Chile,Mexico,thePhilippines,SouthAfrica, andTurkey. TheadvancedeconomygroupconsistsofAustralia,Canada,Denmark,NewZealand, Norway,andSweden. WecollectrealGDP,consumption,andinvestmentfromtheIMF’sInterna- 4Manyapproachesimposerelatedcommon-trendrestrictions;seeBocolaandGornemann(2013)foradiscussion. 7

tional Financial Statistics (IFS) database.5 Due to missing observations, the panel is unbalanced. OurselectionofcountriesfollowsVicondoa(2019),whichisfairlyrepresentativeoftheemerging marketbusinesscycleliterature. Our baseline proxy for interest rate uncertainty uses the text-based monetary policy uncertaintyindexinHustedetal.(2020). Followingtheirapproach,weconstructaninnovationtomonetarypolicyuncertaintythatisorthogonaltocontemporaneousU.S.macroeconomicandfinancial conditions.6 ThisinnovationcapturesunexpectedshiftsinperceivedU.S.interestrateriskconditionalonthosefundamentals. Inrobustnesschecks,wereplacethisproxywith: (i)theVIXindex;(ii)macrouncertaintyfrom Jurado et al. (2015); and (iii) the stochastic volatility of real U.S. short rates following Ferna´ndez- Villaverde et al. (2011). These alternative proxies capture broader dimensions of global financial uncertaintybeyondU.S.monetarypolicyalone. 2.3 Panelstate-spacemodel Weestimateapanelstate-spacemodelthatseparateslow-frequencytrendmovementsfromhigherfrequencycyclicaldynamics. Foreachcountry j,themeasurementequationis            ∆y α ∆y 1 1 j,t j j,t−1               ∆c j,t    =    α j    +Φ      ∆c j,t−1    −    1    aˆ j,t−1    +    1    aˆ j,t +B·Z t US+Σ j (cid:101)m j,t ,            ∆i α ∆i 1 1 j,t j j,t−1 where Φ governsthedynamicsofthestationarycyclecomponent,and Σ isa3×3diagonalmatrix j ofcountry-specificmeasurementshockstandarddeviations. Thetrendcomponentis aˆ = a + ∑ nσ η σMU, j,t j,t s t−s s=0 a = ρ a +σ (cid:101)a . j,t a j,t−1 j,a j,t In ZUS we control for current and lagged U.S. GDP growth and the excess bond premium t 5Weusegrossfixedcapitalformationinsteadofcapitalformationasourinvestmentmeasuretoincreasethenumber ofperiodscoveredinoursample. 6SeeappendixandHustedetal.(2020)fordetails. 8

from Gilchrist and Zakrajsˇek (2012). We also include n growth rates of our uncertainty series σ to capture transitory co-movement at business-cycle frequencies. This specification imposes a separation between (i) effects of uncertainty on the stochastic trend (through η ) and (ii) highers frequencyeffectsabsorbedby ZUS. t Shocks ((cid:101)m,(cid:101)a ) are drawn from a joint normal distribution. The deterministic trend α and j,t j,t j shockvariancesarecountryspecific,whiletheremainingparametersarecommonacrosscountries ineachpanel,astandardrestrictioninpanelmodelsforsmallopeneconomies(e.g.UribeandYue (2006), Akıncı (2013), Vicondoa (2019)). As the effects of uncertainty shocks are often found to buildovertime,wesetn = 12quarterstocaptureeffectsuptothreeyears.7 σ Estimation proceeds by maximum likelihood using the Kalman filter. Standard errors are obtainedviamontecarlosimulations,re-estimatingtheentirestate-spacemodelineachreplication, soconfidenceintervalsforimpulseresponsesaccountforuncertaintyaboutboththefilteredtrend anditsresponsetouncertaintyamongotherthings. TheuncertaintyshockσMU iscommonacross t all countries in a given panel: each emerging and advanced economy is exposed to the same sequence of global monetary policy uncertainty innovations. Differences in responses therefore reflectdifferencesininternalpropagation,notdifferencesintheshockprocessesthemselves.8 2.4 Results Figure1showstheestimatedcumulativeimpulseresponseofthestochastictrendtoaone-standarddeviation monetary policy uncertainty shock, ∑t η . Advanced economies exhibit small and s=0 s typically statistically weak responses. Emerging markets instead experience a sharp and persistentdeclineinthestochastictrend. Becausetheunrestricted η canbenoisyatlongerhorizons, wealsoreportresultsimposinga s flexiblefunctionalformonthelagprofileofη . Thisrestrictionisaregularizationdevice: itisnot s requiredforthequalitativeresult,emergingmarketeconomiesrespondalotmorethanadvanced economies,butitproducessmootherimpulseresponsesandreducessensitivitytohigh-frequency variation being attributed to the trend component. Following Barnichon and Matthes (2018), we (cid:16) (cid:17) set η = aexp −s−b and estimate a,b,c jointly with the other parameters. The restricted estis c 7Weverifiedthatourresultsarerobusttodifferentlengthsofthiswindow. 8WhenconstructingstandarderrorsweincorporatethatallcountriesfacethesamesequenceofU.S.observations. 9

matesareplottedassolidlinesinFigure1andareusedforthebaselineconfidencebands. Figure1: TrendResponsetoMonetaryPolicyUncertaintyShock 0 0 -0.1 -0.1 -0.2 -0.2 -0.3 -0.3 -0.4 -0.4 -0.5 -0.5 -0.6 -0.6 -0.7 -0.7 0 2 4 6 8 10 12 0 2 4 6 8 10 12 Quarter Quarter (a) AdvancedEconomies (b) EmergingMarketEconomies Notes: Thefigurereportsthecumulativeeffectofamonetarypolicyuncertaintyshockonthetrendaftersquarters(∑s t=0 ηt). The solidlineshowsthepointestimatewhenthefunctionalformforηsisimposed;bandsrepresentone-standard-deviationconfidence intervals.Dotsdenotethepointestimatewhennofunctionalformisimposed. Intermsofmagnitude,ata12-quarterhorizontheestimateddeclineinEMEsisbetweenabout 25and65basispoints,dependingonwhetherweimposeaparametricrestrictiononthelagprofile of η (about 25 basis points under the restricted specification; about 65 basis points under the s unrestrictedestimates).9 Figure2confirmsthatthefindingsarerobustacrossalternativeuncertaintyproxies. Wereplace the monetary policy uncertainty innovation with: (1) the VIX index; (2) macro uncertainty from Jurado et al. (2015); and (3) the stochastic volatility of real U.S. short rates following Ferna´ndez- Villaverde et al. (2011).10 We focus on the parametric case in the figures. While magnitudes vary across proxies, the ordering is stable: responses are notably larger for emerging markets than for advanced economies. In addition, for proxies more tightly connected to interest rate uncertainty, thelong-horizoneffectonadvancedeconomiesisfairlyclosetozero.11 9It is worth keeping in mind that ∑t s=0 ηs is the percent deviation in the level of the estimated stochastic trend relativetobaselineathorizontafteranuncertaintyshock. 10ThevolatilitymeasureemployedinFigure2isthestochasticvolatilityoftheU.S.realinterestrate(Ferna´ndez- Villaverdeetal.,2011).AppendixA.1describestheestimationprocedureandresults. 11Figure12intheappendixprovidestheconfidenceintervalsforeachcase. 10

Figure2: TrendResponsetoUncertaintyShocks,Robustness: ShockProxies Baseline 0 0 Macro Uncertainty Volatility VIX -0.1 -0.1 -0.2 -0.2 -0.3 -0.3 -0.4 -0.4 -0.5 -0.5 -0.6 -0.6 -0.7 -0.7 0 2 4 6 8 10 12 0 2 4 6 8 10 12 Quarter Quarter (a) AdvancedEconomies (b) EmergingEconomies Notes:Thisfigureplotsthecumulativeresponseoftheestimatedstochastictrendtoaone-standard-deviationglobaluncertaintyshock foradvancedeconomies(panela)andemergingeconomies(panelb). The“Baseline”linereproducestheresponsetothemonetary policyuncertaintyinnovationusedinFigure1.Theotherlinesreportresponseswhentheuncertaintyshockisproxiedby(i)theVIX index,(ii)macroeconomicuncertaintyfromJuradoetal.(2015),and(iii)thestochasticvolatilityoftheU.S.realshortratefollowing Ferna´ndez-Villaverdeetal.(2011).AllresponsesareestimatedundertheparametricrestrictiononηsandincludethesamesetofU.S. controlsasinthebaselinespecification. 2.5 Empiricalestimatesoftrendgrowth Wenowexaminethecross-sectionaldynamicsofestimatedtrendgrowthacrosscountries. Figure 3 displays the cross-sectional average and standard deviation of country-specific trend growth, demeanedwithincountry, foremergingmarketandadvancedeconomiesoverquarterswithfull data coverage. For each quarter, we subtract each country’s sample mean of the filtered trend growthrateandcompute,withineachgroup,thecross-sectionalaverageanddispersion.12 Two patterns stand out. First, average trend growth among advanced economies is relatively stable. Emerging markets, by contrast, exhibit much larger fluctuations in trend growth, especially during and after the Global Financial Crisis. Second, Emerging Market economies show persistently greater cross-sectional dispersion, with a sharp spike during 2008–2009 that remains elevatedforyears. 12Figure3usesquarterlydatafrom2000Q3onward,whichisthefirstdateatwhichboththeadvancedandemerging economysamplesaresimultaneouslybalanced. 11

Figure3: Cross-SectionalMomentsoftheStochasticTrendGrowthRate 1 0 1− 2− 3− 2004q2 2007q2 2010q2 2013q2 2016q2 2019q2 Emerging Advanced (a) Cross-SectionalAverage 2 5.1 1 5. 0 2004q2 2007q2 2010q2 2013q2 2016q2 2019q2 Emerging Advanced (b) Cross-SectionalStandardDeviation Notes: This figure shows cross-sectional moments of the estimated country-specific stochastic trend growth rates for advanced economiesandemergingmarketeconomies. Ineachquarter, wesubtracteachcountry’saveragetrendgrowth(overthesample) fromitsfilteredtrendgrowthrateandthencompute,withineachgroup,thecross-sectionalaverage(panela)andcross-sectionalstandarddeviation(panelb).Theunderlyingtrendsareobtainedfromthepanelstate-spacemodeldescribedinSection2,usingcommon globaluncertaintyshocksandU.S.controlsforallcountries. These patterns are consistent with the model mechanism developed in Section 4: common volatility shocks generate disproportionately heterogeneous outcomes in financially constrained economies. In Section 4 we show that the calibrated model reproduces both the lower average trendgrowthandthehighercross-sectionaldispersionofemergingmarketsinperiodsofelevated U.S.interestratevolatility. 3 A Small Open Economy with Volatility-Driven Trend Dynamics 3.1 ModelOverview We develop a small open economy model in which volatility in global interest rates, beyond changes in their level, drives persistent fluctuations in long-run productivity growth. The mechanism operates through an occasionally binding collateral constraint on borrowing and endogenous firm dynamics. A representative household owns a continuum of intermediate good producersandcanborrowexternallybypledgingsharesinfirmsascollateral. Theborrowingterms depend not only on the level of the global interest rate but also on its volatility, introducing a channelthroughwhichfinancialconditionsaffectgrowth. The engine of long-run growth is creative destruction among intermediate good producers. 12

Firms expand, contract, or exit through innovation and competition following the framework of Klette and Kortum (2004). These firms sell differentiated intermediate goods to a final good producer,whichaggregatesinputsintoasingletradablefinalgoodunderanaggregateefficiency (TFP)shock. OurmodelextendstraditionalendogenousSuddenStopframeworksinthreekeyways. First, collateral is based on the value of firms’ future profits, directly tying innovation dynamics to borrowingcapacity. Second,endogenoustechnicalchangedeterminestheevolutionoffirmvalue through productivity-enhancing investment and firm entry. Third, both the level (first moment) and volatility (second moment) of international interest rates influence firm dynamics, collateral values, and innovation incentives. Together, these elements generate an endogenous link from second-momentfinancialshockstopersistenttrendgrowthoutcomes. Thekeyequilibriumobjects are the household’s stochastic discount factor and the economy-wide creative destruction rate, whichtogetherdeterminetheevolutionofaggregateproductivityandthusthetrend. 3.2 Households The representative household chooses consumption C and non-state-contingent bond holdings BH each period. Labor supply L¯ is inelastic and remunerated at wage w. In addition to labor income,thehouseholdreceiveslump-sumtransfers T fromincumbentfirms,whichitowns. Thehouseholdsolves: max ∑ ∞ βtE (cid:20) 1 (cid:2) C(st) (cid:3)1−γ (cid:12) (cid:12)s (cid:21) (1) C(st),BH(st) t=0 1−γ (cid:12) 0 subjectto: C(st)+qˆ(st)BH(st) ≤ w(st)L¯ +BH(st−1)+T(st), (2) qˆ(st)BH(st) ≥ −φV(st). (3) Here qˆ(st) denotes the price of debt, defined as the reciprocal of the gross interest rate faced by households, Rˆ(st) ≡ 1/qˆ(st). The household faces a collateral constraint: it cannot borrow more thanafractionφofthetotalvalueofincumbentfirmsV(st),whichitowns. This structure departs from traditional models of endogenous financial crises (Bianchi and 13

Mendoza, 2018), where collateral is typically tied to tradable income or physical assets. Instead, consistentwithprivateequityandventurecapitalpractices,thehouseholdusesthevalueoffuture firmcashflowsascollateral. Thisformulationalignswithrecentempiricalevidenceonearningsbased borrowing constraints (Lian and Ma, 2021; Drechsel, 2023), and mirrors credit assessment practicesintraditionalbanking,whereprojectvaluationsandexpectedcashflowsdisciplinecredit limits. 3.3 FinancialIntermediaries Householdsborrowfromcompetitive,risk-averseinternationalfinancialintermediaries. IntermediariesfaceastochasticgrossfundingcostRandlendtohouseholdsatpriceqˆ. Thegrossfunding costevolvesaccordingtoanAR(1)processwithstochasticvolatility: (cid:16) (cid:17) R(st)−R¯ = ρ R(st−1)−R¯ +σ (st)ω(st), ω(st) ∼ N(0,1), (4) R R log (cid:0) σ (st) (cid:1) = (1−ρ )µ +ρ log (cid:0) σ (st−1) (cid:1) +η ν(st), ν(st) ∼ N(0,1), (5) R σ σ σ R σ where R¯ denotes the average funding cost, ρ and ρ govern the persistence of the funding cost R σ anditsvolatility,andσ (st)denotestheconditionalstandarddeviationofthefundingshock. R Intermediariespricehouseholddebtbysolving: (cid:104) (cid:105) max E mˆ(st+1)b(st) | st −qˆ(st)b(st), (6) b(st) where mˆ(st+1) istheintermediaries’stochasticdiscountfactor. Tocapturetheirrisksensitivityto volatility,weassume: 1 mˆ(st+1) = , R(st+1)+ι +ι (σ (st+1)−σ¯ ) 0 1 R R where ι captures a baseline spread and ι > 0 captures the degree to which spreads widen in 0 1 responsetohigherinterestratevolatility. Thisreduced-formspecificationisconsistentwithmodelsofintermediaryfrictionsunderstochastic volatility, such as Gertler and Karadi (2011) and Gertler and Kiyotaki (2015). Appendix B presents a formal model with these features, showing how increased volatility in funding costs raisesloanspreads. Alternatively,thisstructureisconsistentwithambiguityaversion(seeBianchi 14

et al. (2018a)), and similar reduced-form pricing structures have been employed in Arellano and Ramanarayanan(2012),Bianchietal.(2018b),Johrietal.(2022),andHegartyetal.(2023). Thesolutionto(6)yieldsthebondpricingfunction: (cid:20) (cid:12) (cid:21) qˆ(st) = E 1 (cid:12) (cid:12)st . (7) R(st+1)+ι +ι (σ (st+1)−σ¯ ) (cid:12) 0 1 R R Expectedspreadsthereforerisewithvolatility,evenwhentheconditionalmeanofRisunchanged. Foreignintermediaries’pricingruledeterminesthewedgebetweentheexogenousworldfunding cost and the domestic borrowing rate, while households discount cash flows using their own stochasticdiscountfactor. Thetwoobjectscapturedifferentsourcesofriskandarelinkedthrough thebondpriceqˆ(st). 3.4 FinalGoodProducer Λ The final good producer aggregates a mass of differentiated intermediate goods into a single homogeneousfinaloutputusingaCobb–Douglas-liketechnology: 1 (cid:90) Λ lnY(st) = z(st)+ lny (st)di, (8) Λ i 0 whereY(st)denotesthefinalgood,y (st)isthedemandforintermediatevarietyi,andz(st)isan i aggregateefficiency(TFP)shock. TheaggregateefficiencyshockfollowsanAR(1)process: lnz(st) = ρ lnz(st−1)+(cid:101) , (cid:101) ∼ N(0,η2), z t t z whereρ governspersistenceandη thevolatilityofaggregateproductivityinnovations. Thefinal z z good is the only tradable output in the economy and serves as the numeraire for international borrowingandlending. 15

3.5 IntermediateGoodProducers Acontinuumofintermediategoods, indexedby i ∈ [0, Λ], isproducedbyfirmsoperatingunder monopolisticcompetition. Eachintermediategoodisproducedaccordingto: y (st) = q (st)l (st), (9) i i i whereq (st)denotestheefficiency(productivity)ofvarietyiandl (st)denoteslaborinput. i i The firm with the lowest marginal cost for each variety is the technological leader, earning monopoly rents through Bertrand competition against the second-best producer. Firms can operatemultipleproductlinessimultaneously,expandingbyinnovatingintoadditionalvarietiesor contractingwhenlosingtechnologicalleadership. Firmsexitthemarketiftheylosecontrolofall their product lines. This structure generates endogenous firm dynamics through innovation and creativedestruction,linkingmicro-levelcompetitiontomacroeconomicproductivitygrowth.13 3.5.1 InnovationbyIncumbents The productivity of each intermediate good evolves endogenously through innovation. Innovationsarisewheneitheranincumbentorapotentialentrantsuccessfullyimprovesupontheexisting technology for producing a given variety. When an innovation occurs for variety i, the new technologicalleadergainsaccessto: q (st+1) = (1+σ)q˜ (st), i i whereq˜ (st)denotesthepreviousleader’stechnologylevelandσ > 0istheinnovationstepsize. i Incumbent firms can actively attempt to innovate and capture new product lines. Following thediscrete-timeversionofAtesandSaffie(2021)basedonKletteandKortum(2004),afirmwith 13OurquantitativeresultsdonothingeonthespecificKlette–Kortumstructure. Anyforward-lookingendogenous growthmodelinwhichfirmsinvestininnovationandcreativedestructiongeneratesasimilarlinkbetweenfirmvalues, innovation,andthetrend. Weadoptthisframeworkbecauseitcanbedisciplinedusingfirm-leveldynamicssuchas thedistributionoffirmsizesandexitrates. 16

nproductscanallocateresearchlabor L (st)togenerateaper-productsuccessprobability: r x(st) = ξ (cid:18) L r (st) (cid:19)θ ≡ ξ (cid:0) l (st) (cid:1)θ , r n wherel (st)denotesresearchlaborperproduct. r Theexpansionanddestructionofafirm’sproductportfoliofollowbinomialprocesses. Specifically,afirmwithnproductshasprobability: (cid:18) (cid:19) n B(k,n,x(st)) = x(st)k(1−x(st))n−k, (10) k ofwinningknewproductsthroughinnovation,andprobability: (cid:18) (cid:19) n B(k˜,n, ∆(st)) = ∆(st)k˜ (1−∆(st))n−k˜ , (11) k˜ oflosingk˜ productstocreativedestruction,where ∆(st)istheeconomy-widecreativedestruction rate. Incumbent firms face a fixed innovation cost F(st) per product line successfully innovated, whichscaleswiththeeconomy’ssizeas F(st) = A(st)F. Giventhesedynamics,theincumbent’svaluefunctionwithnproductssolves: (cid:20) (cid:18) x (st) (cid:19)1/θ (cid:21) V (st) = max n π(st)−w(st)α n −(1−α)x (st)F(st) n n xn (st) ξ (cid:34) (cid:35) n n (cid:12) +E m(st+1) ∑ B(k˜,n, ∆(st)) ∑ B(k,n,x (st))V (st+1)(cid:12)st . (12) n n−k˜+k (cid:12) k˜=0 k=0 Here π(st) denotes per-product profits, w(st) the wage, and m(st+1) the household’s stochastic discountfactor. Becausefirmsareatomistic,thetwobinomialprocesses(expansionanddestruction)areindependent, and transitions over firm size are separable. A firm with n products can thus transition withinoneperiodtoanysizein[0,2n].14 We also allow for a depreciation rate δ of each product line’s technology, capturing gradual efficiency losses or evolving consumer preferences. Depreciation affects all producers symmet- 14SeeAppendixDforadetailedderivationoffirmsizedistributiondynamics. 17

rically within a variety and thus does not alter the relative technology gap between leaders and followers. 3.6 EntryofNewFirms Firmentryismodeledanalogouslytoincumbentinnovation. Let M(st) ∈ [0,1]denotetheaggregateentrepreneurialeffortdirectedtowardstartingnewbusinesses. EntrepreneursinvestκM(st) unitsoflaborandsuccessfullycreateanewsingle-productfirminthenextperiodwithprobability M(st)ν. Aswithincumbentinnovation,entryentailsafixedcostF(st),whichscaleswiththeeconomy’s size. Entrepreneurschoose M(st)tomaximizeexpectednetreturns: (cid:104) (cid:12) (cid:105) max (cid:0) M(st) (cid:1)νE m(st+1)V (st+1)(cid:12)st −ακM(st)w(st)−(1−α) (cid:0) M(st) (cid:1)ν F(st). (13) 1 (cid:12) M(st) Here V (st+1) is the expected value of operating a single product line next period. The optimal 1 solution M∗(st) determines the endogenous entry rate of new firms. Together with incumbent innovation, entry shapes the creative destruction rate and thus the economy’s long-run growth dynamics. 3.7 EquilibriumCharacterization Theparsimonyofthemodelenablesaclearmappingbetweeninterestratevolatility,firminnovation,andtheendogenousevolutionofproductivity. HouseholdDiscounting. Thehouseholdstochasticdiscountfactoris: C(st+1)−γ m(st,st+1) = β . (14) C(st)−γ−φµ(st) Here µ(st) is the Lagrange multiplier on the collateral constraint (3). The collateral constraint affectsdiscountingthroughthewedgeµ(st),becausebindingconstraintsraisethemarginalvalue ofrelaxingborrowinglimitsandincreasetheeffectivediscountrateappliedtofuturefirmpayoffs. 18

IntermediateGoodProduction. Intermediategoodproducersfaceaunit-elasticdemandcurve: Y(st) y (st) = , (15) i Λp (st) i where p (st) is the price of variety i. Under Bertrand competition, per-product profits and labor i demandbecomeindependentofthevariety-specificproductivityq (st). Specifically: i σ Y(st) π(st) = , (16) 1+σ Λ Y(st) l(st) = . (17) Λw(st)(1+σ) Becausefirm-leveldecisionsareindependentofindividualq ,firmvalueisproportionaltothe i numberofproducts: V (st) = nV (st). n 1 FirmValueandInnovation. Givenproportionality,thevalueofcontrollingasingleproductline satisfies: V (st) = max (cid:26) π(st)−w(st)α (cid:18) x(st) (cid:19)1/θ −(1−α)x(st)F(st)+E (cid:104) m(st,st+1) (cid:0) 1−∆(st)+x(st) (cid:1) V (st+1) (cid:12) (cid:12)st (cid:105) (cid:27) . 1 1 (cid:12) x(st) ξ (18) Theoptimalincumbentinnovationeffortperproductlineis: (cid:34) θ E(cid:2) m(st,st+1)V (st+1)−(1−α)F(st) | st (cid:3)(cid:35)θ/(1−θ) x ∗(st) = ξ1/θ 1 . (19) α w(st) Similarly,themassofnewentrantfirmsis: (cid:34) ν E(cid:2) m(st,st+1)V (st+1)−(1−α)F(st) | st (cid:3)(cid:35)1/(1−ν) M ∗(st) = 1 . (20) ακ w(st) Inequilibrium,incumbentinnovationandentryjointlypindownthecreativedestructionrate, andmovementsindiscountingandinthenormalizedvalueoffuturefirmpayoffspropagateinto ∆(st)through(19)and(20). 19

Productivity Growth. The aggregate creative destruction rate combines entry and incumbent innovation: (M∗(st))ν ∆(st) = +x ∗(st). (21) Λ Aggregateoutputevolvesaccordingto: Y(st) = ez(st) A(st)l(st), (22) where A(st)istheendogenousproductivityindex: 1 (cid:90) Λ lnA(st) = lnq (st)di. (23) Λ i 0 Thelawofmotionforproductivitysatisfies: ln(A(st,st+1))−ln(A(st)) = ∆(st)ln(1+σ)+ln(1−δ). (24) Productivity growth can be negative if creative destruction is insufficient to offset depreciation. Theendogenousproductivityindex A(st)correspondstothecommonstochastictrendestimated inSection2: changesin A(st)mapintopersistentchangesinthelevelsofGDP,consumption,and investment. Labor Market and Wage Determination. Combining (22) and (17), the equilibrium wage satisfies: ez(st)A(st) w(st) = . (25) Λ(1+σ) HouseholdOptimalityConditions. Thehousehold’sfirst-orderconditionsare: (cid:104) (cid:105) C(st)−γ = µ(st)+βRˆ(st)E C(st+1)−γ | st , (26) C(st)+qˆ(st)BH(st) ≤ w(st)L¯ +BH(st−1)+Λe(st)−καM(st)w(st)−(1−α)(M(st))νF(st), (27) 20

where e(st) captures firm net earnings per product, derived from (18). The collateral constraint remains: qˆ(st)BH(st) ≥ −φ ΛV (st), (28) 1 whereV(st) = ΛV (st)isthetotalcollateralvalue. 1 Stationarity and Solution. Appendix E renders the model stationary by normalizing growing variablesbytheproductivityindexA(st)andsummarizesthefullsystemofstochasticequilibrium conditions. 3.8 TrendDynamicsandInterestRates Equation(24)showsthatstationarydistortionsaffectingtheendogenouscreativedestructionrate ∆(st) can generate permanent shifts in the level of the productivity index A(st), defined in (23). Since A(st) governs the long-run level of the economy, fluctuations in ∆(st) generate hysteresis in output and consumption. In this class of models, stationary shocks can thus produce lowfrequency(trend)dynamicsthroughinternalpropagation. Understanding these endogenous trends requires analyzing how aggregate shocks affect the determinantsofcreativedestruction—firmentry andincumbentinnovationdecisions, characterized by (19) and (20). Two endogenous objects mediate this transmission: (i) the household’s stochastic discount factor, and (ii) the expected future value of a product line relative to the currentwage. EffectsofTFPShocks. ConsiderfirstaTFPshock,z(st). Asourmodelisasmallopeneconomy facinganexogenousinterestrate,TFPshockshavelittleeffectonintertemporaldiscountinginunconstrainedstates. Meanwhile,equation(25)showsthatapositiveTFPshockraiseswages,which increasesthedenominatorofthenormalizedvalueoffuturefirmpayoffs. Atthesametime,profits and innovation costs scale with aggregate activity. As a result, when the collateral constraint is slack, TFP shocks generate limited movements in the normalized incentives that govern x∗(st) 21

and M∗(st).15 When a sufficiently adverse TFP realization pushes the economy into the constrained region, however, the Fisherian deflation channel becomes operative: falling asset values tighten the borrowing constraint, raise the marginal value of relaxing borrowing limits (via µ(st)), and depress firm values and innovation incentives. In this case, TFP shocks can have persistent effects on the trendbytriggeringbindingfinancialconstraints. Effects of Interest Rate Shocks. By contrast, shocks to the international borrowing rate faced by households directly affect discounting without necessarily changing contemporaneous firm profits or innovation costs.16 An increase in financing costs raises the gross borrowing rate Rˆ(st) and,through(26)–(14),increasestheeffectivediscountrateappliedtofuturefirmpayoffs. Lower firmvaluesreducecollateral,tightenborrowinglimitswhenconstraintsarerelevant,anddepress innovationandentryincentivesvia(19)and(20). CollateralConstraintsandAmplification. BothTFPandinterestrateshockscaninfluencetrend growth through collateral constraints. When the borrowing constraint (28) binds, households are forced to delever, lowering current consumption and raising the marginal value of relaxing borrowinglimits. Thisreducesfirmvalues,tightensborrowingconditionsfurther,andcantrigger aFisherianspiral. Accordingly,largeadverseshocks,especiallythosethatmovetheeconomyinto the constrained region, can have persistent effects on the trend through endogenous movements in ∆(st). TheRoleofVolatilityShocks. Finally,evenabsentrealizedinterestrateshocks,volatilityshocks matter. Consider a state in which the borrowing constraint is slack. An increase in interest rate volatility, σ (st), raises the likelihood of large future movements in the borrowing rate. Because R the collateral constraint is occasionally binding, the effects of future tightening and easing are not symmetric: large rate hikes can sharply reduce firm values and push the economy into the 15AfixedresourcecostF(paidingoodsratherthanlabor)breaksexactscaleinvariance,sinceitdoesnotscaleonefor-onewithwagesandaggregateactivity. Quantitatively, thiseffectissmallinourcalibrationandismostrelevant whenxandMarealreadylow(i.e.,nearorinsidetheconstrainedregion),whereFcancontributetoamplificationby furthercompressingcashflowsandfirmvalues. 16Weabstractfromworkingcapitalconstraints,whichwouldotherwisetransmitinterestrateshocksintowagesand operatingcosts. Withworkingcapitalfrictions,interestrateshockswouldaffectwagessimilarlytoTFPshockswith, therefore,limitedadditionaleffectsongrowth. 22

constrained region, while large cuts cannot further relax an already slack constraint. As a result, highervolatilitylowersexpected firmvaluesandreducesinnovation andentryincentivestoday, evenholdingfixedtheconditionalmeanofinterestrates. Thiseffectisstrongerineconomiesthat spendmoretimeneartheconstrainedregion, becausevolatilityraisestheprobabilityofentering statesinwhichtheFisherianamplificationmechanismisoperative. 4 Quantitative Analysis In this section, we show that the model replicates the differential sensitivity of the productivity trendtointerestratevolatilityinemergingandadvancedeconomies. Wefirstcalibratethemodel toMexico. Wethenconstructanadvancedeconomycalibrationbychangingonlytheparameters thatgovernfinancialfrictions,pledgeabilityandthepricingofexternalborrowing,whilekeeping all other parameters and all shock processes common across the two economies. We show that a volatility shock generates a much larger and more persistent decline in the productivity trend in theemergingeconomycalibration,consistentwiththeevidenceinSection2,andtheseimpulseresponsesarenottargetedinthecalibration. Wethenexplainhowourmodelgeneratesthisresult. To give the intuition up front, when the collateral constraint is slack, volatility mainly operates through a risk and discounting channel with relatively linear effects. When, however, low productivitypushestheeconomyintotheconstrainedregion,volatilitytriggersaFisheriancollateral mechanism that amplifies deleveraging and depresses firm values, innovation, and the endogenous trend. Finally, we quantify the sources of the emerging versus advanced gap by separating the role of pledgeability from the role of spreads, and we illustrate the implications for average trenddynamicsandcross-countrydispersionovertherecentglobalvolatilitycycle. 4.1 Calibration: HeterogeneousFinancialFrictions We calibrate the model to match key features of Mexico at a quarterly frequency. The model has 21 parameters. We split them into two groups. The first group consists of 11 parameters that we either take from standard values in the literature or estimate directly. Table 1 reports these values. We estimate the U.S. real interest rate process and its stochastic volatility as described in Appendix A.1. We set the average interest rate to 4% per year (Mendoza, 1991), which corre- 23

spondstoroughly1%perquarter. WesettheTFPprocessparameters(ρ ,η )followingNeumeyer z z and Perri (2005). We set the innovation curvature parameters for incumbents and entrants to 0.5 (Akcigit and Kerr, 2018). We assume CRRA utility with curvature γ = 2, a standard choice in quantitative Sudden Stop models. Finally, we set the depreciation rate of ideas to δ = 0.015 per quarter. This implies that, in the absence of innovation and entry, the efficiency index shrinks at 1.5% per quarter. This magnitude is consistent with the lower tail of our estimated trend growth distributionforemergingeconomies. Table1: ExternallyCalibratedParameters Parameter Symbol Value Source AverageU.S.InterestRate R¯ (1.04)0.25−1 Mendoza(1991) PersistenceofInterestRate ρ 0.91 Estimation,U.S.data R AverageInterestRateVolatility µ 0.17 Estimation,U.S.data σ PersistenceofInterestRateVolatility ρ 0.94 Estimation,U.S.data σ VolatilityofInterestRateVolatility η 0.12 Estimation,U.S.data σ PersistenceofTFPShock ρ 0.95 NeumeyerandPerri(2005) z VolatilityofTFPShock η 0.02 NeumeyerandPerri(2005) z InnovationCurvatureCostbyIncumbents θ 0.50 AkcigitandKerr(2018) InnovationCurvatureCostbyEntrants υ 0.50 AkcigitandKerr(2018) UtilityFunctionCurvature γ 2 Standard DepreciationofIdeas δ 0.015 Estimation,lowertailoftrendgrowth Notes: Thistablereportsexternallycalibratedparameters,theirsymbols,numericalvalues,anddataorliteraturesources. Interest rateandvolatilityparametersareestimatedusingU.S.dataasdescribedinAppendixA.1. The second group consists of 10 internally calibrated parameters, summarized in Table 2. We setthestepsizeσto0.22tomatchanaverageannualizedgrowthrateofabout2%,consistentwith Neumeyer and Perri (2005). We set the entry cost κ to 31 to generate an annualized entry rate of 10%.17 We set the R&D cost level ξ to 0.49 so that the average incumbent firm size relative to entrants is 3. For the cost structure of innovation, we set α = 0.8 so that labor accounts for twothirds of total R&D costs (Moris and Shackelford, 2020), and we set F = F(st)/A(st) = 0.21 so thattotalinnovationandproduct-creationexpenditures(entryandincumbentexpansion)amount to approximately 4 percent of GDP, consistent with estimates of broad intangible investment for Mexico(ValdiviaLo´pezandBorrayoLo´pez,2023).18 Wenormalizethemassofproductsto Λ = 3, ensuringaunitmassoffirmsalongthebalancedgrowthpath. Wesetthediscountfactorβ = 0.98 17INEGI, Mexico’s national statistical office, reports a monthly establishment birth rate of 0.81% in its Business DemographySurvey(EDN2021). Annualizingthisrateyieldsroughly9.7%,whichweroundto10%forcalibration. SeeInstitutoNacionaldeEstad´ısticayGeograf´ıa(INEGI)(2021). 18Firm-level evidence on revenues from new products (INEGI and CONACYT, 2019) and data on startup costs (World Bank, 2020) imply magnitudes of fixed outlays that are consistent with this calibration, providing external validityforthevalueofF. 24

tomatchMexico’slong-runexternalposition,targetinganexternaldebttoGDPratiocloseto33% annually, in line with Lane and Milesi-Ferretti (2017). We set the collateral coefficient φ to 0.62 so that the model produces an annual crisis probability close to 3%, consistent with the Sudden Stops literature.19 We set ι = 0.01, the parameter governing the average spread charged by 0 the representative financial intermediary, to match a 1% quarterly spread in line with Mexico’s averageEMBIspreadbetween1994and2019. Finally,wesetι = 14.58tomatchthesensitivityof 1 Mexico’sEMBIspreadtovolatilityduringtheGreatRecession.20 Table2: InternallyCalibratedParameters Parameter Symbol Value MainIdentification Target StepSize σ 0.22 AnnualGrowthRate 2% CostLevelEntry κ 31 AnnualEntryRate 10% CostLevelR&D ξ 0.49 Avg. FirmSizeRelativetoEntrants 3 VariableCostShareR&D α 0.80 R&DWageBilltoTotalR&DCosts 2/3 FixedCostR&D F 0.21 TotalR&DCoststoFirmValue 5% MassofProducts Λ 3 UnitMassofFirms N/A DiscountFactor β 0.98 AnnualDebt-to-GDPRatio 33% BorrowingConstraint φ 0.62 AnnualProb. ofCrisis 3% FinancialIntermediaryAveragePrice ι 0.01 AverageSpread 1% 0 Spread −Spread FinancialIntermediaryPriceSensitivity ι 14.58 SpreadSensitivity 09Q1 08Q1 1 σ09Q1 −σ¯ Notes:Thistablereportsinternallycalibratedparameters,theirsymbols,values,mainidentificationroles,andcalibrationtargets.All parametersarecalibratedusingtheMexicobenchmark. Theadvancedeconomycalibrationchangesonlyφ,ι0,andι1whilekeeping allotherparametersfixed. Duetothenonlinearnatureofamodelwithanoccasionallybindingborrowingconstraint,we solvethemodelusingglobalmethods. Weemployahybridmethodthatcombinestimeiteration withvaluefunctioniteration. AppendixFprovidesadetaileddescriptionofthesolutionmethod. To highlight the importance of heterogeneous financial frictions, we construct an advanced economy calibration by changing only three parameters from Table 2, namely φ, ι , and ι , and 0 1 keeping all other parameters and all shock processes fixed. We set φ = 0.92 so that the economy experiencesafinancialcrisiswithroughlyhalfthebaselineprobability,around1.5%peryear,consistentwithtargetsusedfordevelopedeconomies(BianchiandMendoza,2020). Wesetι = 0.002 0 andι = 2.16sothattheaveragequarterlyspreadis0.25%andthespreadsensitivitytoU.S.inter- 1 estratevolatilityisconsistentwithwhatwasobservedforapanelofadvancedeconomiesduring 19WedefineacrisisorSuddenStopasaneventinwhichthecurrentaccounttoGDPratioistwostandarddeviations aboveitslong-runmeanandtheborrowingconstraintbinds,following(Mendoza,2010;Bianchietal.,2016). 20Mexico’s annual EMBI spread increased by 2.5 percentage points between 2008Q1 and 2009Q1. The associated spike in U.S. real interest rate volatility, relative to trend, was close to 20%. We map this increase to our stochastic volatilitygrid.Thisimpliesι 1 = ∆Sp ∆ r σ ead ≈ 0 0 .0 .0 0 0 0 6 4 . 25

the Great Recession.21 Only φ, ι , and ι differ between the emerging and advanced economy 0 1 calibrations. 4.2 ModelMeetsData: StochasticVolatilityandEndogenousTrendDynamics We use the main empirical fact described in Section 2 to assess the quantitative implications of the calibrated model. We compute generalized impulse response functions (GIRFs) from modelsimulateddata,followingKoopetal.(1996). Theshockisaonestandarddeviationincreaseinthe volatilityoftheworldinterestrate,themodelanalogueoftheU.S.realinterestrate. Wecompute the response of the accumulated productivity trend by simulating two economies that share the same sequence of shocks, one with a volatility shock in period T and one without, and taking the difference between the two paths. We repeat this exercise 10,000 times and average across simulations.22 Figure 4 reports the impulse responses of the accumulated trend for the baseline and advanced calibrations. Two patterns emerge. First, the advanced economy calibration exhibits a substantially smaller decline in the productivity trend than the baseline calibration. Second, the heterogeneitybetweenthebaselineandadvancedeconomycalibrationisqualitativelyandquantitatively in line with our empirical findings. As these impulse responses are not targeted in the calibrationandtheyprovideanout-of-samplecheckonthemodelsuggestingthattheuncertainty inducedforcesweightingongrowthareintherightballpark.23 21To set ι we calculate the change in five-year mean CDS spreads, relative to the United States, between 2008 1 and 2009 for a group of advanced economies. We follow a process identical to the one described for our baseline calibration. OursampleincludesBelgium,Denmark,Finland,France,Germany,Italy,Netherlands,Norway,Portugal, Spain,Sweden,andtheUnitedKingdom.OurdatawereobtainedfromMarkit. 22Eachsimulationlasts390quarters. Wediscardthefirst350quarterstoremovedependenceoninitialconditions. Foreachdraw,weusethesameunderlyingsequenceofshocksacrossthetreatedandcontroleconomies,andweuse thesameshocksequencesforthebaselineandadvancedcalibrations. 23GiventhepricingformulationinEquation(7),avolatilityshockalsoinducesalevelcomponentintheinterestrate facedbyhouseholds.AppendixCisolatestheeffectofapurechangeininterestratevolatilityandshowsthatvolatility itselfaccountsforroughly30%ofthetotalresponse. 26

Figure4: TrendGrowthRateImpulseResponseFunctionstoaWorldInterestRateVolatilityShock 0 -0.1 -0.2 -0.3 -0.4 Baseline -0.5 Advanced 1 2 3 4 5 6 7 8 9 10 11 12 Horizon Notes: Thisfigurepresentsimpulseresponsefunctionsoftheaccumulatedproductivitytrendtoaonestandarddeviationstochasticvolatilityshockoftheworldinterestrate, forthebaseline(redsolidline)andadvanced(bluedottedline)modelcalibrations. Responsesarecomputedfrommodel-simulateddatausingthegeneralizedimpulseresponseproceduredescribedinSection4.2. 4.3 Mechanism: Constraints,Volatility,andAsymmetry The GIRFs show that a volatility shock has much larger effects on the productivity trend in the emergingeconomycalibration. Inthissubsectionwedelveintothereasonsbehindthisdifference. The key object is the interaction of aggregate productivity Z and interest rate volatility σ with R the collateral constraint. Low productivity realizations move the economy into states in which the constraint binds. In those states, volatility shocks trigger a Fisherian collateral mechanism that amplifies deleveraging and depresses firm values and innovation incentives in addition to any other effects. When the constraint is slack, volatility mainly operates through a risk and discounting channel with relatively symmetric effects (in absolute value) between increases and decreases. 4.3.1 Policyfunctionsandtheconstrainedregion Figure 5 summarizes these forces using policy functions. Panel (a) plots the endogenous trend growth rate g as a function of σ for three values of Z. Volatility reduces trend growth at all R productivity levels, but the decline is much larger when productivity is low. Panel (b) explains thisstatedependence. ItplotstheLagrangemultiplieronthecollateralconstraint,µ˜,asafunction ofσ . Themultipliermeasuresthetightnessoftheborrowingconstraint. Whenproductivityisat R 27

oraboveitsaveragelevel,wehavethatµ˜ = 0forallvaluesofσ ,sovolatilitydoesnottightenthe R constraint. When productivity is sufficiently low, higher volatility increases µ˜ sharply, pushing theeconomydeeperintotheconstrainedregion. Panel(c)plotsµ˜ asafunctionof Z fordifferentlevelsofvolatility. Asproductivityfallsbelow its long-run mean, the constraint starts binding, and the severity of this tightening depends on σ . ForagivendeclineinZ,highervolatilityimpliesalargermultiplierandasharpercontraction R in borrowing capacity. As a result, the same productivity realization can generate very different innovationandgrowthoutcomesdependingonthevolatilitystate. Thisstatedependenceiscentralforunderstandingwhyvolatilityshockshavelimitedeffectsinnormaltimesbutlargeeffects whentheeconomyvisitslowproductivitystates. Figure5: PolicyFunctions: Volatility,FinancialConstraints,andTrendGrowth 12 3 2.5 10 2 8 1.5 1 6 0.5 4 0 2 -0.5 -1 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.1 0.15 0.2 0.25 0.3 0.35 0.4 (a) TrendGrowthRateandVolatility (b) LagrangeMultiplierandVolatility 140 120 100 80 60 40 20 0 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 (c) LagrangeMultiplierandProductivity Notes: Thisfigureplotspolicyfunctionsfortheendogenoustrendgrowthrate, g, andtheLagrangemultiplierontheborrowing constraint,µ˜.VerticallinesdenoteergodicmeansofinterestratevolatilityandTFP.Trendgrowthratesareannualized.Bondholdings andtheinterestratearefixedattheirlong-runmeans. 28

4.3.2 Asymmetryresponsetosymmetricinterestrateshocks Anotherimplicationoftheoccasionalbindingconstraintisthatamorevolatileinterestrateenvironmentcanlowerexpectedfirmvaluesandtrendgrowthevenwheninterestrateinnovationsare symmetric on average. When volatility is higher, interest rate innovations are larger in absolute value,conditionalonhikesorcuts.24 Neartheconstrainedregion,therealeffectsofhikesandcuts ofthesameabsolutesizeneednotbesymmetric. Whenthecollateralconstraintbinds,aninterest ratehiketightensborrowingcapacityandtriggersaFisherianfeedbackthroughcollateralvalues. When the interest rate falls, the relaxation is weaker because the multiplier is bounded below by zero. Asaresult,ahigh-volatilityenvironment,whichmakeslargeinterestratemovementsmore likely,lowerstheexpectedvalueoffirmsandreducesinnovationandentryincentives,eveninthe absenceofacontemporaneousfirst-momentshock. In contrast, when the constraint rarely binds, the main nonlinearity comes from discounting. Since the discount factor is concave in the interest rate, Jensen’s inequality implies that hikes can havesmallerabsoluteeffectsondiscountingthancutsofthesamemagnitude. Thiscanattenuate asymmetry,andforsufficientlylargeshocksitcangenerateamildreversal.25 To quantify asymmetry, we compute impulse responses to symmetric interest rate shocks using an approach similar to a generalized impulse response function. We vary the magnitude of the shock while maintaining symmetry, meaning equal absolute sizes for hikes and cuts. Each simulation lasts 390 quarters, we discard the first 350 quarters, and we repeat the exercise 5,000 timesforeachshocksize. Wecomputetheaverageimpactresponseforthebaselineandadvanced calibrationswhentheinterestrateshockmaterializes,usingthesameunderlyingshocksequences acrosscalibrations.26 Figure 6 summarizes the results. Panel A reports an asymmetry statistic for the trend growth response,definedastheabsoluteimpactresponsetoahikeminustheabsoluteon-impactresponse toacut,withresponsesstandardizedbythelong-runstandarddeviationofg. Interestrateshocks 24Lettheinterestrateinnovationbeω(st)σ(st)withω(st)∼ N(0,1).Conditionalonahike,E[ω(st)σ(st)|ω(st)> 0,st]=σ(st) φ(0) ,andthesamelogicappliestocuts. 1−Φ(0) 25ThisJenseneffectisdominatedwhentheeconomyfrequentlyvisitsconstrainedstates,butitcanbevisibleinthe advancedcalibrationwhentheconstraintbindslessoften. 26Theresponseofgdeclinesmonotonicallyafterthefirstperiodoftheshock,sotheimpactresponseconstitutesalso themaxresponse. 29

are expressed in standard deviations relative to the average level of interest rate volatility. Panel B reports, for each shock size, the probability that the absolute interest rate change exceeds that threshold under two volatility regimes, a low-volatility state one standard deviation below the meanandahigh-volatilitystateonestandarddeviationabovethemean. Figure6: AsymmetryinImpulseResponsestoSymmetricInterestRateShocks 0.1 0.9 0.8 0.08 0.7 0.06 0.6 0.04 0.5 0.02 0.4 0.3 0 0.2 -0.02 0.1 -0.04 0 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Notes: Theasymmetryinresponsesispresentedas|gHike|−|gCut|,wheregHike(gCut)correspondstotheon-impactresponseofthe trendgrowthrateg(standardizedwithrespecttoitslong-runmeanandstandarddeviation)toaninterestratehike(cut). Interest rateshocksareexpressedinstandarddeviations.Low(High)σRcorrespondstointerestratevolatilitythatisonestandarddeviation below(above)itslong-runaverage. Figure 6 reveals two patterns. First, for the emerging market economy asymmetry clearly increases with shock size. For small shocks, the responses to hikes and cuts are similar, but for larger shocks the absolute response to a hike exceeds the absolute response to a cut. Second, asymmetries are mainly present in the baseline calibration. The advanced economy calibration exhibitsnoclearasymmetries,consistentwiththediscountingforcediscussedabove. Panel B shows that the shock sizes for which asymmetries arise are much more likely when volatilityishigh. Forexample,anincreaseintherealinterestrateofatleastonestandarddeviation occurs with about 10% probability in the low-volatility regime, but with almost 50% probability inthehigh-volatilityregime. Takentogether,thetwopanelsimplythathighervolatilityincreases theprobabilitymassonshocksforwhichtheeconomy’sresponsesarestronglyasymmetric. This lowers expected growth in the baseline calibration, and leads households to reduce current consumptionandincreaseprecautionarysavings,generatinganimmediatedeclineintheendogenous trendevenintheabsenceofafirst-momentshock. 30

Toisolatetheroleofstochasticvolatilityinlong-runmoments,wealsoconsideraneconomyin whichthestandarddeviationoftheworldinterestrateisfixedatitsergodicmean. Table3reports selectedlong-runmoments forthebaselineandadvanced calibrationsunderstochasticvolatility andunderdeterministicvolatility. Table3: VolatileRatesandVolatileTrends: DeterministicVolatility Moment Baseline Advanced SV NoSV SV NoSV σ(g)/ E(g) 0.18 0.13 0.11 0.12 σ(CA/Y)% 3.08 2.92 1.11 0.91 E(BH/Y)% -32.49 -33.83 -54.05 -54.23 Spread% 1.00 1.00 0.25 0.25 Prob. SuddenStop% 2.68 3.23 1.61 1.60 Notes: SVdenotesthescenariowithstochasticvolatilityintheworldinterestrate. IntheNoSVcase,thevolatilityprocessisshut downandthestandarddeviationoftheworldinterestrateisfixedatitslong-run(ergodic)mean. Allmomentsarecomputedfrom longsimulatedsamplesundereachregime. Forthebaselinecalibration,shuttingdownstochasticvolatilityreducesthecoefficientofvariationoftrendgrowthbyroughly30%. Fortheadvancedcalibration,thevolatilityoftrendgrowth changeslittle. Botheconomiesexperiencelowercurrentaccountvolatilitywhenvolatilityshocks are removed, reflecting reduced precautionary savings motives and a smoother consumption path. In the baseline calibration, the absence of volatility also encourages higher external borrowing and increases exposure to Sudden Stops, as reflected in their higher probability.27 These results indicate that stochastic volatility is a key driver of trend dynamics in the baseline calibration, and that its effects depend on financial frictions. We next separate the contributions of pledgeabilityandspreads. 4.4 InterestRateRiskandFinancialFrictions The mechanism we have been highlighting depends on two features of the emerging economy calibration: limitedpledgeabilityandhigherborrowingcosts. Inthissubsection,weseparatethe roleofcollateraltightnessfromtheroleofspreads. Weconstructanintermediatecalibrationthat wecalltherelaxedconstrainteconomy. Itisidenticaltothebaselinecalibrationexceptthatweset 27OurSuddenStopdefinitionusesacurrentaccounttoGDPthresholddefinedrelativetoeacheconomy’sownlongrundistribution,andthedistributionchangesacrosscalibrations. Asaresult,differencesincrisisprobabilitiesreflect bothdifferencesinfinancialtightnessandchangesinequilibriumborrowingandcurrentaccountvolatility. 31

the collateral coefficient φ to its advanced-economy value, while keeping the spread parameters (ι ,ι )attheirbaselinevalues. Comparingthebaselineandrelaxedconstrainteconomiesisolates 0 1 the role of pledgeability. Comparing the relaxed constraint and advanced economies isolates the roleofspreads. Table4reportslong-runmomentsforthethreeeconomies. Relaxingtheborrowingconstraint has large effects on volatility. The coefficient of variation of trend growth declines by 22%, and current account volatility falls by half.. In terms of the emerging versus advanced gap in trend volatility,thechangeinpledgeabilityaccountsforroughly60%ofthedifference,withtheremaining share attributed to spreads. Sudden Stop probabilities need not move monotonically across calibrations because they are equilibrium outcomes that reflect endogenous borrowing, precautionarysavings,andthedistributionofcurrentaccountfluctuations.28 Table4: FinancialFrictionsandBusinessCycles Moment Baseline RelaxedConstraint Advanced E(Spread)% 1.00 1.00 0.25 σ(g)/ E(g) 0.18 0.14 0.11 σ(CA/Y)% 3.08 1.49 1.11 corr(DomesticSpread,g) -0.54 0.49 0.49 Prob. SuddenStop% 2.68 1.50 1.61 E(BH/Y)% -32.49 -52.80 -54.05 Notes: Thistablereportslong-runsimulatedmomentsforthreecalibrations: thebaseline,therelaxedconstrainteconomy(sameas baselineexceptforφsettoitsadvanced-economyvalue),andtheadvancedeconomy(baselinewithhigherpledgeabilityandlower, lessvolatility-sensitivespreads).Allmomentsarecomputedunderstochasticvolatilityintheworldinterestrate. We also report the correlation between the domestic spread and trend growth. Standard small open economy models often assume that spreads and productivity are negatively correlated(NeumeyerandPerri,2005). Inourmodel,thisrelationshipisendogenousanddependson the degree of financial tightness. In the baseline calibration, domestic spreads are strongly countercyclicalwithrespecttotrendgrowth,whileintherelaxedconstraintandadvancedcalibrations thecorrelationbecomespositive.29 A key implication of the baseline calibration is the presence of Sudden Stops. These episodes 28Wealsofindexcessconsumptionvolatility(withrespecttooutput)inourbaselinecalibration. Notsurprisingly, wefindthattheexcessvolatilitydecreasesasfinancialconstraintsarerelaxed. Similarpatternsareobservedforthe currentaccount-to-GDPandtradebalance-to-GDPratios. 29Wedefinethedomesticspreadasthedifferencebetweenthedomesticinterestrateandtheratechargedbyintermediaries,E(cid:2) RB(st+1)−Rˆ(st) (cid:3) =µ(st)/E[λ(st+1)|st]. 32

involve sharp reversals in the current account together with severe contractions in consumption andoutput. Theyarisefromoccasionallybindingcollateralconstraintsandendogenouscollateral values, which activate a Fisherian deflation mechanism during periods of financial stress (Mendoza,2005,2010). Unlikebusinesscyclefluctuationswithexogenousgrowth,SuddenStopsinour modelhavepersistenteffectsonproductivityandoutput. AppendixGpresentseventstudiesfor thebaselinecalibrationandhighlightsthepersistenceofthetrendandslowrecoveriesaftercrises. This persistence is consistent with models that integrate financial frictions into growth dynamics (Queralto, 2020; Guerron-Quintana and Jinnai, 2019) and with the hysteresis documented in the empiricalliterature(CerraandSaxena,2008). 4.5 VolatileRatesandFragileGrowth We next study the economic magnitude of the mechanism over the recent global volatility cycle. We use the observed path of the U.S. real interest rate and its volatility (Figure 11 in Appendix A.1). Wedraw10,000TFPsequencesandfeedeachsequence,togetherwiththeobservedinterest rateandvolatilitypaths,intothethreecalibrations. Sincealleconomiesfacethesamerealizations of global rates and volatility and the same TFP process, differences in outcomes reflect internal propagationthroughfinancialfrictions. Figure7reportsaveragedeviationsfromdeterministictrendsforproductivityandforthemultiplierontheborrowingconstraint. Panel(a)showsthatthethreeeconomiesfollowmarkedlydifferentaverage trenddeviations overthe sample. Duringthe low-volatilityperiod withdeclining interestratesbetween1990and2006,emergingmarketsgrewsubstantiallyfasterthantheiraveragerate,whiletheadvancedeconomiesgainedlittlebythismetric. By2006,thebaselineeconomy isabout4%abovetrend. After2006,whenglobalriskrises,thesegainsarereversed. By2018,the baselineeconomyisnearly2%belowtrend,whiletherelaxedconstraintandadvancedeconomies experiencesubstantiallysmallerdeclines. Panel (b) links these outcomes to financial constraints.30 The reversal in the baseline economy coincides with a sharp increase in the multiplier, reflecting tight borrowing conditions and 30Thefigurereportsaveragedeviationsacross10,000TFPpaths. WemeasurelnAt −lnA¯ twithAt =∏ i t =0 (1+g i ) and A¯ t = (1+g¯)t, where g¯ is the ergodic mean of g. For the multiplier we report percentage deviations from its deterministiccounterpart,withµt = A − t γ µ˜tandµ¯t = A¯− t γ µ¯˜. AppendixHpresentsasimilarexercisefortheLagrange multiplierinlevelsandtheprobabilityofabindingborrowingconstraint. 33

a deleveraging episode. The relaxed constraint and advanced economies display much smaller movementsinthemultiplier. Inthebaselinecalibration, theFisherianfeedbackisstrongenough that the economy tends to keep more precautionary slack in normal times, but when adverse volatilityandproductivityrealizationspushitintotheconstrainedregion,thetighteningisabrupt andpersistent. Intherelaxedconstraintandadvancedcalibrations,theeconomyislessexposedto theseamplificationdynamics, soincreasesinglobalriskleadtomilderdeleveragingandsmaller trendlosses.31 Figure7: DeviationsfromTrendBasedonActualInterestRateandVolatilityTimeSeries % 4 2 0 2− 4− 1990q1 1994q1 1998q1 2002q1 2006q1 2010q1 2014q1 2018q1 Baseline Relaxed Advanced (a) lnAt −lnA¯ t % 004 003 002 001 0 001− 1990q1 1994q1 1998q1 2002q1 2006q1 2010q1 2014q1 2018q1 Baseline Relaxed Advanced (b) µt −µ¯t µ¯t Notes: Thisfigureshows,forthethreecalibrations(baseline,relaxedconstraint,advanced),theaveragedeviationofproductivity andoftheLagrangemultiplierfromtheirdeterministictrendswhenalleconomiesaresubjectedtothesamepathofU.S.realinterest ratesandvolatility. Panel(a)reportslnAt −lnA¯ t; panel(b)reportspercentagedeviationsofthemultiplierfromitsdeterministic counterpart.Averagesaretakenacross10,000simulatedTFPpaths. To connect these average outcomes to cross-sectional dynamics, Figure 8 reports the average and dispersion of the trend growth rate g across the 10,000 simulated economies. We construct these series following the same approach as in Section 2.5 and focus on the same sample window. Panel (a) shows that average trend growth in the baseline economy falls sharply during high-volatility episodes. Panel (b) shows that dispersion in g rises substantially for the baseline economy and remains much smaller for the relaxed constraint and advanced calibrations. This pattern mirrors the empirical evidence and highlights that the same global volatility cycle can 31The global risk shock in this experiment is stochastic volatility in the U.S. interest-rate process. Consequently, episodes in which emerging-market risk premia rose for reasons largely orthogonal to uncertainty about U.S. rates (e.g.,the1997–98Asian/Russiancrises)neednotappearaslargerealizationsoftheshockinFigure7. Inthemodel, suchepisodeswouldbebetterrepresentedbyanincreaseinthecountryspread(orbyfeedinginabroadermeasureof globalfinancialrisk/uncertaintyratherthanU.S.-ratevolatility). 34

generatebothloweraveragegrowthandhigherdispersioninemergingmarkets. Figure8: AverageandDispersionofTrendGrowth % 1. 0 1.− 2.− 3.− 2004q2 2007q2 2010q2 2013q2 2016q2 2019q2 Baseline Relaxed Advanced (a) GrowthRateg–Average % 6. 4. 2. 0 2004q2 2007q2 2010q2 2013q2 2016q2 2019q2 Baseline Relaxed Advanced (b) GrowthRateg–StandardDeviation Notes: Foreachquarterinthesamplewindow,wecomputethecross-sectionalaverageandstandarddeviationofthetrendgrowth rategacrosssimulatedeconomies,usingthesamesamplewindowandconstructionasinSection2.5. Panel(a)reportsthecrosssectionalaverage;panel(b)reportsthecross-sectionalstandarddeviation,forthebaseline,relaxedconstraint,andadvancedcalibrations. Figure9isolatestheroleofstochasticvolatilityinthesedynamicsforthebaselinecalibration. We repeat the exercise in Figure 8 under two counterfactual scenarios, one in which the interest rate level is fixed at its mean while volatility follows its stochastic process, and one in which volatilityisfixedatitsmeanwhiletheinterestratefollowsitsstochasticprocess. Thedecomposition shows that aggregate risk is the primary driver of both the decline in average trend growth and the rise in dispersion. When interest rate volatility is held fixed at its mean, the collapse in averagegrowthandtheincreaseindispersionlargelydisappear. The remaining question is why the same panel of productivity shocks generates much larger dispersion in trend growth for emerging markets than for advanced economies. Figure 10 links dispersiontotheinteractionbetweenvolatilityandtheconstrainedregionofthestatespace. The figure plots, for each calibration, the difference in the trend-growth policy function between a high-volatilitystateandalow-volatilitystateasafunctionofTFP,holdingallotherstatevariables fixedattheirergodicmeans. 35

Figure9: AverageandStandardDeviationofGrowthRate gforDifferentInterestRateScenarios 1. 0 1.− 2.− 3.− 2004q2 2007q2 2010q2 2013q2 2016q2 2019q2 Baseline Fixed Rate Fixed Volatility (a) GrowthRateg–Average 7. 6. 5. 4. 3. 2004q2 2007q2 2010q2 2013q2 2016q2 2019q2 Baseline Fixed Rate Fixed Volatility (b) GrowthRateg–StandardDeviation Notes:Thisfigurereports,forthebaseline(Mexico)calibration,thecross-sectionalaverageandstandarddeviationofthetrendgrowth rategunderthreescenarios:(i)fullmodelwithstochasticinterestratesandvolatility,(ii)interestratevolatilityfixedatitsmean,and (iii)interestratelevelfixedatitsmeanwhilevolatilityfollowsitsstochasticprocess.Panel(a)showsthecross-sectionalaverage;panel (b)showsthecross-sectionalstandarddeviation.AllconstructionsmirrorthoseinFigure8. Twoobservationsarekey. First,forproductivitylevelsclosetoorabovetheergodicmean,the effectofvolatilityontrendgrowthissimilaracrossthethreeeconomies: thegapbetweenhighand low volatility is stable and modest. Second, once productivity is sufficiently low for the baseline (emerging-market) calibration to enter the constrained region, the relationship changes sharply. The gap in trend growth across volatility regimes steepens rapidly as productivity declines, reflectingFisherianamplificationwhentheconstraintbinds. Consequently,economiesthatfallinto low-productivity states experience a much larger drop in trend growth in high-volatility states thaneconomiesthatremainoutsidetheconstrainedregion,generatingsubstantialcross-sectional dispersioneventhoughtheglobalvolatilitycycleiscommon. A complementary way to quantify how often the economy is exposed to this nonlinear amplificationistomeasurehowfrequentlythecollateralconstraintbindsinnormaltimes. Inasimulation that fixes (R,σ ) at their ergodic means and feeds the economy only idiosyncratic TFP R shocks(withdebtandotherendogenousstatesadjusting),theborrowingconstraintbinds7.1%of the time in the baseline calibration. This provides a benchmark for the stationary probability of operating in the nonlinear region. During high-volatility episodes, the set of states in which the constraintbindsexpands andthemassofconstrained observations rises, magnifyingdispersion. Incontrast,withintheconstrainedregiontherelaxed-constraintandadvancedcalibrationsareless 36

sensitivetovolatilityincreasesbecausehighercollateralpledgeabilityweakenstheFisherianfeedback. Thisisalsowhythehigh–lowvolatilitygapdoesnotsteepen—andcanevenflatten—inthose calibrations: when financing is less tight, the labor-intensive component of innovation becomes relativelycheaperinbadtimes(wagesfall),soR&Dislesscompressed(andcanbecomepartially countercyclical), offsetting the direct tightening effect of higher volatility. As a result, identical TFP shocks translate into much smaller differences in trend growth across economies and crosssectionaldispersionremainslimited. Thecomparisonbetweenthebaselineandrelaxed-constraint calibrationshighlightstheroleofpledgeability: itgovernshowfrequentlytheeconomyentersthe regionwherevolatilityhaslargemarginaleffectsthroughcollateralfeedback. Figure10: DifferentialEffectsofVolatilityonTrendGrowth 6 5 4 3 2 1 0 0.9 1 1.1 1.2 Notes:Thisfigureplots,foreachcalibration,thedifferenceinthepolicyfunctionfortheendogenoustrendgrowthrategbetweena high-volatilitystateandalow-volatilitystate,asafunctionofTFP.Allotherstatevariablesarefixedattheirergodicmeans(including bondholdingsandtheinterestrate). TheshadedareadenotesthesetofTFPvaluesforwhichtheborrowingconstraintbindsinthe baselinecalibrationwhenevaluatedatergodic-meanvaluesoftheotherstatevariables. Theverticallineindicatestheergodicmean ofTFP.Trend-growthdifferencesarestandardizedbythelong-runstandarddeviationofg. 5 Conclusion Thispaperprovidesempiricalandtheoreticalevidencelinkingglobalfinancialrisktoproductivitytrends,withparticularlylargeeffectsinemergingmarkets. Weoperationalizeglobalfinancial risk using uncertainty about U.S. interest rates. On the empirical side, we show that a one standarddeviationincreaseininterestrateuncertaintylowerstheleveloftheGDPtrendinemerging 37

marketeconomiesbyatleast25basispointsafterthreeyears,withsubstantiallysmallereffectsin advancedeconomies. Onthetheoreticalside,wedevelopasmallopeneconomymodelwithcollateral constraints and endogenous innovation that can account for this heterogeneous response evenwhenadvancedandemergingeconomiesareexposedtothesameglobalshockprocess. Themodel’smechanismoperatesthroughasymmetricresponsesandstatedependence. Interest rate hikes sharply reduce trend productivity in emerging markets when collateral constraints bind, whilecutsofequalmagnitudeproduceonlymodestgainswhenconstraintsareslack. This asymmetryisamplifiedwhenfinancialriskiselevated. Higherratescompressfirmvalues,tighten borrowing constraints through Fisherian deflation, trigger deleveraging, and reduce innovation and entry. Consequently, higher interest rate volatility lowers expected firm values and slows productivitygrowthevenwhenaverageratesareunchanged. In the model, heterogeneity arises from financial conditions rather than from differences in preferences,technology,orexogenousshocks. Advancedandemergingeconomiesshareidentical primitivesandfacethesameglobalprocesses,butdifferincollateraltightnessandspreadlevels. In the emerging market calibration, shutting down interest rate volatility substantially reduces trend-growthvariation,whiletheadvancedeconomycalibrationiscomparativelyinsensitive. The decomposition highlights that collateral constraints are the central source of amplification, with volatilitysensitiveriskpremiaaccountingfortheremainder. Historical simulations illustrate the macroeconomic significance of the mechanism. During low-volatility periods, emerging markets accumulate productivity gains, whereas episodes of elevated global risk generate large and persistent reversals in trend productivity in the emerging market calibration while leaving the advanced economy calibration relatively stable. The model also reproduces higher cross-sectional dispersion of emerging market growth during high-risk periodsdespiteidenticalglobalshocks. Theseresultsimplythatfinancialdevelopmentshapeswhetherglobal financial instabilityremains a short-run cyclical disturbance or translates into persistent damage to productivity and long-run prosperity. Policies that raise effective pledgeability, through stronger contract enforcement and collateral recovery, deeper financial markets, and improved institutional frameworks, reduce the frequency and severity of binding constraint episodes and thereby attenuate the long run consequences of global risk shocks. Finally, because our empirical proxy focuses on uncer- 38

taintyaboutU.S.rates,itneednotcaptureallepisodesofemergingmarketstressdrivenbyother sourcesofglobalorregionalrisk;incorporatingbroadermeasuresofglobalriskisanaturaldirectionforfuturework. 39

References Adjemian,S.,Bastani,H.,Juillard,M.,Mihoubi,F.,Perendia,G.,Ratto,M.,andVillemot,S.(2011). ‘Dynare: Referencemanual,version4’. Aguiar, M. and Gopinath, G. (2007). ‘Emerging market business cycles: The cycle is the trend’. JournalofPoliticalEconomy,vol.115,no.1,69–102. Akcigit,U.andKerr,W.R.(2018). ‘Growththroughheterogeneousinnovations’. JournalofPolitical Economy,vol.126,no.4,1374–1443. Akıncı, O¨. (2013). ‘Global financial conditions, country spreads and macroeconomic fluctuations inemergingcountries’. JournalofInternationalEconomics,vol.91,no.2,358–371. Akinci,O.,Kalemli-O¨zcan, andQueralto,A.(2022). ‘Uncertaintyshocks,capitalflows,andinternationalriskspillovers’. Technicalreport,NationalBureauofEconomicResearch. Arellano, C. and Ramanarayanan, A. (2012). ‘Default and the Maturity Structure in Sovereign Bonds’. JournalofPoliticalEconomy,vol.120,no.2,187–232. Ates, S. T. and Saffie, F. E. (2021). ‘Fewer but better: Sudden stops, firm entry, and financial selection’. AmericanEconomicJournal: Macroeconomics,vol.13,no.3,304–356. Barnichon,R.andMatthes,C.(2018). ‘Functionalapproximationofimpulseresponses’. Journalof MonetaryEconomics,vol.99,41–55. Benguria, F., Matsumoto, H., and Saffie, F. (2022). ‘Productivity and trade dynamics in sudden stops’. JournalofInternationalEconomics,vol.139,103631. Benigno, G., Fornaro, L., and Wolf, M. (2025). ‘The global financial resource curse’. American EconomicReview,vol.115,no.1,220–262. Bhattarai, S., Chatterjee, A., and Park, W. Y. (2020). ‘Global spillover effects of US uncertainty’. JournalofMonetaryEconomics,vol.114,71–89. Bianchi, F., Ilut, C. L., and Schneider, M. (2018a). ‘Uncertainty shocks, asset supply and pricing overthebusinesscycle’. TheReviewofEconomicStudies,vol.85,no.2,810–854. 40

Bianchi, J. (2011). ‘Overborrowing and Systemic Externalities in the Business Cycle’. American EconomicReview,vol.101,no.7,3400–3426. Bianchi, J., Hatchondo, J., and Martinez, L. (2018b). ‘International Reserves and Rollover Risk’. AmericanEconomicReview,vol.108,no.9,2629–70. Bianchi, J., Liu, C., and Mendoza, E. (2016). ‘Fundamentals News, Global Liquidity and MacroprudentialPolicy’. JournalofInternationalEconomics,vol.99,no.1,2–15. Bianchi, J. and Mendoza, E. (2018). ‘Optimal Time-consistent Macroprudential Policy’. Journal of PoliticalEconomy,vol.6126,no.2,588–634. Bianchi, J. and Mendoza, E. (2020). ‘A Fisherian Approach to Financial Crises: Lessons from the SuddenStopsLiterature’. ReviewofEconomicDynamics,vol.37,S254–S283. Bocola,L.andGornemann,N.(2013). ‘Risk,economicgrowthandthevalueofUScorporations’. Boz, E., Daude, C., and Durdu, C. B. (2011). ‘Emerging market business cycles: Learning about thetrend’. JournalofMonetaryEconomics,vol.58,no.6-8,616–631. Carrie`re-Swallow, Y. and Ce´spedes, L. F. (2013). ‘The impact of uncertainty shocks in emerging economies’. JournalofInternationalEconomics,vol.90,no.2,316–325. Cerra, V.andSaxena, S.C.(2008). ‘Growthdynamics: themythofeconomicrecovery’. American EconomicReview,vol.98,no.1,439–57. Chang, R. and Ferna´ndez, A. (2013). ‘On the sources of aggregate fluctuations in emerging economies’. InternationalEconomicReview,vol.54,no.4,1265–1293. Chari,A.,Dilts-Stedman,K.,andForbes,K.(2022). ‘Spilloversattheextremes: Themacroprudentialstanceandvulnerabilitytotheglobalfinancialcycle’. JournalofInternationalEconomics,vol. 136,103582. Comin, D. and Gertler, M. (2006). ‘Medium-term business cycles’. American Economic Review, vol.96,no.3,523–551. Drechsel, T. (2023). ‘Earnings-based borrowing constraints and macroeconomic fluctuations’. AmericanEconomicJournal: Macroeconomics,vol.15,no.2,1–34. 41

Ferna´ndez-Villaverde, J., Guerro´n-Quintana, P., Rubio-Ramirez, J. F., and Uribe, M. (2011). ‘Risk matters: Therealeffectsofvolatilityshocks’. AmericanEconomicReview,vol.101,no.6,2530–61. Garcia-Cicco, J., Pancrazi, R., and Uribe, M. (2010). ‘Real business cycles in emerging countries?’ AmericanEconomicReview,vol.100,no.5,2510–31. Garga, V. and Singh, S. R. (2021). ‘Output hysteresis and optimal monetary policy’. Journal of MonetaryEconomics,vol.117,871–886. Gerding,F.,Henriksen,E.,andSimonovska,I.(2014). ‘Theriskycapitalofemergingmarkets’. Gertler,M.andKaradi,P.(2011).‘Amodelofunconventionalmonetarypolicy’.Journalofmonetary Economics,vol.58,no.1,17–34. Gertler, M. and Kiyotaki, N. (2015). ‘Banking, liquidity, and bank runs in an infinite horizon economy’. AmericanEconomicReview,vol.105,no.7,2011–2043. Gilchrist, S. and Zakrajsˇek, E. (2012). ‘Credit spreads and business cycle fluctuations’. American economicreview,vol.102,no.4,1692–1720. Gornemann,N.,Guerro´nQuintana,P.A.,andSaffie,F.(2025). ‘RealExchangeRatesandEndogenousProductivity’. AmericanEconomicJournal: Macroeconomics,vol.17,no.4,204–261. Gruss, B. and Mertens, K. (2009). ‘Regime switching interest rates and fluctuations in emerging markets’. Guerron-Quintana,P.A.andJinnai,R.(2019). ‘Financialfrictions,trends,andthegreatrecession’. QuantitativeEconomics,vol.10,no.2,735–773. Hegarty, C., Moretti, M., Ottonello, P., and Perez, D. (2023). ‘Global Borrowing Costs and Firms’ RiskinOpenEconomies’. WorkingPaper. Husted, L., Rogers, J., and Sun, B. (2020). ‘Monetary policy uncertainty’. Journal of Monetary Economics,vol.115,20–36. INEGI and CONACYT (2019). ‘INEGI y CONACYT presentan resultados de la Encuesta sobre Investigacio´nyDesarrolloTecnolo´gico(ESIDET)2017’. INEGIStatisticalBulletin,,no.633/19. 42

Instituto Nacional de Estad´ıstica y Geograf´ıa (INEGI) (2021). ‘El INEGI presenta los resultados del Estudio sobre la Demograf´ıa de los Negocios 2021’. Comunicado de prensa Nu´m. 790/21. 21dediciembrede2021. Jarocin´ski,M.andKaradi,P.(2020). ‘Deconstructingmonetarypolicysurprises—theroleofinformationshocks’. AmericanEconomicJournal: Macroeconomics,vol.12,no.2,1–43. Johri, A., Khan, S., and Sosa-Padilla, C. (2022). ‘Interest Rate Uncertainty and Sovereign Default Risk’. JournalofInternationalEconomics,vol.139. Jorda`,O`.,Singh,S.R.,andTaylor,A.M.(2024). ‘Thelong-runeffectsofmonetarypolicy’. Review ofEconomicsandStatistics,pages1–49. Jurado,K.,Ludvigson,S.C.,andNg,S.(2015).‘Measuringuncertainty’.AmericanEconomicReview, vol.105,no.3,1177–1216. Klette,T.J.andKortum,S.(2004).‘InnovatingFirmsandAggregateInnovation’.JournalofPolitical Economy,vol.112,no.5,986–1018. Koop,G.,Pesaran,M.H.,andPotter,S.M.(1996). ‘Impulseresponseanalysisinnonlinearmultivariatemodels’. Journalofeconometrics,vol.74,no.1,119–147. Lakdawala, A., Moreland, T., and Schaffer, M. (2021). ‘The international spillover effects of US monetarypolicyuncertainty’. JournalofInternationalEconomics,vol.133,103525. Lane,P.andMilesi-Ferretti,G.(2017). ‘InternationalFinancialIntegrationintheAftermathofthe GlobalFinancialCrisis’. IMFWorkingPaper17/115. Lian,C.andMa,Y.(2021). ‘Anatomyofcorporateborrowingconstraints’. TheQuarterlyJournalof Economics,vol.136,no.1,229–291. Mendoza,E.(2005).‘RealExchangeVolatilityandthePriceofNontradablesinSudden-StopProne Economies’. Economia,pages103–148. Fall. Mendoza, E. G. (1991). ‘Real business cycles in a small open economy’. The American Economic Review,pages797–818. 43

Mendoza, E. G. (2010). ‘Sudden stops, financial crises, and leverage’. American Economic Review, vol.100,no.5,1941–66. Miranda-Agrippino, S. and Rey, H. (2020). ‘US monetary policy and the global financial cycle’. TheReviewofEconomicStudies,vol.87,no.6,2754–2776. Moran, P. and Queralto, A. (2018). ‘Innovation, productivity, and monetary policy’. Journal of MonetaryEconomics,vol.93,24–41. Moris, F. and Shackelford, B. (2020). ‘Labor Costs Account for Over Two-Thirds of U.S. Business RDPerformancein2020’. NationalCenterforScienceandEngineeringStatistics(NCSES),vol.23. Neumeyer, P. A. and Perri, F. (2005). ‘Business cycles in emerging economies: the role of interest rates’. JournalofmonetaryEconomics,vol.52,no.2,345–380. Queralto, A. (2020). ‘A model of slow recoveries from financial crises’. Journal of Monetary Economics,vol.114,1–25. Rey, H. (2015). ‘Dilemma not trilemma: the global financial cycle and monetary policy independence’. Technicalreport,NationalBureauofEconomicResearch. Reyes-Heroles, R. and Tenorio, G. (2020). ‘Macroprudential policy in the presence of external risks’. JournalofInternationalEconomics,vol.126,103365. Roch,F.,Urquiza,J.,andVicondoa,A.(2025). ‘SpilloversofUSPolicyVolatilityShockstoEMEs’. Mimeo. Tauchen,G.(1986). ‘FiniteStateMarkov-ChainApproximationstoUnivariateandVectorAutoregressions’. EconomicsLetters,vol.20,no.2,177–181. Uribe, M. and Yue, V. Z. (2006). ‘Country spreads and emerging countries: Who drives whom?’ JournalofinternationalEconomics,vol.69,no.1,6–36. ValdiviaLo´pez,M.andBorrayoLo´pez,R.(2023). ‘Unaestimacio´ndelosactivosintangiblespara laeconom´ıamexicana: 1990-2020’. ProblemasdelDesarrollo,vol.54,no.215,55–87. Vicondoa, A. (2019). ‘Monetary news in the United States and business cycles in emerging economies’. JournalofInternationalEconomics,vol.117,79–90. 44

World Bank (2020). ‘Doing Business 2020: Comparing Business Regulation in 190 Economies’. WorldBankReport. Zhou,H.(2024). ‘Thefickleandthestable: Globalfinancialcycletransmissionviaheterogeneous investors’. AvailableatSSRN4616182. 45

Appendices Appendix A Empirical Appendix Inthissectionweprovideadditionaldetailsonthedataconstructionandempiricalmethodsunderlying the results in Section 2. We describe how we measure U.S. interest rate uncertainty, outlinetheestimationofstochasticvolatilityinrealinterestrates,andreportsupportingevidence androbustnesschecksthatvalidateourempiricalimplementation. A.1 DataandStochasticVolatilityinU.S.RealRates For the United States, we utilize data on PCE inflation and Treasury interest rates (3-month, 2year, 5-year) from FRED. We construct a demeaned quarterly time series for the U.S. real interest rate, measured as the real 3-month T-bill rate, for the period of interest.32 Following Ferna´ndez- Villaverde et al. (2011), we adjust nominal rates by the total change in the PCE index over the currentandpriorthreequarters. WeestimatethestochasticvolatilityoftheU.S.realinterestrate usingtheparticlefiltermethodologydescribedbyFerna´ndez-Villaverdeetal.(2011). Specifically, wefilterasequenceσ fromthefollowingmodel,estimatedbymaximumlikelihood: t R t −R¯ = φ(R t−1 −R¯)+σ t rεr t , (29) logσr = (1−ρr)µr +ρr logσr +σ νr, (30) t σ σ σ t−1 r t where R¯ representsthesamplemeanoftherealinterestrate. Table 5 presents our parameter estimates. Both the interest rate and its hidden volatility state arehighlypersistent. Figure11displaystherealinterestrateandthesmoothedpathofthevolatility state. Notably, the hidden volatility state shows substantial variation over time. Volatility declinesfrom1985to2000,correspondingtotherelativestabilityinrealratesduringthisperiod. Afterward, volatility rises over the next decade, paralleling a persistent decline in the average rate and significant fluctuations around this trend. Post-2010, real rates stabilize again, which is reflectedinthestochasticvolatilityprocess. 32Usingthe2-yearor5-yearinterestrateinsteaddoesnotsignificantlyalterourcorefindings, astheseseriesare highlycorrelatedoverthesampleperiod. 46

Table5: U.S.InterestRateModel: EstimatedParameters φ ρr µr σ σ σ r 0.9115 0.9387 −6.3516 0.1181 (0.88,0.93) (0.88,0.95) (−6.61,−6.09) (0.02,0.20) Notes: ThistablereportsmaximumlikelihoodestimatesforthestochasticvolatilitymodeloftheU.S.realinterestratedescribedin equations(29)–(30).Parenthesescontain95%confidenceintervalsobtainedviamontecarlosimulations. Figure11: EstimatedSeriesforU.S.RealRates )ylretrauQ( tnecreP 1 5. 0 5.− 1− 1985q1 1990q1 1995q1 2000q1 2005q1 2010q1 2015q1 2020q1 (a) U.S.RealInterestRate 001*)t 2σ(pxe 53. 3. 52. 2. 51. 1. 1985q1 1990q1 1995q1 2000q1 2005q1 2010q1 2015q1 2020q1 (b) U.S.RealInterestRateStochasticVolatility Notes: Panel(a)plotsthedemeanedquarterlyU.S.real3-monthT-billrate. Panel(b)showsthesmoothedstochasticvolatilitystate impliedbythemodelinequations(29)–(30). A.2 TimeSeriesModels Herewegathermoredetailsontheestimatedtimeseriesmodels. Ourbaselinespecificationis:            ∆y α ∆y 1 1 j,t j j,t−1               ∆c j,t    =    α j    +A·       ∆c j,t−1    −    1    aˆ j,t−1    +    1    aˆ j,t +B·Z t US+Σ j (cid:101)m j,t            ∆i α ∆i 1 1 j,t j j,t−1 (cid:32) (cid:33) aˆ = a + ∑ nσ η σMU j,t j,t s t−s s=0 a = ρ a +σ (cid:101)a . j,t a j,t−1 j,a j,t 47

(cid:16) (cid:17) For most of our results we also impose η = a·exp −s−b . When we estimate the model, we s c imposethat ρ ∈ (−1,1) andthat Σ isdiagonal. Weassumethatallinnovationsaredrawnfrom a j ajointnormaldistributionandthatshockstothetrend((cid:101)a )areindependentfrom(cid:101)m. Toreduce j,t j,t thenumberofparameterstoestimateinourbaselineresultswealsoset   y b  2(cid:32) ns (cid:33) B·Z t US = B 1 ·(∆Y t US, ∆Y t U − S 1 ,EBP t ,EBP t−1 )+    b 2 c    ∑σ η s v∆ σ t M − U s   s=0 bi 2 and impose the same parametric form as discussed above on the ηb. So, while we leave the res sponsetoU.S.growth( ∆YUS)andtheexcessbondpremium(EBP)unrestrictedweimposesome t t restrictionsonthetransitoryeffectsoftheuncertaintyshock. Relaxingthelatterbyallowing B to befullyunrestrictedleadstosimilarpointestimatesfortheη butwidererrorbands. s Tocomputestandarderrorswerepeattheestimationonmodelsimulateddata1000timesand computethepercentilesofinterest. InordertosimulatetheU.S.variablesinthisprocess,wefita VAR(2)totheU.S.timeseries. In addition to using different time series proxies for uncertainty we also performed various variations of the main specification to assess robustness and found our main result survives. As alreadynoted weallowedfor differentrestrictions on B. We alsodroppedsome orallof theU.S. controls. Weestimatedthemodelbothwithandwithouttheparametricrestrictionsontheη . s Finally,weseparatedtheeffectoftheU.S.variablesonthetrendfromother,transitoryeffects, byestimating:            ∆y α ∆y 1 1 j,t j j,t−1               ∆c j,t    =    α j    +A·       ∆c j,t−1    −    1    aˆ j,t−1    +    1    aˆ j,t +B˜ ·Z˜ t US+Σ j (cid:101)m j,t            ∆i α ∆i 1 1 j,t j j,t−1 48

(cid:32) (cid:33) aˆ = a + ∑ nσ η σMU +C·(∆YUS,EBP) j,t j,t s t−s t t s=0 a = ρ a +σ (cid:101)a . j,t a j,t−1 j,a j,t Here B˜ ·Z t US = B˜ 1 ·(∆Y t US−∆Y t U − S 1 , ∆Y t U − S 1 −∆Y t U − S 2 ,EBP t −EBP t−1 ,EBP t−1 −EBP t−2 )   y b  2(cid:32) ns (cid:33) +    b 2 c    ∑σ η s v∆ σ t M − U s .   s=0 bi 2 InthiswayweimposeaseparationbetweenpermanentandtransitoryeffectsofU.S.variables. Results on the η are again robust. We use the smoothed estimate for a + (cid:0) ∑nσ η σMU (cid:1) +C· s j,t s=0 s t−s (∆YUS,EBP) as our estimate of the country trend whenever we display them in the main text to t t allowmoreexplicitlyforotherU.S.effectsonthetrend. Figure 12 shows the confidence intervals when we replace the monetary policy uncertainty shocks with shocks based on other uncertainty metrics as discussed in the text. All of them are identified as the residuals from a VAR including U.S. GDP growth, CPI inflation, interest rates, and the excess bond premium. Figure 13 replaces the uncertainty measure with U.S. monetary policyshocksasmeasuredbyJarocin´skiandKaradi(2020)usingthemedian-rotation. Theshock isscaledsothatitmovesU.S.2-yearratesby25basispoints. 49

Figure12: TrendResponsetoUncertaintyShocks,Robustness: ConfidenceIntervals 0 0 0.04 -0.05 0.02 -0.05 -0.1 -0.15 0 -0.1 -0.2 -0.02 -0.15 -0.25 -0.04 -0.2 -0.3 -0.06 -0.35 -0.08 -0.25 -0.40 2 4 6 8 10 12 -0.10 2 4 6 8 10 12 -0.30 2 4 6 8 10 12 Quarter Quarter Quarter AEMacroUncertainty AEStochasticVolatility AEVIX 0 0 0 -0.1 -0.05 -0.1 -0.2 -0.3 -0.1 -0.2 -0.4 -0.15 -0.3 -0.5 -0.6 -0.2 -0.4 -0.7 -0.25 -0.5 -0.8 -0.90 2 4 6 8 10 12 -0.30 2 4 6 8 10 12 -0.60 2 4 6 8 10 12 Quarter Quarter Quarter EMEMacroUncertainty EMEStochasticVolatility EMEVIX Notes:Thisfigureplotsthecumulativeresponseoftheestimatedstochastictrendtoaone-standard-deviationglobaluncertainty shockforadvancedeconomies(top)andemergingeconomies(bottom).Thelinesreportresponseswhentheuncertaintyshockis proxiedby(i)macroeconomicuncertaintyfromJuradoetal.(2015),(ii)thestochasticvolatilityoftheU.S.realshortratefollowing Ferna´ndez-Villaverdeetal.(2011),(iii)theVIXindex.Allresponsesareestimatedundertheparametricrestrictiononηsandinclude thesamesetofU.S.controlsasinthebaselinespecification.Solidlinesshowthepointestimate,whilethebrokenlinesindicate1-std errorbands. Figure13: TrendResponsetoU.S.MonetaryPolicyShock 0 0 -0.05 -0.1 -0.1 -0.15 -0.2 -0.2 -0.3 -0.25 -0.4 -0.3 -0.35 -0.5 -0.4 -0.6 -0.45 -0.5 -0.7 0 2 4 6 8 10 12 0 2 4 6 8 10 12 Quarter Quarter AE EME Notes:Thisfigureplotsthecumulativeresponseoftheestimatedstochastictrendtoaone-standard-deviationmonetarypolicyshock foradvancedeconomies(left)andemergingeconomies(right). Solidlinesshowthepointestimate,whilethebrokenlinesindicate 1-stderrorbands.Weusethemedian-rotationU.S.monetarypolicyshocksfromJarocin´skiandKaradi(2020)andscaleresponsesso thattheshocksmovetheannualziedU.S.2-yearrateby25basispoints. 50

Appendix B A Simple Model with a Financial Accelerator In this appendix, we characterize a simple model following Gertler and Karadi (2011), Gertler and Kiyotaki (2015), and Akinci et al. (2022), where financial intermediaries in the economy face stochastic volatility in deposit rates. The rest of the features of the model are standard in this literature. B.1 ModelSetup Theoptimizationproblemofanindividualbankis V i,t = max E t [Λ t,t+1 ((1−σ)N i,t+1 +σV i,t+1 )] Li,t,Di,t subjectto V ≥ θL i,t i,t N = Rl L −Rd D i,t t−1 i,t−1 t−1 i,t−1 N +D = L i,t i,t i,t We assume that the loan demand is given by L(Rl) = A−B·Rl. The bond interest rate follows t t thestochasticprocess: Rd = Rd+ρ (Rd −Rd)+σ (cid:101) t 1 t−1 t−1 t logσ t = logσ¯ +ρ 2 (logσ t−1 −logσ¯)+σ¯η t . Lastly, Λ t,t+1 istherelevantdiscountfactorand Λ t,t+1 = R 1 d . t B.2 QuantitativeResults WecalibratethemodeltomatchfeaturesoftheU.S.economy. Table6presentstheexternallycalibratedparameters,alongwiththeircorrespondingvaluesandsourcesinthedata. Theparameters for the stochastic process of the real interest rate and volatility are the ones presented in Section A.1. 51

Table6: CalibrationSummary Parameter Symbol Value Source DepositRate Rd 1.005 U.S.data DemandParameters A,B Internal Normalization L = 1 ExitProbability 1−σ 0.03 U.S.data LeverageRatio L/N 5 U.S.data LoanRate Rl 1.0075 U.S.data Notes:ThistablereportstheexternallycalibratedparametersforthebankingmodelinAppendixB.Thedepositrate,leverageratio, exitprobability,andaverageloanratearechosentomatchU.S.bank-levelandaggregatedata.ThedemandparametersAandBare internallysettonormalizesteady-statelendingtoL=1.Thestochasticprocessesforinterestratesandvolatilityfollowtheestimates inSectionA.1. Ω The rest of the parameters, ,ψ,ν, and θ, are set internally such that equilibrium conditions aresatisfied. Figure14presentstheimpulseresponsefunctionsofthemodelinresponsetoaone standarddeviationincreaseininterestratevolatility.33 Responsesappearaspercentagepointdeviationsfromtheircorrespondingsteadystatevalues. Wealsoaddtheresponsesofanalternative calibration(blackdottedline). Thiscalibrationassumesthattheaverageloan-depositratespread ishigherthaninthebaselinescenario(RL = 1.0085). Thisassumptionisconsistentwithaneconomy that features a larger value of the parameter ι, which controls the average spread faced by agentsintheeconomy. Figure14: ImpulseResponseFunctionstoaStochasticVolatilityShock 3 10-3 1 10-3 1 Baseline Higher Spread 2 0.5 0.8 0 0.6 1 -0.5 0.4 0 -1 0.2 -1 Baseline Higher Spread -1.5 0 2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 16 18 20 LoanInterestRateRl LoansLt StochasticVolatilityσt Notes: Thisfigureshowsimpulseresponsestoaonestandarddeviationincreaseinthevolatilityofthedepositrate. Solidlines correspondtothebaselinecalibration,whiledottedlinesdepictanalternativecalibrationwithahigheraverageloan–depositspread. Panel(a)showstheloanrateRl,panel(b)thequantityofloansLt,andpanel(c)thevolatilitystateσt. 33Wesolvethismodelusing3rdorderperturbationindynare.Astheimpulseresponsefunctionsareobtainedasthe averageovertheergodicsetthroughsimulationsomenoiseremainsinthefigures. FormoreondynareseeAdjemian etal.(2011). 52

The impulse response functions of the baseline case presented in Figure 14 show that an increase in interest rate volatility leads to an increase in the borrowing costs faced by agents in the economy,whichultimatelyleadstoadecreaseinborrowing. Interestingly,theexercisealsoshows thataneconomythathasalargeraverageloan-depositspreadisalsomoresensitivetoavolatility shock: loanrateincreasesandlendingdeclinesaremorepronouncedrelativetothebaseline. Appendix C Financial Intermediation, Risk Aversion and Volatility As seen in Equation (7), a change in the volatility state has a level effect on the interest rate, in additiontoalteringthedispersionofinterestrateinnovations. Toseparatetheseeffects,webuilda counterfactualinwhichtheonlyshockcorrespondstotheleveleffectcomingfromι inEquation 1 (7). In this setup, the only impact is a direct effect on the price of debt, fully isomorphic to a first-moment shock in interest rates. By comparing the impulse response to this shock with the baselineresponsetoavolatilityshock,wecandecomposetheeffectintofirst-andsecond-moment components. Furthermore, we replicate this exercise for the three calibrations examined in the maintext(baseline,advanced,andrelaxedconstrainteconomies).34 To generate the isomorphic interest rate, we proceed as follows. We begin by generating a cross-section of stochastic volatility shocks, as used in Section 4.2. For each of these sequences, we compute the implied interest rate that would produce the same observed movement in the priceqˆ(st). Wethencomputeimpulseresponsestothisimpliedinterestrateshock. Thefirstpanel of Figure 15 presents the cumulative trend responses to the full stochastic volatility shock and to the implied interest rate shock for the baseline model. The second panel shows the difference in responses between the baseline and the two counterfactual models, where in each case we calculate the model-specific implied R sequence. Because the second panel nets out the level effect,thesedifferencescanbeinterpretedasthepuresecond-momenteffectoninterestrates. 34SeeSection4formoredetailsaboutthecalibrationandtheeconomiesstudied. 53

Figure15: CumulativeTrendResponses,StochasticVolatilityandInterestRateShocks 0 0 -0.1 -0.2 -0.05 -0.3 -0.4 -0.1 Baseline -0.5 SV Shock Advanced Implied R Shock Relaxed -0.6 -0.15 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 Horizon Horizon (a) CumulativeResponses (b) DifferentialResponses(SV−ImpliedR) Notes:Panel(a)presentsthecumulativetrendresponsestoaonestandarddeviationvolatilityshockandtotheimpliedfirst-moment interestrateshockforthebaselinecalibration. Panel(b)showsthedifferencebetweenthecumulativeresponsestothestochastic volatilityshockandtheimpliedrateshock,forthebaseline,advanced,andrelaxedconstrainteconomies.Thesedifferencesisolatethe puresecond-moment(volatility)effectontrendproductivity. The results in the first panel of Figure 15 show that pure volatility explains roughly 30% of the total response to a volatility shock. While the level effect varies across models with different ι , the pure second-moment effect can only differ due to the internal propagation mechanisms 1 within each model. The second panel of Figure 15 confirms that the collateral constraint plays a keyroleinthispropagation. Interestingly,thereremainsanimportantdifferencebetweentheadvancedandrelaxedeconomies,whichdifferonlyintheiraveragespreadandinthefirst-moment channel of stochastic volatility. This difference arises from the fact that the relaxed economy featuresadifferentergodicdistributionandadistinctfrequencyandseverityofSuddenStops. Thus, morevolatileratescanstilltriggerrelativelyasymmetriceffectsthroughtheinteractionofthetwo channels. Appendix D Calculating the Firm Size Distribution Because there is a continuum of products we can use the law of large numbers to track the distribution of firms. In particular, denote by Ω (st) the mass of firms with n products. The law of n motionofthisdistributionischaracterizedbyasystemofdynamicequationsthatonlydependon 54

theinnovationrateofincumbentsandthemassofentrants: Ω (st) = (cid:16) M ∗(st−1) (cid:17)υ + ∑ ∞ Ω (st−1) ∑ 1 B (cid:16) k,n,x ∗(st−1) (cid:17) B (cid:16) (k+n−1,n, ∆(st−1) (cid:17) 1 n n=1 k=0 (cid:40) (cid:41) n˜ n (cid:16) (cid:17) (cid:16) (cid:17) Ω n˜>1 (st) = ∑ Ω n (st−1) ∑ B k,n,x ∗(st−1) B k−(n˜ −n),n, ∆(st−1) n=I+(n˜) k=n˜−n 2 (cid:40) (cid:41) ∞ n˜ (cid:16) (cid:17) (cid:16) (cid:17) + ∑ Ω (st−1) ∑ B k,n,x ∗(st−1) B k−(n˜ −n),n, ∆(st−1) , n n=n˜+1 k=0 where I+(a) refers to the integer closest to a such that I+(a) ≥ a.35 The first equation has two terms, the first one tracks the entry of new firms with one product while the second term tracks firmsthatusedtohavemorethan1productandcontractedtoexactly1product. Thesecondline showsananalogouslawofmotionforcategoriesoffirmswithmorethanoneproductwherethe first component are firms that started with less than n˜ products and had net gains that left them at n˜, while the second term reflects firms that were above n˜ and experienced net losses that left themexactlyat n˜.36 TheBGPdistributioncanbefoundbyiteratingintheselawsofmotionuntil themassoffirmsineachproductcategoryisconstant. Appendix E Dynamic System of Equations E.1 RepresentativeHousehold&FinancialIntermediation C˜(s )−γ m˜(st,s t+1 ) = β C˜(st)−γ t+ − 1 φµ˜(st) (1+g(st,s t+1 ))−γ β (cid:104) (cid:105) C˜(st)−γ = µ˜(st)+ qˆ(st) E C˜(st+1)−γ|st (1+g(st,s t+1 ))−γ C˜(st)+qˆ(st)B˜H(st)(1+g(st,s t+1 )) = w˜(st)+B˜H(st−1)+T˜(st) qˆ(st)B˜H(st)(1+g(st,s t+1 )) ≥ −φ ΛV˜ 1 (st) (cid:20) (cid:12) (cid:21) qˆ(st) = E 1 (cid:12) (cid:12)st . (1+R(st+1)+ι +ι (σ(st+1)−σ¯))(cid:12) 0 1 35Afirmwithnproductscanbecomeafirmwithn(cid:48) ∈ [0,2n]inoneperiod,soatmostitcandoubleitssizeinone period. 36Theconditionthatensuresthatthemassofproductsisalwaysequaltooneisgivenby∑∞ n=1 nΩ n (st)=Λ. 55

E.2 FinalGoodProducer Y˜(st) = ez(st) l(st). E.3 IntermediateGoodProducer Y˜(st) l(st) = w˜(st)Λ(1+σ) σ π˜(st) = Y˜(st) Λ(1+σ) (cid:18) x(st) (cid:19)1 θ V˜ (st) = π˜(st)−αw˜(st) −(1−α)x(st)F+ 1 ξ (cid:104) (cid:105) E m˜(st+1)(1−∆(st)+x(st)) (cid:0) 1+g (cid:0) st,s t+1 (cid:1)(cid:1) V˜ 1 (st+1)|st x ∗(st) = (cid:34) θ ξ 1 θ E(cid:2) m˜(st+1) (cid:0) 1+g (cid:0) st,s t+1 (cid:1)(cid:1) V˜ 1 (st+1) (cid:12) (cid:12)s t (cid:3) −(1−α)F (cid:35) 1− θ θ α w˜(st) (cid:18) x(st) (cid:19)1 θ l (st) = . r ξ E.4 Entry M ∗(st) = (cid:34) υ E(cid:2) m˜(st+1) (cid:0) 1+g (cid:0) st,s t+1 (cid:1)(cid:1) V˜ 1 (st+1)|st (cid:3) −(1−α)F (cid:35) 1− 1 υ . ακ w˜(st) E.5 AggregateVariables 1+g(st,s t+1 ) = (1+σ) ∆ (1−δ) = (1+σ)x∗(st)+(M∗ Λ (st))υ (1−δ) T˜(st) = Λ (cid:34) π˜(st)−w˜(st)α (cid:18) x(st) (cid:19)1 θ −(1−α)x(st)F (cid:35) −καM ∗(st)w˜(st)−(1−α) (cid:0) M ∗(st) (cid:1)ν F ξ ez(st) w˜(st) = Λ(1+σ) 1 = Λ(cid:0) l(st)+l (st) (cid:1) +κM ∗(st). r 56

E.6 ExogenousShocks lnz(st) = ρ lnz(st−1)+(cid:101) , with (cid:101) ∼ N(0,η2) z t t z (cid:16) (cid:17) R(st)−R¯ = φ R(st−1)−R¯ +σ(st)ω(st), with ω(st) ∼ N(0,1), R log(σ(st)) = (1−ρ )µ +ρ log(σ(st−1))+η ν(st), with ν(st) ∼ N(0,1), σ σ σ σ 57

Appendix F Solution Method Oursolutionalgorithmforthedecentralizedequilibriumfollowsacombinationofthetime-iteration method employed in Bianchi et al. (2016) with value function iteration. We extend it in order to updateguessesforthecontinuationvalueofaproductline. Wediscretizetheprocessesforaggregateefficiencyz,interestrateRandvolatilityσ following r Tauchen (1986). We consider grids of 7 points for aggregate efficiency, 21 points for the interest rate, and 9 points for interest rate volatility. Our bond holdings grid consists of 60 points, and is skewedtowardslargerdebtholdings.37 In what follows we drop the superscript H from bond holdings BH in order to save notation. All functions presented below are stationary, unless otherwise noted. We start with a conjecture forthebondholdingspolicyfunction,B(cid:48),definedoverthestatespace(z,R,σ ,B).38 Wealsomake r aguessforinnovationintensity x(z,R,σ ,B). Fornotationalsimplicity,assumeS = (z,R,σ ). r r Thestepsofthesolutionalgorithmarethefollowing: 1. Start iteration j with a guess for B(cid:48)(S,B) and innovation intensity x (S,B). Using these j j guessesconstruct: (cid:34) x j (S,B)1− θ θ ν (cid:35) 1− 1 ν M (S,B) = (31) j ξ 1 θθ κ g (S,B) = (1+σ)xj (S,B)+ Mj( Λ S,B)ν (1−δ)−1 (32) j M (S,B)ν ∆ (S,B) = x (S,B)+ j (33) j j Λ (cid:18) x (S,B)(cid:19)1 θ j l (S,B) = (34) rj ξ (1−κM (S,B)) j l (S,B) = −l (S,B) (35) j Λ rj Y(S,B) = zl (S,B) (36) j j σ π (S,B) = Y(S,B) (37) j Λ(1+σ) j 37Sinceweinterpolatepolicyfunctions,ourresultsdonotvarysubstantiallywithmorepopulatedgrids. 38Note that this guess corresponds to a matrix with dimensions Nz ×N R ×Nσ ×N B , where Nz, N R , Nσ and N B correspond to the number of elements in the grid of aggregate efficiency, interest rate, volatility of interest rate and debt,respectively. 58

t (S,B) = Λ(π (S,B)−αw(z)l (S,B)−(1−α)Fx (S,B)) j j rj j −ακM (S,B)w(z)−(1−α)M (S,B)νF (38) j j exp(z) w(S) = (39) Λ(1+σ) c (S,B) = w(S)+B−B (cid:48)(S,B)(1+g (S,B))qˆ(S)+t (S,B) (40) j j j j Lastly,computethediscountedexpectedmarginalutility 1 (cid:104) (cid:105) β E u (S (cid:48) ,B (cid:48)(S,B)) (1+g (S,B))−γ, (41) qˆ(S) j j j whereu (S,B) = c (S,B)−γ. j j 2. Using the above guesses compute a guess for the value of a product line and the stochastic discountfactor. Forthevalueofaproductlineweiterateoverthefollowingvaluefunction: (cid:18) x (S,B)(cid:19)1 θ j V (S,B) = π (S,B)−αw(S) −(1−α)x (S,B)F 1,k+1 j j ξ +E(cid:2) m (S,B)(1−∆ (S,B)+x (S,B)) (cid:0) 1+g (S,B) (cid:1) V (S,B) (cid:3) (42) j j j j 1,k until||V (S,B)−V (S,B)|| < tol. V (S,B)istheconvergedvaluefunction. 1,k+1 1,k 1,j 3. Assume the borrowing constraint binds. Note that when the constraint binds we have that consumptionis c (S,B) = w(S)+B+φ ΛV (S,B)+t (S,B). (43) j+1 1,j j WethencheckwhetherthisassumptionholdsbycalculatingtheresidualoftheEulerequation: R(S,B) = u (S,B) j+1 1 (cid:104) (cid:105) −β E u (S (cid:48) ,B (cid:48)(S,B)) (1+g (S,B))−γ. (44) qˆ(S) j j j 59

If R(S,B) > 0, we keep the values for c (S,B), and we set B(cid:48) (S,B) = − φΛV 1,j (S,B) , j+1 j+1 (1+gj (S,B))qˆ(S) µ (S,B) = R(S,B). Otherwise, the constraint does not bind for that point of the state j+1 space and we discard c (S,B) and B(cid:48) (S,B). We then numerically solve for the value of j+1 j+1 c (S,B)thatsatisfies j+1 1 (cid:104) (cid:105) u (S,B) = β E u (S (cid:48) ,B (cid:48)(S,B)) (1+g (S,B))−γ. (45) j+1 qˆ(S) j j j Wethenset B(cid:48) (S,B) = w(S)+B+tj (S,B)−cj+1 (S,B) andµ (S,B) = 0. j+1 (1+gj (S,B))qˆ(S) j+1 4. Using the updated guesses c (S,B) and B(cid:48) (S,B), compute an updated guess for the j+1 j+1 stochasticdiscountfactor: c (S˜(cid:48),B(cid:48) (S,B))−γ m (S,B) = β j+1 j+1 (1+g (S,B))−γ, (46) j+1 c (S,B)−γ−φµ (S,B) j j+1 j+1 whereS˜(cid:48) arenext-periodrealizations. 5. Recomputethevalueofaproductlineusingtheupdatedstochasticdiscountfactor. Thatis, usevaluefunctioniterationoverthevalueofaproductline: (cid:18) x (S,B)(cid:19)1 θ j V (S,B) = π (S,B)−αw(S) −(1−α)x (S,B)F 1,k+1 j j ξ +E(cid:2) m (S,B)(1−∆ (S,B)+x (S,B)) (cid:0) 1+g (S,B) (cid:1) V (S,B) (cid:3) (47) j+1 j j j 1,k until||V (S,B)−V (S,B)|| < tol. V (S,B)istheconvergedvaluefunction. 1,k+1 1,k 1,j+1 6. Updatetheguessforinnovationintensityofincumbents:   x j+1 (S,B) = max  (cid:34) α θ ξ 1 θ E(cid:2) m j+1 (S,B) (cid:0) 1+g j (S, w B ( ) S (cid:1) ) V 1,j+1 (S,B) (cid:3) −(1−α)F (cid:35) 1− θ θ ,0  .   (48) 7. Check for convergence. If ||B(cid:48) (S,B)− B(cid:48)(S,B)|| < (cid:101) and ||x (S,B)− x (S,B)|| < (cid:101) j+1 j j+1 j thentheproblemissolved. Otherwise,discardB(cid:48)(S,B)andx(cid:48)(S,B),anduseB(cid:48) (S,B)and j j j+1 x(cid:48) (S,B)asnewguessesfortheproblem(gobacktostep1). j+1 60

Appendix G Persistent Effects of Sudden Stops WeconductaneventanalysisaroundSuddenStopsendogenouslygeneratedbythemodelunder the baseline calibration. Using a time window of 10 quarters before and after each event, we average relevant time series.39 Figure 16 illustrates the Sudden Stop dynamics for the baseline scenario. Our focus is on the dynamics of five key variables: the value of a product line, the Lagrange multiplier,thecurrentaccount-to-GDPratio,theendogenoustrend,andlogGDP(inlevels). Panel (a)showstheevolutionofthemodel’sthreeshocksaroundtheevent. Inourframework,Sudden Stopstypicallyoccurunderthreeconditions: (1)borrowingcostsarebelowtheirlong-runaverage, (2)interestratevolatilityislowandbelowitslong-runaverage,and(3)asudden,significantdrop in aggregate efficiency takes place. Low and stable borrowing costs promote excessive borrowing,ashouseholdsdonotfullyinternalizetheconsequencesoftheirborrowingdecisions,leading tooverborrowing.40 Theseepisodesareparticularlypronouncedwhenborrowingconditionsare favorable. Because efficiency shocks are persistent, the combination of high leverage and a protracteddeclineinproductivitytriggerssharpadjustmentsinborrowing, asdepictedinpanel(b), whereasteepcurrentaccountreversalfollows. 39WedefineaSuddenStopasanepisodewherethecurrentaccount-to-GDPratioexceedsitslong-runaverageby twostandarddeviationsandtheborrowingconstraintbinds. 40Thisbehaviorischaracteristicofmodelswithoccasionallybindingborrowingconstraintsandendogenouscollateral values. See Bianchi (2011) and Bianchi and Mendoza (2018) for a detailed analysis of pecuniary externalities in endowmentandproductionmodels. 61

Figure16: SuddenStopDynamics-EmergingEconomy 0 14 2.4 12 2.2 -0.2 10 2 8 -0.4 6 1.8 -0.6 4 1.6 2 1.4 -0.8 0 -2 1.2 -1 -4 1 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 (a)Shocks (b)CA/GDP (c)EndogenousTrendGrowthg 0 5 -1.12 -1.14 4 -1.16 -5 3 -1.18 2 -1.2 -10 -1.22 1 -1.24 -15 0 -1.26 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 -10 -5 0 5 10 (d)ValueofaProductLineV (e)Lagrangemultiplierµ (f)LogGDP 1 Notes:SuddenStopsaredefinedaseventswheretheborrowingconstraintbindsandwherethecurrentaccount-to-GDPratioistwo standarddeviationsaboveitslong-runmean.Thethreeshocksofthemodelarestandardizedbytheircorrespondinglong-runmeans andstandarddeviations. CA/GDPdenotesthecurrentaccount-to-GDPratio,andlogGDPcorrespondstothelogofGDPinlevels. TheredsolidlineinthelogGDPpaneldenotestheaveragetrend,whichisconstructedbyaveragingthelineargrowthusingthetrend growthrate10quartersbeforeaSuddenStop. Panel (c) depicts the trend growth response: a decline of approximately 1 percentage point (annualized),followedbyarapidrecovery. However,asshowninpanel(d),thevalueofaproduct line experiences a sharp drop and fails to return to its pre-Sudden Stop level. This persistent declineisdrivenbyboththesustainedlowaggregateefficiencyandtheincreasedlikelihoodofa bindingborrowingconstraintpost-event(panel(e)). Adepressedproductlinevaluealsoimplies thatcollateralvaluesremainbelowtheirlong-runaverage, contributingtothesluggishrecovery. Finally, panel (f) clearly demonstrates the long-lasting consequences, or hysteresis, of a Sudden Stop: outputsuffersanabruptandpermanentdeviationfromitspre-eventtrend. It is important to distinguish between the crises driven by U.S. interest rate volatility and the Sudden Stops analyzed in this appendix. In the main text, we focus on how increased volatility in U.S. interest rates negatively impacts growth, as agents anticipate larger future interest rate 62

shocks. This is because adverse rate shocks tend to be more damaging than rate reductions are beneficial for growth in emerging economies. However, as shown here, Sudden Stops are different. Theseeventsinvolveasharpcurrentaccountreversalandaretypicallytriggeredbylarge negativeTFPshocks. NoteveryinstanceofabindingborrowingconstraintleadstoaSuddenStop by this definition; the constraint can bind without causing such a large current account reversal. SuddenStopsaremorecloselylinkedtodeepcontractionsinaggregateefficiencyandborrowing needsforconsumptionsmoothing,whereasthemaintextcentersonthedynamicsofinterestrate volatility and its asymmetric effects on growth due to a binding constraint, without requiring a sharpcurrentaccountreversal. Appendix H Additional Results: Binding Borrowing Constraints Figure17displayssimulationsoftheLagrangemultiplierandtheprobabilityofabindingborrowing constraint across three scenarios: baseline, advanced economy calibrations, and an intermediatecasewitharelaxedborrowingconstraint. Thesesimulationsincorporateactualinterestrate and interest rate volatility data and follow the methodology outlined in Section 4.5. To facilitate comparison,Lagrangemultipliersarenormalizedbytheirrespectiveergodicmeans. AsdetailedinSection4.5, ouremergingeconomycalibrationhighlightsstrongprecautionary motives among households, as the probability of a binding borrowing constraint remains below 10% during periods of low risk. However, in times of heightened interest rate uncertainty, this probabilityrisessignificantly,accompaniedbyasubstantialincreaseintheeffectivemultiplier. In theothertwoscenarios,economiesgenerallyoperateneartheborrowinglimit,withepisodesofincreasedvolatilitypromptingdeleveraging,therebymovingawayfromtheendogenousborrowing limit. Thebehaviorofadvancedeconomiesisconsistentwiththerelativelypainlessamplification triggeredbyashockthatforcesdeleverage. 63

Figure 17: Borrowing Constraint Multiplier & Binding Probability Based on Actual Interest Rate andVolatilityTimeSeries 4 3 2 1 0 1990q1 1994q1 1998q1 2002q1 2006q1 2010q1 2014q1 2018q1 Baseline Relaxed Advanced (a) AverageMultiplierµ˜ 1 8. 6. 4. 2. 0 1990q1 1994q1 1998q1 2002q1 2006q1 2010q1 2014q1 2018q1 Baseline Relaxed Advanced (b) Prob.ofBindingConstraintPr(µ˜t >0) Notes: Thisfigureshows,forthethreecalibrations(baseline,relaxedconstraint,andadvanced),theaveragenormalizedLagrange multiplierandtheprobabilityofobservingabindingborrowingconstraintwhenalleconomiesaresubjectedtothesamepathofU.S. realinterestratesandvolatility.Averagesaretakenacross10,000simulatedTFPpaths. 64