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1、BIS Working PapersNo 958Sharing asymmetric tail risk:Smoothing,asset pricingand terms of tradeby Giancarlo Corsetti,Anna Lipiska andGiovanni LombardoMonetary and Economic DepartmentAugust 2021JEL classification:F15,F41,G15.Keywords:international risk sharing,asymmetry,fattails,welfare.BIS Working Pa
2、pers are written by members of the Monetary and EconomicDepartment of the Bank for International Settlements,and from time to time by othereconomists,and are published by the Bank.The papers are on subjects of topicalinterest and are technical in character.The views expressed in them are those of th
3、eirauthors and not necessarily the views of the BIS.This publication is available on the BIS website(www.bis.org).Bank for International Settlements 2021.All rights reserved.Brief excerpts may bereproduced or translated provided the source is stated.ISSN 1020-0959(print)ISSN 1682-7678(online)Sharing
4、 Asymmetric Tail Risk:Smoothing,Asset Pricing and Terms of TradeGiancarlo CorsettiAnna LipinskaAugust 10,2021Giovanni LombardoAbstractCrises and tail events have asymmetric effects across borders,raising thevalue of arrangements improving insurance of macroeconomic risk.Using a two-country DSGE mode
5、l,we provide an analytical and quantitative analysis of thechannels through which countries gain from sharing(tail)risk.Riskier countriesgain in smoother consumption but lose in relative wealth and average consump-tion.Safer countries benefit from higher wealth and better average terms oftrade.Calib
6、rated using the empirical distribution of moments of GDP-growthacross countries,the model suggests significant quantitative effects.We offer analgorithm for the correct solution of the equilibrium using DSGE models undercomplete markets,at higher order of approximation.Keywords:International Risk Sh
7、aring,Asymmetry,Fat Tails,Welfare.JEL Classification:F15,F41,G15.University of Cambridge and CEPR.International Finance Division,Federal Reserve Board.Bank for International Settlements and University of Basel.The views expressed in this paper do not necessarily reflect the views of the BIS and of t
8、he USFederal Reserve System.We thank Fernando Alvarez for an insightful discussion.Giancarlo Corsettigratefully acknowledges the generous support and hospitality of the BIS when working on the firstdraft of this paper.Corsettis work on this paper is part of the project“Disaster Risk,Asset Pricesand
9、the Macroeconomy”(JHUX)sponsored by the Keynes Fund at Cambridge University.1 IntroductionThe Global Financial Crisis,the sovereign risk crisis in the euro-area,the early ef-fects of the looming Climate Change and more recently the COVID-19 pandemic haveprogressively exposed the lack of resilience o
10、f the global economy to large financialand macroeconomic distress and disasters.Policymakers around the world are bracingfor a new global environment with heightened tail riskthe risk of rare but disrup-tive events.Agents perceptions of tail risk may hinder economic recovery from largedisturbances(B
11、aker et al.,2020),or even weigh on long-term growth prospects(Ko-zlowski et al.,2020).While the recent large crises have a strong global component,it has become increasingly clear that regions and countries have a very different ex-posure to disaster shocks.Global crises and tail events transmit qui
12、te asymmetricallyacross borders,widening the international divide in wealth and welfare.Hence tail risk,even when associated to global disturbances,raises the value of international risk shar-ing,achievable either through capital market development and integration,or throughinstitutional arrangement
13、s.In the context of heightened perception of tail risk,risk sharing arrangementsat global level are seen as highly desirable as they give regions and countries oppor-tunities for smoothing consumption and moderate the costs of adjustment to adverseshocks.However,insuring disaster risk has potentiall
14、y significant macroeconomic andfinancial implications.For any given distribution of fundamentals,going from a lowto a high degree of risk insurance changes the equilibrium valuation of national assets.Any change in asset pricing in turn translates into an equilibrium adjustment in rel-ative wealth a
15、nd demand,possibly leading to a re-allocation of labor and productionacross regions and countries.This means that insurance may also affect trade and theinternational prices of goods.In this paper,we study the joint financial,macroeconomic and welfare im-plications of enhancing risk sharing in the p
16、resence of disaster risk.In the traditionof open macroeconomics,we focus on GDP fluctuations as the fundamental source ofmacroeconomic risk.Drawing on financial theory and asset pricing,we bring forwardthe analysis of kurtosis and skewness,in addition to variance,in the distribution ofthe variable u
17、nderlying macroeconomic risk.Relative to the literature,we explicitlyaccount for cross-border heterogeneity in both second and higher moments of the dis-tribution of national GDP.For analytical clarity and tractability,we focus our analysisby contrasting the extreme cases of financial autarky(no rol
18、e for insurance via finan-cial markets)to complete markets(perfect insurance).1 We carry out our analysis1This guarantees that,in the absence of economic distortions,trade in financial assets will unam-1both analytically and numerically,setting parameters based on evidence on the GDPdistribution acr
19、oss countries.To motivate our analysis,we present a set of stylized facts on the variance,kurtosis and the skewness of output for a large sample of countries.We show that,first,there is substantial heterogeneity in these moments across countries.Second,thevariance of output is positively correlated
20、with kurtosis but negatively correlated toskewness.As one would expect,especially in light of the past decades of data,highervolatility of output is associated with higher frequency of large downturns.Our theoretical contribution is threefold.First,we offer a novel decompositionof the gains from ris
21、k sharing into a“smoothing effect”(SE)and a“level effect”(LE).The former captures welfare gains from risk diversification in terms of the distributionof marginal utility growth.The latter synthesizes welfare gains or losses through theaverage consumption of goods and leisure.These in turn materializ
22、e via interrelatedchannels.The relative wealth channel works via the revaluation of a country assets,including physical,financial and human capital,at the equilibrium prices with perfectinsurance(relative to imperfect insurance).Asset prices reflect any adjustment notonly in the equilibrium discount
23、 factor,but also in the(average)international price of acountrys output the good price channel associated to the equilibrium reallocationof production and demand.We specifically highlight the terms of trade as a novelchannel by which perfect insurance may affect social welfare:for a given relative w
24、ealth,the country experiencing an improvement in its average terms of trade gains in higherconsumption and lower labor effort.An important advantage of our decompositionconsists of clarifying how varying the relative riskiness of national GDPs may move thesmoothing and level effects(SE and LE)in opp
25、osite directions.Riskier countries gain interms of smoother consumption and labor,but lose out in terms of average consumptionand labor effort.Instead,safer countries benefit from higher average consumption andlower labor effort in excess of possible smoothing losses.Our decomposition maps thesemove
26、ments into aggregate quantities and prices.Intuitively,these movements are thegeneral equilibrium analog of a premium paid or received by a country to benefit fromor offer macro insurance.Second,we derive analytically and numerically the independent and jointcontribution of different moments of the
27、GDP distribution to a countrys gains fromrisk sharing,by different channels.We show that smoothing and level effects tend tocompensate each other with asymmetries in second moments(volatility of income)with substantial macroeconomic adjustment to risk sharing via relative wealth andbiguously bring a
28、bout positive welfare gains.2terms of trade movements.With fat tails asymmetric to the left(third and fourthmoments)in the distribution of GDP,the gains from risk sharing are instead dominatedby improvement in consumption smoothing of the riskier country.Relatively safecountries gain in terms of hig
29、her average asset prices and better average terms oftrade.Model simulations accounting for the correlation across moments based oncountry-pair comparison corroborate the empirical relevance of both the smoothingand the level components of the gains from risk sharing.Overall,tail risk enhancesthe rel
30、ative gains from capital market integration of countries that are more exposedto it.We quantify this effect by drawing country pairs from the empirical distributionof countries according to their GDP-growth variance,skewness and kurtosis,and usingthe resulting moments in our theoretical model.Our si
31、mulation suggests that riskiercountries in the 95-th percentile of the distribution of outcomes can have a relative gainadvantage of about 10%of the total gains from risk sharing(total gains are defined assum of Home and Foreign country gains form risk sharing).This relative advantageresults from di
32、fferent contributions from the SE and LE components of the gains acrosscountries.For example,the advantage for riskier countries in the 95-th percentile ofthe distribution,the consumption smoothing component is about 15%,in part offsetby a negative LE.The opposite mechanism is at work for the safer
33、countries,who aregaining mainly from the level effect.Our third and last contribution is related to the way we carry out our study,both analytically and numerically,using perturbation methods.2 For the purpose ofstudying tail risk,these methods are preferable to alternative(global)methods,asthey nat
34、urally yield a decomposition of the solution in the higher moments of thedata generating process.As a methodological contribution to the literature,we spellout a theoretically consistent algorithm applicable in general equilibrium models.Thealgorithm yields an efficient solution to the problem of so
35、lving for the initial distri-bution of wealth under complete markets,using perturbation.The usefulness of thiscontribution is best appreciated in light of a widespread practice in the literature,consisting of omitting the specification of the budget constraint under the assumptionof complete markets
36、.This practice is not necessarily consequential when countriesare assumed to be sufficiently symmetrical in economic structure and distribution ofdisturbances.It becomes problematic in exercises realistically allowing for large asym-metries in structure and risk across borders,as omitting the budget
37、 constraint fromthe solution algorithm rules out by construction the level effect component driving thegains from risk sharing.32See e.g.Holmes(1995),Judd(1998),Schmitt-Grohe and Uribe(2007),Lombardo and Sutherland(2007),Kim et al.(2008),Andreasen et al.(2018),and Lombardo and Uhlig(2018).3It is eas
38、y to produce examples where a model solved using this practice erroneously predictswelfare losses for a country when moving from autarky to complete markets.3Analytical tractability allows us to explore in detail how the structure of theeconomy translate the properties of the fundamental process dri
39、ving output into incomerisk.We provide insight on non-loglinearities in the economic structure that drive thetransmission of tail risk,and specifically discuss how income risk varies with the intra-and intertemporal elasticity of substitution.For some parameterizations of the model,standard in the l
40、iterature,we are able to derive sharp and instructive propositions.Oneinstance is the proposition of“equal gains”from risk sharing,applied to symmetriccountries differing only in the volatility of output:asymmetries in risk do not translateinto differences in welfare gains,but only affect the compos
41、ition of these gains.Theriskier country gains more in consumption smoothing,the other benefits from higheraverage consumption.Our decomposition of the gains from risk sharing into smoothing and leveleffects has policy relevance.In the policy literature,the gains from risk sharing are typ-ically asse
42、ssed in terms of consumption smoothing only(e.g.Vinals(2015),Constancio(2016),i.e.it focuses only on the first leg of our decomposition.Consistently,mostof the empirical evidence and indicators of risk sharing published in policy reportsare based on measures of consumption volatility and cross count
43、ry correlations of con-sumption.4 Relying on these indicators to assess international risk diversification raisesa number of logical issues.As shown in our analysis,the SE is only one componentof the total gains from diversification:an assessment of these gains based on theseindicators is at best in
44、complete.When a relatively safe and a relatively risky countryintegrate their capital markets,it is plausible that the safe country mainly gains interm of higher average wealth and consumption,and despite diversification may evenlose out in terms of consumption volatility.By no means this implies th
45、at the safecountry derives no gain from asset trade,as the wealth and consumption level effectsof asset revaluation at the new equilibrium price would more than compensate lossesin smoothing,if any.Vice versa,the risky country is likely to lose out in terms of rela-tive wealth and consumption.The“im
46、plicit transfer”via asset revaluation and termsof trade adjustment is typically disregarded in policy debate,arguably because it isdifficult to quantify.Yet,it is a key channel through which countries benefit from theintegration of frictionless financial markets.5 This channel cannot be ignored in p
47、olicy4The empirical literature is large.See for example Obstfeld(1994)and the literature review inKose et al.(2009).One popular approach consists of testing directly the consumption risk-sharingcondition,which predicts a perfect correlation of consumption growth of two economies trading incomplete f
48、inancial markets.Another popular approach measures the correlation between domesticconsumption growth and domestic output growth:the more a country is globally financially integrated,the less domestic consumption depends on idiosyncratic domestic disturbances.5This point is apparent in the theoretic
49、al literature,starting from textbook treatments(e.g.Ljungqvist and Sargent,2012),and including recent research(e.g.Engel,2016;Coeurdacier et al.,2019).4debates on the pros and cons of capital market integration among countries differingin their risk profile and economic features.Our analysis draws o
50、n a long standing body of literature highlighting theeffects of higher moments on asset prices and risk premia.Early on,Samuelson(1970)already warned against limiting the analysis of optimal portfolio choices to first andsecond moments(mean-variance models),which in his view can be justified only in
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