Assessing Macroeconomic Tail Risk

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Assessing Macroeconomic Tail Risk Francesca Loria, Christian Matthes, and Donghai Zhang 2019-026 Please cite this paper as: Loria,Francesca,ChristianMatthes,andDonghaiZhang(2019). “AssessingMacroeconomic Tail Risk,” Finance and Economics Discussion Series 2019-026. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2019.026. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) 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 Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Assessing Macroeconomic Tail Risk Francesca Loria* Christian Matthes† Donghai Zhang‡ April 3, 2019 Click Here for the Latest Version Abstract What drives macroeconomic tail risk? To answer this question, we borrow a definition of macroeconomic risk from Adrian et al. (2019) by studying (left-tail) percentiles of the forecastdistributionofGDPgrowth. Weuselocalprojections(Jordà,2005)toassesshow this measure of risk moves in response to economic shocks to the level of technology, monetarypolicy,andfinancialconditions. Furthermore,bystudyingvariouspercentiles jointly,westudyhowtheoveralleconomicoutlook—ascharacterizedbytheentireforecast distribution of GDP growth—shifts in response to shocks. We find that contractionaryshocksdisproportionatelyincreasedownsiderisk,independentlyofwhatshock welookat. Keywords: MacroeconomicRisk,Shocks,LocalProjections JELClassification: C21,C53,E17,E37 WethankMarvinNöllerforexcellentresearchassistance.Disclaimer:Theviewspresentedhereinarethose of the author and do not necessarily reflect those of the Federal Reserve Board, the Federal Reserve Bank of Richmond,theFederalReserveSystemortheirstaff. *BoardofGovernorsoftheFederalReserveSystem,francesca.loria@frb.gov. †FederalReserveBankofRichmond,christian.matthes@rich.frb.org. ‡InstituteforMacroeconomicsandEconometrics—UniversityofBonn,donghai.zhang@uni-bonn.de.

1 Introduction Economicpolicymakersandmarketparticipantsaregenerallynotonlyworriedaboutwhat changes to economic conditions will do to the economy on average, but also how these changes affect the probability of large losses materializing.1 Standard impulse response functions in linear models such as Vector Autoregressions (VARs) are not built to answer thesequestionsastheytrackaverageoutcomes. Ourgoalistoprovideaflexible,yetsimple framework that can directly tackle these issues. In the finance literature, the notion of value at risk is prevalent. What is meant by value-at-risk is the evolution of left-tail percentiles of the variable of interest under various scenarios. We borrow this idea to operationalize the conceptofmacroeconomicrisk. Tobemoreprecise,wefollowAdrianetal.(2019)andstudy the distribution of macroeconomic risk by estimating a quantile forecast regression of GDP growthfourquartersaheadforvariousquantiles. Wefocusonthe10thpercentileand,asreference points, the median and 90th percentiles. We interpret this 10th percentile of the forecastdistributionoffutureGDPgrowthasmacroeconomictailrisk. Withthatmeasureathand, we ask how macroeconomic risk changes after structural shocks hit the economy by studying local projections as introduced by Jordà (2005). To do so, we collect various measures of a suite of macroeconomic shocks. In particular, we use various measures of technology shocks,monetarypolicyshocks,aswellasameasureofshockstofinancialconditions. Here we follow the large literature that directly uses measures of (or instruments for) structural shocks—see for example Ramey and Zubairy (2018), Romer and Romer (2004), or Mertens andRavn(2013). Withthechangesinthe10thpercentileaswellasthemedianandthe90th percentileinhand,wecanfurtherfollowinthefootstepsofAdrianetal.(2019)andfitaflexible (skewed-t) distribution to match various estimated quantiles as well as trace out how the entire distribution of real GDP growth four quarters ahead changes after a shock hits the economy. We view changes in this distribution as summarizing changes in the economic outlook afterashockhitstheeconomy. One key point to emphasize is that our approach is constructed to be as flexible as possible: In the initial quantile regression stage, we model each quantile separately instead of assuming a specific distribution for the forecast distribution of real GDP growth. In the second stage, we use local projections to impose as few restrictions on the data generating process as possible.2 Just as Adrian et al. (2019), we only use the skewed-t distribution after 1ForresearchshowingthattheFederalReserveisconcernedbydownsiderisk,seeKilianandManganelli (2008). For direct evidence of a policymaker thinking about downside risk, see this March 2019 speech Lael Brainard,memberoftheBoardofGovernorsoftheFederalReserveSystem: https://www.federalreserve. gov/newsevents/speech/brainard20190307a.htm. 2As shown by Plagborg-Møller and Wolf (2019), local projections and VARs asymptotically estimate the sameimpulseresponses,butareondiametricallyoppositeendsofthebias-variancetrade-offinfinitesamples. 2

having estimated the quantiles separately. A common pattern emerges when we study our shocks: ExpansionaryshockscompressthedistributionoffutureGDPgrowth,thusmaking “bad” outcomes (those in the left tail) more tolerable. Unfortunately, as we show later, this result also implies that contractionary shocks make the 10th percentile fall more than the median—hence leading not only to poor average outcomes, but also to a further increase in downside risk. Complementing the analysis in Adrian et al. (2019), we find that the key channelthroughwhichshocksaffectmacroeconomicriskisviatheireffectonfinancialconditions. Theremainderofthepaperisorganizedasfollows. Section(2)presentseconometricmethodology. Section(3)provides anintuitionhowshocks mightaffecttheshape ofdistributionin differentmanners. Section(4)presentsthemainfindingsandSection(5)concludes. 2 Econometric Methodology 2.1 Conditional Quantiles We compute conditional quantiles for annualized real GDP growth following the method proposed by Adrian et al. (2019). In particular, we run a quantile regression (Koenker and Bassett, 1978) for real GDP growth over the subsequent 4 quarters by conditioning on a constant,theNationalFinancialConditionsIndex(NFCI)andrealGDPgrowthattime t.3 Formally, let y denote the average value of real GDP growth between t and t+h and t+h let x denotethevectorofconditioningvariables,thenthequantileregressionisgivenby: t T−h(cid:16) (cid:17) βˆ =argmin ∑ τ·1 |y −x β |+(1−τ)·1 |y −x β | , (2.1) τ (y t+h ≥xtβ) t+h t τ (y t+h <xtβ) t+h t τ βτ ∈Rk t=1 where 1 denotestheindicatorfunctionandτ∈(0,1)indicatestheτthquantile. Thequan- (·) tile of y conditional on x is then given by the predicted value from that regression4, t+h t definedas Qˆ (τ|x )= x βˆ ≡q . (2.2) y t+h |xt t t τ τ,t Inthefollowingwewillanalyzehowdifferentquantilesreacttoaggregateshocks. 3InAppendixCweshowthatourfindingsarerobusttoaddingadditionalcontrols. 4WhileAdrianetal.(2019)definethepredictedvalueofy t+h astheconditionalquantileatt+h,wedefine thepredictedvalueastoday’srisk. Thatis,thepredictedvalueofy t+h correspondstot. 3

2.2 Impulse Responses We estimate responses of different GDP growth quantiles to a variety of aggregate shocks by applying the local projection method based on Jordà (2005). As a baseline we run the followinglinearregression: q τ,t+s =α τ,s +β τ,s shock t +ψ τ,s controls+(cid:101) τ,t+s , (2.3) fors=0,...,Sandwhereq τ,t+s isthemeasureofriskatperiodt+sfortheτthquantile(i.e., the quantile τ of the distribution of y conditional on information at time t + s), and t+s+h controls is a vector of control variables that include the lagged quantiles and model-specific controlsthatwewillexplaininthenextsection. Notethatthattherearetwodistinctnotions of “horizon” in our application. First, the horizon in the quantile regression h, which we keep fixed at 4 quarters. This first horizon captures how forward looking our measure of risk is. The second notion of horizon is s in the local projection, which we vary as we trace outhowriskrespondsatdifferenthorizonstoashockattime t. Theresponseofquantile q τ attimet+stoashockattimetisthengivenbyβ . Thus,weconstructtheimpulse-response τ,s functionsbytheestimatingthesequenceofthe β ’sinaseriesofunivariateregressionsfor τ,s each horizon. Confidence bands are based on Newey-West corrected standard errors that control for serial correlation in the error terms induced by the successive leading of the dependentvariable. At this point it is useful to contrast our approach with another approach that aims to combine quantile regressions with local projections, an approach advocated for by Linnemann and Winkler (2016). We want to interpret the 10th percentile of 4-quarters ahead GDP growth as a measure of downside risk and we then ask how this measure of risk reacts to different shocks. Furthermore, by not only looking at the 10th percentile in isolation but various quantiles jointly, we can construct how the distribution of four-quarters ahead real GDP growth changes as shocks hit the economy. We study a number of shocks and find it useful to use the same quantile (or measure of risk) for all shocks we study in our local projections. Linnemann and Winkler (2016), instead, are interested in one shock only and model the conditional quantiles conditional on, among other things, a fiscal shock and thus includetheshockdirectlyinthequantileregression. Byfollowingtheirapproach,Linnemann and Winkler (2016) can not distinguish between the two horizons h and s that we emphasizedabove(giventhattheyaskadifferentquestion,theyprobablywouldnotwantto). With impulse responses to various quantiles at hand, we fit a flexible distribution to our estimatedpathofGDPgrowthdistributionsaftereachshock. Tobespecific,westartwiththe average distribution of real GDP growth four quarters ahead using the sample of Adrian 4

et al. (2019). We then change four quantiles according to the estimated impulse response functions(IRFs)5toproducepathsofthosefourquantiles. Foreachhorizon,wethenchoose the four parameters of the skewed-t distribution (Azzalini and Capitanio, 2003) to exactly match those four quantiles. The skewed-t distribution is given by the following density functionforadatapoint y:   (cid:18) (cid:19) (cid:118) 2 y−µ y−µ(cid:117) ν+1 f(y|µ,σ,α,ν)= t ;ν Tα (cid:117) ;ν+1. (2.4) σ σ  σ (cid:116) ν+ (cid:16) y−µ (cid:17)2  σ AsdiscussedinAdrianetal.(2019),tandTarethedensityandcumulativedistributionfunction of the common t-distribution, µ is a location parameter, σ is a scale parameter, ν controls how fat the tails are (similar to the degrees of freedom in the common t-distribution), whereas α governs skewness because it controls how much the standard t-distribution is twisted(orskewed)accordingto T. 2.3 Data We estimate responses in different quantiles of GDP growth to various aggregate shocks. All regressions are estimated at quarterly frequency and as a baseline we use four lags for all control variables. This section gives a brief overview of the various specifications and datatransformations. MostoftheshocksconsideredherearereviewedinRamey(2016)and can be thus found in her data appendix. More details on our data sources are provided in AppendixA. NarrativeMonetaryPolicyShocks Weexploretwotypesofmonetarypolicyshocks. First, weusetheRomerandRomer(2004)(RRhenceforth)narrative-basedmonetaryshocks. They regress the federal funds target rate on Greenbook forecasts at each FOMC meeting date and use the residuals as the monetary policy shock. We aggregate these monthly shocks by adding up the monthly values within each quarter. The sample period runs from 1973Q1 to 2007Q4. As a second measure, we use the monetary policy shocks identified by Antolín- Díaz and Rubio-Ramírez (2018) (AR henceforth) who add narrative sign restrictions to the VAR model in Uhlig (2005). Also in this case, monthly values are aggregated to quarterly frequency. Herethesampleperiodrunsfrom1973Q1to2007Q3. Forbothtypesofshockswe includethefollowingcontrolsinthelocalprojectionregression: Laggedvaluesoftheshock 5Following Adrian et al. (2019), we use impulse responses for the 5th, 25th, 75th, and 95th percentiles to matchthepercentilesthatAdrianetal.(2019)usedtocomputethedistributionsintheirpaper. Weshowthe impulseresponsesforthosequantilesinAppendixB.Theytellthesamestoryasourchoiceofpercentiles. 5

itself,thelogofboththeconsumerandthecommoditypriceindex(aggregatedtoquarterly frequency by simple averaging) in first-differences, the log of real GDP in first-differences, the federal funds rate (quarterly average) and the unemployment rate. We refrain from includingcontemporaneouscontrols. ExcessBondPremiumShocks WetaketheGilchristandZakrajšek(2012)excessbondpremium(EBPhenceforth)updatedbyFavaraetal.(2016)toconstructanaggregateshock6. The excess bond premium can transformed into an exogenous shock by setting the additional controlsappropriatelyifweassumethatthebondpremiumaffectsinterestratescontemporaneouslybuthasnoimpactonpricesandeconomicactivitywithinaquarter.7 Thus,theset of controls consists of the contemporaneous federal funds rate and lags of the EBP, the log of the consumer price index, and the log of real GDP (the last two in first-differences). All other shocks we study are identified in a separate estimation. For EBP we can instead identify the shock in the local projection step along the lines of Barnichon and Brownlees (2016) by controlling for the relevant variables. In this one step approach, the lagged “shocks” are implicitly controlled for in lags of endogenous variables. The sample period runs from 1973Q1to2015Q4. Unanticipated and Anticipated Technology shocks We consider three different technology shocks. First, a technology shock à la Galí (1999), constructed by imposing that a technology shock is the only shock affecting labor productivity in the long-run. For the Galí (1999) shock, we estimate a VAR with four lags that includes three variables: changes in labor productivity, changes in hours, and changes in the GDP deflator. The technology shock is identified as the only shock affecting labor productivity in the long-run. Second, we constructtechnologyshocksbytakingthegrowthrateoftheFernald(2012)utilization-adjusted TFP series for the aggregate economy. We refer to these shocks as “JF-TFP” shocks. Third, we consider the Barsky and Sims (2012) TFP news shocks. The news shock is identified in a VAR with four lags that includes TFP, consumption, real output, and hours per capita. The identification assumption is that the news shock is orthogonal to the innovation in current TFP that best explains variation in future TFP (in the subsequent 10 years). For the Galí (1999) shock and the TFP news shock the sample period runs from 1975Q1 to 2007Q3. The JF-TFP shock is available from 1974Q1 up to 2015Q3. For all technology shocks we include the following controls in local projections: lags of the shock itself, lagged log of real GDP percapitainfirst-differencesandlaggedlogofproductivityinfirst-differences. Thelatteris 6Wetransformittoquarterlyfrequencybyaveragingthemonthlyvalueswithineachquarter. 7Forafurtherdiscussionofhowtimingrestrictionssuchasthiscanbeincorporatedinlocalprojectionssee BarnichonandBrownlees(2016). 6

measuredasrealGDPdividedbytotalhours. 3 Some Intuition for Impulse Responses of Quantiles This section gives three examples where an initial distribution of an outcome changes after ashockhits. Weshowtheseexamplestoconveyhowthechangeinquantilesislinkedtothe change in the distribution as a whole and how changes in specific moments translate into changes in quantiles. Our scenario is as follows: After an initial univariate distribution of an outcome is hit by a shock, we trace out how this distribution changes on impact and in theperiodafterimpact. Weconsiderthreeexperiments: 1. Theshockleadstoanincreaseinthevarianceofourdistribution,whichisGaussian. 2. Theshockleadstoanincreaseinthemeanofourdistribution,whichisGaussian. 3. The shock leads to an increase in the shape parameter of our distribution, which is distributedaccordingtoaGammadistribution. Figure1plotsthreepanelsforeachexperiment. Thefirstpanelineachrowshowstheinitial distribution, the distribution when the shock hits and the distribution in the period after the shock has materialized. The middle panel in each row shows the evolution of the 10th and 90th percentile for those three periods. The last panel in each row gives the impulse responses for the 10th and 90th percentiles under the assumption that if the shock that moved the distributions did not materialize, the distribution would have remained at its original position. As the impulse response plots the difference between the relevant percentiles and the original values, the impulse response figures only show values for two time periods (the period where the shock hits and the period after). Each row presents the figures for one experiment. Note that the levels of the percentiles are not directly interpretable as IRFs because we do not subtract the baseline value from the quantiles in those figures. As we can see, an increase in the variance of a symmetric distribution makes the quantiles drift apart in a mirror-image fashion, whereas a change in the mean of a symmetric distribution makes thequantilesmoveinparallel,whichinturnmakestheimpulseresponseslieontopofeach other. Withanon-symmetricdistribution(orifashockmakesadistributionnon-symmetric) the quantiles can drift apart, but not necessarily in a mirror-image fashion, as is the case in thelastexample. Interpreting changes in multiple quantiles jointly can be challenging because we have to envision how the entire distribution might change. We will later also plot changes in distributions to help the reader with interpretation. Nonetheless, it is useful to dig a bit deeper 7

at this point. As an example, let us focus on the third experiment. As can be seen from the lastpanelonthebottomrowofFigure1,the10thand90thpercentiledriftapartbecausethe 90th percentile increases faster than the 10th percentile. Thus the distribution spreads out as a result of the shock—this can also be seen by looking at the leftmost panel of the bottom row, where the yellow distribution is more spread out than the original blue distribution. Let us for a second imagine that this impulse response is the response to a “positive” shock andthatquantilesreactlinearlytothoseshocks(aswillbethecaseinourlocalprojections), so that the response to a “negative” shock would just be the mirror image of the rightmost panelofthebottomrow. Whatwouldhappentothedistributioninthatcase? The90thpercentile would decrease faster than the 10th percentile. Hence the distribution would actually compressinthatscenario. distributions, change in variance quantiles, change in variance IRF of quantiles, change in variance 0.4 10 3 initial impact 8 2 0.3 after impact 10th percentile 1 90th percentile 6 10th percentile 0.2 0 90th percentile 4 -1 0.1 2 -2 0 0 -3 0 2 4 6 8 10 0 1 2 1 2 distributions, change in mean quantiles, change in mean IRF of quantiles, change in mean 0.4 9 2 8 1.8 0.3 7 1.6 0.2 6 1.4 5 0.1 1.2 4 0 3 1 0 2 4 6 8 10 0 1 2 1 2 distributions, change in shape quantiles, change in shape IRF of quantiles, change in shape 0.2 30 16 25 14 0.15 12 20 10 0.1 15 8 10 6 0.05 5 4 0 0 2 0 5 10 15 20 0 1 2 1 2 Figure1: IllustrationofChangesinPercentiles. 8

4 Results In this section, we present various impulse responses (i.e. βˆ ) based on equation 2.3. The s βˆ coefficientscanbeinterpretedasresponsestoonestandarddeviationshocks. Wepresent s resultsforthreegroups: monetarypolicyshocks,creditshocks,andtechnologyshocks. Additional figures can be found in Appendix B. We first plot the impulse responses of the 10th percentile, the median, and the 90th percentile in Figure 2. We show the error bands for the response for the median in the main text, the corresponding error bands for the other percentiles can be found in Appendix B. We then follow Adrian et al. (2019) and use those estimated quantiles to fit a flexible (skewed-t) distribution to match the quantiles. In Figure 3 we plot how various shocks change this distribution. In particular, we first compute the average distribution of four-quarters ahead real GDP growth in our total sample and then plotthedifferencebetweenthisinitialdistributionandthedistributionaffectedbyaspecific shock at various horizons. In order to facilitate interpretation, each panel of Figure 3 plots three lines: the 10th percentile (in red), the median (in black), and the 90th percentile (in blue)oftheoriginal(average)distribution. Thishelpscheckinwhatdirectionashockshifts the distribution. In particular, whenever a line is visible it means that posterior mass at that quantileoftheoriginaldistributionhasdecreased. 4.1 Monetary Policy Shocks The first panel of Figure 2 plots the responses to a contractionary RR monetary shock estimated via local projections. Those shocks affect the distribution of GDP growth disproportionately across quantiles. A contractionary (i.e., positive) monetary policy shock decreases the 10th percentile more than the median or the 90th percentile. This means that not only willamonetarypolicyshockleadtoadecreaseinmedianforecastedGDPgrowthfourquarters ahead, but it will also make “bad” outcomes substantially worse by spreading out the lefttailofthedistribution. The above result is robust to the use of an alternative monetary shock measure, namely the AR monetary shock (see the second panel in the top row of Figure 2). This shift is also evident from the top two panels of Figure 3, which plot the implied changes in the entire distributionofforecastedGDPgrowth. 4.2 Credit Spread Shock The third panel of Figure 2 plots the responses to a contractionary (i.e., positive) shock to the excess bond premium, which we interpret as an unexpected deterioration of financial 9

conditions,justasGilchristandZakrajšek(2012). TheentireconditionaldistributionofGDP growth is shifted, with the left tail being affected disproportionately more. On impact and up to one year, the interpretation of the effects of a contractionary credit shock is similar to the interpretation of the monetary policy shock given above. After one year, however, the responses of the 10th and 90th percentile cross, leading the distribution of future GDP growth to actually compress since the 10th percentile grows faster than the 90th percentile. Oneinterpretationoftheseresultsisthatpolicymakerscounteractfinancialshocks,butthat it takes arounda year for these measures totake effect (potentially and partiallydue to lags inpolicyimplementation). 4.3 Technology Shocks The effects of a technology shock identified along the lines of Galí (1999) is shown in the second panel of the middle row of Figure 2. The bottom row of that figure shows the corresponding effects for a technology shock identified using Fernald (2012) and a TFP news shock following Barsky and Sims (2012). We discuss the findings together since the results for both risk (the effects on the 10th percentile of the forecast distribution) and the entire shapeoftheeconomicoutlookaresimilaracrossthesespecifications. Anexpansionarytechnology shock of any of the three types we consider here compresses the distribution of real GDP growth one year ahead. This means that not only does a technology shock raise median GDP growth one year ahead, but it also makes low outcomes of future GDP growth moretolerablebyshiftingthedistributiontotheright—ascanbeseeninFigure3. Theonly slight caveat to this interpretation is that at large horizons (more than three years out) the impulseresponseofthe10thpercentiletoaFernaldTFPshockbecomesnegative. Thispositiveviewofanexpansionarytechnologyshockcomeswithadownside: Acontractionary technology shock will increase downside risk. Indeed, the response to a negative shockwouldbethemirrorimageofthecorrespondingpanelsinFigure2. 10

RR monetary AR monetary 0.2 1 0.5 0 0 -0.5 -0.2 5 10 15 20 5 10 15 20 EBP Credit Gali Tech 0.6 1 0.4 0 0.2 -1 0 -2 5 10 15 20 5 10 15 20 TFP News JF TFP 0.4 0.1 0.2 0 0 -0.1 5 10 15 20 5 10 15 20 10th quantile median 90th quantile Figure2: ImpulseResponsesofVariousQuantiles. Note: Red (dashed) is response of the 10th quantile, black (solid) is the median response, blue (dotted) is responseofthe90thquantile. Confidencebandscorrespondtomedianresponse,90%significancelevel,based onNewey-Weststandarderrors. Source: Authors’calculations. Figure3: DifferenceinFitted t-Distributions. Note: Straightlinesare10thpercentile(red), median(black), and90thpercentile(blue)oftheaveragedistributionof4-quartersaheadrealGDPgrowthinoursample. Source: Authors’calculations.

4.4 Inspecting the Economic Mechanism ThroughwhichchanneldomacroeconomicshocksaffecttheconditionaldistributionofGDP growth? To answer this question we look at how the conditioning variables used to construct the quantiles of GDP growth in (2.1) respond to the shocks studied in this paper. In particular,inFigure4wereporttheimpulseresponsesoftheNationalFinancialConditions Index (NFCI). Positive values indicate that financial conditions are tighter, while negative values indicate financial conditions that are looser. As expected, while contractionary monetarypolicyshocksandcreditspreadshocksmakefinancialconditionstighter,thereverseis trueforexpansionarytechnologyshocks. Akeydifferenceisthatwhilethereis,onaverage, strong mean reversion in the response to the shocks that make financial conditions tighter, technology shocks improve financial conditions for much longer. Notice that the impulse responsesofthe10thquantileoftheconditionalGDPgrowthdistributioninFigure2inherit the(inverse)patternoftheresponseoffinancialconditions.8 Thisresultsuggeststhatofour two conditioning variables, i.e., financial conditions and current GDP growth, it is through the former channel that shocks affect macroeconomic tail risk. Our finding is in line with Adrian et al. (2019), who point out that including the NFCI as a conditioning variable is importanttocapturedownsiderisk. Adrianetal.(2019)discussvariousequilibriummodelsin the literature that help explain the central role of financial conditions in shaping future real GDPgrowth. We can thus conclude that contractionary monetary policy shocks and credit spread shocks temporarilyincreasemacroeconomictailriskbytighteningfinancialconditions. Onthecontrary, expansionary technology shocks reduce tail risk for substantially longer by loosening financial conditions. Over a horizon of five years, which is the largest horizon we study here, movements in the forecast distribution of GDP growth due to expansionary technologyshocksarenotundoneandhenceshifttheentiredistributiontotheright. Another feature of our results that stands out is that upside risk reacts substantially less to economic shocks than downside risk, as is evident from Figure 2. This is in line with the finding in Adrian et al. (2019) that upside risk moves substantially less over time relative to downsiderisk. 8In Appendix B we show the corresponding figure for the other conditioning variable in the quantile regressions,GDPgrowth. Therearesubstantiallymorepronounceddifferencesintheresponsesofthatvariable totheshockrelativetohowthe10thpercentileoftheGDPgrowthforecastdistributionreactstoshocks. 12

RR monetary AR monetary 0.4 0.1 0 0 -0.4 -0.1 5 10 15 20 5 10 15 20 EBP Credit Gali Tech 1 0 0.5 0 -0.2 -0.5 -0.4 5 10 15 20 5 10 15 20 TFP News JF TFP 0.1 0 0.05 -0.1 0 -0.2 -0.05 -0.3 -0.1 5 10 15 20 5 10 15 20 Figure4: ImpulseResponsesoftheChicagoFEDNationalFinancialConditionsIndex. Source: Authors’calculations. 5 Conclusion Theimpactofmacroeconomicshocksonaverageeconomicactivityhasbeenstudiedextensively,whereastheeffectonlowerquantiles—commonlyreferredtoas“tailrisk”—hasbeen studied substantially less, even though it is of utmost importance to policymakers. This paper fills this gap by focusing on how macroeconomic shocks affect both tail risk and the entiredistributionoffutureGDPgrowth. Wefindthatallshocksweconsider(monetarypolicy, credit conditions, and productivity shocks) affect the tail risk disproportionately more than other quantiles. This means that contractionary shocks deserve even more attention than what their effect on average outcomes suggests to the extent that they make poor economic conditions much more likely. Since this is also true of monetary policy shocks, there is reason to be especially wary of the consequences of contractionary policy shocks. We complement the findings in Adrian et al. (2019) by showing that financial conditions are the key channel through which shocks affect macroeconomic risk. This suggests that research onhowstructuralshocksaffectfinancialconditionsiskeytostudyeconomicgrowthandits vulnerability. 13

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A Data Thissectiongivesabriefoverviewofthedataweusethroughoutthispaper,whichismostly availableatFRED.Additionaldatasourcesareprovided. ToestimatethequantileregressionweuseseasonallyadjustedandannualizedrealGDP growth as well as the Chicago FED National Financial Conditions Index (NFCI). This index isnotseasonallyadjustedanddownloadedatquarterlyfrequencybyrelyingontheaverage ofweeklyvalueswithinaquarter. The control variables in the local projection stage are given as follows. At quarterly frequencywetakeseasonaladjustedrealGDP,theseasonaladjustedcivilianunemployment rate,totalpopulation(includingarmedforcesoverseas)andtotalhoursworkedgivenbythe hours of wage and salary workers on non-farm payrolls. The latter two series are used to compute per capita GDP and productivity (real GDP divided by hours), respectively. Both thecommoditypriceindexandtheconsumerpriceindexareavailableatmonthlyfrequency. We take the CRB commodity index provided by Ramey (2016) and headline CPI (defined in FRED as “Consumer Price Index for all Urban Consumers: All Items”). Additionally, we take the monthly federal funds rate. All monthly series are aggregated to quarterly frequencybytakingthequarterlyaverage. Finally, we utilize the following aggregate shocks. The Romer and Romer (2004) monetaryshockisprovidedbyRamey(2016). Weaggregatethemonthlyshockseriestoquarterly frequency by taking the quarterly sum. We take the narrative monetary policy shock provided by Antolín-Díaz and Rubio-Ramírez (2018), again aggregated to quarterly frequency by calculating the quarterly sum. To identify the credit shock we use the Gilchrist and Zakrajšek (2012) excess bond premium, frequently updated by Favara et al. (2016)9. The three technologyshocksareidentifiedbyrunningtheVARsdescribedinSection(2). 9Theseriescanbedownloadedathttps://www.federalreserve.gov/econresdata/notes/feds-notes/ 2016/updating-the-recession-risk-and-the-excess-bond-premium-20161006.html. 16

B Additional Impulse Responses Inthissectionweshowtheerrorbandsforthe10thand90thpercentileresponsesthatwere notpresentedinthemaintext. RR monetary AR monetary 1 0.2 0 0 -0.2 -1 -0.4 5 10 15 20 5 10 15 20 EBP Credit Gali Tech 1 1 0 0.5 -1 0 -2 5 10 15 20 5 10 15 20 TFP News JF TFP 0.2 0.6 0.4 0.2 0 0 -0.2 -0.2 5 10 15 20 5 10 15 20 10th quantile 90th quantile Figure5: ImpulseResponsesofVariousQuantiles. Note: Red(dashed)isresponseofthe10thquantile,blue(dotted)isresponseofthe90thquantile. Confidence bands correspond to 10th quantile response, 90% significance level, based on Newey-West standard errors. Source: Authors’calculations. 17

RR monetary AR monetary 0.2 1 0.5 0 0 -0.5 -0.2 5 10 15 20 5 10 15 20 EBP Credit Gali Tech 1 0.4 0 -1 0 -2 -0.4 5 10 15 20 5 10 15 20 TFP News JF TFP 0.4 0.1 0.2 0 0 -0.2 -0.1 5 10 15 20 5 10 15 20 5th quantile 25th quantile 75th quantile 95th quantile Figure6: ImpulseResponsesofQuantilesUsedtoFit t-Distributions. Source: Authors’calculations. RR monetary AR monetary 1 0.2 0 0 -0.2 -1 -0.4 5 10 15 20 5 10 15 20 EBP Credit Gali Tech 1 0 0.5 -1 0 -2 -3 -0.5 5 10 15 20 5 10 15 20 TFP News JF TFP 0.6 0.2 0.4 0.1 0.2 0 0 -0.2 -0.1 5 10 15 20 5 10 15 20 Figure7: ImpulseResponsesofAverageGDPGrowth y . t+h Source: Authors’calculations. 18

C Allowing for More Controls in Quantile Regressions To check whether or not our results are robust to adding additional controls in the quantile regression stage, we add the controls from the local projections stage already at the first quantile regression stage (except for the shock measures). This means that each impulse responseisnowbasedonadifferentsetofquantiles. Nonetheless,theresultsfromthemainsectionarebroadlyinlinewithwhatwefindforthis robustnesscheck,inparticularwhenitcomestotheresponsesofthe10thpercentile. RR monetary AR monetary 0.5 0.2 0 0 -0.5 -0.2 5 10 15 20 5 10 15 20 EBP Credit Gali Tech 1 0.6 0 0.4 0.2 -1 0 -0.2 5 10 15 20 5 10 15 20 TFP News JF TFP 0.4 0.1 0.2 0 0 -0.2 -0.1 5 10 15 20 5 10 15 20 10th quantile median 90th quantile Figure8: ImpulseResponsesofVariousQuantiles. Note: Red (dashed) is response of the 10th quantile, black (solid) is the median response, blue (dotted) is responseofthe90thquantile. Confidencebandscorrespondtomedianresponse,90%significancelevel,based onNewey-Weststandarderrors. Source: Authors’calculations. 19

RR monetary AR monetary 0.4 1 0.2 0.5 0 0 -0.5 -0.2 5 10 15 20 5 10 15 20 EBP Credit Gali Tech 1 1 0 0.5 -1 0 -2 5 10 15 20 5 10 15 20 TFP News JF TFP 0.6 0.2 0.4 0.2 0 0 -0.2 -0.2 5 10 15 20 5 10 15 20 10th quantile 90th quantile Figure9: ImpulseResponsesofVariousQuantiles,MoreControlsinQuantileRegression. Note: Red (dashed) is response of the 10th quantile, blue (dotted) is response of the 90th quantile. Confidence bands correspond to 90% significance level, based on Newey-West standard errors. Source: Authors’ calculations. 20