The Economic Effects of Firm-Level Uncertainty: Evidence Using Subjective Expectations

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 1320 June 2021 The Economic Effects of Firm-Level Uncertainty: Evidence Using Subjective Expectations Giuseppe Fiori and Filippo Scoccianti Please cite this paper as: Fiori, Giuseppe and Filippo Scoccianti (2021). “The Economic Effects of Firm-Level Uncertainty: Evidence Using Subjective Expectations,” International Finance Discussion Papers 1320. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/IFDP.2021.1320. 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.

The Economic Effects of Firm-Level Uncertainty: ∗ Evidence Using Subjective Expectations Giuseppe Fiori Filippo Scoccianti June 7, 2021 Abstract This paper uses over two decades of Italian survey data on business managers’ expectationstomeasuresubjectivefirm-leveluncertaintyandquantifyitseconomiceffects. Wedocumentthatfirm-leveluncertaintypersistsforafewyearsandvariesacrossfirms’demographic characteristics. Uncertainty induces long-lasting economic effects over a broad array of real and financial variables. The source of uncertainty matters with firms responding only to downsideuncertainty,thatis,uncertaintyaboutfutureadverseoutcomes. Economy-wideuncertainty, constructed aggregating firm-level uncertainty, is countercyclical but uncorrelated with typical proxies in the literature, and accounts for a sizable amount of GDP variation duringcrises. JELClassification: D24,E22,E24 Keywords: Uncertainty, business cycles, investment, expectations, cash holdings, downside uncertainty ∗First version: April 13, 2020. We are grateful to Danilo Cascaldi-Garcia, Brian Doyle, Thiago Ferreira, Steffen Henzel, Matteo Iacoviello, Cosmin Ilut, Andrea Lanteri, Francesca Lotti, Hyunseung Oh, Andrea Prestipino, PlutarchosSakellaris,EnricoSette,FrankWarnock,andparticipantstovariousseminarsandtothe"11th IFOConference on Macro and Survey Data" for useful comments. Giuseppe Fiori: Board of Governors of the Federal ReserveSystem,DivisionofInternationalFinance,20thandCSt. NW,WashingtonD.C.20551,UnitedStates(email: giuseppe.fiori@frb.gov;webpage: http://www.giuseppefiori.net);FilippoScoccianti: Bancad’Italia,ViaNazionale 91,Rome,Italy(email: filippo.scoccianti@bancaditalia.it). TheviewsexpressedinthispaperaresolelytheresponsibilityoftheauthorsandshouldnotbeinterpretedasreflectingtheviewsoftheBoardofGovernorsoftheFederal ReserveSystem(orofanyotherpersonassociatedwiththeFederalReserveSystem)ortheBankofItaly.

1 Introduction Economictheoryemphasizestherolethatuncertaintyaboutfuturemacroeconomicandmicroeconomic outcomes (such as GDP and growth rate of firms’ sales) plays for firms’ decisions. The subject of economic uncertainty has a long tradition in economics, and, on the heels of Bloom (2009), a vast literature has greatly improved the measurement and the understanding of the nature and economic consequences of macroeconomic, or aggregate, time-varying uncertainty. Theliteratureonfirm-leveluncertaintyisinsteadscantandmostlylimitedbydataavailability. WeadvancetheliteratureonsubjectiveuncertaintybyusingItaliansurveydataonfirm-level expectations that span over 20 years and cover multiple business cycle episodes.1 Our analysis yieldsthreemaininsights. First,weconstructameasureofexanteuncertaintyusingsurveydataonfirm-levelexpectationsaboutfuturesalesforarepresentativesampleofItalianfirms. Wedocumentthatfirm-level uncertaintyismostlyanidiosyncraticprocessthatpersistsforafewyears. Theseresultssuggest thatchangesinconsumers’tastesorshiftsintechnologyaremorerelevantsourcesofuncertainty thanaggregatefactors. Also,weshowthattheleveloffirmsuncertaintyabouttheirfuturebusiness prospects depends upon demographic characteristics, such as age, size, and the sector in whichfirmsoperate. Second,wecharacterizethepropagationmechanismoffluctuationsinfirm-leveluncertainty over a broad set of real and financial variables. While most of the existing literature typically focusesontheroleofuncertaintyforcapitalaccumulation,weshowthatthisemphasisneglects labor’scriticalrole(inbothhoursandnumberofworkers)andcapacityutilization. Uncertainty also affects the financial structure of firms that increase their cash holdings when perceived uncertainty increases. We obtain our results controlling for a plethora of confounding factors, including changes in the first moment of the probability distribution of future sales. Also, our data’s granularity allows disentangling the source of uncertainty fluctuations between "down- 1TheBankofItalysurveyconstitutesaunicumintheexistingliterature,asmostsurveysthattrackuncertainty onfirmleveloutcomesspanonlyafewyears. Inparticular, fortheUnitedStates, Altigetal.(2020b)developeda monthly panel Survey of Business Uncertainty (SBU) starting in 2014 that features about 1,750 firms in 50 states. In Germany, the IFO Institute surveyed firms’ expectations from 2013 to 2016, see Bachmann et al. (2018) and Bachmannetal.(2020). Alongermonthlytime-seriesstartingin1980andbasedonqualitativeexpectations,isused inBachmann,ElstnerandSims(2013)andMassenotandPettinicchi(2018). FortheUnitedKingdom,theDecision MakerPanel(DMP)surveywaslaunchedinAugust2016. 1

side"or"upside"uncertainty—thatis,uncertaintyaboutadverseorpositiveoutcomes. Third, we construct an economy-wide measure of uncertainty for the Italian economy, aggregating individual firm-level data, and find it to be countercyclical. While this countercyclicality reproducestheliterature’stypicalresult,weemphasizethatourmeasureisuncorrelatedtostandard proxies for macroeconomic uncertainty employed in the literature. This little correlation indicates that typical proxies based on ex post outcomes, such as dispersion in sales or innovations in total factor productivity (TFP), may understate the amount of ex ante uncertainty perceivedbyfirms. The source of the data on expectations is the Survey of Industrial and Service Firms (or IN- VIND), an extensive annual business survey conducted by the Bank of Italy on a sample of Italianfirmsrepresentativeoftheaggregateeconomy. AsdiscussedinSection2,thesurveyelicits managers’ expectations over the average, the minimum, and the maximum one-year ahead growth rates of sales. Thus, we directly observe the first moment of the subjective probability distribution of future sales and the distribution’s support, i.e. the range between the maximum and minimum expected outcome, or max–min range. Using the 2005 and 2017 waves of IN- VINDthatelicitedthefullprobabilitydistributionofexpectedsales,weshowthatthemax–min range measures the dispersion of future expected outcomes while being orthogonal to the third moment of the distribution, or skewness. The nearly deterministic relationship between the max–min range and the dispersion of future sales allows us to use the max–min range to measure firm-level uncertainty for the whole sample. Directly observing the first and the second momentsofthedistributionofexpectedoutcomesenablesustoovercomeoneoftheexistingliterature’s main challenges, disentangling the economic effect of fluctuations in uncertainty from changestothefirstmoment. In Section 3, we show that, in a given year, the median firm perceives uncertainty equal to 8 percentage points around its mean expectation. Uncertainty varies with specific demographic characteristics. Smallandmedium-sizedfirms(lessthan50workers)andyoungfirms(lessthan five years) tend to display higher uncertainty than large and mature firms. Interestingly, the source of uncertainty for young firms is upside uncertainty (caused by the maximum expected future sales). Instead, it is downside uncertainty for small and medium-sized firms (driven by theminimum). 2

Toshowthatuncertaintyisapersistentprocess,weexploitthe2017waveofINVIND,which elicits the full probability distribution of expected sales one year and three years ahead. On average, these two measures of uncertainty are strongly and positively correlated (0.64). If a firmdisplayshighuncertaintyaboutitsfuturesalesoneyearahead,thesameistrue,onaverage, threeyearsahead,indicatingthatuncertaintydoesnotabatequicklyatthefirmlevel. In Section 4, we further match INVIND expectations with balance sheet data to measure the impact of uncertainty on real and financial outcomes, such as hours, investment, labor, capacity utilization, and cash holdings. The availability of a broad cross-section and a long time-series dimension allows us to perform a panel regression analysis to characterize, at various horizons, howfirmsadjustfollowingfluctuationsinuncertainty. While the existing microeconomic literature has mainly focused on the response of investment,wehighlightthatfirmsalsouseothermarginstoadjusttouncertaintyfluctuations. Specifically,followinganincreaseinuncertainty,firmsimmediatelyreducetheextensiveandintensive margins of labor (number of workers and hours per worker), decrease capacity utilization, and hoard cash for a few periods. With a lag, firms reduce the accumulation of capital that persists for a few periods. Over time the dynamics are reversed, with investment overshooting its steady-state level before converging back to it as the shock dissipates. Results are confirmed when we instrument current uncertainty with its lagged values. Our evidence on investment aligns well with model predictions in Bloom (2009) and Bloom et al. (2018). Also, our evidence on the negative effects of uncertainty complements models emphasizing financial frictions that leadtohighercostoffinance(Arellano,BaiandKehoe,2019;Gilchrist,SimandZakrajšek,2014), andprecautionarysavingeffects(Fernández-Villaverdeetal.,2015;BasuandBundick,2017). In Section5,wedecomposetotalfirm-leveluncertaintyintoadownsideandanupsidecomponent to investigate whether all uncertainties are all alike. Specifically, we study what are the economic effects of higher dispersion in positive and negative outcomes. While both components are significant contributors of the total variance of uncertainty, we find that only the downside component matters—that is, only uncertainty about future negative outcomes generates significant economic effects. Instead, firms are unresponsive to the upside component, indicating that the sourceofuncertaintydeterminesitseconomiceffects. The differentiated response to downside and upside uncertainty provides practical overi- 3

dentifying restrictions against which to test competing macro theories aimed at quantifying the aggregate effects of uncertainty (see Section 6). In the context of real options theories, the response to downside or upside uncertainty is informative about the frictions faced by firms to increase or decrease durable inputs, (see the discussion in Abel et al., 1996). Our evidence emphasizes costly downsizing of capital or labor, such as the one induced by input irreversibility andtheensuing"badnewsprinciple"discussedbyBernanke(1983). Downsideuncertaintymay also increase the likelihood of firms becoming financially constrained in the future, leading to a decreaseintheaccumulationofinputsseeLin,BloomandAlfaro(2017). Also,totheextentthat theminimumoffuturesalesisinterpretedasasummarystatisticoftheworst-casescenario,the sensitivity to downside uncertainty may be loosely interpreted as agreeing with the predictions of theories that emphasize ambiguity aversion, as in Hansen, Sargent and Tallarini (1999) and IlutandSchneider(2014). Inthosemodels,agentsformbeliefsoverarangeofpossiblescenarios andactasiftheworstscenariowilloccur. After studying the microeconomic dimension of uncertainty, we exploit our representative sample and construct an economy-wide measure by aggregating firm-specific uncertainty (see Section 7). We consider this bottom-up approach noteworthy because our proxy is the first ex antemeasureofaggregateuncertaintycoveringovertwodecadesoffirm-levelexpectationsand spanning multiple business cycle episodes. Notwithstanding the little correlation with typical proxies for aggregate uncertainty, we find that our measure increased sharply during economic crises, such as the Great Financial Crisis and the latest COVID-19 recession, as well as periods withelevatedpoliticaluncertainty. Using our firm-level estimates that isolate the "pure" effect of uncertainty from changes to the mean, we find that uncertainty is a significant contributor to aggregate fluctuations, over and beyond fluctuations induced by first-moment shocks. On average, uncertainty accounts for about 15 percent of GDP response over the 2009 and 2012 recessions. Also, the unprecedented spike in aggregate uncertainty due to the COVID-19 pandemic reduced GDP’s growth rate by about 1 percentage point in 2020. Moving forward, we expect uncertainty to have more muted effectsasthedownsidecomponentlargelyrecoveredin2021. Thepaperisorganizedasfollows. InSection1.1,wereviewtheexistingliterature. InSection 2,wedescribethedata. InSection3,wedetailtheconstructionofourmeasureofex-anteuncer- 4

tainty based on subjective expectations. We characterize the economic effects of uncertainty in Sections4and5. InSection6,wediscusstheimplicationsofourresultsformacroeconomicmodeling. In Section 7, we construct a measure of aggregate uncertainty based on firm-level uncertainty and quantify the aggregate effects of uncertainty across multiple business cycle episodes. Section8concludes. 1.1 Literature Review Our work connects to many strands of the existing literature on uncertainty and aggregate fluctuations. While the existing literature provides a sizeable number of surveys eliciting consumer expectations, less is known about quantitative measures of uncertainty at the firm level.2 Our data source INVIND is the forerunner of DMP for the United Kingdom discussed in Altig et al. (2020a) and SBU for the United States described in Altig et al. (2020b). Another important example is the IFO survey employed in Bachmann et al. (2018) and Bachmann et al. (2020).3 The critical advantage of INVIND is that it has surveyed firms’ expectations for over two decades, allowing us to study how uncertainty has evolved over multiple business cycles. In contrast, DMPandSBUstartedonlyinrecentyears,albeitatahigherfrequency. In relating survey data to economic outcomes, our paper is related to the pioneering work of Guiso and Parigi (1999) and Bontempi, Golinelli and Parigi (2010).4 Relative to these contributions that also use INVIND, the panel dimension of our sample allows us to expand the scope of the analysis characterizing the effect of uncertainty on a broad array of real and financialvariables(notonlyinvestment). Besides,weshowthatthesourceofuncertaintymattersfor its economic effects. Our sample includes important business cycle episodes in recent history, both on the upside in the years 2005 to 2007 and in the deep financial recession that followed 2ExamplesofconsumersurveysincludetheU.S.HealthandRetirementStudy(HurdandMcGarry,2002), the BankofItaly’sSurveyonHouseholdIncomeandWealth(Guiso,JappelliandTerlizzese,1992;Guiso,Jappelliand Pistaferri, 2002), the Survey of Economic Expectations (Dominitz and Manski, 1994), the University of Michigan Surveys of Consumers (Dominitz and Manski, 2004) and the New York Fed’s very recent Survey of Consumer Expectations(Armantieretal.,2015). 3Ben-David and Graham (2013) and Gennaioli, Ma and Shleifer (2016) study executives’ stock return expectations. 4Another example is Morikawa (2013) that uses two-point distributions from the survey conducted at the Research Institute of Economy, Trade and Industry. He focuses on uncertainty related to the tax system and trade policymattersforfirms’capitalinvestmentandoverseasactivities. 5

from2008to2013andthesubsequentrecovery. A second strand of the literature has investigated the economic effects of uncertainty, typically focusing on investment and pointing to a negative uncertainty-investment relationship when dealing with micro-level uncertainty. Leahy and Whited (1996) and Bloom, Bond and VanReenen(2007)userealizedstockreturnvolatilityasameasureoffirm-leveluncertaintyand show a negative relationship between uncertainty and business investment. Stein and Stone (2013) use the option price to create a forward-looking measure of uncertainty and arrive at a similarconclusionontheuncertainty-investmentrelationship. GulenandIon(2016)usethepolicyuncertaintyindexdevelopedbyBaker,BloomandDavis(2016)toshowthatfirm-levelcapital investment is negatively affected by the uncertainty associated with future policies. Moreover, firm-level uncertainty appears to vary in both the cross section and the time series. Bachmann, Elstner and Hristov (2017) and Senga (2015) find substantial cross-sectional heterogeneity and time variation in measures of firm-idiosyncratic uncertainty using survey data. Senga (2015) also finds that smaller and younger firms face greater uncertainty. Based on our results, we argue that uncertainty is more detrimental for small firms rather than young firms because it originatesfromdownsideuncertainty. Besides differences in the considered measure of uncertainty, our analysis shows that the effects of uncertainty extend beyond capital accumulation and affect the labor market and financial decisions. The broad focus on firm-level economic outcomes aligns our work with Lin, BloomandAlfaro(2017)withthreecriticaldistinctionsrelatedtoouruncertaintymeasure. First, ratherthanrelyingontherealizedorimpliedannualvolatilityofstockreturns,weemployanex ante measure of uncertainty that allows us to tease out changes in the dispersion of expected outcomes from fluctuations in the first moment of future expectations. Second, our empirical analysis shows that the economic effects of uncertainty last for a few years, with investment overshooting its steady-state level. Third, we distinguish the source of fluctuations in uncertaintybetweenadownsideandanupsidecomponent,showingthatonlytheformermattersfor itseconomiceffects. Our work also connects to the literature that studies aggregate uncertainty and its cyclical propertiesalongthebusinesscycle. Arobustfindingintheliteratureisthatcross-sectionalmeasures of uncertainty rise in recessions. Bloom (2009) finds that a variety of cross-sectional dis- 6

persion measures, like the standard deviation of firms’ profit growth, positively correlates with time-series stock market volatility. Bloom et al. (2018) show that the cross-sectional dispersion of establishment-level TFP shocks is countercyclical (see also Kehrig (2015) and Bloom (2014) for discussion on the cyclicality of uncertainty measures). Bachmann, Elstner and Sims (2013) use disagreement among professional forecasters as a proxy for aggregate uncertainty and find that forecaster disagreement is higher in downturns. Baker, Bloom and Davis (2016) develop a measureofeconomicpolicyuncertaintybasedonthefrequencyofarticlesmentioningthewords “uncertain" or "uncertainty” and find this measure is also countercyclical.5 Our economy-wide measureofuncertaintyisalsocountercyclical,butuncorrelatedtomostoftheexistingproxiesof aggregate uncertainty. We interpret this finding as indicating that current proxies may not fully capturetheaggregatedimensionofex-antefirm-leveluncertainty. Wereferthereaderinterested in a comprehensive review of the literature to Datta et al. (2017) and Fernández-Villaverde and Guerrón-Quintana(2020). 2 Data: Subjective Firm-Level Expectations This section describes the data sources that constitute the basis for measuring firm-level uncertainty and its economic effects. We first provide details about our data source in Section 2.1. Then, we describe the measures of firm-level expectations and their statistical properties in Section2.2andinSection2.3,respectively. 2.1 Data Sources We obtained our data set by combining different sources. We first construct our measure of uncertainty using data on firm-level expectations from INVIND. INVIND is an annual business survey conducted between February and April of every year by the Bank of Italy on a representative sample of firms operating in industrial sectors (manufacturing, energy, and extractive industries) and non-financial private services, with administrative headquarters in Italy. The sampleis representativeof theItalian economy, based on thebranch ofactivity(according toan 5InasimilarveinofresearchHassanetal.(2019)andCaldaraetal.(2020)usetextualanalysistostudyfirm-level politicaluncertaintyandexplorethequantitativeimplicationsoftradepolicyuncertainty,respectively. 7

11-sectorclassification),sizeclass,andregioninwhichthefirm’sheadofficeislocated. Wethen use detailed information on yearly balance sheets from Cerved Group S.P.A. (Cerved Database) to obtain data on investment (equipment and structures), cash holdings, and realized sales. Total hours, number of employees, and capacity utilization are part of INVIND. Industry-specific price deflators are obtained from the Italian National Institute of Statistics. The sample period extends over 25 years, from 1993 to 2018. The matched data set includes about 25,000 firm-year observations from an average of more than 900 firms per year. We refer the reader to Appendix A for more details. We note that the number of firm-year observations in INVIND depends on the variable of interest and includes more than 30,000 observations. However, not all of the observations can be matched with balance sheet data in Cerved, reducing the sample to about 25,000 observations. Next we report statistics using all the available data and accounting for eachfirm’sshareinthepopulationofItalianfirms. 2.2 Firm-Level Expectations: Variables Description INVIND elicits expectations about future sales from surveyed firms. Specifically, the survey reportsthreecriticalvariablesforourpurposes: 1. Theexpected,oraverage,growthrateofsalesoneyearahead,denotedby se . avg,f,t 2. The maximum, or best-case scenario, future growth rate of sales one year ahead, denoted by se . max,f,t 3. The minimum, or worst-case scenario, future growth rate of sales one year ahead, denoted by se . min,f,t Shaped by idiosyncratic and aggregate factors, these variables allow us to directly observe the first moment of the probability distribution of the expected growth rate of sales and the range of subjective uncertainty around this point. We emphasize that we do not directly observe the probability mass over the support except for the 2005 and 2017 waves. We overcome this limitation in Section 3 by showing that there is a near-deterministic relationship between the range andthestandarddeviation,orsecondmoment,oftheprobabilitydistributionofexpectedsalesat the firm level. We connect the range with the dispersion in future sales exploiting the 2005 and 8

2017 waves of the survey that elicit the entire probability distribution, asking firms to provide a quantitativeassessmentoftheirbusinessprospects. Wenowdescribethestatisticalpropertiesof se , se ,and se . avg min max 2.3 Statistical Properties: Minimum, Maximum, and Average of Expected Future Sales Growth Table 1 reports a set of statistics comparing actual outcomes (the growth rate of sales) and the minimum (worst-case scenario), the maximum (best-case scenario), and the average expected growthratesofsales. Statisticsarereportedforthewholesampletakingintoaccounteachfirm’s weightintheentirepopulationoffirms. Growthratesareexpressedinpercent. Table1: Firm-LevelExpectations: DescriptiveStatistics No. ofObs. Mean St. Dev. Skew. P P P P P 10 25 50 75 90 se 49674 3.56 11.30 1.07 -7.20 0.00 2.60 7.20 14.30 avg,f,t se 30958 -3.89 9.91 -0.01 -12.00 -10.00 -2.00 1.00 5.00 min,f,t se 30976 7.07 9.82 1.37 0.00 2.00 5.00 12.00 15.00 max,f,t ∆ Sales 41934 0.93 18.70 -0.51 -19.90 -7.51 1.76 10.40 21.10 t,t−1 Note: Statistics are computed over the whole sample period 1996 to 2018, weighting firm-specific observations based on the share of the entire population they represent. The number of observations refers to the numberoffirmseffectivelysampledinthedata. Tableentriesarecomputedovergrowthrates(expressedin percent). se , se , se denotetheaverage,minimum,andmaximumexpectedgrowthratesofsalesone-year avg min max ahead,while∆Salesreportsthegrowthrateofrealizedsales. P reportstheXth percentileofthedistribution. X We start from describing the properties of se . The median firm expects sales to grow by avg 2.6 percentage points, in line with the median of actual sales. Turning to se and se , we find min max that the median firm expects the worst-case scenario to result in a decrease of sales of about 2 percentage points and the best-case scenario in an expansion of 5. Also, for both variables, the interquartilerange(P −P )isabout10percentagepoints. Thethreemeasuresofexpectations 75 25 display a lower standard deviation than the realized growth rate of sales. As shown in Table 2, the se , se ,and se areasprocyclicalasactualsales. avg min max 9

Table2: CyclicalityofExpectations se se se ∆ Sales avg,f,t min,f,t max,f,t f,t ∆ GDP 0.25 0.28 0.18 0.28 t,t−1 Note: Statisticsarecomputedoverthewholesampleperiod 1996to2018,weightingfirm-specificobservationsbasedon theirshareoftheentirepopulation.Thenumberofobservationsreferstothefirmsdirectlyobservedinthedata. Table entries report the unconditional correlation between se , avg se ,se andthegrowthrateofGDP.se ,se ,se denote min max avg min max the average, minimum, and maximum expected growth rates of sales one year ahead. ∆GDP denotes the yearly growth rateofrealGDP. Notably, we find that the statistical properties of expectations display sizeable differences conditioning on firms’ size, age, and sector in which they operate. Results are reported in Table A.1 in Appendix B. Starting from firms’ size, small and medium-sized firms (defined as firms employing between 20 and 50 workers) display a lower expected growth rate in the worst- and the best-case scenarios than large firms (with more than 50 employees).6 This property shows despite a similar expected growth rate, se . We note that small and medium-sized firms do not avg perfectly overlap with the definition of young firms. Young firms (less than five years) tend to expect higher growth both on average and in the best-case scenario than mature and old ones (more than five years). Intuitively, this outcome lines up with firms’ life-cycle dynamics that, conditional on survival, grow to reach their optimal size. Finally, firms in the manufacturing sector expect faster growth than those in the service sector. This result reflects the faster growth rate of sales experienced by the manufacturing sector that we conjecture is being driven by the higherdegreeofinternationalopennessrelativetotheservicesector. 6Becauseofthedesignofthesurvey,wedonotobservefirmswithlessthan20employees. 10

3 Measuring Firm-Level Uncertainty with Subjective Expectations WenowdescribehowweuseINVINDexpectationstoconstructatime-varyingmeasureofindividual firms’ subjective uncertainty and provide a set of stylized facts on firm-level uncertainty. In Section 3.1, we show that there is a near equivalence in the range between the maximum and minimum future expect sales (or the best- and worst-case scenario, se − se ) and max,f,t min,f,t the dispersion (or second moment) of future expected sales. Exploiting this link, we use the max–min range as a measure of firm-level uncertainty and establish a new set of stylized facts on the properties of uncertainty conditioning across age, size, and sector in which the firms operate in Section 3.2. In Section 3.3, we exploit the granularity of our data to trace back the sourceoffirm-leveluncertaintytoitsupside(drivenbyuncertaintyaboutpositiveoutcomes)or downside(negativeoutcomes)component. Finally,weanalyzehowfirm-specificandaggregate variables covariate with uncertainty in Section 3.4 and conclude by showing that uncertainty is apersistentprocessthatdoesnotabatequicklyinSection3.5. 3.1 The Max–Min Range Measures Dispersion in Future Expected Sales INVIND provides us with the range between the best- and the worst-case scenario about the expected growth rate of sales one-period ahead. We now show that this range, denoted by σ , measures the second moment of the probability distribution of expected outcomes.7 max−min To do so, we use data from the 2005 and 2017 waves of INVIND. Unlike other years in our sample,thesewaveselicitedthefullprobabilitydistributionofexpectedsalesoveradiscretized supportofintervalsrangingfrom<-10percentto>10percent.8 We compute the mean, standard deviation, and skewness of the subjective probability distribution of expected sales for every firm. Our calculations are carried out applying standard 7Bachmannetal.(2018)refertothemax–minrangeasspan. 8In 2005, the support of the probability distribution of expected sales x was discretized using 11 bins: ≤-10 percent,-10percent<x≤-6percent,-6percent<x≤-4percent,-4percent<x≤-2percent,-2percent<x<0percent,0,0 percent<x≤2percent,2percent<x≤4percent,4percent<x≤6percent,6percent<x≤10percent,≥10percent.In2017, thegridbetween-6percentand+6percentwasfiner,withintervalsofonepercentagepointratherthantwo. Bythe natureofINVIND,the2005and2017wavesasksagentsaboutonedistributionofexpectedoutcomes. Bachmann etal.(2020)innovatesonthisfrontdistinguishingbetweenBayesianandKnightianagents. 11

Table3: σ andMomentsoftheSubjectiveProbabilityDistribution max−min St.Dev. Skew. St.Dev. Skew. f f f f (1) (2) (3) (4) ∗∗∗ σ 0.29 -0.10 f,max−min (0.00) (0.21) se -0.29 ∗∗∗ 0.11 f,min (0.00) (0.17) se 0.29 ∗∗∗ -0.10 f,max (0.00) (0.20) R2 0.88 0.00 0.88 0.00 Observations 920 920 920 920 Note: Each equation is estimated with ordinary least squares using2005waveoftheSurveyofIndustrialandServiceFirmsdata. P values in parentheses. Stars denote significance level of the coefficient they refer to: * p-value<0.10, ** p value<0.05, *** pvalue<0.01. The dependant variable reported on columns is the second moment (St.Dev. ) and the third-moment (Skew. ) of the f f firm-specificprobabilitydistributionofexpectedsalesfortheyear 2005. Foreveryfirm f,σ f,max−min denotesthedifferencebetween se , and se , the maximum and minimum expected growth f,max f,min rateofsaleone-yearahead. formulasandusing,foreachbin,themidpointoftherespectiveintervalanditsassociatedprobability. Notably, as we observe the probability distribution of future sales, we do not need to imposeanydistributionalassumption. Finally,weregresseachmomentofthesubjectivedistributiononσ ,and,inaseparate max−min regression, the best- and worst-case scenarios. Table 3 reports the results for the 2005 wave of INVIND. The main result is that the range between the best- and worst-case scenarios measures the second moment of the probability distribution of future sales. Specifically, firms with higher dispersioninexpectedoutcomesalsodisplayawiderrangeofσ . Column1showsanear max−min equivalence between σ and the true standard deviation of the probability distribution. maxmin,f The coefficient on σ is statistically significant, and the R2 is very close to one, indicatmax−min ing that the range accounts for almost the total variance of the dependent variable. The fit is similar when se and se enter the specification as separate regressors. A decrease in se f,max f,min f,min 12

(a deterioration in the worst-case scenario) and an increase in se (an improvement in the f,max best-case scenario) increase uncertainty. Interestingly, se is virtually orthogonal to the max−min,f third moment, the skewness, allowing us to rule out that the range captures fluctuations in the skewness. Werunthesameregressionusingthe2017waveofINVIND.Results(notshown)aremainly unchanged both in terms of estimated coefficients and fit, providing additional support that the range σ captures the standard deviation of the probability distribution of expected max−min outcomes.9 Finally, we connect measures of the worst- and best-case future sales with the probability massoffuturesales(notshown). Firmswithlowerse exhibitahigherprobabilitymassinbins min associated to intervals close to se . The same association holds for se and mass probability min max for intervals close to se . We exploit this result in Section 5 when we study the sources of max uncertaintyfluctuations. 3.2 Firm-Level Uncertainty Varies by Age, Size, and Sector Our measure of firm-level uncertainty has three advantages. First, σ is an ex ante meamax−min sure of the uncertainty perceived by firms about future outcomes. Second, σ reflects the max−min managers’ expectations—that is, the decision-makers of the firm. Third, σ can be easily max−min interpretedasitrelatestoeconomicoutcomes. Table 4 reports descriptive statistics on σ . The data indicate that, on average, firms’ max−min uncertainty around their average expected future sales is 9.33 percentage points. The median uncertainty is instead 8. Using the results in Table 3, we find that the coefficient of variation, the ratio between the standard deviation and the mean se , is for the median firm about 1. avg Moreover, σ is virtually acyclical, as its correlation with the growth rate of real GDP is max−min -0.07.10 Wefindsignificantheterogeneityinfirms’uncertainty,basedontheirage,size,andthesector in which they operate. Young firms (less than five years), on average, perceive the higher level 9Usingthe2017wave, wefindthatthe R2 is0.76forthespecificationincolumn1and0.86incolumn3. Asin Table3,independentlyofthespecification,σ max−min,f explains,atmost,4percentoftheskewnessvariance. 10Thecorrelationbetweenfirm-leveluncertaintyandthefirstlag(thefirstlead)ofrealGDPis-0.03(0.00). 13

Table4: Firm-LevelUncertainty σ : DescriptiveStatistics max−min No. ofObs. Mean St. Dev. Skew. P P P P P 10 25 50 75 90 FullSample 30735 11.00 9.81 1.35 1.00 3.00 8.00 20.00 24.00 SmallandMediumFirms: 20 ≤ LaborForce ≤ 50 5082 13.70 10.60 0.82 1.20 4.00 11.00 24.00 24.00 LargeFirms: LaborForce > 50 25443 9.50 8.99 1.78 1.00 3.00 6.00 13.00 24.00 YoungFirms: Age ≤ 5 866 13.30 10.30 1.05 2.00 5.00 10.00 24.00 24.00 MatureandOldFirms: Age > 5 29869 11.00 9.79 1.35 1.00 3.00 7.50 20.00 24.00 ManufacturingSector 21450 11.00 9.59 1.47 2.00 4.00 8.00 19.00 24.00 ServiceSector 9285 11.00 10.10 1.20 1.00 2.60 7.00 24.00 24.00 Note:Statisticsarecomputedoverthewholesampleperiod1996to2018,weightingfirm-specific observationsbasedontheirshareoftheentirepopulation. Thenumberofobservationsrefersto the firmsdirectly observed inthe data. σ max−min denotes thedifference between se max and se min , themaximumandminimumexpectedgrowthratesofsalesoneyearahead. of uncertainty, together with small and medium-sized firms (defined here as having less than 50 employees). The drivers of uncertainty are also heterogeneous across firms’ characteristics, as young firms expect, on average, a higher growth rate in the best-case scenario, se . In commax parison, small and medium-sized firms expect a lower growth rate in the worst-case scenario. Large firms perceive a lower level of uncertainty than smaller and medium companies, a result consistentwithlife-cycledynamicssuggestingthattheyhavealreadyreachedtheiroptimalsize or achieved a better knowledge of their demand curve. Finally, firms in the service sector face, onaverage,ahigherlevelofuncertaintythanthoseinthemanufacturingsector. Oldfirms(with ageequaltomorethanfiveyears)andmanufacturingfirmsdrivethefullsampleresultsasthey 14

accountforalargefractionofit. Interestingly,σ isacyclical,exceptforyoungfirmsandsmallandmedium-sizedfirms max−min thatdisplayanegativecorrelationwithrealGDPequalto-0.22and-0.11,respectively. Asshown inSection3.4,thisoveralllackofcyclicalityisduetothelimitedexplanatorypowerofaggregate factorsforthevariabilityof σ . max−min 3.3 Sources of Firm-Level Uncertainty: Downside and Upside Uncertainty We now investigate the source of firm-level uncertainty and whether an increase in uncertainty is driven by firms being more uncertain about positive outcomes, negative outcomes, or both. Answering this question is not just an intellectual curiosity. As discussed in Section 6, it carries critical theoretical implications providing useful restrictions against which to test competing theoretical frameworks employed to rationalize the economic effects of uncertainty. We assess the individual contribution of positive outcomes, se , and negative outcomes, se , to the max min variance of the max–min range. We first compute a standard variance decomposition using data for every firm, and then pool the results to construct the unconditional distribution across firms. For every firm f, we compute the shares of the variance attributed to se and se as max min β cov,se min ,f ≡ cov v ( a s r e m (σ in m ,σ ax m − ax m − in m ) in ) and β cov,se max ,f ≡ cov v ( a s r e m ( a σ x m ,σ ax m − a m x− in m ) in ) . This decomposition shows that both margins contribute to fluctuations in uncertainty, with 42 percent of its variance accounted for by downside uncertainty β cov,se ,f , and the remaining min 58percentattributableto β cov,se ,f . max 3.4 Firm-LevelUncertaintyCorrelateswithCurrentandFutureBusinessConditions Thissectionanalyzesmoreformallywhethermeasuresofexpectationsanduncertaintycorrelate withasetoffirm-levelcharacteristics. Specifically, we regress se , se , and σ on measures of current and future min,f,t max,f,t max−min,f,t business prospects for the firm (proxied by the actual growth rate of sales and se , respecavg,f,t tively),thenumberofemployees(size),cohorteffects(ageofthefirm),andfirm-specific,industry,andyeareffects. Concerningtheroleoffirmcharacteristics,wefindasmallbutpositivecor- 15

relationbetweentheaverageexpectedgrowthrateofsales(se )anduncertainty(σ ). avg,f,t max−min,f,t This result suggests that part of fluctuations in uncertainty may be driven by changes in the meanoftheprobabilitydistributionofexpectedoutcomes. Uncertaintyalsorespondstocurrent businessconditions: Apositivegrowthrateofcurrentsalesisassociatedwithloweruncertainty, althoughtheeffectisrathersmall. TurningtoColumns2and3,wefindthathighercurrentsales tendtoincrease se ,whileuncertaintytendstobesmallerforlargerfirms. min Table5: UncertaintyCovariates σ se se max−min,f,t min,f,t max,f,t (1) (2) (3) se 0.10 ∗∗∗ 0.67 ∗∗∗ 0.78 ∗∗∗ avg,f,t (0.00) (0.00) (0.00) ∆ ∗∗∗ ∗ ∗∗∗ Sales -0.03 0.01 -0.01 f,t−1 (0.01) (0.08) (0.00) Size -0.23 -0.01 -0.20 f,t−1 (0.64) (0.25) (0.63) 0 ≤ Age ≤ 5 1.28 0.0271 1.32 ∗ f,t (0.30) (0.97) (0.10) Observations 12038 12124 12145 R2 0.42 0.77 0.82 Note:Eachregressionisestimatedbyordinaryleastsquares over the sample period 1996 to 2018, and it includes yearand industry-effects. σ max−min measures firm-level uncertainty; se , se , and se denote the maximum, average, max avg min and minimum one-year-ahead expected growth rates of sales,respectively. Asexpected,youngfirmsdisplayhigheruncertaintyastheylearnabouttheirbusinessprospects. Finally, average expected sales se covariates positively with se and se . We emphaf,t,avg min,f,t max,f,t size that we do not attach any causal interpretation to the results in Table 5, as the estimated coefficientscapturecorrelationsbetweenthevariablesofinterest. 16

3.5 Firm-Level Uncertainty Persists for a Few Years We now turn to study the persistence of firm-level uncertainty. Our analysis’s main takeaway is that, on average, firm-level uncertainty does not abate quickly but lasts for a few years. We exploit the 2017 wave of INVIND that elicits the full probability distribution of expected sales one year ahead and three years ahead. After computing the respective standard deviation of futureexpectedsales,weregresstheone-year-aheaddispersiononthethreeyearsaheadandestimateacoefficientof0.64,yieldinganautoregressivecoefficientof0.8. Fittinganautoregressive processoforderoneto σ yieldsanestimatedcoefficientof0.5. Bothestimatesindicate max−min,f,t that uncertainty does not abate quickly but lasts for a few years, with the half-life of a shock to uncertaintyestimatedtobetwoyears. 4 The Economic Effects of Uncertainty on Capital, Labor and Cash Holdings We now study the economic effects of uncertainty by tracing the dynamic responses of a large setofrealandfinancialvariables,broadeningtheanalysis’sscoperelativetomostoftheexisting literature. Our analysis’s critical advantage is that the richness of the data allows us to separate theeffectsinducedbytime-varyinguncertaintyfromfluctuationsinthemeanexpectationabout future sales. In Section 4.1, we describe our empirical approach. In Section 4.2, we show that fluctuations in uncertainty are associated with sizeable effects not only on investment but also on labor variables and cash holdings. Importantly, these effects do not abate quickly but last for a few years. In Section 4.3, we show that our results are robust to instrumenting firm-level uncertaintywithitslaggedvaluesandincludingmorelagsofcontrolvariables. 4.1 Empirical Methodology Weestimatetheeconomiceffectsoffluctuationsinuncertainty,byrelyingonthelocalprojection technique, discussed in Jordà (2005). We face a critical challenge because subjective expectations and the resulting uncertainty perceived by firms are jointly determined by aggregate and 17

idiosyncratic factors, such as current and future business prospects. To tackle this issue, we proceedinsteps. We first isolate the unpredictable component of firm-level uncertainty by controlling for firmspecific and aggregate conditions. Specifically, we project σ on current and future max−min,f,t business conditions, lags of capacity utilization, lags of growth rates of labor inputs and real investment, firms’ leverage, "sales surprises" (or forecast errors) defined as the difference between lagged expected (se ) and the growth rate of real sales realized at time t ( ∆ Sales ). f,t−1 f,t,t−1 The empirical specification also includes firm-specific, sector, and year dummies to account for time-invariant firm characteristics, as well as industry-specific or policy factors. The resulting estimatedresidual,denotedbyσX ,isusedinthesecondstage(describednext)tocharacmax−min,f,t terize the propagation mechanism of fluctuations in uncertainty. This empirical strategy allows us to isolate the component of firm-level uncertainty not driven by aggregate or firm-specific factorsrelatedtoobservablevariablesorreflectedinchangesinexpectations. To tease out the unpredictable component of uncertainty, we proxy current business conditions with the current growth rate of sales and future business conditions with se the first avg,f,t moment of the probability distribution of expected sales one year ahead. In so doing, we explicitly control for fluctuations in the first moment of the probability distribution of expected sales that may potentially affect uncertainty and confound its effect. We also consider lags of capacity utilization and labor, as these margins of adjustment may signal news about the future not explicitly accounted for by current or future business conditions. The set of regressors also controls for firm leverage, proxied by the ratio between debts and assets. Finally, we include time t sales surprises (or forecast errors) to control for unexpected outcomes that may influence firms’expectations,aswellastheirperceptionofrealizedcurrentoutcomes. Forinstance,howa firmassessestherealizedgrowthratesalemaydependonwhatthefirmexpectedoneyearago. Armed with the unpredictable component of uncertainty, we then trace the dynamic economic effects of uncertainty fluctuations over a broad range of outcomes by projecting firm-level real and financial variables at different horizons on contemporaneous σX . The variables we max−min,f,t look at include investment, the growth rate of total hours (distinguishing between the number of workers and hours-per-worker), the capacity utilization rate, and the growth rate of liquid assets,orcash,heldbythefirm. 18

4.2 Real and Financial Effects of Uncertainty We now show that the economic effects of uncertainty are not limited to investment but extend to the labor market and the firm’s financial structure. Table 6 reports the dynamic response of firm-levelvariablesfollowinga1percentagepointincreaseinfirm-leveluncertainty. Entriesare expressedinpercent. Fluctuations in uncertainty induce economic effects that are statistically and economically significant. Notably, these effects do not abate quickly and last for a few years. This result is due to both the persistence of firms’ perceived changes in uncertainty (as shown in Section 3.5) andthesluggishnessoffirms’endogenousresponsesthatfirstadjustsoftmarginslikelaborand onlythenchangeinvestment. Table6: RealandFinancialEffectsofFirm-LevelUncertainty ImpulseResponses-IncreaseinUncertainty1p.p. Horizon=h 0 1 2 3 4 ∗∗∗ CapacityUtil. Rate(t+h) -0.138 -0.005 0.005 0.045 -0.012 (0.00) (0.34) (0.94) (0.44) (0.43) ∗∗∗ TotalHours(t+h) -0.126 0.019 0.026 0.004 0.042 (0.01) (0.42) (0.60) (0.93) (0.58) ∗∗ ∗∗ RealInvestment(t+h) 0.058 -0.554 -0.785 0.229 0.387 (0.75) (0.03) (0.00) (0.41) (0.12) ∗ ∗∗ ∗∗ RealCashHoldings(t+h) 0.299 0.783 0.722 0.526 -0.599 (0.08) (0.04) (0.03) (0.15) (0.23) Note: Each equation is estimated with ordinary least squares over the sample period 1996 to 2018, and it includes firm- and sector-specific dummies, and year effects. P-values are in parentheses. Starsdenotethesignificancelevelofthecoefficienttheyreferto: *p-value<0.10, **p-value<0.05,and***p-value<0.01.Standarderrorsclusteredintwo-waysbyfirmandyear. Entries are expressed in percent, and report the estimated coefficient on σX . See the max−min,f,t textformoredetails. On impact, firms also increase their cash holdings, signaling a precautionary behavior that anticipates reducing investment. We discuss these results in turn. On the real side, after an increase in perceived uncertainty equal to 1 percentage point, the firm reduces its capacity uti- 19

lization rate and the growth rate of total hours by about 0.13 percentage points, equivalent to one standard deviation of both variables. Also a reduction in employed workers’ growth rate, smaller than that of hours, signals that the intensive margin of labor is adjusted more swiftly. Over the same period, on the financial side, firms also increase their cash holdings. After one year, the firm starts cutting on investment, by more than 1 percent over two years (or about one-half of the investment standard deviation).11 As the increase in uncertainty is reabsorbed, investment overshoots its steady-state level before converging, but the coefficient is not statisticallysignificant. Overall, our results indicate that we are capturing the effects induced by pure uncertainty rather than first-moment shocks associated with changes to the current or future business conditions(giventhatbothareincludedinthesetofcontrols). 4.3 Evidence Based on Instrumental Variables In thissection, weprovide someevidence onthe causallink betweenuncertainty and economic outcomes. Towards this goal, we instrument current uncertainty using its second lag. As in the previous section, the set of controls includes current and expected business prospects, financial variables, and aggregate and industry-specific factors. In the specification reported in Table 7, we instrument contemporaneous uncertainty using its second lag. F-statistics lie above the usual value of 10 (not reported), indicating that the instrument is relevant and captures the strong persistence of uncertainty. As in the case with ordinary least squares, instrumental variablesestimatesconfirmthatanincreaseinuncertaintypromptsfirmstoreducetotalhours(with the brunt of the adjustment sustained by hours per worker), increase cash holdings, and lower investment. Wenotethatutilizationisnegativebutnotsignificant,withap-valueof0.13. 5 Effects of Uncertainty through "Downside Uncertainty" Wenowstudywhethertheeconomiceffectsofuncertaintydependonthesourcedrivingtheincreaseindispersionoffutureexpectedsales—thatis,whetheritcomesfromdownsideorupside 11Investmentisdeflatedusingsector-specificdeflatorsandincludescapitalexpendituresonequipmentandstructures. 20

Table7: IVEvidenceontheEffectsofFirm-LevelUncertainty IV-ImpulseResponses-IncreaseinUncertainty1p.p. Horizon=h 0 1 2 3 4 CapacityUtil. Rate(t+h) -0.389 0.296 0.128 0.106 -0.370 (0.13) (0.37) (0.75) (0.80) (0.45) ∗∗ ∗ TotalHours(t+h) -0.918 0.836 0.016 -0.310 -0.690 (0.02) (0.06) (0.97) (0.59) (0.37) ∗ RealInvestment(t+h) 0.478 -0.100 -0.712 0.363 1.224 (0.34) (0.18) (0.06) (0.39) (0.12) ∗∗ ∗∗∗ RealCashHoldings(t+h) 0.078 0.121 0.069 0.015 -0.076 (0.03) (0.01) (0.13) (0.77) (0.34) Note: Each equation is estimated with instrumental variables over the sample period1996to2018,anditincludesfirm-andsector-specificdummies,andyeareffects. We use the second lag of uncertainty as an instrument. P-values are in parentheses. Stars denote the significance level of the coefficient they refer to: * p-value<0.10, ** p-value<0.05, and***p-value<0.01. Entriesareexpressed inpercent. See thetextfor moredetails. uncertainty. Typically,theexistingliteraturedoesnotdistinguishbetweenthesourceoffluctuationsinuncertainty,mostlybecauseofthelimitationimposedbyexistingdata.12 Understanding this issue is important for at least two reasons. From an empirical standpoint, the source of the increase in uncertainty is important to predict future effects. For instance, an increase in uncertainty may signal an increase (decrease) in labor and capital if driven by dispersion in positive or upside (negative or downside) outcomes. From a theoretical standpoint, measuring the effectsofdownsideandupsideuncertaintyprovidesoveridentifyingrestrictionsagainstwhichto test competing models aimed at quantifying the aggregate effects of uncertainty. (We return to this issue in Section 6.) Following the terminology in Bernanke (1983), we define an increase in uncertainty driven by se (a reduction in se holding se constant) as an increase in downside min min max uncertainty—that is, an increase in dispersion in negative outcomes.13 Similarly, we denote up- 12Segal,ShaliastovichandYaron(2015)constituteanimportantexception. Theystudytheroleofdownsideand upside(orbadandgood)uncertaintyforaggregatemacroeconomicseriesandfinancialmarkets,findingthatboth matter. 13Intheempiricalanalysis,wecontrolforchangesinthemeanoffutureexpectedsales. 21

sideuncertaintyasanincreaseinuncertaintydrivenbyse (holdingse constant). Asdiscussed max min in Section 3.1, firms that display a lower se (higher se ) also display more probability mass min max associatedwithnegativegrowthrates(positivegrowthrates)ofsales. How do we distinguish downside and upside uncertainty? We exploit the definition of σ as the difference between se and se . Operationally, we follow the same empirical max−min max min strategyinSection4.1. FirstweconstructsX ,theunpredictablecomponentoftheupsideunmax,f,t certainty (or best-case scenario), and sX , the unpredictable component of the downside unmin,f,t certainty(orworst-casescenario). Second,weregressfirm-leveloutcomesonsX andsX . min,f,t max,f,t Everyspecificationincludesbothvariablessimultaneously. The main takeaway is that firms respond to fluctuations in uncertainty only if it originates with downside uncertainty. Results are reported in Table 8. Panel A shows that an increase in downside uncertainty induces negative economic effects. Instead, Panel B shows that the coefficients on upside uncertainty are not statistically significant (except for hours per worker that increase; see Table A.2). The propagation mechanism of fluctuations in downside uncertainty (or equivalently an increase in uncertainty driven by a deterioration in the worst-case scenario, or downside uncertainty) is similar to the one discussed in Section 4.2. In response to an increase in downside uncertainty, firms first reduce capacity utilization and total hours and then investment. Overtime,astheinitialeffectoftheshockwanes,thedynamicsarereverted. Disentangling the individual contribution of upside and downside uncertainty sheds light on the dynamics induced by an increase in σ . We emphasize two aspects. First, the estimax−min matedeffectsofanincreaseinuncertaintyconfoundthesignificantsensitivityoffirms’decisions to the rise in downside uncertainty and its unresponsiveness to upside uncertainty. Dynamics triggered by fluctuations in downside uncertainty are statistically and economically significant, moving each variable in Panel A of Table 8 by about one standard deviation. As upside uncertainty accounts for about one-half of the variance in uncertainty, responses following shocks to σ areabouthalfoftheonesfollowingshockstodownsideuncertainty. max−min Second, fluctuations in downside uncertainty generate "boom-bust" dynamics, with investment overshooting its steady-state level after the initial drop. On impact, firms reduce capacity utilization and hours (with two-thirds of the response accounted for by hours per worker; see Table A.2) and then investment. Cash holdings also increase for the first two periods. As the 22

Table8: RealandFinancialEffectsofFirm-LevelUncertainty PanelA-ImpulseResponses: IncreaseinDownsideUncertainty1p.p. Horizon=h 0 1 2 3 4 ∗∗ CapacityUtilizationRate(t+h) -0.198 -0.077 -0.007 0.001 0.000 (0.02) (0.26) (0.88) (0.16) (0.94) ∗∗∗ TotalHours(t+h) -0.217 0.045 0.024 -0.014 0.091 (0.00) (0.27) (0.68) (0.77) (0.30) ∗∗∗ ∗ ∗ RealInvestment(t+h) -0.108 -0.875 -0.977 -0.094 0.731 (0.75) (0.01) (0.07) (0.82) (0.06) ∗∗ ∗ RealCashHoldings(t+h) 0.624 0.832 -0.151 -0.534 0.262 (0.01) (0.09) (0.71) (0.31) (0.64) PanelB-ImpulseResponses: IncreaseinUpsideUncertainty1pp Horizon=h 0 1 2 3 4 CapacityUtilizationRate(t+h) -0.063 -0.006 0.017 -0.000 -0.030 (0.14) (0.90) (0.84) (1.00) (0.61) TotalHours(t+h) -0.024 -0.011 0.023 0.035 -0.008 (0.53) (0.76) (0.63) (0.34) (0.91) RealInvestment(t+h) 0.005 -0.185 -0.520 0.659 -0.102 (0.99) (0.60) (0.28) (0.29) (0.82) RealCashHoldings(t+h) 0.014 0.003 0.022 -0.008 -0.032 (0.28) (0.92) (0.25) (0.86) (0.35) Note: Each equation is estimated with ordinary least squares over the sample period 1996 to 2018,anditincludesfirm-andsector-specificdummies,andyeareffects. P-valuesareinparentheses. Stars denote the significance level of the coefficient they refer to: * p-value<0.10, ** pvalue<0.05,and***p-value<0.01. Standarderrorsareclusteredintwoways,byfirmandyear. Entriesareexpressedinpercent.PanelAreportstheresponseofeachvariabletoa1percentage point decrease in sX , or equivalently an increase in downside uncertainty. Panel B reports min,f,t theresponseofeachvariabletoa1percentagepointincreaseinsX ,or,equivalently,aninmax,f,t creaseinupsideuncertainty. Seethetextformoredetails. 23

shock dissipates, the initial dynamics are reversed. The total effect is mostly zero for capacity utilization,whileitisnegativefortheothervariables. 6 Implications for Macroeconomic Modeling Our microeconomic evidence shows that the adverse economic effects of firm-level uncertainty results from fluctuations in downside uncertainty. Instead, firms’ decisions are insensitive to changesinupsideuncertainty. Howdoesourevidencedisciplineexistingtheoriesofuncertainty,andwhataretheimplications for macroeconomic models? As discussed in Bloom (2014), to reproduce the negative effectsofuncertainty,macroeconomicframeworksrelyonmodelsof"realoptions"ormodelsthat emphasize financial or behavioral considerations.14 Theories of real options emphasize "wait and see" motives due to the presence of adjustment costs that give firms the option to delay investment(orhiring)inthepresenceofuncertaintyandmakereversingdecisionscostly.15 Examples of these frictions include non-convex adjustment costs and input irreversibility that have received widespread attention in the quantitative macroeconomic literature; see, for instance, Bloom(2009)andBachmannandBayer(2014). AsdiscussedinAbeletal.(1996),inthecontextofrealoptionstheoriesthespecificationofthe capital(orlabor)adjustmentcostfunctiondictatesthefirms’sensitivitytodownsideuncertainty, upside uncertainty, or both. With capital irreversibility due to firm specificity or the absence of secondary markets, Bernanke’s bad news principle applies with firms responding only to fluctuations in downside uncertainty. This choice increases firm’s profits in low future productivity states in which the irreversibility constraint is binding and the firm cannot downsize. Frictions 14On theoretical grounds, it is well known that the economic effects of uncertainty are in general ambiguous and depend on the assumptions about the production technology, competition in product markets, the shape of adjustmentcosts,andmanagementattitudestowarduncertainty. Uncertaintycanpotentiallyhavepositiveeffects. Bar-IlanandStrange(1996)showthatinthepresenceof"timetobuild"or"gestationlags,"uncertaintymayincrease investment. We refer the reader to the discussion of the literature in Dixit and Pindyck (1994), Guiso and Parigi (1999),and,morerecently,Bloom(2014). 15Cooper and Haltiwanger (2006) estimate high capital adjustment cost, while Ramey and Shapiro (2001) emphasize sectoral specificity of physical capital and substantial costs of redeploying the capital. Similarly, there is evidenceofsignificanthiringadjustmentcostsrelatedtorecruitment,training,andseverancepay;see,forinstance, Nickell(1987)andBloom(2009). 24

that result in costly accumulation of capital prompt firms to respond to upside uncertainty.16 Our empirical evidence supports theories of real options delivering an asymmetric adjustment costfunction,inwhichdownsizingcapital(orlabor)iscostly. Thispointisalsodemonstratedby the reliance of the firms in using "soft margins" like the intensive margin of hours and capacity utilization rates to cope with fluctuations in uncertainty. We numerically illustrate the role of inputirreversibilitybysolvingtheproblemofasinglefirmsubjecttofluctuationsinuncertainty inAppendixF. Another strand of the literature emphasizes financial and behavioral considerations. Higher downside uncertainty about future sales could increase the firm’s likelihood of facing financial constraints, leading to a drop in investment and hiring. Hansen, Sargent and Tallarini (1999) andIlutandSchneider(2014)highlighttheimportanceof"ambiguityaversion."Intheirmodels, agents cannot form a probability distribution about future events behaving as if the worst-case scenario will occur. Assuming that the minimum of future sales is a summary statistic for the probability distribution under the worst-case scenario, our evidence is also consistent with this classofmodels. Agentsrespondtoadeteriorationintheworst-casescenariowhilebeinginsensitivetoimprovementsinthebest-casescenario. Overall, our empirical analysis provides a set of restrictions based on microeconomic evidenceagainstwhichtovalidatemacroeconomictheoriesaimedtoquantifytheaggregateeffects ofuncertainty. 7 Measurement and Consequences of Aggregate Uncertainty We now derive an economy-wide measure of ex ante uncertainty. We describe the detail of the aggregation of firm-level uncertainty in Section 7.1. In Section 7.2, we discuss how economywideuncertaintyhasevolvedoverthepast25yearsandusefirm-levelestimatestoquantifythe contributionofuncertaintytotheGDPdynamicsexperiencedbytheItalianeconomyduringthe pastthreerecessions. 16Abeletal.(1996)refertothegeneralizationofthebadnewsprincipleasthe"Goldilocksprinciple". 25

7.1 A Bottom-Up Measure of Ex Ante Aggregate Uncertainty Weconstructaneconomy-widemeasureofuncertaintybasedonanaggregationofthemax–min range at the firm level. Uncertainty perceived by each firm is affected by both aggregate and idiosyncraticfactors. Byaveragingacrossfirms,wewashouttheidiosyncraticcomponent,leavingtheaggregateone. Ourbottom-upapproachprovidesaunicumintheliterature,asitcovers multiple business cycles. Similarly, Altig et al. (2020a) and Altig et al. (2020b) use survey data toconstructanaggregateproxyofaggregateuncertainty. Still,dataavailabilitylimitsthelength of their series extending (albeit a monthly rather than yearly frequency) to the past five years. AlternativestrategiesincludeBloom(2009),andBloometal.(2018)thathaveproxiedaggregate uncertaintyusingdispersioninrealizedoutcomes,suchasthecross-sectionaldispersioninTFP shocks. Bachmann, Elstner and Sims (2013) construct uncertainty measures based on both ex ante disagreement and ex post forecast error about future outcomes. Jurado, Ludvigson and Ng (2015) adopted a latent-variable approach to extract a measure of the common variation in uncertaintyacrossmorethan100macroeconomicseries. Our aggregate measure, σ , is constructed averaging firm-level uncertainty, using agg,max−min as weights each firm’s value added and the share of each firm over the entire population. The meanandthestandarddeviationofσ are8.53and1.60percentagepoints,respectively. agg,max−min Unsurprisingly,thevolatilityoftheseriesissmallerthanitsfirm-levelcounterpart. Asshownin Section3roughlytwothirdsofthevariationinσ atthefirmlevelisidiosyncratic. Unlike max−min firm-leveluncertainty,wefindthataggregateuncertaintyisnegativelycorrelatedwithrealGDP growth(-0.58). Whilethiscountercyclicalityistypicallyobtainedintheliterature,weemphasize that the correlation of our measure of ex-ante aggregate uncertainty, σ , is uncorreagg,max−min lated with typical proxies currently used in the literature. For instance, the correlation between σ and the cross-sectional dispersion in TFP innovation and sales is zero or slightly agg,max−min negative, respectively. This disconnection between ex ante and ex post measures occurs even if the measures of cross-sectional dispersion are markedly countercyclical and remained elevated since2009. Wesuggestthatσ capturesadimensionofex-anteuncertaintythat,almostby max−min construction, is distinct from realized uncertainty captured by standard proxies, suggesting that thesemeasuresdonotcapturethefullextentofaggregateuncertainty. 26

Figure1reportsourmeasure σ togetherwiththegrowthrateofrealGDP.(Theseries max−min foraggregate σ isdemeaned.) max−min 8 6 4 2 0 -2 -4 -6 -8 1997 2000 2003 2006 2009 2012 2015 2018 2021 stniop egatnecrep (demeaned) agg,max-min GDP Growth Rate Figure1: UncertaintyandGDPGrowth Note: Thefigurereportsthedemeanedseriesforaggregate σ max−min , togetherwith thegrowthrateofrealGDP.Sampleperiodsi1997to2021. Excluding the current spike due to the COVID-19 pandemic, uncertainty peaked in the 2009 Global Financial Crisis (GFC) and rose, although to a lesser extent, in 2012 during the sovereign debt crisis (SDC). During the GFC and SDC, uncertainty increased more in the manufacturing sector relative to the service sector. In contrast, in 2020 at the peak of the COVID-19 pandemic, uncertainty nearly doubled in the service sector, and it increased by 50 percent in the manufacturing sector. For both sectors, in 2021 uncertainty is still historically high but is now driven by itsupsidecomponent(thedownsidecomponentrecovered). Beyond business cycle effects, our measure was also affected by political considerations in 2019,reachinglevelscomparabletotheSDCduetoelevatedpoliticaluncertainty. Beforeturning to quantify the economic effects of aggregate uncertainty, we also note that in periods of high 27

aggregate uncertainty, aggregate expected sales, se , have been particularly negative, see agg,avg Figure A.1inAppendixE.17 7.2 Economic Effects of Aggregate Uncertainty Using survey data for the Italian economy, we find that uncertainty significantly contributed to theItalianeconomy’sGDPlossesinthepastthreerecessions. WeusetheestimatesinTable6tomeasuretheeffectsofuncertaintyonGDPandassumethat the same uncertainty shock hits all firms in the economy. Our calculations implicitly balanced outaggregatepriceresponsesthatmayreducetheGDPlossesduetouncertaintyandaggregate demandeffectsthatmayincreaseGDPlossesthroughinput—outputlinkages. To pin down the size of the shock, we compute the variation in aggregate uncertainty between consecutive years. These changes are reported in the first column of Table A.5 in Appendix G. For the Italian economy, while the increase in uncertainty was of similar magnitude in2009and2012,the2020spikeisunprecedentedasuncertaintydoubledrelativetotheGFC. According to our estimates, a deterioration in uncertainty weighs on the Italian economy’s recovery,reducingcapacityutilizationandthegrowthrateoftotalhoursandinvestment.18 WelinktheestimateduncertaintyeffectsoncapitalandlaborintoaGDPequivalentemployingagrowthaccountingapproach. Throughgrowthaccountingidentity,weexpressthegrowth rate of real GDP ( ∆ GDP) as ∆ GDP= ∆ TFP + α ∆ K + (1-α ) ∆ TH, where ∆ K and ∆ TH de- K K notethegrowthrateofcapitalaccumulationandtotalhours,respectively. Weset α toatypical K value of 1/3 and assume that capacity utilization reduces TFP one-to-one. The economic effects ∆ ∆ of total hours directly map to TH. Obtaining K is slightly more involved. Given that the median investment rate is about 20 percent, the 4 percent reduction in investment decreases the investmentrate(orthegrowthrateofcapital)byabout1percentagepoint. Table9reportsthefinalresultsofthesecalculations. WecomparetheactualdropinrealGDP ∆ ( GDP) and the corresponding contribution of uncertainty for every recession. The main take- 17Similarly with the aggregate measure of uncertainty, se is constructed averaging the firm-level expected agg,avg salesusingasweightseachfirm’svalueaddedandtheshareofeachfirmovertheentirepopulation. 18The total effect on capacity utilization and the growth rate of hours is obtained by multiplying the estimated coefficientathorizonh=0inTable8,-0.138and-0.126,timestheuncertaintyshock. Thecumulativeeffectofinvestmentiscomputedanalogouslyusingthecoefficientsathorizonh=1(-0.554)andh=2(-0.785). 28

Table9: GDPEffectsofAggregateUncertainty GlobalFinancialCrisis 2009 2010 2011 ∆ GDP Italy -5.43 1.70 0.70 ContributionofUncertainty -0.69 -0.14 -0.20 SovereignDebtCrisis 2012 2013 2014 ∆ GDP Italy -3.02 -1.85 -0.01 ContributionofUncertainty -0.45 -0.09 -0.13 Note: Entriesareexpressedinpercentagepoints. ∆GDPrefers tothegrowthrateofrealGDP.Theentry"ContributionofUncertainty" reports the estimated GDP contribution of the observed increase in uncertainty during the corresponding period.SeethetextfordetailsonthecalculationonGDPeffects. away is that uncertainty has significant GDP effects, with an average contribution of about 15 percent to the Italian economic activity drop. Results are robust to using downside uncertainty ratherthantotaluncertainty;seeTable A.6inAppendixG. Concerning the Covid-19 pandemic, we highlight that the source of uncertainty dynamics have driven its economic effects. In 2020 spike in uncertainty accounted for about 1.2 percentage points of the 8.9 percent GDP contraction, owing to the significant decrease in downside uncertainty. As indicated by the 2021 wave of INVIND, overall uncertainty is still high. Still, the recovery in the downside component, more than the value predicted by the recovery in the mean,pointstoasmallerdragonGDPmovingforward. 8 Final Remarks We study the economic effects of time-varying uncertainty and offer a unique perspective that addressessomeofthemostpressingmeasurementissuesregardinguncertaintyatthefirm-level. Access to microeconomic data allows us to construct, for a representative panel of firms, a measure of subjective ex ante uncertainty based on business managers’ expectations that span over twodecadesandmultiplebusinesscycleepisodes. 29

We document the properties of time-varying uncertainty across firms’ size, age, and sectors. Ourempiricalanalysisdetailsthepropagationmechanismofuncertaintyfluctuationsatthefirm level showing that they induce long-lasting economic effects across various real and financial variables,suchascapacityutilization,hours,investment,andcashholdings. We provide evidence that not all uncertainties are all alike and the source of uncertainty mattersforitsoveralleffect. Ourevidenceprovidesapracticalsetofoveridentifyingrestrictions againstwhichtotestcompetingmacroeconomicmodels. Weconstructanexanteeconomy-widemeasureofuncertainty. Ourbottom-upmeasurecaptures a new dimension of aggregate uncertainty distinct from existing proxies. Although both are markedly countercyclical, our measure is uncorrelated with typical proxies of uncertainty employed in the existing literature, such as dispersion in realized TFP shocks or sales. This resultindicatesthatexistingproxiesmaynotcapturethefullextentofaggregateuncertainty. Our estimates indicate that uncertainty amplifies GDP losses during economic downturns, accounting for about 15 percent of the GDP losses during the past three recessions. Higher uncertainty has contributed to the 2020 GDP hit. Still, we expect these forces to subside given thelargerecoveryindownsideuncertaintyandexertaminordragontherecoveryoftheItalian economyfromtheCOVID-19crisis. 30

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APPENDIX A Data Sources Our data on expected sales growth (the average, the minimum and the maximum) comes from theSurveyofIndustrialandServiceFirms(INVIND),alargeannualbusinesssurveyconducted by the Bank of Italy on a representative sample of firms. Since 2002, the reference universe in INVIND consists of firms with at least 20 employees operating in industrial sectors (manufacturing,energy,andextractiveindustries)andnon-financialprivateservices,withadministrative headquarters in Italy. The survey adopts a one-stage stratified sample design. The strata are combinations of the branch of activity (according to an 11-sector classification), size class (in termsofnumberofemployeesclassifiedin7buckets),andregioninwhichthefirm’sheadoffice is located. In recent years, each wave has around 4,000 firms (3,000 industrial firms and 1,000 servicefirms). ThedataarecollectedbytheBankofItaly’slocalbranchesbetweenFebruaryand April every year. The question between the minimum and maximum expected growth rate of sales(min—maxgap)coversaround900firmsonaverageperyear,from1993to2007,and1,677 firms on average per year from 2008 to 2018. The data set has a panel dimension. The firms observed in the previous edition of the survey are always contacted again if they are still part of the target population. In contrast, those no longer wishing to participate are replaced with othersinthesamebranchofactivityandsizeclass. B Heterogeneity in Firm-Level Expectations Table A.1describesthepropertiesoffirms’expectationsconditioningonsize,age,andsectors. C Estimation Details We characterize the dynamic response of investment, labor, and capacity utilization after an increase in the unpredictable component of uncertainty, σX . Towards this goal, we estif,t,max−min 36

Table A.1: Firm-LevelExpectations: DescriptiveStatistics No. ofObs. Mean St. Dev. Skew. P P P P P 10 25 50 75 90 FullSample se 49674 3.59 11.60 1.00 -7.10 0.00 2.70 7.10 14.50 avg se 30958 -3.57 10.40 -0.20 -12.00 -10.00 -2.00 1.00 5.00 min se 30976 6.91 10.70 1.63 -1.00 1.50 5.00 12.00 15.00 max SmallandMediumFirms: 20 ≤ LaborForce ≤ 50 se 3059 3.53 10.20 1.07 -4.80 0.00 2.40 5.90 14.30 avg se 5115 -5.97 10.60 -0.42 -14.00 -12.00 -5.00 0.00 4.00 min se 5120 6.63 10.40 0.75 -2.00 1.00 5.10 12.00 12.70 max LargeFirms: LaborForce ≥ 50 se 46339 3.60 11.70 0.99 -7.40 0.00 2.80 7.30 14.60 avg se 25630 -2.14 10.00 -0.01 -12.00 -6.00 -1.00 2.00 7.00 min se 25646 7.09 10.80 2.09 -1.00 2.00 5.00 12.00 16.20 max YoungFirms: Age ≤ 5 se 1367 6.27 14.90 1.20 -7.40 0.00 4.00 10.50 22.30 avg se 873 -3.60 11.60 0.66 -12.00 -12.00 -3.00 1.00 8.00 min se 871 9.91 12.00 1.60 0.00 3.00 10.00 12.00 21.00 max OldFirms: Age > 5 se 48307 3.54 11.50 0.98 -7.00 0.00 2.70 7.10 14.40 avg se 30085 -3.57 10.30 -0.23 -12.00 -10.00 -2.00 1.00 5.00 min se 30105 6.85 10.60 1.62 -1.00 1.50 5.00 12.00 15.00 max ManufacturingSector se 33873 4.28 12.20 0.83 -7.50 0.00 3.50 8.50 16.00 avg se 21592 -3.08 11.00 -0.26 -12.00 -10.00 -1.20 2.00 7.00 min se 21607 7.48 11.20 1.41 -1.00 2.00 5.60 12.00 18.00 max ServiceSector se 15801 2.55 10.40 1.30 -6.40 -0.10 1.80 5.10 11.30 avg se 9366 -4.25 9.43 -0.16 -12.00 -12.00 -2.00 0.20 4.00 min se 9369 6.14 9.82 2.00 -1.00 1.00 5.00 12.00 12.00 max Note: Statistics are computed pooling all the firm-specific observations over the whole sample period 1996 to 2018. Tableentriesarecomputedovergrowthratesexpressedinpercent. se ,se ,andse denotetheaverage, avg min max minimum,andmaximumexpectedgrowthratesofsalesone-yearahead,while∆Salesreportsthegrowthrateof realizedsales. P reportstheXth percentileofthedistribution. X 37

matethefollowingspecificationatdifferenthorizons: Y = α+β σX +(cid:101) ,∀h = 0...4 (A.1) f,t+h h max−min,f,t f,t for every h ≥ 0. The firm-level dependent variables Y are, the log of investment, the f,t growth rate of total hours at the firm level, the capacity utilization rate, and the growth rate of cashholdings. Weremindthereaderthatincludingfirm-andindustry-specificeffects,andyear dummiesinEquation A.1isirrelevantgiventhatthoseeffectshavealreadybeenextractedfrom σX . The set of control variables depends on the dependent variable. Importantly, we max−min,f,t includethestockofcapital(inlogs)whenthedependentvariableisinvestment. D Firm-Level Uncertainty and Labor Market Dynamics Table A.2 reports the decomposition of the impulse responses of the growth rate of total hours into the intensive margin, the growth rate of hours-per-worker, and the extensive margin, the number of employees. Panel A reports the impulse responses following an increase in overall uncertainty. Panel B reports the labor market dynamics following an increase in downside uncertainty. Panel C reports the responses following an increase in upside uncertainty. The key messageisthatmostoftheadjustmenttototalhoursoccursthroughtheintensivemargin. 38

Table A.2: Firm-LevelUncertainty: LaborMarketDynamics PanelA-ImpulseResponses-IncreaseinUncertainty1p.p. Horizon=h 0 1 2 3 4 ∗∗ GrowthRateofHours-per-Worker(t+h) -0.072 0.041 0.022 -0.025 0.059 (0.02) (0.22) (0.48) (0.29) (0.25) ∗∗ GrowthRateofNo. ofEmployees(t+h) -0.058 -0.017 -0.006 0.035 -0.016 (0.02) (0.53) (0.79) (0.49) (0.69) PanelB-ImpulseResponses-IncreaseinDownsideUncertainty1pp Horizon=h 0 1 2 3 4 ∗∗∗ ∗ ∗ GrowthRateofHours-per-Worker(t+h) -0.176 0.072 0.045 -0.020 0.103 (0.01) (0.10) (0.31) (0.40) (0.05) ∗∗∗ GrowthRateofNo. ofEmployees(t+h) -0.055 -0.018 -0.015 0.016 0.003 (0.01) (0.59) (0.44) (0.77) (0.93) PanelC-ImpulseResponses-IncreaseinUpsideUncertainty1pp Horizon=h 0 1 2 3 4 ∗ GrowthRateofHours-per-Worker(t+h) 0.043 0.003 -0.009 -0.015 0.010 (0.09) (0.93) (0.82) (0.68) (0.92) GrowthRateofNo. ofEmployees(t+h) 0.059 -0.013 0.005 0.054 -0.037 (0.14) (0.65) (0.89) (0.37) (0.52) Note: Each equation is estimated with ordinary least squares over the sample period 1996 to 2018, and it includes firm- and sector-specific dummies, and year effects. P-values are in parentheses. Starsdenotethesignificancelevelofthecoefficienttheyreferto: *p-value<0.10,**p-value<0.05,*** p-value<0.01. Standarderrorstwo-wayclusteredbyfirmandyear. Entriesareexpressedinpercent andreporteachvariable’sresponsetoa1percentagepointinuncertainty. Seethetextformoredetails. 39

E Aggregate Expected Sales and GDP Growth Figure A.1 reports the evolution of se , an aggregate measure of the expected growth rate agg,avg of sales one period ahead. We aggregate firm-level expected growth rates using as weights each firm’s share in the population and value added. The series se in the figure has been agg,avg demeaned. 8 6 4 2 0 -2 -4 -6 -8 -10 1997 2000 2003 2006 2009 2012 2015 2018 2021 stniop egatnecrep e s agg,avg GDP Growth Rate Figure A.1: ExpectedAggregateSalesandGDPGrowth Note:Thefigurereportsthe(demeaned)seriesforaggregateexpectedgrowthrateof salesone-yearahead,denotedbyse ,togetherwiththegrowthrateofGDP. agg,avg F Theory: Input Irreversibility Thissectiondescribesthetheoreticalframeworkthatweemploytostudythelinkinourevidence on the economic effects of uncertainty playing through downside uncertainty and economic theory. The main goal is to reconcile the sensitivity of investment to fluctuations in downside 40

uncertainty (and the muted response to upside uncertainty) with the optimizing behavior of a profit-maximizingfirm. The model features input irreversibility as in Bernanke (1983), where firms cannot disinvest. WedescribetheenvironmentinSectionsF.1andF.2andthefirm’sproblemfeaturinginputirreversibilityinSectionF.3. Wedetailthemodel’sparameterizationandtheresultofournumerical simulationinSectionsF.4andF.5. F.1 Production Each firm has access to an increasing and concave production function that combines predeterminedcapitalstock k withitsavailabletechnology ε toproduceoutput y: y = εkθ, (A.2) where θ > 0 and 0 < θ < 1. ε denotes the idiosyncratic productivity. The latter follows a firstorder Markov with autocorrelation ρ with time-varying conditional standard deviation, σ . In ε ε turn, σ follows an autoregressive process with persistence ρ and volatility σ . Fluctuations in ε σε σε σ capturethetime-varyinguncertaintyfacedbythefirm.19 ε F.2 Firm’s Input Accumulation Decision We consider two alternative scenarios: input irreversibility and non-convex adjustment cost. Under input irreversibility, the firm can adjust the accumulation of input without incurring any cost, while decreasing input above its depreciation rate is not feasible, in the spirit of Bernanke (1983). (Assumingthatthefirmcansellitsinputatadiscount,asinBloom(2009),doesnotalter ourconclusions.) F.3 Value of a Firm and Profit Maximization LetV1(ε ,σ ,k)denotetheexpecteddiscountedvalueofafirmenteringtheperiodwith(ε ,σ ,k). l ε l ε The dynamic optimization problem for the typical firm is described using a functional equation 19Tobeprecise,σ(cid:48) = σ¯(1−ρ )+ρ σ +(cid:101) . ε ε σε σε ε σε 41

definedby(A.3)and(A.4). Thefirm’sprofitmaximizationproblemisthendescribedby    [F(ε,k)+(1−δ)k]+  V1(ε,σ ,k,ξ) = max (A.3) ε k∗  +R(ε,σ (cid:48) ,k ∗)  ε s.t. k ∗ ≥ k(1−δ) (cid:48) (cid:48) where R(ε,σ ,k ) represents the continuation value associated with a given combination of the ε idiosyncraticshock,firstandsecondmoments,andthestockofcapital: R(ε,σ (cid:48) ,k (cid:48) ) ≡ −γk (cid:48) +β ∑ Nε πε V0(ε ,σ (cid:48) ,k (cid:48) ) (A.4) ε lm m ε m=1 F.4 Model Parameterization We solve the problem of the individual firm defined in Section F.3 by value function iteration. WereferthereadertoAppendixF.6fordetailsonthecomputation. As is customary in the quantitative business cycle literature, we parameterize the model to reproduce key characteristics of Italian firms. Table A.3 summarizes parameter values and data sources. We are to assign values to six parameters related to the production process (δ, θ) , discount factor (β), and the persistence and the volatility of the idiosyncratic productivity process anditstime-varyingvolatility(ρ , σ¯ , ρ ,and σ ). Oneperiodinthemodelrepresentsoneyear, ε ε σε σε which corresponds to the frequency of the data employed in Section 4.2. The depreciation rate is estimated by the Italian National Institute of Statistics and is equal to 9 percent. The discount factor β is set to 0.975 to reproduce the data’s real annual interest rate. The elasticity of output to capital is estimated from the data using the procedure in Bachmann and Bayer (2014). This strategyresultsin θ equalto0.19. To select the remaining parameters, we calibrate the persistence using the estimates in Fiori andScoccianti (2018)anduse theestimateddispersion inexpectedfuturesales fromoursurvey data. This choice yields ρ and σ¯ equal to 0.87 and 0.031, respectively. ρ and σ are instead ε ε σε σε equalto0.64and0.03. 42

Table A.3: BenchmarkCalibration Parameter Value Target Depreciationrate δ 0.091 Data Discountfactor β 0.975 Annualrealinterestrate=2.3% Elasticityofoutputw.r.t. capital θ 0.19 Data Persistenceidiosyncraticproductivity ρ 0.87 Data ε Meanst.devidiosyncraticproductivity σ¯ 0.081 Data ε Persistencest.devidiosyncraticproductivity ρ 0.84 Data σε F.5 Data and Model Comparison The goal of this section is to take the model to the data. Can the framework in Section 6 reproduce qualitatively the asymmetry of the estimated investment responses following an increase indownsideandupsideuncertainty? ∗ Toanswerthisquestion,wecomputehowthefirm’soptimalcapitalk variesacrossdifferent uncertaintyregimesσ . Weassumethatthefirm’sproductivity(ε)isunchanged. Weassumethat ε volatility can take three regimes: (i) a baseline value, (ii) uncertainty increases driven by higher downsideuncertainty,and(iii)uncertaintyincreasesdrivenbyupsideuncertainty. Scenarios(ii) and(iii)aremean-preserving,inthattheydonotimplyachangeinthemean. As is well known in the literature, without input irreversibility, an increase in uncertainty increases investment. This result occurs because the marginal value product of capital is a convex function of the firm’s uncertainty. Thus, more significant uncertainty increases investment via the usual Jensen inequality effect: Greater uncertainty raises the marginal valuation of one additional unit of capital. Increasing the fixed cost or introducing input irreversibility reverses theneoclassicalresult: Greateruncertaintyreducescapitalaccumulation. Table A.4 shows how the optimal k varies with downside and upside uncertainty. Panel A shows that the model with input irreversibility reproduces the asymmetric response between downsideandupsideuncertainty. Afteranincreaseindownsideuncertainty,thefirmreduces k by 0.28 percent, while the response to upside uncertainty is muted. The firm reduces its capital today to avoid being stuck with too much capital if adverse states materialize. In contrast, the responsetoupsideuncertaintyismutedbecausethefirmcanalwaysreadjustitscapitalupward. 43

Table A.4: DownsideandUpsideUncertainty: OptimalCapital InputIrreversibility Baseline DownsideUncertainty UpsideUncertainty ∆ ∗ k n.a. -0.28% 0.04% Note: ∆k∗ indicates how optimal capital changes across different volatility regimesinpercentrelativetothebaseline. n.a. Notavailable F.6 Computational Details: Value Function Iteration Thevaluefunctiontosolvethefirm’sproblemdefinedinequations(A.3)and(A.4)isthebasisof ournumericalsolutionoftheeconomy. Thesolutionalgorithminvolvesrepeatedapplicationof thecontractionmappingtosolveforfirms’valuefunction. Morespecifically,thefirm’sproblem (cid:48) amounts to find the next-period value of capital k . To do so, we resort on a golden section search to allow for continuous control. We discretize the state space using a fine grid between 0.1 and 8.5 for capital k. We approximate the process for the idiosyncratic processes ε and σ ε using the procedure in Tauchen (1986) over 91 and 22 possible values. We compute the value function exactly at the grid points above and interpolate for in-between values. This procedure isimplementedusingamultidimensionalcubicsplinesprocedure,withaso-called"‘notaknot"’ condition to address the large number of degrees of freedom problem, when using splines; see Judd(1998). G GDP Effects of Aggregate Uncertainty: Downside Uncertainty Table A.5reportshowthevariationinuncertainty(σ ),thebest-casescenario(se ), agg,max−min agg,max the worst-case scenario (se ) and the average expectation (se ) about future sales fluctuagg,min agg,avg atesduringtheGlobalFinancialCrisis,thesovereigndebtcrisis,andtheCOVID-19pandemic. Table A.6reportstheestimatedeffectsofuncertaintyonGDPusingdownsideuncertainty. 44

Table A.5: CrisesandAggregateUncertainty GlobalFinancialCrisis σ se se se agg,max−min agg,max agg,min agg,avg 2008 8.52 7.22 -1.26 6.11 2009 10.52 -1.33 -11.82 -5.30 ∆ 2009−2008 2.00 -8.55 -10.56 -11.41 SovereignDebtCrisis σ se se se agg,max−min agg,max agg,min agg,avg 2011 7.86 6.54 -1.37 3.72 2012 9.55 3.32 -5.15 0.28 ∆ 2012−2011 1.69 -3.22 -3.78 -3.44 Covid-19Pandemic σ se se se agg,max−min agg,max agg,min agg,avg 2019 9.77 7.17 -2.12 3.99 2020 14.55 2.02 -11.56 -5.86 2021 13.00 12.34 -0.11 9.92 ∆ 2020−2019 4.78 -5.14 -9.44 -9.85 ∆ 2021−2020 -1.55 10.32 11.45 15.78 Note: Entriesareexpressedinpercentagepoints. σ agg,max−min denotes our measure of aggregate uncertainty. se , se , and se agg,avg agg,min agg,max denote the aggregate measure of average, minimum, and maximum expectedgrowthratesofsalesoneyearahead. ∆referstothechange betweentwoconsecutiveyears. 45

Table A.6: GDPEffectsofAggregateDownsideUncertainty GlobalFinancialCrisis 2009 2010 2011 ∆ GDP Italy -5.43 1.70 0.70 ContributionofDownsideUncertainty -1.00 -0.21 -0.23 SovereignDebtCrisis 2012 2013 2014 ∆ GDP Italy -3.02 -1.85 -0.01 ContributionofDownsideUncertainty -0.51 -0.10 -0.12 Note:Entriesareexpressedinpercentagepoints. ∆GDPreferstothegrowth rate of real GDP. The entry "Contribution of Downside Uncertainty" reports the estimated GDP contribution of the observed increase in downside uncertainty during the corresponding period purged by fluctuations inse . SeethetextfordetailsonthecalculationonGDPeffects. agg,avg,t 46