The Origins of Aggregate Fluctuations in a Credit Network Economy

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. The Origins of Aggregate Fluctuations in a Credit Network Economy Levent Altinoglu 2018-031 Please cite this paper as: Altinoglu,Levent(2018). “TheOriginsofAggregateFluctuationsinaCreditNetworkEconomy,”FinanceandEconomicsDiscussionSeries2018-031. Washington: BoardofGovernors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2018.031. 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.

The Origins of Aggregate Fluctuations in a Credit Network Economy Levent Altinoglu∗ FederalReserveBoardofGovernors Abstract I show that inter-firm lending plays an important role in business cycle fluctuations. I first build a tractable network model of the economy in which trade in intermediate goods is financed by supplier credit. In the model, a financialshocktoonefirmaffectsitsabilitytomakepaymentstoitssuppliers. Thecreditlinkagesbetweenfirmspropagatefinancialshocks,amplifyingtheir aggregate effects by about 30 percent. To calibrate the model, I construct a proxyofinter-industrycreditflowsfromfirm-andindustry-leveldata. Ithen estimate aggregate and idiosyncratic shocks to industries in the US and find thatfinancialshocksareaprominentdriverofcyclicalfluctuations,accounting fortwo-thirdsofthedropinindustrialproductionduringtheGreatRecession. Furthermore,idiosyncraticfinancialshockstoafewkeyindustriescanexplain aconsiderableportionoftheseeffects. Incontrast,productivityshockshada negligibleimpactduringtherecession. ∗Email: levent.altinoglu@gmail.com. Phone: +1617-817-6669. Address: ConstitutionAve& 20thStNW,Washington,DC20551. Website: https://sites.google.com/site/leventaltinoglu/ I am very grateful to my advisers Stefania Garetto, Simon Gilchrist, and Adam Guren for their guidance. IalsothankGiacomoCandian, MaryamFarboodi, MirkoFillbrunn, IlleninKondo, and FabioSchiantarelliforcommentswhichsubstantiallyimprovedthispaper. Allerrorsaremyown. The views expressed in this paper are solely the responsibility of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of anyoneelseassociatedwiththeFederalReserveSystem.

1. INTRODUCTION The recent financial crisis and ensuing recession have underscored the importanceofexternalfinancefortherealeconomy. Generally,firmsborrowextensively from their suppliers in the form of trade credit, or delayed payment terms provided by suppliers to their customers. Indeed, trade credit is the single most important source of short-term external financing for firms in the US, yet it has been largely absentfromthebusinesscycleliterature. Inthispaper,Ishowthattradecreditplays animportantroleinbusinesscyclefluctuations. To this end, I introduce trade credit into a network model of the economy and showthatthecreditinterlinkagesbetweenfirmscangeneratelargefluctuationsfrom small financial disturbances. I then use the framework to empirically shed light on the sources of observed fluctuations in the US. Accounting for the effects of the interlinkages between firms turns out to be crucial for identifying the sources of aggregate fluctuations in the US. In particular, I find financial shocks to be a key driver of cyclical fluctuations, particularly during the Great Recession. In contrast, productivityshocksplayonlyaminorrole. ThecreditlinkagesIconsidertaketheformoftradecreditrelationshipsbetween non-financial firms, in which a firm purchases intermediate goods on account and pays its supplier at a later date. Trade credit accounts for more than half of firms’ short-termliabilitiesandmorethanone-thirdoftheirtotalliabilitiesinmostOECD countries. In the US, trade credit was three times as large as bank loans and fifteen times as large as commercial paper outstanding on the aggregate balance sheet of non-financial corporations in 2012.1 These facts point to the presence of strong creditlinkagesbetweennon-financialfirms. An important feature of trade credit is that it leaves suppliers exposed to the financial distress of their customers.2 A number of studies - including Jacobson 1SeetheFederalReserveBoardFlowofFunds. 2 Forexample, thegovernmentbailoutoftheUSautomotiveindustryin2008wasprecipitated 1

andvonSchedvin(2015),BoissayandGropp(2012),Raddatz(2010),andKalemli- Ozcan et al. (2014) - have found that firm- and industry-level trade credit linkages areanimportantchannelthroughwhichfinancialshocksaretransmittedfromfirms to their suppliers. Yet the macroeconomic implications of trade credit have been largelyoverlookedintheliterature. IconsideraneconomysimilartothatofBigioandLa’O(2016),inwhichfirms are organized in a production network and trade intermediate goods with one another. Limited enforcement problems require firms to make cash-in-advance payments to their suppliers before production takes place. As a result, firms face cashin-advanceconstraints ontheir production. However, Iassumethat firmscan delay part of these payments by borrowing from their suppliers. To obtain this credit, a firmcancrediblypledgesomefractionofitsfuturecashflowtorepayitssuppliers. Whereas in Bigio and La’O (2016), the tightness of financial constraints is fixed exogenously,tradecreditinthisframeworkimpliesthatthetightnessofconstraints fluctuatesendogenouslywiththecash-flowofdownstreamfirms. Asaresult,credit linkagesgeneraterichnetworkeffectsbywhichfinancialshockspropagatethrough theeconomy. When one firm is hit with an adverse shock to its cash on hand, there are two channels by which other firms in the economy are affected. First is the standard input-output channel: the shocked firm cuts back on production, reducing the supply of its good to its customers.3 Second is a new credit linkage channel which tightens the financial constraints of upstream firms. That is, the shocked firm reducestheup-frontpaymentsitmakestoitssuppliers. Beingmorecash-constrained, these suppliers may be forced to cut back on their own production, and reduce the up-frontpaymentstotheirownsuppliers,etc. Inthisway,creditinterlinkagespropagate the firm-level financial shock across the economy. This additional upstream propagationturnsouttobeapowerfulmechanismbywhichthefinancialconditions byanacuteshortageofliquidity,whichcameaboutlargelyduetoextendeddelaysinpaymentfor goodsalreadydelivered. 3ThischannelhasbeenthefocusofstudiessuchasAcemogluetal. (2012)andBigioandLa’O (2016). 2

intheeconomyaretightenedendogenously.4 Next, I evaluate the quantitative relevance of the mechanism. In order to overcome the paucity of data on trade credit, I first construct a proxy of inter-industry tradecreditflowsbycombiningfirm-levelbalancesheetdatafromCompustatwith industry-level input-output data from the Bureau of Economic Analysis (BEA). I thus produce a map of the credit network of the US economy at the three-digit NAICSlevelofdetail,withwhichIcalibratethemodel. Counterfactual exercises reveal the amplification mechanism to be quantitatively significant, amplifying financial shocks by 30-40 percent. Furthermore, the aggregateimpactofanidiosyncratic(industry-level)financialshockdependsjointly ontheunderlyingstructuresofthecreditandinput-outputnetworksoftheeconomy. Based on this analysis, certain industries emerge as systemically important to the US economy, such as auto manufacturing and petroleum and coal manufacturing. Moreover, the systemic importance of an industry is closely related to the intensity of trade credit use by its largest trading partners. Thus, credit interlinkages play a significant role in exacerbating the effects of financial shocks and amplifying their aggregateeffects. Intheempiricalpartofthepaper,Iusethistheoreticalframeworktoinvestigate which shocks drive cyclical fluctuations once we account for the network effects created by credit interlinkages. Accounting for these effects turns out to be crucial for identifying the sources of business cycle fluctuations in the US. My framework is rich enough to permit an empirical exploration of the sources of these fluctuations along two separate dimensions: the importance of productivity versus financial shocks, and that of aggregate versus idiosyncratic shocks. To address these issues,Iusetwomethodologicalapproaches. My first approach involves identifying financial and productivity shocks without imposing the structure of my model on the data. To do this, I first construct 4 This upstream propagation of financial shocks is consistent with industry- and firm-level evidence on trade credit, including in Jacobson and von Schedvin (2015) and Raddatz (2010), who find that the trade credit relationships between firms transmit financial distress from firms to their suppliers. 3

quarterly measures of bank lending based on data from Call Reports collected by theFFIEC.IthenaugmentanidentifiedVARofmacroandmonetaryvariableswith this measure of bank lending, and with the excess bond premium of Gilchrist and Zakrajsek (2012), which reflects the risk-bearing capacity of the financial sector. I constructfinancialshocksaschangesinbanklendingwhicharisefromorthogonalized innovations to the excess bond premium. 5 For productivity shocks, I use the quarterly, utilization-adjusted changes in total factor productivity (TFP) estimated byFernald(2012). Feeding these estimated shocks into the model, I find that, before 2007, productivity and financial shocks played a roughly equal role in generating cyclical fluctuations, together accounting for half of observed aggregate volatility in US industrial production. However, during the Great Recession, productivity shocks had virtually no adverse effects on industrial production - in fact, they actually mitigated the downturn. On the other hand, two-thirds of the peak-to-trough drop in aggregateindustrialproductionduringtherecessioncanbeaccountedforbyfinancial shocks, with the remainder unaccounted for by either shock. By propagating financial shocks across firms and exacerbating the financial conditions in the economy,tradecreditlinkagesthusamplifiedthedropinaggregateindustrialproduction duringtherecession. Withmysecondmethodologicalapproach,Iempiricallyassesstherelativecontribution of aggregate versus idiosyncratic, industry-specific shocks in generating cyclical fluctuations. This involves estimating the model using a structural factor approach similar to that of Foerster, Sarte, and Watson (2011), using data on the output and employment growth of US industrial production industries. I first use a log-linear approximation of the model to back-out the productivity and financial shocks to each industry required for the model to match the fluctuations in the output and employment data. Then, I use standard factor methods to decompose each oftheseshocksintoanaggregatecomponentandanidiosyncraticcomponent. 5 I construct the measure of bank lending in such a way that changes in the demand for bank lending are largely netted out. Therefore, changes in my measure of bank lending mostly reflect supply-sidechanges. 4

Through variance decomposition I show that, while the idiosyncratic componentofproductivityshockscanaccountforafractionofaggregatevolatilitybefore 2007, it played virtually no role during the Great Recession. Rather, nearly threequarters of the drop in industrial production during the recession can be accounted for by aggregate financial shocks. In addition, the remainder can be accounted for byidiosyncraticfinancialshockstoafewsystemicallyimportantindustrialproduction industries - namely the oil and coal, chemical, and auto manufacturing industries. Furthermore, the credit and input-output linkages between industries played asignificantroleinpropagatingtheseindustry-levelshocksacrosstheeconomy. The broad picture which emerges from these two empirical analyses is that financial shocks have been a key driver of aggregate output dynamics in the US, particularly during the Great Recession.6 Thus, when we account for the amplification mechanism of trade credit and input-output interlinkages, financial shocks seem to displace aggregate productivity shocks as a prominent driver of the US businesscycle. RelatedLiterature This paper contributes to several strands of the literature. A growing literature examines the importance of network effects in macroeconomics, including Acemoglu et al. (2012), Shea (2002), Dupor (1999), Horvath (2000), Acemoglu et al. (2015), Baqaee (2016), and Carvalho and Gabaix (2013). These abstract away fromfinancialfrictions. TheseminalworkofAcemogluetal. (2012)showthatthe networkstructureofaneconomycangenerateaggregatefluctuationsfromidiosyncratic,firm-levelshocks,usingafrictionlessinput-outputmodeloftheeconomy. The notable work of Bigio and La’O (2016) explores the interaction between financial frictions and the input-output structure of an economy by introducing financial constraints to the Acemoglu et al. (2012) economy. However, they do not explicitly model any credit relationships between firms. As a result, the financial 6 While shocks to aggregate TFP have long been relied upon as a principal source of cyclical fluctuations, the lack of direct evidence for such shocks has raised questions about their empirical viability. 5

constraints that firms face are fixed exogenously, and do not become tighter in response to shocks. Luo (2016) embeds an input-output structure in the framework of Gertler and Karadi (2011), with a role for trade credit. However, trade credit linkages do not propagate shocks across the economy per se.7 Kiyotaki and Moore (1997) study theoretically how a shock to a firm in a credit chain can cause a cascade of defaults in a partial equilibrium framework. Gabaix (2011), Foerster et al. (2011), and Stella (2014) evaluate the contribution of idiosyncratic shocks to aggregate fluctuations, the latter two using a structural factor approach. Jermann and Quadrini(2012)evaluatetheimportanceoffinancialshocksbyexplicitlymodeling the tradeoff between debt and equity financing. Ramirez (2017) uses an inputoutputmodeltoexplaincertainempiricalfeaturesofassetprices. Therestofthepaperisorganizedasfollows. InsectionI,Iintroducethestylized modelandderivetheanalyticalresults. InsectionsII-IV,Igeneralizetheproduction networkstructure,discusstheconstructionofmyproxyforcreditflowsandcalibration, and summarize the quantitative results. In section V, I perform the empirical analyses. 2. STYLIZEDMODEL:VERTICALPRODUCTIONSTRUCTURE Inthissection,Ibuildintuitionwithasimplemodel. Thestylizednatureoftheproduction structure of the economy permits closed-form expressions for equilibrium variables. Iwilllatergeneralizeboththeproductionstructureandpreferences. Thereisonetimeperiod,consistingoftwoparts. Atthebeginningoftheperiod, contracts are signed. At the end of the period, production takes place and contracts aresettled. Therearethreetypesofagents: arepresentativehousehold,firms,anda bank. ThereareM goods,eachproducedbyacontinuumofcompetitivefirmswith constant returns-to-scale in production. We can therefore consider each good as beingproducedbyarepresentative,price-takingfirm. Eachgoodcanbeconsumed 7 Inthatpaper,creditlinkagesonlyaffecttheinterestratethatthebankchargesfirms. Assuch, allnetworkeffectsareduetoinput-outputlinkages,asinBigioandLa’O(2016). 6

Figure1: VerticalProductionChain bythehouseholdorusedintheproductionofothergoods. The representative household supplies labor competitively to firms and consumes a final consumption good. It has preferences over consumption C and labor N given by U(C,N), and a standard budget constraint, where w denotes the competitivewageearnedfromworking,andπ theprofitearnedbyfirmi. i M U(C,N)=logC−N C=wN+∑π (1) i i=1 There are M price-taking firms who each produce a different good, for now arrangedinasupplychain,whereeachfirmproducesanintermediategoodforone otherfirm. Thelastfirminthechainproducestheconsumptiongood,whichitsells to the household. Firms are indexed by their order in the supply chain, with i=M denotingtheproducerofthefinalgood. TheproductiontechnologyoffirmiisCobb-Douglasoverlaborandintermediategoods,wherex denotesfirmi’soutput,n itslaboruse,andx itsuseofgood i i i−1 i−1,z denotesfirmi’stotalfactorproductivity,η theshareoflaborinitsproduci i tion (and η = 1), and ω the share of good i−1 in firm i’s total intermediate 1 i,i−1 gooduse(equalto1fornow). Let p denotethepriceofgoods. s x =zn ηix ωi,i−1 (1−ηi ) (2) i i i i−1 Limited enforcement problems between firms create a need for ex ante liquidity to finance working capital. The household cannot force any debt repayment. Therefore,firmimustpaythefullvalueofwagebill,wn,upfronttothehousehold i beforeproductiontakesplace. Inaddition,eachfirmimustpayforsomeportionof its intermediate goods purchases p x up front to its supplier. Thus, firms are i−1 i−1 required to have some funds at the beginning of the period before any revenue is realized. Firm i can delay payment to its supplier by borrowing some amount τ from i−1 7

its supplier, representing the trade credit loan given from i−1 to i. In addition, I assume each firm has some other exogenous source of funds b, which I interpret i as a cash loan from an outside bank, for ease of exposition. The net payment that firm i−1 receives from its customer at the beginning of the period is therefore p x −τ . Firmi’scash-in-advanceconstrainttakestheform i−1 i−1 i−1 wn + p x −τ ≤ b + px −τ . (3) i i−1 i−1 i−1 i i i i (cid:124)(cid:123)(cid:122)(cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124)(cid:123)(cid:122)(cid:125) (cid:124) (cid:123)(cid:122) (cid:125) wagebill CIApaymenttosupplier bankloan CIA fromcustomer Thus,thecashthatfirmiisrequiredtohaveinordertoemployn unitsoflaborand i purchase x units of intermediate good i−1, is bounded by the amount of cash i−1 that firm i can collect at the beginning of the period. Note that trade credit appears onbothsidesoftheconstraint. Firmsfaceborrowingconstraintsonthesizeofloanstheycanobtainfromtheir suppliersandthebank. Firmicanobtaintheloanb fromthebankatthebeginning i of the period by pledging a fraction B of its total end-of-the-period revenue px, i i i andafractionα ofitsaccountsreceivableτ ,whereαε(0,1].8 i+1 b ≤B px +ατ (4) i i i i i Firms are also constrained in their ability to obtain trade credit from their suppliers. In particular, firm i can credibly pledge a fraction θ of its end-of-the-period i revenuetorepayitssupplier. τ ≤θ px (5) i−1 i i i Underlying this constraint is a contracting problem outlined in the seminal work on trade credit contracts in Burkart and Ellingsen (2004), in which a moral hazardproblembetweensupplierandproducerismanagedbypledgingtheproducer’s 8 I will later show that α parameterizes the degree of substitutability between cash and bank credit. Nevertheless, thecollateralizingaccountsreceivablesforborrowing, sometimesreferredto asfactoring,isprevalent. SeeMianandSmithJr. (1992)andOmiccioli(2005). 8

receivablesascollateralforthetradecreditloan.9 How do firms choose how much to lend to their customers and borrow from their suppliers? Recall that representative firm i is actually comprised of a continuum of competitive firms with CRS production. Perfect competition amongst these suppliers forces them to offer their customers the maximum amount of trade credit permitted by the constraint. This result holds even when these suppliers are cash-constrainedinequilibrium.10 (Ileavetheproofofthistoanonlineappendix.) While this pins down the supply of trade credit, I study firms’ demand for trade creditbelow. Wecanre-writefirmi’scash-in-advanceconstraintas wn +p x ≤ χ px (6) i i−1 i−1 i i i (cid:124) (cid:123)(cid:122) (cid:125) liquid funds where b τ τ i i−1 i χ ≡ + + 1− . (7) i px px px i i i i i i (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) debt/revenueratio cash/revenueratio Therefore, a firm’s expenditure on inputs is bounded by the amount of funds it has at the beginning of the period. The variable χ describes the tightness of firm i’s i cash-in-advanceconstraint,andwillplayakeyroleinthemechanismofthemodel. Thetightnessofafirm’scash-in-advanceconstraintiscomprisedofthefirm’sdebtto-revenue ratio and its cash-to-revenue. These describe how much of the firm’s revenue is financed by debt, and how much of its revenue is collected as a cash-in- 9 Constraints of this form have found empirical support in studies using micro-data on trade credit,suchasPetersenandRajan(1997). Thatpaperalsofindthattheassetholdingsofafirmare notasignificantpredictorofpurchasesmadeoncreditasaratiooverassets,suggestingthatphysical capitalholdingsarenotusedascollateralfortradecredit,astheymightbeforfinancinglonger-term investmentprojects. 10Theseresultsaresupportedbymicro-levelevidenceontradecredit: competitionamongstsuppliers is is often sufficiently high that they are forced to offer their customers extended payment terms,evenwhentheyarecash-constrained. See,forinstance,Barrot(2015). 9

advance payment, respectively. Notice that χ is decreasing in τi , the amount of i px i i i’s output sold on credit: the more credit that i gives its customer, the less cash it collectsatthebeginningoftheperiod. Firm i chooses its input purchases n and x , and how much trade credit to i i−1 borrow τ , to maximize its profits subject to its cash-in-advance constraint. (Rei−1 call that because of perfect competition, the firm takes its trade credit lending τ as i given.) max px −wn −p x i i i i−1 i−1 n i ,x i−1 ,τi−1 s.t. wn +px ≤χ(τ )px (8) i i i−1 i i−1 i i τ ≤θ px (9) i−1 i i i Denotebyτ∗ firmi’schoiceofhowmuchtradecredittoborrowfromitssupplier. i−1 I show in online appendix O.A1 that if firm i’s cash-in-advance constraint (8) is bindinginequilibrium,thenitborrowsthemaximumamountoftradecreditoffered by its supplier, pinning down τ∗ =θ px. For much of this paper, I consider this i−1 i i i moreinterestingcaseinwhichfirmsareconstrainedinequilibrium.11 If firms are constrained in equilibrium, we can re-write the tightness χ of a i firm’sconstraintusingfirms’bindingborrowingconstraintstoreplaceτ andb. i i p x i+1 i+1 χ = B +θ +1−(1−α)θ (10) i i i i+1 (cid:124) (cid:123)(cid:122) (cid:125) p i x i debt/revenueratio (cid:124) (cid:123)(cid:122) (cid:125) cash/revenueratio Crucially, equation (4) shows that χ is an equilibrium object - it is an endogenous i variable which depends on the firm’s forward credit linkage θ and the revenue i+1 of its customer.12 Hence, changes in the price of its customer’s good affect the tightness of firm i’s cash-in-advance constraint. 13 Here, the endogeneity of χ will i 11Neverthelessthat(9)bindsinequilibriumisnotcrucialforthequalitativeresults, andmayin factunderstatethequantitativeresults. 12 Notice that the firm’s debt-to-revenue ratio is fixed, because firms collateralize their end-ofperiodrevenueforborrowing. 13ThisakeydifferencewithBigioandLa’O(2016), inwhichthetightnessofeachfirm’scashin-advanceisanexogenousparameterbecausethereisnointer-firmlending. 10

beacriticaldeterminantofhowtheeconomyrespondstoshocks. Firm i’s optimality conditions equate the ratio of expenditure on each type of input with the ratio of their share of production. I show in online Appendix O.A1 thatfirmi’scash-in-advanceconstraint(3)bindsinequilibriumifandonlyifχ <1. i Combining the first order conditions with the cash-in-advance constraint yields the optimalityconditionsbelow.14 px px i i i i w=φη , p =φω (1−η) (11) i i i−1 i i,i−1 i n x i i−1 Here,φ ≡min{1,χ}describesfirmi’sshadowvalueoffunds.15 φ isstrictlyless i i i than one if and only if firm i’s cash-in-advance is binding in equilibrium. Equations(5)saysthat,ifbinding,thecash-in-advanceconstraintinsertsawedgeφ <1 i between the marginal cost and marginal benefit of each input, representing the distortion in the firm’s input use created by the constraint. A tighter cash-in-advance (lower χ) corresponds to a greater distortion, and lower output. Through χ , φ i i i endogenously dependsonshadowvaluefundsofdownstreamfirmsφ ,reflecting i+1 thatfirms’constraintsareinterdependentduetotradecredit. Note that there are two types of interlinkages between firms: input-output linkages, represented by input shares ω in production; and credit linkages, reprei,i−1 sented by the borrowing limits θ between firms. Each of these interlinkages will i playadifferentroleingeneratingnetworkeffectsfromshocks. 2.1. Equilibrium I close the model by imposing labor and goods market clearing conditions N = ∑ M i=1 n i andC=Y ≡x M . Definition: Anequilibriumisasetofprices{p ,w},andquantitiesx,n,τ iiεI i i iiεI that (i) maximize the representative household’s utility, subject to its budget constraint; (ii) maximize each firm’s profits subject to its cash-in-advance, bank bor- 14Sinceτ isimportantonlyinsofarasitaffectsthetightnessesoffirms’constraints, itshows i−1 upinfirmi’sfirstorderconditionsonlythroughφ. i 15Moreprecisely,theshadowvalueoffundsoffirmiisgivenby 1 −1. φi 11

rowing, and supplier borrowing constraints; and (iii) clear goods markets and the labormarket. Equilibriumaggregateoutputintheeconomyisdeterminedbyeachfirm’sproduction function and financial constraint. To see this, let Y¯ denote the aggregate output that would prevail in a frictionless input-output economy (à la Acemoglu et al. (2012)),givenbyY¯ ≡∏ M η˜η˜ izω˜ i.16 Defineaggregateliquidityintheeconomy i=1 i i asΦ¯ ≡∏ M φ ∑i j=1 η˜ j ,anaggregationofallfirm’sshadowvalueoffunds. Andsince i=1 i theproductionstructureoftheeconomyissimplyasupplychain,theshareoffirms i−1’s good in firm i’s production is ω = 1 for all i. Then an analytical exi,i−1 pressionforequilibriumaggregateoutput,derivedinonlineappendixO.A1,shows outputtobelog-linearinY¯ andtheaggregateliquidityintheeconomy. Y =Y¯Φ¯ (12) Intuitively, (12) says that equilibrium aggregate output is constrained by aggregate liquidity - the funds available to all firms to finance working capital at the beginning of the period. Note that if all firms are unconstrained, then Φ¯ = 1 and Y = Y¯. If one firm i is constrained, aggregate output depends on how its constraint affects the supply of intermediate good i for all downstream firms, given by ∑ i j=1 η˜ j .17 To summarize, firms’ financial constraints distort production in a way whichdependsontheunderlyingstructuresofthecreditandinput-outputnetworks oftheeconomy. 2.2. AggregateImpactofFirm-LevelShocks I now examine how the economy responds to firm-level financial shocks and productivity shocks. I model a financial shock to firm i by a change in B, the i fraction of firm i’s revenue that the bank will accept as collateral for the bank loan. This is a reduced-form way to capture a reduction in the supply of bank credit to 16Here, ω˜ i ≡∏M j=i+1 ω j,j−1 denotesfirmi’sshareintotalintermediategooduse, andη˜ i ≡η i ω˜ i denotesfirmi’sshareoflaborinaggregateoutput. 17Notethatthecreditnetworkoftheeconomy-i.e. theset{θ} -showsupimplicitlyin(12) i ∀iεI througheachφ. i 12

firmi,andrepresentsanexogenoustighteninginfirmi’sfinancialconstraint.18 If firm i is unconstrained in equilibrium, a marginal financial shock dB has i no effect on its production - the firm has deep pockets and can absorb the shock. However, if the firm is constrained, then it is forced to reduce production as it can no longer finance as many inputs with up front payments. In addition to this direct effect,therearetwotypesofnetworkeffectsbywhichtheshockaffectsotherfirms intheeconomy: input-outputchannelandthecreditlinkagechannel. Network Effects: Standard Input-Output Channel: Through the first channel, whichIcallthestandardinput-outputchannel,theshockpropagatesthroughinputoutput interlinkages, increasing firms’ input costs. This is the standard channel analyzedintheinput-outputliterature,includingAcemogluetal. (2012)andBigio and La’O (2016). The reduction in firm i’s output increases the price p of good i i. This acts as a supply shock to the customer downstream (firm i+1), who is now faced with a higher unit cost of its intermediate good. In response, firm i+1 cuts back on production, which causes the p to increase, etc. Thus, as a result i+1 of the shock to firm i, all firms downstream experience a supply shock to their intermediate goods, and cut back on production. This amplifies the shock because as firms reduce production, they cut back on employment which, in turn, reduces the wage and household consumption.19 In addition, the shock travels upstream as suppliers adjust their output to respond to the fall in demand for their intermediate goods. NetworkEffects: CreditLinkageChannel: Thereisalsoanew,additionalchannel of transmission - which I call the credit linkage channel - which describes how 18Inthegeneralnetworkmodelinthefollowingsection,eachfirmsellssomeportionofitsoutput directly to the household. In this setting, one could alternatively interpret the fall in B as a failed i paymentbyfinalconsumer. Ineithercase,theseareidiosyncraticshockstothefirm’sliquidfunds suchthat dχi >0,andarenotwell-representedbyachangeinitsproductivityortechnology. dBi 19 Thischannelisultimatelydrivenbytheinputspecificityineachfirm’sproductiontechnology, aseachdownstreamfirmisunabletooffsetthesupplyshockbysubstitutingawayfromusinggood iintheirproduction,andeachupstreamfirmisunabletooffsetthedemandshockbyfindingother customersforitsgood. 13

the financial constraints of upstream firms are tightened endogenously in response totheshock. Recall that when firm i cuts back on production, the price p of its good rises. i This increases the collateral value of its future cash flow, allowing it to delay paymentforalargerfractionofitspurchasefromsupplieri−1.20 Asaresult,supplier i−1’s cash/revenue ratio falls, meaning the fraction of its revenue collected as up frontpaymentfalls. Thistightensitscash-in-advanceconstraint-i.e. χ falls.21 i−1 τ i−1 χ ↓≡ B +θ + 1− (13) i−1 i−1 i−1 p x (cid:124) (cid:123)(cid:122) (cid:125) i−1 i−1 debt/revenueratio (cid:124) (cid:123)(cid:122) (cid:125) cash/revenueratio↓ Thus,withlesscashon-hand,thesupplieri−1isnowfacedwithatighterfinancial constraintitself. Thesuppliermaythereforebeforcedtoreduceproductionfurther, and thereby pass the shock to its own suppliers and customers. (This continues up the chain of firms). In this manner, the initial effect of the shock is amplified as upstreamfirmsexperiencetighterfinancialconditions. But why doesn’t firm i−1 reduce the trade credit loans it makes in order to increase its cash holdings and relax its own constraint? Recall that representative firmi−1consistsofacontinuumoffirms,andthatperfectcompetitionforcesthem to offer the maximum trade credit, even when they are themselves constrained.22 Note also that α mitigates the transmission, allowing firm i−1 to partially offset the lost up-front cash payments with a larger bank loan. Thus, α parameterizes the substitutabilitybetweencashandbankcredit. 20This is true even though the volume of trade credit τ may actually fall in response to the i−1 shock. 21 More precisely, there are three effects of the shock d B on χ . Recall from (10) that firm i i−1 i−1’scash/revenueratiodependsinverselyon pixi . First, theshockincreases p, asdiscussed pi−1xi−1 i above. Second, the fall in firm i’s output increases the ratio xi due to the decreasing returns to xi−1 x . And third, the fall in i’s demand reduces the price p of good i−1. All of these effects i−1 i−1 unambiguouslyreduceχ . i−1 22Thismechanismisinlinewithstrongempiricalevidencethatfirmsinfinancialdistressreduce theup-frontpaymentstheymaketotheirsuppliers,therebytransmittingthefinancialdistresstotheir suppliers. SeeJacobsonandvonSchedvin(2015),Raddatz(2010),andBoissayandGropp(2012). 14

Figure2: FeedbackEffect FeedbackEffectCreatedbyTransmissionChannels: Importantly,thetwotransmissionchannelsproduceafeedbackeffectwhichamplifiestheshock,asillustrated in Figure 2. Suppose that firm 2 is hit with an adverse financial shock, causing its cash-in-advance constraint to become tighter, and forcing it to cut back on production. The standard input-output channel, represented by the blue arrow, transmits theshockdownstreamintheformofahigherintermediategoodprice. Inaddition,thecreditlinkagechanneltightenstheconstraintsofupstreamfirms, as firm 2 reduces the cash-in-advance payments it makes to its supplier. With a tighter financial constraint the supplier is forced to reduce production, which feeds back to firm 2 again in the form of higher price for the intermediate good. Thus, firm2ishitnotonlywithatighterfinancialconstraint,butalsoendogenouslyhigher input costs, (which it passes on to its customer, and so on). In this manner, the two channels interact to create a feedback loop represented by the red arrows, which exacerbatestheinitialshock.23 2.3. ImpactofFirm-LevelShockonAggregateOutput In light of these mechanisms, I now derive analytical expressions for how a firm-levelfinancialshockaffectsaggregateoutput,andshowthatthecreditnetwork effects amplify the shock in a manner which depends on the structure of the credit linkages. From(12),Idecomposethechangeinaggregateoutputduetoafinancialshock tofirmiintocomponentsreflectingthestandardinput-outputchannelandthecredit 23Afirm-levelfinancialshockinmymodelthereforeisisomorphictoanaggregatefinancialshock toallfirmsinamodelwithfixedconstraints,e.g. BigioandLa’O(2016). 15

linkagechannel. dlogY M dlogφ j = ∑v¯ (14) j dB dB i j=1 i Here,theterms dlogφj capturethecreditlinkagechannel,andreflecthowthefinandB i cial shock to firm i affects the shadow value of funds of every other firm j in the network. The terms v¯ capture the standard input-output channel, and map these j j changesineachφ j intoaggregateoutput. (v¯ j ≡∑ k=1 η˜ k dependsontheshareoflaborinaggregateoutputofeachfirm.) Thisdecompositionwillallowmetoquantify theaggregateeffectsofeachchannellateron. Inaneconomywithoutthecreditlinkagechannel,suchBigioandLa’O(2016), eachφ isfixedsothat dlogφj =0forall j(cid:54)=i. Inwords,financialconstraintswould j dB i dlogY notrespondendogenouslytoashock. Therefore,(14)wouldreduceto =v¯. dB i i However, credit network effects amplify the effects of the firm-level financial shock on aggregate output. This is because dlogφj ≥0 and therefore dlogY = dB dB i i ∑ M j=1 v¯ j dl d o B gφj > v¯ i (proved in online appendix O.A2). In addition, the credit neti work effects dlogφj are weakly increasing in θ for all firms i,j, and k. Thus, the dB jk i aggregateimpactofthefinancialshockdependsonthelocationoffirmiwithinthe networks,andthestrengthofinput-outputandcreditlinkagesbetweenfirms. 2.4. ImpactofFirm-LevelProductivityShockonAggregateOutput Now consider a productivity shock to firm i, represented by a fall in i’s total factor productivity(TFP)z. Itturnsoutthat,duetoCobb-Douglasproduction,eachfirm’s i cash/revenueratio,andthereforethetightnessoftheirconstraintφ ,isindependent j oftheproductivityoffirmsz.24 Asaresult,whilethestandardinput-outputchannel i amplifiestheproductivityshockjustasinAcemogluetal. (2012),thecreditlinkage channeldoesnot. Summary of Theoretical Results: To summarize, the credit linkages between firms create a multiplier effect which amplifies the aggregate effects of firm-level 24Acemoglu, Akcigit, and Kerr (2015) argue that Cobb-Douglas is a good approximation for productionattheindustrylevel. 16

shocks. The aggregate impact of these shocks depends on structure of the credit network,i.e. howfirmsborrowfromandlendtooneanother. 3. GENERALMODEL To capture more features of the economy, I now allow for an arbitrary network structure so that each firm may trade with and borrow from or lend to any other firmintheeconomy. IassumethateachoftheMgoodscanbeconsumedbytherepresentativehousehold or used in the production of other goods. The household’s total consumption C isCobb-DouglasovertheM goods,andithasGHHpreferences.25 1 (cid:18) 1 (cid:19)1−γ M U(C,N)= C− N1+ε , C≡∏c βi (15) 1−γ 1+ε i i=1 Here, ε and γ respectively denote the Frisch and income elasticity of labor supply. Thehouseholdmaximizesitsutilitysubjecttoitsbudgetconstraint(1). Thisyields optimality conditions which equate the ratio of expenditure on each good with the ratio of their marginal utilities, and the competitive wage with the marginal rate of substitutionbetweenaggregateconsumptionandlabor. pc β i i = i , N1+ε =C (16) p c β j j j Each firm can trade with all other firms. Firm i’s production function is again Cobb-Douglasoverlaborandintermediategoods. (cid:32) m (cid:33)1−ηi x =z ηin ηi ∏x ωij (17) i i i ij j=1 25 Quantitativelysimilarresultsholdforpreferenceswhichareadditivelyseparableinaggregate consumptionCandlaborN. 17

Here, x denotes firm i’s output and x denotes firm i’s use of good j. Since ω i ij ij denotes the share of j in i’s total intermediate good use, I assume ∑ M j=1 ω ij = 1 so that each firm has constant returns to scale. The input-output structure of the economycanbesummarizedbythematrixΩofintermediategoodsharesω .26 ij   ω ω ··· ω 11 12 1M   ω ω  21 22  Ω≡  . . . ...     ω ω M1 MM Note that the production network is defined only by technology parameters. As we will see, the presence of financial frictions will distort inter-firm trade in equilibrium. Hence, Ω describes how firms would trade with each other in the absence of frictions. Each firm’s cash-in-advance constraint takes the same form as in the stylized model, with the exception that each firm has M suppliers and M customers instead of just one of each. τ denotes the trade credit loan that firm i receives from each is ofitssupplierss. M M wn + ∑(p x −τ ) ≤b + px − ∑τ (18) i s is is i i i ci s=1 c=1 (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) netCIApaymenttosuppliers netCIAreceived fromcustomers Firmifacesborrowingconstraintswitheachofitssuppliers,towhichitcanpledge fractions θ of its future cash flow to repay the loans. Each firm can also borrow is b from the bank by pledging B of its revenue and α of its accounts receivable i i ∑ M c=1 τ ci . M τ ≤θ px b ≤B px +α ∑τ (19) is is i i i i i i ci c=1 Asbefore,competitionamongstsuppliersinindustrysforcesthemtoofferthemaximum trade credit permitted by the limited enforcement problem, so that the trade 26Thisissimplyageneralizationoftheinput-outputstructureinthestylizedmodel. Inthatcase, the Ω would be given by a matrix of zeros, with one sub-diagonal of ones, reflecting the vertical productionstructureandtheconstantreturnstoscaletechnologyoffirms. 18

credit borrowing constraint always binds when industries are cash-constrained in equilibrium. The structure of the credit network between firms can be summarized bythematrixofθ ’s. ij   θ θ ··· θ 11 12 1M   θ θ  21 22  Θ≡  . . . ...     θ θ M1 MM Plugging the binding borrowing constraints into (18) yields a constraint on i’s total input purchases, where χ describes the tightness of i’s cash-in-advance coni straint. M wn +∑ p x ≤χ px (20) i s is i i i s=1 Justasinthestylizedversion,χ isananequilibriumobject,wherefirmi’scash/revenue i ratiodependsontheprices p ofitscustomer’sgoodsanditsforwardcreditlinkages c θ . ci M M p x χ = B +∑θ +1−(1−α)∑θ c c (21) i i is ci px s=1 c=1 i i (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) debt/revenueratio cash/revenueratio Firms choose labor and intermediate goods to maximize profits subject to their cash-in-advance constraint. Again, firm i’s constraint inserts a wedge φ between i themarginalcostandmarginalrevenueproductofeachinput p p i i n =φη x x =φ (1−η)ω x (22) i i i i ij i i ij i w p j where the wedge φ = min{1, χ} is determined by the firm’s shadow value of i i funds. Market clearing conditions for labor and each intermediate good are given by M M N = ∑n x =c + ∑x . (23) i i i ci i=1 c=1 19

The equilibrium conditions of this generalized model take the same form as in the stylized model, and the economy will behave in qualitatively the same way in responsetoshocksasinthestylizedmodel. Whentakingthismodeltoindustry-level data, the calibration of the model will allow industries to differ in how financially constrainedtheyare. RelationshipBetweenFirmInfluenceandSize A well-known critique of frictionless input-output models such as Acemoglu et al. (2012) is that the size of a firm, as measured by its share s of aggregate sales, is i sufficienttodeterminetheaggregateimpactofashocktosectori,andonedoesnot needtoknowanythingabouttheunderlyinginput-outputstructureoftheeconomy. BigioandLa’O(2016),however,showthatthisresultbreaksdownwhentheeconomy has financial frictions. My model shows that when credit linkages between firms propagate shocks across the economy, the aggregate impact of an idiosyncratic shock depends also on the underlying structure of the credit network of the economy,summarizedbythematrixΘ. 4. QUANTITATIVEANALYSIS Havingestablishedanalyticallythatthecreditnetworkoftheeconomycanamplify firm-levelshocks,Inowaskwhetherthismechanismisquantitativelysignificantfor theUS,andexaminemorecarefullytherolethatthestructureofthecreditnetwork plays. But before these questions can be addressed, I need disaggregated data on tradecreditflowsinordertocalibratethecreditnetworkoftheUSeconomy. 4.1. MappingtheUSCreditNetwork Calibration of the trade credit parameters θ requires data on credit flows between ij industrypairs;butdataon credit flowsatanylevelofdetailisscarce. Toovercome 20

Figure3: ConstructingProxyforTradeCreditFlows this paucity of data, I construct a proxy for trade credit flows τ between industry ij pairs using industry-level input-output data and firm-level balance sheet data. I use input-output tables from the Bureau of Economic Analysis (BEA) and Compustat NorthAmericaovertheperiod1997-2013. TheBEApublishesannualinput-output data at the three-digit NAICS level, at which there are 58 industries, excluding the financialsector. Fromthisdata,Iobserveannualtradeflowsbetweeneachindustrypair, which corresponds to p x in my model for every industry pair {i, j}. Comj ij pustat collects balance-sheet information annually from all publicly-listed firms in the US. The available data includes each firm’s total accounts payable, accounts receivable,costofgoodssold,andsalesineachyearofthesample. My strategy for constructing the proxy is illustrated in Figure 3. From the payables and receivables data, I observe how much, on average, firms in each industry have borrowed from all of their suppliers collectively, and lent to all of their customerscollectively.27 However,Idonotobservehowanindustry’sstockoftrade credit and debt breaks down across each of its suppliers and customers. Therefore, I combine the input-output data with the payables and receivables data to approximate the fraction of sales from firms in industry j to firms in industry i made on credit,onaverage,yieldingaproxyfortradecreditflowsτ betweeneachindustry ij pair. Many studies have found that large firms on average use trade credit less intensivelythantheirsmallercounterparts,presumablybecausetheyhavegreateraccess to other forms of financing.28 Since the publicly-traded firms in the Compustat database tend to be large, my use of this data likely biases downward the extent of trade credit linkages between firms, and therefore potentially underestimates their quantitativeimportanceinamplifyingbusinesscycles. 27The vast majority of accounts receivables and payables of US corporations consists of trade credit. 28See,forinstance,PetersenandRajan(1997). 21

4.2. Calibration With the proxy for trade credit flows at hand, I calibrate the general model to match US data. I calibrate technology parameters η and ω to match the BEA i ij input-output tables of the median year in my sample, 2005. The firm optimality conditionsandCRStechnologyimply wn i +∑ M j=1 p j x ij φ = . (24) i px i i The right-hand side of (12) is directly observable from the BEA’s Direct Requirementstable. Looking through the lens of the model, the observed input-output tables reflect bothtechnologyparametersanddistortionscreatedbythefinancialconstraints. My calibration strategy respects this feature. In particular, I calibrate technology parametersusingfirmi’soptimalityconditionsforeachinputandmycalibratedφ’s. i wn p x i j ij η = ω = (25) i ij φ px (1−η)φ px i i i i i i i Againtheratios wn i and p j x ij aredirectlyobservablefromtheDirectRequirements px px i i i i tablesforeveryindustryiand j. Icalibratetheparametersθ ,representingthecreditlinkagesbetweenindustries ij j and i, to match my proxy of inter-industry trade credit flows τˆ using industry i’s ij bindingborrowingconstraint. τˆ ij θ = (26) ij px i i Industry i’s total revenue px is directly observable from the Uses by Commodity i i tables. (RecallthatIusetheinput-outputtablesforyear2005). TocalibrateB,theparametersreflectingtheagencyproblembetweenfirmiand i thebank,recallthedefinitionofφ givenby(11),whichdependsonthetechnology i parameters (calibrated as described above) and the tightness χ of each industry’s i cash-in-advance,where 22

M M p x χ =B +∑θ +1−(1−α)∑θ c c . (27) i i is ci px s=1 c=1 i i The total revenue of each industry px is observable from the Uses by Commodity i i tables, and φ and θ for all s were calibrated as described above. I therefore use i is (13) and (11) to back out B for each industry. Thus, the calibration of B ensures i i thatφ <1,sothatallindustriesareconstrainedtosomedegreeinequilibrium.29 i I follow the standard literature and set ε = 1 and γ = 2, which represent the Frisch and income elasticity, respectively. I set α =0.2 in my baseline calibration, butcheckthesensitivityofthequantitativeresultstovaryingα.30 5. AQUANTITATIVEEXPLORATIONOFTHEMODEL With my model calibrated to match the US economy, I am in a position to examine the quantitative response of the economy to industry-level and aggregate productivityandfinancialshocks. In this more general setting, the presence of higher-order linkages means there arenowadditionalspillovereffects. Toillustrate,considerFigure4. Thepetroleum and coal manufacturing industry and the utilities industry are linked by a common supplier, the oil and gas extraction industry. Suppose that firms in petroleum and coalmanufacturingexperiencetighterfinancialconstraints,forcingsometoreduce production, and raising the price of petroleum. This corresponds to the standard input-output channel represented by the blue arrow.31 In the absence of the credit linkage channel of transmission, firms in the utilities industry will remain largely 23

Figure4: TransmissionMechanismintheGeneralModel unaffectedbytheshock. However, the shock causes petroleum and coal manufacturers to reduce the up front payments they make to their oil and gas suppliers. With tighter financial constraints, these suppliers reduce production, raising the price of oil and gas. As a result utilities firms pass thesehigher input costs downstream in the form of higher energyprices. Theseadditionalcreditnetworkeffectsfurtheramplifytheeffectsof theshock. Howlargearethesecreditnetworkeffectslikelytobe? Toanswerthis,Ihitthe USeconomywithanaggregatefinancialshock,andindustry-levelfinancialshocks, andmeasuretheresponseinaggregateoutputtoalog-linearapproximation. 5.1. ResponsetoanAggregateFinancialShock Suppose that the economy is hit with a one percent aggregate financial shock: each industry i’s cash-in-advance constraint is tightened by one percent. 32 Under my conservative, baseline calibration, I find that US GDP falls by 2.92 percent - a 29Recallthatforacreditsupplyshocktohaveanyeffectonindustryi, anecessaryconditionis thattheindustrybeconstrainedinequilibrium. 30 Recallthatα isthefractionofreceivablesthatindustriescancollateralizetoborrowfromthe bank. Omiccioli(2005)findsthatthemedianItalianfirminasamplecollateralizes20percentofits accountsreceivableforbankborrowing. 31In addition, the suppliers in the oil and gas industry will face lower demand from their customers,andreduceproductionaccordingly. 32 MorespecificiallydB =0.01forallindustriesi. Thiscanbeinterpretedasaonepercentfall i intheaggregatesupplyofcredit. 24

Figure5: Notes:ThischartshowsthetenmostsystemicallyimportantUSindustriesbasedonthecounterfactualdropinGDPinresponsetoa1percentindustry-levelfinancial shock.Thecontributionofcreditnetworkeffectsiscomputednumerically.Thisexerciseisdoneexcludingfinancialindustries. large drop. Shutting off the credit linkage channel, I find that GDP falls by only 2.28 percent in response to the same aggregate shock. Thus, the credit network effectsamplifythefallinGDPbyabout30percent. Thisisaconservativeestimate of the quantitative relevance of the mechanism, given that the calibration uses data ononlylarge,publicly-tradedfirmswhousetradecreditlessintensivelythanother. Table3intheappendixreportsthesensitivityoftheseresultstothespecificationof α =0.2,theparametercontrollingthesubstitutabilityofcashandbankcredit. 5.2. ResponsetoIndustry-LevelFinancialShocks Next, I ask which industries are likely to be systemically important to the US economy, in light of these network effects. I measure the systemic importance of industry i by the how much GDP falls in response to a 1 percent financial shock to industry i. This industry-specific shock should be interpreted as an exogenous tighteningofthefinancialconstraintsofatleastsomefirmsintheindustry. Figure 5 shows a bar graph of the ten most systemically important industries in theUS,basedonthisexercise. Foreachindustryi,thebluebarsshowtheelasticity of GDP with respect to B, or the percentage change in GDP in response to a 1 i 25

percentfinancialshocktoindustryi. The model implies that an industry-level financial shock can have a strong impactonUSGDP.Forexample,althoughthetechnicalservicesindustryaccountsfor only 0.069 percent of US GDP, a one percent financial shock this industry causes a fall in GDP of 0.19 percent - a multiplier of 2.75. The red bars indicate the magnitude of the credit network effects of the shock.33 These credit network effects contribute substantially to this amplification, accounting for between one-fifth to half of the fall in GDP in response to an industry-level shock, depending on the industry. 5.3. MappingtheModeltotheData In order to map the model to the data, I extend the static model to be a repeated cross-section. Let X , N , B , and z denote the M-by-1 vectors of output growth, t t t t employment growth, financial shocks, and productivity for each industry respectively, in quarter t. The log-linearized model yields closed-form expressions for how the output and employment of each industry respond to financial and productivityshocks. X =G B +H z N =G B +H z (28) t X t X t t N t N t The M-by-M matrices G and H (G and H ) map industry-level financial and X X N N productivity shocks, respectively, into output growth (employment growth), and capture the effects of input-output and credit interlinkages in propagating shocks acrossindustries. Theelementsofthesematricesdependonlyonthemodelparameters,andthereforetaketheirvaluesfrommycalibration. I construct the observed, quarterly cyclical fluctuations in the output Xˆ and t employment Nˆ of US industrial production industries using data from the Federal t 33 ThisiscomputedbysubtractingthedropinGDPthatoccurswithcreditlinkagechannelshut off, from the total drop in GDP. I shut off the credit linkage channel by imposing that financial constraintsdonotrespondendogenouslytofinancialshocks,i.e. dlogφj =0forall j(cid:54)=i. dBi 26

Reserve Board’s Industrial Production Indexes, which includes data on the output growth of these industries, and the Bureau of Labor Statistics’ Quarterly Census of Employment and Wages, from which I observe the number of workers employed byeachoftheseindustries. Atthethree-digitNAICSlevelthereare23suchindustries.34 Foreachdataset,Itake1997Q1through2013Q4asmysampleperiod,and seasonally-adjustandde-trendeachseries. Intheempiricalanalysistofollow,Iuse this data and the expressions (28) to decompose observed cyclical fluctuations into variouscomponents. 6. EMPIRICALANALYSES Intheempiricalpartofthepaper,Iusemytheoreticalframeworktoinvestigate which shocks drive observed cyclical fluctuations in the US, once we account for the network effects created by credit and input-output linkages between industries. The framework is rich enough to permit an empirical exploration of the sources of these fluctuations along two separate dimensions: the importance of productivity versusfinancialshocks,andthatofaggregateversusidiosyncraticshocks. To this end, I use two methodological approaches to identifying shocks. In the first,Iidentifyshockswithoutimposingthestructureofmymodelonthedata. This permits a cleaner identification of financial and productivity shocks, and estimates a residual component of fluctuations which are not explained by either of these shocks. In the second approach, I identify shocks using a structural estimation of themodel. Whilethisattributesallfluctuationstofinancialandproductivityshocks only,itallowsforadecompositionbetweenaggregateversusindustry-levelshocks. 6.1. FirstMethod: EstimatingShockswithouttheModel My first approach involves identifying financial and productivity shocks without imposing the structure of my model on the data - the identifying assumptions are 34Hoursworkedisnotdirectlyavailableatthislevelofindustrydetailandthisfrequency. 27

completely independent of the model. An added advantage of this method is that it permitstheestimationofaresidualcomponentofobservedfluctuations-acomponent which is not explained by either shock. However, the shocks estimated using thismethodareassumedtobecommontoallindustries. 6.1.1. Estimating financial shocks To identify credit supply shocks to the US economy,IestimateanidentifiedVARusingasimilarapproachasGilchristandZakrajsek(2011). Todothisrequiresfirstconstructingameasureofbank-intermediated businesslending. I construct a measure of aggregate business lending by US financial intermediariesusingquarterlyCallReportdatacollectedbytheFFIEC.Tocapturelendingto the business sector, I use commercial and industrial loans outstanding and unused loancommitments-acyclically-sensitivecomponentofbanklending.35 Ithusconstruct a measure called the business lending capacity of the financial sector, as the sum of unused commitments and commercial and industrial loans outstanding in eachquarter.36 To empirically identify credit supply shocks, I augment a standard VAR of macroeconomicandfinancialvariableswiththemeasureofbusinesslendingcapacity, and the excess bond premium of Gilchrist and Zakrajsek (2012) - a component ofcorporatecreditspreadsdesignedtocapturechangesintherisk-bearingcapacity of financial intermediaries.37 The endogenous variables included in the VAR, ordered recursively, are: (i) the log-difference of real business fixed investment; (ii) the log-difference of real GDP; (iii) inflation as measured by the log-difference of 35Gilchrist and Zakrajsek (2011) show that the contraction in unused loan commitments was concomitantwithonsetofthefinancialcrisisin2007,whilebusinessloansoutstandingcontracted onlywithalagofaboutfourquarters. 36Changesinbusinesslendingcapacitymostlyreflectsupply-sidechanges. Toseewhy,consider the following example. Suppose that a business draws down an existing line of credit it has with itsbank. Thisisrecordedasafallinunusedcommitments, butreflectsanincreaseindemandfor creditratherthanacontractioninthesupplyofcredit. However,theloanisnowrecordedasanonbalancesheetcommercialorindustrialloan. Therefore, thefallinunusedcommitmentsisexactly offsetbytheincreaseincommercialandindustrialloansoutstanding,leavingbanklendingcapacity unchanged. Sothismeasureofbusinesslendingcapacityislargelyunresponsivetofirmsdrawing downtheirlinesofcredit. 37IthankSimonGilchristforkindlysharingtheexcessbondpremiumdata. 28

the GDP price deflator; (iv) the quarterly average of the excess bond premium; (v) the log difference business lending capacity (vi) the quarterly (value-weighted) excess stock market return from CRSP; (vii) the ten-year (nominal) Treasury yield; and (viii) the effective (nominal) federal funds rate. The identifying assumption impliedbythisorderingisthatstockprices,therisk-freerate,andbanklendingcan react contemporaneously to shocks to the excess bond premium, while real economic activity and inflation respond with a lag. I estimate the VAR using two lags ofeachendogenousvariable. To map the orthogonalized innovations in the excess bond premium into the financial shocks B˜ of my model, I make use of the impulse response function of t business lending capacity, and construct financial shocks as changes in the supply of bank lending which arise due to orthogonalized innovations in the risk-bearing capacityofthefinancialsector. Figure6plotsthetimeseriesofthisshock. To allow for credit supply shocks to affect industries differentially depending on their dependence on external finance, I also load the financial shocks onto each industrybasedonameasureofthetheindustry’sexternalfinancedependence,constructed according to Rajan and Zingales (1998).38However, the results reported hereafterareforfinancialshocksBˆ whichloadequallyontoallindustries. t 6.1.2. Estimating productivity shocks The Federal Reserve Bank of San Francisco produces a quarterly series on TFP for the US business sector, adjusted for variations in factor utilization, according to Fernald (2012). As such, this series is readilymappedintomymodelasanaggregateproductivityshockz˜ . Figure6plots t time series for this productivity shock. Let zˆ ≡ z˜(cid:126)1 denote the M-by-1 vector of t t theseshocks. 6.1.3. Decomposing Observed Fluctuations in Industrial Production With the estimatedshocksathand,Iuselog-linearizedexpression(28)todecomposeobserved 38Inthismanner, Iobtainatime-varying, industry-specificfinancialshockB˜ whichcanbefed it intothemodel.Althoughtheyvariesacrossindustriesinanygivenquarter,theseshockstoeachindustryareperfectlycorrelatedacrosstime,andsoshouldnotbeinterpretedasidiosyncraticshocks. 29

Figure6: 10 5 0 −5 −10 2002 2003 2004 2005 2006 2007 2008 2009 2010 egnahC tnecreP Externally Estimated Financial and Productivity Shocks Estimated credit supply shock Utilization−adjusted TFP Notes: Thisfigureshowstheseriesofquarter-to-quartergrowthinutilization-adjustedTFPmeasureofFernald(2012)andthecreditsupplyshocks,estimatedas changesinthebusinesslendingcapacityofthefinancialsectorwhichareduetoorthogonalizedinnovationstotheexcessbondpremium. Financialshockswere estimatedusinganidentifiedVAR..TFPdatawasobtainedfromtheSanFranciscoFeddatabase. cyclical fluctuations in industrial production into components coming from the financialshocks,productivityshocks,andaresidual. Xˆ =G Bˆ +H zˆ +ε (29) t X t X t t Theresidualε isthecomponentofthesefluctuationswhichisunexplainedbyeither t of these shocks. I then feed these shocks into the model and perform a variance decompositionofaggregateindustrialproduction. The variance decomposition of output before 2007 is given in Table 1. In the period2001-2007,productivityandfinancialshocksplayedaroughlyequalrolein generatingcyclicalfluctuations,togetheraccountingforhalfofobservedaggregate volatility in US industrial production. The remaining half is unaccounted for by eithertypeofshock. However, the story is different for the Great Recession. Figure 7 plots the time series of aggregate industrial production during the Great Recession, as well as a simulationforeachofitscomponents.39 Thesecounterfactualseriesareconstructed by feeding each of the estimated components through the model one at a time, and thus represents how aggregate industrial production would have evolved in the 39The time series for observed aggregate IP is constructed from the cyclical component of IP growth. Itisconstructedasanaggregateindexoftheobservedindustry-levelgrowthrates. 30

Table1: VarianceDecompositionofIP:2001Q4:2007Q3 Shareof AggregateVolatility ProductivityShocks 0.205 FinancialShocks 0.279 Residual 0.516 Notes: Thistablereportstheresultsofthevariancedecompositionofthequarterlytimeseriesofaggregateindustrialproductionoverthepre-recessionaryperiod 2001Q4-2007Q3. Aggregatevolatilityiscomputedasthesamplevarianceofobservedaggregateindustrialproduction. Financialshockswereestimatedusing anidentifiedVAR,andcapturequarterlycreditsupplyshockstotheproductivesector. ProductivityshocksareestimatedbyFernald(2012)asquarter-to-quarter, utilization-adjustedchangesinTFPintheUS,obtainedfromtheSanFranciscoFeddatabase.Theresidualisthecomponentofaggregateindustrialproductionwhich isunexplainedaftertheseshocksarefedthroughthelog-linearizedmodel. absenceofothershocks,beginningin2007Q3. Duringtherecession,productivityshockshadvirtuallynoadverseeffectsonindustrialproduction-infact,theyactuallymitigated thedownturn. Rather,financial shocksarethemainculprit,accountingfortwo-thirdsofthepeak-to-troughdropin aggregateindustrialproductionduringtherecession. Theremainingone-thirdisnot accounted for by either shock. Furthermore, the credit network of these industries played a quantitatively significant role during this period, amplifying the effects of the financial shocks by about 15% (i.e. adding 3.98 percentage points to the peak-to-troughdropinthefinancialcomponentofaggregateindustrialproduction). 6.2. SecondMethod: StructuralFactorAnalysis With my second methodological approach, I empirically assess the relative contribution of aggregate versus idiosyncratic shocks in generating cyclical fluctuations. Thisinvolvesestimatingthemodelusingastructuralfactorapproachsimilartothat of Foerster et al. (2011)40, using data on the output and employment growth of US IP industries. The procedure involves two steps. I first use a log-linear approximationofthemodeltoback-outtheproductivityandfinancialshockstoeachindustry requiredforthemodeltomatchthefluctuationsintheoutputandemploymentdata. Then, I use dynamic factor methods to decompose each of these shocks into an 40Foersteretal. (2011)allowonlyforproductivityshocksindrivingobservedfluctuations. 31

Figure7: 130 120 110 100 90 80 70 60 2007Q42008Q12008Q22008Q32008Q42009Q12009Q22009Q3 leveL xednI Aggregate IP and Its Components Observed Aggregate IP Financial Component Productivity Component Residual Notes:Thisfigureshowsthetimeseriesofaggregateindustrialproductionanditscomponents.Observedaggregateindustrialproductionisanindexconstructedfrom thede-trended,seasonally-adjustedindustry-levelquarter-to-quartergrowthratesintheoutputofthe23industrialproductionindustriesatthethree-digitNAICSlevel, obtainedfromFRBIPIndexes.Eachoftheotherseriesdepictcounterfactualindexesconstructedfromtherespectivecomponentsoftheobservedseries,beginningin 2007Q3,andrepresenthowaggregateIPwouldhaveevolvedintheabsenceofothershocks.FinancialshockswereestimatedusinganidentifiedVARProductivity shocksareestimatedbyFernald(2012)asquarter-to-quarter,utilization-adjustedchangesinTFPintheUS,obtainedfromtheSanFranciscoFeddatabase. aggregatecomponentandanidiosyncratic,industry-specificcomponent.41 6.2.1. Step1: StructuralEstimationofShocks I first use a log-linear approximation of the model to back-out the productivity and financial shocks to each industry required for the model to match the fluctuations in the output and employment data. To do this, recall that from equations (28) I have an exactly identified system of equations. Given the observations Xˆ and Nˆ , t t I then invert the system to back-out industry-level each quarter over my sample period 1997 Q1 to 2013 Q4. Denote by Bˇ and zˇ the M-by-1 vectors of financial t t and productivity shocks estimated with this procedure in quarter t. And let Q ≡ H −G G−1H . X X N N Bˇ =G−1(cid:0) Nˆ −H zˇ (cid:1) zˇ =Q−1Xˆ −Q−1G G−1Nˆ (30) t N t N t t t X N t 41AsinFoersteretal. (2011),theselattershocksarespecifictoeachindustry,butidiosyncraticin thesensethattheyareuncorrelatedacrossindustries. 32

Figure8: 30 20 10 0 −10 −20 −30 −40 1998 2000 2002 2004 2006 2008 2010 2012 egnahC tnecreP Auto Manufacturing: Financial and Productivity Shocks Financial Shock Productivity Shock Notes:Thisfigureshowsthequarterlytimeseriesoftheproductivityandfinancialshockstotheautomanufacturingindustryoverthesampleperiod.Financialshocks arecapturedbypercentchangesinparametersBiinthemodel,andthusrepresentexogenoustightneninginthecash-in-advanceconstraintofanindustry.Productivity shocksarechangesinTFP.Theseshockswereestimatedusingthelog-linearizedmodel,andquarterlydataontheemploymentandoutputgrowthofIPindustries, obtainfromtheBLSQuarterlyCensusofEmploymentandWagesandtheFRBIPIndexes,respectively. Thus, I construct industry-level shocks as the observed fluctuations, filtered for the the network effects created by interlinkages. The model is able to separately identify these shocks because each type of shock has quantitatively differential effects onanindustry’soutputandemployment.42 Figure8showsthetimeseriesoftheestimatedfinancialandproductivityshocks whichhittheUSautomanufacturingindustryeachquarteroverthesampleperiod. Between 2007 and 2009, the output and employment of industrial production industries took a sharp drop for a number of quarters. As illustrated in the figure, this contraction shows up in the model as an acute tightening in the financial constraintsofthesefirms,reachinguptoa25percentdeclineinasinglequarter.43 6.2.2. Step2: DynamicFactorAnalysis Next, I use factor methods to decompose the financial and productivity shocks, Bˇ t andzˇ ,intoaggregateandidiosyncraticcomponents. t 42Namely, productivity shocks affect an industry’s output relative to its employment through Cobb-Douglas production functions. On the other hand, financial shocks do not affect production functions,buttightensthecash-in-advanceconstraints. 43Thesefeaturesbroadlyholdacrossmostindustriesinindustrialproduction. 33

Bˇ =Λ FB+u , zˇ =Λ Fz+v (31) t B t t t z t t Here, FB and Fz are scalars denoting the common factors affecting the output and t t employment growth of each industry at quarter t, and are assumed to follow an AR(1) process; the residual components, u and v , are the idiosyncratic shocks. t t Hence, I estimate two dynamic factor models; one for the financial shocks Bˇ and t onefortheproductivityshockszˇ .44 t Togaugetheexternalvalidityofthestructuralfactoranalysis,Icomparetheaggregatefinancialshockstotheexcessbondpremium. Thelargeaggregatefinancial shocks estimated by the structural factor analysis is broadly reflective of the severe creditcrunchthatoccurredduringthisperiod. 6.2.3. DecomposingObservedFluctuationsinIndustrialProduction To perform a variance decomposition of observed industrial production from 1997 Q1 to 2013 Q4, I follow the procedure described in Appendix A3. For the full sample period, aggregate volatility is about 0.19%.45 The results are summarized inTable2. Before the Great Recession, aggregate volatility was driven primarily by aggregate financial shocks and idiosyncratic productivity shocks; aggregate financial shocks account for nearly a half of aggregate volatility. Nevertheless, idiosyncratic productivityshocksaccountforaquarterofaggregatevolatility. Furthermore, the credit network of industrial production industries amplified theseshocks,accountingfornearlyone-fifthofobservedaggregatevolatility. 44 I use standard methods to estimate the model. To predict the factors, I use both a one-step predictionmethodandKalmansmoother. TheKalmansmootheryieldsfactorswhichexplainmore of the data. Since it utilizes more information in predicting the factors, I use this method as my baseline. AllsubsequentreportedresultsusedthefactorspredictedusingaKalmansmoother. 45This is roughly in line with the findings of Foerster et al. (2011). If I compute growth rates andaggregatevolatilityusingthesamescalingconventionsasthey,Ifindaggregatevolatilitytobe about9.35comparedtotheir8.8for1972-1983and3.6for1984-2007. ThehighervolatilitythatI getcomesfromincludingtheGreatRecessioninmysampleperiod. 34

Table2: Pre-RecessionCompositionofAgg. Vol.: 1997Q1:2006Q4 FractionofAgg.Vol. Explained ProductivityShocks 0.365 Agg.Component 0.133 Idios.Component 0.232 FinancialShocks 0.635 Agg.Component 0.45 Idios.Component 0.185 Notes:Thistablereportstheresultsofthevariancedecompositionofthequarterlytimeseriesofaggregateindustrialproductionovertheperiod1997Q1-2006Q4. Aggregatevolatilityiscomputedasthesamplevarianceofobservedaggregateindustrialproduction.Shockstoindustrialproductionindustrieswereestimatedusing thestructuralfactoranalysisoftheseindustries’quarterlyoutputandemploymentgrowth,obtainedfromtheBLSQuarterlyCensusofEmploymentandWagesand theFRBIPIndexes,respectively.Theaggregateandidiosycnraticcomponentswereestimatedbydynamicfactoranalysisoftheindustry-levelfinancialshocks,where thecommoncomponentsareassumedtofollowanAR(1)process. Aggregate financial shocks were the primary driver of the Great Recession. I perform an accounting exercise to evaluate how much of the peak-to-trough drop in aggregate industrial production over 2007Q4: 2009Q2 can be explained by each typeofshock. Ifindthatchangesinproductivitydidnotcontributetothedeclinein aggregate industrial production during the recession. In contrast, 73 percent of the dropinaggregateindustrialproductionisduetoanaggregatefinancialshock,anda sizablefractionofthetheremaindercanbeaccountedforbyidiosyncraticfinancial shockstothethreemostsystemicallyimportantindustries Figure 9 depicts the relationship between industry-level financial shocks and an industry’s contribution to aggregate output, for industrial production industries duringtheGreatRecession. Largefinancialshockstoafewsystemicallyimportantindustriescanexplainthe bulk of the decline in aggregate industrial production during the Great Recession. In fact, idiosyncratic shocks to the oil and coal products manufacturing, chemical products manufacturing, and auto manufacturing industries account for about 9 percent of the decline (or one-third of the decline unaccounted for by aggregate shocks), despite comprising only about 25 percent of aggregate industrial production. This suggests that idiosyncratic financial shocks to a few systemically importantindustriesplayedaquantitativelysignificantroleduringtheGreatRecession. In contrast, both the aggregate and idiosyncratic components of productivity shocks were slightly positive during this period on average. As such, changes in 35

Figure9: 0.25 0.2 0.15 0.1 0.05 0 −0.05 −0.1 −0.35 −0.3 −0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 Mean Financial Shock to Industry PI etagerggA ni llaF ot noitubirtnoC Financial Shocks and IP During the Great Recession C E o l m e p c u t t r e o r n i & cs Manuf. P & M e a t C n r o u o a f l l . eum C M h a e n m u i f c . al Utilities Auto Manuf. Metal Products Manuf. Printing Mining Notes: Thisfigureshowsascatterplotofindustrialproductionindustriesbythemeanquarterlyfinancialshocktoeachindustryduringtherecessionaryperiod 2007Q4-2009Q2,andbyeachindustry’scontributiontothepeak-to-troughfallinaggregateindustrialproductionobservedoverthisperiod. Eachindustry’s spotisweightedbyameasureoftheindustry’ssystemicimportancetotheUSeconomy,computedusingnumericalsimulations.Thefigureincludesaleast-squares line.Shockswereestimatedusingastructuralfactorapproachandquarterlydataontheemploymentandoutputgrowthofindustrialproductionindustries,obtained fromtheBLSQuarterlyCensusofEmploymentandWagesandtheFRBIndustrialProductionIndexes,respectively.Theshocksconsistofboththeaggregateand idiosyncraticcomponents.Anindustry’scontributiontothepeak-to-troughdropinaggregateindustrialproductioniscomputedbysimulatingthepathofanindex ofeachindsutry-levelcomponentofaggregateindustrialproduction(i.e.howaggregateindustrialproductionwouldevolvewithshockstoexactlyoneindustry)and computingthepeak-to-troughchangebetween2007Q4and2009Q2. productivitydidnotcontributetothedeclineinaggregateindustrialproductionduringtherecession. 6.3. Take-AwaysfromtheTwoEmpiricalAnalyses The broad picture which emerges from these empirical analyses is that financial shockshavebeenakeydriverofaggregateoutputdynamicsintheUS,particularly during the Great Recession. While much of the previous literature has relied on shocks to aggregate TFP drive the business cycle, the dearth of direct evidence for such shocks has raised concerns about their empirical viability. I have argued that the credit and input-output interlinkages of firms can create a powerful mechanism by which a shock to one firm’s financial constraint propagates across the economy. The confluence of my empirical results suggest that once we account for these interlinkages, financial shocks seem to displace aggregate productivity shocks as a prominentdriveroftheUSbusinesscycle. 36

7. CONCLUSION In this paper, I showed that inter-firm lending plays an important role in business cycle fluctuations. First, I introduced supplier credit into a network model of the economy and show that trade credit interlinkages can create a powerful amplification mechanism. To evaluate the model quantitatively, I constructed a proxy of the credit linkages between US industries by combining firm-level balance sheet data andindustry-levelinput-outputdata. Finally,IusedthemodeltoinvestigatewhichshocksdrivetheUSbusinesscycle when we account for the linkages between industries. To do so, I identified shocks both structurally and without the use of my model. Feeding these shocks though the model showed financial shocks to be a key driver of aggregate fluctuations, particularly during the Great Recession, and productivity shocks to play only a minor role. Thus, accounting for the role that credit and input-output interlinkages play helps to capture the empirical importance of financial shocks in US business cyclefluctuations. Appendix A1. DemandforTradeCredit Firmi’sproblemistochooseitsinputpurchasesandtradecreditborrowingtomaximize its profits, subject to its cash-in-advance constraint. Recall that competition amongst suppliers forces each firm to offer the maximum trade credit allowed by theborrowingconstraint. Therefore,firmitakesτ asgiven. i max px −wn −p x i i i i−1 i−1 n i ,x i−1 ,τi−1 s.t. wn +px ≤χ(τ )px i i i−1 i i−1 i i τ ≤θ px i−1 i i i Notice that in general, there is a tradeoff to taking more trade credit (i.e. to increasingτ ). Ahigherτ relaxesfirmi’scash-in-advanceconstraint,allowing i−1 i−1 it to purchase more inputs ceteris paribus. But a higher τ may also tighten its i−1 37

supplier’s cash in advance constraint, causing the price of its intermediate good p toincrease. Letτ∗ denotetheoptimalamountoftradecreditborrowing. We i−1 i−1 can solve for optimal τ∗ separately from n and x . In particular, there are three i−1 i i−1 relevantcases. Case 1) If both i and i−1 are unconstrained in equilibrium, then there is no tradeoff to firm i taking marginally more τ . So there is a continuum of τ i−1 i−1 betweenwhichfirmiisindifferent: thesetofallτ suchthatbothfirmiandfirm i−1 i−1 are unconstrained in equilibrium, i.e. χ,χ <1. Without loss of generality, i i−1 wecantakeτ∗ =minτ | χ,χ <1. i−1 i−1 i i−1 Case 2) If i is unconstrained in equilibrium, but i−1 is constrained in equilibrium, then the tradeoff mentioned above applies. The optimal τ will be the i−1 minimum such that i’s cash-in-advance constraint is not binding. Any τ >τ∗ i−1 i−1 will further constrain supplier i−1, and therefore i will face a higher input price p . And any τ <τ∗ will mean that firm i will be constrained in equilibrium i−1 i−1 i−1 andwillhavetoreduceproduction. Case3) Iffirmiisconstrainedinequilibrium,τ∗ isthemaximumallowableby i−1 thetradecreditborrowingconstraint: τ∗ =θ px. Toseethis,firstrecallthatfirm i−1 i i i i actually consists of a continuum of identical firms with CRS production. Being constrained, each individual firm has an incentive to take the maximum amount of trade credit. They do not internalize the fact that, when all firms do this, they may increasetheprice p ofinputsthattheyface.46 Thus,inanyequilibriuminwhich i−1 firm i is constrained (i.e. its cash-in-advance constraint is binding), the trade credit borrowingconstraintsbindandτ =θ px. i−1 i i i Given its choice of τ∗ , firm i then chooses its inputs to solve the problem i−1 outlinedinthetext. max px −wn −p x i i i i−1 i−1 n,x i i−1 s.t. wn +px ≤χ(τ ∗ )px . i i i−1 i i−1 i i 46Therefore,evenifthereisaτ˜ <θ px suchthatindustry-wideprofitswillbehigher(taking i−1 i i i intoaccounttradeoffoflowerinputprice p ),thesefirmsareunabletocoordinateonthatτ˜ . i−1 i−1 38

Table3: α P(αˆ ≤α) %ChangeinGDP CreditNetworkAmplification 0 0.18 4.04% 77.2% 0.1 0.32 3.26% 43.0% 0.2 0.5 2.92% 28.1% 0.4 0.66 2.59% 13.6% 0.5 0.75 2.50% 9.6% 1 0.97 2.28% 0% Notes: Thistablereportstheresultsofthesensitivityanalysis. Recallthatαisthefractionofaccountsreceivablethatbankscancollateralizetoborrowfromthe bank,andcontrolsthesubstitutabilityofcashandbankcreditforfirmsinthemodel.Thefirstcolumnindicatesthevalueofαused.Thesecondcolumnyieldsthe fractionofItalianfirmswhichcollateralizeslessthanαoftheirreceivablestoborrowfrombanks,asestimatedbyOmiccioli(2005).Thethirdcolumnliststhetotal percentagechangeinGDPinresponsetoa1percentfinancialshocktoallUSindustries.Thefourthcolumnlistsbyhowmuchthecreditnetworkeffectsamplifythe dropinGDPinresponsetotheshock.Theboldrowindicatesthebaselinecalibration. A2. SensitivityAnalysis In the quantitative analysis, I computed the change in GDP to a counterfactual one percet aggregate financial shock. Table 3 reports these results for different values ofα. Whilethemultipliereffectofthecreditnetworkindeedfallsasα approaches1, creditnetworkeffectsarequantitativelysignificantforreasonablevaluesofα. A3. StructuralFactorAnalysis: AggregateVolatility AssumetheshocksB andz in(28)arecomposedofanaggregateandidiosyncratic t t components. B =Λ FB+u FB =γ FB +ι B (32) t B t t t B t−1 t z =Λ Fz+v Fz =γ Fz +ι z (33) t z t t t z t−1 t Then letting Σ denote the variance-covariance matrix of X , and s¯a vector of in- XX t dustrysharesofaggregateoutput,aggregatevolatility(ofoutput)isapproximately σ2 ≡s¯(cid:48)Σ s¯=s¯(cid:48)G Σ G(cid:48) s¯+s¯(cid:48)H Σ H(cid:48) s¯. (34) XX X BB X X zz X For Online Publication Only 39

O.A1. SolutionforSytlizedModel I solve in closed form for aggregate output in the stylized (vertical) economy. I proceedrecursively,beginningwiththefinalfirminthechain,firmM. FirmM Recall that firm M collects none of its sales from the household up front (does not givethehouseholdanytradecredit,τ =0). Thenitsproblemistochooseitsinput M purchases, loan from the bank, and the trade credit loan from M−1, to maximize its profits, subject to its cash-in-advance, supplier borrowing, and bank borrowing constraints. max p x −wn −p x M M M M−1 M−1 n M ,x M−1 ,b M ,τM−1 s.t. wn +p x ≤b +τ +p x −τ M M−1 M−1 M M−1 M M M b ≤B p x +ατ M M M M M τ p x ≤θ p x M−1 M−1 M−1 M M M Wecancombinetheconstraintstore-writetheproblem. max p x −wn −p x M M M M−1 M−1 n M ,x M−1 ,b M ,τM−1 s.t. wn +p x ≤χ p x M M−1 M−1 M M M where χ = τ M ∗ −1 +B . Here, τ∗ denotes firm M’s choice of trade credit bor- M p x M M−1 M M rowing, based on the arguments given in Appendix A1. (Notice that when firm M isconstrained, χ =θ +B ). M M,M−1 M IffirmMisunconstrainedinequilibrium,thentheoptimalityconditionsequate themarginalcostofeachtypeofinputwiththemarginalrevenue. p x p x M M M M w=η p =(1−η ) (35) M M−1 M n x M M−1 FirmM’sexpenditureininputsisthen wn +p x =(η +(1−η ))p x . (36) M M−1 M−1 M M M M 40

Therefore,firmMisthenunconstrainedinequilibriumifandonlyifitsexpenditure atitsunconstrainedoptimumislessthanitsliquidityatthisoptimum. p x <χ p x i.e. χ >1 (37) M M M M M M If firm M is constrained in equilibrium, then its binding cash-in-advance pins down its level of output. The only choice left to make is how much labor to hire n versushowmuchintermediategoodsx topurchase,givenitslevelofoutput M M−1 x . Becauseχ isindependentofM’schoiceofn andx ,theproblemofmax- M M M M−1 imizing profits subject to the binding cash-in-advance is equivalent to minimizing its expenditure n +x subject to producing x . Thus, it solves the following M M−1 M cost-minimizationproblem. min wn +p x n M ,x M−1 M M−1 M−1 s.t.x =z n ηMx (1−ηM ) M M M M−1 Then firm M’s optimality condition equates the ratio of expenditure on each input withtheratioofeachinput’sshareinproduction. wn η M M = (38) p x (1−η ) M−1 M−1 M Usingthis,wecanrewriteM’sbindingcash-in-advanceas p x M M w=η χ . M M n M Together, the constrained and unconstrained cases imply that we can write the optimalityconditionas p x M M w=φ η . (39) M M n M φ ≡min{1, χ } represents the distortion in firm M’s optimal labor usage due to M M its cash-in-advance. Financial frictions introduce wedge between firm’s marginal benefit and cost of production. The wedge between these two objects is increasing in the tightness χ of M’s constraint, and decreasing in the returns-to-scale of firm M M’sproductionfunction. GivenfirmM’ssolution,wecancontinuerecursivelyand solvefirmM-1’sproblem. 41

Equilibrium Eachotherfirm’sproblemissymmetric. Continuingrecursively,Iobtaintheclosedpx form solution for each firm. To summarize, I have, for each firm i w = φη i i. i i n i MarketclearingconditionsaregivenbyC=Y ≡x M andN =∑ M i=1 n i Given the firm optimality conditions, we can write each n as a function of i aggregateoutputx M (cid:32) (cid:33)(cid:32) (cid:33) M M−1 wn = p x ∏φ ∏ ω (1−η ) η (40) i M M j j+1,j j i j=i j=i Thehousehold’spreferencesandoptimalityconditionsimply V(cid:48)(N) w= =x (41) U(cid:48)(x ) M M Let good M be the numeraire. Combining (40) with (41) yields a closed-form expressionforeachfirm’slaboruse. M n =η ∏ ω (1−η )φ (42) i i j,j−1 j j j=i+ Byrecursivelypluggingintheproductionfunctionsintooneanother,wecanobtain aggregateoutputasafunctionofthelaboruseofeachfirm,whereδ M−i ≡∏ i j − = 1 0 (1− η ). M−j (cid:32) (cid:33)(cid:32) (cid:33) M−1 M−1 Y = ∏ z δM−i ∏ n ηM−iδM−i (43) M−i M−i i=0 i=0 Thencombining(42)and(43)yieldsaclosed-formexpressionforaggregateoutput (12). O.A2. ProofofAmplification Fromthedefinitionsof χ andφ,wehave i i (cid:26) (cid:18) (cid:19)(cid:27) 1 1 φ =min 1, B +θ −θ . i i i,i−1 i+1,i r φ ω (1−η ) i i+1 i+1,i i+1 42

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