The origins of aggregate fluctuations in a credit network economy

The Origins of Aggregate Fluctuations in a Credit Network Economy

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The Origins of Aggregate Fluctuations in a Credit Network Economy Levent Altinoglu PII: DOI: Reference:

S0304-3932(18)30561-0 https://doi.org/10.1016/j.jmoneco.2020.01.007 MONEC 3215

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Journal of Monetary Economics

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22 September 2018 20 December 2019 22 January 2020

Please cite this article as: Levent Altinoglu, The Origins of Aggregate Fluctuations in a Credit Network Economy, Journal of Monetary Economics (2020), doi: https://doi.org/10.1016/j.jmoneco.2020.01.007

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Highlights

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• Build a network model in which trade credit linkages amplify financial distress.

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• Impact of a firm-level financial shock depends on the structure of credit network between

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firms.

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• Construct a proxy of inter-industry credit flows from firm- and industry-level data.

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• Estimate aggregate and sectoral financial and productivity shocks to US industries.

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• Credit network of US amplified financial shocks during the Great Recession.

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The Origins of Aggregate Fluctuations in a Credit Network Economy

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Levent Altinoglu∗ Federal Reserve Board of Governors

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Abstract Inter-firm lending plays an important role in business cycle fluctuations. I build a network model of the economy in which trade in intermediate goods is financed by supplier credit. A financial shock to one firm affects its ability to make payments to its suppliers. The credit linkages between firms propagate financial shocks, amplifying their aggregate effects. To calibrate the model, I construct a proxy of inter-industry credit flows from firm- and industry-level data. I estimate aggregate and idiosyncratic shocks to US industries and find that financial shocks are a prominent driver of cyclical fluctuations, particularly during the Great Recession. Keywords: Credit Network, Input-Output Economy, Trade Credit, Financial Frictions, Business Cycles JEL classification: C67, E32, G10

∗

I am very grateful to my advisers Stefania Garetto, Simon Gilchrist, and Adam Guren for their guidance. I also thank Giacomo Candian, Bora Durdu, Maryam Farboodi, Mirko Fillbrunn, Illenin Kondo, Carlos Madeira, Fabio Schiantarelli, and seminar participants at Boston University, the Federal Reserve Board, the Central Bank of Chile, Columbia University, Georgetown University, University of Miami, University of South Carolina, University of Tokyo, and the Bank of Japan for comments which substantially improved this paper. All errors are my own. The author acknowledges financial support from the Institute for New Economic Thinking. 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 anyone else associated with the Federal Reserve System. Email: [email protected]. Phone: +1 202-721-4503. Address: Constitution Ave & 20th St NW, Washington, DC 20551. Website: https://sites.google.com/site/leventaltinoglu/

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1. Introduction

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The recent financial crisis and ensuing recession have underscored the importance of external

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finance for the real economy. Generally, firms borrow extensively from their suppliers in the form

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of trade credit, or delayed payment terms provided by suppliers to their customers. Indeed, trade

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credit is the single most important source of short-term external financing for firms in the US, yet

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it has been largely absent from the business cycle literature. In this paper, I show that trade credit

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plays an important role in business cycle fluctuations.

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To this end, I introduce trade credit into a network model of the economy and show that

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the credit interlinkages between firms can generate large fluctuations from small financial distur-

30

bances. I then use the framework to empirically shed light on the sources of observed fluctuations

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in the US. Accounting for the effects of the interlinkages between firms turns out to be crucial for

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identifying the sources of aggregate fluctuations in the US. In particular, I find financial shocks

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to be a key driver of cyclical fluctuations, particularly during the Great Recession. In contrast,

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productivity shocks play only a minor role.

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The credit linkages I consider take the form of trade credit relationships between non-financial

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firms, in which a firm purchases intermediate goods on account and pays its supplier at a later date.

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Trade credit accounts for more than half of firms’ short-term liabilities and more than one-third of

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their total liabilities in most OECD countries. In the US, trade credit was three times as large as

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bank loans and fifteen times as large as commercial paper outstanding on the aggregate balance

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sheet of non-financial corporations in 2012.1 These facts point to the presence of strong credit

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linkages between non-financial firms.

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An important feature of trade credit is that it leaves suppliers exposed to the financial distress

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of their customers.2 A number of studies - including Jacobson and von Schedvin (2015), Boissay 1

See the Federal Reserve Board Flow of Funds. 2

1

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and Gropp (2012), Raddatz (2010), and Kalemli-Ozcan et al. (2013) - have found that firm- and

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industry-level trade credit linkages are an important channel through which financial shocks are

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transmitted upstream from firms to their suppliers. Yet the macroeconomic implications of trade

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credit have been largely overlooked in the literature.

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I consider an economy similar to that of Bigio and La’O (2019), in which firms are organized

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in a production network and trade intermediate goods with one another. A moral hazard problem

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requires firms to make cash-in-advance payments to their suppliers before production takes place.

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As a result, firms face cash-in-advance constraints on their production. However, I assume that

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firms can delay part of these payments by borrowing from their suppliers. In particular, the moral

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hazard problem places a borrowing constraint on the amount of trade credit a firm can obtain from

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its suppliers, which depends on the firm’s total cash flow. I show how the market structure and the

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contracting environment pin down the trade credit contracts which emerge in equilibrium.

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Whereas in Bigio and La’O (2019) the tightness of financial constraints is fixed exogenously,

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trade credit in this framework implies that the tightness of constraints fluctuates endogenously with

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the cash-flow of downstream firms. As a result, credit linkages generate rich network effects by

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which financial shocks propagate through the economy.

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When one firm is hit with an adverse shock to its cash on hand, there are two channels by which

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other firms in the economy are affected. First is the standard input-output channel: the shocked firm

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cuts back on production, reducing the supply of its good to its customers.3 Second is a new credit

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linkage channel which tightens the financial constraints of upstream firms. That is, the shocked

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firm reduces the up-front payments it makes to its suppliers. Being more cash-constrained, these

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suppliers may be forced to cut back on their own production, and reduce the up-front payments to

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their own suppliers, etc. In this way, credit interlinkages propagate the firm-level financial shock

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across the economy. This additional upstream propagation turns out to be a powerful mechanism For example, the government bailout of the US automotive industry in 2008 was precipitated by an acute shortage of liquidity, which came about largely due to extended delays in payment for goods already delivered. 3 This

channel has been the focus of studies such as Acemoglu et al. (2012) and Bigio and La’O (2019).

2

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by which the financial conditions in the economy are tightened endogenously.

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This mechanism is consistent with empirical evidence that, in response to tighter financial

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conditions, firms use trade credit more intensively, as their suppliers extend more trade credit to

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their distressed customers either through financing a higher proportion of purchased goods, or by

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extending the agreed maturity of the loans. It is also consistent with the evidence that trade credit

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linkages transmit financial distress upstream from firms to their suppliers.4 In online appendix

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O.A4, I present a brief review of the empirical evidence on the role of trade credit in the business

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cycle.

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I show analytically that the aggregate impact of a firm-level shock depends on a new measure

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of network centrality, which I call the firm’s financial influence. Mathematically, a firm’s financial

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influence is a linear transformation of a measure of the firm’s centrality in the production network,

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called its production influence vector, where the transformation matrix is determined by the un-

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derlying structure of the economy’s credit network. Intuitively, the aggregate impact of a shock

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depends on how the structure of the credit network distorts the propagation of shocks through the

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production network. While the literature thus far has centered around the production influence vec-

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tor as the key measure of network centrality, I show that this is insufficient in any setting with trade

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credit or financial relationships: a financial shock has highest impact when it hits firms who are not

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necessarily the most central in the production network, but those who have suppliers who are si-

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multaneously important suppliers of intermediate goods to the rest of the economy, and prominent

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creditors to their customers.

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Next, I evaluate the quantitative relevance of the mechanism. In order to overcome the paucity

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of data on trade credit, I first construct a proxy of inter-industry trade credit flows by combining

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firm-level balance sheet data from Compustat with industry-level input-output data from the Bu4

For a discussion of why suppliers extend more trade credit to distressed customers, see Cunat (2007), Calomiris et al. (1995), and Nilsen (2002). For evidence for the upstream transmission of shocks via trade credit, see Jacobson and von Schedvin (2015), Boissay and Gropp (2012), Raddatz (2010), Jorion and Zhang (2009), and Carbo-Valverde et al. (2016).

3

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reau of Economic Analysis (BEA). I thus produce a map of the credit network of the US economy

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at the three-digit NAICS level of detail, with which I calibrate the model.

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Counterfactual exercises reveal the amplification mechanism to be quantitatively significant,

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amplifying financial shocks by 30-40 percent. Furthermore, the aggregate impact of an idiosyn-

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cratic (industry-level) financial shock depends jointly on the underlying structures of the credit

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and input-output networks of the economy. Based on this analysis, certain industries emerge as

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systemically important to the US economy, such as auto manufacturing and petroleum and coal

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manufacturing. Moreover, the systemic importance of an industry is closely related to the intensity

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of trade credit use by its largest trading partners. Thus, credit interlinkages play a significant role

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in exacerbating the effects of financial shocks and amplifying their aggregate effects.

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In the empirical part of the paper, I use this theoretical framework to investigate which shocks

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drive cyclical fluctuations once we account for the network effects created by credit interlinkages.

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Accounting for these effects turns out to be crucial for identifying the sources of business cycle

104

fluctuations in the US. My framework is rich enough to permit an empirical exploration of the

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sources of these fluctuations along two separate dimensions: the importance of productivity versus

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financial shocks, and that of aggregate versus idiosyncratic shocks. To address these issues, I use

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two methodological approaches.

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My first approach involves identifying financial and productivity shocks without imposing the

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structure of my model on the data. To do this, I first construct quarterly measures of bank lending

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based on data from Call Reports collected by the FFIEC. I then augment an identified VAR of

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macro and monetary variables with this measure of bank lending, and with the excess bond pre-

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mium of Gilchrist and Zakrajsek (2012), which reflects the risk-bearing capacity of the financial

113

sector. I construct financial shocks as changes in bank lending which arise from orthogonalized

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innovations to the excess bond premium.

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For productivity shocks, I use the quarterly, utilization-

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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-side changes.

4

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adjusted changes in total factor productivity (TFP) estimated by Fernald (2012).

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Feeding these estimated shocks into the model, I find that, before 2007, productivity and fi-

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nancial shocks played a roughly equal role in generating cyclical fluctuations, together accounting

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for half of observed aggregate volatility in US industrial production. However, during the Great

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Recession, productivity shocks had virtually no adverse effects on industrial production - in fact,

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they actually mitigated the downturn. On the other hand, two-thirds of the peak-to-trough drop in

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aggregate industrial production during the recession can be accounted for by financial shocks, with

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the remainder unaccounted for by either shock. By propagating financial shocks across firms and

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exacerbating the financial conditions in the economy, trade credit linkages thus amplified the drop

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in aggregate industrial production during the recession.

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With my second methodological approach, I empirically assess the relative contribution of

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aggregate versus idiosyncratic, industry-specific shocks in generating cyclical fluctuations. This

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involves estimating the model using a structural factor approach similar to that of Foerster et al.

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(2011), using data on the output and employment growth of US industrial production industries. I

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first use a log-linear approximation of the model to back-out the productivity and financial shocks

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to each industry required for the model to match the fluctuations in the output and employment

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data. Then, I use standard factor methods to decompose each of these shocks into an aggregate

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component and an idiosyncratic component.

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Through variance decomposition I show that, while the idiosyncratic component of produc-

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tivity shocks can account for a fraction of aggregate volatility before 2007, it played virtually no

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role during the Great Recession. Rather, nearly three-quarters of the drop in industrial produc-

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tion during the recession can be accounted for by aggregate financial shocks. In addition, the

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remainder can be accounted for by idiosyncratic financial shocks to a few systemically important

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industrial production industries - namely the oil and coal, chemical, and auto manufacturing in-

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dustries. Furthermore, the credit and input-output linkages between industries played a significant

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role in propagating these industry-level shocks across the economy.

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The broad picture which emerges from these two empirical analyses is that financial shocks

5

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have been a key driver of aggregate output dynamics in the US, particularly during the Great Reces-

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sion. Thus, when we account for the amplification mechanism of trade credit and input-output in-

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terlinkages, financial shocks seem to displace aggregate productivity shocks as a prominent driver

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of the US business cycle.?

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Related literature

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This paper contributes to several strands of the literature. A growing literature examines the

148

importance of network effects in macroeconomics, beginning with the seminal work of Long and

149

Plosser (1983), and continuing with Dupor (1999), Horvath (2000), Shea (2002), Acemoglu et al.

150

(2012), Acemoglu et al. (2015), Carvalho and Gabaix (2013), Jones (2013), Baqaee (2018), and

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Liu (2017). These abstract away from financial frictions. The seminal work of Acemoglu et al.

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(2012) show that the network structure of an economy can generate aggregate fluctuations from

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idiosyncratic, firm-level shocks, using a frictionless input-output model of the economy.

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The notable work of Bigio and La’O (2019) explores the interaction between financial frictions

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and the input-output structure of an economy by introducing financial constraints into a version of

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the Acemoglu et al. (2012) economy. However, they do not explicitly model any credit relation-

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ships between firms. As a result, the financial constraints that firms face are fixed exogenously, and

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do not become tighter in response to shocks. Reischer (2019) studies a network model in which

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both the price and quantity of trade credit are endogenous. She shows that endogenous price ef-

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fects transmit shocks downstream as well as upstream, and uses the model to quanitify both the

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amplifying and stabilizing roles of trade credit. Luo (2016) embeds an input-output structure in

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the framework of Gertler and Karadi (2011), with a role for trade credit. However, trade credit

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linkages do not propagate shocks across the economy per se.6 Kiyotaki and Moore (1997) study

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theoretically how a shock to a firm in a credit chain can cause a cascade of defaults in a partial

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equilibrium framework. Gabaix (2011), Foerster et al. (2011), Stella (2015), and Atalay (2017) 6

In that paper, credit linkages only affect the interest rate that the bank charges firms. As such, all network effects are due to input-output linkages, as in Bigio and La’O (2019).

6

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evaluate the contribution of idiosyncratic shocks to aggregate fluctuations. Jermann and Quadrini

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(2012) evaluate the importance of financial shocks by explicitly modeling the tradeoff between

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debt and equity financing. Ramirez (2017) uses an input-output model to explain certain empirical

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features of asset prices.

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2. Stylized Model: Vertical Production Structure

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In this section, I build intuition with a simple model. The stylized nature of the production

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structure of the economy permits closed-form expressions for certain equilibrium variables. I will

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later generalize both the production structure and preferences.

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There is one time period, consisting of two parts. At the beginning of the period, contracts are

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signed. At the end of the period, production takes place and contracts are settled. There are three

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types of agents: a representative household, firms, and a bank. There are M goods, each produced

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by a continuum of competitive firms with constant returns-to-scale in production. We can therefore

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consider each good as being produced by a representative, price-taking firm. I discuss the market

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structure in further detail below. Each good can be consumed by the household or used in the

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production of other goods.

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The representative household supplies labor competitively to firms and consumes a final con-

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sumption good. It has preferences over consumption C and labor N given by U(C, N), and a

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standard budget constraint, where w denotes the competitive wage earned from working, and πi

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the profit earned by firm i. M

U(C, N) = logC − N 186

C = wN + ∑ πi

(1)

i=1

The household’s optimality condition is given by w = C.

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There are M price-taking firms who each produce a different good, for now arranged in a supply

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chain, where each firm produces an intermediate good for one other firm, as shown in Figure 1.

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The last firm in the chain produces the consumption good, which it sells to the household. Firms

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are indexed by their order in the supply chain, with i = M denoting the producer of the final

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consumption good.

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The production technology of firm i is Cobb-Douglas over labor and intermediate goods, where

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xi denotes firm i’s output, ni its labor use, and xi−1 its use of good i − 1, zi denotes firm i’s total

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factor productivity, ηi the share of labor in its production, and ωi,i−1 the share of good i − 1 in firm

195

i’s total intermediate good use. ω

i,i−1 xi = zi nηi i xi−1

(1−ηi )

(2)

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Note that since in this supply chain economy each firm has one supplier and one customer, ωi,i−1 =

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1 for all i, and η1 = 1. Let ps denote the price of good s, where the final consumption good M is

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the numeraire and I normalize pM = 1.

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Limited enforcement problems between firms create a need for ex ante liquidity to finance

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working capital. The household cannot force any debt repayment. Therefore, firm i must pay the

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full value of wage bill, wni , up front to the household before production takes place. In addition,

202

each firm i must pay for some portion of its intermediate goods purchases pi−1 xi−1 up front to its

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supplier. Thus, firms are required to have some funds at the beginning of the period before any

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revenue is realized.

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Firm i can delay payment to its supplier by borrowing some amount τi−1 from its supplier,

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where τi−1 represents the trade credit loan given from i − 1 to i. In addition, I assume each firm has

207

some other exogenous source of funds bi , which I interpret as a cash loan from an outside bank,

208

for ease of exposition. The net payment that firm i − 1 receives from its customer at the beginning

209

of the period is therefore pi−1 xi−1 − τi−1 . Firm i’s cash-in-advance constraint takes the form wn + pi−1 xi−1 − τi−1 ≤ bi + |{z} |{z}i {z } |

wage bill

CIA payment to supplier

bank loan

p xi − τi | i {z }

.

(3)

CIA f rom customer

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Thus, the cash that firm i is required to have in order to employ ni units of labor and purchase xi−1

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units of intermediate good i − 1, is bounded by the amount of cash that firm i can collect at the 8

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beginning of the period. Note that trade credit appears on both sides of the constraint. Contracting environment

Firms face borrowing constraints on the size of loans they can

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obtain from their suppliers. Namely, the trade credit that firm i can obtain from its supplier i − 1 is

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bounded from above by a fraction θi of its end-of-period revenue.

τi−1 ≤ θi pi xi

(4)

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Underlying this borrowing constraint is a moral hazard problem described in detail in online ap-

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pendix O.A2 in which firms have access to a diversion technology specific to each intermediate

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good. (Although this resembles a collateral constraint, suppliers cannot recover any of their cus-

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tomer’s funds in the event of default.)7

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Firms have similar diversion technologies for funds lent by banks. I assume that there are two

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types of banks, one of whom observes each firm’s total revenue, and another who observes only a

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firm’s accounts receivables τi .8 The severity of the moral hazard problem between firm i and each

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type of bank is parameterized respectively by Bi and α ε (0, 1]. Therefore, the total bank borrowing

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firm i can receive is subject to the constraint

bi ≤ Bi pi xi + ατi .

(5)

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The purpose of introducing two types of banks is only to incorporate two features into the model in

226

a tractable way: the role of Bi is to allow for some exogenous shock to tightness of firm i’s finan-

227

cial constraint, while α simply introduces in a reduced-form way some degree of substitutability 7

The parameter θi reflects the threshold above which the private benefit to diversion exceeds the cost. Alternatively, one could consider a collateral constraint in which firm i’s accounts receivables τi serves as collateral for the trade credit loan, so that the constraint would be of the form τi−1 ≤ θi τi . It is easy to show that this would yield qualitatively similar results, as trade credit linkages would still transmit shocks upstream from firms to their suppliers. 8

The indexing of bank loans to accounts receivables, sometimes referred to as factoring, is prevalent in the data. See Mian and Smith Jr (1992) and Omiccioli (2005), and Ahn et al. (2011).

9

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between cash and bank credit, whereby a firm can partially offset a fall in the up-front payment

229

it collects from its customers by borrowing more from a bank. This will dampen the quantitative

230

importance of trade credit in transmitting shocks, to be discussed in section 2.2.9

231

Therefore, the variable bi represents the external funds available to firm i other than trade credit

232

or customer payments, such bank credit, and in equilibrium will be increasing in a firm’s revenue

233

through the borrowing constraint (5). The parameter Bi controls the extent to which the firm’s

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revenue affects its external funds bi .

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Market structure and equilibrium contracts

How do firms choose how much to lend to

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their customers and borrow from their suppliers? Here, I briefly characterize firms’ supply of and

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demand for trade credit and the trade credit contracts which emerge in equilibrium. The online

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appendix O.A3 explains derives these results in detail.

239

Recall that each representative firm or industry i is actually comprised of a continuum of com-

240

petitive firms with constant returns to scale production. These atomistic suppliers compete with

241

one another along two margins by posting contracts at the beginning of the period which specify

242

both a price of output and the trade credit to offer. Atomistic firms in industry i choose which con-

243

tracts to accept, and given these contracts, how many inputs to buy and borrow from each supplier.

244

In online appendix O.A3, I setup the game between suppliers and characterize the contracts which

245

emerge in the Nash equilibrium. In order to compete with other firms in the industry, each firm is

246

forced to offer its customers in the downstream industry both the maximium trade credit allowed

247

by the borrowing constraint, and the lowest price feasible given its budget constraint. This result

248

holds even when these suppliers are cash-constrained in equilibrium, as free entry ensures that the

249

suppliers’ surplus is minimized.10 Therefore, the equilibrium amount of trade credit offered by 9

As discussed in the contracting problem outlined in appendix OA.2., the firm’s revenue or receivables do not serve as collateral for bank loans, since banks cannot recover any of the firm’s assets in the event of default. Therefore, there is no issue of double-pledging of revenue to different creditors. 10

These results are supported by micro-level evidence on trade credit: competition amongst suppliers is often sufficiently high that they are forced to offer their customers extended payment terms, even when they are cash-constrained. See, for instance, Barrot (2015).

10

250

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suppliers is pinned down by the customers’ borrowing constraint. Representative firm’s problem

We can re-write firm i’s cash-in-advance constraint as

wni + pi−1 xi−1 ≤ 252

where

χi ≡

τi−1 bi + + pi xi pi xi | {z }

debt/revenue ratio

χpx | i{zi }i

(6)

liquid f unds

τi 1− px | {z i }i

.

(7)

cash/revenue ratio

253

Therefore, a firm’s expenditure on inputs is bounded by the amount of funds it has at the beginning

254

of the period. The variable χi describes the tightness of firm i’s cash-in-advance constraint, and

255

will play a key role in the mechanism of the model. The tightness of a firm’s cash-in-advance

256

constraint is comprised of the firm’s debt-to-revenue ratio and its cash-to-revenue. These describe

257

how much of the firm’s revenue is financed by debt, and how much of its revenue is collected as a

258

cash-in-advance payment, respectively. Notice that χi is decreasing in

259

sold on credit: the more credit that i gives its customer, the less cash it collects at the beginning of

260

the period.

τi pi xi , the amount of i’s output

261

Firm i chooses its input purchases ni and xi−1 , and how much trade credit to borrow τi−1 ,

262

to maximize its profits subject to its cash-in-advance constraint. Because competition pins down

263

prices pi and trade credit supply τi , the firm takes these as given.

max

ni , xi−1 , τi−1

pi xi − wni − pi−1 xi−1

s.t. wni + pi−1 xi−1 ≤ χi (τi−1 )pi xi

11

(8)

τi−1 ≤ θi pi xi

(9)

264

Recall that contracts are such that firms borrow the maximum trade credit in equilibrium, implying

265

the borrowing constraints (9) are always binding. I will show in section 2.2 on the credit linkage

266

channel this is not crucial for the qualitative results.

267

Notice that a firm’s production is constrained by how much liquid funds it has at the beginning

268

of the period, given by the tightness of its cash-in-advance constraint (8). Henceforth, I refer to a

269

firm whose cash-in-advance constraint is binding in equilibrium as a “constrained” firm. If firms

270

are constrained in equilibrium, we can re-write the tightness χi of a firm’s constraint using firms’

271

binding borrowing constraints to replace τi and bi .

χi =

+ 1 − (1 − α)θi+1 {z debt/revenue ratio | B +θ | i {z }i

pi+1 xi+1 pi xi }

(10)

cash/revenue ratio

272

Crucially, equation (10) shows that χi is an equilibrium object - it is an endogenous variable which

273

depends on the firm’s forward credit linkage θi+1 and the revenue of its customer. Hence, changes

274

in the price of its customer’s good affect the tightness of firm i’s cash-in-advance constraint.

275

Here, the endogeneity of χi will be a critical determinant of how the economy responds to shocks.

276

Firm i’s optimality conditions equate the ratio of expenditure on each type of input with the

277

ratio of their share of production. I show in section 2.1 that firm i’s cash-in-advance constraint (3)

278

binds in equilibrium if and only if χi < 1. Combining the first order conditions with the cash-in-

279

advance constraint yields the optimality conditions below.

w = φ i ηi

pi xi , ni

pi−1 = φi ωi,i−1 (1 − ηi )

pi xi xi−1

11

(11)

11

This a key difference with Bigio and La’O (2019), in which the tightness of each firm’s cash-in-advance is an exogenous parameter because there is no inter-firm lending.

12

280

Here, φi ≡ min {1, χi } describes firm i’s shadow value of funds. φi is strictly less than one if and

281

only if firm i’s cash-in-advance is binding in equilibrium. Equations (11) says that, if binding, the

282

cash-in-advance constraint inserts a wedge φi < 1 between the marginal cost and marginal benefit

283

of each input, representing the distortion in the firm’s input use created by the constraint. A tighter

284

cash-in-advance (lower χi ) corresponds to a greater distortion, and lower output. Through χi , φi

285

endogenously depends on the shadow value funds of downstream firms φi+1 , reflecting that firms’

286

constraints are interdependent due to trade credit.

287

Note that there are two types of interlinkages between firms: input-output linkages, represented

288

by input shares ωi,i−1 in production; and credit linkages, represented by the borrowing limits θi

289

between firms. Each of these interlinkages will play a different role in generating network effects

290

from shocks.

291

2.1. Equilibrium

292

I close the model by imposing labor and goods market clearing conditions N = ∑M i=1 ni and

293

C = Y ≡ xM . An equilibrium is a set of prices {pi iεI , w }, and quantities xi , ni , τi iεI that (i) maximize

294

the representative household’s utility, subject to its budget constraint; (ii) maximize each firm’s

295

profits subject to its cash-in-advance, bank borrowing, and supplier borrowing constraints; and

296

(iii) clear goods markets and the labor market.

297

Solving for the equilibrium

The concavity in the household utility function pins down

298

the equilibrium uniquely. This concavity means that, in general equilibrium, prices respond to

299

firm production decisions. (This can be seen from equation (14) below). That prices enter cash-

300

in-advance constraint means that firm production decisions affect the ’tightness’ of the constraint.

301

Solving for the equilibrium amounts to solving this fixed point problem. I now outline the closed-

302

form solution for the equilibrium.

303

Let the final consumption good be the numeraire, and normalize its price to pM = 1. First

304

note from equation (10) that, since the final firm in the supply chain collects all revenue from the

305

household up front, the tightness of its cash-in advance constraint is given by χM = BM + θM , 13

306

which pins down its equilibrium wedge φM = min{1, χM }. Then, using the expression (10) and

307

the optimality conditions (11) for each firm’s intermediate goods, we can recursively solve for the

308

tightness χi of each firm’s constraint and wedges φi = min{1, χi }, where χi = Bi + θi + 1 − (1 − α)θi+1

1 . φi+1 (1 − ηi+1 )

(12)

309

Here, I have imposed that the share ωi,i−1 of good i − 1 in the intermediate good use of firm i is

310

unity, reflecting the vertical structure of the supply chain.

311

312

We can also recursively use the optimality conditions for labor (11) to obtain an expression for each firm’s labor expenditure as function of final output. For each firm i

wni = xM φi ηi

M

∏

j=i+1

φ j ω j, j−1 1 − η j




wnM = xM φM ηM .

∀i 6= M

(13)

313

Recall that the household’s optimality condition, derived from (1), is w = C. Combining this

314

condition with the market clearing condition C = xM for the consumption good yields

(14)

w = xM . 315

From (14) we can see that the concavity in the household utility functions implies that prices are

316

increasing in final output in equilibrium. Combining (14) with the expressions (11) for each firm’s

317

labor expenditure yields expressions for each firm’s labor use.

ni = φi ηi

M

∏

j=i+1

φ j ω j, j−1 1 − η j




nM = φM ηM

∀ i 6= M

(15)

318

Using the inter-linked production functions (2) of each firm, we can produce an expression for

319

equilibrium aggregate output as function of each firm’s wedge φi and labor use (15)

Y 320

≡ xM = zM nηMM


where ϕi ≡ ∏M j=i+1 ω j, j−1 1 − η j . 14

M−1

∏ i=1

zi nηi i


ϕi

(16)

321

Thus, equilibrium aggregate output in the economy is determined by each firm’s produc-

322

tion function and financial constraint. To see this, let Y¯ denote the aggregate output that would

323

324

prevail in a frictionless input-output economy (as in Acemoglu et al. (2012)), given by Y¯ ≡ h ih i ηM ηi
ϕi ∑i−1 M j=1 ϕ j η j . Define aggregate liquidity in the econzM ηM z η ω (1 − η ) ∏M−1 ∏ i i i,i−1 i=2 i i=1 i

325

∑ j=1 ϕ j η j ¯ ≡ φ ηM ∏M , an aggregation of all firm’s shadow value of funds. Then we omy as Φ i=1 (φi ) M

326

can write the analytical expression (16) for equilibrium aggregate output as an expression which is

327

log-linear in Y¯ and the aggregate liquidity in the economy.

¯ Y = Y¯ Φ

(17)

328

Intuitively, (17) says that equilibrium aggregate output is constrained by aggregate liquidity -

329

the funds available to all firms to finance working capital at the beginning of the period. Note that

330

¯ = 1 and Y = Y¯ . If one firm i is constrained, aggregate output if all firms are unconstrained, then Φ

331

depends on how its constraint affects the supply of intermediate good i for all downstream firms,

332

given by ∑ij=1 ϕ j η j . To summarize, firms’ financial constraints distort production in a way which

333

depends on the underlying structures of the credit and input-output networks of the economy.

334

Note that the size of firms is determined in equilibrium by two things: the scale of economy as

335

a whole, and the size of firms relative to one another in equilibrium. In the presence of constant

336

returns-to-scale, the scale of the economy as a whole, given by equation (17), is pinned down by

337

the household’s marginal rate of substitution, the total factor productivity of each firm, and the

338

tightness of firm’s financial constraints, while the relative size of a firm is determined by firms’

339

production functions and the tightness of their financial constraint φi (which depends on the credit

340

network.

341

2.2. Aggregate Impact of Firm-Level Shocks

342

I now examine how the economy responds to firm-level financial shocks and productivity

343

shocks. I model a financial shock to firm i by a change in Bi , the fraction of firm i’s revenue

344

that the bank will accept as collateral for the bank loan. This is a reduced-form way to capture a 15

345

reduction in the supply of bank credit to firm i, and represents an exogenous tightening in firm i’s

346

financial constraint.

347

If firm i is unconstrained in equilibrium, a marginal financial shock d Bi has no effect on its

348

production - the firm has deep pockets and can absorb the shock. However, if the firm is con-

349

strained, then it is forced to reduce production as it can no longer finance as many inputs with up

350

front payments. In addition to this direct effect, there are two types of network effects by which

351

the shock affects other firms in the economy: input-output channel and the credit linkage channel.

352

Network effects: Standard input-output channel Through the first channel, which I call the

353

standard input-output channel, the shock propagates through input-output interlinkages, increasing

354

firms’ input costs. This is the standard channel analyzed in the input-output literature, including

355

Acemoglu et al. (2012) and Bigio and La’O (2019). The reduction in firm i’s output increases the

356

price pi of good i. This acts as a supply shock to the customer downstream (firm i + 1), who is

357

now faced with a higher unit cost of its intermediate good. In response, firm i + 1 cuts back on

358

production, which causes the pi+1 to increase, etc. Thus, as a result of the shock to firm i, all firms

359

downstream experience a supply shock to their intermediate goods, and cut back on production.

360

This amplifies the shock because as firms reduce production, they cut back on employment which,

361

in turn, reduces the wage and household consumption. In addition, the shock travels upstream as

362

suppliers adjust their output to respond to the fall in demand for their intermediate goods.

363

Network effects: Credit linkage channel

There is also a new, additional channel of trans-

364

mission - which I call the credit linkage channel - which describes how the financial constraints of

365

upstream firms are tightened endogenously in response to the shock.

366

Recall that when firm i cuts back on production, the price pi of its good rises. This increases

367

the collateral value of its future cash flow, allowing it to delay payment for a larger fraction of

368

its purchase from supplier i − 1.12 As a result, supplier i − 1’s cash/revenue ratio falls, meaning 12

This is true even though the volume of trade credit τi−1 may actually fall in response to the shock.

16

369

the fraction of its revenue collected as up front payment falls. This tightens its cash-in-advance

370

constraint - i.e. χi−1 falls.13 τi−1 χi−1 ↓ ≡ Bi−1 + θi−1 + 1 − | {z } pi−1 xi−1 | {z } debt/revenue ratio

(18)

cash/revenue ratio ↓

371

Thus, with less cash on-hand, the supplier i − 1 is now faced with a tighter financial constraint

372

itself. The supplier may therefore be forced to reduce production further, and thereby pass the

373

shock to its own suppliers and customers. (This continues up the chain of firms). In this manner,

374

the initial effect of the shock is amplified as upstream firms experience tighter financial conditions.

375

But why doesn’t firm i − 1 reduce the trade credit loans it makes in order to increase its cash

376

holdings and relax its own constraint? Recall that representative firm i − 1 consists of a continuum

377

of firms, and that perfect competition forces them to offer the maximum trade credit, even when

378

they are themselves constrained. Note also that α mitigates the transmission, allowing firm i − 1

379

to partially offset the lost up-front cash payments with a larger bank loan. Thus, α parameterizes

380

the substitutability between cash and bank credit.

381

Importantly, this mechanism is consistent with two well-documented stylized facts on trade

382

credit. First, in response to a liquidity shock, firms generally use trade credit more intensively

383

to finance their intermediate goods: when a customer experiences a financial shock, suppliers

384

extend more trade credit to their distressed customer either through financing a higher proportion

385

of purchased goods, or by extending the agreed maturity of the trade credit loans. (See Cunat

386

(2007), Calomiris et al. (1995), and Nilsen (2002) for evidence and discussion.) This is captured

387

in my stylized model: in response to a financial shock, firm i increases

388

intermediate goods that firm i finances with trade credit.

τi−1 pi−1 xi−1 ,

the fraction of

13

More precisely, there are three effects of the shock d Bi on χi−1 . Recall from (10) that firm i − 1’s cash/revenue pi xi ratio depends inversely on pi−1 xi−1 . First, the shock increases pi , as discussed above. Second, the fall in firm i’s output xi increases the ratio xi−1 due to the decreasing returns to xi−1 . And third, the fall in i’s demand reduces the price pi−1 of good i − 1. All of these effects unambiguously reduce χi−1 .

17

389

Second, empirical evidence strongly suggests that trade credit linkages transmit financial dis-

390

tress upstream from firms to their suppliers. This is consistent across studies which use firm-level

391

and industry level data on trade credit, such as Jacobson and von Schedvin (2015), Boissay and

392

Gropp (2012), and Raddatz (2010), Jorion and Zhang (2009), and Carbo-Valverde et al. (2016).14

393

In the model, the credit linkage channel implies that trade credit transmits a financial shock up-

394

stream from firms to their suppliers, consistent with the evidence.15

395

Feedback effect created by transmission channels Importantly, the two transmission chan-

396

nels produce a feedback effect which amplifies the shock, as illustrated in Figure 2. Suppose that

397

firm 2 is hit with an adverse financial shock, causing its cash-in-advance constraint to become

398

tighter, and forcing it to cut back on production. The standard input-output channel, represented

399

by the blue arrow, transmits the shock downstream in the form of a higher intermediate good price.

400

In addition, the credit linkage channel tightens the constraints of upstream firms, as firm 2

401

reduces the cash-in-advance payments it makes to its supplier. With a tighter financial constraint

402

the supplier is forced to reduce production, which feeds back to firm 2 again in the form of higher

403

price for the intermediate good. Thus, firm 2 is hit not only with a tighter financial constraint,

404

but also endogenously higher input costs, (which it passes on to its customer, and so on). In this

405

manner, the two channels interact to create a feedback loop represented by the red arrows, which

406

exacerbates the initial shock.

407

408

Misallocation and the real effects of financial shocks

The real effect of financial shocks,

and the amplification of these shocks generated by credit linkages, operates through a misalloca14 While

aggregate accounts receivable fell during the Great Recession, this likely reflects the fall in trade of intermediate goods rather than the intensity of trade credit, which the above papers showed increase during episodes of financial distress. 15

It is not crucial for the qualitative results that the borrowing constraints (9) are binding in equilibrium. Even if equilibrium trade credit were defined by an interior optimum in which the borrowing constraints (9) do not bind, there would still be an upstream transmission of shocks as long as trade credit does not declined as a fraction of suppliers’ revenue in response to a financial shock to industry i. In fact, this upstream transmission may be stronger if borrowing constraints are not binding in equilibrium: in response to a financial shock, firm i can borrow more from its supplier, further tightening its supplier’s financial constraint.

18

409

tion of labor across firms in the production network. The mapping between labor and output is

410

determined by the production structure of economy and financial constraints, which distort the al-

411

¯ in equation (17), as . constraints introduce location of labor along the supply chain, captured by Φ

412

a wedge between the firms’ marginal cost and marginal revenue product of labor (see equation

413

(11)). Moreover, the presence of credit linkages between firms implies that these sectoral distor-

414

tions are endogenously magnified in response to a financial shock, depending on the structure of

415

the underlying credit network, thereby exacerbating the misallocation of labor.

416

3. Financial Influence and Network Centrality

417

418

In this section, I introduce a new notion of network centrality, called financial influence, which

419

captures the aggregate impact of a firm-level financial shock, and derive it analytically from two

420

measures of centrality: one which captures its centrality in the production network, and the other

421

which captures its centrality in the credit network of the economy. Online appendix O.A5 gives

422

these results in more detail.

423

I first derive analytical expressions for the impact of a firm-level financial shock on aggregate d logY d Bi ,

the marginal effect on aggregate out-

424

output. Define firm i’s total financial influence as

425

put of a financial shock to firm i. From (17), I decompose firm i’s total financial influence into

426

components reflecting the standard input-output channel and the credit linkage channel. d logY = d Bi d log φ j d Bi

M

∑ v¯ j δ ji

(19)

j=1

427

Here, the terms δ ji ≡

428

to firm i affects the shadow value of funds of every other firm j in the network. These terms are

429

expressed in closed form in online appendix O.A5.

capture the credit linkage channel, and reflect how the financial shock

430

For each firm i, I define the vector of δ ji as the firm’s financial influence vector, which is a

431

measure of its centrality in the credit network of the economy and describes how a financial shock

432

to the firm affects the aggregate financial conditions of the economy through the credit network 19

433

effects outlined in the previous section. Each firm’s financial influence vector is determined by the

434

structure of the credit network of the economy, through its dependence on credit parameters θk .16

435

logY The terms v¯ j ≡ ∂∂logφ capture the standard input-output channel, and map these changes in each j

436

φ j into aggregate output. These expressions are given in closed form in online appendix O.A5. I

437

refer to the scalar v¯i as firm i’s production influence, which is a measure of its centrality in the input-

438

output network of the economy and captures how a fall in its production due to a tighter financial

439

constraint affects aggregate output through its input-output linkages with other firms.

440

441

442

Defining v¯ to be the M-by-1 defined by v¯ vector of all firms’ production influences, and defining   1 M we can then the financial centrality matrix ∆ to be the M-by-M matrix given by ∆ ≡ δ · · · δ re-write the expression for a firm’s financial influence (19) in matrix notation. 

d logY d B1

···

d logY d BM

0

= ∆0 v¯

(20)

443

Notice that the elasticities of output to the shocks is a linear transformation of the economy’s

444

production influence vector v, ¯ where the transformation matrix is ∆. The financial centrality matrix

445

matrix ∆ captures the way that the trade credit linkages between firms distort the propagation of

446

financial shocks through the economy, depending on the underlying structure of the economy’s

447

trade credit network.

448

Note that the highest impact firms are not necessarily those with the highest production influ-

449

ence or the highest financial influence. The fact that the aggregate impact of a shock depends on

450

the interaction between these two measures of centrality implies that the firms with the highest

451

impact are those who have suppliers who are simultaneously important suppliers of intermediate 16

In particular, higher-order upstream linkages are an important determinant of a firm’s financial influence: the effect of the financial shock to i on firm j’s financial constraint depends not only on how much credit j is extending directly to i (which is 0 in this stylized model), but also on how much credit it is extending to i indirectly through all firms along the credit chain in between i and j. As a result, a financial shock to i has a larger effect on j’s financial constraint if trade credit is used more intensively amongst all firms between i and j. In online appendix O.A5, I prove that d log φ j d Bi ≥ 0, which implies that the credit network effects amplify the initial firm-level financial shock.

20

452

goods to the rest the of economy, and prominent creditors to their customers.17

453

4. General Model

454

455

456

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 firm in the economy.

457

I assume that each of the M goods can be consumed by the representative household or used in

458

the production of other goods. The household’s total consumption C is Cobb-Douglas over the M

459

goods, and it has Greenwood-Hercowitz-Huffman preferences.18  1−γ 1 1 1+ε C− N , U(C, N) = 1−γ 1+ε

M

β

C ≡ ∏ ci i

(21)

i=1

460

Here, ε and γ respectively denote the Frisch and income elasticity of labor supply. The household

461

maximizes its utility subject to its budget constraint (1). This yields optimality conditions which

462

equate the ratio of expenditure on each good with the ratio of their marginal utilities, and the

463

competitive wage with the marginal rate of substitution between aggregate consumption and labor. pi ci βi = , p jc j β j

464

465

N 1+ε = C

(22)

Each firm can trade with all other firms. Firm i’s production function is again Cobb-Douglas over labor and intermediate goods. 17

Intuitively, if a firm i borrows heavily from its suppliers, then a financial shock will be transmitted upstream more intensively as firms reduce the cash-in-advance payments they make to their suppliers, captured by δ i . As these suppliers become more constrained, they will reduce their output. The impact of this lower output will have greater effects on downstream firms if those same suppliers are also important suppliers of intermediate goods, captured by a high measure of production influence v¯ j . 18

See Greenwood et al. (1988). Quantitatively similar results hold for preferences which are additively separable in aggregate consumption C and labor N.

21

xi = zηi i nηi i

m

∏

j=1

ω xi ji j

!1−ηi

(23)

466

Here, xi denotes firm i’s output and xi j denotes firm i’s use of good j. Since ωi j denotes the

467

share of j in i’s total intermediate good use, I assume ∑M j=1 ωi j = 1 so that each firm has constant

468

returns to scale. The input-output structure of the economy can be summarized by the matrix Ω of

469

intermediate good shares ωi j .19 

 ω ω · · · ω 12 1M   11    ω21 ω22    Ω≡ .  ...  ..      ωM1 ωMM

470

Note that the production network is defined only by technology parameters. As we will see, the

471

presence of financial frictions will distort inter-firm trade in equilibrium. Hence, Ω describes how

472

firms would trade with each other in the absence of frictions.

473

Each firm’s cash-in-advance constraint takes the same form as in the stylized model, with the

474

exception that each firm has M suppliers and M customers instead of just one of each. The variable

475

τis denotes the trade credit loan that firm i receives from each of its suppliers s. M

M

wni +

∑ (psxis − τis)

s=1

|

{z

}

≤ bi +

net CIA payment to suppliers

pi xi − ∑ τci

|

c=1

{z

(24)

}

net CIA received f rom customers

476

Firm i faces borrowing constraints with each of its suppliers, in which the loan from each supplier

477

s is bounded above by a fraction θis of its total cash flow. Each firm can also borrow bi from the

478

bank up to a fraction Bi of its cash flow, and by pledging a fraction α of its accounts receivable 19

This is simply a generalization of the input-output structure in the stylized model. In that case, the Ω would be given by a matrix of zeros, with one sub-diagonal of ones, reflecting the vertical production structure and the constant returns to scale technology of firms.

22

479

∑M c=1 τci as collateral.

τis ≤ θis pi xi

bi ≤ Bi pi xi + α

M

∑ τci

(25)

c=1

480

Underlying these constraints is the same moral hazard problem described in the stylized model. As

481

in the stylized model, competition amongst suppliers in industry s forces them to offer the maxi-

482

mum trade credit permitted by the limited enforcement problem, so that the trade credit borrowing

483

constraint always binds when industries are cash-constrained in equilibrium. The structure of the

484

credit network between firms can be summarized by the matrix of θi j ’s. 



 θ11 θ12 · · · θ1M     θ21 θ22    Θ≡ .  ...  ..      θM1 θMM

485

486

Plugging the binding borrowing constraints into (24) yields a constraint on i’s total input purchases, where χi describes the tightness of i’s cash-in-advance constraint. M

wni + ∑ ps xis ≤ χi pi xi

(26)

s=1

487

Just as in the stylized version, χi is an an equilibrium object, where firm i’s cash/revenue ratio

488

depends on the prices pc of its customer’s goods and its forward credit linkages θci . M

M

s=1

c=1

χi = Bi + ∑ θis + 1 − (1 − α) ∑ θci |

{z

}

debt/revenue ratio

|

{z

pc xc pi x i }

(27)

cash/revenue ratio

489

Firms choose labor and intermediate goods to maximize profits subject to their cash-in-advance

490

constraint. Again, firm i’s constraint inserts a wedge φi between the marginal cost and marginal

491

revenue product of each input

23

ni = φi ηi

pi xi w

xi j = φi (1 − ηi ) ωi j

pi xi pj

(28)

492

where the wedge φi = min {1 , χi } is determined by the firm’s shadow value of funds. Market

493

clearing conditions for labor and each intermediate good are given by M

N = ∑ ni i=1

M

xi = ci + ∑ xci .

(29)

c=1

494

The equilibrium conditions of this generalized model take the same form as in the stylized model,

495

and the economy will behave in qualitatively the same way in response to shocks as in the stylized

496

model. When taking this model to industry-level data, the calibration of the model will allow

497

industries to differ in how financially constrained they are.

498

Relationship between firm influence and size

Bigio and La’O (2019) showed that in a

499

multisector model with financial frictions, Hulten’s theorem breaks down.20 My model shows that

500

when credit linkages between firms propagate shocks across the economy, the aggregate impact

501

of an idiosyncratic shock depends also on the underlying structure of the credit network of the

502

economy, summarized by the matrix Θ.

503

5. Quantitative Analysis

504

505

Having established analytically that the credit network of the economy can amplify firm-level

506

shocks, I now ask whether this mechanism is quantitatively significant for the US, and examine

507

more carefully the role that the structure of the credit network plays. But before these questions

508

can be addressed, I need disaggregated data on trade credit flows in order to calibrate the credit

509

network of the US economy. 20 Attributed

to Hulten (1978), this states that under certain conditions, the size of a firm, as measured by its share si of aggregate sales, is sufficient to determine the aggregate impact of a shock to sector i, and one does not need to know anything about the underlying input-output structure of the economy.

24

510

5.1. Mapping the US Credit Network

511

Calibration of the trade credit parameters θi j requires data on credit flows between industry

512

pairs; but data on credit flows at any level of detail is scarce. To overcome this paucity of data, I

513

construct a proxy for trade credit flows τi j between industry pairs using industry-level input-output

514

data and firm-level balance sheet data. I use input-output tables from the Bureau of Economic

515

Analysis (BEA) and Compustat North America over the period 1997-2013.21

516

My strategy for constructing the proxy is illustrated in Figure 3. From the payables and re-

517

ceivables data, I observe how much, on average, firms in each industry have borrowed from all

518

of their suppliers collectively, and lent to all of their customers collectively.22 However, I do not

519

observe how an industry’s stock of trade credit and debt breaks down across each of its suppliers

520

and customers. Therefore, I combine the input-output data with the payables and receivables data

521

to approximate the fraction of sales from firms in industry j to firms in industry i made on credit,

522

on average, yielding a proxy for trade credit flows τi j between each industry pair. Importantly, the

523

trade credit flows are allowed to vary across industry pairs.

524

5.2. Calibration

525

With the proxy for trade credit flows at hand, I calibrate the general model to match US data.

526

I calibrate technology parameters ηi and ωi j to match the BEA input-output tables of the median

527

year in my sample, 2005. The firm optimality conditions and CRS technology imply

φi =

wni + ∑M j=1 p j xi j pi xi

.

(30)

21

The BEA publishes annual input-output data at the three-digit NAICS level, at which there are 58 industries, excluding the financial sector. From this data, I observe annual trade flows between each industry-pair, which corresponds to p j xi j in my model for every industry pair {i, j}. Compustat 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, cost of goods sold, and sales in each year of the sample. 22

The vast majority of accounts receivables and payables of US corporations consists of trade credit.

25

528

The right-hand side of (30) is directly observable from the BEA’s Direct Requirements table.

529

Therefore, the assumptions of CRS and Cobb-Douglas production, which are assumptions used in

530

many multisector models in the literature (Acemoglu et al. (2015), Acemoglu et al. (2012), Atalay

531

(2017), Baqaee (2018), Baqaee and Farhi (2019), Foerster et al. (2011), Long and Plosser (1983)),

532

imply that the ratio of an industry’s expenditure on inputs to its revenue is informative about the

533

tightness of the industry’s financial constraint. This calibration implies that, at the industry level,

534

financial constraints are binding.23

535

Looking through the lens of the model, the observed input-output tables reflect both technology

536

parameters and distortions created by the financial constraints. My calibration strategy respects

537

this feature. In particular, I calibrate technology parameters using firm i’s optimality conditions for

538

each input and my calibrated φi ’s.

ηi = 539

Again the ratios

540

industry i and j.

wni pi xi

and

p j xi j pi xi

wni φi pi xi

ωi j =

p j xi j (1 − ηi )φi pi xi

(31)

are directly observable from the Direct Requirements tables for every

541

I calibrate the parameters θi j , representing the credit linkages between industries j and i, to

542

match my proxy of inter-industry trade credit flows τˆi j using industry i’s binding borrowing con-

543

straint.

θi j =

τˆi j pi xi

(32)

23

This is consistent with empirical evidence. In the context of the model, that φi < 1 amounts to saying that, at the margin, a financial shock to industry i has nonzero effects on the output of that industry. Conversely, a value of φi = 1 would imply that a financial shock to industry i has zero real effects, since the financial constraint is slack for that industry. The conditions for this to hold empirically are very general and plausible: that at least some firms in each industry face financial constraints. Viewed in this light, the result from the calibration that φi < 1 for all industries is consistent with empirical evidence that sectoral level shocks to the financial conditions of firms have measurable, nonzero effects on real activity in that sector. Examples of such evidence is presented in Alfaro et al. (2017), Manaresi and Pierri (2018), and firm level evidence in Jacobson and von Schedvin (2015).

26

544

Industry i’s total revenue pi xi is directly observable from the Uses by Commodity tables. (Recall

545

that I use the input-output tables for year 2005). This implies that the credit linkages vary across

546

industry pairs - thus, we have a matrix of credit linkages which characterize the credit network of

547

the economy.

548

To calibrate Bi , the parameters reflecting the agency problem between firm i and the bank,

549

recall the definition of φi given by (11), which depends on the technology parameters (calibrated

550

as described above) and the tightness χi of each industry’s cash-in-advance, where M

M

s=1

c=1

χi = Bi + ∑ θis + 1 − (1 − α) ∑ θci

pc xc . pi xi

(33)

551

The total revenue of each industry pi xi is observable from the Uses by Commodity tables, and φi

552

and θis for all s were calibrated as described above. I therefore use (30) and (32) to back out Bi for

553

each industry. Thus, the calibration of Bi ensures that φi < 1, so that all industries are constrained

554

to some degree in equilibrium.

555

I follow the standard literature and set ε = 1 and γ = 2, which represent the Frisch and income

556

elasticity, respectively. I set α = 0.2 in my baseline calibration, but check the sensitivity of the

557

quantitative results to varying α.24

558

6. A Quantitative Exploration of the Model

559

560

With my model calibrated to match the US economy, I am in a position to examine the quanti-

561

tative response of the economy to industry-level and aggregate productivity and financial shocks.

562

Since this general environment precludes closed-form solutions, I use quantitative methods to ex24

Recall that α is the fraction of receivables that industries can collateralize to borrow from the bank. Omiccioli (2005) finds that the median Italian firm in a sample collateralizes 20 percent of its accounts receivable for bank borrowing.

27

563

plore the role that the structures of the credit and input-output networks play.

564

In this more general setting, the presence of higher-order linkages means there are now addi-

565

tional spillover effects. To illustrate, consider Figure 4. The petroleum and coal manufacturing

566

industry and the utilities industry are linked by a common supplier, the oil and gas extraction

567

industry. Suppose that firms in petroleum and coal manufacturing experience tighter financial con-

568

straints, forcing some to reduce production, and raising the price of petroleum. This corresponds

569

to the standard input-output channel represented by the blue arrow. In the absence of the credit

570

linkage channel of transmission, firms in the utilities industry will remain largely unaffected by the

571

shock.

572

However, the shock causes petroleum and coal manufacturers to reduce the up front payments

573

they make to their oil and gas suppliers. With tighter financial constraints, these suppliers reduce

574

production, raising the price of oil and gas. As a result utilities firms pass these higher input costs

575

downstream in the form of higher energy prices. These additional credit network effects further

576

amplify the effects of the shock.

577

How large are these credit network effects likely to be? To answer this, I hit the US economy

578

with an aggregate financial shock, and industry-level financial shocks, and measure the response

579

in aggregate output to a log-linear approximation.

580

6.1. Response to an Aggregate Financial Shock

581

Suppose that the economy is hit with a one percent aggregate financial shock: each indus-

582

try i’s cash-in-advance constraint is tightened by one percent. Under my conservative, baseline

583

calibration, I find that US GDP falls by 2.92 percent - a large drop.

584

To gauge the extent to which this fall is driven by the effect of credit linkages in amplifying the

585

shock, I consider the same shock under a counterfactual version of the model in which industry

586

financial constraints are fixed exogenously, which I refer to as the Fixed Constraints Model. This

587

counterfactual effectively involves shutting off the credit linkage channel described in section 2.2.

588

of the paper, so that a financial shock to industry i has no effect on the tightness φ j of any other 28

589

industry j. Any difference between the response of aggregate output between these two versions

590

is due solely to the effect of trade credit linkages in propagating shocks across sectors, thereby

591

generating an endogenous tightening in sectoral financial constraints, depending on the structure

592

of the credit network of the economy. Under the Fixed Constraints Model, I find that GDP falls by

593

only 2.28 percent in response to the same aggregate shock. Thus, the credit network effects amplify

594

the fall in GDP by about 30 percent. This is a conservative estimate of the quantitative relevance

595

of the mechanism, given that the calibration uses data on only large, publicly-traded firms who use

596

trade credit less intensively than other. The table in appendix A1 reports the sensitivity of these

597

results to the specification of α = 0.2, the parameter controlling the substitutability of cash and

598

bank credit.

599

In appendix A2, I ask which industries are likely to be systemically important to the US econ-

600

omy in light of these network effects, and show that the credit network implies that an industry-

601

level financial shock can have a strong impact on US GDP.

602

6.2. Mapping the Model to the Data

603

In order to map the model to the data, I extend the static model to be a repeated cross-section.

604

Let Xt , Nt , Bt , and zt denote the M-by-1 vectors of output growth, employment growth, financial

605

shocks, and productivity for each industry respectively, in quarter t. The log-linearized model

606

yields closed-form expressions for how the output and employment of each industry respond to

607

financial and productivity shocks.

Xt = GX Bt + HX zt

Nt = GN Bt + HN zt

(34)

608

The M-by-M matrices GX and HX (GN and HN ) map industry-level financial and productivity

609

shocks, respectively, into output growth (employment growth), and capture the effects of input-

610

output and credit interlinkages in propagating shocks across industries. The elements of these

611

matrices depend only on the model parameters, and therefore take their values from my calibration.

612

I construct the observed, quarterly cyclical fluctuations in the output Xˆt and employment Nˆ t of

29

613

US industrial production industries using data from the Federal Reserve Board’s Industrial Pro-

614

duction Indexes, which includes data on the output growth of these industries, and the Bureau of

615

Labor Statistics’ Quarterly Census of Employment and Wages, from which I observe the number

616

of workers employed by each of these industries. At the three-digit NAICS level there are 23

617

such industries.25 For each dataset, I take 1997 Q1 through 2013 Q4 as my sample period, and

618

seasonally-adjust and de-trend each series. In the empirical analysis to follow, I use this data and

619

the expressions (34) to decompose observed cyclical fluctuations into various components.

620

7. Empirical Analyses

621

622

In the empirical part of the paper, I use my theoretical framework to investigate which shocks

623

drive observed cyclical fluctuations in the US, once we account for the network effects created by

624

credit and input-output linkages between industries. The framework is rich enough to permit an

625

empirical exploration of the sources of these fluctuations along two separate dimensions: the im-

626

portance of productivity versus financial shocks, and that of aggregate versus idiosyncratic shocks.

627

To this end, I use two methodological approaches to identifying shocks. In the first, I identify

628

shocks without imposing the structure of my model on the data. This permits a cleaner identifica-

629

tion of financial and productivity shocks, and estimates a residual component of fluctuations which

630

are not explained by either of these shocks. In the second approach, I identify shocks using a struc-

631

tural estimation of the model. While this attributes all fluctuations to financial and productivity

632

shocks only, it allows for a decomposition between aggregate versus industry-level shocks.

633

7.1. First Method: Estimating Shocks without the Model

634

My first approach involves identifying financial and productivity shocks without imposing the

635

structure of my model on the data - the identifying assumptions are completely independent of the

636

model. An added advantage of this method is that it permits the estimation of a residual component 25

Hours worked is not directly available at this level of industry detail and this frequency.

30

637

of observed fluctuations - a component which is not explained by either shock. However, the

638

shocks estimated using this method are assumed to be common to all industries.

639

To identify credit supply shocks to the US economy, I estimate an identified VAR using a

640

similar approach as Gilchrist and Zakrajsek (2011). To do this requires first constructing a measure

641

of bank-intermediated business lending.

642

I construct a measure of aggregate business lending by US financial intermediaries using quar-

643

terly Call Report data collected by the FFIEC. To capture lending to the business sector, I use

644

commercial and industrial loans outstanding and unused loan commitments - a cyclically-sensitive

645

component of bank lending.26 I thus construct a measure called the business lending capacity

646

of the financial sector, as the sum of unused commitments and commercial and industrial loans

647

outstanding in each quarter.27

648

To empirically identify credit supply shocks, I augment a standard VAR of macroeconomic

649

and financial variables with the measure of business lending capacity, and the excess bond pre-

650

mium of Gilchrist and Zakrajsek (2012) - a component of corporate credit spreads designed to

651

capture changes in the risk-bearing capacity of financial intermediaries.28 The endogenous vari-

652

ables included in the VAR, ordered recursively, are: (i) the log-difference of real business fixed

653

investment; (ii) the log-difference of real GDP; (iii) inflation as measured by the log-difference

654

of the GDP price deflator; (iv) the quarterly average of the excess bond premium; (v) the log dif26

Gilchrist and Zakrajsek (2011) show that the contraction in unused loan commitments was concomitant with onset of the financial crisis in 2007, while business loans outstanding contracted only with a lag of about four quarters. 27

Changes in business lending capacity mostly reflect supply-side changes. To see why, consider the following example. Suppose that a business draws down an existing line of credit it has with its bank. This is recorded as a fall in unused commitments, but reflects an increase in demand for credit rather than a contraction in the supply of credit. However, the loan is now recorded as an on-balance sheet commercial or industrial loan. Therefore, the fall in unused commitments is exactly offset by the increase in commercial and industrial loans outstanding, leaving bank lending capacity unchanged. So this measure of business lending capacity is largely unresponsive to firms drawing down their lines of credit. 28

I thank Simon Gilchrist for kindly sharing the excess bond premium data.

31

655

ference business lending capacity (vi) the quarterly (value-weighted) excess stock market return

656

from CRSP; (vii) the ten-year (nominal) Treasury yield; and (viii) the effective (nominal) federal

657

funds rate. The identifying assumption implied by this ordering is that stock prices, the risk-free

658

rate, and bank lending can react contemporaneously to shocks to the excess bond premium, while

659

real economic activity and inflation respond with a lag. I estimate the VAR using two lags of each

660

endogenous variable.

661

To map the orthogonalized innovations in the excess bond premium into the financial shocks B˜t

662

of my model, I make use of the impulse response function of business lending capacity, and con-

663

struct financial shocks as changes in the supply of bank lending which arise due to orthogonalized

664

innovations in the risk-bearing capacity of the financial sector. The plot in appendix A3 shows the

665

time series of this shock.

666

667

7.1.2. Estimated productivity shocks

668

The Federal Reserve Bank of San Francisco produces a quarterly series on TFP for the US

669

business sector, adjusted for variations in factor utilization, according to Fernald (2012). As such,

670

this series is readily mapped into my model as an aggregate productivity shock z˜t . The plot in

671

appendix A3 shows the time series for this productivity shock. Let zˆt ≡ z˜t~1 denote the M-by-1

672

vector of these shocks.

673

674

7.1.3. Decomposing observed fluctuations in industrial production

675

With the estimated shocks at hand, I use log-linearized expression (34) to decompose observed

676

cyclical fluctuations in industrial production into components coming from the financial shocks,

677

productivity shocks, and a residual.

Xˆt = GX Bˆt + HX zˆt + εt 678

(35)

The residual εt is the component of these fluctuations which is unexplained by either of these 32

679

shocks. I then feed these shocks into the model and perform a variance decomposition of aggregate

680

industrial production. The variance decomposition of output before 2007, given in appendix A3,

681

shows that productivity and financial shocks played a roughly equal role in generating cyclical

682

fluctuations in the period 2001 - 2007, together accounting for half of observed aggregate volatility

683

in US industrial production. The remaining half is unaccounted for by either type of shock.

684

In order to quantify the importance of the credit network in generating aggregate volatility

685

from these shocks during this period, I also take the shocks estimated using the full model, and

686

feed them through the Fixed Constraints Model, a version of the model described in section 6.1 in

687

which industry financial constraints are fixed exogenously. By comparing the results from the full

688

model to the results from the fixed constraints economy, I find that that accounting for the credit

689

linkages of the economy increases the relative importance of financial shocks in driving aggregate

690

fluctuations. Moreover, the credit network of the economy amplifies the contribution of financial

691

shocks to aggregate volatility by 29 percent. The results are presented in the table in appendix A8.

692

While productivity shocks and financial shocks seem to have played a comparable role before

693

2008, the story is different for the Great Recession. Figure 5 plots the time series of aggregate

694

industrial production during the Great Recession, as well as a simulation for each of its compo-

695

nents.29 These counterfactual series are constructed by feeding each of the estimated components

696

through the model one at a time, and thus represents how aggregate industrial production would

697

have evolved in the absence of other shocks, beginning in 2007 Q3.

698

During the recession, productivity shocks had virtually no adverse effects on industrial produc-

699

tion - in fact, they actually mitigated the downturn. Rather, financial shocks are the main culprit,

700

accounting for two-thirds of the peak-to-trough drop in aggregate industrial production during the

701

recession. The remaining one-third is not accounted for by either shock. Furthermore, the credit

702

network of these industries played a quantitatively significant role during this period, amplifying 29

The time series for observed aggregate IP is constructed from the cyclical component of IP growth. It is constructed as an aggregate index of the observed industry-level growth rates.

33

703

the effects of the financial shocks by about 15% (i.e. adding 3.98 percentage points to the peak-to-

704

trough drop in the financial component of aggregate industrial production).

705

In order to quantify the importance of the credit network in generating the dynamics of ag-

706

gregate output during the recession given the estimated shocks, I take the shocks estimated using

707

the full model, and feed them through the Fixed Constraints Model described above, and plot the

708

financial component of aggregate IP under each model, where the financial component is the coun-

709

terfactual path of aggregate industrial production when feeding only the estimated financial shocks

710

into the model. In addition, I perform the same exercise for a version of the model in which fi-

711

nancial constraints never bind, called the Frictionless Model. I plot these paths in appendix A8.

712

Unsurprisingly, financial shocks have no effect on aggregate output the Frictionless Model. By

713

comparing the paths of the financial component of aggregate industrial production in the Baseline

714

Model with that in the Fixed Constraints Model, I find that, even under my conservative calibration,

715

the credit linkages between industries amplify the effects of the financial shocks, causing aggre-

716

gate industrial production to decline by about 6 percentage points more than it otherwise would -

717

an increase of 21 percent.

718

719

7.2. Second Method: Structural Factor Analysis

720

With my second methodological approach, I empirically assess the relative contribution of

721

aggregate versus idiosyncratic shocks in generating cyclical fluctuations. This involves estimating

722

the model using a structural factor approach similar to that of Foerster et al. (2011), using data

723

on the output and employment growth of US IP industries. The procedure involves two steps. I

724

first use a log-linear approximation of the model to back-out the productivity and financial shocks

725

to each industry required for the model to match the fluctuations in the output and employment

726

data. Then, I use dynamic factor methods to decompose each of these shocks into an aggregate

727

component and an idiosyncratic, industry-specific component.

728

34

729

7.2.1. Step 1: Structural estimation of shocks

730

I first use a log-linear approximation of the model to back-out the productivity and financial

731

shocks to each industry required for the model to match the fluctuations in the output and em-

732

ployment data. To do this, recall that from equations (34) I have an exactly identified system

733

of equations. Given the observations Xˆt and Nˆ t , I then invert the system to back-out industry-

734

level each quarter over my sample period 1997 Q1 to 2013 Q4. Denote by Bˇt and zˇt the M-by-1

735

vectors of financial and productivity shocks estimated with this procedure in quarter t. And let

736

Q ≡ HX − GX G−1 N HN . ˆ Bˇt = G−1 N Nt − HN zˇt




ˆ zˇt = Q−1 Xˆt − Q−1 GX G−1 N Nt

(36)

737

Thus, I construct industry-level shocks as the observed fluctuations, filtered for the the network

738

effects created by interlinkages. The model is able to separately identify these shocks because each

739

type of shock has quantitatively differential effects on an industry’s output and employment.30

740

The figure in appendix A5 shows the time series of the estimated financial and productivity

741

shocks which hit the US auto manufacturing industry each quarter over the sample period. Between

742

2007 and 2009, the output and employment of industrial production industries took a sharp drop

743

for a number of quarters. As illustrated in the figure, this contraction shows up in the model as an

744

acute tightening in the financial constraints of these firms, reaching up to a 25 percent decline in a

745

single quarter, which is broadly representative of most industrial production industries.

746

747

748

749

7.2.2. Step 2: Dynamic factor analysis Next, I use factor methods to decompose the financial and productivity shocks, Bˇt and zˇt , into aggregate and idiosyncratic components. 30

Namely, 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, but tightens the cash-in-advance constraints.

35

Bˇt = ΛB FtB + ut ,

zˇt = Λz Ftz + vt

(37)

750

Here, FtB and Ftz are scalars denoting the common factors affecting the output and employment

751

growth of each industry at quarter t, and are assumed to follow an AR(1) process; the residual

752

components, ut and vt , are the idiosyncratic shocks. Hence, I estimate two dynamic factor models;

753

one for the financial shocks Bˇt and one for the productivity shocks zˇt .

754

To gauge the external validity of the structural factor analysis, I compare the aggregate finan-

755

cial shocks to the excess bond premium. The large aggregate financial shocks estimated by the

756

structural factor analysis is broadly reflective of the severe credit crunch that occurred during this

757

period.

758

759

7.2.3. Decomposing observed fluctuations in industrial production

760

To perform a variance decomposition of observed industrial production from 1997 Q1 to 2013

761

Q4, I follow the procedure described in appendix A6. For the full sample period, aggregate volatil-

762

ity is about 0.19 percent. The results are summarized in Table 1.

763

Before the Great Recession, aggregate volatility was driven primarily by aggregate financial

764

shocks and idiosyncratic productivity shocks; aggregate financial shocks account for nearly a half

765

of aggregate volatility. Nevertheless, idiosyncratic productivity shocks account for a quarter of

766

aggregate volatility. Furthermore, the credit network of industrial production industries amplified

767

these shocks, accounting for nearly one-fifth of observed aggregate volatility.

768

Aggregate financial shocks were the primary driver of the Great Recession. I perform an ac-

769

counting exercise to evaluate how much of the peak-to-trough drop in aggregate industrial pro-

770

duction from 2007Q4 to 2009Q2 can be explained by each type of shock. I find that changes in

771

productivity did not contribute to the decline in aggregate industrial production during the reces-

772

sion. In contrast, 73 percent of the drop in aggregate industrial production is due to an aggregate

773

financial shock, and a sizable fraction of the the remainder can be accounted for by idiosyncratic

36

774

financial shocks to the three most systemically important industries

775

The figure in appendix A10 depicts the relationship between industry-level financial shocks, an

776

industry’s contribution to aggregate output, and the systemic importance of an industry for indus-

777

trial production industries during the Great Recession. Large financial shocks to a few systemically

778

important industries can explain the bulk of the decline in aggregate industrial production during

779

the Great Recession. In fact, idiosyncratic shocks to the oil and coal products manufacturing,

780

chemical products manufacturing, and auto manufacturing industries account for about 9 percent

781

of the decline (or one-third of the decline unaccounted for by aggregate shocks), despite com-

782

prising only about 25 percent of aggregate industrial production. This suggests that idiosyncratic

783

financial shocks to a few systemically important industries played a quantitatively significant role

784

during the Great Recession.

785

In contrast, both the aggregate and idiosyncratic components of productivity shocks were

786

slightly positive during this period on average. As such, changes in productivity did not contribute

787

to the decline in aggregate industrial production during the recession.

788

789

790

8. Conclusion

791

Inter-firm lending plays an important role in business cycle fluctuations. To show this, I first

792

introduced supplier credit into a network model of the economy and showed that trade credit in-

793

terlinkages can create a powerful amplification mechanism. To evaluate the model quantitatively, I

794

constructed a proxy of the credit linkages between US industries by combining firm-level balance

795

sheet data and industry-level input-output data, and I used the model to investigate which shocks

796

drive the US business cycle when we account for the linkages between industries.

797

The broad picture which emerges from these empirical analyses is that financial shocks have

798

been a key driver of aggregate output dynamics in the US, particularly during the Great Recession.

799

While much of the previous literature has relied on shocks to aggregate TFP drive the business

800

cycle, the dearth of direct evidence for such shocks has raised concerns about their empirical 37

801

viability. I have argued that the credit and input-output interlinkages of firms can create a powerful

802

mechanism by which a shock to one firm’s financial constraint propagates across the economy. The

803

confluence of my empirical results suggest that once we account for these interlinkages, financial

804

shocks seem to displace aggregate productivity shocks as a prominent driver of the US business

805

cycle.

806

One limitation of this framework is that it abstracts away from capital goods. While trade credit

807

is most pertinent for the exchange of intermediate goods and primarily affects firms’ working cap-

808

ital, accounting for inter-industry trade in capital goods could nevertheless considerably affect the

809

quantitative results presented here. I abstract away from these considerations in order to keep the

810

model tractable, as adding capital accumulation to the model, or trying to model the inter-industry

811

trade of capital goods in the presence of financial constraints, would substantially complicate the

812

analysis. For these reasons, I leave the these considerations for future work.

38

813

814

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815

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Mian, S., Smith Jr, C., 1992. Accounts receivable management policy: theory and evidence. Journal of Finance 47 (1), 169–200. Nilsen, J., 2002. Trade credit and the bank lending channel. Journal of Money, Credit and Banking 34, 226–253. Raddatz, C., 2010. Credit chains and sectoral comovement: does the use of trade credit amplify sectoral shocks? Review of Economics and Statistics 92 (4), 985–1003. Ramirez, C., 2017. Inter-firm relationships and asset prices. Finance and Economics Discussion Seris 2-17-014. Board of Governors of the Federal Reserve System. Reischer, M., 2019. Finance-thy-neighbor. trade credit origins of aggregate fluctuations. Working paper. Shea, J., 2002. Complementarities and comovements. Journal of Money, Credit and Banking 34 (2), 412–433. Stella, A., 2015. Firm dynamics and the origins of aggregate fluctuations. Journal of Economic Dynamics and Control 55, 71–88.

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Figures

889

890

Figure 1: Vertical Production Chain

891 Notes: The production structure of the economy in the stylized model consists of a vertical supply chain in which each firm produces an intermediate good. The final firm in the chain produces the consumption good.

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892

893

Figure 2: Feedback Effect

894

Notes: In response to a financial shock, firm 2 reduces production, increasing the price of inputs for downstream firms. This standard input-output channel is represented by the blue arrow in the top panel. Experiencing a tighter financial constraint, firm 2 also reduces the up-front payments to its supplier, firm 1. As a result, the financial constraint of firm 1 also becomes tighter, causing firm 1 to reduce production. Therefore, the credit linkage channel creates a feedback effect represented by the red arrows.

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895

896

Figure 3: Constructing Proxy for Trade Credit Flows

897 Notes: I construct the proxy of trade credit flows from an industry A to industry B using firm-level data on industry A’s accounts receivable, industry B’s accounts payable, and industry-level data on the sales from industry A to industry B.

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898

899

Figure 4: Transmission Mechanism in the General Model

900 Notes: In the general model, trade credit linkages create rich spillover effects across industries. For example, when firms in the petroleum and coal manufacturing industry are hit with a financial shock, they reduce their up-front cash payments to their suppliers in the oil and gas manufacturing industry, tightening these firms’ financial constraints. These firms then reduce production, causing oil and gas prices to increase for firms in the utilities industry.

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901

902

Figure 5: Aggregate Industrial Production and Its Components

903 Notes: This figure shows the time series of aggregate industrial production and its components. Observed aggregate industrial production is an index constructed from the de-trended, seasonallyadjusted industry-level quarter-to-quarter growth rates in the output of the 23 industrial production industries at the three-digit NAICS level, obtained from FRB IP Indexes. Each of the other series depict counterfactual indexes constructed from the respective components of the observed series, beginning in 2007 Q3, and represent how aggregate IP would have evolved in the absence of other shocks. Financial shocks were estimated using an identified VAR Productivity shocks are estimated by Fernald (2012) as quarter-to-quarter, utilization-adjusted changes in TFP in the US, obtained from the San Francisco Fed database.

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904

905

Table 1: Pre-Recession Composition of Aggregate Volatility Fraction of Agg. Vol. Explained

Productivity Shocks

906

0.365

Agg. Component

0.133

Idios. Component

0.232

Financial Shocks

0.635

Agg. Component

0.45

Idios. Component

0.185

Notes: This table reports the results of the variance decomposition of the quarterly time series of aggregate industrial production over the period 1997 Q1 - 2006 Q4. Aggregate volatility is computed as the sample variance of observed aggregate industrial production. Shocks to industrial production industries were estimated using the structural factor analysis of these industries’ quarterly output and employment growth, obtained from the BLS Quarterly Census of Employment and Wages and the FRB IP Indexes, respectively. The aggregate and idiosycnratic components were estimated by dynamic factor analysis of the industry-level financial shocks, where the common components are assumed to follow an AR(1) process. 907

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