Propagation of financial shocks in an input-output economy with trade and financial linkages of firms

Journal Pre-proof Propagation of financial shocks in an input-output economy with trade and financial linkages of firms

Shaowen Luo

PII:

S1094-2025(18)30273-4

DOI:

https://doi.org/10.1016/j.red.2019.10.004

Reference:

YREDY 963

To appear in:

Review of Economic Dynamics

Received date:

21 June 2017

Revised date:

18 October 2019

Please cite this article as: Luo, S. Propagation of financial shocks in an input-output economy with trade and financial linkages of firms. Review of Economic Dynamics (2019), doi: https://doi.org/10.1016/j.red.2019.10.004.

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Highlights • • • •

Trade credit plays an important role in the propagation of financial shocks and the aggregate economic fluctuation. Trade credit attenuates the propagation of financial shocks when shocks are relatively small through the sharing of liquidity. Trade credit amplifies the propagation of financial shocks when shocks are relatively large through illiquidity contagion. The upstream propagation of financial shocks is stronger than the downstream propagation (based on the U.S. data).

Propagation of Financial Shocks in an Input-Output Economy with Trade and Financial Linkages of Firms

Shaowen Luo∗ Virginia Tech

Abstract Firms are connected through the production network, in which the production linkages coincide with financial linkages owing to delays in input payments that amount to a form of trade credit. In this paper, I investigate the roles of these interconnected production and financial linkages in the propagation of financial shocks. Empirically, I find, based on U.S. input-output matrix and loan data, that the upstream propagation of financial shocks is stronger than the downstream propagation. Theoretically, I elaborate a model that can capture this pattern of shocks, of which trade credit is an important component. Moreover, the model reflects the fact that trade credit attenuates the propagation of financial shocks when shocks are relatively small through the sharing of liquidity and amplifies their propagation when shocks are relatively large through illiquidity contagion. JEL code: E23, E32, E44 Keywords: production network, financial friction, trade credit

∗ Department of Economics, Virginia Tech, 3016 Pamplin Hall, 880 West Campus Drive, Blacksburg, VA 24061, United States. Email address: [email protected].

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1

Introduction

An economy is an entangled network of specialized productions that are interconnected through inter-firm trade within and across sectors. In the course of this trade, the products of one firm may be purchased and consumed by another firm as inputs. In addition, there is often a waiting period between the moment when a cost is incurred and the later point when the corresponding cash flow materializes. In this respect, the production network also creates and sustains a trade credit network.1 A financial shock may, therefore, spread through firms’ production and financial linkages. This paper studies how the interaction between the production network and the trade credit network affects the propagation of financial shocks. The automotive industry crisis of 2008-2010 offers an example of how a financial shock to one firm impacts its suppliers and customers. First, a firm that endures a financial shock may reduce its demand for the goods and services of its suppliers. Thus, for example, General Motors Co. (GM) significantly reduced its demand during the crisis owing to a severe liquidity problem.2 As a consequence, American Axle & Manufacturing Holdings Inc., one of GM’s major suppliers, experienced a net loss of $112.1 million in the fourth quarter of 2008.3,4 Fitch Ratings likewise downgraded the long-term ratings for Johnson Controls, Inc., another of GM’s major suppliers.5 Second, when a firm experiences a financial shock, it may postpone repaying trade credit to its suppliers and reduce its provision of trade credit to its customers. GM and Chrysler Group LLC., 1

Trade credits are short-term loans that a supplier provides to customers upon purchase of its products and that thus constitute a form of deferred payment. See Appendix A for further detail. 2 A combination of tight credit and declining sales caused the 2008-2010 crisis in the U.S. auto industry. The focus here is on the impact of the credit contraction on the production network. 3 “American Axle CEO: ‘2008 Is the Year From Hell’.” 30 January 2009, Dow Jones International News. 4 Similarly, during the 1997 Korean financial crisis, Kia Motors suffered liquidity problems that affected its 16,000 domestic suppliers. Source: “South Korea’s Kia Buckles, And Suppliers Begin to Break.” 22 August 1997, The Wall Street Journal. 5 “Fitch Downgrades Johnson Controls IDR to ‘BBB’; Places ST ‘F2’ on Watch Negative.” 26 January 2009, Business Wire.

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for example, had in excess of $21 billion in domestic trade payables as of September 30, 2008.6 The failure to meet these trade payments quickly crippled GM’s suppliers during the crisis. Notably, trade credit is an important source of short-term external finance for firms of all sizes. It is to be found on the balance sheets of almost every firm (in the forms of accounts-receivable and accounts-payable), where it accounts for more than 20% of the median firm’s total assets (see Boissay and Gropp, 2007; Klapper et al., 2012; Peterson and Rajan, 1997). Moreover, the choice of trade credit terms has been used as a screening device in order to make inferences regarding firms’ credit worthiness by financial institutions (see Smith, 1987). Despite its importance, however, trade credit has not been examined thoroughly in macroeconomics, especially in the context of the transmission of shocks. This paper presents an input-output model that takes into account trade credit in order to facilitate the study of the propagation of financial shocks. Specifically, the model reflects the fact that, when shocks are sufficiently small, trade credit attenuates their propagation through the sharing of liquidity within the network. During severe financial crises, by contrast, trade credit amplifies the propagation of shocks through illiquidity contagion within the network. To start with, I present a partial equilibrium model in an effort to explain the mechanism behind the propagation of financial shocks. Specifically, the model involves a production network structure and financial linkages among firms. To capture financial frictions, I assume that firms have a working capital requirement for inputs and therefore need to pay wages and intermediate input costs in advance of production. To satisfy this requirement, firms obtain bank credit from financial institutions and trade credit from suppliers. Accordingly, firms are financially interlocked through trade, for suppliers can use payments from customers as working capital, and, at the same time, 6

“US CREDIT - A GM failure risks more debt losses, default chain.” 11 December 2008, Reuters News.

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the balance sheets of trading parties become interlocked through accounts-payable and accountsreceivable. Trade credit in this way creates a liquidity-sharing channel that reallocates liquidity among firms. The production and financial linkages among firms serve to propagate financial shocks both upstream and downstream. For example, a positive interest rate shock to bank credit increases the input cost, reduces intermediate input demand, and affects intermediate input suppliers, which results in upstream propagation. The same shock increases the production price, creates a supply impact, and affects consumers, which results in downstream propagation. Two countervailing effects, the output effect and the input substitution effect of financing cost variation, determine the extent of upstream propagation. Two other types of effects, the cost effect and the discount effect of financing cost variation, determine the extent of downstream propagation. An important aspect of trade credit is that it affects the relative strength of upstream compared with downstream propagation. While my model indicates that the propagation of financial shocks depends on the nature of the credit frictions in conjunction with the input-output structure in the economy, the U.S. data that I have investigated suggest that upstream propagation of financial shocks is stronger than downstream propagation. Using Dealscan syndicated loan data (to measure liquidity shocks to 102 subsectors of the U.S. economy) and the industrial production (of 49 subsectors in the manufacturing and utility industries), I find both a significant negative impact of financial shocks on the focal subsector and significant upstream propagation of these shocks. In particular, my results show that subsectors are more sensitive to financial shocks that impact their customers than to shocks that impact their suppliers. Specifically, a 1% exogenous decline in the bank loan supply of a subsector’s customers generates a 2.9% decrease in the output of the focal subsector during the 4

2008-2009 financial crisis. Afterwards, I present a calibrated general equilibrium model for studying the U.S. economy along with two types of trade credit adjustments, namely adjustments of credit size and of its payment schedule. In the model, when a firm experiences a negative financial shock, size adjustment serves to increase its accounts-payable and to decrease its accounts-receivable so that the liquidity pressure can be absorbed through liquidity sharing. In this way, trade credit increases firms’ output correlation and attenuates both the propagation and the aggregate impact of financial shocks. Furthermore, during temporary illiquidity, firms tend to delay repayments of trade credit, which means that suppliers are exposed to counter-party risk and may be penalized by their creditors owing to debt rollover. Because liquidity pressure thus readily spills over to surrounding firms, trade credit amplifies the propagation and the aggregate impact of financial shocks. One key finding from the general equilibrium model is that trade credit leads to a “robustyet-fragile” production network.7 When the magnitude of negative shocks falls below a certain threshold, the liquidity-sharing channel serves as a kind of shock absorber, stabilizing the production network. In the event of large negative shocks, by contrast, deferred payments on trade credit lead to illiquidity contagion and fragility of the production network. This finding is related to the discussion in Acemoglu et al. (2015b) that a more densely interconnected financial network is associated with a more stable financial system when shocks are sufficiently small but with greater fragility when shocks are sufficiently large. The architecture of a network, then, has significant implications for systemic risk. The rest of the paper is organized as follows. After a literature review, Section 2 presents a

7

Haldane (2013) uses this phrase to describe the densely interconnected nature of financial networks, and this conjecture has been confirmed by Acemoglu et al. (2015b).

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partial equilibrium model to illustrate the propagation of financial shocks. Section 3 discusses my empirical findings on the propagation of shocks. Section 4 presents a general equilibrium model with size adjustment and deferred payments on trade credit, and Section 5 calibrates the model and forms quantitative predictions. Finally, Section 6 summarizes the findings and discuss their implications. Literature review. This project fits into three strands of literature, namely (1) production networks, (2) trade credit, and (3) financial frictions. Long and Plosser (1983) inaugurate the study of sectoral co-movements using a network model, sowing the seeds of a rich literature that has focused on the aggregate volatility generated by idiosyncratic shocks.8 As di Giovanni et al. (2014) present, two effects are at work. First, owing to the linkages effect, idiosyncratic shocks have sizable aggregate effects when the input-output linkages among firms are strong (Acemoglu et al., 2012, 2015c; Bak et al., 1993; Conley and Dupor, 2003; Dupor, 1999; Foerster et al., 2011; Horvath, 1998, 2000; Jones, 2011, 2013; Levine, 2012; Shea, 2002, etc.). Second, owing to the direct effect, idiosyncratic shocks can contribute directly to aggregate fluctuations (Carvalho and Gabaix, 2013; Gabaix, 2011; Jovanovic, 1987). Of particular note in this regard is the study by Acemoglu et al. (2015a) of the propagation of supply and demand shocks through input-output and geographic networks. My emphasis here, however, is on the transmission of financial shocks in the input-output structure. In research on the production network, financial frictions were not considered until the study by Bigio and La’O (2016). The present paper, like those of Su (2014) and Altinoglu (2018), build on Bigio and La’O (2016) by taking network-based approaches to the study of the propagation of

8

There is also a branch of the literature on the propagation of shocks in financial networks, e.g., Allen and Gale (2000), Acemoglu et al. (2015b). This paper focuses on the propagation of financial shocks in production networks.

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financial shocks. My paper and these other three address these issues in distinct ways, particularly with regard to the nature of the financial friction investigated. Unlike Bigio and La’O (2016), my approach considers firms’ financial linkages; and while Su (2014) presents a network model that accommodates financial frictions in the capital input, that model does not account for financial frictions in inter-firm trade. The independent work by Altinoglu (2018) has demonstrated the importance of trade credit in business fluctuations, but there are a number of substantive differences with my paper. In Altinoglu (2018), trade credit always amplifies financial shocks, whereas in my paper it may either amplify or attenuate financial shocks depending on the nature of the shocks. Moreover, in my paper, trade credit is allowed to adjust through size variation and deferred payments. Firms commonly increase trade borrowing during the contraction period of bank loans (see Nilsen, 2002) and delay repayments of trade debt during times of financial distress (see Cu˜nat, 2007). Incorporation of these features into the model is important when assessing the role of trade credit in the propagation of financial shocks. Several theories have been put forward to explain why suppliers provide trade credit to their customers (e.g., Burkart and Ellingsen, 2004; Cu˜nat, 2007; Peterson and Rajan, 1997). My analysis follows that of Kiyotaki and Moore (1997) in emphasizing the role of trade credit in the propagation of shocks. Regarding the third strand of inquiry, financial frictions have been extensively studied in the literature on the 2008-2009 financial crisis (e.g., C´urdia and Woodford, 2011; Gertler and Karadi, 2011; Gertler and Kiyotaki, 2010; Jermann and Quadrini, 2012; Perri and Quadrini, 2018). In particular, Perri and Quadrini (2018) present the international transmission of credit shocks through the cross-country ownership of shares of firms. This paper builds on these previous approaches in order to elaborate an input-output model that incorporates trade credit for the study of the impact 7

of financial shocks.

2

The Production Network with Trade Credit

In this section, I present a partial equilibrium model of an input-output economy in which the interconnected production and financial linkages among firms lead to the propagation of shocks.

2.1

The Environment

Unlike the situation in a horizontal economy, firms in a network are interconnected through trade. I consider here a network economy with exogenous interest rates and levels of trade credit. In particular, there are N sectors indexed by i = 1, · · · , N , each of which produces one type of product. The firms within each sector are homogeneous and competitive. Those in Sector i produce product mi using a Cobb-Douglas production function given by ij 1−αi mi = zi liαi (ΠN , j=1 mij )

ω

(1)

where mij denotes the amount of product j used by Firm i, li represents labor, and zi denotes technology. The exponent ωij denotes the share of good j in the total intermediate input use of Firm i and captures the production network structure. There is a working capital requirement for labor and intermediate inputs. Thus, firms need to borrow from banks at the beginning of the production period in order to pay for the labor cost and for the part of intermediate inputs that is not financed through trade credit. The interest rate of bank credit, Ri , is exogenous. Financial shocks in this paper refer to unexpected changes in Ri . To reduce the need to borrow from banks, producers could defer a proportion of their inter-

8

mediate input payments using trade credit. A proportion θij of the intermediate input payments to Supplier j is paid after production without any explicit borrowing costs.9 Nonetheless, as discussed below, the trade credit interest rate is implicit in the product price. All firms supply inputs that enter the production of the final good. The final output of the economy is −ζi ζi yi , Y = ΠN i=1 ζi

where yi represents the intermediate output i used in the final production and ζi the share of product i in the final output. Unlike intermediate firms, final producers pay the inputs at the end of the production period at price pi . Price normalization implies that the aggregate price of the economy ζi is P = ΠN i=1 pi = 1. The market clearing condition of goods is mi =

2.2

 j

mji + yi .

Solving the Model

In this economy, each firm solves the following problem: max

N li ,{mij }N j=1 ,{mji }j=1 ,yi

N 

[(1 − θji )Ri + θji ]pji mji + pi yi − wli Ri −

j=1

+Φi

 ω zi liαi (Πj mijij )1−αi

−



 mji − yi ,

N 

[(1 − θij )Ri + θij ]pij mij

j=1

(2)

j

where pij denotes the price of product j paid by Firm i, w is wages, and Φi is the Lagrangian multiplier, which corresponds to the marginal benefit of producing one unit of product. The first term represents the benefit of selling products to downstream firms. The marginal benefit of selling one unit of mji is [pji + (Ri − 1)(1 − θji )pji ], where the second part of this term represents the 9

Following Kiyotaki and Moore (1997), the implicit trading contract involves a form of debt contract; thus, product payments are staggered, and a proportion is paid in advance as a form of down payment while the rest is paid upon the delivery of products.

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benefit derived from savings in borrowing costs. The total working capital requirement for intermediate inputs is

N

j=1 (1−θij )pij mij .

Likewise,

Firm i also receives (1 − θji )pji mji from Customer j and has account receivables θji pji mji . The total working capital gain from trade is

N

j=1 (1

− θji )pji mji . In these ways, firms are linked

through both production and trade credit networks, and trade credit generates a liquidity-sharing channel among firms. I draw attention to differences between the model presented here and that of Bigio and La’O (2016). While firms in both models face a working capital requirement for intermediate inputs, in Bigio and La’O (2016), firms are not linked financially, while they are here. That study assumes, rather, that (i) payments are settled upon the delivery of products and that (ii) firms pay intermediate inputs in advance of production (i.e., at the beginning of the production period) - although the sale revenue therefrom is not realized until the delivery of the product (i.e., at the end of the production period). In the absence of financial linkages among firms, therefore, the working capital requirement is stronger in the model of Bigio and La’O (2016) than in the one presented here. I discuss these issues further in Section 5.3. The first-order conditions indicate that the price of product i paid by Firm j can be expressed as pji = pi /[θji + (1 − θji )Ri ].

(3)

In practice, price and trade credit are bundled together in the contracts. Because producers value early payments, higher trade credit is associated with relatively higher product prices; that is, the implicit cost of trade credit is presented in the intermediate input price. Thus, for instance, according to the terms of a typical 2/10 Net 30 two-part trade credit contract, customers who

10

pay within 10 days of delivery receive a 2% discount while those who do not have to pay the full amount within 30 days. The implicit annual interest rate for this type of agreement is 43.5% (see Peterson and Rajan, 1997). The high interest rate arises because of an insurance premium and a default premium as argued by Cu˜nat (2007). From this perspective, firms offer trade credit as a means of price discrimination. Moreover, the model assumes that a firm’s trade credit cost depends on the borrowing costs of its suppliers but not on its own. In reality, suppliers have both an information advantage and a comparative advantage over banks in terms of liquidating collateral assets (see Appendix A). In light of these considerations, I simplify the model by assuming that there is neither friction in the inter-firm financing nor any explicit cost of trade credit. The equilibrium levels of firm-level output and the aggregate output are functions of productivity levels and interest rates. Let Ω denote the input matrix with entries (1 − αi )ωij , which capture the amount of j used as an input in producing $1 worth of i output (i.e.,

Salesj→i ). Salesi

Further, v de-

notes the Leontief inverse matrix of (I − Ω )−1 . ζ is a vector of the final share (ζi ). v is a vector of zi ). vζ with entries vi . z denotes a vector of the log productivity deviation from steady state level (˜ ˜ i ). R is a vector of the log interest rate deviation from steady state level (R Proposition 1. For any labor input l, the aggregate output (GDP) is given by

Y =

Πi Ξvi i zivi Ri−αi vi Πj



(1−θij )Ri +θij (1−θij )Rj +θij

1 − Θ2 (I − Θ1 )−1 ζ

−ωij (1−αi )vi l.

(4)

1. When interest rates are homogeneous across firms, i.e., Ri = Rj , ∀i, j, then Y = Πi Ξvi i zivi l. ¯ the log deviation of the 2. Assuming that the steady state borrowing costs of all firms are R, aggregate output from its steady state is given by  Y˜ = ζ [v  z − R − v  (I1 ◦ Ω − I2 )R] + f (R).

11

(5)

In Equation 4, Ξi ≡ αiαi (1 − αi )(1−αi ) Π(ωij )ωij (1−αi ) is a constant. ◦ represents the Hadamard (1−θ )R +θ

ωij (1−θijij )Rji +θijij . Θ2 is a vector with entries product. Θ1 is a matrix with entries (1 − αi )ˆ 1) +



ωij (1−αi ) j (1−θij )Ri +θij (1 − θij )(Ri

− Rj ). In Equation 5, I1 is a matrix with entries

is a diagonal matrix with diagonal elements (1 − αi )



ωij θij ¯ ij ] . j [(1−θij )R+θ

αi (Ri Ri

−

θij ¯ ij ] . [(1−θij )R+θ

I2

f (R) is a term that includes

the log deviation of l and the denominator of Equation 4. Finally, the aggregate labor l equals 

i li .

Proofs of the proposition are presented in Appendix B.

Notably, the coefficient for the aggregate labor l in Equation 4 represents the total factor productivity of the network economy. This coefficient is affected by the production cost owing to financial friction, which is captured by the numerator; it is further affected by the profits, which are captured by the denominator. In a hypothetical situation in which financial profits are discarded, the denominator would be 1. In another situation in which financial shocks are symmetric (i.e., Ri = Rj , ∀i, j), the input price discount 1/[(1 − θij )Rj + θij ] would cancel out the borrowing cost of the intermediate input (represented by [(1 − θij )Ri + θij ]) according to Equation 3. Thus, the liquidity-sharing channel perfectly absorbs the financial distortion, and Proposition 1.1 holds. However, when financial shocks are asymmetric (i.e., Ri = Rj , for at least one pair of {i, j}), the liquidity-sharing channel cannot eliminate the financial distortion. In fact, the trade credit network structure plays an important role in the aggregate effect of asymmetric financial shocks, which in turn not only affects the marginal cost of production but also distorts the allocation of commodities. This is related to the finding by Bigio and La’O (2016) and Jones (2013) that sectoral distortions create aggregate effects by means of the network architecture. The input misallocation at the micro level, then, affects the total factor productivity at the aggregate level. Trade credit, however, may attenuate or amplify the aggregate impact of financial shocks, as discussed presently. In Equation 5, the coefficients for productivity z and borrowing cost R are the influence vectors. 12

These vectors capture the propagation of firm-level changes in productivity and in borrowing costs to other firms and, ultimately, the aggregate impact of the changes. The productivity influence vector equals v and resembles the one discussed in the existing network literature (e.g., Acemoglu et al., 2012; Bigio and La’O, 2016). Each element vi of the vector corresponds to the well-known notion of the Bonacich centrality (e.g., Acemoglu et al., 2015c). Nonetheless, the influence vector of financial friction (or financial influence vector) is distinct from both the productivity influence vector and the Bonacich centrality. Because this vector is a non-log-linear function of R, the financial influence vector cannot be expressed analytically. Equation 5, however, shows that the vector depends on [I + v  (I1 ◦ Ω − I2 )] ζ. The second term in the square brackets captures the aggregate effect of the trade credit structure. In Section 5.4, I use a numerical approach to present the financial influence vector. The financial influence vector also carries a credit policy implication. Thus, for example, should policymakers wish to facilitate lending during times of financial distress, they must choose the types of sectors to target. Given that financial influence is equal to the aggregate impact of changes in Ri , an effective credit policy would involve injecting liquidity into those sectors with the largest ratio of sectoral financial influence to total sectoral borrowing. This conclusion is connected to the notion of “distortion centrality” by Liu (2017), a statistic defined as the ratio of sectoral influence in a frictionless economy to Domar weight. Specifically, Liu (2017) shows that distortion centrality is associated with the effect of micro-level subsidies on the aggregate output. Proposition 2. In this economy, the vector of Domar weight, defined as the sectoral size relative to the total factor income

pi mi , wl

equals 

(I − Θ1 )−1 ζ . d= 1 − Θ2 (I − Θ1 )−1 ζ 13

This vector thus differs from the productivity and financial influence vectors in an economy characterized by financial friction. Hulten (1978), Bigio and La’O (2016), and Liu (2017) have also found that the influence vector cannot be equal to the vector of equilibrium shares of sales - i.e., the Domar weight - in situations of market imperfection. On the contrary, the Domar weight equals the productivity influence vector in the absence of financial friction, in which case Ri = 1 ∀i, Θ1 = Ω, and Θ2 = 0.

2.3

Upstream vs. Downstream Propagation of Financial Shocks

ˆ denote the output I turn now to the propagation of financial shocks in the production chain. Let Ω mi p i , which correspond to matrix with entries (1 − αi )ωij m j pj

from j to i normalized by the sales of Firm j (i.e.,

mij pij . mj pj

ˆ captures the sales Entry-ij of Ω

Salesj→i ). Salesj

¯ the vector of Proposition 3. Assuming that the steady-state borrowing costs of all firms are R, output deviation from the steady state level follows ˆ  ◦ I3 − I4 )]R + f (R) · 1, −R −[v  (I1 ◦ Ω − I2 ) + vˆ (Ω m = v  z  

 

  own effect

downstream effect

(6)

upstream effect

ˆ −1 . Trade credit affects the relative strength of upstream compared with downwhere vˆ ≡ (I − Ω) stream propagation of financial shocks. In particular, it amplifies the downstream propagation and attenuates the upstream propagation. In Equation 6, I3 is a matrix with entries elements

 j

¯ (1−αj )ˆ ωji (1−θji )R ¯ ji ] . [(1−θji )R+θ

¯ (1−θji )R ¯ ji ] . [(1−θji )R+θ

I4 is a diagonal matrix with diagonal

Proofs of the proposition are presented in Appendix B.

Notably, in a general network structure, Firm i could deliver products to Firm j and also deliver products to suppliers of Firm j. It is therefore important to characterize both the direct and the 14

indirect linkages among firms. The mathematical representations of upstream and downstream propagations follow the discussion by Acemoglu et al. (2015a). Financial shocks propagate downstream to customer industries. Mathematically, the geometric summation of the input matrix Ω, which equals v  , captures both the direct use (represented by Ω) and the indirect use (represented by the higher-order terms, Ωn , n = 2, 3, . . . ) of inputs in the production network.10 The automobile production chain provides a good example. In this case, ωauto,glass measures the direct input of glass in the production of automobiles, and ωglass,sand measures the direct use of sand in the production of glass. ωauto,glass · ωglass,sand , which appears in Ω2 , captures the indirect use of sand in automobile production and describes the propagation of shocks from sand mining factories to the automotive industry. Thus, the first term in the square brackets of Equation 6 captures the impact of the downstream propagation of financial shocks. Matrices I1 and I2 capture the role of trade credit in the downstream propagation, as discussed below. In addition, financial shocks propagate upstream to input-supplying industries. vˆ captures both ˆ Thus, to the direct and the indirect supply of a product to other firms through the output matrix Ω. ˆ glass,sand captures the indirect supply that sand mining return to the previous example, ω ˆ auto,glass · ω factories provide to the automotive industry. This term therefore describes the propagation of shocks from automobile production to sand mining. In turn, the second term in the square brackets of Equation 6 captures the impact of the upstream propagation of financial shocks. Matrices I3 and I4 capture the role of trade credit in the upstream propagation, as discussed below. Upstream propagation. The upstream propagation that affects suppliers can be characterized In v = I + Ω + Ω2 + · · · + Ω∞ , the second term captures the direct use and the following terms capture the ˆ + ···Ω ˆ n , the second term captures the direct supply and the following terms indirect use. Similarly, in vˆ = I + Ω capture the indirect supply. Notably, v is the Leontief inverse of the economy. 10

15

by the change in intermediate input demand. When Firm j is a supplier of Firm i, two factors impact the intermediate input demand mij after a positive Ri shock, namely (i) the output effect (or scale effect) and (ii) the input substitution effect of financing cost variation. The output effect reduces the intermediate input demand because firms decrease the quantities that they produce after increases in the cost of production. Conversely, the input substitution effect increases the intermediate input demand. Because the presence of trade credit in effect defers a portion of the intermediate input payments, the response of the marginal cost of the intermediate input, pij [(1 − θij )Ri + θij ], is less sensitive to Ri shocks than is the response of the marginal cost of labor, wRi . For this reason, Firm i substitutes labor with intermediate inputs after positive Ri shocks. The substitution effect, then, attenuates the negative impact on upstream firms. Notably, as trade credit increases, the substitution effect becomes stronger and the upstream propagation diminishes. Mathematically, these two effects are captured by I3 and I4 . In the extreme case that θij = 1 ∀i, j, I3 = I4 = 0, no upstream propagation occurs because the output and substitution effects cancel each other out in the Cobb-Douglas production structure. Downstream propagation. The downstream propagation that affects customers can be characterized by the change in product prices. When Firm k is a customer of Firm i, two factors impact the product price pki after a positive Ri shock, namely (i) the cost effect and (ii) the discount effect of financing cost variation. The cost effect would increase pki ; the discount effect, by contrast, would decrease pki . Because firms value early payments, they engage in price discrimination with regard to downstream buyers through discounts, as represented in Equation 3. As the financing cost of Firm i increases, the discounts that it offers customers for early payments

16

also increase. Thus, the discount effect attenuates the negative impact of the shock to buyer k.11 As trade credit decreases, the discount effect becomes stronger and the downstream propagation diminishes. Mathematically, the two effects are captured by I1 and I2 . In the extreme case that θki = 0 ∀i, k, I1 = I2 = 0, the downstream propagation effect disappears. The last term in Equation 6 is a constant term multiplying the vector of ones (see Appendix B for further detail). As discussed in the previous subsection, this term is a product of the profits; it does not work through the input-output linkage and impacts firm-level production homogeneously. In sum, trade credit amplifies the downstream propagation of financial shocks and attenuates their upstream propagation. Its ultimate effect on the aggregate impact of financial shocks differs depending on the locations (within the network) of the firms that are subject to the shocks. Specifically, when the shock affects more directly upstream firms, trade credit amplifies the aggregate impact, whereas it attenuates the aggregate impact if the shock affects downstream firms. This conclusion is confirmed by the qualitative analyses presented in Section 5.

3

Empirical Evidence

I now present some empirical evidence about the propagation of financial shocks. In particular, I compare the strength of upstream and downstream propagation in a manner similar to the method employed by Acemoglu et al. (2015a). The main estimating equation is a direct analog of Equation 6 that takes the form of

Δmi = β si shocki + β up U Pi + β down DOW Ni + i + constant, 11

(7)

Notably, in the absence of price discrimination, the discount effect disappears while the downstream propagation becomes stronger than is suggested by the model. See Appendix F for a quantitative analysis of the propagation of financial shocks in this scenario.

17

where Δmi is the change in sectoral output, and shocki is the idiosyncratic financial shock. U Pi and DOW Ni stand for shocks working through the network. Specifically, U Pi measures the shocks to customers of a sector that flow up the production chain, while DOW Ni measures the shocks to suppliers of a sector that flow down the production chain. These shocks are calculated as follows: U Pi =



ij vup · shockj ,

(8)

ij vdown · shockj ,

(9)

j

DOW Ni =

 j

ij ˆ  ◦I3 −I4 ) and v ij is the i, j−th element of v  (I1 ◦Ω−I2 ). where vup is the i, j−th element of vˆ (Ω down

3.1

Data and the Construction of Idiosyncratic Financial Shocks

The industry-level data for manufacturing are obtained from the Industrial Production Index. This index, released monthly by the U.S. Federal Reserve Board, is accessed to construct Δmi . Specifically, I utilize the data at the four-digit NAICS level and match 49 subsectors (in the manufacturing and utilities industries) to the U.S. input-output table discussed below. The total output of these subsectors accounts for 33% of the output of the entire economy and 25% of the GDP in the U.S.. ˆ I employ the make-use table of the 2002 In order to measure links among industries (Ω and Ω), Input-Output (IO) Accounts created by the Bureau of Economic Analysis (BEA) at the 4-digit NAICS level but exclude FIRE (finance, insurance, and real estate) industries.

12

I construct the idiosyncratic financial shock (shocki ) using the Dealscan syndicated loan database

12

The BEA reports the IO tables at the detailed industry level at five-year intervals. The input-output network at the sectoral level is relatively stable; thus the results are unaltered when the 2007 IO table is applied instead.

18

following the method of Chodorow-Reich (2014).13,14 Let shocki,k be a measure of the change in the loan supply of bank k to all borrowers apart from Firm i before and during the financial crisis, so that

 shocki,k =

0.5

pD k,j,crisis Dk,j,crisis

j=i j=i

pD k,j,normal Dk,j,normal

,

where Dk,j,t equals 1 when bank k makes a loan to Firm j within period t and pD k,j,t denotes bank k’s share in this loan.15 crisis represents the 9-month period from October 2008 to June 2009 and normal the cumulative 18-month period from October 2005 to June 2006 and from October 2006 to June 2007. Next, I calculate shocki =



pD k,i,last shocki,k ,

k∈s

where s denotes the set of banks that participate in the last pre-crisis loan issuance of Firm i. Finally, I construct sector-level financial shocks using the median shocki of all firms within each subsector according to the BEA IO classification.16 This method identifies financial shocks to 102 subsectors during the 2008-2009 financial crisis, the total output of which accounted for 85% of the U.S. economy excluding FIRE industries. These subsectors are the suppliers and customers of the 49 subsectors with the Δmi measure. shocki , along with U Pi and DOW Ni , capture both the direct and the indirect liquidity impacts to these 49 subsectors.

13

The Dealscan syndicated loan database contains the borrowing history of both public and private firms in the syndicated loan market; the sample used here contains loans issued to non-FIRE U.S. firms. 14 Similar methodologies have been applied by Ivashina and Scharfstein (2010) and Santos (2011), though the focus in those papers is on bank outcomes. 15 In most cases, Dealscan does not report the actual loan shares; when these data are missing, I use the average share retained by lead lenders (who retain 60%) and participants (who share the rest) following Chodorow-Reich (2014). Furthermore, “lead arranger” and “agent” are considered lead banks following Ivashina and Scharfstein (2010). 16 In particular, firms in the Dealscan data are assigned to BEA IO industries based on their primary SIC code and a SIC-IO list that I compiled manually.

19

Table 1: Empirical Results: The Impact of Financial Shocks (1)

(2)

(3)

(4)

Δm2009.09 i Shocki UPi

No trade credit

Full trade credit

US average

No trade credit

1.808**

2.302***

1.906**

[0.710]

[0.847]

[ 0.739]

1.227

1.997**

[ 2.002]

[ 0.814]

0.935 [0.990]

DOWNi DownMeasure R

2

(5)

(6)

(7) Δm2009.06−2010.05 i

Δm2009.12 i Full trade credit

US average

1.667***

0.878

1.554**

[ 0.584]

[ 0.749]

[ 0.606]

[ 0.439]

4.143**

2.933**

[ 1.642 ]

[ 1.189 ]

1.360***

2.072

0.724

0.585

-0.833

-0.727

[1.472]

[ 1.358]

[ 1.302]

[1.114 ]

[0.807 ]

-0.255**

-0.212*

-0.237*

-0.225**

-0.194*

-0.246**

-0.182**

[ 0.115]

[ 0.115]

[ 0.120]

[ 0.094]

[ 0.102]

[ 0.099]

[ 0.072]

0.20

0.20

0.22

0.21

0.11

0.22

Δm2009.09 i

log(m2009.09 ) i

log(m2008.09 ). i

0.27 Δm2009.12 i

Notes: denotes the year-on-year sectoral output change as of September 2009, calculated as − denotes the denotes the average 12-month output change compared with 1-year before, calculated year-on-year sectoral output change as of December 2009. Δm2009.06−2010.06 i 2010.05 2009.05 as [log( 2009.06 mti ) − log( 2008.06 mti )]/12. The dependent variables are the changes in industrial production of the 49 subsectors. The independent variables are constructed using the financial data of the 104 subsectors that are the suppliers and customers of the 49 subsectors as described above. ∗ ∗ ∗, ∗∗, and ∗ represent coefficients significant at the 1%, 5%, and 10% level. Absolute values of t−stats are in brackets.

3.2

Empirical Results

Table 1 presents the empirical results following regression 7 while controlling for the location of each sector in the production network denoted by DownMeasure.17 The dependent variable, Δmi , is measured at various time horizons following the shock. Columns (1) and (4) present the regression results imposing θi = 0 so that vdown = 0. Columns (2) and (5) present the regression results imposing θi = 1 so that vup = 0. Finally, Columns (3), (6), and (7) present the regression results imposing θi = 0.45, which is the average trade credit level in the United States (as explained in Section 5). Clearly, the upstream effects that result from financial shocks to a sector’s customers strongly influence the output of the focal sector. As shown in the last column, a 1% decrease in the loan supply of a sector translates into a 1.4% decrease in its output, and a 1% decrease in the loan supply of its customers would decrease its output by 2.9%. Although this exercise accounts for only the impact of financial shocks on the manufacturing and utility subsectors, these subsectors represent 17

DownMeasure estimates the relative downstreamness of a sector; it is constructed using the methodology of Antr´as and Chor (2013) and the 2002 IO table. Specifically, DownMeasure = {[I − Ω]−2 ζ}−1 .

20

a significant portion of the U.S. economy.

4

General Equilibrium

In this section, I extend the model presented in Section 2 to a general equilibrium setting for calibrating and studying the U.S. economy. I also introduce two ways to adjust trade credit, namely size and payment schedule. The trade credit is exogenous in Section 2 but flexible in this section.

4.1

Households

The preference of households is given by U (C, l) =

l1+ψ C 1−χ − . 1−χ 1+ψ

(10)

The budget constraint faced by households is C = wl + Π,

(11)

where Π represents profit transfers to households.

4.2

Adjustment of Trade Credit Size

According to empirical studies of trade credit, firms increase their accounts-payable during periods of contraction in bank loans and open market credits and shrink it when their suppliers are suffering financially (e.g., Costello, 2018; Nilsen, 2002). This finding motivates the inclusion of the adjustment of trade credit size in the model. With this addition, Firm i can adjust its level of accounts-payable θij while Supplier j offers a price schedule pij based on θij according to Equation 3. The supplier is indifferent because the price schedule homogenizes the marginal benefit of 21

selling products to customers who request various levels of θij . In addition, there is a quadratic adjustment cost C(θij , θ¯i ) = ς(θij − θ¯i )2 per dollar unit of input purchases paid by Firm i, where θ¯i is the steady state trade credit of firms in Sector i. The cost is zero when θij = θ¯i . The cost size is controlled by ς, the magnitude of which correlates negatively with the flexibility of the adjustment. Under such circumstances, managers make a two-step decision. Initially, they set the level of trade credit (θij ) for each intermediate input purchase. Next, they choose {li , mij , mji , yi } given {θij , θji }. The Optimal Level of Trade Credit. pij increases with θij , since suppliers naturally value early payments, and managers accordingly choose a trade credit level θij in the first step so as to minimize the unit intermediate input cost. The trade-off for adjusting trade credit is as follows. On the one hand, increasing θij confers the benefit of reducing bank credit and interest costs. On the other hand, increasing θij increases the intermediate input price pij . Managers must, then, solve the following problem: min [(1 − θij )Ri + θij ] pij + C(θij , θ¯i )pij θij

s.t.

pij = pj /[(1 − θij )Rj + θij ]

(12)

Therefore, the optimal level of trade credit is θij = f (ς, θ¯i , Ri , Rj )

(13)

with ∂θij /∂Ri > 0,

∂θij /∂Rj < 0,

and

θij = θ¯i , if Ri = Rj .

θij is an increasing function of Ri and a decreasing function of Rj . Further, trade credit is more

22

sensitive to the financial conditions of the two trading parties when ς is small. In the extreme case that ς = 0, trade credit becomes fully flexible, under which conditions θij = 1 when Ri > Rj and θij = 0 when Ri < Rj . The structural form of C(θij , θ¯i ) governs the flexibility of the adjustment and the equilibrium of trade credit. It is natural, for instance, to assume that the downward adjustment of trade credit is less costly than its upward adjustment. Should, for example, C(θij , θ¯i ) = max{ς(θij − θ¯i )3 , 0}, the asymmetric adjustment cost function would involve a positive upward adjustment cost and zero downward adjustment cost; consequently, θij = 0 when Ri < Rj and θij = f (ς, θ¯i , Ri , Rj ) otherwise. In fact, the downward adjustment of trade credit is nonzero. One implicit cost of reducing trade credit is the loss of the opportunity to receive help with financing from suppliers, for example in the case of temporary illiquidity, by delaying repayment on trade credit. I will return to this issue in the next subsection. Notably, the trade credit adjustment mechanism strengthens the liquidity-sharing channel further and facilitates the extension of credit from less costly sources. That is, a firm increases accounts-payable when it finds that bank loans are becoming more costly than trade credit and shrinks its accounts-payable otherwise. This is consistent with the empirical literature on trade credit adjustment. According to Gao (2014), trade credit plays an important role as an inter-firm financing channel in terms of sharing liquidity, and, according to Costello (2018), suppliers pass on negative liquidity shocks to downstream firms through reductions in trade credit offered on each sale. Besides, Raddatz (2008) finds that an increase in the use of trade credit along the product chain that links two sectors increases the correlation between them.18

18

Other channels may also play significant roles in these production correlations, such as employment comovements at the sectoral level, by means of the intersectoral linkages presented by Kim and Kim (2006).

23

Once trade credits have been determined, each firm solves the following problem: max

N li ,{mij }N j=1 ,{mji }j=1 ,yi

N 

[(1 − θji )Ri + θji ]pji mji + pi yi − wli Ri −

j=1

−

N 

N 

[(1 − θij )Ri + θij ]pij mij

j=1



C(θij , θ¯i )pij mij + Φi zi liαi (Πj mijij )1−αi − ω

j=1



 mji − yi .

(14)

j

This problem differs slightly from Equation 2 owing to the addition of one additional cost term, N j=1

C(θij , θ¯i )pij mij . The first-order conditions are presented in Appendix C. Obviously, the

size adjustment of trade credit attenuates the direct impact of a Ri shock through the reduction of Firm i’s financing cost. Thus, this adjustment also weakens the spillover effect of the shock along the supply chain. In addition, the size adjustment averages out the interest rates paid by firms through liquidity reallocation, thereby weakening the commodity misallocation effect of asymmetric shocks (as discussed in Section 2).

4.3

Adjustment of Trade Credit Payment Schedule

When faced with financial distress, firms tend to obtain credit from their suppliers by delaying their repayment of trade credit (e.g., Cu˜nat, 2007; Cu˜nat and Garcia-Appendini, 2012). Cu˜nat (2007) finds that 46% of the firms covered in the 1998 National Survey of Small Business Finance data had made some trade credit payments after the due date in the preceding year. According to Love et al. (2007), a temporary increase in trade credit during a financial crisis is likely to result from the accumulation of unpaid credit. Suppliers are willing to extend more credit because they have an implicit equity stake in the firms with which they do business (see Peterson and Rajan, 1997), for whom they serve as both debt collectors and insurance providers (see Cu˜nat, 2007). On the one hand, suppliers prefer to maintain business relationships because of the high

24

cost of establishing them; on the other hand, they may have both an information advantage and a comparative advantage over banks in terms of liquidating collateral. It is for these reasons that suppliers tend to renegotiate their claims when a client firm encounters financial distress, whereas banks tend to follow a strict liquidation policy (e.g., Berger and Udell, 1998; Huyghebaert et al., 2007; Mann, 1997; Peterson and Rajan, 1997). The following discussion extends the model with trade credit forbearance in light of these considerations. To incorporate trade credit forbearance, suppose that the production process repeats over time. Goods and labor markets clear in each period, but trade credit terms can be extended for one more period. I further assume that Ri of the current period is realized before the repayment of accountspayable for the previous period. When Firm j is a supplier of Firm i, Firm i can delay repayment of a portion τij of its accounts-payable for the previous period to Firm j as a means to release its financial tightness. However, renegotiation of the trade credit payment schedule comes at the cost of a steep interest rate penalty, for Firm j charges an interest rate of (Rj + η) on the deferred payment, with Rj denoting the interest rate of Firm j’s bank credit and η capturing the penalty for the forbearance. In order to extend additional credit to Firm i, Firm j rolls over its bank loans from the previous period. As a consequence, banks raise Firm j’s interest rate to Rj = Rj0 + ρ



ˆ ij , τij λ

(15)

i

where Rj0 denotes the interest rate without debt rollover. The second part of the equation accounts for the facts that banks charge a premium on debt rollover and that Firm j is exposed to counterparty risk.



ˆ represents the ratio of the total rollover to the total bank loan of the previous

i τij λij

25

period, with ˆ ij ≡ λ

wˆ ˆlj +



ˆ ij pˆij θˆij m

k (1

 − θˆjk )m ˆ jk pˆjk − k (1 − θˆkj )m ˆ kj pˆkj

.

λij denotes the ratio of accounts-receivable from Firm i to Firm j’s total bank loan. Variables with ˆ denote corresponding values from the previous period. Finally, ρ controls for the sensitivity of the interest rate to debt rollover and measures the contagion effect of financial shocks. When ρ = 0, suppliers are unaffected by trade credit forbearance. By contrast, when ρ is sufficiently large, suppliers may encounter severe financial difficulties and be forced to defer payments on their own trade credit, thus creating further illiquidity problems along the supply chain in a kind of chain reaction similar to the one discussed by Kiyotaki and Moore (1997).19 Under these circumstances, managers make a two-step decision. First, they negotiate the amount of the deferred payments with their firms’ suppliers, i.e., τij . Following these negotiations, the effective interest rate of Firm i becomes Ri∗ =

1−

N 

τij νij

Ri +

j=1

N 

τij νij (Rj + η) ,

(16)

j=1

with νij ≡

wli +



ˆ ij pˆij θˆij m  . k (1 − θik )mik pik − k (1 − θki )mki pki

τij νij represents the ratio of the deferred trade credit to Firm i’s total bank loan. Thus, the effective interest rate is an average of the rates for bank credit and deferred trade credit weighted by their relative sizes, this rate being less than or equal to Ri . Afterward, firms produce products in the manner discussed in Section 2 or Section 4.2 but with Ri∗ replacing Ri (see Appendix C). 19

The model in Altinoglu (2018) also takes into account the upstream spillover of the liquidity pressure, but, in that model, trade credit affects the financial constraint of firms directly through the assumption that the fraction of earning that constrains input cost (and thus serves as a parameter for Bigio and La’O, 2016) decreases exogenously in step with the firm’s level of accounts-receivable.

26

The Optimal Level of Payment Postponement. I assume that, during the negotiations, managers know the interest rates of connected firms and take them as given. Moreover, to simplify the problem, I assume that the negotiation is done separately and simultaneously with each supplier by minimizing the effective interest rate, as follows: min

{0≤τij ≤1}N j=1

1−

N 

τij νˆij

Ri +

j=1

N 

  ˆ ij + η τij νˆij Rj−i + ρτij λ

j=1

where Rj−i is the bank rate of Firm j before the negotiations (i.e., when τij = 0). Notably, each firm takes the interest rate of its suppliers before the negotiations as given, thereby creating a negative externality for the entire production sector. Managers approximate νij using the past period’s level νˆij .20 A trade-off is involved in delaying the repayment of trade credit. Notably, deferred payment occurs only when Ri > Rj−1 + η; otherwise, τij = 0. Thus, the benefit of increasing τij is a reduction in high-interest bank credit, while the cost is an increase in the interest rate on the deferred trade credit, which occurs because Rj increases with τij . Under these conditions, the optimal level of τij is as follows: ⎧ −i ⎪ ⎪ ⎨ Ri −Rˆj −η , if Ri > Rj−1 + η; 2ρλij τij = ⎪ ⎪ ⎩ 0, if Ri ≤ Rj−1 + η. Accordingly, firms delay repayment of trade credit and force the liquidity pressure upstream whenever the bank rate exceeds a threshold that is equal to the supplier’s interest rate plus η. At this point, suppliers would have to roll over their bank loans and thus be exposed to counter-party 20

I make this assumption for two reasons. First, the negotiations take place before either the finalization of the effective borrowing costs for all firms or the production process. Managers cannot predict νij without knowing the effective interest rate for all firms because {li , mik , pik , mki , pki } ∀k depends on the collective financial condition of all firms (see the derivation in Appendix B). Second, the optimal level of τij appears to be independent of νij as discussed below.

27

risk and high borrowing costs. It is in these respects that an idiosyncratic financial shock readily spills over to surrounding firms. Therefore, trade credit forbearance amplifies the propagation of financial shocks, in particular the upstream propagation. Ultimately, it also amplifies the aggregate economic fluctuations. The model proposed here thus has the capacity to explain the strong and sudden transmission of the financial distress from the U.S. automobile producers to their suppliers during the 2008-2010 automotive industry crisis, as discussed in the Introduction.

4.4

The Differing Effects of Large and Small Financial Shocks

In an economy that features both size adjustment and deferred payments on trade credit, firms use both margins only when shocks are sufficiently large to justify the forbearance option; otherwise, they adjust only the size. Generally speaking, the macroeconomic effect of trade credit forbearance dominates in the former case for two reasons. First, forbearance leads to illiquidity contagion and increases the borrowing cost of surrounding firms. Second, in practice, once forbearance occurs, suppliers increase the cost of the upward adjustment of trade credit as a consequence in the likelihood of default, thereby rendering the structure of the size adjustment more rigid. Trade credit, therefore, leads to a “robust-yet-fragile” production network, the typology of which plays an important role in the propagation of shocks. A production network that is highly interconnected financially is especially susceptible to large negative shocks but tends to be robust during moderate downturns. This finding is related to the argument of Acemoglu et al. (2015b) regarding the resilience of the financial system. In particular, highly connected financial networks remain relatively stable in the face of small shocks but become unstable in the face of severe shocks.

28

5

Quantitative Predictions

Now I quantitatively study the importance of trade credit for the propagation of financial shocks in the network economy.

5.1

Calibration

I calibrate the model using the U.S. data at the two-digit NAICS level, excluding the government, finance, and insurance subsectors.21 Input-output Structure, Labor, Intermediate Input Share, and Final Output Share. The inputoutput structure ωij is calibrated using the BEA IO table (as illustrated in Appendix Figure D.1), as is the final share ζi . The labor share αi and intermediate input share (1 − αi ) are calibrated using the BEA GDP by Industry Value-added Components Table (1998-2013) and the calibration method proposed by Su (2014) (see Appendix D). Parameters at the sectoral level are listed in Appendix Table D.1. Trade Credit. The trade credit size θij corresponds to accounts-payable over cost of goods sold.22 Table A.1 in the Appendix presents accounts-payable over cost of goods sold from all sectors based on the Compustat data (measured as the median of each sector in each time period and averaged from 2000 to 2014).23 Additionally, the U.S. Census Bureau’s Quarterly Financial Report (QFR) collects quarterly aggregate statistics on the financial results and positions of U.S.

21

The objective of the government is not profit maximization. The finance and insurance firms cannot be formulated using the production problem presented in Section 2 owing to the complexity of their investment strategies and balance sheet composites. Moreover, the trade credit of these two types of firms differs from that of goods producers. 22 Although accounts-payable is a stock variable, it is close to its flow value because the length of the trade credit period is generally less than a single quarter. 23 The financial and insurance sectors have accounts-payable over cost of goods sold at a level of 60. The balance sheets of these financial sectors are complicated, and the definition of accounts-payable therein differs from that used in other production sectors.

29

corporations. The QFR is more comprehensive than Compustat, but it only covers four industry sectors, namely mining, manufacturing, wholesale, and retail. All four measures of the standardized trade credit are relatively stable over the QFR’s sample period (2000q4-2014q4), as shown in Appendix Table A.2. Moreover, these measures using the QFR data are close to the measures using the Compustat data. I therefore calibrate θ¯i using the Compustat measure. I simulate the model for various values of ρ and η as well as for various types of adjustment cost functions. In the benchmark model, I set ς = 0.2, ρ = 1, η = 0.04 and use a quadratic cost function for size adjustment.24 Finally, I set χ = 0.2 and ψ = 0.5 following Bigio and La’O (2016) and many other studies.

5.2

Application: The Propagation of Financial Shocks along the Supply Chain

I now consider the importance of trade credit for the propagation of financial shocks and quantify the strength of their upstream and downstream propagation. Factors that are specific to certain firms, such as intermediate input share, final share, and trade credit, all have strong effects on the sensitivity of these firms’ output to shocks. In order to focus on the propagation effect along the production chain, I simulate a three-firm circle economy with the network structure illustrated in Appendix Figure F.2. Specifically, Firm 1 delivers to Firm 2; Firm 2 delivers to Firm 3; and Firm 3 delivers to Firm 1. The only difference among the firms is their relative location along the supply chain. 24

The choice of these three parameters is meant to be suggestive. In the calibrated economy, the trade credit size adjustment is 36% on average in the financial crisis exercise. In the case of forbearance, η = 0.04 corresponds to an annual rate of 17% on the forbearance penalty, which is close to the average annualized penalty rate measured by Cu˜nat and Garcia-Appendini (2012). ρ is at a level that leads to a non-trivial amount of deferred payments on trade credit and a premium on bank loan rollovers.

30

Table 2: 3-Firm Circle Economy: Responses to R2 Shocks (1) Size of R2 shock Trade credit structure

=0

(2) = 0.45

(3) 1% =1

(4)

(5)

(6)

10% Fixed Flexible

Flex (at 0.45)

(7)

(8)

20% Fixed Flexible

Δ%R1∗ Δ%R2∗ Δ%R3∗

0 1% 0

0 1% 0

0 1% 0

0 1% 0

0 10% 0

3.02% 9.85% 0

0 20% 0

7.98% 18.42% 2.04%

Δ%m1 Δ%m2 Δ%m3

-0.40% -0.76% -0.25%

-0.34% -0.76% -0.32%

-0.25% -0.76% -0.40%

-0.32% -0.74% -0.31%

-3.22% -7.07% -3.05%

-4.45% -6.82% -2.98%

-6.13% -13.10% -5.78%

-9.57% -12.58% -6.86%

Δ%Y

-0.47%

-0.47%

-0.47%

-0.46%

-4.49%

-5.19%

-8.49%

-10.69%

I calibrate this economy using the average levels of labor share and trade credit for the U.S. economy (as presented in the last row of Appendix Table D.1), the final share of each firm being 1/3. The percentage deviations for each variable are constructed in comparison with an economy that faces a long-run (or steady state) interest rate. The long-run interest rate is calibrated at a quarterly frequency and has an annual spread of 100 basis points between the corporate borrowing rate and the risk-free rate (following Gertler and Karadi, 2011).25 Table 2 presents how a R2 shock affects firms along the supply chain. The shock propagates upstream to affect Firm 1, downstream to affect Firm 3, and, ultimately, leads to aggregate changes in output. The first three rows of the table present the change in the effective borrowing rate of each firm and the following three rows the change in firm-level output. Result 1. trade credit, when its structure is exogenously fixed, amplifies the downstream propagation and attenuates the upstream propagation of financial shocks. The results of the simulation presented in the first three columns confirm this finding, which is consistent with the prediction in Section 2. Furthermore, owing to the homogeneity of firms, trade credit plays a limited role in the aggregate impact of financial shocks when the trade credit structure is fixed. Liquidity reallocation 25

Thus, the quarterly interest rate is 1.25% in an economy with a discount factor of 0.99.

31

among homogeneous firms generates no aggregate output impact. Result 2. The adjustment of trade credit size attenuates the propagation of financial shocks. A sufficiently small shock, such as a 1% increase in R2 , triggers only the size adjustment of trade credit, which in turn facilitates the extension of credit from less costly sources. Hence, both the propagation of the shock and its aggregate impact are attenuated, as is evident from a comparison of Columns (2) and (4). Result 3. Trade credit forbearance amplifies the propagation of financial shocks, especially upstream. Large financial shocks trigger both credit size adjustment and payment schedule adjustment. As shown in Columns (5)-(8), although trade credit forbearance relaxes the financial tightness of Firm 2, it generates a credit chain reaction. Specifically, a 10% R2 shock triggers forbearance of Firm 2’s trade debt and raises R1 . On the other hand, a 20% R2 shock not only raises R1 but also triggers forbearance of Firm 1’s trade debt and increases R3 . In other words, the credit forbearance transmits the liquidity pressure upstream along the supply chain, amplifying both the propagation and the aggregate impact of financial shocks. Finally, Table 2 also shows that the upstream propagation of financial shocks is stronger than the downstream propagation in economies with either a flexible trade credit structure or a fixed structure that has been calibrated to the U.S. data, which finding is consistent with the empirical exercise.26

26

It is also important to model trade credit as a means of price discrimination. As Table F.3 in the Appendix shows, in the absence of price discrimination, the downstream propagation is stronger than the upstream propagation, and liquidity reallocation among homogeneous firms generates an impact on the aggregate output. Both outcomes contradict my predictions here, and the former is also inconsistent with my empirical findings.

32

Table 3: Aggregate Effect of Financial Shocks (1)

(2)

Input-Output Trade credit Shock

US IO Fixed Asym

US IO Size adj. Asym

Δ%Y Δ%L Production cost Profits

-6.86% -6.73% -4.78% 4.65%

-6.19% -6.07% -4.31% 4.19%

-10.80% -10.75% -7.66% 7.61%

-10.53% -10.48% -7.46% 7.41%

0.036

0.032

0.025

0.023

std(Δ%mi )

5.3

(3)

(4)

(5)

(6)

(7)

US IO =1 Asym

US IO Fixed Sym

-6.95% -6.80% -4.84% 4.68%

-6.22% -6.07% -4.32% 4.17%

-6.34% -6.34% -4.48% 4.48%

-6.22% -6.07% -4.32% 4.17%

-10.08% -9.77% -7.01% 6.70%

-11.38% -11.16% -7.99% 7.77%

0.038

0.034

-

-

-

-

Benchmark economy US IO US IO US IO Delay Size + delay =0 Asym Asym Asym

(8)

(9)

(10)

Other economy Horizontal US IO US IO NA BL version Asym Asym Sym

Application: The Role of Trade Credit during the 2008-2009 Financial Crisis

I now apply the model to study the 2008-2009 financial crisis in order to explicate the aggregate impact of trade credit. Table 3 reports the impacts of the calibrated financial shocks on aggregate variables. The change in output (presented in the first row) has three components: change in labor, change in production cost, and change in profits (presented in the following three rows). In mathematical terms, the first term of Equation (5) captures the change in production cost and the second term captures the changes in both labor and profits. To begin this exercise, I simulate the benchmark model with two types of financial shocks, asymmetric and symmetric. The sectoral-level financial shocks were asymmetric during the 20082009 financial crisis and can be measured using the loan data described in Section 3. I present the sectoral-level liquidity contraction in Table E.1 and Figure E.1 in Appendix E. The liquidity contraction varied from 19% in the construction industry to 0.3% in the manufacturing industry. In the simulation, I consider a borrowing cost increase at a level that corresponds to the measured liquidity contraction, with Δ%Ri = −Δ%Liquidityi , such that the simulated liquidity contraction

33

approximates the observations in the data.27 The simulation results using asymmetric shocks are presented in Columns (1)-(6) of Table 3. In addition, I simulate the model with symmetric financial shocks constructed to be homogeneous across sectors and equal to the average of the sectoral-level shocks.28 The results are presented in Column (7). Furthermore, I simulate the model using six types of trade credit structures - fixed, with size adjustment, with forbearance, with both adjustment options, no credit, and full credit - as shown in Columns (1)-(6). Result 1. Trade credit, when its structure is exogenously fixed, attenuated the aggregate impact of financial shocks during the 2008-2009 financial crisis. As discussed in Section 2, trade credit amplifies the impact of shocks that affect upstream firms and attenuates the impact of shocks that affect downstream firms.29 Figure E.1 in the Appendix shows that, during the crisis, U.S. downstream sectors in general experienced stronger liquidity contractions than did upstream sectors. The implication is that the response of the aggregate output weakens as trade credit increases in the context of a fixed trade credit structure, as a comparison of Columns (1), (5), and (6) makes clear. When interest rate shocks are symmetric, however, the total factor productivity is independent of trade credit, in accordance with Proposition 1.1. The benchmark economy has an equilibrium Y that is the same as that in an economy with only a working capital requirement for labor. The change in aggregate output is thus equal to the change in labor, as shown in Column (7). Result 2. The adjustment of trade credit size attenuates the aggregate impact of financial shocks. First of all, firms substitute trade credit for bank credit as the latter becomes increasingly

27

As demonstrated in Bigio and La’O (2016), interest rates map onto the liquidity constraint of firms as Liquidity constraint = R−1 . 28 The weight used to calculate the symmetric shock is the labor share multiplied by the Bonacich centrality αi vi . According to Equations 4 and B.3, the level of financial friction of Firm i can be approximated by Riαi vi . Moreover,  the proof that i αi vi = 1 is straightforward. 29 In Appendix F (Figure F.3), I further confirm this finding by studying a two-firm, chain economy in which financial shocks impact negatively either the upstream firm or the downstream firm.

34

expensive. In addition, the adjustment mechanism dampens the commodity distortion and efficiency loss by averaging out the interest rates that firms pay. Column (2) presents the simulation results of an economy that allows the size adjustment of trade credit. The adjustment size is 36% on average. Table F.2 in the Appendix reports the simulation results of the model with various trade credit adjustment structures, including an asymmetric one; these results hold qualitatively. In particular, when trade credit is fully flexible, Δ%Y is -4.41%, the magnitude of which is much less than is the case when trade credit is fixed, -6.85%. Result 3. Trade credit forbearance amplifies the aggregate impact of financial shocks. Columns (3) and (4) present the results of a model with trade credit forbearance. The aggregate impact of financial shocks under these circumstances is clearly much stronger than it is in the absence of forbearance. When the benchmark model features both options for adjusting trade credit, as presented in Column (4), the effect of trade credit forbearance dominates. Even in the case of perfect size adjustment, the aggregate output declines by 9.25%, much more than in the case of a fixed tradecredit structure. I present the realized bank rate after debt rollover and the effective borrowing rate (Ri∗ ) of the simulated economy in Appendix Table F.1 and the simulation results using various values of η and ρ in Appendix Table F.2. Moreover, the simulation results show that the U.S. production network, which features trade credit forbearance, is more sensitive to negative shocks than networks with no trade credit, as is evident from a comparison of Columns (3), (4), and (5). Therefore, when shocks are large enough to trigger forbearance, a production network that is more densely interconnected in terms of trade credit is more fragile than one that is relatively less interconnected. Result 4. Trade credit increases firm-level output correlations. The last row of Table 3 reports the standard deviations of the percentage change in sectoral output following asymmetric financial 35

shocks. The output correlation clearly increases with the level of trade credit as well as with its adjustment flexibility. As discussed in Section 4.2, there is evidence that, in practice, firms share liquidity with surrounding firms through trade credit, thereby increasing the output correlation among the members of a production network. In order to explore the role of the production network in the model, I compare the responses ˆ = 0). A horizontal of the network economy with those of a horizontal economy (in which Ω = Ω economy can be constructed in a number of ways, for example by varying the input and final shares. In this case, I construct an “equivalent” horizontal economy that is directly comparable to a network one. As can be seen in Appendix B, a horizontal economy is allocationally equivalent to a network economy with full trade credit when its labor share equals 1 and its final share equals α ◦ v, as aggregate labor and aggregate output in the two economies are identical (see Columns 6 and 8). The aggregate impact of a horizontal economy is weaker than either the benchmark economy with calibrated trade credit or the one that allows for credit forbearance. Finally, I simulate a “BL version” of the model that is comparable to that of Bigio and La’O (2016) and apply that study’s payment schedule of the intermediate inputs. Trade payments are settled upon the final delivery of products, but firms pay intermediate inputs in advance of production at the beginning of the production period. In this economy, the working capital requirement is greater than in the benchmark model. Furthermore, there is no liquidity sharing. The simulation results are presented in Columns (9)-(10). Unsurprisingly, the aggregate impact of financial shocks is stronger in the BL version than it is in my model when the trade credit structure is fixed. Another important difference is that the aggregate effects of the changes in production cost and the changes in profits in this economy do not cancel each other out after symmetric shocks. Rather, financial friction exists in the context of inter-firm trade, even when shocks are symmetric owing 36

to the absence of the liquidity-sharing channel.

5.4

Application: Sectoral Financial Influence

Finally, I study the aggregate impact of idiosyncratic shocks so as to capture the sectoral financial influence. Figure 1 is a scatter plot of the change in aggregate output after 2% and 10% idiosyncratic interest rate shocks to each sector. The former shock occurs during moderate downturns and the latter during severe financial distress. The size of each marker corresponds to each sector’s Domar weight, and the color represents the ratio of trade credit to bank credit for each sector. Manufacturing is the most important sector in the production network owing to its size and intense use of trade credit. Notably, the order of sectoral financial influence can be captured by ranking the size of ΔY following sectoral shocks.30 Figure 1: Aggregate Output Response to Sectoral-Level Ri Shocks

Flexible trade credit structure

0

2%
Ri


10 -3

Agriculture Mining Utility Transportation Information Other services Wholesale Construction Arts Retail

-1 -2

-0.02

-0.03

Real Estate

-4

Agriculture Utility Transportation Other services Wholesale Mining Arts Information Construction Retail

-0.01

PBS

-3

10%
Ri

0

Real Estate -0.04

-5

Education Manufacturing

Manufacturing -6

-6

-5

0.38

PBS

Education

1.64

-4

-3

-2

-1

Rigid trade credit structure
10

0

-0.05 -0.05

-0.04

-0.03

-0.02

-0.01

0

0.11

Rigid trade credit structure

-3

Two findings deserve emphasis here with regard to the sectoral financial influence. First, the financial influence is distinct from the Domar weight, for the issue of trade credit complicates the 30

In addition, Figure F.1 in the Appendix is a bar chart of the aggregate output response to 2% sectoral-level interest rate shocks in which sectors are ordered according to their DownMeasure for an economy with a fixed trade-credit structure. In general, trade credit amplifies the aggregate impact of financial shocks that affect upstream sectors.

37

assessment of a firm’s role in the propagation of financial shocks. Second, the financial influence vector varies depending on the size of a given financial shock. Furthermore, by comparing the scatter plots in the figure with the 45-degree line (in black), I find that the adjustment features of trade credit attenuate the aggregate impact when shocks are sufficiently small but amplify the impact when they are sufficiently large. Trade credit forbearance occurs in the latter case, as illustrated in the right panel of Figure 1.

6

Conclusions

In this paper, I investigate how the interaction between the production network and trade credit network affects the propagation of financial shocks. Using the U.S. input-output matrix and the loan data, I find strong upstream propagation of financial shocks. To model this propagation, it is important to take into account the financial friction in trade and the interlocked balance sheets of the trading parties. Generally speaking, trade credit creates a liquidity-sharing channel among firms so that liquidity is reallocated. During times of financial distress, firms share liquidity through adjustments of trade credit with respect to size and the payment schedule. The size adjustment attenuates both the propagation and the aggregate impact of financial shocks while adjustment of the schedule amplifies them. My findings here suggest avenues for further research. Thus, for example, important results might be obtained using a model based on a micro-founded trade credit structure. Moreover, if a trade credit default were allowed in addition to forbearance discussed in Section 4.3, a strong liquidity shock to one firm could cause a cascade of defaults throughout the trade credit network, resulting in large-scale production failure and a persistent contraction in the aggregate output.

38

Also, in practice, both a complicated production network and an entangled financial network are at work under these circumstances, so that an idiosyncratic financial shock not only spreads through the input-output network but also spills over into the banking network. In a follow-up paper Luo (2019), I present a model with endogenous interest rates and examine the interplay between bank credit and trade credit. It is my hope that the present paper will encourage further theoretical and empirical studies on the role of trade credit in the input-output economy.

Acknowledgement I am grateful to Ricardo Reis for his constant guidance and support. I would also like to thank Jushan Bai, Richard Clarida, Jennifer La’O, Emi Nakamura, Stephanie Schmitt-Grohe, J´on Steinsson, Alireza Tahbaz-Salehi, Martin Uribe, Michael Woodford as well as the editor, Vincenzo Quadrini, and anonymous referee for helpful comments and discussions. All remaining errors are mine. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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42

A

Trade Credit

Trade credit is a short-term loan that suppliers provide to their customers upon purchase of their products. This form of credit is the single most important source of external finance for firms (Boissay and Gropp, 2007) and underpins 90% of world merchandise trade in 2007.31 Tables A.1 and A.2 present the summary statistics regarding trade credit. Two types of trade credit rules are common (Nilsen, 2002). One involves a one-part contract known as Net-30, with suppliers extending to buyers 30-day, interest-free loans covering the cost of their purchases. The other type of trade credit involves a two-part contract, known as 2/10 Net 30; in this case, customers who pay within 10 days of delivery receive a 2% discount and those who do not have up to 20 more days to complete payment. Empirical evidence shows that the implicit interest rate in a trade credit agreement is usually much higher than the rate on bank credit.32 According to a conservative estimate by Peterson and Rajan (1997), for example, trade credit cost is more expensive than 99.8% of the loans. The high interest rate on trade credit reflects the associated insurance and default premiums (Cu˜nat, 2007). Suppliers help with financing through trade credit or defer payments when their customers have exhausted their lines of bank credit and, as they have an implicit equity stake in the firms (Peterson and Rajan, 1997). Suppliers tend to renegotiate their claims when a firm encounters financial distress, whereas banks tend to follow a strict liquidation policy (e.g. Berger and Udell, 1998; Huyghebaert et al., 2007; Mann, 1997; Peterson and Rajan, 1997). Several theories have been put forward to explain why suppliers extend credit to firms that are unable to secure additional banking credit. On the one hand, the cost to suppliers of losing customers is high. On the other hand, suppliers may have an information advantage over banks and have a comparative advantage in liquidating collateral that a borrower may put up to secure a loan. Moreover, according to the transaction argument, trade credit reduces the transaction cost of paying bills. Lastly, some studies have looked at the role of trade credit in mitigating moral hazards associated with supply chains. The focus of this paper is on, not explaining the exsistence or identifying the optimal type of trade credit, but rather the impact of trade credit on the propagation of financial shocks.

31 32

“World Bank urged to lift trade credit finance.” 11 November 2008, Financial Times. Be aware that the price may be in the form of intrinsic interest.

43

Table A.1: Trade Credit (Compustat)

Agriculture Mining Utilities Construction Manufacturing Wholesale trade Retail trade Transportation Information FIRE PBS Educational Arts Other services

AP/COGS 0.38 1.01 0.49 0.40 0.50 0.43 0.42 0.29 0.61 0.63 0.37 0.25 0.20 0.37

AP/S 0.28 0.51 0.36 0.33 0.32 0.33 0.28 0.21 0.27 0.35 0.23 0.16 0.15 0.24

AR/S 0.33 0.56 0.53 0.62 0.58 0.44 0.08 0.35 0.57 0.60 0.68 0.53 0.07 0.20

AP/TA 0.04 0.05 0.04 0.09 0.07 0.16 0.14 0.04 0.04 0.02 0.06 0.05 0.04 0.05

AR/TA 0.04 0.04 0.04 0.15 0.13 0.22 0.04 0.06 0.09 0.04 0.20 0.14 0.02 0.06

Note: AP represents accounts-payable; AR represents accounts-receivable; COGS represents cost of goods sold; S represents sales; TA represents total asset. FIRE sector calibration excludes finance and insurance firms.

Table A.2: Trade Credit (QFR)

Mining Manufacturing Wholesale trade Retail trade

AP/S 0.49 0.31 0.33 0.28

AR/S 0.64 0.45 0.36 0.14

AP/TA 0.05 0.07 0.20 0.16

AR/TA 0.06 0.10 0.22 0.08

Note: AP represents accounts-payable; AR represents accountsreceivable; S represents sales; TA represents total asset.

44

B

Solve the Partial Equilibrium Model

Proof of Proposition 1. Denote ⎡ ⎢ ⎢ Ω=⎢ ⎢ ⎣

(1 − α1 )ω11 (1 − α2 )ω21 .. .

(1 − α1 )ω12 (1 − α2 )ω22 .. .

··· ··· .. .

(1 − α1 )ω1N (1 − α2 )ω2N .. .

⎤ ⎥ ⎥ ⎥, ⎥ ⎦

(1 − αN )ωN 1 (1 − αN )ωN 2 · · · (1 − αN )ωN N From firms’ first-order conditions, I obtain (1 − θij )Ri + θij pj mij = (1 − αi )ωij pi mi , (1 − θij )Rj + θij wli Ri = αi pi mi . From the goods market clearing condition pi m i = p i y i +



pi mji

j

= pi yi +



(1 − αj )ωji pj mj

j

Normalize P =

 i

(1 − θji )Ri + θji . (1 − θji )Rj + θji

pζi i = 1. Give that pi yi = ζi Y,

and denote gi ≡ pi mi , I obtain g = (I − Θ1 )−1 ζY,

(B.1) (1−θ )R +θ

where g is the vector of gi . Θ1 is a matrix with the ij−entry (1 − αi )ωij (1−θijij )Rji +θijij . By the zero profit condition, pi =

αi−αi (1

− αi )

−(1−αi )

Thus w

αi

= Ξi pi Πj

Π(ωij )



−ωij (1−αi )

−ω (1−αi ) pj ij



ω (1−αi )  1 αi αi N [(1 − θij )Ri + θij ] ij w Ri Πj=1 pj . zi [(1 − θij )Rj + θij ]

zi Ri−αi Πj



(1 − θij )Ri + θij (1 − θij )Rj + θij

−ωij (1−αi )

,

where Ξi ≡ αiαi (1−αi )(1−αi ) Π(ωij )ωij (1−αi ) is a constant. Aggregate the previous condition across

45

firms, I get Πi w

αi v i

=

Πi Ξvi i pvi i Πj



−ω (1−αi )vi pj ij



zivi Ri−αi vi Πj



(1 − θij )Ri + θij (1 − θij )Rj + θij

−ωij (1−αi )vi

,

where vi is the Bonacich centrality of firm i, v ≡ (I − Ω )−1 ζ and v ≡ (I − Ω )−1 . It is easy to proof that,



Πi pvi i Πj

αi vi = 1;

i



−ω (1−αi )vi pj ij



= Πi pζi i = P = 1.

With some algebra, I obtain w=

Y

Πi Ξvi i zivi Ri−αi vi Πj



(1 − θij )Ri + θij (1 − θij )Rj + θij

−ωij (1−αi )vi

;

   ωij (1 − αi )  αi mi pi (Ri − 1) + mi pi (1 − θij )(Ri − 1) = wl + R (1 − θ )R + θ i ij i ij i j −

 j

= wl +

i  Θ2 g,

ωij (1 − αi ) mi pi (1 − θij )(Rj − 1) (1 − θij )Ri + θij (B.2)

where Θ2 is a vector with entry Rαii (Ri − 1) + Combing equation B.1, I obtain

Y =



Πi Ξvi i zivi Ri−αi vi Πj



ωij (1−αi ) j (1−θij )Ri +θij (1

(1−θij )Ri +θij (1−θij )Rj +θij

− θij )(Ri − Rj ).

−ωij (1−αi )vi

1 − Θ2 (I − Θ1 )−1 ζ

l.

It is interesting to notice that if θ = 1, Πi Ξvi i zivi Ri−αi vi  l. Y = 1 − i αi vi (1 − 1/Ri )

(B.3)

If shocks are symmetric Ri = Rj , then Y = Πi Ξvi i zivi l. An “allocationally equivalent” horizontal economy. Equation 4 implies that a horizontal economy

46

ζH

with Y = Πi Ξvi i (ζiH )−ζi yi i , final share ζiH = αi vi and labor share αiH = 1 has H

ζH

i i = 1, P = Πi Ξ−v i pi

ζH

−ζ H

Πi Ξvi i zi i Ri i l  . Y = 1 − i ζiH (1 − 1/Ri ) Y response to Ri in this case equals to that in a network economy with full trade credit. Also, if shocks are symmetric, Ri = Rj , ∀i, j, then ζH

Y = Πi zi i l. Linearize the system of equations. Define the following vectors, ⎡ ⎢ ⎢ z=⎢ ⎢ ⎣

z˜1 z˜2 .. .

⎤ ⎥ ⎥ ⎥, ⎥ ⎦

z˜N

⎡ ⎢ ⎢ R=⎢ ⎢ ⎣

˜1 R ˜2 R .. . ˜N R

⎤ ⎥ ⎥ ⎥, ⎥ ⎦

⎡ ⎢ ⎢ p=⎢ ⎢ ⎣

p˜1 p˜2 .. .

⎤ ⎥ ⎥ ⎥, ⎥ ⎦

p˜N

Let A denote a diagonal matrix with diagonal elements αi + (1 − αi ) denote a matrix with entries

¯ (1−θij )R ¯ ij . (1−θij )R+θ



¯ ωij (1−θij )R ¯ ij . j (1−θij )R+θ

Let B

Log linearize:

Y˜ = ζ  v  [z − (A − B ◦ Ω)R] + f (R). where B ◦ Ω presents the Hadamard product of B and Ω. f (R) is a constant and is a function of R. Rearrange, Y˜ = ζ  v  [z − (A − BΩ)R] + f (R)

(B.4)

= ζ  [v  z − R − v  (−I + A + (I − B)Ω)R] + f (R) = ζ  [v  z − R − v  (I1 ◦ Ω − I2 )R] + f (R), where I1 is a matrix with ij-th entry of  θ element of (1 − αi ) j ωij [(1−θij ij)R+θ ¯ ij ] . Thus,

θij ¯ ij ] [(1−θij )R+θ

and I2 is a diagonal matrix with diagonal

y = v  [z − (A − B ◦ Ω)R] + f (R)ζ = [v  z − R − v  (I1 ◦ Ω − I2 )R] + f (R) · 1

47

Proof of Proposition 3. From goods market clearing condition, I obtain mi = yi +



mji

j

= yi +



(1 − αj )ωji mj

j

yi ζj [(1 − θji )Ri + θji ] , yj ζi [(1 − θji )Rj + θji ]

 mi mj [(1 − θji )Ri + θji ] . = ζi + (1 − αj )ωji ζj ζi yi y [(1 − θ )R + θ ] j ji j ji j Denote ti =

mi , yi

I obtain ζi t¯i t˜i =

 j



 ¯ (1 − θ ji )R ˜ ˜ (1 − αj )ωji ζj t¯j t˜j + ¯ + θji ] (Ri − Rj ) . [(1 − θji )R

ˆ be a matrix with ij−entry (1 − αi )ˆ ˆ ji ≡ ωji m¯ ji p¯ji and let Ω ωij , then Further replace ωji by ω m ¯ p¯

t˜i =

 j

 (1 − αj )ˆ ωji

 ¯ (1 − θ ji )R ˜ ˜ t˜j + ¯ + θji ] (Ri − Rj ) . [(1 − θji )R

Thus ˆ  ◦ I3 ]R, ˆ  ]−1 [I4 − Ω t = [I − Ω  ¯ (1−θ )R ωji [(1−θji )jiR+θ where I4 is a diagonal matrix with diagonal element j (1 − αj )ˆ ¯ j ] . I3 is a matrix with

¯ (1−θ )R ˜ ˜ i − y˜i , so t = m − y. Thus, the vector of the log ij-th element [(1−θji )jiR+θ ¯ ji ] . Given that, ti = m deviation of firm output from the steady state (m ˜ i ) follows,



ˆ  ]−1 (Ω ˆ  ◦ I3 − I4 ) R + f (R) · 1.(B.5) m = [I − Ω] z − R − [I − Ω]−1 (I1 ◦ Ω − I2 )] + [I − Ω −1

The first term in the brace captures the downstream propagation of an interest rate shock and the second term captures the upstream propagation. This equation indicates that trade credit affects the strength of the two propagations. It is straightforward to show that entry−i of vector (I1 ◦Ω−I2 )R   (1−αi )ωij θij is j=i (1−θij )R+θ ¯ ij (Rj − Ri ). The magnitude of the term in square brackets increases with θ.   ¯ (1−αj )ˆ ωji (1−θji )R ˆ  ◦ I3 − I4 )R is  Entry−i of vector (Ω (Rj − Ri ). The magnitude of the term ¯ j=i (1−θji )R+θji in square brackets term decreases with θ. Thus, trade credit amplifies the downstream propagation and attenuates the upstream propagation.

48

C

Firm’s Problem in the General Equilibrium Set-up

Size Adjustment. The first-order conditions for Problem 14 are ∂li : αi Φi mi = wli Ri ; ! " ∂mij : (1 − θij )Ri + θij + C(θij , θ¯i ) pij mij = Φi (1 − αi )ωij mi ; ∂mji : pji [(1 − θji )Ri + θji ] = Φi ; ∂yi : Φi = pi . Credit Forbearance. When forbearance occurs, the first step is to solve for the equilibrium τij and the new bank rate Ri (according to Equation 15). To simplify the problem, the negotiation is done separately and simultaneously with each of the firms’s suppliers. First, firms choose τij based on the initial realized bank rate. Multiple rounds of negotiation may then occur, until the equilibrium τij is achieved and the updated Ri leads to no further changes to any of the firms involved. In the second step, firms produce products in the manner discussed in Section 2 (without size adjustment) or Section 4.2 (with size adjustment), using Ri∗ that satisfies Equation 16.

D

Calibrations

Calibration of labor share. αi is calibrated using the BEA GDP by Industry Value-added Components Table (1998-2013). Following Su (2014), Labor share = Compensation of employees +1/2 of the noncorporate part of other gross operating surplus. Capital share = Gross operating surplus + taxes on production and imports less subsidies −1/2 of the noncorporate part of other gross operating surplus. The labor share in the model αi is assumed to be equal to the calibrated labor share plus the calibrated capital share. Thus, the intermediate input share is set equal to 1−αi . Table D.1 presents the calibrated values. The input-output matrix. Figure D.1 plots the input-output matrix (Ω) of the U.S..

E

Liquidity Contraction During the 2008-2009 Financial Crisis

Table E.1 presents the measured sectoral-level liquidity contraction during the 2008-2009 financial crisis. Notably, the information in the Dealscan data is insufficient to estimate the size of the liquidity contraction for firms in the FIRE industries. In the simulation, I assume instead zero shock to FIRE firms, for which reason the levels of aggregate response are conservative.

49

Table D.1: Sectoral Level Parameters Sector

Labor share αi

Intermediate share 1 − αi

Final share ζi

Trade credit θ¯i

Agriculture Mining Utility Construction Manufacturing Wholesale Retail Transportation Information real estate PBS Education Arts Other services

0.42 0.63 0.58 0.52 0.36 0.69 0.68 0.50 0.55 0.72 0.63 0.60 0.56 0.62

0.58 0.37 0.42 0.48 0.64 0.31 0.32 0.50 0.45 0.28 0.37 0.40 0.44 0.38

0.01 0.01 0.02 0.07 0.21 0.04 0.10 0.02 0.04 0.15 0.06 0.17 0.07 0.04

0.38 1.00 0.49 0.40 0.50 0.43 0.42 0.29 0.62 0.63 0.37 0.25 0.20 0.37

Average

0.58

0.42

0.07

0.45

Table E.1: % of Liquidity Contraction 2008.10-2009.06 Sector Agriculture Mining Utilities Construction Manufacturing Wholesale Retail Transportation Information FIRE PBS Education Arts Other services

F

Weighted average -5.57% -2.49% -2.87% -19.36% -0.30% -19.12% -14.45% -2.79% -3.06% NA -1.63% -4.17% -4.26% -5.25%

Additional Simulation Results

In a two-firm chain economy with the kind of structure illustrated in panel (a) of Figure F.3, Firm 1 is upstream and Firm 2 is downstream. A chain network model of this sort makes it possible to focus on the aggregate impact of financial shocks by targeting firms with various locations along the supply chain. I calibrate the economy using the average levels of labor share and trade credit 50

Figure D.1: The U.S. Input-Output Matrix Input-Output Matrix

Agriculture Mining Utility

Suppliers (Input)

Construction Manufacturing Wholesale Retail Transportation Information FinInsurRealEst ProfBusiServ Education Arts OtherServices

re g ty n g le ail n n te rv n ts s ltu inin Utili uctio turin lesa Ret rtatio atiolEstasiSe catio Ar rvice u c o e tr ric M po orm ea Bu du ns ufa Wh erS Ag ns Inf urR Prof E h t a Co Man r O T Ins an n i F

Destination Industry (Output)

Figure E.1: % of Liquidity Contraction (2008.10-2009.06) V.S. DownMeasure

Size of Sectoral Liquidity Contraction

0.2 Wholesale

Construction

0.15 Retail

0.1 Agriculture

0.05

Other services

Information Arts Mining Transportation PBS Manufacturing

0 0.2

0.4

Education

Utility Real Estate

0.6

0.8

1

DownMeasure

Note: DownMeasure is constructed using the methodology of Antr´as and Chor (2013) and the 2002 BEA IO table.

51

for the U.S. economy (as presented in the last row of Table D.1 in Appendix D) and set the final share of each firm at 0.5. Figure F.3 illustrates the aggregate output responses to R1 shock and R2 shock in economies with no trade credit, with calibrated trade credit, and with full trade credit. Clearly, trade credit amplifies the aggregate impact of financial shocks that upstream firms suffer and attenuates that which downstream firms suffer. In the absence of price discrimination, the discount effect discussed in Section 2.3 disappears while the downstream propagation of financial shocks becomes stronger than is the case in the benchmark model. I have simulated a version of my benchmark model without price discrimination; the results for a three-firm circle economy such as the one presented in Section 5.2 are shown in Table F.3. In this case, the downstream propagation is obviously stronger than the upstream propagation - an outcome that my empirical findings contradict. The sectoral output and the aggregate output responses to financial shocks are also obviously stronger than the output in the benchmark model. In addition, the aggregate output response varies with the level of trade credit so that the liquidity reallocation among homogeneous firms generates the aggregate output impact - another outcome inconsistent with the prediction in Section 5.2. Table F.1: Illiquidity Contagion (η = 0.04 and ρ = 1) Sector Agriculture Mining Utilities Construction Manufacturing Wholesale Retail Transportation Information FIRE PBS Education Arts Other services

Original bank rate Ri0

Realized bank rate after debt rollover Ri

Effective borrowing rate Ri∗

1.0689 1.0377 1.0415 1.2085 1.0156 1.2061 1.1589 1.0407 1.0434 1.0125 1.0290 1.0548 1.0556 1.0657

1.0793 1.0708 1.0835 1.2085 1.0832 1.2061 1.1638 1.1166 1.0761 1.0638 1.1075 1.0565 1.0668 1.0939

1.0793 1.0708 1.0835 1.1819 1.0832 1.1809 1.1576 1.1159 1.0761 1.0638 1.1075 1.0565 1.0668 1.0939

Note: The original bank rates are measured according to Table E.1. Firms in sectors with Ri∗ < Ri = Ri0 delay repayments on their trade credit whenever the magnitude of their bank rate exceeds their suppliers’ rate plus η, as illustrated in the rows highlighted in blue.

52

Table F.2: Aggregate Effect of Financial Shocks Cont. (1) Adjut. option

(2)

Size adjustment Perfect Asymmetric Adjustment Adjustment

Δ%Y Δ%L Production cost Profits

(3)

-4.41% -4.24% -3.02% 2.86%

-5.99% -5.86% -4.16% 4.03%

(4)

(5)

Forebearance ρ=1 η = 0.1

ρ=1 η = 0.15

ρ = 0.5 η = 0.04

-9.48% -9.41% -6.70% 6.62%

-8.08% -7.98% -5.67% 5.57%

-9.00% -8.94% -6.36% 6.29%

Note: In the case of asymmetric adjustment, downward adjustment of trade credit is free while upward adjustment is not allowed. In the perfect adjustment case, the cost of adjustment is zero, i.e., C(θij , θ¯i ) = 0.

Table F.3: 3-Firm Circle Economy without Price Discrimination: Firm-Level Output Response to 2% R2 Shock Trade credit structure Calibrated

Fixed =0

=1

Δ%m1 Δ%m2 Δ%m3

-1.20% -2.21% -1.34%

-1.76% -2.76% -1.76%

-0.51% -1.51% -0.81%

Δ%Y

-1.32%

-1.63%

-0.94%

53

Figure F.1: Fixed Trade Credit Structure: Aggregate Output Response to 2% ΔRi and DownMeasure

Co nst ruc tio n Re tai l Ed uca tio n

ati on Oth er ser vic Ar es ts

orm

sta

Inf

e

al E

sal

Re

ole Wh

y ilit Ut

te

on ati ort nsp Tra

Ag ric ult ure Ma nuf act uri PB ng S

0

Mi

nin g

DownMeasure

% change of Y

-1 -2 -3 -4 -5 -6


10-3 no tc

calibrated tc

full tc

Note: Sectors are ordered according to their downstreamness. Moving to the right, the larger is the DownMeasure of a sector. DownMeasure is constructed using the methodology of Antr´as and Chor (2013) and the 2002 BEA IO table.

Figure F.2: Two Simple Network Structure  
 


 


   


  

 




 

 



  
 

Note: Upstream shock refers to a 2% increase in R1 . Downstream shock refers to a 2% increase in R2 .

54

Figure F.3: 2-Firm Chain Economy: Aggregate Output Response to Ri Shocks 0

Upstream shock

Downstream shock


%Y

-0.005

-0.01

-0.015 no tc

calibrated tc

55

full tc