Trade Credit as a Signal of Quality

Trade Credit as a Signal of Quality by Eric de Bodt*, Frédéric Lobez and Jean-Christophe Statnik April, 2008

Abstract Trade Credit is a major source of financing. Over the past decade, it has represented more than 20% of the total assets of US listed firms. Different arguments have been suggested in the academic literature to explain why there is a strong industry pattern to trade credit usage (including the nature of the firm’s assets, the degree of liquidity of the firm’s inputs, and the degree of competition among suppliers), but little is known about the factors underlying the variance of trade credit usage among firms in the same industry. We argue that trade credit can be used by firms as a signal of quality. Our theoretical predictions are empirically verified using a large sample of US firms observed during the 1977−2005 period. JEL classification: G32; G21 Keywords: trade credit, signaling

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De Bodt Université de Lille 2 Lille School of Management 1 place Déliot - BP381 59020 Lille Cédex France

Frédéric Lobez Université de Lille 2 Lille School of Management 1 place Déliot - BP381 59020 Lille Cédex France

Jean-Christophe Statnik Université de Lille 2 Lille School of Management 1 place Déliot - BP381 59020 Lille Cédex France

+33-3-2090-7477 +33-3-2090-7629 [email protected]

+33-3-2090-7624 +33-3-2090-7629 [email protected]

+33-3-2090-7479 +33-3-2090-7629 [email protected]

*Corresponding author

Trade Credit as a Signal of Quality

1. Introduction Trade credit is a major source of financing in our modern economies. Rajan and Zingales (1995) reported that trade credit (estimated using account payables) amounted to 15% of total assets for a large sample of non-financial US firms. We found a similar proportion. On our sample of 10,687 firm/year observations (based on US listed firms between 1977 and 2005, see Section 3.1), trade credit represented 28% of total debts and 16% of total assets, while Mian and Smith (1994) reported that trade credit comprised 26% of the total debts of non financial firms listed on the NASDAQ at the end of 1992. Moreover, the usage of trade credit increased significantly during the first half of the 1990s, especially for bigger firms (defined as firms with total assets of over 50 million USD). The importance of trade credit as a financing source also applies outside of the US. In France, for example, trade credit represents four times the value of short-term financing by financial institutions (€ 604 billion against € 133 billion at the end of 2005 (Kremp, 2006)). These are not small figures. Such a generalized usage of trade credit is in fact puzzling. As a shortterm financing source obtained from non-financial suppliers, by any standard, trade credit is very expensive. The implicit cost of trade credit is the rebate for cash payment the firm renounces in order to benefit from payment delays. Let us take an example. As pointed out by Boyer (2007), if the rebate is 2% for payment within the 10 days following a delivery, while the maximum payment delay is 30 days, the implicit interest rate on an annual basis is over 44%!1 Why are firms using such an expensive source of financing so much? Many academic studies have attempted to find the answer to this challenging question. It is well-known that trade credit displays a strong industry pattern: payment delays vary considerably from industry to industry. This common knowledge is confirmed by the statistics. In our sample, a simple regression of the trade credit on the total debt ratio for the 49 Fama/French industry classification2 yielded an 𝑅2 of 58.7%! It is therefore not surprising that the determinants that have been investigated by academics are mostly industry-wide factors: -

Several early contributions emphasize the potential use of trade credit terms as a tool for implementing price discrimination between low and high quality customers (see e.g. Meltzer, 1960). As highlighted by Burkart et al. (2008), the price discrimination argument fundamentally

1 2

365

The implicit interest rate 𝑖 is obtained as a solution of 98 (1 + 𝑖) 20 = 100 in the present case. See http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

depends on the degree of concentration in the suppliers’ industry: the stronger the suppliers’ market power, the stronger their incentives to put a price discrimination strategy in place. Concentration is an industry-specific attribute. -

Frank and Maksimovic (1998) introduced a theory based on collateral liquidation. The authors based their analysis on the fact that, in cases of default, suppliers can repossess their goods and sell them through their distribution network. The cost of default is far higher for financial institutions that do not benefit from such an opportunity. Petersen and Rajan (1997) and Davydenko and Franks (2008) provide empirical support for this claim. Under this collateral liquidation theory, the suppliers’ advantage depends on the nature of the inputs (the possibility of selling them back to other customers) and the extent to which inputs are transformed by customers. These are clearly also industry-wide factors.

-

Another argument pointed out by Petersen and Rajan (1997) is the potential advantage to suppliers of controlling the buyer: suppliers can threaten to cut the delivery of supplies to customers who have a bad payment history. And the more the supplier is in a monopolistic situation with respect to the customer (the higher the supplier’s market power), the more credible is this threat. This again will vary from industry to industry, depending on the power balance between suppliers and customers.

-

Burkart and Ellingsen (2004) developed a theoretical contract model of trade credit based on the degree of input liquidity. The less liquid an input (note that again, the degree of input liquidity is an industry-wide factor), the less it can be diverted by opportunistic borrowers. As suppliers provide less liquid inputs than banks, they can lend more liberally. Burkart et al. (2008) provide empirical evidence supporting this diversion vulnerability theory. It is interesting to note that these authors emphasize that one of the two main innovations of their paper is the “extensive use of variables that capture industry characteristics”. The authors adopt a “classification scheme motivated by the crucial role of industry characteristics in many trade credit theories” (Burkart et al. (2008), p. 1).

Even if industry determinants clearly play a central role in explaining trade credit patterns, variations of trade credit usage inside industries are not insignificant. Our regression of trade credit on total debt ratio leaves more than 40% of the variation in trade credit usage unexplained after accounting for industry membership. In Section 3, we report the ratio of the intra-industry to inter-industry variance of trade credit in our sample during the period 1977−2005. This ratio was almost always above one, with an average value of 2.4 over the whole period. So, even after exhausting industry-

wide explanations of trade credit usage, much remains to be said. This is the issue we address in this paper. Why does trade credit usage varies inside industries? At first sight, the financial health of the customer seems to be an obvious reason: suppliers are ready to concede payment delays to healthy customers and less ready to do so when repayment is at risk. It is, moreover, frequently argued that suppliers benefit from an informational advantage with respect to other creditors (in particular financial institutions): the commercial relationships that they maintain with their customers allow them to be tracked faster and more accurately. This was pointed out by Smith (1987), who showed how trade credit terms are a channel for extracting information about the risk of the buyer defaulting. However these arguments only explain why suppliers are ready to offer trade credit.3 The question of why buyers are willing to use such a costly financing source (the demand side of the issue) remains open. Probably the most promising avenue of research has that initiated by Biais and Gollier (1997). They developed a signaling model in which trade credit is used by buyers to indicate their quality. The starting point of their analysis is the same as Smith’s (1987): suppliers possess an informational advantage over financial institutions to judge the health of their buyers. As this informational advantage is recognized by all participants (in particular, by banks), buyers agree to finance part of their activities through trade credit, despite its costly nature, in order to signal their quality. It is even, in fact, the high cost of trade credit that renders the signal credible. Signaling theory can indeed explain the demand for trade credit, but, to the best of our knowledge, few direct empirical investigations of this theory have been undertaken. Burkart et al. (2008) probably present the most relevant results, but they are not very encouraging. The authors used data from the National Survey of Small Businesses Finances (NSSBF) and input/output industry matrices published by the US Bureau of Economic Analysis to investigate the determinants of trade credit contracts. They report that their results provide little support for the informational-advantage hypothesis. Maybe the most troubling evidence is that “firms buying relatively more inputs from firms in closely related business lines do not receive more trade credit” (Burkart et al. 2008, p. 2). If the informational advantage of suppliers is not supported by the data, this casts doubt on the signaling role of trade credit, as introduced by Biais and Gollier (1997).

3

Other recent contributions to the literature suggest ways of gaining a better understanding of the supply side of the short-term financing market. Boyer (2007), for example, argues that banks can credibly commit to auditing a firm which declares bankruptcy. This ex-ante commitment allows banks to charge lower interest rates than non-financial firms. In the author’s framework, banks are constrained, and trade credit supplies the residual fraction of short-term financing needed by firms.

In this paper, we propose an alternative source for the signaling role of trade credit: the illiquidity of inputs. As previously mentioned, the role of input illiquidity as a determinant of trade credit was introduced by Burkart and Ellingsen (2004). In their theoretical contract model, input illiquidity explains why suppliers can lend more liberally than financial institutions (the supply side): it is an industry-wide factor driving the offer of trade credit. But if input illiquidity may be the foundation of signaling activities by buyers, it will also be a factor driving the intensity of trade credit demand inside industries. This is the precise issue that we explore here. We start our analysis with a theoretical investigation of whether input illiquidity drives signaling activities. We develop a classic model of asymmetric information in which the firm manager chooses the proportion of trade credit to be used to finance activities. The model has three periods. In the first period, the manager takes the financing decision. In the second period, the manager receives information indicating whether the firm will succeed or not. The information is private to the manager and perfectly informative. On this basis, the manager decides either to go on with the activity or to stop it. During the third period, if the activity has been maintained, the cash-flow is produced. The central question is what the firm’s assets are if activity is disrupted. This depends on the degree of input illiquidity. Cash provided by banks can be fully diverted: cash is perfectly liquid and banks do not have the right to recover it when activity is disrupted. The status of inputs delivered by suppliers is different: these are physical goods that can be repossessed by suppliers (see Frank and Maksimovic, 1998)). Liquidity can act in two directions: (i)

as argued by Burkart and Ellingsen (2004), the more liquid suppliers’ inputs are, the more the manager can divert them to an alternative use. We will refer to this argument as the liquidity hypothesis;

(ii) in the spirit of Frank and Maksimovic (1998), the more liquid inputs are, the more incentive suppliers have to incur the costs of repossessing them and reselling them on the secondary market. In such a case, no diversion is possible as the manager loses possession of the goods. We will refer to this argument as the repossession hypothesis. Our model is compatible with these two interpretations. The key point is that the diversion of inputs is the foundation of the signaling role of trade credit. Although a close form solution of the model cannot be found in its most general form, we show that a signaling equilibrium is theoretically possible. This opens the door to an alternative foundation for the use of trade credit as a signaling activity. The two main implications of this theoretical analysis are (i) that the use of trade credit

increases with firm quality; and (ii) that the intensity of the relation between trade credit and firm quality depends on the degree of input diversion in the event of activity failure (the sign of the relation depends on whether the liquidity hypothesis or the repossession hypothesis dominates). We then provide an in-depth empirical investigation of these predictions. Our sample is composed of 1958 US listed firms, observed over the period 1977 to 2005 (10,893 firm/year observations). The three main features of our method are (i) the use of the Altman (1968) ZScore as a proxy for the firm quality, computed in such a way that it is unobservable to market participants at the time when it is taken into account (a key condition for being a proxy for private information subject to signaling activities); (ii) controlling for firms’ time invariant characteristics using a panel fixed-effect estimator (estimations are undertaken both on the whole 29-year period and by decade); and (iii) the focus on intra-industry variations in trade credit use. Our two main results are: -

Trade credit use increases with firm quality. This result holds for the whole period, and for (almost) every decade separately, and is confirmed in cross-sectional year-by-year regressions;

-

As predicted by our theoretical analysis, the potential diversion of inputs affects the intensity of signaling activities by firms. The empirical evidence indicates that, at the intra-industry level, it is the repossession hypothesis that drives this result: the more liquid are the inputs (and therefore the more potentially likely they are to be repossessed by suppliers), the more intense is the signaling activity.

These results clearly support the idea that the signaling hypothesis is a factor in explaining the demand for trade credit by firms. They also support the role of input diversion as a driving factor in this signaling activity. These are, in our eyes, our main contributions. Our work is related to Antov and Atanasova’s (2007) recent contribution. They focused on the dynamics of firms’ choice of short-term external funding (intermediate loans or trade credit), and developed a signaling model based on the liquidity advantage to suppliers suggested by Frank and Maksimovic (1998). The main prediction of their model is that trade credit can serve as a reputational signal, giving firms using trade credit easier access to intermediate financing. The authors then provide supporting empirical evidence: the more trade credit is used, the more available institutional loans become to borrowers. While the main prediction of our model is essentially the same (the use of trade credit can serve as a signal of quality), there are two significant differences in our approach. These are the source of the signal (the degree of input diversion), and our direct tests of the signaling role of trade credit. Our empirical evidence confirms in particular that input diversion is a factor driving trade credit as a signal of quality.

In the second section of this paper, we introduce our theoretical analysis with the aim of determining whether input diversion can explain the use of trade credit as a signal of quality. The third section is dedicated to comparing our theoretical analysis with empirical results. Section 4 presents our conclusions.

2. Using Trade Credit to Signal Quality Our model does not include the trade credit features classically put forward in the literature (price discrimination, collateral liquidity, monopoly rent and informational advantage) with the exception of two of them: the high (implied) cost of trade credit and the degree of potential diversion of the inputs. As mentioned in the introduction, the high (implied) cost of trade credit has been reported by many previous researchers. Burkart and Ellingsen (2004) focused on the degree of illiquidity of suppliers’ deliveries. Some suppliers’ goods are standardized commodities, traded on active secondary markets; others are highly specialized goods, produced at the request and according to the specifications of customers. Burkart and Ellingsen (2004) examined the demand-side role of illiquidity: the more specialized the goods, the more restricted the buying firm’s managers are in their usage. In other words, the more illiquid are the suppliers’ goods, the more difficult it is for managers to divert them from their intended usage. We refer to this argument as the input liquidity hypothesis. In a world of asymmetric information, this limits the moral hazard issues faced by suppliers. Input illiquidity can, however, also be analyzed from the perspective of suppliers (the supply side) in the spirit of Frank and Maksimovic (1998): the more liquid the inputs, the more incentives suppliers have to repossess them and to sell them back on the secondary market, and the lower is the probability that the manager will keep them if business activity is disrupted (in which case no asset diversion is possible). We refer to this second argument as the input repossession hypothesis. We note also that the more at risk and close to bankruptcy the firm, the more potentially severe these issues. In such a situation, managers have greater incentives to divert existing assets to their own benefit (under the input liquidity hypothesis) or the more they are exposed to the risk of having their inputs repossessed by suppliers repossessing (under the input repossession hypothesis). So, under both hypotheses, the possibility of diverting assets affects managers of low quality firms more than managers of high quality firms. In such a context, using trade credit to signal quality may make sense: managers of high quality firms would accept the financing of a fraction of the firm’s activities through an expensive source of funds since it could be interpreted by outside investors as a signal of

the firm’s quality. The signal is credible because its marginal cost decreases with the quality of the firm, and it can therefore not be replicated by low-quality firms. This is the intuition that drives our theoretical analysis. 2.1. Firms and activities Consider a firm managing one single risky activity, the size of which can be normalized to one without loss of generality. We model the risk of the firm’s activity in the form of a probability of success, denoted 𝑥. As the firm is managing only one activity, we assimilate below the firm and the probability of success of its activity. Firms are distributed in the range 𝑐, 𝑑 (with 0 ≤ 𝑐 < 𝑑 ≤ 1) according to the cumulative density function 𝐹 (with a corresponding probability density function 𝑓). The firm has access to two sources of finance: bank loans and trade credits. More specifically, each firm can choose a mix between bank loans and trade credits to finance its activity. We distinguish three periods, denoted 0, 1 and 2. In period 𝑡 = 0, the firm 𝑥 invests 1 unit of capital into an activity generating a unique flow of cash 𝐾 two periods later with probability 𝑥 (the firm/activity probability of success). With probability (1 − 𝑥), the activity fails. A fraction 𝛼 of this activity is funded by trade credits and the remainder (1 − 𝛼) by bank loans. 2.2. Information and decisions The managers are assumed to have perfect knowledge of the probability of success 𝑥 of their firms. Banks and suppliers are also assumed to be perfectly informed about the riskiness of firms asking for funding. However we assume that the interest rate charged by banks 𝑟𝑏 (𝑥) and the (implicit) interest rate charged by suppliers 𝑟𝑠 (𝑥) are non-informative4: 𝑟𝑏 (𝑥) and 𝑟𝑠 (𝑥) cannot be inverted to infer the level of risk of the firms. Many academic studies have indeed shown that interest rates are only slightly, if at all, related to borrowers’ riskiness (see Petersen and Rajan 1994, Cole 1998, Elsas and Krahnen 1998, Harhöff and Körting 1998). Interest rates appear to include a premium which is a function of the power balance between creditors and borrowers. The exact state of this balance of power is private information between the parties involved. External investors (referred to below as the financial market), by observing interest rates, obtain therefore, at best, a noisy signal of the creditor’s riskiness. We model the market power of banks and suppliers explicitly by two parameters 𝜋𝑏 and 𝜋𝑠 , that represent the monopoly rents these creditors capture at the equilibrium of the economy.5 If there is

4 5

The corresponding gross rates are 𝑅𝑏 (𝑥) and 𝑅𝑠 (𝑥). For the theoretical foundation of the informational monopoly argument, see Sharpe (1990).

perfect information (Section 2.4), the financial market knows the firm’s risk level and, if there is no information (Section 2.5), the financial market ignores it. In period 𝑡 = 0, the financial market infers the firm’s probability of success 𝑥 from the share of the firm’s activity financed by trade credit (𝑥 = 𝑥 𝛼 ). In period 𝑡 = 1, the firm’s manager receives some information 𝑠 that perfectly informs him or her about the outcome of the activity (𝑠 = 𝐷 if the activity will fail in period 𝑡 = 2 and 𝑠 = 𝑆 if the activity will succeed in period 𝑡 = 2). Remember that, if the activity is successful it produces the cash flow 𝐾, but if it fails no cash flow is generated. Using this information, the manager decides either to maintain the activity (if 𝑠 = 𝑆) or to discontinue the activity immediately (𝑠 = 𝐷). In the latter case (𝑠 = 𝐷), the manager diverts all the financed assets to his or her own profit (which illustrates the moral hazard issue with which creditors are faced).6 2.3. Agent utilities All agents are risk neutral and 𝑟, the interest rate of the economy, is equal to the risk-free rate. Without loss of generality, we can normalize this to zero. The manager-expected utility in period 𝑡 = 0 incorporates two components. The first is related to the firm’s market value 𝑉(𝑥)7 and represents the classical incentive contracts put into place by shareholders (see, for example, Hall and Liebman 1998). The second comes from the firm’s assets diversion to the manager that will occur if the activity is stopped in period 𝑡 = 1. We define the manager utility of a firm with probability success 𝑥, financing a fraction 𝛼(𝑥) of its activity by trade credit, as 𝑈 𝑥 = 𝑏𝑉 𝑉 𝑥 + 𝑏𝐷 (1 − 𝑥) 1 − 𝛼(𝑥) + 𝛽𝛼(𝑥)

(1)

where 𝑏𝑉 captures the manager contract incentives to maximize the firm’s value 𝑉 𝑥 , and 𝑏𝐷 captures the valuation of the firm’s asset diversion in the eyes of the manager in the event of activity failure. Activity failure happens with probability 1 − 𝑥 and asset diversion originates from two sources: (i) assets financed by the bank can fully be diverted; and (ii) assets financed by trade credit can only be partially diverted. The coefficient 𝛽 captures the degree to which suppliers’ inputs are

6

7

If we assume that, in the 𝑠 = 𝐷 case, there is only a positive probability (not certainty) that the firm will cease trading, and/or that, if it does stop trading, only a fraction of the financed assets will be diverted, the conclusions of our analysis are unchanged. However adopting these assumptions would force us to introduce more notation. Note that, because in our setup the firm realizes only one project and only projects with positive net present value are undertaken, 𝑉(𝑥) must be positive.

diverted. Its interpretation depends on the view that we adopt of the role of the illiquidity of suppliers’ inputs8: (i)

Under the input liquidity hypothesis (Burkart and Ellingsen, 2004), only a fraction 𝛽 (with 𝛽 < 1) of suppliers’ inputs can be diverted because they are less liquid than bank loans.

(ii) Under the input repossession hypothesis (Frank and Maksimovic, 1998), the more liquid suppliers’ inputs are, the higher is the probability that they will be repossessed. In this case 𝛽 is the fraction of suppliers’ inputs that will be left in the firm. Under assumption (i), 𝛽 is a positive function of the liquidity of suppliers’ inputs, whereas under assumption (ii), 𝛽 is a negative function of the liquidity of suppliers’ inputs. Figure 1 summarizes our model and its notation. 2.4. Perfect information We start our analysis by considering the case of perfect information: the financial market knows the firm’s risk level 𝑥. The risk-free rate being normalized to zero, the market value of the firm in period 𝑡 = 0 can then be written: 𝑉 𝑥 = 𝑥 𝐾 − 𝛼 𝑥 𝑅𝑠 𝑥 − 1 − 𝛼 𝑥 𝑅𝑏 (𝑥) .

(2)

The firm is exposed to the market power of its creditors (the banks and the suppliers). The main difference between bank loans and trade credits lies in the degree of diversion of the inputs supplied: while bank loans can be fully diverted from their intended use, only a fraction 𝛽 of suppliers’ deliveries can be diverted, which means that the suppliers are guaranteed to get back at least (1 − 𝛽) of their credits if activity is disrupted. As we denote by 𝜋𝑏 and 𝜋𝑆 the monopoly rents of the banks and the suppliers respectively in the economy at equilibrium, and as the risk-free rate is normalized to zero, the (implicit) interest rates 𝑅𝑠 𝑥 and 𝑅𝑏 𝑥 obtained by the firm must satisfy conditions (3) and (4): 𝑥𝑅𝑠 𝑥 + 1 − 𝑥 1 − 𝛽 = 1 + 𝜋𝑠 𝑥𝑅𝑏 𝑥 = 1 + 𝜋𝑏 8

(3) (4)

Note that, assuming that only a fraction of the assets financed by banks can be diverted does not change our analysis. The key condition is that assets financed by trade credit are easier to divert than those financed by financial institutions.

By substituting Equations (2) to (4) into Equation (1), the manager utility function can be reformulated as: 𝑈 𝑥 = 𝑏𝑉 𝐾𝑥 − 𝑏𝑉 1 + 𝜋𝑏 + 𝑏𝐷 1 − 𝑥 + 𝛼(𝑥) 𝑏𝑉 𝜋𝑏 − 𝜋𝑠 + 𝑏𝑉 1 − 𝑥 1 − 𝛽 − 𝑏𝐷 1 − 𝛽 (1 − 𝑥)

(5)

From Equation (5), it appears that it will be optimal for the firm to finance its activities exclusively by banks if condition (6) is fulfilled: 𝑏𝑉 𝜋𝑏 − 𝜋𝑠 + 𝑏𝑉 − 𝑏𝐷 1 − 𝛽 1 − 𝑥 < 0

(6)

Proof: if 𝑏𝑉 𝜋𝑏 − 𝜋𝑠 + 𝑏𝑉 − 𝑏𝐷 1 − 𝛽 1 − 𝑥 < 0, 𝑏𝑉 𝜋𝑏 − 𝜋𝑠 + 𝑏𝑉 1 − 𝑥 1 − 𝛽 − 𝑏𝐷 1 − 𝛽 (1 − 𝑥) is negative and 𝑈(𝑥) is maximized by choosing 𝛼(𝑥) = 0.

Condition (6) deserves some interpretation. At equilibrium, the manager will choose the least expensive source of funding. In the case of perfect information, the two effects of using trade credit are (i) 𝑏𝑉 𝜋𝑏 − 𝜋𝑠 , which captures the interest rate differential between bank loans and trade credit, and (ii) 𝑏𝑉 − 𝑏𝐷 1 − 𝛽 1 − 𝑥 , which captures the loss of utility due to the limited opportunities that the manager enjoys to divert assets financed by suppliers. If the sum of these two effects is negative, only bank loans will be used. In practice, as trade credit is known to be far more expensive than bank loans 𝑟𝑠 𝑥 ≫ 𝑟𝑏 (𝑥) , we expect 𝜋𝑠 ≫ 𝜋𝑏 . We also expect 𝑏𝐷 ≫ 𝑏𝑉 (benefits from the diversion of direct assets should be an order of magnitude bigger than the fraction of the firm’s value captured by the manager through incentive contracts, unless the manager owns a large fraction of the firm personally). Therefore, with perfect information, trade credit should not be used as it cumulates disadvantages: it is more expensive and it limits the opportunities for asset diversion. We will assume below that Condition (6) is fulfilled to see whether, under imperfect information, some interest in the use of trade credit can be restored. 2.5. Imperfect information and the signaling role of trade credit We now consider the case in which the manager, banks and suppliers have perfect knowledge of the firm’s probability of success, but the financial market does not. Outside investors can, however, observe the firm’s financial structure and they can try to infer information from that. In our model, as the firm’s activity is only financed by bank loans and/or trade credit, 𝛼(𝑥) characterizes the firm’s financial structure.

Consider the manager of a firm with probability of success 𝑦. Assume that this manager decides to cheat, and tries to persuade investors that the firm has a probability of success 𝑥, with 𝑥 > 𝑦. To do this, the manager will mimic the behavior of firms with a probability of success 𝑥, and will choose a fraction 𝛼(𝑥) of trade credit financing. The expected utility of this manager in period 𝑡 = 0 can be expressed as: 𝑈 𝑥, 𝑦 = 𝑏𝑉 𝑥 𝐾 − 𝛼 𝑥 𝑅𝑠 𝑦 − 1 − 𝛼 𝑥 𝑅𝑏 (𝑦) + 𝑏𝐷 (1 − 𝑦) 1 − 1 − 𝛽 𝛼(𝑥) (7) where 𝑦 represents the real risk level of the firm and 𝑥, the risk level reported by the manager. It is important to note that: (i)

banks and suppliers being perfectly informed, 𝑅𝑠 . and 𝑅𝑏 (. ) are functions of the real risk level of the firm (𝑦);

(ii) the market value of the firm is the product of its cash flow 1 − 𝛼 𝑥 𝑅𝑏 (𝑦)

𝐾 − 𝛼 𝑥 𝑅𝑠 𝑦 −

and 𝑥, the firm’s risk level chosen by the manager, as the financial

market infers the firm’s risk level from the signal 𝛼(𝑥); (iii) the expected value of asset diversion (1 − 𝑦) 1 − 1 − 𝛽 𝛼(𝑥)

is a function of the real

risk level of the firm (𝑦) as it is known by the manager. The manager chooses the signal to be sent to the financial market 𝛼(𝑥) in order to maximize his or her expected utility. The first order condition is: 𝜕𝑈 (𝑥,𝑦 ) 𝜕𝑥

= 0.

(8)

This leads to the following first order differential equation: 𝑏𝑉 𝐾 − 𝛼 𝑥 𝑅𝑠 𝑦 − 1 − 𝛼 𝑥 𝑅𝑏 𝑦 +𝑏𝑉 𝑥 −𝛼 ′ 𝑥 𝑅𝑠 𝑦 + 𝛼 ′ 𝑥 𝑅𝑏 (𝑦) − 𝑏𝐷 1 − 𝑦 1 − 𝛽 𝛼 ′ 𝑥 = 0

(9)

By the revelation principle (Myerson, 1981), a signaling equilibrium is obtained when the manager truthfully reports the risk level of the firm i.e. when 𝑥 = 𝑦. The signaling constraint is therefore obtained by substituting 𝑥 for 𝑦 in Equation (9): 𝑏𝑉 𝐾 − 𝛼 𝑦 𝑅𝑠 𝑦 − 1 − 𝛼 𝑦 𝑅𝑏 𝑦 +𝑏𝑉 𝑦 −𝛼 ′ 𝑦 𝑅𝑠 𝑦 + 𝛼 ′ 𝑦 𝑅𝑏 (𝑦) − 𝑏𝐷 1 − 𝑦 1 − 𝛽 𝛼 ′ 𝑦 = 0

(10)

Equation (10) holds for every 𝑦 in the economy, so it holds for any value of 𝑥. By substituting 𝑅𝑏 𝑦 and 𝑅𝑠 𝑦 by their corresponding expressions in Equations (3) and (4), we obtain: 𝑏𝑉 𝐾 − 𝛼 𝑥

𝜋𝑠 − 𝜋𝑏 − 1 − 𝑥 1 − 𝛽 1 + 𝜋𝑏 − 𝑥 𝑥

= 𝑏𝑣 𝛼 ′ (𝑥) 𝜋𝑠 − 𝜋𝑏 +

𝑏𝐷 𝑏𝑉

−1

1 − 𝛽 (1 − 𝑥)

(11)

Equation (11) leads to proposition 1. Proposition 1 If Equation (6) is satisfied, the share of assets financed by trade credit 𝛼 𝑥 is a credible signal of the firm’s risk level 𝑥. In this case, 𝛼 𝑥 is an increasing function of the firm quality 𝑥. Proof: see Appendix A. The intuition behind Proposition 1 is that the higher the firm quality (i.e. the higher the probability of success 𝑥), the lower the probability that the firm will receive negative information in the period 𝑡 = 1 (𝑠 = 𝐷). This lowers the expected value of asset diversion. It is therefore less costly for the manager of a high quality firm to finance the activity using trade credit. Remember that trade credit is characterized by the degree of liquidity of the inputs, and that, under both the liquidity hypothesis and the repossession hypothesis; this limits the diversion opportunities of the manager if divesture becomes necessary.9 Managers of high quality firms can afford to finance a high share of their activity using trade credit. The reverse is true for managers of low quality firms. Because the probability of divesture is high, the opportunity to divert a large fraction of the assets contributes significantly to their expected utility. Managers of low quality firms are therefore more reluctant to use trade credit. A different signaling equilibrium is reached: the marginal cost of the signal (the diversion opportunities of the trade credit inputs) is lower for high quality firms than for low quality firms. In equilibrium, high quality firms will therefore send a stronger signal (they will choose a higher level of 𝛼(𝑥)) than low quality firms. This verifies Spence’s (1973) condition. 2.6. Implications Equation (11) has no close form solution, except when 𝜋𝑏 = 𝜋𝑠 and the ratio of 𝑏𝑉 to (𝑏𝐷 − 𝑏𝑉 ) is an integer value. In Appendix B we provide the explicit solution in this specific case and in this

9

The liquidity hypothesis and the repossession hypothesis do, however, predict different signs for the relation between the degree of liquidity of the suppliers’ inputs and diversion opportunities.

section we explore numerically the behavior of Equation (11) without imposing this restriction. Our numerical simulations were obtained using the Runge and Kutta method, with Order 4 level of precision. Our simulation parameters are: -

the probability of success 𝑥 is uniformly distributed between 0.625 and 0.925;

-

the manager’s incentives to maximize the firm’s market value 𝑏𝑉 and assets diversions 𝑏𝐷 are set to 1 and 0.1 respectively;

-

the market power coefficients of suppliers 𝜋𝑠 and banks 𝜋𝑏 equal 0.1 and 0.03 respectively;

-

the activity cash flow 𝐾 is set at 1.65;

-

the degree of diversion of the suppliers’ inputs 𝛽 varies between 0 and 1.

Figure 2 summarizes our results. Panel A shows clearly that the proportion of a firm’s assets financed by trade credit 𝛼(𝑥) increases as the probability of success 𝑥 increases: the use of trade credit is a signal of quality. Panel B adds another dimension to the analysis: the diversion of the suppliers’ inputs 𝛽 (remember that 𝛽 represents the fraction of a firm’s assets that are financed by trade credit that can be diverted in the event of activity disruption). So, the lower is 𝛽, the lower are the diversion opportunities and vice-versa. Panel B shows that an increase in diversion opportunities strengthens the relation between trade credit use and the firm’s probability of success. In other words, firms with high 𝛽 coefficients will use trade credit aggressively to signal their quality (trade credit is not very costly as suppliers’ inputs can easily be diverted), while firms with low 𝛽 coefficients will use trade credit more cautiously, as trade credit use strictly limits their opportunities to divert assets. Panels A and B of Figure 2 are graphical representations of the two hypotheses that we will test empirically in Section 3: Hypothesis 1 – The signaling role of trade credit Trade credit increases with firm quality. Hypothesis 2 – The opportunities for the diversion of suppliers’ inputs are a source of the signaling role of trade credit

For a given level of firm quality, the higher the suppliers inputs diversion opportunities, the more trade credit is used to signal quality.

3. Empirical Evidence 3.1. Data, sample and method Industry classification As mentioned in the introduction, we are interested in the determinants of the intra-industry variation in the use of trade credit. Choosing the right industry classification is therefore a key empirical issue. All classification schemes are known to suffer from shortcomings (Bhojra et al. 2003). The use of CRSP provided SIC codes has the advantage of reflecting historical information. The choice between two or three digit SICs is delicate, the two-digit classification being very raw and the three-digit one producing very small sub-samples of firms. To find the right balance between homogeneity and sub-sample sizes, we decided to use the 49-industry Fama/French classification scheme. The conversion between the historical SIC codes and Fama/French classification has been achieved by using the conversion table provided by Ken French on his web site.10 Firm quality proxy In order to test the main predictions of the model introduced in Section 2 (the signaling role of trade credit and the opportunities for diverting inputs as a source of signaling), we had to build an empirical proxy of the firm quality (the probability of success 𝑥, as described in Section 2). This is challenging: signaling only makes sense if the information is private while, as external analysts, we only have access to external public information. To solve this conundrum, our strategy was the following: (i)

We computed the Altman ZScore (1968, 2000) for each firm as a proxy of the probability of success. The ZScore (and closely related scoring models) has been extensively used in the financial community (by financial intermediaries, among others) as an indicator of the probability of bankruptcy.11 As such, the ZScore allows us to capture the firm quality as perceived by professionals.

10 11

See http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html The ZScore model has become such a commonplace that nowadays interactive web sites (e.g. http://www.insolvencyhelpline.co.uk/interactive-tools/z-calc.htm) provide free ZScore computation.

(ii) We studied the relationship between the use of trade credit at the end of the fiscal year 𝑡 and the value of the ZScore at the end of the same fiscal year. As financial statements are published several months after the end of the fiscal year, the ZScore is, at the moment at which we observe the trade credit use, still private information. (iii) In our robustness checks, we went one step further, studying the relationship between the use of trade credit at the end of the fiscal year 𝑡 with the ZScore at the end of the fiscal year 𝑡 + 1. This forward-looking approach alleviates any risk of using only public information as a proxy for private information. This is, however, at the cost of obtaining a noisier estimator of the firm’s quality at the end of fiscal year 𝑡, as it involves (potentially many) exogenous shocks between the end of fiscal year 𝑡 and the end of fiscal year 𝑡 + 1. It is finally worthwhile stressing that, although the ZScore clearly incorporates public information, its use as a proxy of private information rests on its positive correlation with firm quality. From this point of view, the use of the ZScore is clearly judicious. Sample composition The use of the ZScore as a proxy form firm quality drives the composition of our sample. Many previous empirical studies of trade credit (e.g. Petersen and Rajan 1997 and Burkart et al. 2008) use the National Survey of Small Business Finance (NSSBF) database. The NSSBF database is provided by the Board of Governors of the Federal Reserve System12 and includes detailed information on the financing and history of relations between small business firms and financial institutions. It is based on surveys undertaken in 1987, 1993, 1998 and 2003. The firms involved are really small: Petersen and Rajan (1997) report, for the 1987 edition, a sample of 3,404 firms with median total assets of USD 130,000 and median total sales of USD 300,000. This database has attracted the focus of academics due to the richness of the information it provides. Moreover, as stressed by Petersen and Rajan (1997), “this dataset focuses on small firms, which are more likely to face constraints on their ability to raise capital”. However, the main drawback of the NSSBF database is that most of the firms included are not listed, and the computation of the ZScore requires an estimate of the firm’s market value to be available. It is therefore not a viable source of information for our purposes. Our empirical study relies on an extensive sample of firms extracted from the CRSP/Compustat universe. The main drawback of this approach is that we do not have access to the richness of information provided by the NSSBF database but, in exchange, we get some important benefits:

12

The database is freely available at http://www.federalreserve.gov/boarddocs/surveys/

(i) First and foremost, we are able to compute the ZScore. (ii) We can work on a very long time horizon (from 1977 to 2005), collecting yearly data. This allows us to test the stability of our results by sub-periods and to use a fixed effect panel data approach to control for time-invariant unobservables. (iii) Our sample involves much larger firms (median total assets of USD 55 million and median total sales of USD 44 million), which are less subject to credit constraints. So the use of trade credit is a deliberate choice, a situation which is more suited to testing signaling theories. Table 1 presents our dataset. We analyzed the period from 1977 to 2005, starting from the CRSP/Compustat universe. We retained firm/year observations for which all the CRSP/Compustat items we needed were available (see below for our variable definitions). Our final sample included 1,958 different listed firms and 10,893 firm/year observations. The main facts that emerge from Table 1 are: (i)

The importance of trade credit in financing US firms. On average, during the period 1977 to 2005, trade credit represented 28% of total debts and 16% of total assets. Both these statistics increased through time. By the end of 2005, trade credit amounted to 25% of total assets!

(ii) The large difference in the use of trade credit between small companies (total assets below USD 50 million) and large companies (total assets above USD 50 million). Maybe unexpectedly, trade credit is consistently used more by large companies than by small ones. By the end of 2005, trade credit financing reached 38.61% of the total assets of large companies! Welch (2006) reports similar evidence (non-financial liabilities representing more or less 50% of US firms’ total assets). (iii) The increase in trade credit use is driven by large companies. Close inspection of Table 1 reveals a significant shock at the beginning of the 1990s. At that time, trade credit jumped by at least 10% for large companies. The reasons for such a change remain to be explored. A first guess might be that this change in financing behavior is related to the important regulatory changes (such as, the Instate Banking and Branching Efficiency Act of 1994) that the US banking sector underwent at that time.

Our dataset allows us also to study the evolution of the variance of trade credit use through time. Table 2 focuses on the ratio of trade credit to total debts (which is more closely related to the proportion of the firm’s activity financed by trade credit 𝛼(𝑥) introduced in Section 2 than is the ratio of trade credit to total assets). We present the year-by-year development of the total variance of the trade credit to total debts ratio (i.e. the variance of the ratio among the firms included in our dataset in a given year), the average of the intra-industry variance (the average of the variance of the trade credit to total debts ratio computed for each industry), the variance of the inter-industry averages (the variance of the average ratio of trade credit to total debts by industry) and, finally, the ratio of the intra- and the inter-industry variance. Table 2 highlights the importance of the intraindustry variation in trade credit use with respect to the inter-industry variation: the ratio of these variances is on average 2.39, and it reached a peak at the beginning of the 1990s. This corresponds to the period in which trade credit use by large companies increased. These statistics justify the importance of understanding the determinants of trade credit use beyond the industry determinants already identified up to now. Variables We compute the ZScore using the Altman (1968, 2000) formula: 𝑍𝑆𝑐𝑜𝑟𝑒 = 0.012 𝑋1 + 0.014 𝑋2 + 0.033 𝑋3 + 0.006 𝑋4 + 0.999 𝑋5

(12)

where: -

𝑋1 is the ratio of working capital (Compustat Item 4 minus Compustat Item 5) to total assets (Compustat Item 6);

-

𝑋2 is the ratio of retained earnings (Compustat Item 36) to total assets (Compustat Item 6);

-

𝑋3 is the ratio of earnings before interest and taxes (Compustat Item 13 minus Compustat Item 14) to total assets (Compustat Item 6);

-

𝑋4 is the ratio of market value of equity (Compustat Item 25 times Compustat Item 199) to the book value of total debts (Compustat Item 6 minus Compustat Item 60);

-

𝑋5 is the ratio of total sales (Compustat Item 12) to total assets (Compustat Item 6).

We also use the ratio of intangibles (Compustat Item 33) to total assets (Compustat Item 6), and the ratio of trade credit (Compustat Item 70) to the book value of total debts (Compustat Item 6 minus Compustat Item 60) or total assets (Compustat Item 6) in our empirical investigations. All our ratios are winsorized to percentiles 0.01 and 0.99 to neutralize the effects of outliers. The ratio of intangibles to total assets is used as a control variable because it may proxy for factors driving the use of trade credit. Intangibles may be due to the intensive research and development activities of growing firms, potentially subject to financial constraints (a determinant of trade credit, as already pointed out by Petersen and Rajan 1997). But intangibles may also proxy for opacity and information asymmetry, a context in which signaling activities using trade credit may take place (as argued by Biais and Gollier 1997). Both arguments lead to a positive relationship between intangibles and trade credit use. We therefore expect a positive coefficient in our empirical analyses when trade credit is regressed on intangibles but, even if this is found, we will not be able to identify the cause of the effect. Table 3 presents some descriptive statistics, including the mean, median and standard deviation of each ratio. Comparisons of means to medians show that most ratios (except the ZScore, total sales to total assets and trade credit use) display significant skewness (left or right). The coefficients of variation highlight the high dispersion of several ratios (working capital to total assets, retained earnings to total assets, earnings before interest and taxes to total assets, market value of equity to book value of total debts, intangibles to total assets and, for industry adjusted values, trade credit to total assets). Some interesting figures are the mean ratio of working capital to total assets (working capital amounts to around 19% of total assets), the mean ratio of market value of equity to book value of total debts (around 10), the mean ratio of total sales to total assets (close to 1) and the mean ratio of intangibles to total assets (near 5%). The values for trade credit use ratios confirm the evidence presented in Table 1. We also use the data provided in Appendix 1 of Burkart et al. (2008) to build an industry input illiquidity index. Burkart et al. (2008) follow Rauch’s (1999) product classification, and distinguish between standardized goods (products that can be sold as easily by their producer as by any other agent), differentiated goods (products from more advanced manufacturing sectors) and services (all other sectors). Burkart et al. then use the input-output matrices from the US Bureau of Economic Analysis to construct proxies for the input characteristics of each sector. More specifically, their Appendix 1 provides us, by two digits SIC codes, with the share of inputs coming from the standardized, differentiated and services sectors. These estimates are produced for the year 1999. Our input illiquidity index is computed as:

𝐼𝑙𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑠 = %𝐼𝑛𝑝𝑢𝑡𝑠𝑆𝑡𝑎𝑛𝑑 ,𝑠 × 1 + %𝐼𝑛𝑝𝑢𝑡𝑠𝐷𝑖𝑓𝑓 ,𝑠 × 2 + (%𝐼𝑛𝑝𝑢𝑡𝑠𝑆𝑒𝑟𝑣 ,𝑠 × 3) (13) where: -

𝐼𝑙𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑠 is the input illiquidity index of sector 𝑠;

-

%𝐼𝑛𝑝𝑢𝑡𝑠𝑆𝑡𝑎𝑛𝑑 ,𝑠 is the percentage of inputs to sector 𝑠 coming from sectors producing standardized goods;

-

%𝐼𝑛𝑝𝑢𝑡𝑠𝐷𝑖𝑓𝑓 ,𝑠 is the percentage of inputs to sector 𝑠 coming from sectors producing differentiated goods;

-

%𝐼𝑛𝑝𝑢𝑡𝑠𝑆𝑒𝑟𝑣 ,𝑠 is the percentage of inputs to sector 𝑠 coming from service sectors.

We also built a dummy version of our Illiquidity index variable that takes the value 1 for firms having an Illiquidity index value above the median of our sample. Econometric approach Taking into consideration the panel data structure of our sample, most of our multivariate analyses rely on the classical fixed effect estimator. The choice between the fixed effect estimator and a random effect estimator was dictated by the results of Hausman tests of specification. The use of the fixed effect estimator theoretically allows us to control for unobservables but, it can be argued that nothing is really constant across the long time-period that we are using. So, we also report estimation results by ten-year sub-periods to test for the robustness of our results using a fixedeffect estimator, as well as year-by-year cross-sectional regressions. For panel data estimations, we also include year dummies to control for time-specific effects (to avoid cluttering the tables, the coefficients for the year dummies are not shown). The model developed in Section 2 predicts a positive relation between firm quality and trade credit use but provides no specific clues about the form of the relation. In particular, there is, a priori, nothing that leads us to expect that it should be linear. We therefore included the square of the ZScore in our specification to test for the presence of a second-order effect. As it has also been argued that trade credit is used more aggressively by credit-constrained firms (Petersen and Rajan 1997), we also added a default dummy variable that takes the value 1 when the firm is in the last decile of the ZScore distribution to our specification. The default dummy variable identifies the firms most likely to go bankrupt according to the Altman ZScore. Finally, in order to be sure that our proxy

variable for firm quality (ZScore) does not include a firm size effect, we added the natural logarithm of a firm’s total assets as a control variable. Our base specification is therefore: 𝑇𝑟𝑎𝑑𝑒 𝐶𝑟𝑒𝑑𝑖𝑡 𝑇𝑜𝑡𝑎𝑙 𝐷𝑒𝑏𝑡𝑠 𝑖,𝑡

𝐼𝑛𝑡𝑎𝑛𝑔𝑖𝑏𝑙𝑒𝑠

2 = 𝛼𝑖 + 𝛽1 𝑍𝑆𝑐𝑜𝑟𝑒𝑖,𝑡 + 𝛽2 𝑍𝑆𝑐𝑜𝑟𝑒𝑖,𝑡 + 𝛽3 log 𝑇𝑜𝑡𝑎𝑙𝐴𝑠𝑠𝑒𝑡𝑠𝑖,𝑡 + 𝛽4 𝑇𝑜𝑡𝑎𝑙

𝛽5 𝐷𝑒𝑓𝑎𝑢𝑙𝑡𝑖,𝑡 + 𝑌𝑒𝑎𝑟 𝐷𝑢𝑚𝑚𝑖𝑒𝑠 + 𝜀𝑖,𝑡

𝐴𝑠𝑠𝑒𝑡𝑠 𝑖,𝑡

+

(14)

where 𝑖 is the firm index and 𝑡 is the period index. We also used 𝑇𝑟𝑎𝑑𝑒 𝐶𝑟𝑒𝑑𝑖𝑡 𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠𝑖,𝑡 as a dependent variable to check, once again, the robustness of our results. The ratio 𝑇𝑟𝑎𝑑𝑒 𝐶𝑟𝑒𝑑𝑖𝑡 𝑇𝑜𝑡𝑎𝑙 𝐷𝑒𝑏𝑡𝑠𝑖,𝑡 is, however, a more direct proxy of the fraction of a firm’s assets financed by trade credit 𝛼(𝑥) as defined in Section 2. Let us finally stress that we only worked with industry adjusted ratios (this is to say, on the differences between the value of a ratio for a given firm and year and its corresponding industry mean), as we were looking for the determinants of intra-industry variance in the use of trade credit. 3.2. Results Trade credit use and firm quality Figure 3 presents a first analysis of the relation between our proxy for firm quality, the ZScore, and trade credit use, measured by 𝑇𝑟𝑎𝑑𝑒 𝐶𝑟𝑒𝑑𝑖𝑡 𝑇𝑜𝑡𝑎𝑙 𝐷𝑒𝑏𝑡𝑠𝑖,𝑡 . The figure shows the dataset (firm/year observations) divided into quartiles by ZScores trade credit use. ZScore 1 is the quartile of firms with the lowest ZScores, and ZScore 4 the quartile with the highest scores. TC1 is the quartile of firms with the lowest values of trade credit use and TC4 is the quartile with the highest ones. So, for example, 6.27% of firm/year observations are in the quartile of highest ZScore and highest trade credit use. The figure clearly highlights the existence of a relation between firm quality and trade credit use. For the lowest quartile of trade credit use (TC1), the proportion of firms using trade credit decreases as the firm quality improves. For the three other quartiles of trade credit use (TC2 to TC4), the proportion of firms using trade credit is an increasing function of the firm quality, with one exception: there is a high percentage of firms of low quality (Zscore1) using a lot trade credit (TC4), namely 12.68%. Table 4 reports estimates of Equation (14). In Panel A, the dependent variable is 𝑇𝑟𝑎𝑑𝑒 𝐶𝑟𝑒𝑑𝑖𝑡 𝑇𝑜𝑡𝑎𝑙 𝐷𝑒𝑏𝑡𝑠𝑖,𝑡 , while in Panel B, it is 𝑇𝑟𝑎𝑑𝑒 𝐶𝑟𝑒𝑑𝑖𝑡 𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠𝑖,𝑡 . In each case,

the results are given for the whole 1977 to 2005 period, and by ten-year sub-periods (9 years for the last sub-period). The main results that emerge are: (i) The coefficient of ZScore is positive and significant with two exceptions: in Panel A, for the 1997−2005 sub-period, the significance is marginal and in Panel B, for the same sub-period, the coefficient is negative and significant. This brings some early evidence supporting the signaling role of trade credit use (our hypothesis 1) over the last 30 years, but suggests that this use of trade credit may have weakened at the end of the 1990s and the early years of the new century. The coefficient of ZScore squared is always negative and usually significant. This highlights the existence of some concavity in the relationship between firm quality and trade credit use (the marginal impact of ZScore on the trade credit use decreases as firm quality increases). Equation (14) is a second-order polynomial in ZScore and therefore, the marginal effect of ZScore on trade credit use is given by 𝛽1 + 2 𝛽2 𝑍𝑆𝑐𝑜𝑟𝑒𝑖,𝑡 . For the whole period, this gives a marginal effect of firm quality on trade credit as a proportion of total debts of 0.027 at the mean value of ZScore (0.85, see Table 3). The corresponding figure for trade credit as a proportion of total assets is 0.005. Trade credit use is clearly increasing in ZScore. In economic terms, this signifies that, at the mean value of ZScore, if the ZScore of a firm improves by 10%, the share of trade credits in totals debts increases by 1%. (ii) The coefficient of the log of total assets is positive and significant in both panels for the 1977−2005 period. However sub-periods show differing results. Overall this supports the evidence reported in Table 1: bigger firms use relatively more trade credit. This result must, however, be treated with some care, as sub-period analyses reveal some time variation. (iii) Intangibles decrease the use of trade credit (except during the first decade where the results are not statistically significant). This is an unexpected result in the light of the theoretical arguments driving the inclusion of this control variable (firm opacity and/or growth financing) and needs to be investigated further. (iv) Finally we note that the default dummy variable has a positive coefficient in both panels for the 1977−2005 period; in Panel B this is significant. However the coefficients are not significant for the 1977−1986 sub-period; they are negative and significant in the 1987−1996 period and only positive and significant during the last period. The findings reported in Figure 3 (12.68% of low quality firms using a lot trade credit) thus seem to be a

recent phenomena. This is probably related to the weakening of the use of trade credit as a signal of quality during the most recent period (see Point (i) above). In Table 5, we present two robustness checks of these results. In Panel A, we use the ZScore estimated at the end of the fiscal year 𝑡 + 1 as a proxy for firm quality. This forward-looking approach strengthens the private-information dimension of the proxy, but at same time increases its noisiness, as many exogenous events may affect the firm’s quality during the period 𝑡 to 𝑡 + 1. All our conclusions are broadly confirmed: (i) the coefficient of the ZScore is positive and remains highly significant when 𝑇𝑟𝑎𝑑𝑒 𝐶𝑟𝑒𝑑𝑖𝑡 𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠𝑖,𝑡 is used as the dependent variable; (ii) the relation between trade credit use and ZScore is concave; (iii) firm size (measured by the log of total assets) increases trade credit use; (iv) intangibles still have a negative coefficient. The coefficient of the default dummy variable is more affected by the change of approach. It becomes negative and significant when 𝑇𝑟𝑎𝑑𝑒 𝐶𝑟𝑒𝑑𝑖𝑡 𝑇𝑜𝑡𝑎𝑙 𝐷𝑒𝑏𝑡𝑠𝑖,𝑡 is used as the dependent variable. A possible explanation of this change of sign is that firms currently in financial difficulties currently use more trade credit (due to credit constraints), but will have less access to trade credit in the future as their financial difficulties become more apparent and their suppliers more restrictive. In Table 5 Panel B, we report year by year cross-sectional estimates of Equation (14). The dependent variable is 𝑇𝑟𝑎𝑑𝑒 𝐶𝑟𝑒𝑑𝑖𝑡 𝑇𝑜𝑡𝑎𝑙 𝐷𝑒𝑏𝑡𝑠𝑖,𝑡 . Only the coefficient of ZScore, ZScore squared and the marginal effect of ZScore on 𝑇𝑟𝑎𝑑𝑒 𝐶𝑟𝑒𝑑𝑖𝑡 𝑇𝑜𝑡𝑎𝑙 𝐷𝑒𝑏𝑡𝑠𝑖,𝑡 (estimated at the mean value of Zscore) are presented. During the period 1977 to 1992, the cross-sectional regressions lead (qualitatively) to the same conclusions as those reported in Table 4: (i) Trade credit use increases with firm quality. Only for 1984 is the coefficient of ZScore negative, but even then it is not significant. (ii) The relationship between trade credit use and ZScore is concave for 27 out of 29 years, and the coefficient of ZScore squared is usually highly significant.

(iii) The marginal effect of ZScore, estimated at the ZScore mean value, is positive each year, with the exception of 1984. Finally it is interesting to note that the weakening of the positive relation between trade credit use and ZScore during the 1997−2005 period highlighted in Table 4 is not apparent is our cross-sectional regressions. As the Table 4 results were obtained using a panel data fixed-effect estimator (and therefore controlled for time-constant omitted variables), this may suggest that the results of crosssectional regressions are affected by a problem of omitted variables. The role of input illiquidity We now turn to the exploration of the relation between trade credit use, firm quality and input illiquidity. Under Hypothesis 2, the greater the opportunities for input diversion, the more trade credit should be used by firms to signal quality (see Figure 2 Panel B for a graphical representation). The chances of the manager diverting assets depend on the liquidity of the inputs. The relation between input illiquidity and asset diversion can, however, be either positive or negative: (i) under the liquidity hypothesis (Bukart and Ellingsen, 2004), the relationship should be negative: liquid inputs are easier for managers to divert; (ii) under the repossession hypothesis (Frank and Maksimovic, 1998), it should be positive: liquid inputs are more prone to be repossessed by suppliers. We therefore expect a significant impact of our Illiquidity index variable (and its dummy variable version) on the slope of the relationship between trade credit use and ZScore. The sign of this impact is an empirical issue. The regression model that we estimate at this stage is a modified version of Equation (14) which includes the cross-product between our Illiquidity index (or its dummy version) and the ZScore variable: 𝑇𝑟𝑎𝑑𝑒 𝐶𝑟𝑒𝑑𝑖𝑡 𝑇𝑜𝑡𝑎𝑙 𝐷𝑒𝑏𝑡𝑠 𝑖,𝑡

2 = 𝛼𝑖 + 𝛽1 𝑍𝑆𝑐𝑜𝑟𝑒𝑖,𝑡 + 𝛽2 𝑍𝑆𝑐𝑜𝑟𝑒𝑖,𝑡 +𝛽3 𝑍𝑆𝑐𝑜𝑟𝑒𝑖,𝑡 × 𝐼𝑙𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑖,𝑡

+𝛽4 log 𝑇𝑜𝑡𝑎𝑙𝐴𝑠𝑠𝑒𝑡𝑠𝑖,𝑡 + 𝛽5

𝐼𝑛𝑡𝑎𝑛𝑔𝑖𝑏𝑙𝑒𝑠 𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠 𝑖,𝑡

+ 𝛽6 𝐷𝑒𝑓𝑎𝑢𝑙𝑡𝑖,𝑡 + 𝑌𝑒𝑎𝑟 𝐷𝑢𝑚𝑚𝑖𝑒𝑠 + 𝜀𝑖,𝑡 (15)

Table 6 presents the results. The period of analysis is limited to 1989−1999. As explained in Section 3.1, we used data from Burkart et al. (2008) to build the Illiquidity index and these are only available from the end of 1999. Since relations among industrial sectors are quite stable through time, a 10-

year period seems a reasonable compromise between having a large number of observations and the validity of the Illiquidity index. Choosing a 5-year window does not affect our results qualitatively. Some particularly interesting aspects of the results presented in Table 6 are: (i) Input illiquidity has a positive and significant impact on the slope of the relationship between ZScore and trade credit use. This is true with and without control variables and using the Illiquidity index or its dummy variable version. (ii) The negative coefficients of ZScore in Columns (3) and (4) do not mean that the marginal effect of ZScore on trade credit use is negative. Remember that the marginal effect in such regressions must be evaluated at the mean values of the ZScore and Illiquidity index. In Column (3), the marginal effect of ZScore, evaluated in this way is 0.07. In Column (4), it is 0.064. These results confirm the role of input illiquidity as a determinant of the use of trade credit by firms to signal their quality. The positive relationship between the illiquidity of inputs and the use of trade credit supports the repossession hypothesis: liquid inputs are more prone to be repossessed by suppliers. As our analysis focuses on the intra-industry determinants of the use of trade credit, it should be noted that our results do not contradict those reported by Burkart et al. (2008): trade credit use can be higher, on average, in industries with less liquid inputs (the Burkart and al. (2008) results) because suppliers anticipate a lower risk of asset diversion and, simultaneously, inside a given industry, firms may signal their quality by trade credit use more aggressively when their inputs are illiquid because they are less exposed to asset repossession by suppliers in the event of financial difficulties. Let us finally note that these results are quite striking given the noisiness of our proxy of illiquidity. It is based on a classification of industries into three broad categories, using input/output tables published by the US Bureau of Economic Analysis and based on the two-digit SIC code industrial classification. Moreover we have assumed that the relationships between industries were stable over the 1989−1999 period.

4. Conclusion Trade credit is a major financing channel in modern economies. It has therefore legitimately attracted the attention of the academic community. Because one of the key features of trade credit use is its significant variation between industries, most studies have tried to establish the inter-

industry determinants of trade credit. Price discrimination (Meltzer 1960), collateral liquidation (Frank and Maksimovic 1998), information (Petersen and Rajan 1997) and input liquidity (Burkart and Ellingsen (2004)) have all been shown to play a role. Intra-industry variation in trade credit use remains, however, largely unexplored. This is somewhat surprising. Our results show that the intra-industry variance in trade credit use is at least as great as the inter-industry variance. Among the first to tackle this issue, Biais and Gollier (1997) opened a promising avenue of research: trade credit can be used by firms to signal their quality. These authors argue that the cost of using trade credit is marginally lower for high quality firms than for low quality firms because suppliers benefit from an informational advantage. High quality firms can therefore use trade credit to signal their quality. However the empirical evidence reported by Burkart et al. (2008) does not support this informational advantage hypothesis. In this paper we have introduced an alternative argument about the signaling role of trade credit use: input diversion. We argue that the costs associated with limits on input diversion decrease as firm quality increases. This is because the probability that diversion will take place is less in high quality firms. Our theoretical analysis shows that a signaling equilibrium can be built on this basis. Our empirical results, using a large sample of U.S. listed firms, clearly validate our predictions. The trade credit use is an increasing function of the firm Altman ZScore (1968), used as a proxy for the firm quality. Our empirical results also confirm that inputs diversion is one of the factors driving the signaling role of trade credit use: the more liquid are the inputs, the more intense is the signaling activity.

References Altman, E., 1968, Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy, Journal of Finance, vol. 23/4, pp. 589−609 Altman, E., 2000, Predicting Financial Distress of Companies: Revisiting the ZScore and Zeta Models, Stern School of Business, Working Paper Antov, D. and C. Atanasova, 2007, How Do Firms Choose between Intermediary and Supplier Finance? Paris, December Finance International Meeting AFFI-EUROFIDAI Paper Available at SSRN: http://ssrn.com/abstract=1069875 Bhojra, S., C. Lee and O. Derek, 2003, What’s My Line? A Comparison of Industry Classification Schemes for Capital Market Research, Journal of Accounting Research, vol. 41, pp. 745−774 Biais, B. and C. Gollier, 1997, Trade Credit and Credit Rationing, Review of Financial Studies, vol. 10, No. 4, pp. 903−937 Boyer, M., 2007, Why Are Trade Credits so Damn Expensive? It’s a Commitment Problem, Working Paper, Available at SSRN: http://ssrn.com/abstract=972647 Burkart, M. and T. Ellingsen, 2004, In-kind Finance: A Theory of Trade Credit, American Economic Review, vol. 94, No. 3, pp. 569−590 Burkart, M., T. Ellingsen and M. Giannetti, 2008, What You Sell is What You Lend? Explaining Trade Credit Contracts, Review of Financial Studies, forthcoming Cole, R., 1998, The Importance of Relationships to the Availability of Credit, Journal of Banking and Finance, vol. 22, pp. 959−977 Davydenko and Franks, 2008, Do Bankruptcy Codes Matter? A Study of Defaults in France, Germany and the UK, Journal of Finance, forthcoming Elsas, R. and J.P. Krahnen, 1998, Is Relationship Special? Evidence from Credit File Data in Germany, Journal of Banking and Finance, vol. 22, pp. 1283−1316 Frank, M. and V. Maksimovic, 1998, Trade Credit, Collateral, and Adverse Selection, World Bank, Policy Research Working Paper Hall, B., and J. Liebman, 1998, Are CEOs Really Paid Like Bureaucrats? Quarterly Journal of Economics, vol. 113, pp. 653−691 Harhöff, D. and T. Körting, 1998, Lending Relationships in Germany: Empirical Evidence from Survey Data, Journal of Banking and Finance, vol. 22, pp. 1317−1354 Kremp, E., 2006, Rapport annuel de l’observatoire des délais de paiement, Présidé par J.-P. Betbèze, Banque de France, Direction des Entreprises, Décembre, 143 pages Meltzer, A.H., 1960, Mercantile Credit, Monetary Policy and Size of Firms, Review of Economics and Statistics, vol. 42, pp. 429−437 Mian, S. and C. Smith, 1994, Extending Trade Credit and Financing Receivables, Journal of Applied Corporate Finance, vol. 7, pp. 75−84 Myerson, R., 1981, Optimal Auction Design, The Mathematics of Operations Research, vol. 6, pp. 58−73 Petersen, M. and R. Rajan, 1994, The Benefits of Lending Relationships: Evidence from Small Business Data, Journal of Finance, vol. 49, pp. 3−37 Petersen, M. and R. Rajan, 1997, Trade Credit: Theories and Evidence, Review of Financial Studies, vol. 10, No. 3, pp. 661−691

Rajan, R. and L. Zingales, 1995, What Do We Know about Capital Structure? Some Evidence from International Data, Journal of Finance, vol. 50, pp. 1421−1460 Rauch, J, 1999, Networks versus Markets in International Trade, Journal of International Economics, vol. 48, No. 1, pp. 7−35 Sharpe, M., 1990, Asymmetric Information, Bank Lending and Implicit Contracts: a Stylized Model of Customer Relationships, Journal of Finance, vol. 45, pp. 1069−1087 Smith, J., 1987, Trade Credit and Information Asymmetry, Journal of Finance, vol. 4, pp. 863−869 Spence, M., 1973, Job Market Signaling, Quarterly Journal of Economics, vol. 90, pp. 1−23 -

Welch, I, 2006, Common Flaws in Empirical Capital Structure Research, Available at SSRN: http://ssrn.com/abstract=931675

Figure 1. Our model Figure 1 presents the model developed in Section 2. There are three time periods: 𝑡 = 0, 𝑡 = 1 and 𝑡 = 2. 𝑥 is the probability of success of the firm (or activity). 𝛼(𝑥) is the fraction of the firm’s assets financed by trade credit, while (1 − 𝛼 𝑥 ) is the fraction financed by bank loans. 𝑅𝑏 (𝑥) is the gross interest rate charged by banks and 𝑅𝑆 (𝑥) is the (implicit) gross interest rate charged by suppliers. 𝑠 represents the information received by the manager in period 𝑡 = 1, which can be either 𝑆 for success or 𝐹 for failure. 𝐾 is the cash flow produced by the activity if it is successful.

𝒕=𝟎

𝒕=𝟏

𝒕=𝟐

𝑠=𝑆

𝑠=𝐹 Information -

Manager: 𝑥

-

Banks/suppliers: 𝑥

-

Financial market:

Information -

Manager: 𝑠 ∈ 𝑆, 𝐹

-

perfect info: 𝑥

Decision

-

imperfect info: 𝛼(𝑥)

-

Decision -

Manager: 𝛼(𝑥)

-

Banks: 𝑅𝑏 (𝑥)

-

Suppliers: 𝑅𝑠 (𝑥)

Manager: activity disruption

Activity cash flows

𝐾 0

Figure 2. The results of the numerical simulations Figure 2 presents the result of the numerical simulations of the model developed in Section 2. Panel A explores the relation between the probability of success of the firm’s activity (𝑥) and the percentage of the firm’s activity financed by trade credit (𝛼(𝑥)). Panel B adds a third dimension, the degree of liquidity of suppliers’ inputs (𝛽).

1.2

Trade credit financing

1

0.8 0.6

0.4 0.2

0.625 0.635 0.645 0.655 0.665 0.675 0.685 0.695 0.705 0.715 0.725 0.735 0.745 0.755 0.765 0.775 0.785 0.795 0.805 0.815 0.825 0.835 0.845 0.855 0.865 0.875 0.885 0.895 0.905 0.915 0.925

0

Probability of Success

Panel A

100% 90% 70% 60% 50% 40% 30% 20% 10% 0% 0.625

0.75

0.675

0.725

0.775

0.825

Probability of Success

Panel B

0 0.875

0.925

Diversion

Trade Credit

80%

Figure 3. The relationship between firm quality and the use of trade credits Figure 3 shows the relationship between ZScores and Trade Credit Total Debtsi,t for each quartile of ZScore and quartile of trade credit use. ZScore 1 is the quartile of firms with the lowest ZScores and ZScore 4 the quartile with the highest scores. TC1 is the quartile of firms with the lowest values of Trade Credit Total Debtsi,t and TC4 the quartile with the highest ones.

14.00%

Z-Score Quartile

12.00% 10.00% 8.00%

6.00% 4.00%

ZScore 4

2.00%

ZScore 3 ZScore 2

0.00%

TC 1

ZScore 1

TC 2

TC 3

TC 4

TC 1

TC 2

TC 3

TC 4

ZScore 1

7.63%

2.40%

2.29%

12.68%

ZScore 2

10.10%

6.62%

4.91%

3.38%

ZScore 3

4.85%

9.80%

7.67%

2.67%

ZScore 4

2.43%

6.18%

10.13%

6.27%

Trade Credit Quartile

Table 1. Our dataset Table 1 presents our dataset. # Firms is the number of firms for which data is available in each year. The next columns report the development of the use of Trade Credit by US firms year by year during the period 1977−2006. Trade Credit is estimated using Account Payables (Compustat Item 70). Total Debt is the difference between Total Assets (Compustat Item 6) and Common Equity (Compustat Item 60). The composition of the dataset is described in Section 3.1.

Table 2. The ratio of Trade Credit to Total Debts Table 2 shows year-by-year data on the total variance of the ratio of Trade Credit to Total Debts (i.e. the variance of the ratio among the firms included in our sample for a given year), the average intra-industry variance (the average of the variance of the ratio of Trade Credit to Total Debts computed for each industry), the variance of inter-industry averages (the variance of the average ratio of Trade Credit to Total Debts by industry) and, finally, the ratio of intra- to inter-industry variance.

Total Variance

All firms Average Intra Industry Variance of Inter Variance Industry average

Intra to Inter Industry Ratio

Year 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Average

0.0215 0.0216 0.0159 0.0153 0.0207 0.0268 0.0468 0.0261 0.0301 0.0495 0.0522 0.0545 0.0550 0.0525 0.0558 0.0577 0.0769 0.1135 0.1022 0.0994 0.0962 0.0948 0.0885 0.0823 0.0877 0.0871 0.0849 0.0854 0.0851

0.0135 0.0123 0.0103 0.0087 0.0127 0.0218 0.0311 0.0189 0.0240 0.0442 0.0464 0.0501 0.0474 0.0449 0.0485 0.0448 0.0473 0.0449 0.0412 0.0404 0.0370 0.0385 0.0287 0.0260 0.0244 0.0215 0.0209 0.0299 0.0307

0.0123 0.0151 0.0122 0.0088 0.0105 0.0080 0.0192 0.0096 0.0089 0.0078 0.0092 0.0130 0.0163 0.0094 0.0106 0.0122 0.0160 0.0183 0.0183 0.0197 0.0188 0.0157 0.0118 0.0159 0.0155 0.0213 0.0198 0.0186 0.0205

1.10 0.81 0.85 0.98 1.21 2.73 1.62 1.96 2.70 5.67 5.04 3.85 2.92 4.76 4.59 3.67 2.96 2.46 2.24 2.05 1.97 2.44 2.43 1.63 1.57 1.01 1.06 1.61 1.50 2.39

Table 3. Descriptive statistics for the financial ratios Table 3 presents the descriptive statistics for the variables that we use in Section 3. All ratios are winsorized at percentiles 0.01 and 0.99. The ratio of working capital to total assets is computed as Compustat Item 4 minus Compustat Item 5 divided by Compustat Item 6. The ratio of retained earnings to total assets is computed as Compustat Item 36 divided by Compustat Item 6. The ratio of earnings before interest and taxes to total assets is computed as Compustat Item 13 minus Compustat Item 14 divided by Compustat Item 6. The ratio of the market value of equity to the book value of total debts is computed as Compustat Item 25 times Compustat Item 199 divided by Compustat Item 6 minus Compustat Item 60. The ratio of total sales to total assets is computed as Compustat Item 12 divided by Compustat Item 6. The ZScore is computed as in Altman (1968, 2000) (see Equation (12)). The ratio of intangibles to total assets is computed as Compustat Item 33 divided by Compustat Item 6. The ratio of trade credit to the book value of total debts is computed as Compustat Item 70 divided by Compustat Item 6 minus Compustat Item 6, and the ratio of trade credit to total assets is computed as Compustat Item 70 divided by Compustat Item 6.

Table 4. Estimates of credit use Table 4 reports estimates of Equation (14). In Panel A, the dependent variable is Trade Credit Total Debtsi,t , while in Panel B, it is Trade Credit Total Assetsi,t . We used the classical fixed effect estimator. Reported standard errors are robust to heteroskedasticity. In each Panel, the results are reported for the whole period (1977−2005) and for each ten-year subperiod.

Panel A

Trade credit on total debts All Sample

Variables

Coef

1977/1986

t-stat

Coef

1987/1996

t-stat

Coef

1997/2005

t-stat

Coef

t-stat

ZScore ZScore2 log of total assets Intangibles Default

0.050

21.52

0.067

5.63

0.056

9.21

0.013

1.42

-0.014 0.005 -0.187 0.009

-13.39 2.65 -8.40 1.21

-0.013 -0.018 -0.113 -0.008

-1.46 -4.91 -1.12 -0.46

-0.014 -0.004 -0.189 -0.025

-6.18 -1.33 -6.05 -2.63

-0.009 0.022 -0.211 0.037

-2.47 5.51 -5.14 2.65

Fisher N

47.7 10893

16.6 1424

Panel B

9.9 2895

Trade credit on total assets All Sample

Variables

47.4 6574

Coef

1977/1986

t-stat

Coef

1987/1996

t-stat

Coef

1997/2005

t-stat

Coef

t-stat

ZScore ZScore2 log of total assets Intangibles Default

0.020

6.00

0.055

9.52

0.016

4.20

-0.023

-3.30

-0.008 0.013 -0.079 0.017

-7.10 10.58 -5.25 4.83

-0.005 -0.005 0.057 0.009

-1.16 -2.66 1.19 1.06

-0.005 0.007 -0.044 -0.009

-3.43 3.41 -2.29 -1.59

-0.006 0.025 -0.198 0.043

-2.40 8.36 -6.46 4.20

Fisher N

36.4 10893

20.35 1424

24.87 6574

33.51 2895

Table 5. Robustness checks on the estimates of credit use In Table 5, we present two robustness checks. In Panel A, we estimate Equation (14) as in Table 4 but using the ZScore estimated at the end of fiscal year t + 1 as the proxy of firm quality. A fixed effect panel data estimator was used. Standard errors are robust to heteroskedasticity. In Panel B, we report year by year cross-sectional estimates of Equation (14), with Trade Credit Total Debtsi,t as the dependent variable. Only the coefficient of ZScore, ZScore2 and the marginal effect of ZScore on the dependent variable (estimated at the mean value of ZScore) are presented. An ordinary least square estimation was used. Standard errors are robust to heteroskedasticity. The marginal effect of the ZScore on β1 + 2 β2 ZScorei,t was estimated at the mean value of the ZScore. Panel A

All Sample Trade Credit on Total Trade Credit on Total Debts Assets

Variables

Coef

Zscore t+1

t-stat

Coef

t-stat

0.004

1.05

0.008

2.98

Zscore2 t+1 log of total assets Intangibles Default

-0.003 0.002 -0.200 -0.035

-1.64 1.13 -8.93 -5.58

-0.004 0.013 -0.082 0.004

-3.41 10.55 -5.48 0.87

Fisher N

27.5 10893

29.4 10893

Panel B - Year by Year cross-sectional regressions

R2

Year 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

44.79% 16.17% 30.39% 22.59% 19.42% 13.68% 9.47% 11.74% 12.75% 9.20% 6.08% 9.58% 4.54% 4.70% 3.32% 4.92% 6.89% 4.72% 4.58% 5.71% 3.49% 3.93% 5.75% 7.50% 7.99% 8.21% 8.12% 5.01% 3.82%

ZScore 0.207 0.011 0.065 0.086 0.047 0.052 0.056 -0.002 0.076 0.076 0.089 0.095 0.071 0.054 0.032 0.068 0.093 0.052 0.065 0.056 0.043 0.031 0.103 0.101 0.119 0.123 0.141 0.104 0.040

t-stat 6.570 0.281 2.663 3.305 1.724 1.858 1.785 -0.059 2.211 2.465 4.548 5.733 4.019 3.033 1.690 3.312 4.531 2.538 2.854 2.571 1.829 1.231 3.786 3.516 4.046 4.344 4.383 2.899 0.912

ZScore2 -0.059 0.005 -0.019 -0.061 -0.021 -0.011 -0.013 0.007 -0.003 -0.026 -0.026 -0.017 -0.025 -0.012 -0.006 -0.021 -0.030 -0.022 -0.026 -0.019 -0.019 -0.021 -0.022 -0.013 -0.022 -0.034 -0.034 -0.028 -0.021

t-stat -4.603 0.313 -1.492 -3.180 -2.152 -1.014 -0.939 0.478 -0.237 -1.996 -3.333 -2.478 -3.749 -1.857 -0.878 -2.747 -4.091 -3.125 -3.429 -2.777 -2.531 -2.718 -2.510 -1.261 -2.285 -3.616 -3.261 -2.271 -1.462

Mean Value of ZScore -0.009 0.022 -0.038 -0.091 -0.007 0.025 0.017 0.040 0.021 -0.011 0.029 0.017 0.020 0.017 -0.003 0.014 0.040 0.008 0.023 -0.011 -0.001 0.001 0.025 -0.003 0.020 0.031 -0.003 0.056 0.039

ZScore Marginal Effect 0.208 0.011 0.066 0.097 0.047 0.051 0.055 -0.001 0.076 0.077 0.088 0.094 0.070 0.053 0.032 0.067 0.091 0.052 0.064 0.057 0.043 0.031 0.102 0.101 0.118 0.120 0.141 0.101 0.039

Table 6. Estimates of trade use, including an illiquidity index Table 6 presents our estimates of Equation (15). The dependent variable is Trade Credit Total Debtsi,t and the effects were estimated using the classical fixed effect estimator. Reported standard errors are robust to heteroskedasticity. The Illiquidity variable was build using data provided by Bukart and al. (2005) as explained in Section 3.1, and the analysis covers the period 1989−1999.

Coef

t-stat (1)

Zscore Year Zscore2 Year Zscore x Illiquidity Zscore x Illiquidity Dummy log of total assets Intangibles Default Fisher N

Trade Credit on Total Debts (1989-1999) Coef t-stat Coef t-stat (2) (3)

0.059 -0.013

8.55 -4.82

0.050 -0.011

6.40 -3.72

0.031

3.22

0.033 -0.011 -0.116 -0.011

3.37 -3.37 -3.66 -1.10

62.3 4125

31.5 4125

-0.077 -0.013 0.089

-2.38 -4.80 4.70

Coef

t-stat (4)

-0.0855 -2.63702 -0.011 -3.68 0.089 4.70 -0.011 -0.115 -0.011

66.4 4125

33.1 4125

-3.26 -3.66 -1.16

Appendix A. Proof of proposition In Section 2.5, we assumed that Condition (6) is fulfilled, i.e. that:

  b  bD  bv   b   s   v  1  1 x  bv  







  0 . 

(A.1)

On the other hand, the project is financed if its market value is positive. So, using equations (3) and (4), the market value can be written as:

   b  1  x 1    1   b   V x   x  K   x  s  0 . x x  

(A.2)

Consequently, the first part and the term in brackets in the second part of Equation (11) are positive, so   x  is positive too.

Appendix B. An exact solution for optimal trade credit use

bv

We can solve the differential Equation (11) when s=b and

is an integer. When s=b,

bD  bv

Equation (11) becomes:

1 x 1    

 x 

x

 bD

 1  b   1 1  1 x  = K. x  

x  b 



v





(B1)

At first, we resolve the differential equation without the second term:

1 x 1    

 x 

x

 bD 

1  x 1      

 x 

  1 1  1 x 

x  b

x

  x   x 



v

 bD





 =0

(B2)



   1 1   1  x   

x  b 





v





bv

1 bD  bv x





bv ln  x   ln x  Cte bD  bv bv

 x  Cx

bD  bv

.

(B3)

Now, we use the classical method of constant variation to give:

 x  C x x   x  C  x x

bv bD  bv

bv bD  bv

 b

2bv  bD

bv

C x

D

 bv

x

bD  bv

.

(B4)

Equation (B1) then becomes:



C x x

bv bD  bv

1 x 1    C x





C  x x

x x

bv bD  bv

 b

C x

bv

D

bv bD  bv

 bv

2bv  bD

x

bD  bv

  b    D  1 1  1 x   bV 





 bD   1  b K .   1 1  1 x  = x   bV 









1  b



x

 =

K

(B5)

Integration of C', as given by Equation (B5), yields



C x x

bv bD  bv

 bD   1  b K   1 1  1 x  =x   bV 





C  x =-

We insert p 

bv bD  bv

bv bD  bv





x



bv bD  bv

 1  b   x  K 

1  1 x 

.

(B6)

in Equation (B6), and we assume that p is an integer greater than 1 (the case

where p=1 is easy to solve). We must now integrate the expression

1  C  x  =-px

p

 1  b   K  x 

1 x 





 1  C(x)    px  p1

In a first step we seek the anti-derivatives of

Let us first explore the anti-derivative of

1  b 1 x

dx   px  p

K dx  cte 1 x

x p x  p1 and . 1 x 1 x

x p in the simple case where p=2. 1 x

1 dx 1  1     x 2 1 x   x 2 x 1 x dx   x  ln(x)  ln(1 x) .  









Now, we can use a proof by induction for the general case p=n.

Our starting point is :

n1 dx 1 1    ln(x)  ln(1 x)  x n 1 x  k k 1 k x





We have already checked that this expression holds for n=2, and now we have to show that if it holds for n, then it also holds for n+1. Assume that for n: n  1  dx 1 1 1 dx 1 1  ln(x)  ln(1 x)  x n1 1 x    x n1  x n 1 x dx   n x n   x n 1 x   k k 1 k x  













So the expression holds for n+1. By induction, we can conclude that the statement holds for all natural numbers greater than 1. This leads to : p1 x p 1 1  ln(x)  ln(1  x) and k  1  xdx   k 1 k x

p x  p1 1 1  ln(x)  ln(1  x) k  1  x dx   k 1 k x

Now, we can determine the anti-derivative of C'(x).



  p 1 1  1 1  ln(x)  ln(1  x)  pK   ln(x)  ln(1  x)  C k k    k 1 k x   k 1 k x  p1

1- C(x)   p 1   b  

p1  x 1 1 1  K p C 1- C(x)  p K  1   b  ln k  x  1  x k 1 k x 

Hence, the solution of the differential Equation (12) is: p1   1  p x 1 1 p  x   px K  1   ln   K  Cx    b  k   1      1  x k 1 k x 

(B7)

The boundary condition  c =0 permits us to determine the constant C, so: p1  c 1 1 K C  p K  1   b   ln  k  p . 1  c k 1 k c  c 

(B8)

And finally the solution is:

 1  c x p1 1  1  xP   1  p 1   x      k  k    K  p  1   px K  1   b  ln 1    x  c   .  1  x c k 1 k  c

(B9)