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

De Bodt Frédéric Lobez Jean-Christophe Statnik

Address

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



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*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 short-

term 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 The implicit interest rate 𝑖 is obtained as a solution of 98 (1 + 𝑖)

36520 = 100 in the present case.

2 See http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

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 The corresponding gross rates are 𝑅𝑏(𝑥) and 𝑅𝑠(𝑥).

5 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 = 𝑏𝑉𝑉 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 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. 7 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.

<Insert Figure 1 about here>

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 (3)

𝑥𝑅𝑏 𝑥 = 1 + 𝜋𝑏 (4) 8 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 = 𝑏𝑉𝐾𝑥 − 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 = 𝑏𝑉𝑥 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 𝐾 − 𝛼 𝑥 𝑅𝑠 𝑦 −

1 − 𝛼 𝑥 𝑅𝑏(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

+𝑏𝑉𝑥 −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

+𝑏𝑉𝑦 −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

𝑥−

1 + 𝜋𝑏

𝑥

= 𝑏𝑣𝛼′(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 See http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html 11

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.

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

http://www.insolvencyhelpline.co.uk/interactive-tools/z-calc.htm

(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/

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.

<Insert Table 1 about here>

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 intra-

industry 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 fixed-

effect 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= 𝛼𝑖 + 𝛽1𝑍𝑆𝑐𝑜𝑟𝑒𝑖,𝑡 + 𝛽2𝑍𝑆𝑐𝑜𝑟𝑒𝑖,𝑡

2 + 𝛽3 log 𝑇𝑜𝑡𝑎𝑙𝐴𝑠𝑠𝑒𝑡𝑠𝑖,𝑡 + 𝛽4𝐼𝑛𝑡𝑎𝑛𝑔𝑖𝑏𝑙𝑒𝑠

𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠 𝑖,𝑡+

𝛽5𝐷𝑒𝑓𝑎𝑢𝑙𝑡𝑖,𝑡 + 𝑌𝑒𝑎𝑟 𝐷𝑢𝑚𝑚𝑖𝑒𝑠 + 𝜀𝑖 ,𝑡 (14)

where 𝑖 is the firm index and 𝑡 is the period index.

We also used 𝑇𝑟𝑎𝑑𝑒 𝐶𝑟𝑒𝑑𝑖𝑡 𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠 𝑖 ,𝑡 as a dependent variable to check, once again, the

robustness of our results. The ratio 𝑇𝑟𝑎𝑑𝑒 𝐶𝑟𝑒𝑑𝑖𝑡 𝑇𝑜𝑡𝑎𝑙 𝐷𝑒𝑏𝑡𝑠 𝑖,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 𝐷𝑒𝑏𝑡𝑠 𝑖 ,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 𝐷𝑒𝑏𝑡𝑠 𝑖,𝑡 , while in Panel B, it is 𝑇𝑟𝑎𝑑𝑒 𝐶𝑟𝑒𝑑𝑖𝑡 𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠

𝑖,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 𝛽2𝑍𝑆𝑐𝑜𝑟𝑒𝑖,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 𝐴𝑠𝑠𝑒𝑡𝑠 𝑖 ,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 𝐷𝑒𝑏𝑡𝑠 𝑖,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 𝐷𝑒𝑏𝑡𝑠 𝑖,𝑡 . Only the coefficient of ZScore, ZScore squared and the

marginal effect of ZScore on 𝑇𝑟𝑎𝑑𝑒 𝐶𝑟𝑒𝑑𝑖𝑡 𝑇𝑜𝑡𝑎𝑙 𝐷𝑒𝑏𝑡𝑠 𝑖 ,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 cross-

sectional 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= 𝛼𝑖 + 𝛽1𝑍𝑆𝑐𝑜𝑟𝑒𝑖,𝑡 + 𝛽2𝑍𝑆𝑐𝑜𝑟𝑒𝑖,𝑡

2 +𝛽3 𝑍𝑆𝑐𝑜𝑟𝑒𝑖,𝑡 × 𝐼𝑙𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑖,𝑡

+𝛽4 log 𝑇𝑜𝑡𝑎𝑙𝐴𝑠𝑠𝑒𝑡𝑠𝑖,𝑡 + 𝛽5𝐼𝑛𝑡𝑎𝑛𝑔𝑖𝑏𝑙𝑒𝑠

𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠 𝑖 ,𝑡+ 𝛽6𝐷𝑒𝑓𝑎𝑢𝑙𝑡𝑖,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

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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

http://ssrn.com/abstract=1069875


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

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- 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

Activity cash flows

Information

- Manager: 𝑥

- Banks/suppliers: 𝑥

- Financial market:

- perfect info: 𝑥

- imperfect info: 𝛼(𝑥)

Decision

- Manager: 𝛼(𝑥)

- Banks: 𝑅𝑏(𝑥)

- Suppliers: 𝑅𝑠(𝑥)

Information

- Manager: 𝑠 ∈ 𝑆, 𝐹

Decision

- Manager: activity disruption

𝑠 = 𝑆

𝑠 = 𝐹

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).

Panel A

Panel B

0

0.2

0.4

0.6

0.8

1

1.2

0.6

25

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35

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95

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Trad

e c

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it f

inan

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0.75

0%

10%

20%

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40%

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100%

0.6250.675

0.7250.775

0.8250.875

0.925

Div

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Probability of Success

Figure 3. The relationship between firm quality and the use of trade credits

Figure 3 shows the relationship between ZScores and Trade Credit Total Debts i,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 Debts

i,t and TC4 the quartile with the

highest ones.

ZScore 1

ZScore 2

ZScore 3

ZScore 4

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

TC 1TC 2

TC 3TC 4

Z-Sc

ore

Qu

arti

le

Trade Credit Quartile

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%

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

Average Intra

Industry

Variance

Variance of Inter

Industry average

Intra to Inter

Industry Ratio

Year

1977 0.0215 0.0135 0.0123 1.10

1978 0.0216 0.0123 0.0151 0.81

1979 0.0159 0.0103 0.0122 0.85

1980 0.0153 0.0087 0.0088 0.98

1981 0.0207 0.0127 0.0105 1.21

1982 0.0268 0.0218 0.0080 2.73

1983 0.0468 0.0311 0.0192 1.62

1984 0.0261 0.0189 0.0096 1.96

1985 0.0301 0.0240 0.0089 2.70

1986 0.0495 0.0442 0.0078 5.67

1987 0.0522 0.0464 0.0092 5.04

1988 0.0545 0.0501 0.0130 3.85

1989 0.0550 0.0474 0.0163 2.92

1990 0.0525 0.0449 0.0094 4.76

1991 0.0558 0.0485 0.0106 4.59

1992 0.0577 0.0448 0.0122 3.67

1993 0.0769 0.0473 0.0160 2.96

1994 0.1135 0.0449 0.0183 2.46

1995 0.1022 0.0412 0.0183 2.24

1996 0.0994 0.0404 0.0197 2.05

1997 0.0962 0.0370 0.0188 1.97

1998 0.0948 0.0385 0.0157 2.44

1999 0.0885 0.0287 0.0118 2.43

2000 0.0823 0.0260 0.0159 1.63

2001 0.0877 0.0244 0.0155 1.57

2002 0.0871 0.0215 0.0213 1.01

2003 0.0849 0.0209 0.0198 1.06

2004 0.0854 0.0299 0.0186 1.61

2005 0.0851 0.0307 0.0205 1.50

Average 2.39

All firms

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 Debts i,t, while in

Panel B, it is Trade Credit Total Assets i,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 sub-period.

Panel A

Variables Coef t-stat Coef t-stat Coef t-stat Coef t-stat

ZScore 0.050 21.52 0.067 5.63 0.056 9.21 0.013 1.42

ZScore2-0.014 -13.39 -0.013 -1.46 -0.014 -6.18 -0.009 -2.47

log of total assets 0.005 2.65 -0.018 -4.91 -0.004 -1.33 0.022 5.51

Intangibles -0.187 -8.40 -0.113 -1.12 -0.189 -6.05 -0.211 -5.14

Default 0.009 1.21 -0.008 -0.46 -0.025 -2.63 0.037 2.65

Fisher 47.7 16.6 47.4 9.9

N 10893 1424 6574 2895

Panel B

Variables Coef t-stat Coef t-stat Coef t-stat Coef t-stat

ZScore 0.020 6.00 0.055 9.52 0.016 4.20 -0.023 -3.30

ZScore2-0.008 -7.10 -0.005 -1.16 -0.005 -3.43 -0.006 -2.40

log of total assets 0.013 10.58 -0.005 -2.66 0.007 3.41 0.025 8.36

Intangibles -0.079 -5.25 0.057 1.19 -0.044 -2.29 -0.198 -6.46

Default 0.017 4.83 0.009 1.06 -0.009 -1.59 0.043 4.20

Fisher 36.4 20.35 24.87 33.51

N 10893 1424 6574 2895

Trade credit on total debts

1977/1986 1987/1996 1997/2005All Sample

Trade credit on total assets

All Sample 1977/1986 1987/1996 1997/2005

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 Debts

i,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 β2ZScorei,t was estimated at the mean value of the ZScore.

Panel A

Variables Coef t-stat Coef t-stat

Zscore t+1 0.004 1.05 0.008 2.98

Zscore2 t+1 -0.003 -1.64 -0.004 -3.41

log of total assets 0.002 1.13 0.013 10.55

Intangibles -0.200 -8.93 -0.082 -5.48

Default -0.035 -5.58 0.004 0.87

Fisher 27.5 29.4

N 10893 10893

All Sample

Trade Credit on Total

Debts

Trade Credit on Total

Assets

Panel B - Year by Year cross-sectional regressions

Year R2ZScore t-stat ZScore2

t-stat

Mean

Value of

ZScore

ZScore

Marginal

Effect

1977 44.79% 0.207 6.570 -0.059 -4.603 -0.009 0.208

1978 16.17% 0.011 0.281 0.005 0.313 0.022 0.011

1979 30.39% 0.065 2.663 -0.019 -1.492 -0.038 0.066

1980 22.59% 0.086 3.305 -0.061 -3.180 -0.091 0.097

1981 19.42% 0.047 1.724 -0.021 -2.152 -0.007 0.047

1982 13.68% 0.052 1.858 -0.011 -1.014 0.025 0.051

1983 9.47% 0.056 1.785 -0.013 -0.939 0.017 0.055

1984 11.74% -0.002 -0.059 0.007 0.478 0.040 -0.001

1985 12.75% 0.076 2.211 -0.003 -0.237 0.021 0.076

1986 9.20% 0.076 2.465 -0.026 -1.996 -0.011 0.077

1987 6.08% 0.089 4.548 -0.026 -3.333 0.029 0.088

1988 9.58% 0.095 5.733 -0.017 -2.478 0.017 0.094

1989 4.54% 0.071 4.019 -0.025 -3.749 0.020 0.070

1990 4.70% 0.054 3.033 -0.012 -1.857 0.017 0.053

1991 3.32% 0.032 1.690 -0.006 -0.878 -0.003 0.032

1992 4.92% 0.068 3.312 -0.021 -2.747 0.014 0.067

1993 6.89% 0.093 4.531 -0.030 -4.091 0.040 0.091

1994 4.72% 0.052 2.538 -0.022 -3.125 0.008 0.052

1995 4.58% 0.065 2.854 -0.026 -3.429 0.023 0.064

1996 5.71% 0.056 2.571 -0.019 -2.777 -0.011 0.057

1997 3.49% 0.043 1.829 -0.019 -2.531 -0.001 0.043

1998 3.93% 0.031 1.231 -0.021 -2.718 0.001 0.031

1999 5.75% 0.103 3.786 -0.022 -2.510 0.025 0.102

2000 7.50% 0.101 3.516 -0.013 -1.261 -0.003 0.101

2001 7.99% 0.119 4.046 -0.022 -2.285 0.020 0.118

2002 8.21% 0.123 4.344 -0.034 -3.616 0.031 0.120

2003 8.12% 0.141 4.383 -0.034 -3.261 -0.003 0.141

2004 5.01% 0.104 2.899 -0.028 -2.271 0.056 0.101

2005 3.82% 0.040 0.912 -0.021 -1.462 0.039 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 Debts i,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 Coef t-stat Coef t-stat Coef t-stat

Zscore Year 0.059 8.55 0.050 6.40 -0.077 -2.38 -0.0855 -2.63702

Zscore2 Year -0.013 -4.82 -0.011 -3.72 -0.013 -4.80 -0.011 -3.68

Zscore x Illiquidity 0.089 4.70 0.089 4.70

Zscore x Illiquidity Dummy 0.031 3.22 0.033 3.37

log of total assets -0.011 -3.37 -0.011 -3.26

Intangibles -0.116 -3.66 -0.115 -3.66

Default -0.011 -1.10 -0.011 -1.16

Fisher 62.3 31.5 66.4 33.1

N 4125 4125 4125 4125

Trade Credit on Total Debts (1989-1999)

(1) (2) (3) (4)

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

bv

b

s

bv b

D

bv

1 1 x

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:

V x x K x s b 1 x 1

x

1bx

0 . (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

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

bv

bD b

v

is an integer. When s=b,

Equation (11) becomes:

x 1 x 1

x x

bD

bv

1

1 1 x

=1

b

x K . (B1)

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

x 1 x 1

x x

bD

bv

1

1 1 x

=0 (B2)

x 1 x 1

x x

bD

bv

1

1 1 x

x x

b

v

bD b

v

1

x

ln x

bv

bD b

v

ln x Cte

x Cx

bv

bDb

v . (B3)

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

x C x x

bv

bDb

v

x C x xb

v

bDb

v C x b

v

bD b

v

x

2bvb

D

bDb

v . (B4)

Equation (B1) then becomes:

C x xb

v

bDb

v

1 x 1 x

C x xb

v

bDb

v C x b

v

bD b

v

x

2bvb

D

bDb

v

bD

bV

1

1 1 x

=1

b

x K

C x xb

v

bDb

vb

D

bV

1

1 1 x

=1

b

x K . (B5)

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

C x xb

v

bDb

vb

D

bV

1

1 1 x

=-1

b

x K

C x =-b

v

bD b

v

x

bv

bDb

v

1 b

x K

1 1 x . (B6)

We insert

p b

v

bD b

v

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

x K

1 x 1 C(x) px p1

1 b

1 x dx px p K

1 x dx cte

In a first step we seek the anti-derivatives of

x p

1 x and

x p1

1 x.

Let us first explore the anti-derivative of

x p

1 x in the simple case where p=2.

dx

x2 1 x 1

x2

1

x 1 x

dx 1

x ln(x) ln(1 x) .

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

Our starting point is :

dx

xn 1 x 1

k

1

xkk1

n1

ln(x) ln(1 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:

dx

xn1 1 x 1

xn1

1

xn 1 x

dx 1

n

1

xn

dx

xn 1 x 1

k

1

xkk1

n

ln(x) ln(1 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 :

x p

1 x dx 1

k

1

xkk1

p1

ln(x) ln(1 x) and x p1

1 x dx 1

k

1

xkk1

p

ln(x) ln(1 x)

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

1- C(x) p 1 b 1

k

1

xkk1

p1

ln(x) ln(1 x)

pK

1

k

1

xkk1

p

ln(x) ln(1 x)

C

1- C(x) p K 1 b lnx

1 x

1

k

1

xkk1

p1

K

1

x pC

Hence, the solution of the differential Equation (12) is:

x 1

1 px p K 1b ln

x

1 x

1

k

1

xkk1

p1

K Cx p

(B7)

The boundary condition c =0 permits us to determine the constant C, so:

C p K 1b lnc

1 c

1

k

1

ckk1

p1

K

cp. (B8)

And finally the solution is:

x 1

1 px p K 1 b ln

1 c x1 x c

1

k

1

ck

1

xk

k1

p1

K

xP

c p1

. (B9)

trade credit as a signal of quality

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