---
title: "Trade Credit without Systemic Risk"
authors:
  - name: "Alexis Direr"
    affiliation: "École Normale Supérieure and CEPREMAP, URA 928"
date: "2001-02"
doi: "10.3917/rel.683.0371"
keywords: [asymmetric information, trade credit, corporate finance, systemic risk, default propagation, domino effect, interfirm credit]
jel_codes: [D82, G30, G11]
language: en
type: research-article
journal: "Recherches Économiques de Louvain"
---

# Trade Credit without Systemic Risk

**Author**
- Alexis Direr — École Normale Supérieure and CEPREMAP, URA 928 — *direr@ens.fr*

**DOI**: [10.3917/rel.683.0371](https://doi.org/10.3917/rel.683.0371)
**Journal**: *Recherches Économiques de Louvain*.
**Keywords**: asymmetric information, trade credit, corporate finance, systemic risk, domino effect.
**JEL codes**: D82, G30, G11.

---

## Abstract

An incentive to grant trade credit is shown in two simple frameworks in which the amount lent may be alternatively invested in a riskless asset. In the first one, productive risks of the buyer and the supplier are independent. A systemic risk emerges, as a risky account receivable increases the default risk of the supplier. This mechanism is however absent in the second framework in which the productions of the buyer and the seller are positively correlated. In this case, trade credit entails no systemic risk.

---

## 1. Motivation and contributions

In France, the number of firm defaults rose at an average annual rate of 10% between 1970 and 1993 (Longueville 1992); in Canada, an average rate of 6.6% between 1980 and 1992 (Martel 1995). A common conjecture attributes part of this increase to **trade credit** — the financial intermediation operated by firms themselves through accounts payable and accounts receivable.

A simple measure of trade-credit pass-through is the ratio $\min(b, d)/\max(b, d)$ where $b$ denotes accounts receivable and $d$ accounts payable. Direr (2000), on a sample of 2,760 French firms in 1997, finds an average value of **61%** — most trade credit is genuinely intermediated, not merely held as a buffer. In France, accounts payable are roughly twice short-term banking debt and of the same order as internal funds (Biais, Hillion & Malécot 1995); UFB-Locabail (cited in Longueville 1992) attributes 20% of French firm defaults to customer failure.

The paper formalises the **domino effect** described as far back as Marshall (1923) — a risky account receivable can damage a supplier's net worth and propagate to its own creditors — and asks two distinct questions:

1. **Why do firms grant trade credit at all** rather than holding the same liquidity in safe assets?
2. **Does trade credit generate financial contagion** between firms (systemic risk in the credit channel sense)?

The paper makes three contributions.

1. **A new financial incentive to grant trade credit.** The standard literature has explained trade credit through informational advantages of suppliers (Petersen & Rajan 1997), collateralisation of supplied goods (Mian & Smith 1992), price discrimination (Schwartz & Whitcomb 1979) or transaction-cost minimisation (Ferris 1981). The paper adds a leverage-based incentive: because the supplier itself carries debt, debt returns are concave in the stochastic cash flow (Jensen & Meckling 1976; Stiglitz & Weiss 1981), so risk-shifting toward a risky account receivable raises shareholder expected profit relative to a safe asset.

2. **A clean characterisation of trade-credit-induced systemic risk under independent risks.** When buyer and supplier have independent productive risks, granting trade credit *strictly raises* the supplier's default probability at equilibrium. The classical domino mechanism operates.

3. **A neutrality result under perfectly correlated risks.** When the two firms' production levels are perfectly correlated — capturing the commercial link between supplier and customer — trade credit leaves the supplier's default probability **unchanged**. The default-premium compensation built into the trade-credit rate exactly offsets the increase in fundamental risk. This contradicts the common view that trade credit always amplifies systemic risk.

The paper isolates the **financial-propagation channel** (loss transmission via balance-sheet exposures) from the competing **demand-cancellation channel** (a financially constrained customer cancels orders), which can operate even without trade credit. Only the financial channel is studied here.

---

## 2. Model with independent productive risks

### 2.1 Setup

A two-period model with two firms, $i = 1, 2$. Firm 2 (the supplier) sells to firm 1 (the buyer). Firm 2 holds an exogenous liquid amount $b$ for unforeseen spending and chooses, at date 0, whether to:

- hold $b$ as a **safe asset** (gross return $X$), or
- lend $b$ to firm 1 as an **account receivable**.

Productions $\tilde{y}_i$ require real assets $k_i$ and are stochastic.

- **Firm 1 (buyer):** $\tilde{y}_1 = y_1^r$ with probability $p$, $y_1^f < y_1^r$ with probability $1 - p$.
- **Firm 2 (supplier):** $\tilde{y}_2$ distributed over $[0, \bar{y}]$ with twice continuously differentiable cumulative $F(\cdot)$ and density $f(\cdot)$.

For symmetry, both firms have $d_1 = d_2 = d$, $b_1 = b_2 = b$, $k_1 = k_2 = k$, internal funds $w_1 = w_2 = w$, with the balance-sheet identity $k + b = w + d$. Firm 1 holds $b$ as a safe asset by assumption. All agents are risk-neutral.

A financial friction is imposed: creditors cannot observe firm 2's choice between trade credit and safe asset, so debt cannot be contracted on this choice. Default of firm 1 in the bad state is assumed: $y_1^f + Xb < R_1 d$.

### 2.2 Expected profits and bankruptcy thresholds

If firm 2 holds a safe asset, expected profit is

$$E[\pi_2(0)] = \int_{y'}^{\bar{y}} (y + Xb - R_2 d)\, f(y) \, dy, \quad y' = R_2 d - Xb.$$

If firm 2 grants trade credit, expected profit decomposes by buyer's success/failure:

$$E[\pi_2(1)] = p \int_{\hat{y}_b}^{\bar{y}} [y + R_1 b - R_2 d]\, f(y) \, dy + (1 - p) \int_{\hat{y}_e}^{\bar{y}} \big[ y + (b/d)(y_1^f + Xb) - R_2 d \big]\, f(y) \, dy$$

with bankruptcy thresholds:

$$\hat{y}_b = R_2 d - R_1 b, \qquad \hat{y}_e = R_2 d - (b/d)(y_1^f + Xb).$$

### 2.3 Results

**Proposition 1 (incentive to grant trade credit).** *For any fixed $R_2$, $E[\pi_2(1)] > E[\pi_2(0)]$.*

> **Intuition.** Using the no-arbitrage condition (4) at firm 1's debt, $y' = p \hat{y}_b + (1 - p) \hat{y}_e$. Defining $g(x) = \int_x^{\bar{y}} (y - x)\, dF(y)$, the desired inequality reduces to Jensen's inequality $p\, g(\hat{y}_b) + (1 - p)\, g(\hat{y}_e) > g\big[p \hat{y}_b + (1 - p) \hat{y}_e\big]$, which holds because $g'' = f > 0$. The supplier's payoff is convex in the realised cash flow inherited from firm 1, so a mean-preserving spread (trade credit vs. safe asset) is strictly preferred — the standard Jensen–Meckling / Stiglitz–Weiss risk-shifting motive.

**Proposition 2 (systemic risk under independent risks).** *Let $R_2^1$ (resp. $R_2^0$) denote the equilibrium interest rate on the supplier's debt when it grants trade credit (resp. holds a safe asset). Then:*

(i) $R_2^1 > R_2^0$;
(ii) $p F(\tilde{y}_b) + (1 - p) F(\tilde{y}_e) > F(\tilde{y}'_e)$.

The unconditional default probability of the supplier strictly rises when it grants trade credit. Trade credit therefore **increases systemic risk** when productive risks are independent. Result (i) reflects the rationally anticipated risk transfer: lenders charge a higher rate on firm 2 because its asset is riskier; result (ii) follows from the no-arbitrage condition holding in expectation across regimes.

---

## 3. Model with correlated productive risks

### 3.1 Setup

The framework is identical except that productions are now perfectly positively correlated:

$$\tilde{y}_1 = \tilde{y}_2 = \tilde{y}$$

with the common density $f(\cdot)$ over $[0, \bar{y}]$. This captures the commercial link: the buyer and supplier face essentially the same demand shock.

### 3.2 Three default thresholds

When firm 2 holds trade credit, it faces two distinct break-even thresholds depending on whether firm 1 defaults:

$$\hat{y}_b + R_1 b = R_2 d, \quad \hat{y}_e + (b/d)(\hat{y}_e + Xb) = R_2 d, \quad y' + Xb = R_2 d.$$

Algebra gives the ordering $\hat{y}_b < \hat{y}_e < y'$. Crucially, the supplier defaults if and only if $\tilde{y} < \hat{y}_e$, regardless of $\hat{y}_b$, because $\hat{y}_b$ is also (by symmetry) the buyer's default threshold.

### 3.3 Results

**Proposition 3 (incentive to grant trade credit, correlated risks).** *For any fixed $R_2$, $E[\pi_2(1)] > E[\pi_2(0)]$.*

> **Intuition.** Under perfect correlation, the supplier *always* defaults when the buyer does — the loss is mechanically passed through to the supplier's own creditors. Conversely, conditional on the buyer paying back, the supplier's survival is much more likely than for unrelated debt issuers. The compounded effect: the supplier captures the full risky return $R_1$ in those (favourable) states with elevated frequency, and this exceeds the expected return on a safe asset by the strictly positive risk premium $(R_1 - X) b$.

**Proposition 4 (no systemic risk under correlated risks).** *$\tilde{y}_e = \tilde{y}'_e$.*

The supplier's equilibrium default threshold — and therefore its default probability — is **identical** under trade credit and under a safe asset.

> **Mechanism.** Two opposing effects exactly offset. (i) When the buyer defaults, the supplier's asset value falls and credit-worthiness deteriorates — the classical domino effect, which raises default risk *ceteris paribus*. (ii) The supplier is compensated for that default risk by a higher interest rate $R_1$ on its loan to the buyer; this premium strengthens the supplier's ability to repay its own debt in the buyer's non-default states. Under perfect correlation, the gain in non-default states exactly cancels the loss in default states.

> **Authors' critical reading.** The neutrality result *contradicts the common opinion about the effect of trade credit on systemic risk*. Trade credit is not intrinsically a contagion channel: whether it amplifies or leaves systemic risk unchanged depends on the correlation structure of the underlying real shocks. The polar cases bracket the empirically relevant intermediate cases.

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## 4. Summary table of results

| Setting | Incentive to grant trade credit | Effect on supplier default risk |
|:---|:---:|:---:|
| Independent risks (Section 2) | Yes (Proposition 1) | **Increases** (Proposition 2) |
| Perfectly correlated risks (Section 3) | Yes (Proposition 3) | **Unchanged** (Proposition 4) |

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## 5. Conclusion

The paper provides a unified two-firm framework in which the supplier's choice between trade credit and a safe asset is endogenous, and asks how this choice interacts with default risk.

The incentive to grant trade credit is robust: in both the independent-risk and the perfectly-correlated-risk model, the supplier strictly prefers trade credit. The economic rationale, however, differs: under independent risks, it is the standard risk-shifting incentive arising from the concavity of debt returns in cash flow; under correlated risks, it is the privileged informational and timing position of the supplier as a creditor — survival on its loan is concentrated in states where its own survival is highly likely.

Where the two settings diverge is on the systemic-risk implication. Trade credit raises the supplier's default probability under independent risks but leaves it unchanged under perfectly correlated risks. The default premium charged on trade credit acts as a hedge against the additional fundamental risk in the correlated-risks case, and the two effects cancel exactly at the perfect-correlation polar.

### Limitations and research extensions

The author flags the simplicity of the framework: only two firms, two-period horizon, polar correlation cases (zero and one), and a financial friction limited to non-observability of the supplier's short-term asset choice. Extensions to multi-firm networks, intermediate correlation values, and richer financial frictions are natural next steps but are not pursued in the paper. The empirical relevance of the polar correlated-risks case to specific supplier-customer dyads is suggested but not tested.

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## Acknowledgments

The author thanks Frédéric Boissay and Patrick Fève for helpful comments and the two referees of *Recherches Économiques de Louvain*. The paper is drawn from chapter 4 of the author's PhD thesis, *Imperfections financières et dynamiques du marché du crédit* (Université de Nantes, 2000).

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## Main references

Biais, B., Hillion, P., Malécot, J. F. (1995). La structure financière des entreprises: une investigation empirique sur données françaises. *Économie et Prévision* 120(4), 15–28.

Direr, A. (2000). *Imperfections financières et dynamiques du marché du crédit*. PhD Thesis, Université de Nantes.

Ferris, J. S. (1981). A Transactions Theory of Trade Credit Use. *Quarterly Journal of Economics* 94, 243–270.

Jensen, M., Meckling, W. (1976). Theory of the Firm: Managerial Behavior, Agency Costs, and Capital Structure. *Journal of Financial Economics* 11, 5–50.

Longueville, G. (1992). La multiplication des défaillances d'entreprises: contexte permissif et fragilité financière. *Lettre de Conjoncture de la BNP*, juillet–août.

Marshall, A. (1923). *Money, Credit and Commerce*. Macmillan.

Martel, J. (1995). Commercial Bankruptcy in Canada. *Canadian Business Economics* 3, 53–64.

Mian, S., Smith, C. W. (1992). Accounts Receivable Management Policy: Theory and Evidence. *Journal of Finance* 47, 169–200.

Petersen, M. A., Rajan, R. G. (1997). Trade Credit: Theories and Evidence. *Review of Financial Studies* 10(3), 661–691.

Ramey, V. (1992). The Source of Fluctuations in Money: Evidence from Trade Credit. *Journal of Monetary Economics* 30, 171–193.

Schwartz, R. A., Whitcomb, D. (1979). The Trade Credit Decision. In J. Bicksler (ed.), *Handbook of Financial Economics*, North Holland.

Smith, J. (1987). Trade Credit and Information Asymmetry. *Journal of Finance* 4, 863–869.

Stiglitz, J., Weiss, A. (1981). Credit Rationing in Markets with Imperfect Information. *American Economic Review* 71, 393–410.

*The full reference list appears in the PDF.*