---
title: "Concurrence interbancaire et sélection des investissements"
title_en: "Interbank Competition and Investment Screening"
authors:
  - name: "Alexis Direr"
    affiliation: "École Normale Supérieure, CEPREMAP URA 928, and EUREQUA, Université de Paris 1"
date: "2002-10"
keywords: [banks, asymmetric information, externalities, screening, interbank competition, banking crises, strategic complementarities, multiple equilibria]
jel_codes: [G21, D82, D62]
language: en
type: working-paper
---

# Interbank Competition and Investment Screening

*Original title (French): "Concurrence interbancaire et sélection des investissements".*

**Author**
- Alexis Direr — École Normale Supérieure, CEPREMAP URA 928, and EUREQUA, Université de Paris 1 — *direr@ens.fr*

**Keywords**: banks, asymmetric information, externalities, screening, strategic complementarities, banking crises.
**JEL codes**: G21, D82, D62.

---

## Abstract

**Original (French) — verbatim.**
> Nous étudions le mode d'allocation des crédits quand les banques se concurrencent en faisant varier leur degré d'expertise des projets soumis. La concurrence interbancaire conduit à la possibilité d'équilibres multiples impliquant des degrés d'expertise et des expositions au risque différents. L'article propose une théorie du conformisme des banques en matière d'expertise et contribue à expliquer pourquoi les banques ont généralement été touchées dans leur ensemble par l'accumulation de mauvaises créances lors des crises bancaires apparues ces vingt dernières années.

**Working English translation (not from the paper).**
The paper studies how credit is allocated when banks compete by varying the degree of expertise (screening intensity) they exert on submitted projects. Interbank competition can give rise to multiple equilibria with different screening intensities and different aggregate risk exposures. The paper proposes a theory of bank conformism in screening and contributes to explaining why banks have, as a group, been exposed to bad-loan accumulation during the banking crises of the past two decades.

---

## 1. Motivation and contributions

The paper is motivated by the observation that banking crises in industrialised and emerging economies during the 1980s and 1990s — France, Japan, the United States, Mexico, Venezuela, and the Scandinavian countries — repeatedly involved system-wide bad-loan accumulation rather than failures concentrated at a few institutions (Lambert et al. 1997; Miotti & Plihon 2001). Empirical work also documents cyclical variation in bank screening intensity, with a flight-to-quality during recessions (Bernanke, Gertler & Gilchrist 1996; Lang & Nakamura 1995; Asea & Blomberg 1998; Rajan 1994). Variation in bank screening effort is often invoked to rationalise these patterns, but few microeconomic models directly study the credit market when the screening intensity is itself an endogenous, strategic choice.

The paper contributes the following.

1. **A model of endogenous interbank screening competition.** Building on Broecker (1990) and Gehrig (1998), the paper studies a credit market with $n \geq 2$ banks and one firm that visits banks sequentially. Each bank chooses both whether to screen ($\alpha \in \{0, 1\}$) and what interest rate to offer. Unlike Broecker (1990) — where the screening intensity is exogenous and pure-strategy equilibria fail to exist — sequential search restores existence; unlike Gehrig (1998) — where the focus is on screening as a function of the interest rate — this paper allows an arbitrary number of banks and isolates the strategic-complementarity dimension of screening.

2. **The role of information about firm "age" on the credit market.** A central informational variable is whether banks observe the number of times a firm has previously been rejected. Empirical evidence (Shaffer 1998) suggests banks typically do not. The paper shows that the *absence* of this information radically changes the screening equilibrium and aggregate risk exposure.

3. **A theory of bank conformism via strategic complementarities in screening.** When banks do not observe firm age, the screening decisions become strategic complements in the sense of Bulow, Geanakoplos & Klemperer (1985) and Cooper & John (1988): one bank's screening raises the value of screening for the others. This generates multiple Pareto-rankable equilibria — one in which all banks screen, one in which none do — for the same fundamentals. The mechanism rationalises why entire banking systems can drift simultaneously into lax credit standards before a crisis.

4. **An empirical-distinction implication.** When firm age is *known*, all $n$ banks remain active but jointly close to firms with too many prior rejections; identity of the visited bank varies across applicants. When firm age is *unknown*, a strict subset of banks is active and screens every applicant; the rest do not serve the segment at all. The two informational regimes produce observationally distinct credit-market structures.

---

## 2. Model setup

### 2.1 Players and projects

- One firm, of type $j \in \{G, B\}$ (good / bad). Probability of $G$: $\lambda$; probability of $B$: $1 - \lambda$.
- The firm has a unit-size investment project. Type $j$ succeeds with probability $p_j$, paying $y$ on success and $0$ on failure. Risk-free gross interest rate: $X$.
- $n \geq 2$ risk-neutral banks, each able to fund at the risk-free rate.

**Assumption H1.** $p_G y - X > 0 > p_B y - X$ — type-$G$ projects are socially profitable, type-$B$ projects are not.

### 2.2 Screening technology

**Assumption H2.** Each bank chooses $\alpha \in \{0, 1\}$. If $\alpha = 1$, the bank pays cost $c > 0$ and observes a private signal $s \in \{g, b\}$ correlated with project type:

$$\psi \equiv P(g \mid G), \quad \phi \equiv P(b \mid B), \quad \psi, \phi \leq 1, \quad \psi > 1 - \phi.$$

If $\alpha = 0$, no signal is observed.

### 2.3 Sequential search

- No public price posting and no auctioneer. The firm cannot observe a bank's interest-rate offer until it visits.
- A visited bank chooses to (i) finance without screening, (ii) screen and then accept or reject, or (iii) reject without screening.
- The firm must accept or definitively refuse each offer before visiting the next bank, with discount factor $\beta < 1$.
- Up to $n$ banks may be visited.

### 2.4 Bank profit

Let $\lambda_i$ be the bank-$i$ posterior that the firm is type $G$ before $i$'s screening decision. Net profit (after risk-free funding cost $X$):

$$\pi(\alpha_i, R_i; \lambda_i) = \lambda_i [1 + \alpha_i(\psi - 1)](p_G R_i - X) + (1 - \lambda_i)[1 - \alpha_i \phi](p_B R_i - X) - c\alpha_i$$

The relevant signal-value functions, depending on whether the project is profitable absent the signal, are:

- **If profitable without signal** (signal serves to *exclude* bad risks):
$$v(R_i; \lambda_i) \equiv (1 - \lambda_i) \phi (X - p_B R_i) - \lambda_i (1 - \psi)(p_G R_i - X)$$

- **If not profitable without signal** (signal serves to *retain* good projects):
$$V(R_i; \lambda_i) \equiv \lambda_i \psi (p_G R_i - X) - (1 - \lambda_i)(1 - \phi)(X - p_B R_i)$$

Screening is optimal when $v > c$ (resp. $V > c$). The two functions have opposite comparative statics in $\lambda_i$: $\partial v / \partial \lambda_i < 0$ (rejection role) versus $\partial V / \partial \lambda_i > 0$ (retention role) — a property that drives the strategic-complementarity result.

---

## 3. Equilibrium when banks know firm age

The firm visits banks $1, 2, \dots, n$ in indexed order; each bank knows how many times the firm has already been rejected.

### 3.1 Pricing

**Proposition 1.** *In any equilibrium, $R_i^* = y$ for all $i$ and any screening profile $(\alpha_1^*, \dots, \alpha_n^*) \in \{0, 1\}^n$.*

The intuition is backward induction: bank $n$ extracts the firm's full surplus ($R_n = y$), so the no-deviation constraint at bank $n-1$ is $R_{n-1} = y$, and so on.

### 3.2 Case A — firm financeable without screening

Assume $\pi(0, y; \lambda_1) > 0$.

**Proposition 2.** *If the first bank prefers to screen, every subsequent bank also screens (until the expected profitability of the project becomes negative, at which point the firm is definitively rejected).*

The mechanism: a rejection at bank $i$ updates the posterior toward $B$ (since $\psi > 1 - \phi$ implies $\lambda_{i+1} < \lambda_i$). Because the signal-value $v$ is decreasing in $\lambda$, deterioration in expected quality strengthens the case for screening at the next bank. The process unwinds either with an acceptance after a positive signal, or with an outright rejection once expected profit turns negative.

### 3.3 Case B — firm not financeable without screening

Assume $\pi(0, y; \lambda_1) < 0$.

**Proposition 3.** *If a bank screens, expected profitability and signal-value $V$ decrease for each subsequent bank. The firm is either continuously screened or definitively rejected.*

Here $V$ is *increasing* in $\lambda$, so each rejection makes screening less attractive. The firm exits the credit market once $V(y; \lambda_i) \leq c$.

In both cases, screening policy is uniquely determined; **no multiple equilibria can arise when firm age is known**.

---

## 4. Equilibrium when banks do not know firm age

The firm still visits up to $n$ banks, but each bank is uncertain about its position in the sequence.

### 4.1 Pricing

**Proposition 4.** *Even without age information, $R_i^* = y$ for all $i$.*

Sketch: any candidate equilibrium with two distinct rates allows the lowest-rate bank to deviate upward (since the firm cannot do better by waiting due to discounting). Convergence to a common rate, and then to $R^* = y$, follows by an iterative deviation argument exploiting $\beta < 1$.

### 4.2 The ex-ante posterior with $I$ screening banks

**Lemma 1.** *If the firm visits bank $i$ and $I \leq n - 1$ of the other $n - 1$ banks screen (with $n - I - 1$ not screening), the bank-$i$ pre-screening posterior is*

$$\lambda_I = \frac{\lambda \, [1 + (1 - \psi) + \dots + (1 - \psi)^I]}{\lambda \, [1 + (1 - \psi) + \dots + (1 - \psi)^I] + (1 - \lambda)[1 + \phi + \dots + \phi^I]}.$$

*Furthermore $\lambda_I < \lambda_{I-1}$ for $I = 1, \dots, n - 1$.*

The posterior degrades monotonically with the number of screening competitors: more screening on the market means surviving applicants are increasingly drawn from rejected (likely $B$-type) firms.

### 4.3 Case I — firm financeable without screening

Assume $\pi(0, y; \lambda_{n-1}) \geq 0$.

**Proposition 5 (multiple equilibria).** *Suppose the firm is financeable without screening even when all other banks screen. There exist parameter values (in particular, screening costs $c$ in the non-empty interval $\big] v(y; \lambda_{n-1}), v(y; \lambda_0) \big]$) such that both an "$n$-equilibrium" (all banks screen) and a "$0$-equilibrium" (no bank screens) exist for the same fundamentals.*

> **Mechanism.** Screening by bank $j$ asymmetrically removes good projects from the credit market (accepted firms exit, rejected firms continue searching), degrading the average quality of applicants seen by other banks. This raises $v$ — the value of screening — for everyone else and validates the high-screening conjecture. Symmetrically, low screening keeps bad risks on the market briefly (they are quickly funded), so the surviving applicant pool is on average good, validating the low-screening conjecture. The decision problem features strategic complementarities in the sense of Bulow, Geanakoplos & Klemperer (1985) and Cooper & John (1988).

This is the paper's central theoretical result and the foundation of the conformism interpretation.

### 4.4 Case II — firm not financeable without screening when others screen

Assume $\pi(0, y; \lambda_{n-1}) < 0$.

**Proposition 6.** *In equilibrium, fewer than $n$ banks screen. The non-screening banks reject the firm directly (rather than financing without screening).*

Concretely, there exists a threshold $J \in \{1, \dots, n-1\}$ above which $\pi(0, y; \lambda_{J-1}) \geq 0$ and below which $\pi(0, y; \lambda_J) < 0$. For $c$ in a non-empty interval $\big] V(y; \lambda_{I-1}), V(y; \lambda_I) \big]$ with $I \in \{J+1, \dots, n-1\}$, an "$I$-equilibrium" prevails: exactly $I$ banks screen; the remaining $n - I$ exit the segment.

### 4.5 Empirical signature of the two regimes

The paper highlights an observable distinction:

- **Age known.** All $n$ banks are nominally active, but the chain of visits closes once expected profit goes negative. Different applicants visit different identifying banks; participation is universal but conditional.
- **Age unknown.** A strict subset of banks operates on the segment and screens everyone; the rest never serve it at all. Rejected applicants visit *all* the active banks.

---

## 5. Conclusion

The paper compares the screening equilibrium under two informational regimes (firm age on the credit market known vs. unknown) and shows they have very different positive content:

- **Known age:** uniqueness of the screening profile, with screening either intensifying (Case A) or weakening (Case B) along the chain of visits.
- **Unknown age:** multiplicity of equilibria when the firm is financeable without screening (Case I), driven by strategic complementarities in screening; and bank-segment retreat when it is not (Case II).

The conformism interpretation links the model to the empirical observation that banking crises tend to be system-wide rather than bank-specific. If a few banks reduce screening, others have less reason to expertise (the surviving applicant pool is on average better), so the system can drift toward a low-screening / high-risk equilibrium. The reverse — a flight to quality during recessions, documented for example in the Japanese banking crisis (Kanaya & Woo 2000) and the U.S. data of Asea & Blomberg (1998) and Rajan (1994) — is consistent with the rejection-role variant of the signal: as the credit market deteriorates, the value of excluding bad risks rises, validating tighter screening.

### Limitations and research extensions

The author flags two main extensions:

- **Cycle dynamics.** A natural next step is to embed the screening game in a business-cycle model to study how aggregate-risk exposure of bank balance sheets co-moves with macroeconomic variables.
- **Empirical separation of the two cases.** Distinguishing Case I (financeable without screening) from Case II (not financeable) is non-trivial in practice, but the cyclical evidence on screening intensity offers indirect support for the rejection-role variant — the one that produces multiple equilibria.

The paper also abstracts from collateral, repeated lending relationships, and bank heterogeneity; these are not addressed.

---

## Acknowledgments

The author thanks Patrick Fève, Jean-Marc Tallon and Frédéric Boissay for comments on an earlier version, and the EUREQUA laboratory at Paris 1 for hosting the doctoral work from which the paper is drawn. The current version benefited substantially from the comments of an anonymous referee at the *Annales d'Économie et de Statistique*.

---

## Main references

Asea, P. K., Blomberg, B. (1998). Lending Cycles. *Journal of Econometrics* 83, 89–128.

Bernanke, B., Gertler, M., Gilchrist, S. (1996). The Financial Accelerator and the Flight to Quality. *Review of Economics and Statistics* 78(1), 1–15.

Broecker, T. (1990). Credit-Worthiness Tests and Interbank Competition. *Econometrica* 58, 429–452.

Bulow, J., Geanakoplos, J., Klemperer, P. (1985). Multimarket Oligopoly: Strategic Substitutes and Complements. *Journal of Political Economy* 93, 488–511.

Cooper, R., John, A. (1988). Coordinating Coordination Failures in Keynesian Models. *Quarterly Journal of Economics* 103, 441–463.

Gehrig, T. (1998). Screening, Cross-Border Banking and the Allocation of Credit. *Research in Economics* 52(4), 387–407.

Kanaya, A., Woo, D. (2000). The Japanese Banking Crisis of the 1990s: Sources and Lessons. Essays in International Economics No. 222, Princeton University.

Lang, W. W., Nakamura, L. I. (1995). 'Flight to Quality' in Banking and Economic Activity. *Journal of Monetary Economics* 36(1), 145–164.

Lambert, T., Le Cacheux, J., Mahuet, A. (1997). L'épidémie de crises bancaires dans les pays de l'OCDE. *Revue de l'OFCE* 61, 93–138.

Miotti, L., Plihon, D. (2001). Libéralisation financière, spéculation et crises bancaires. *Économie Internationale* 85.

Rajan, R. G. (1994). Why Bank Credit Policies Fluctuate: A Theory and Some Evidence. *Quarterly Journal of Economics* 109(2), 399–441.

Sah, R., Stiglitz, J. (1986). The Architecture of Economic Systems: Hierarchies and Polyarchies. *American Economic Review* 76, 716–722.

Shaffer, S. (1998). The Winner's Curse in Banking. *Journal of Financial Intermediation*, December, 359–392.

*The full reference list appears in the PDF.*