14.1 Adverse Selection in the Credit Market

Credit plays a fundamental role in the functioning of the economy: it allows resources to be shifted over time, enabling households and firms to finance consumption and investment, thereby improving the allocation of resources. However, in both recent and past history, episodes of financial crises have shown how unstable the functioning of the credit market can become. The subprime mortgage crisis of 2008 is one of the clearest examples: in that case, the banking system granted credit far too freely, often to high-risk borrowers, triggering a collapse of the financial system.

One of the causes of these crises lies in the presence of asymmetric information. When granting a loan, the lender does not know exactly the risk being taken, or cannot easily observe the actions that the borrower will take after being financed. These two types of uncertainty give rise to two problems:

• adverse selection, when the hidden information concerns a characteristic of the borrower (e.g., the riskiness of the financed investment);
• moral hazard, when the hidden information concerns a future action of the borrower (e.g., the effort exerted or how carefully the funds are used).

In this section we will focus on adverse selection; in the next, we will examine moral hazard. We will use a simple numerical example to illustrate how asymmetric information can undermine the efficiency of the credit market.

Observable Types: Efficient Allocation of Credit

Consider an entrepreneur who asks a bank for a loan of $60$ (thousands euros, say) to finance a project. The project can either succeed and yield a return of $100$, or fail and yield zero. There are two types of project: a good one, which has a 75% probability of success, and a bad one, which has only a 50% probability. Only the entrepreneur knows the project’s type. The bank cannot observe it and assigns a probability pp that the project is good.

Assume that both parties are risk neutral and that the entrepreneur is protected by limited liability: if the project fails, they are not required to repay the bank.

It is easy to see that financing a good project generates a positive expected total surplus and is therefore socially efficient. In this case, the expected value of the project is $0.75\times100=75$, which is greater than the cost of $60$. Financing a bad project, on the other hand, generates a negative expected surplus and is therefore socially inefficient: the expected value is only $0.5\times 100=50$, less than the cost.

Let us suppose for a moment that the bank can observe the project type. In this case, the surplus generated by the loan is known to both parties, who will have an incentive to create it — and then split it — if and only if it is positive. The way the surplus is split depends, of course, on the relative bargaining power of the two parties. As we did in Chapter 12, we will assume here that the more informed party, the entrepreneur, captures the entire surplus — for instance, because the bank is competing with other banks to attract clients.

The two parties will therefore sign a loan contract such that If, instead, the bank had all the bargaining power, it would ask the entrepreneur — who would accept — to repay the maximum amount possible, $100$, in the event of success. the expected profit for the bank is zero. The bank lends $60$ to the entrepreneur, who agrees to repay $80$ if the project succeeds: the expected repayment to the bank is $0.75\times 80=60$, which exactly covers the loan. The entrepreneur’s payoff is $0.75\times(100−80)=15$, which is the expected total surplus of the project.

An entrepreneur with a bad project, on the other hand, has no way of obtaining financing. Due to limited liability, even if the bank asked for full repayment in case of success — $100$ — the expected repayment would be only $0.5\times 100=50$, which is less than the amount loaned: the bank would not agree.

In the ideal situation where the type is observable, the credit market achieves the socially efficient allocation: only entrepreneurs with good projects — that is, those for which the expected value exceeds the cost — are financed.

Unobservable Types: Underinvestment and Overinvestment

Let us now return to the case in which the type is not observable. The bank cannot distinguish between entrepreneurs with good and bad projects, so it must offer a single contract to everyone — or choose not to lend at all.

Let $R$ denote the amount the entrepreneur agrees to repay in case of success. For the contract to yield an expected profit of at least zero to the bank, the expected repayment must cover the amount loaned:

\(\begin{gathered} [ p \times 0.75 + (1 - p) \times 0.5 ] \times R \geq 60 \end{gathered}\)

which simplifies to:

\(\begin{gathered} R \geq \frac{60}{0.5 + 0.25p} \end{gathered}\)

However, limited liability imposes an upper bound: the entrepreneur can repay at most $100$ in case of success. So the contract must also satisfy $R\leq100$. In order for a contract (a value of $R$) to satisfy both limited liability and the bank’s participation, it must be that

\(\begin{gathered} \frac{60}{0.5 + 0.25p} \leq 100 \end{gathered}\)

from which we obtain:

\(\begin{gathered} p \geq 0.4 \end{gathered}\)

So if the probability that an entrepreneur has a good project is less than 40%, no contract exists that satisfies both the bank and the limited liability constraint. The result is that no entrepreneur is financed, not even those with socially efficient projects: this is a case of underinvestment relative to the social optimum. There is credit rationing: entrepreneurs with efficient projects want to be financed — and it would be socially desirable to finance them — but they cannot find a bank willing to lend. This happens even though their willingness to pay (up to $100$ in case of success, or $0.75\times100=75$ in expected terms) exceeds the bank’s cost ($60$).

If $p\geq0.4$, on the other hand, the bank is willing to finance everyone. But this means that entrepreneurs with bad projects — which have expected value below cost — also get financed. The result is overinvestment: the market finances activities that destroy value.

Good-project entrepreneurs end up worse off than in the observable case. Previously, they received $0.75\times(100−80)=15$. Now they get only

\(\begin{gathered} 0.75 \times \left( 100 - \frac{60}{0.5 + 0.25p} \right) < 15 \end{gathered}\)

Conversely, entrepreneurs with bad projects benefit. In the observable-type case, they were not financed and had zero payoff. Now they get

\(\begin{gathered} 0.25 \times \left( 100 - \frac{60}{0.5 + 0.25p} \right) > 0 \end{gathered}\)

In other words, entrepreneurs with good projects implicitly subsidize those with bad ones: the high expected repayments from the former allow the bank to avoid losses while still lending to the latter.