The applicant arrives carrying information the application cannot quite contain. He knows something about the risk he wants insured, or the project he wants financed, that the institution on the other side must infer. Nothing requires him to be dishonest. A truthful answer to every question on a form can leave much unsaid, including facts too subtle to describe or too costly to verify. The contract offered to him then helps decide whether he stays. A premium attractive to someone expecting frequent losses can repel someone expecting few. A promise to repay a high interest rate can come from a project whose owner expects to keep an unusually large gain if it succeeds. The terms are doing two jobs at once: exchanging money for a promise, and selecting the people willing to make the exchange.
Consider two equally numerous groups, each beginning with wealth of 100 and facing a possible loss of 64. One group has a one-in-ten chance of loss; the other, a one-in-two chance. Each person values wealth according to its square root, and each knows his own probability. A risk-neutral insurer can observe the loss but cannot distinguish the groups. Ignore expenses and offer only full insurance. If everyone joined, the average expected claim would be 19.20, so that premium would balance expected receipts and claims. Yet the low-risk person's maximum acceptable premium is only 7.84; the high-risk person's is 36. At 19.20, only the high-risk group buys, leaving expected claims of 32 per policy. The proposed pool cannot finance itself. A premium of 32 can insure the high-risk group alone. The example loses the low-risk customers without losing the entire insurance market.1
If the insurer could identify the groups, full coverage at their respective expected losses, 6.40 and 32, would attract both. Each would surrender a certain premium in return for protection against an uncertain loss. Charging an actuarially fair price does not abolish insurance. It removes the transfer between these risk classes while preserving the transfer between the fortunate and unfortunate realizations within each class. That distinction matters when asking what an insurance arrangement is meant to accomplish. A society can want protection against an accident and assistance with the cost of being an unusually risky person. The first purpose does not automatically supply the second. When a common premium is intended to serve both, its financing depends on which people can leave and on what other support the arrangement receives. The arithmetic of the pool and the choice of whom to help are connected questions, each requiring an answer.
Contracts can also differ in coverage. Rothschild and Stiglitz studied competing insurers offering exclusive price-and-quantity contracts to two privately informed risk classes. In their model, a pooling contract can be undercut by an offer attracting only the low risks. The sole possible separating equilibrium gives high risks full insurance and low risks partial insurance, at each group's actuarially fair terms. The partial coverage discourages the high risks from choosing the low-risk contract. Even this candidate can fail to be an equilibrium, depending on the population and preferences. The result depends on the specified competition and information. It does not say every pool must unravel. It shows how a deductible can carry a second burden: asking a person to retain risk so that his choice becomes credible evidence about the risk he brings.2
The credit application presents a related difficulty. A lender is interested in what it expects to collect, which can differ from what a borrower promises. Stiglitz and Weiss showed that a higher loan rate can worsen selection or alter borrowers' actions enough to lower the lender's expected return. Their model can therefore sustain rationing: some observationally identical applicants receive loans while others are refused, even when the refused applicants offer to pay more. Collateral is not an automatic escape; their analysis also considers circumstances in which demanding more of it worsens the composition or incentives of borrowers. The result is a possibility under stated conditions, not a diagnosis of every rejection. Its force is that bidding up the promise need not improve the promise's expected fulfillment. Quantity can remain restricted even when applicants are willing to accept a higher price.3
Selection and inducement must nevertheless be kept apart. In the first, changing the offer changes who accepts it. In the second, the person who accepts changes what he subsequently does. An insurer unable to observe a pre-existing probability faces one problem; an insurer unable to observe the care taken after coverage begins faces another. A lender may encounter both, but the distinction determines which evidence would help. Learning a borrower's project before lending can improve selection without ensuring that the project remains unchanged afterward. Monitoring later conduct can govern action without revealing every earlier difference between applicants. The form, the investigation, and the continuing obligation reach different parts of the uncertainty. Their usefulness has to be assessed against the specific missing fact, with the costs of acquiring and acting on it included.4
The applicant's silence need not be a refusal to cooperate. Sometimes the useful information cannot be demonstrated by an answer, however candidly given. Anyone can describe himself as prudent, able, or committed; the institution still needs a reason to distinguish one description from another. The burden can then fall on an action whose cost differs across the people taking it. The ensuing signal may reveal a characteristic, consume resources, and exclude someone who possesses the characteristic but cannot afford the demonstration. These consequences belong to the account together. A market's response to ignorance has a price of its own. The Diploma follows the applicant into a setting where the evidence is acquired before the application is made, and where a costly qualification can carry information beyond the knowledge it teaches.5