Plate iv in print

The Screen

Stiglitz and the screen: how the uninformed side can design a menu — the deductible, the cheaper version, the test — that makes the informed sort themselves.

Let the uninformed offer not one bargain but a choice of bargains, each shaped so that a different type prefers it; then each, in choosing, confesses what he is, and sorts himself without ever being asked.

— the principle of this plate, after Joseph Stiglitz, 1976

Signaling is the work of the side that knows. Its mirror image is the work of the side that does not: rather than wait for the informed to prove what they are, the uninformed party can design the terms of the deal so cunningly that the informed, simply by choosing which terms they prefer, reveal themselves. This is screening, and where signaling burns resources to send a message, screening builds a sieve to extract one.

The principle, worked out by Joseph Stiglitz and others, is to replace a single take-it-or-leave-it offer with a menu of offers, each item shaped so that a particular type finds it the best of the lot. The classic case is insurance. The insurer cannot tell the careful from the reckless, but it can offer two policies: one with full coverage at a high premium, and one with a large deductible at a low premium. The reckless, who expect to claim often, prefer the full coverage and will pay for it; the careful, who expect to claim rarely, prefer the cheaper policy with a deductible they are unlikely to trigger. Each type, choosing the policy that suits its own private knowledge of its risk, sorts itself into the right category — and the insurer, who could not ask "are you reckless?", has induced an honest answer by the mere shape of the choice.1

1. Screening (Rothschild and Stiglitz, "Equilibrium in Competitive Insurance Markets," 1976): the uninformed party offers a menu designed so different types self-select — high-coverage/high-premium versus high-deductible/low-premium insurance separates high from low risks. Choice reveals the private information no question could extract.

Like the signal, the screen, once recognized, is seen to be everywhere a seller faces buyers of unknown type. The airline offers a costly flexible fare and a cheap restricted one, knowing the business traveler, who values flexibility and time, will pay for the former while the price-sensitive tourist accepts the latter, sorting willingness to pay by the choice of ticket. The software comes in a crippled free version and a full paid one; the publisher issues the dear hardback before the cheap paperback; the shop runs the coupon that only the price-sensitive will trouble to clip. In every case the seller cannot see who values the product highly, so it builds a menu whose options are tuned to make the high-value and low-value buyers separate themselves — and charges each, in effect, closer to what the good is worth to them.2

2. Self-selection screening is pervasive: versioning (crippled free versus full paid), fare classes (flexible versus restricted), hardback-then-paperback, and coupons all present menus that sort buyers by willingness to pay or by type. It is the mechanism behind much second-degree price discrimination; the seller extracts hidden information through the buyer's own choice.
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Screening, like signaling, is not free, and its cost takes a revealing form. To make the types separate, the screener must distort the deal offered to at least one of them, away from what would be best if information were complete. The careful driver, in the separating insurance equilibrium, cannot buy the full coverage he might actually want — it is priced to repel the reckless, so it is dear — and must instead accept a policy with a deductible he would not have chosen under symmetric information, bearing risk he would rather have insured. The low-risk type is left worse off than he would be if the insurer could simply see his type and price for it. The distortion is the price of separation: to sort the types apart, the menu must be bent away from efficiency, and the good type pays for the existence of the bad in the coin of a contract worse than he deserves.3

3. Screening imposes a distortion: to deter the bad type from choosing the good type's contract, the good type's contract must be worsened away from the full-information optimum — the low-risk insured ends up under-insured. The good type bears a real cost for the existence of the bad; this is the second-best outcome.

There is a deeper and stranger trouble, which Rothschild and Stiglitz proved and which marks how radically asymmetry can break a market. In their model of competitive insurance, a pooling outcome — everyone on the same policy — cannot survive, because a rival can always lure away the good risks with a policy tailored to them, leaving the bad risks behind to ruin the pool. But the separating outcome may not survive either: if the good risks are numerous enough, a pooling policy could be offered that they would prefer, undercutting the separating menu. So each candidate equilibrium can be upset by some deviation, and the competitive market may have no stable equilibrium whatever — left not merely with a distorted outcome but with no settled outcome at all, churning without rest. That asymmetric information can deprive a competitive market of any equilibrium is among the most striking results in the field.4

4. Rothschild and Stiglitz (1976) showed competitive insurance under adverse selection may have no equilibrium: no pooling equilibrium survives (good risks can be skimmed off), and a separating equilibrium can be upset by a profitable pooling deviation when low risks are numerous. Asymmetry can deny a competitive market any stable resting point.

Signaling and screening are the two faces of the market's response to hidden information, and they often work together. The worker signals with a diploma; the employer screens with a probationary period and a battery of tests. The borrower signals with collateral; the lender screens with a credit score and a graduated limit. The seller signals with a warranty; the buyer screens by demanding an independent inspection. Between them they accomplish what the price alone cannot — they move the hidden information into view, or extract it through choice — and so hold open markets that adverse selection would otherwise close. But both, we have insisted, cost: the signal in resources burned to prove, the screen in deals distorted to sort. The bill for the asymmetry is paid in both currencies, and the flagship will total it.5

5. Signaling (the informed party reveals) and screening (the uninformed party induces revelation) are complementary responses to adverse selection and frequently combine. Both sustain trade that would otherwise unravel, and both are costly — signaling in resources expended, screening in efficiency sacrificed. The flagship, The Signal, assesses the total cost.

The screen is the uninformed side's answer to the silence: not to wait for proof, but to set out a choice so shaped that to choose it is to confess, and let the informed sort themselves. With the signal and the screen, the market has its two great devices against the lemon's unravelling, and between them much honest trade is saved. But we have so far considered only one kind of hidden thing — hidden information, what the other side already knows and will not, or cannot, truthfully say. There is a second kind, hidden not in what a party knows but in what a party does, once the deal is struck and no one is watching. The next plate turns from the hidden type to the hidden action, and to the temptation that every insurance against loss contains.