Rothschild–Stiglitz Insurance Screening Model

The Rothschild–Stiglitz insurance screening model is a foundational model of competitive markets under hidden information in business and economics theory. Michael Rothschild and Joseph Stiglitz published it in the 1976 Quarterly Journal of Economics article "Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information". It analyzes an insurance market in which customers know their own accident probability but insurers do not, and it shows that adverse selection reshapes the form of equilibrium contracts. The central findings are that pooling equilibria cannot exist, that a separating equilibrium exists only under restrictive conditions, and that otherwise no equilibrium in pure strategies exists at all.

Every individual has initial wealth W and faces a potential loss d that occurs with probability p. Two types exist: high-risk individuals with accident probability p^H and low-risk individuals with p^L < p^H. The population share of high-risk types is λ. Individuals are identical risk-averse expected-utility maximizers with a concave utility function u, and they know their own type. Insurers are risk-neutral, competitive, and earn zero expected profit in equilibrium.

An insurance contract is a pair (α₁, α₂), where α₁ is the premium paid in all states and α₂ the payout when an accident occurs. Insurers observe the contracts that customers buy, and they assume exclusivity: each customer can purchase insurance only from one firm. They cannot observe types, so the contract itself is the only screening instrument. This is a market-level counterpart to information asymmetry in bilateral contracts.

State-contingent wealth is W − α₁ without an accident and W − d − α₁ + α₂ with one. The expected utility of type i is

V_i = (1 − pⁱ) u(W − α₁) + pⁱ u(W − d − α₁ + α₂).

In the contract space, zero-profit lines have slope determined by the accident probability: the line for low-risk types is flatter than that for high-risk types, since actuarially fair insurance is cheaper for them. The indifference curves of high-risk individuals are flatter than those of low-risk individuals, which satisfies the single-crossing property that makes screening possible. Because high-risk buyers value additional coverage more, they are willing to pay more for it.

If insurers could identify types, competition would give each type full insurance at an actuarially fair premium, with pⁱ d paid by type i. Risk-averse individuals prefer complete smoothing of wealth across states, and the allocation is Pareto efficient in the sense of Pareto efficiency, conditional on risk. With hidden information, this allocation is not incentive compatible: high-risk individuals would prefer the low-risk contract, which offers full coverage at a lower price.

Suppose a pooling contract that both types buy earns zero profit at the average accident probability p̄ = λp^H + (1 − λ)p^L. Rothschild and Stiglitz show that a rival insurer can always offer a contract just below the pooling point that attracts only low-risk buyers. Because the low-risk indifference curve through the pooling contract is steeper than the high-risk curve, there is a region of contracts that low-risk individuals prefer to the pooling contract and high-risk individuals do not. A firm offering such a contract, which has slightly less coverage at a lower price, cream skims the low-risk customers and earns positive profits, while the original pooling contract is left with only high-risk customers and incurs losses. The pooling contract is therefore not robust to entry, and no pooling equilibrium exists. This resembles a deviation argument in a Nash equilibrium in which each firm best-responds to others' contracts.

The only possible equilibrium consists of two contracts, one per type. High-risk individuals receive full insurance at their fair premium, since distorting their contract would give no screening benefit. Low-risk individuals receive partial insurance at their own fair price, with coverage rationed to the level at which high-risk individuals are just indifferent between the two contracts. The binding condition is the incentive-compatibility constraint of the high-risk type. Partial coverage is the cost low-risk individuals pay to signal their type: they sacrifice risk-sharing so that the contract is unattractive to high-risk buyers. The equilibrium is a second-best result, with low-risk types worse off than under full information. It also links to mechanism design, where a menu of contracts implements truthful self-selection through the revelation principle.

An externality is at work. High-risk individuals impose a cost on low-risk individuals simply by existing, because their presence forces the low-risk contract to be distorted. Low-risk individuals would be better off if high-risk individuals were to disappear, but the high-risk type's presence cannot be changed by the market.

The separating pair is an equilibrium only if no pooling contract can profitably break it. A pooling contract that lies above the low-risk separating contract's indifference curve and below the pooling zero-profit line (at the average probability) would attract both types and earn non-negative profit. Such a contract exists when the proportion of low-risk individuals in the population is sufficiently high, so that the pooled price is not much above the low-risk fair price, and when the degree of risk aversion is low enough that low-risk individuals value partial separation less than a cheap pooled full cover. In this case, the separating contracts are destroyed by the pooling deviation, but the pooling deviation is destroyed by cream-skimming, and no pure-strategy equilibrium exists. The result challenges the generality of competitive equilibrium and provoked attempts to restore existence by changing the equilibrium concept.

• Wilson (1977): proposed the anticipatory equilibrium in which a firm considers that other firms will withdraw contracts that become unprofitable after its own entry. Under this concept a pooling contract can survive when it cannot be profitably broken after anticipating withdrawals. It is the equilibrium consisting of the best pooling contract for low-risk types, with high-risk types receiving a subsidy.
• Miyazaki (1977) and Spence (1978): extended the Wilson approach to allow cross-subsidization between contracts. With cross-subsidies, the low-risk type receives more coverage in a separating equilibrium that is constrained efficient, and an equilibrium always exists. High-risk types then receive contracts with negative profit and low-risk contracts earn positive profit, with the aggregate at zero.
• Riley (1979): introduced the reactive equilibrium in which entrants anticipate reactions of incumbents, which yields the separating contract pair as the unique reactive equilibrium.

These refinements show that existence and efficiency are sensitive to assumptions about firm behavior and exclusivity. Later research on non-exclusive contracting, such as in Jaynes (1978) and Hellwig (1988), found different results.

The model's logic extends beyond insurance to credit markets, labor markets, and health-care policy. It is the template for screening in the Stiglitz–Weiss credit rationing model and informs debates about mandatory insurance, community rating, and risk adjustment in health markets. Empirical tests have found evidence of adverse selection in some markets, such as annuities and health insurance, while others show advantageous selection in which low-risk individuals purchase more coverage because they are more risk averse. The paper is a pillar of the information economics recognized by the 2001 Nobel Memorial Prize in Economic Sciences.

1. Rothschild, M., & Stiglitz, J. (1976). Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information. The Quarterly Journal of Economics, 90(4), 629–649. https://doi.org/10.2307/1885326
2. Wilson, C. (1977). A Model of Insurance Markets with Incomplete Information. Journal of Economic Theory, 16(2), 167–207. https://doi.org/10.1016/0022-0531(77)90004-190004-1)
3. Akerlof, G. A. (1970). The Market for "Lemons": Quality Uncertainty and the Market Mechanism. The Quarterly Journal of Economics, 84(3), 488–500. https://doi.org/10.2307/1879431
4. Stiglitz, J. E. (2000). The Contributions of the Economics of Information to Twentieth Century Economics. The Quarterly Journal of Economics, 115(4), 1441–1478. https://doi.org/10.1162/003355300554827