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Insurance Markets with Adverse Selection

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contract-theory insurance

Core Idea

In insurance markets, individuals know their risk type better than insurers. High-risk individuals demand more insurance, but pooled pricing (average risk) is unattractive to low-risk customers, who exit. The remaining pool becomes riskier, forcing higher premiums, driving out more low-risk customers—market unraveling. Insurers use screening (deductible menus) to separate types and stabilize the market.

Explainer

From adverse selection and screening, you know that when one side of a market has private information, the uninformed side faces a fundamental problem: the people most eager to trade are often the worst deals. Insurance is the textbook case because the information asymmetry is stark and the consequences dramatic. You know your health, driving habits, and family medical history far better than any insurer can. This private knowledge creates a market dynamic that can spiral toward collapse.

Consider a simple model with two types of drivers: safe types (10% accident probability) and risky types (40% accident probability). If the insurer cannot distinguish them, it must offer a single pooling contract priced at the average risk. Suppose the population is half safe and half risky — the average accident probability is 25%, and the actuarially fair pooling premium reflects this. But the safe drivers know their true risk is only 10%. They are being asked to subsidize the risky drivers, and many will decide the insurance is not worth the price. When safe drivers exit, the remaining pool shifts toward risky types, raising the average risk. The insurer must increase premiums, which drives out more safe types. This is adverse selection spiral or market unraveling — first described by Akerlof in the "lemons" context and formalized for insurance by Rothschild and Stiglitz.

The Rothschild-Stiglitz model shows how insurers can fight back through menu design. Instead of one contract, the insurer offers two: a full-coverage contract with a high premium (designed for risky types) and a partial-coverage contract with a low premium and high deductible (designed for safe types). The key is the incentive compatibility constraint: the risky types must prefer their contract to the safe types' contract, and vice versa. Risky types, facing high expected losses, value full coverage enough to pay the steep premium. Safe types, with low expected losses, prefer the cheaper contract despite the deductible. The deductible is not a cost-saving measure — it is a screening device that induces self-selection. By making the cheap contract unattractive to high-risk types (who would face large out-of-pocket costs), the insurer separates the pool without needing to observe private information.

This framework explains real-world insurance design: health insurance deductibles, copays, and plan tiers are not arbitrary — they are calibrated to separate risk types. It also explains persistent policy debates. Mandatory insurance (as in auto or health insurance) solves the unraveling problem by forcing safe types to remain in the pool, enabling cross-subsidization. Community rating (charging everyone the same premium regardless of risk) achieves equity but requires mandates to prevent adverse selection. Without these interventions, the equilibrium may be separating but inefficient: safe types get less coverage than they would in a world of full information, bearing a welfare cost that is a direct consequence of the information asymmetry.

Practice Questions 5 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Literal Equations → Slope-Intercept Form → Point-Slope Form → Writing Linear Equations → Parallel and Perpendicular Line Slopes → Graphing Linear Equations → Piecewise Functions → One-Sided Limits → Continuity Definition → Limits and Continuity in Multiple Variables → Functions of Several Variables → Continuity in Multiple Variables → Partial Derivatives: Definition and Computation → Differentiability in Multiple Variables → Differentiability in Multivariable Functions → Total Differential and Linear Approximation → Chain Rule for Multivariable Functions → Implicit Differentiation → Related Rates → Optimization Problems → Critical Points of Multivariable Functions → Critical Points and Classification of Extrema → Second Partial Test for Local Extrema (Hessian) → The Hessian Matrix and Second Derivative Test → Unconstrained Optimization: Finding Extrema → Optimization in Multiple Variables → Lagrange Multipliers → Constrained Optimization and Lagrange Multipliers → Utility and Preferences → Marginal Utility and Diminishing Returns → Profit Maximization → Perfect Competition → Shutdown and Breakeven Decisions → Monopoly → Monopolistic Competition → Oligopoly and Strategic Behavior → Game Theory Basics → Nash Equilibrium → Nash Equilibrium Refinements → Strategic Form Games and Nash Equilibrium → Extensive Form Games and Game Trees → Subgame Perfect Equilibrium → Perfect Bayesian Equilibrium → Pooling and Separating Equilibria → Adverse Selection and Screening Mechanisms → Insurance Markets with Adverse Selection

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