Module 7 — Information Economics and Contracts

Core question

What allocation can be sustained when one side privately knows its type or can take an action that the other side cannot observe?

Learning outcomes

You will be able to:

• classify hidden-type and hidden-action problems by timing;
• solve a simple lemons market and signalling equilibrium;
• write participation and incentive-compatibility constraints;
• design a screening menu or performance contract;
• distinguish predictive accuracy, allocative effects, and fairness in algorithmic credit.

1. Diagnose what is hidden and when

“Information asymmetry” is not yet a model. Identify who knows what, whether it is verifiable, and which actions or transfers can depend on it.

2. Adverse selection: a numerical lemons market

Cars are high (H) or low (L) quality. Buyers value them at 12 and 6; sellers' reservation values are 10 and 4. Under observable quality, both types trade and each trade creates surplus 2.

If quality is hidden and buyers believe fraction θ is high, the maximum pooling price is:

High-quality sellers participate only if:

If buyers expect fewer high-quality cars, high-quality sellers leave. The pool then becomes worse, validating a lower price. Mutually beneficial high-quality trade disappears.

The model does not say every used-goods market collapses. Warranties, inspections, reputation, repeat trade, certification, and law can change information and incentives.

3. Signalling: informed agents move first

A signal is costly and observed. It can separate types when the cost differs enough by type.

Suppose high productivity earns 10, low productivity earns 6. Education has no productivity effect, but costs:

For education e* to separate types:

Thus any e*∈[2,4] satisfies these incentive constraints given supporting beliefs. The signal conveys information because imitation is more expensive for the low type.

4. Screening: the uninformed side offers a menu

An insurer offers contracts (premium, coverage) so types select themselves. For types H and L, a menu must satisfy:

Participation (individual rationality)

Truthful self-selection (incentive compatibility)

In a standard competitive insurance model, the high-risk type may receive full insurance while the low-risk contract is distorted toward a deductible to deter imitation. The distortion is a cost of private information, not a technological need.

5. Moral hazard: reward observable outcomes

A principal observes output but not effort. High effort creates success probability 0.8 and costs the agent 1; low effort creates probability 0.4 and costs 0. A success bonus is b, with zero base pay and risk-neutral parties.

High effort is incentive compatible when:

so:

If successful output is worth 10, the principal's expected profit at b=2.5 is:

versus 0.4(10)=4 under low effort and no bonus. Incentivising effort is profitable in this benchmark.

With a risk-averse agent, a stronger outcome-contingent bonus also transfers more uncontrollable risk. Optimal contracts trade off incentives against insurance. Limited liability, multitasking, manipulation, team production, and repeated reputation can change the result.

6. First-best and second-best

• First-best: type and action are contractible; choose the surplus-maximising allocation and transfer.
• Second-best: impose IC, IR, observability, budget, and enforcement constraints.

The information rent earned by a type may be necessary to preserve truthful participation. Calling it “overpayment” ignores the counterfactual: removing the rent can destroy the allocation or induce misreporting.

7. Current case: machine learning in mortgage credit

Fuster, Goldsmith-Pinkham, Ramadorai, and Walther compare statistical models using roughly 10 million US mortgages and embed predictions in a competitive lending model. Their machine-learning models slightly expand access and reduce disparity in acceptance, yet increase cross-group disparity in equilibrium interest rates; model flexibility, not only proxying for race, drives the distributional pattern (2022).

The example separates four questions:

1. prediction: who is estimated likely to default?
2. decision: which loss or regulatory objective converts risk into approval and price?
3. equilibrium: how do lenders and applicants respond?
4. distribution: which groups gain on access and interest-rate margins?

Better prediction does not mechanically imply lower inequality or higher welfare. The study uses a historical US mortgage setting and counterfactual models; deployment data, newer underwriting rules, causal responses, and alternative fairness criteria can change conclusions.

8. Contract and algorithm audit

For a contract, score, or recommendation rule, record:

• target variable and whose welfare enters the objective;
• data available to each party at each stage;
• action/report that can be manipulated;
• IC and IR constraints;
• false-positive and false-negative incidence;
• equilibrium adaptation and appeals;
• external validity and monitoring plan.

Practice

1. Change the lemons values and find the minimum high-quality share for pooling trade.
2. In the signalling example, make c_H=e/2; find the separating interval.
3. Write all four IC/IR inequalities for a two-type insurance menu.
4. Resolve the moral-hazard bonus when high effort succeeds with probability 0.7 and costs 1.5.
5. Explain why equal approval rates, equal default rates, and equal interest rates are different policy targets.

Quick check

• Adverse selection concerns hidden type before contract; moral hazard hidden action after.
• A credible signal must be differentially costly or beneficial across types.
• Screening designs a menu so private types sort themselves.
• Incentive pay transfers risk as well as motivation.
• Predictive accuracy, equilibrium welfare, and fairness are separate claims.

Next: design rules for truthful reports and strategic bids.