A Welfare Analysis of Competitive Insurance Markets with Vertical Differentiation and Adverse Selection
Bibliographic record
Abstract
A feature of many insurance markets is that they combine vertical differentiation (all consumers prefer high to low-coverage policies) and adverse selection (high cost customers prefer highcoverage plans).Building on Novshek and Sonnenschein (1978) and Azevedo and Gottlieb (2017), this paper characterizes the competitive equilibria in a vertically differentiated market characterized by adverse selection.This provides a simple, dynamic model of the market, along with their welfare consequences over time in response to policy changes.The model makes predictions consistent with recent evidence on the ACA exchange in the US (Frean et al. (2017)).Moreover, it provides a complete characterization of the health insurance "death spiral".The death spiral leads to an inefficient outcome, but does not lead to a complete breakdown of the market.Rather, it predicts a large number of plans, with coverage that falls with an individual's willingness to pay.It is shown that introducing a minimum coverage standard combined with an insurance mandate cannot restore efficiency.The optimal system depends on both the valuation of public funds and the social value of insurance.Depending on these parameters, a number of different types of systems may be optimal, including a single payer system with mandatory participation for all, such as the Canadian system, a mixed private-public system, as one sees in many countries, or a pure, free market system.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.010 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".