Measuring Ex Ante Welfare in Insurance Markets
Abstract The willingness to pay for insurance captures the value of insurance against only the risk that remains when choices are observed. This article develops tools to measure the ex ante expected utility impact of insurance subsidies and mandates when choices are observed after some insurable information is revealed. The approach retains the transparency of using reduced-form willingness to pay and cost curves, but it adds one additional sufficient statistic: the percentage difference in marginal utilities between insured and uninsured. I provide an approach to estimate this additional statistic that uses only the reduced-form willingness to pay curve, combined with a measure of risk aversion. I compare the approach to structural approaches that require fully specifying the choice environment and information sets of individuals. I apply the approach using existing willingness to pay and cost curve estimates from the low-income health insurance exchange in Massachusetts. Ex ante optimal insurance prices are roughly 30% lower than prices that maximize observed market surplus. While mandates reduce market surplus, the results suggest they would actually increase ex ante expected utility.
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Publication Date:
NSF-PAR ID:
10237587
Journal Name:
The Review of Economic Studies
Volume:
88
Issue:
3
Page Range or eLocation-ID:
1193 to 1223
ISSN:
0034-6527
3. Abstract We conduct a comparative welfare analysis of 133 historical policy changes over the past half-century in the United States, focusing on policies in social insurance, education and job training, taxes and cash transfers, and in-kind transfers. For each policy, we use existing causal estimates to calculate the benefit that each policy provides its recipients (measured as their willingness to pay) and the policy’s net cost, inclusive of long-term effects on the government’s budget. We divide the willingness to pay by the net cost to the government to form each policy’s Marginal Value of Public Funds, or its MVPF''. Comparing MVPFs across policies provides a unified method of assessing their effect on social welfare. Our results suggest that direct investments in low-income children’s health and education have historically had the highest MVPFs, on average exceeding 5. Many such policies have paid for themselves as the government recouped the cost of their initial expenditures through additional taxes collected and reduced transfers. We find large MVPFs for education and health policies among children of all ages, rather than observing diminishing marginal returns throughout childhood. We find smaller MVPFs for policies targeting adults, generally between 0.5 and 2. Expenditures on adults have exceededmore »
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5. The actuarially fair insurance premium reflects the expected loss for each insured. Given the dearth of cyber security loss data, market premiums could shed light on the true magnitude of cyber losses despite noise from factors unrelated to losses. To that end, we extract cyber insurance pricing information from the regulatory filings of 26 insurers. We provide empirical observations on how premiums vary by coverage type, amount, policyholder type, and over time. A method using Particle Swarm Optimization is introduced to iterate through candidate parameterized distributions with the goal of reducing error in predicting observed prices. We then aggregate the inferred loss models across 6,828 observed prices from all 26 insurers to derive the County Fair Cyber Loss Distribution. We demonstrate its value in decision support by applying it to a theoretical retail firm with annual revenue of $50M. The results suggest that the expected cyber liability loss is$428K, and that the firm faces a 2.3%chance of experiencing a cyber liability loss between $100K and$10M each year. The method could help organizations better manage cyber risk, regardless of whether they purchase insurance.