Insurer Risk and Public Risk-Sharing: Quantifying the Value of Reinsurance

Kim and Li study how publicly provided reinsurance affects insurer behavior and market outcomes in health insurance markets where firms face substantial cost uncertainty. The central question is whether standard expected-profit models—which predict that reinsurance reducing only cost volatility (not expected cost) should leave prices unchanged—miss an important mechanism: insurers internalizing the implicit financial cost of bearing claims uncertainty through “risk charges.”

The paper develops a stylized monopoly-insurer model in which the insurer’s objective includes both expected claims cost and a risk charge term L(S), where S is a risk measure (e.g., standard deviation of total claims). This yields a first-order condition in which effective marginal cost includes both standard expected claims cost and a marginal risk charge. The model predicts that public reinsurance acts through two distinct channels: (1) a cost subsidy—reimbursing a share of high-cost claims reduces expected cost; and (2) risk protection—reducing the variance of claims lowers the risk charge and thus effective marginal cost. When both channels operate, the model predicts pass-through of public reinsurance to premiums can exceed unity, in contrast to the standard less-than-one pass-through under market power.

Empirically, the authors use three primary data sources for the U.S. individual health insurance exchange market. NAIC Schedule S filings (2014–2023) provide transaction-level private reinsurance contracts, including ceded premiums, realized claims, and financial solvency measures. CMS Public Use Files and MLR reports provide plan-level premiums, enrollment, and claims. The Colorado All Payer Claims Database (CO APCD, 2014–2022) and Connect for Health Colorado administrative records (2015–2021) provide individual-level claims and insurance choices for structural analysis.

Descriptive evidence establishes that 62% of exchange insurers purchase private reinsurance despite average reinsurance markups of 1.54 (reinsurance margin of 0.54), and that smaller, less financially solvent insurers are disproportionate buyers—consistent with risk charges driving demand for risk protection even at above-actuarially-fair prices.

An event study exploiting staggered adoption of state-level public reinsurance programs finds that public reinsurance reduces premiums by approximately 14.5% on average (27% in Colorado Tiers 1–2, 46% in Tier 3), with a pass-through rate of 1.3—significantly greater than one (p = 0.037 one-sided). Public reinsurance reduces the probability of purchasing private reinsurance by 26 percentage points (a 42% reduction from baseline) and per-member private reinsurance expenditures by $19.5 (a 68% reduction from baseline). Premium and private reinsurance effects are larger for financially constrained insurers (RBC ratio below 3). No significant effects are found on insurer entry/exit, total medical expenses (ruling out moral hazard), or private reinsurance markups.

The structural model, estimated on the Colorado exchange for 2017–2020, finds that the risk charge coefficient for regional insurers averages rho = 0.25, implying regional insurers face 9.8% higher effective costs than national insurers due to risk charges and private reinsurance expenses. Risk charges account for at least half the premium-cost wedge for small regional insurers. Counterfactual decomposition of Colorado’s program shows the direct cost subsidy accounts for approximately 75% of equilibrium price reductions; risk protection and competition effects together account for the remaining 25%. In a bang-for-buck comparison, public reinsurance dominates premium subsidies of equal government expenditure by approximately 20–30%, because reinsurance uniquely reduces risk charges and enhances competition by reducing smaller regional insurers’ cost disadvantage.

Q: What is the core theoretical innovation of the paper? A: The paper adds a risk charge term L(S) to the standard expected-profit objective, where S is a risk measure of the insurer’s cost distribution. This makes the insurer behave “as if risk averse,” with effective marginal cost including both expected claims cost and a marginal risk charge that decreases with insured pool size due to risk pooling. When rho = 0, the model collapses to the standard monopoly case; when rho > 0, cost uncertainty directly inflates prices and creates a novel role for reinsurance even when reinsurance is actuarially fair priced.

Q: What are the two distinct mechanisms through which public reinsurance affects insurer pricing? A: The first is a cost subsidy: by reimbursing a portion of high-cost claims without requiring an actuarially fair premium upfront, public reinsurance lowers the insurer’s net expected cost. The second is risk protection: by providing ex-post payments for extreme health shocks, reinsurance reduces the variance of claims costs, lowering the risk charge component of effective marginal cost. Together, these channels can produce pass-through exceeding unity even under imperfect competition, where standard cost-subsidy pass-through is typically below one.

Q: What does Proposition 1 say about actuarially fair reinsurance (theta = 1)? A: Proposition 1(i) states that actuarially fair reinsurance—which does not alter net expected cost—still lowers the insurer’s price if and only if the insurer faces a risk charge (rho > 0). An insurer without risk charges is entirely unaffected by actuarially fair reinsurance. This result isolates the risk-protection channel as theoretically distinct from cost subsidization and establishes that pass-through exceeding one requires risk charges to be operative.

Q: Why would an insurer purchase costly private reinsurance (theta > 1)? A: Proposition 1(iii) shows that an insurer with no risk charge would never purchase private reinsurance with theta > 1, since it increases net expected cost with no offsetting benefit. An insurer facing a risk charge (rho > 0) may purchase private reinsurance because the risk-protection benefit—the reduction in cost variance and thus the risk charge—can outweigh the net cost increase. The paper documents that 62% of exchange insurers buy private reinsurance at an average markup of 1.54 (reinsurance margin 0.54), with smaller and financially weaker insurers more likely to purchase, consistent with this mechanism.

Q: How does the paper establish empirically that insurers face and internalize cost uncertainty? A: Three lines of evidence are presented. First, the CO APCD shows the claims distribution has a long right tail: the top 5% (1%) of consumers account for 68% (38%) of total expenses, and 2.5% of consumers exceed the $30,000 reinsurance threshold. Second, simulations show that with 1,000 enrollees, the probability that realized claims exceed expected costs by 25% is approximately 7%; even at 10,000 enrollees there is a 17% probability of exceeding expected costs by 5%. Third, in over 24% of insurer-year observations premium revenue falls short of realized claims costs, and the within-firm standard deviation of the claims-to-premium ratio is 0.15.

Q: What are the event study findings on premiums? A: Using staggered introduction of state-level public reinsurance programs, the event study finds premiums fell by 14.5% on average following program adoption. In Colorado specifically, Tiers 1 and 2 experienced 27% decreases and Tier 3 (highest reinsurance generosity) experienced a 46% decrease. The implied pass-through rate for 2020 is 1.3, meaning for every dollar the government spent on reinsurance, health insurance premiums fell by $1.30. A one-sided t-test rejects pass-through equal to one at p = 0.037.

Q: What are the event study findings on private reinsurance? A: Public reinsurance reduces the probability that an insurer purchases private reinsurance by 26 percentage points, a 42% decline from the pre-program baseline. Average per-member private reinsurance expenditures fall by $19.5, a 68% reduction from baseline. The substitution away from private reinsurance is consistent with the model prediction that public reinsurance displaces the demand for risk protection previously met by private markets, and reinforces the interpretation that risk management is a key driver of private reinsurance demand.

Q: Do financially constrained insurers respond differently to public reinsurance? A: Yes. The premium-reduction effect is significantly larger for insurers with RBC ratios below 3 (an additional interaction effect of -0.161 log points on top of the baseline -0.135). The reduction in per-member private reinsurance expenditures is also significantly larger for insurers with significant prior private reinsurance purchases (-$108.8 vs. baseline of -$19.5). This heterogeneity supports the hypothesis that the risk protection channel is more valuable for financially constrained insurers who face higher implicit costs of bearing risk.

Q: Does public reinsurance affect insurer entry/exit, moral hazard, or private reinsurance markups? A: The event study finds no statistically significant effect on market entry, total monthly medical expenses per enrollee, the probability that individual expenses exceed the reinsurance threshold (ruling out insurer moral hazard), or private reinsurance markups paid by primary insurers. These null results support the interpretation that premium reductions reflect reduced cost uncertainty rather than cost containment distortions, and that the competitive structure of the private reinsurance market is not directly altered by public programs.

Q: What are the structural estimates of risk charges? A: The estimated risk charge coefficient for regional insurers averages rho = 0.25. This implies that regional insurers incur, on average, 9.8% higher effective costs than national insurers (who are assumed not to face risk charges due to scale and diversification), stemming from both direct risk charges and private reinsurance expenses required to manage risk. Risk charges account for at least half the observed wedge between premiums and marginal claims costs for small regional insurers.

Q: How does the structural model decompose the impact of Colorado’s reinsurance program? A: Counterfactual analysis decomposes the equilibrium price reduction into three channels. The direct cost subsidy effect—reimbursing a share of high-cost claims between the $30,000 attachment point and $400,000 cap—accounts for approximately 75% of the price reduction. The risk protection effect (reduction in risk charges from lower portfolio variance) and the competition effect (smaller regional insurers facing lower cost disadvantages and competing more aggressively with national insurers) together account for the remaining 25% of the equilibrium price reduction.

Q: How does public reinsurance compare to premium subsidies in bang-for-buck terms? A: For equal government expenditure, public reinsurance is estimated to be approximately 20–30% more cost-effective than premium subsidies at reducing premiums. The advantage stems from two sources: reinsurance reduces risk charges, shifting down the marginal cost curve for regional insurers in a way demand-side premium subsidies do not; and reinsurance enhances competition by reducing the cost disadvantage of smaller regional insurers relative to national ones. The dominant effect is risk reduction rather than markup inflation, making reinsurance the more efficient instrument when the degree of financial risk is considerable.

Q: What is the role of market size in risk charges, and why does this create a competitive asymmetry? A: The model shows that the marginal risk charge decreases as the insured population grows (risk pooling), with marginal standard deviation equal to sigma_0 / (2*sqrt(q)), which vanishes as q approaches infinity. This implies that larger national insurers, covering very large populations, effectively face no risk charges, while smaller regional insurers face meaningful marginal risk charges. This size-asymmetry is the fundamental reason why public reinsurance disproportionately benefits smaller insurers—by reducing their risk charges, it narrows the cost gap with national insurers and intensifies competition.

Q: What scope conditions apply to the structural findings? A: The structural estimates are based on the Colorado individual health insurance exchange, covering years 2017–2020, chosen to avoid unsatisfactory early data quality and to net out systematic pandemic effects. The model assumes national insurers do not face risk charges in the baseline specification, and that aggregate (correlated) risk is not the primary driver during the sample period. Results are robust to staggered-treatment corrections (Callaway-Sant’Anna 2021; Borusyak et al. 2024), alternative outcome measures (benchmark premiums, Silver plan averages), alternative aggregation levels, and sensitivity analyses allowing for insurer entry/exit, correlated risks, moral hazard, and alternative risk charge functional forms.

Q: What are the broader policy implications of the framework? A: The framework applies to any market where firms face substantial cost uncertainty and internalize financial risk, including property and casualty insurance, flood insurance, wildfire insurance, and government loan guarantee programs. The analysis suggests that ignoring the risk protection channel causes policymakers to underestimate the effectiveness of public reinsurance relative to demand-side subsidies. Supply-side risk-sharing policies are particularly important for markets with small, financially constrained firms, where cost uncertainty most severely distorts pricing and competition, and where the competitive benefits of risk reduction are largest.

Risk Charge: An additional cost term in the insurer’s objective function representing the implicit financial cost of bearing claims uncertainty, formalized as L(S) where S is a risk measure of total cost. Risk charges make the insurer behave “as if risk averse,” raising effective marginal cost above expected claims cost. In the baseline model the risk charge equals rho times the standard deviation of total claims.

Risk Charge Coefficient (rho): The parameter governing the insurer’s marginal cost of financial risk, estimated structurally at an average of 0.25 for regional insurers in Colorado. It can be interpreted as either a direct risk-aversion parameter, the marginal cost of regulatory capital, or a reduced-form representation of financial and regulatory frictions that make bearing cost uncertainty costly.

Risk Protection Channel: The mechanism through which reinsurance (public or private) reduces claims cost variance and thereby lowers the insurer’s risk charge, distinct from the cost-subsidy channel. The risk protection channel is operative even for actuarially fair reinsurance (theta = 1) and is responsible for pass-through rates exceeding unity under public reinsurance programs.

Cost Subsidy Channel: The mechanism through which subsidized public reinsurance (theta less than 1) lowers the insurer’s net expected claims cost by reimbursing a share of high-cost claims without charging an actuarially fair premium. This channel operates regardless of whether the insurer faces risk charges and is the primary channel in standard models.

Pass-Through Rate: The ratio of premium reduction to government expenditure on reinsurance. In standard models with market power, pass-through of cost subsidies is typically below one; the paper documents a pass-through rate of 1.3 in Colorado (p = 0.037 for the null of pass-through equal to one), attributing the excess to the risk protection channel reducing both expected cost and cost uncertainty simultaneously.

Stop-Loss Reinsurance: A contract structure in which the reinsurer reimburses the primary insurer for individual claims costs exceeding a deductible (attachment point) kappa up to a cap. In Colorado’s program the attachment point is $30,000 and the cap is $400,000, with government coinsurance rates of 40–80% depending on county tier. More generous reinsurance corresponds to lower kappa; full reinsurance is kappa = 0.

Risk-Based Capital (RBC) Ratio: The ratio of capital surplus (assets minus liabilities) to required risk-based capital, used by NAIC as a measure of insurer solvency. NAIC scrutinizes companies with RBC ratios below 200%; the paper uses RBC ratio below 3 as a proxy for financial constraint in heterogeneity analysis, finding larger premium and private reinsurance responses among constrained insurers.

Tail-End Risk: The risk arising from the possibility that a small fraction of enrollees incurs extremely high medical costs, concentrated in the right tail of the claims distribution. In Colorado, the top 5% of consumers account for 68% of total expenses; tail-end risk is especially severe for small insurers with fewer than 10,000–100,000 enrollees and is the primary motivation for private reinsurance purchases even at above-actuarially-fair prices.