Adam Solomon

This paper studies imperfectly-perceived private information in insurance markets when contracts endogenously respond. Equilibrium contracts, pooling and welfare depend on the joint distribution of risk and misperception. In the Health and Retirement Study (HRS), I show that misperceptions typically co-vary with (medical, long-term care, disability and mortality) risk type: high types under-perceive their risk, low types over-perceive. I develop a general model and algorithm to estimate the equilibrium contracts, pooling and welfare impact of misperceptions that is applicable in many settings. I offer suggestive evidence from US annuity markets that contracts are distorted due to misperceptions, with welfare likely increasing.

We study Colonel Blotto games with sequential battles and a majoritarian objective. For a large class of contest success functions, the equilibrium is unique and characterized by an even split: Each battle that is reached before one of the players wins a majority of battles is allocated the same amount of resources from the player's overall budget. As a consequence, a player's chance of winning any particular battle is independent of the battlefield and of the number of victories and losses the player has accumulated in prior battles. This result is in stark contrast to equilibrium behavior in sequential contests that do not involve either fixed budgets or a majoritarian objective. We also consider the equilibrium choice of an overall budget. For many contest success functions, if the sequence of battles is long enough the pay

Transfer receipt is voluntary and costly, generating "self-targeting" through selective take-up among the eligible. How does self-targeting select on need, and what are its policy implications? We show self-targeting is advantageous in eight U.S. transfers: On average, recipients have lower consumption and lifetime incomes than eligible nonrecipients with similar current incomes. Due to self-targeting, these transfers provide 50 to 75 percent more to the consumption-poorest and lifetime-poorest than would automatic transfers that are distributionally equivalent by income. Self-targeting makes automatic transfers undesirable: We estimate the social benefits of self-targeting are approximately six cents per transfer dollar, generally exceeding the social costs of ordeals.

Every insurance contract bundles risks at some level, and insurers commonly offer discounted contracts with explicit bundling. In a two-risk model, I characterize when bundling occurs in equilibrium and when regulations on bundling can improve welfare. I show theoretically that bundling arises whenever within-person correlations between risk types enable ''cream-skimming'': the willingness to pay (WTP) for insurance against one risk must be negatively correlated with expected costs from the other risk. Regulations that mandate bundling can enhance welfare if they reduce selection, whereas regulations that ban bundling can increase welfare if bundling has lead to substantial unravelling in the separate markets. I use the model to analyze the market for long-term care insurance (LTCI), in which both-spouse bundles are often discounted relative to actuarially-equivalent separate contracts. Using Health and Retirement Study (HRS) data, I show that spousal WTP is negatively correlated with own cost, and model-predicted equilibrium bundling discounts closely match empirical discounts. In counterfactuals, I find that a ban on both-spouse discounts would raise welfare, and mandatory spousal bundling would reduce it, because the advantageous selection in LTCI makes mandatory bundling cost-increasing, and a ban on bundling substantially corrects the unravelling in the singles markets.

Estimates the expected present discounted value (EPDV) of future payouts on both immediate and deferred annuities are sensitive to the discount rate used to value future payment streams and assumptions about future mortality rates. This paper illustrates this with respect to annuities that were available in the US retail insurance market in 2020. The spread between the interest rates on Treasury and corporate bonds was high by historical standards as a share of the riskless Treasury yield during much of 2020, making the choice of discount rate more consequential than in the past. The EPDV estimates also depend on whether the rapid but since-attenuated decline in US old-age mortality rates during the 1990s and early 2000s is extrapolated to future decades. The “money's worth” is the EPDV divided by the annuity's purchase price. Our central estimates, using discount rates drawn from the corporate BBB yield curve and future mortality rates that combine a Society of Actuaries individual annuitant mortality table with projections of future mortality improvements from the Social Security Administration, suggest money's worth values for annuities offered to 65-year-old men and women of about 92 cents per premium dollar. Recent Department of Labor rulemaking requires defined contribution plan sponsors to provide participants with estimates of the annuity income stream that their plan balance could purchase. These estimates, like EPDVs, are also sensitive to both prospective rate of return and mortality rate assumptions.

Mortality rates for those who choose to purchase annuities are lower than the corresponding rates for those who do not, reflecting in part the role that private information about health and mortality risk plays in the purchase decision. This paper explores the nature of this information, by comparing the mortality risk of recent annuity buyers and those who purchased annuities a number of years ago. Using data on the universe of annuity owners in the US, we find clear evidence of vintage effects in the mortality experience of annuitants. The mortality rate for 70-year-old male annuitants who purchased their annuities in the last two years is 77 percent of that for annuitants of the same age who purchased their annuity between five and seven years earlier, and 65 percent of that for those buying between ten and twelve years earlier. Similar patterns are found for men at later ages, and for women. At all ages, the annuitant mortality rates are lower than the population mortality rates, but the disparity at each age declines in the time since annuity purchase. These findings provide evidence on the decay rate of private information about mortality, and shed light on the potential role of deferred annuity products in providing retirement security.

Medical services often have opaque prices. Medical insurance that uses a dollar copayment for cost sharing mitigates this opacity, while coinsurance maintains it. I present experimental evidence that individuals of all risk levels are willing to pay for more transparent contracts, conditional on state-contingent payoffs. To explain why opacity nevertheless prevails in equilibrium, I theoretically show and experimentally verify that when distaste for opacity is more pronounced among the high risk than the low risk, opacity can have a welfare-improving screening function. I offer empirical evidence from the Covered California healthcare exchange that shows demonstrates that individuals are opacity averse but that the aversion increases in risk level, consistent with the theory.

These are the materials I made as the TA for Prof. Amy Finkelstein in Fall 2022