1 Measuring Inefficiencies from Adverse Selection Jonathan Levin Gaston Eyskens Lectures November 7, 2013
2 Roadmap Lectures 1. Technology and Asymmetric Information 2. High Risk Consumer Credit Markets 3. Measuring Inefficiencies from Adverse Selection 4. Can Markets for Health Insurance Work?
3 Introduction Generally taken for granted that asymmetric information creates significant inefficiencies in insurance markets. Several related types of inefficiency: Mispricing due to adverse selection Distortion of available products Complete market breakdown Today s lecture: describe recent work on two questions. Can we detect asymmetric information in insurance markets? Can we estimate the welfare losses from adverse selection? Based on Einav, Finkelstein, Levin (2010, Ann Rev), and especially Bundorf, Levin, Mahoney (2012, AER).
4 Testing for Adverse Selection Key prediction: People who are higher risk buy more insurance. - This self-selection drives up the price of generous insurance, so equilibrium coverage is inefficiently low. Seems easy to test Identify people who choose more versus less insurance while facing the same prices (important if self-selection is to apply). Look ex post to see who makes a claim or costs more to cover. If individuals who buy more insurance have higher realized risk, taken as evidence for the theory. If not, evidence against the theory. Moral hazard complicates interpretation: Individuals might generate more claims because they have more insurance.
5 Evidence: Puelz and Snow (JPE, 1994) Sample of 3,280 individuals who bought auto collision insurance in Georgia in 1986, choosing deductible level. Number of individuals Number incurring a loss Deductible Level $100 $200 $250 1, , Fraction w/ loss 3.03% 2.28% 1.59% Regression of deductible choice on indicator for a subsequent loss, controlling for the prices of the different plans, shows deductible choices is correlated with loss conditional on Xs.
6 Evidence: Chiappori and Salanie (JPE 2000) Large sample of auto insurance contracts in France in Test whether deductible choice is correlated with having subsequent accident, conditional on individual characteristics used in pricing. Main finding: cannot reject that conditional on (rich) covariates: deductible choice is not correlated with driver having an accident. Interpretation: if rich individual data is used for pricing, there may not be much self-selection within risk categories.
7 Evidence: Life Insurance and Long-Term Care Cawley and Philipsson (AER 1999) on life insurance People with more life insurance have lower mortality than those with less insurance, and lower self-reported risk of death. Finkelstein-McGarry (AER 2005) on long-term care insurance No correlation between LTC insurance and subsequent use. Although people who say that they expect to use a nursing home are more likely to buy LTC insurance, and more likely to use LTC. Interpretation: there is an offsetting effect, e.g. wealthier people are more likely to buy insurance but less likely to need LTC.
8 Evidence: Hendren (EMA 2013) Attempts to reconcile apparently puzzling evidence Life insurance (high risk insure less) Long-term care (high risk insure same) Disability (high risk insure more) Argues that pattern is consistent with asymmetric info theory, in fact is explained by Akerlof-style market breakdowns. High risks don t insure because their applications are rejected. As in Akerlof, no price works for insurers given enough private info. Uses subjective risk assessments to estimate private information, and argues that for life + long-term care insurance, no trade is predicted for high-risk applicants => they can t get coverage. Implication: failure of correlation test market is efficient.
9 From Testing to Measurement Lessons from testing papers Extent of adverse selection seems to vary across markets, depending on what is priced, and specific nature of risk. In markets where risk is not accurately priced, can we quantify how important are the distortions? This requires some additional structure. Need to understand how incorrect pricing affects choices. And need to understand cost structure to measure the misallocation, and whether key products aren t offered. Remainder of the talk Outline textbook model of insurance demand + welfare. Two applications using slightly stylized approaches.
10 Canonical Insurance Model Individual with characteristics ζ (risk, preferences, etc.) Possible outcomes S (e.g. accident of no accident) Insurance contract: characteristics φ and premium p Expected utility from contract φ, p given v φ, p, ζ = u s, ζ, φ, p π s ζ s S Probability of outcomes π s ζ, utility u s, ζ, φ, p See EFL (2010) for general model that allows for MH.
11 Canonical Insurance Model Consumer choice: Select contract j if for all alternatives k v φ j, ζ p j v φ k, ζ p k I m assuming no income effects v φ, p, ζ = v φ, ζ p Let τ(s, φ) denote payments by the insurer. c φ, ζ = τ(s, φ)π s φ, ζ s S Key point: unit costs depend on risk type ζ.
12 Measuring Welfare Total surplus measure of welfare W = v φ i, ζ j(i) c φ i, ζ j(i) i I Note: j(i) is insurance product selected by consumer i. W maximized if each i faces prices: p ij = c φ i, ζ j + a i What information do we need to learn W? Just v and c (not u!) Choice data to measure indirect utility v : e.g. Einav, Finkelstein, Cullen, 2010; Bundorf, Levin and Mahoney, Structural models of underlying risk preferences (estimate u): e.g. Cardon-Hendel (2001), Cohen-Einav (2007), Handel (2013).
13 Modeling Adverse Selection Einav-Finkelstein-Cullen (2011, QJE) Employees at a large employer (Alcoa) choosing more or less generous health insurance. Health care costs are higher for employees who chose the more generous coverage. Linear model of demand and costs, as a function of price. Prices faced by the employees varied by location. Estimate using data on insurance choices and claims. Measure welfare as the difference between WTP and cost.
14 Einav-Finkelstein-Cullen Linear Model Price As price decreases, more people buy (extra) insurance The cost of covering the extra enrollees is lower they re healthier. P =AC P =MC Avg Cost Marg. Cost Demand Comp. Q Efficient Q Quantity
15 Measuring Adverse Selection Deadweight loss from adverse selection is not that large. Why? Because demand is inelastic! Estimates from Einav, Finkelstein and Cullen (2010, QJE): Data from Alcoa
16 Modeling Self-Selection Bundorf, Levin and Mahoney (2012, AER) Choice between differentiated health plans An integrated HMO plan with specific doctors. A traditional PPO insurance plan. Choice isn t just more/less generous insurance No obvious problem of adverse selection, but will see that self-selection can still create inefficiencies.
17 Self-Selection with Differentiation Two plans: A and B. Consumers differentiated by WTP and coverage cost Willingness to pay v = v B v A Cost of coverage c = c B c A Joint distribution of v and c --- not perfectly correlated. Efficiency: assign to plan B if and only if v c 0 Self-selection: choose plan B if and only if v p 0
18 Self-Selection and Inefficiency WTP Δv Assume: (1) plan A relatively more effective at covering high cost patients; (2) prices aren t personalized. Δc( ) Δp Choose A inefficiently Choose B efficiently Choose A efficiently Choose B inefficiently Risk ( )
19 Data and Environment Data from a company that helps small to mid-sized employers offer choice of health insurance plans. How the plan choice process works Insurers submit bids to cover employees at a firm. Firm sets employee premiums. Employees select plans. Data includes bids, premiums, employee info, including predictive risk scores, plan choices and subsequent costs. As noted above, plans provided by two insurers a (low-cost) integrated and a (higher-cost) standard insurer.
20 Key Features of the Environment 1. Standard insurer is higher cost, especially for less healthy people. Standard insurer has higher average ex post costs and also bids higher, with difference most pronounced for high-risk (less-healthy) people. 2. Individuals at a firm face the same subsidized plan prices, not dependent on individual health status (federal regulation). Individual premiums are higher for standard insurer. Average premiums are $41 for integrated and $54 for standard insurer. 3. Majority of individuals choose the low-priced integrated insurer. 71% compared to 29% for standard insurer. 4. No obvious adverse selection Enrollee risk is 1.02 for standard insurer versus 0.99 for integrated.
21 Cost Structure of Insurers
22 Bids of Insurers
23 Puzzling Feature of Pricing Employers in the our data (and US generally) do not face employees with full cost of health insurance. Instead, use simple rules to set employee contributions The following rule explains 99% of price variation in our data! p j = βb + γ B f B where B is the bid of the cheapest plan. Two strategies are common Constant pass through β = γ Incremental pass through β < γ Only occasionally full incremental pass-through γ 1.
24 Puzzling Feature of Pricing
25 Household utility model BLM Empirical Model u hj = φ j α φ + x h α xj + ψ r h + μ h ; α rj p j + σ ε ε hj where μ h ~iid N 0, σ h 2 and ε hj ~iid Logit Choice probabilities (set v hj = u hj σ ε ε hj ) Pr q hj = 1 X hj, μ h = exp v hj k J h exp v hk Cost model c ij = a j + b j r i + μ i 1 + η ij
26 Estimating Insurance Demand + Costs Household demand for health plans Little evidence of important risk-based preferences. Relatively little price elasticity, in line with other studies. Optimal assignment by risk score As risk increases from 1 to 2.5, WTP for standard insurer increases by $22, but incremental cost increases by $101. Efficient to put high-cost individuals into low-cost plan, but to provide price incentive for this sort of self-selection, requires making high-cost plan very expensive for all individuals
27 Inefficiency in the Estimated Model
28 Assessing Inefficiency Calculate social surplus under alternative types of pricing - Efficient: each household faces actuarially fair prices. - Feasible: each household faces prices equal to predicted costs, not including private information. - Uniform: employees at each firm face most efficient uniform prices, i.e. independent of their health status. - Actual: uniform prices as observed in data, not optimal. Main finding: differences in social surplus are relatively modest, about 2-11% of coverage costs. - Could eliminate ¼ with optimal uniform prices. - Could eliminate ½ with risk-rated individual prices.
29 Assessing Inefficiency
30 Welfare and Consumer Choice EFC and BLM (and other recent studies) find very modest welfare losses from adverse / self-selection. Main reason is inelastic demand Typical finding in studies of (health) insurance. Why does it matter? The source of inefficiency is that individuals don t face efficient personalized prices. With inelastic demand, price distortions don t have much effect on the allocation, which is what matters for efficiency! So why isn t demand more price-sensitive?
31 Switching Costs / Inertia? Handel (2013, AER) Example Existing Employees New Employees Available Plans Year 1 Year 2 Year 2 PPO % 21% 11% PPO % 26% 43% PPO % 14% 14% HMOs (A+B) 40% 39% 32% Choices are very persistent. The surprise here is that in Year 2, the price of PPO 250 went up so much that PPO 500 was cheaper regardless of how much care you got and yet people picked it.
32 Inertia and Adverse Selection Handel goes on to study a more general model of choice similar to above, but incorporating switching costs. Finds that inertia in plan choice helps explain inelastic demand and (to some extent) failure to find inefficiencies from adverse selection. Then makes an interesting observation forcing active decisions in insurance markets: Increases price sensitivity and potentially avoids dominated choices, but also exacerbates adverse selection, by creating more sorting / self-selection.
33 Choice Behavior Missing Pieces Insurance products are complicated, and unlike in these models consumers choose poorly (Handel + Kolstad, others). Moral Hazard Talk has focused on adverse selection problems, and not on moral hazard, through which insurance affects behavior. Maybe not a big deal in life insurance and annuities, or even auto insurance. But a very big deal in health insurance. Reclassification Risk Risk-based pricing helps mitigate adverse selection, but it creates re-classification risk: individuals who get (persistently) sick in year t will face high risk-rated prices in years t+1, t+2, etc.
34 Competition Papers I ve discussed do not focus on competition Einav et al.: just assumes p = AC Bundorf et al: prices set by administrative rules But unlike in our models, insurance markets often have a limited set of firms and presumably imperfect competition. Raises some questions for next lecture Are inefficiencies from imperfect competition a bigger issue than inefficiencies from adverse selection? What sort of models can we use to analyze markets where there is self-selection and imperfect competition?
35 Summary Recent work has begun to explore and measure the extent of selfselection in insurance markets and the resulting distortions. Exciting area rich data and interesting theories to analyze large and economically important markets. Mixed evidence on importance of adverse selection Risk-based pricing seems to offset AS in many settings. In others, can observe clear self-selection, but misallocation of resources does not seem large. Of course, some markets simply may not exist the inefficiency from missing markets could be large. Plenty of missing pieces for future work!
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