Woolhandler, et al. (2003) note that Seattle alone had 757 distinct health insurance products. Our discussions with executives in the insurance industry suggest that this number is not atypical for metropolitan areas and may be conservative. Recent experience with the new market for pharmaceutical insurance under Medicare part D illustrates well the tendency for health insurance markets to proliferate vast numbers of products (Thaler and Sunstein, 2008).
Exogenous switches could be the result of shocks that cause clients to drop insurance coverage or become self-insured, or changes in client preferences or even miscalculations. Brokers, who receive commissions from insurers for bringing in new business, may also be an exogenous source of switches. A more complex back-story that we don’t develop is that insurers find it difficult to estimate insurance costs in the coming year. Some will bet high and others low. As a result some low cost insurers will suddenly become high cost and vice versa. One way to model this would be to randomly reassign a subset of insurers and their current customers to different parts of the premium distribution . This would provide the needed exogenous reshuflling needed for the distribution not to collapse into a single price. Another way to introduce this reshuffling is to simply take a sample of current insurers and randomly assign them to policies on the premium distribution.
The fact that the highest premium is pR follows from the assumption that the efficiency of searching for insurance is the same whether the group is currently insured or not.
Notice as market frictions approach 0, average and median converge to c.As frictions approach infinity, average and median approach the reservation price.A result we will use later is that maximum observed price equals reservation price if search efficiency is the same for insured and uninsured. Mechanically, the right skew arises because the distribution is bounded from below by the marginal cost of insurance, c. This is what accounts for the right skew.In labor markets, the distribution of premiums is bounded from above by the value of the marginal product of labor. B-M predicts a left-skewed distribution of wages
Insurers must update their computer systems to accommodate new members and match them with the terms of their policies, a surprisingly difficult task made more complex by the continuous movement of employees in and out of firms and by the very large variety of offered plans (see, e.g., Cebul, Rebitzer, Taylor, and Votruba, 2008, and Hall, 2008). In addition, it takes insurers time to learn about the needs and expenditure patterns of new members. One insurance industry executive with whom we spoke said it can take up to a year to accumulate enough billing data to identify a diabetic. Employees whose employer switches insurers may have to find new primary care physicians, new specialists and new hospitals. Because the U.S. lacks a portable electronic medical records system, it is often the job of individual patients themselves to transfer information to new providers. Of course the job of searching for a new insurance policy also consumes employer time, attention and (if a broker is hired) money.
Our analysis focuses on 5,261 establishments that offered a non-HMO plan as their dominant plan option when surveyed. Table 6 provides a breakdown of these establishments by insurance type and FI/SI status. Within this sample, the strongest predictor of SI status is firm size (see Table 7). Among firms with 35 or fewer workers, only 2.5% of establishments offered SI plans, while SI plans dominate establishments within larger firms. Our variable of interest is the “single monthly premium” recorded for the dominant plan at the surveyed establishment. A plan was identified as the "dominant plan" if >90% of the coveredworkers from the group were covered by that plan.There were two reasons why we decided to exclude HMO plans. The first reason is that very few (<5%) of the HMO plans were self-insured.Another justification for excluding them is that HMO premiums are expected to vary for reasons not captured by the plan characteristicsSee the Data Appendix for detail on data exclusions.
Our variable of interest is the “single monthly premium” recorded for the dominant plan at the surveyed establishment.Ceteris paribus, our model leads us to expect relatively higher premiums in FI plans, but in comparing FI with SI plans all else is probably not equal. Large employers, who tend to self insure, offer higher wages than smaller employers (Brown and Medoff, 1989). We would therefore expect SI plans to offer richer and more expensive insurance because health insurance is a normal good and because the tax breaks for health insurance are most valuable for high-income employees.
Specification of the premium prediction model followed the advice presented in Manning and Mullahy (2001) for the modeling of skewed health care cost distributions. The link and distributional family assumptions were supported by the Box-Cox test and modified Part test. See the Data Appendix for additional details and estimate results.
Calculated mean and median by counting distance from the bottom 1 percentile.The patterns in the data are what we would expect if there are search frictions in the market for FI plans. Even after conditioning on group and plan characteristics, the residual premium variance is much higher for FI plans than SI plans. The included covariates explain a much smaller fraction of the original variance in premiums in FI plans (about 20%) than for SI plans (about 54%). The distribution of residuals for FI plans also has a pronounced right skew not evident among SI plans, as our model would predict. Table 10 gives calculations of the mean premium residual in different quintiles of the residual distribution. Here again the results suggest that variation in premium residuals is larger for FI plans.There are fewer SI than FI plans in our data. This naturally reduces residual variation because each observation has some influence in pulling the regression line towards it. Can perhaps solve this by a “jacknife” procedure where the fitted line for each observation is calculated by dropping that observation. Very computationally intensive for an effect not likely to be important at sample sizes near 1000.
Results omitted for categories with small sample sizes (N<100). Bootstrap standard errors, with 300 replications, are presented in parentheses.
To understand this result, consider the Burdett-Mortensen model in its original labor market context. If it is more effective for workers to search when employed, then some employees will accept a wage less than their reservation wage in order to gain access to a more efficient search process. In this case, the lowest observed wage will be less than the reservation wage. Conversely, if it is more effective to search when one isn’t employed, some employees will pass up jobs with wages above reservation wages in order to gain access to more efficient search processes. If job search is as efficient for employed and unemployed workers, the minimum observed wage is the reservation wage. The analysis holds in our insurance context: if the efficiency of insurance search is independent of insurance status, then the maximum observed price is equal to pR.
Unhealthy Insurance Markets: Search Frictions and the Cost and Quality of Health Insurance
Unhealthy Insurance Markets: Search Frictions and the Cost and Quality of Health Insurance<br />Randal Cebul<br />School of Medicine and Center for Health Care Research and Policy<br />Case Western Reserve University<br /> <br />James B. Rebitzer<br />Department Markets, Public Policy and Law<br />Boston University School of Management,<br />Case Western’s Center for Health Care Research and Policy,<br />NBER, The Levy Institute, and IZA<br /> <br />Lowell J. TaylorH. John Heinz III School of Public Policy and Management<br />Carnegie Mellon University<br />Mark Votruba<br />Department of Economics, Weatherhead School<br />School of Medicine and Center for Health Care Research and PolicyCase Western Reserve University<br />
A Prosaic Beginning: The Shopping Problem <br />
The Health Insurance Shopping Problem<br />Health Insurance is a complex multi-attribute service.<br />Savvy purchasers must consider:<br />which drugs are in the insurer’s formularies, <br />which local physicians are part of the insurer’s provider network, <br />what co-pays and deductibles apply to which pharmaceuticals, providers and services<br />Delivery of services under hard-to-anticipate contingencies.<br />Medical underwriting and the great profusion of insurance products increases administrative costs and search complexity.<br />Overcoming these challenges entails costs and these costs create search frictions.<br />
The Health Insurance Shopping Problem<br />In the US, large and sophisticated employers can simplify the shopping problem by “self insuring” and hiring insurers simply to administer their plans.<br />Smaller and less sophisticated firms “fully insure”, i.e. they buy both administrative services and insurance. <br />These “fully insured” employers have a particularly daunting shopping problem: they know less and the service they buy is more complex.<br />Brokers can, in theory, help.<br />In practice broker advice influenced by the fact that they receive commissions from insurers.<br />
The Effects of Search Frictions<br />We study the effect of search frictions on the operation of the commercial health insurance market – especially the “fully insured” market segment.<br />Little attention has been given to the issue of search frictions. Important exceptions:<br />Brown and Goolsbee’s (2002) study showing significant search frictions in the term life insurance market prior to advent of the internet-based comparison shopping. <br />Frank and Lamiraud ( 2008) report evidence of significant price dispersion for homogenous products in Swiss health insurance markets.<br />
The Effects of Search Frictions: Theory Results<br />Burdett-Mortensen model adapted to health insurance setting.<br />Key results:<br />Law of One Price doesn’t hold. Identical products priced differently and the distribution of prices is right skewed.<br />Moderate frictions high policy-holder turnover rates <br />The magnitude of frictions can be inferred from the distribution of premiums<br />Search frictions lead insurers to adopt inefficiently high marketing expenditures.<br />
Theory Results: Why Inefficiently High levels of Marketing?<br />In frictional insurance markets p> MC, so insurers always want more clients and will spend resources to attract them.<br />Insurance companies with high p gets greater return from marketing than low price plan and so will pay higher commissions.<br />The result is an arms race in marketing –especially in FI plans.<br />Social welfare would be improved with lower commissions, but no insurer will unilaterally cut their payments.<br />Not much data on insurance plans, but Litow using data from large actuary firm reports that administrative expenses were 21% of premium in small group market and 11.5% in large groups. Almost all this diff is due to commissions that are 8.5% of premiums<br />
Empirical Results I : Excess Insurance Turnover<br />Data: Household Survey component of the Community Tracking Study (CTS); proprietary information from the enrollment records of a large regional insurer.<br />We find<br />High rates of health insurance cancellation rates (20%/year).<br />Rates of turnover are higher for “fully insured” groups (30%/year) than for self insured (14%)<br />For the average “fully insured”, roughly 60% of this turnover is in fact due to cancellations by entire employer groups. <br /> For “self insured”, only 10% of turnover due to employer group turnover.<br />
Empirical Results II: Excess Price Dispersion<br />Data: The Robert Wood Johnson Foundation Employer Health Insurance Survey (EHIS) from 1997<br />The variance in the residual distribution of premiums is greatest in the fully insured market segment where frictions are greatest.<br />The skewness of the residual distribution is greatest for fully insured. <br />
Empirical Results III: Structural Estimates <br />Fitting our theoretical model directly to the data yields parameter estimates suggesting moderate search frictions.<br />Market frictions are severe enough to:<br />Transfer ~ 13.2% of consumer surplus to insurers (~$34B in 1997).<br />Increase the insurance turnover about 64% for the average insurance policy.<br />Caveat: structural estimation presumes a correct model. <br />If the fit to the data is poor or if parameter values are crazy, can cast doubt on adequacy of the chosen model.<br />Structural estimation does not rule the possibility that other models might do as well or better.<br />
Policy Implications<br />Moderate search frictions transfer substantial surplus to insurers; and support high levels of insurance turnover.<br />Friction induced turnover reduces incentives to invest in future health of policy holders. <br />Policy Responses?<br />Use IT to make comparison shopping easier.<br />Reduce excess variety of plans.<br />Thin the right tail of premium distribution: <br />public option? Medical loss ratio regulation?<br />Regulate brokers?<br />
Plan of Talk<br />Sketch out search model and its key predictions for insurance turnover and insurance premiums.<br />Examine the distribution of premiums. Is residual variance and skewness greatest where frictions are greatest?<br />Fit the theoretical model to the data to estimate “search friction” parameter.<br />Are the parameters we uncover consistent with other data?<br />What implications do these parameters have for the efficiency of insurance markets?<br />What implications do these parameters have for incentives to invest in future health. For public insurance options?<br />
Modeling Insurance Search: Setup<br />Two market actors: <br />insurances companies and clients<br />Clients are employers who purchase on behalf of their employees.<br />Problematic Information flows<br />Insurers post a premium. Offers arrive at clients via a random process at rate, l. <br />Clients choose the lowest price plan. Contracts last one year <br />Clients exit the relationship in one of two ways. <br />Exogenous separation: which occurs at rate d. <br />Endogenous separation: the client finds a better deal elsewhere. <br />Market friction parameter, g = d/l. As g increases so do frictions.<br />Solve for steady state solutions in continuous time.<br />
Modeling Insurance Search: Price Dispersion<br />Insurers can reach only a limited number of clients.<br />Perhaps due to the costs of marketing, e.g. the costs of hiring sales people or paying brokers<br />Perhaps due to client’s limited “mental shelf space”.<br />Offers arrive randomly, so some clients will receive many offers and others only one or two.<br />This latter possibility makes it profitable for some insurers to charge high prices for their product. <br />Many, perhaps most, clients will decline these high priced products.<br />For a few clients, however, the high priced offer will be the best they receive.<br />
Modeling Search Frictions: Price Dispersion<br />Suppose all firms set p=c, so p=0<br />A maverick firm could earn positive expected profits by charging a discretely higher premium, p. <br />The high offer will sometimes be accepted if the contacted client receives no better offer. <br />Supposed all firms set p>c, so p>0<br />A maverick firm will do better by charging a price slightly less than p, thereby increasing the number of clients while reducing profit per client by a negligible amount.<br />Insurers must therefore be playing mixed strategies.<br />
Modeling Search Frictions: the equilibrium distribution of premiums.<br />In order for profits to be identical for all insurers, the entire distribution of offers and acceptances must take a certain shape. <br />For a high priced insurer, if there are too many competitors offering a lower price, the rate of acceptance of offers and hence expected profits will be too low.<br />Conversely if there are too few competitors offering a lower price, the rate of acceptance of high priced offers and expected profits will be too high.<br />Requiring that high price insurers make the same profit as lower priced insurers therefore determines the shape of the cdf of premiums, F(p)<br />Somewhat miraculously, the B-M framework allows for a simple closed-form solution for the cdf of premiums.<br />
Modeling Search Frictions: The equilibrium distribution of premiums<br />Knowing the equilibrium cdf of premiums allows us to know the premium that prevails at every quantile of the distribution<br />Thus, the lowest premium in the distribution is: <br />Note: even the lowest premium exceeds cost because frictions give insurers market power. <br />As frictions increase, insurers gain market power and so the lowest premium offered rises higher above costs.<br />
Modeling Search Frictions: More on The Distribution of Accepted Offers<br />We can generalize the previous result for any quantile, q,<br /> Integrating over the distribution gives us average price<br />So long as the market friction parameter is neither zero nor infinity, the average premium exceeds the median premium, p.5<br />Competition pushes the distribution of premiums towards their lower bound, c, but so long as markets have moderate frictions, there will be a long right tail of premiums.<br />
Search Frictions and Switching Costs:<br />Firms switch insurers when the gains in terms of better premiums exceed the costs of switching<br />If market frictions were quite small (g ~0) or, large (gapproaching infinity), the distribution of premiums would be narrow and gains from switching insurers would likely not exceed the switching costs. <br />High insurance turnover rates with positive switching costs is evidence for intermediate levels of market frictions. <br />Key: Friction induced churn involves the movement of entire employer groups as clients exit after having found a better deal at a competing insurer. This is what we find, especially in the fully-insured market segment.<br />
Premiums Data For FI and SI Plans from EHIS<br />
Distribution of Raw Premiums: Mean premiums are very close, but variance and skew is larger for FI <br />
Frictions Create Premium Variation For Similar Plans at Similar Firms<br />Search frictions result produce price dispersion for “identical” products. If frictions are greater in FI than SI employer group markets, we should expect to see greater variance and skewness of “residual” distributions where the influence of observable client and product characteristics are removed.<br />The premium prediction models were estimated via GLM using the log “link” function and gamma distributional family. Similar results from OLS. Separate regressions were run for FI and SI plans<br />Both regressions included identical covariates measuring plan and establishment characteristics<br />Plan type (PPO/POS), deductible level, co-payment for typical office visit, the inclusion of prescription drug coverage, <br />firm and establishment size, percent of workers who are full-time, percent female, age distribution of workers, state and mean payroll. <br />
Premium Variance in FI vs. SI by Firm Size<br />
Assessment<br />We find that the variance and skewness of residual premium distributions is greatest for the FI market segment where search frictions are more important.<br />It turns out that one can do much more than this. It is possible to fit the theoretical distribution of premiums to the empirical distribution and back out some of the deeper parameters of the model.<br />
Fitting our Search Model to the Data<br />r(θiEi) is the residual due to the firms random draw from distribution of premiums due to search frictions and the random draw from a nuisance distribution.<br />We assume that e is a mean zero random variable with variance equal to variance in residual in the SI market.<br />We begin assuming that θi=Ei and then “fit” the model to the data to get starting values of parameters.<br />With these starting values we create a simulates distribution of premiums by taking 100,000 independent draws of θi, and Ei .<br />We calculate the values of θ and E at each percentile and use these to re-fit the model.<br />Results are based on 20 iterations, <br />
Table 12. Estimates of Market Frictions and Insurance Cost for Fully Insured Employers<br />
The Model Fitted at Each Percentile<br />Mean Absolute Deviation is<br />$1.7 / month<br />
Is c = $136 per month plausible? <br />Estimates of c using aggregate data<br />Total private insurer spending on health care was $320b in 1997, and 188 million persons were covered by private insurance at some point during the year. (320b/188m)/12 = $142 per member per month<br />The implied load factor<br />If c =$136 pmpm then monthy premiums exceed costs in the FI market by 27% in 1997. <br />Brown and Finkelstein ( 2007 ) find that for long-term care insurance; policy holders receive $0.82 in benefits for every premium dollar spent. This result implies that the ratio of the discounted present value of premiums to the discounted present value of expenditures by insurers is 1.22.<br />
Is PR= $433 reasonable?<br />Hornstein, Krusell and Violante ( 2007) note, in frictional markets the maximum willingness to pay will equal the maximum observed premium so long as the efficacy of search for insurance is unrelated to current insurance status. <br />Our model 1 estimate of pR= $433.9 seems reasonable as it lies about 5% above the premium at the 99th percentile of the adjusted distribution ($415.2) <br />
What does γ= 0.152 mean? Transfer of surplus from employers to insurance companies<br />The monthly consumer surplus is pR– c = $297.5 <br />The fraction of this accruing to insurers is γ/(g+1) = .132<br />Summing over 73.1 million policy holders in the FI market, the implied transfer is $34.4B in 1997<br />
What does γ= 0.152 mean? High Rates of Turnover <br />We observe the distribution of accepted offers, but turnover is determined by the distribution of offers.<br />The average accepted offer sits at the 27th percentile of the distribution of offers.<br />the fraction of group turnover due to endogenous separations is <br />Thus at the mean, frictions increase turnover by .27/(.27+.152)= 64%<br />
What does γ= 0.152 mean? Uninsurance<br /> In the Burdett-Mortensen framework, the distribution of prices is bounded from above by employers’ maximum willingness to pay. <br />In the real world, of course, many employer groups don’t offer insurance because the price exceeds their reservation price. To the extent that “affordability” contributes uninsurance, we would expect our estimate to understate total rates of uninsurance – perhaps by substantial amounts. <br />Consistent with this expectation, our estimate of implies a frictional uninsurance rate = 0.135, far less than the 41.7 percent of employers in the EHIS who report not offering health insurance in 1997. <br />
We attribute excess price dispersion to seach frictions.<br />Our calculation of excess price dispersion rests on the assumptions that <br />premiums in the self insured market reflect variations in the marginal cost of insurance, and <br />unobservables in the self insured market have the same effect on premiums in the fully insured market as they do in the self insured market. <br />If assumption 1 is wrong, our approach leads us to understate the extent of search frictions.<br />
We attribute excess price dispersion to seach frictions.<br />Our calculation of excess price dispersion rests on the assumptions that <br />premiums in the self insured market reflect variations in the marginal cost of insurance, and <br />unobservables in the self insured market have the same effect on premiums in the fully insured market as they do in the self insured market. <br />If assumption 2 is violated by adverse selection from SI to FI market, this will reduce the right skew of premium distributions and cause us to underestimate frictions.<br />
Implications for Health Policy I<br />Make shopping easier:<br />Recent IRS, HHS and DOL guidelines might help, but recent guidelines don’t seem very effective. See here<br />Clever uses of IT might be helpful.<br />Reduce excessive variety of plans<br />
Implications for Health Policy II<br />In a frictional insurance market, heightened turnover and rent transfer reduce the payoff to investing in the future health of employees.<br />True for relationship specific investments<br />True general investments whether financed by employer or employee<br />This has important implications for the problem of managing chronic diseases.<br />
Implication for Health Policy III: Thin the Right Tail of Price Distribution<br />The marketing arms race is driven by the small number of plans on the right tail of the premium distribution. These plans have highest markups and will benefit most from raising commissions.<br />Lower priced plans have to match these payments to brokers in order to attract clients.<br />How to thin right tail?<br />Subsidized public option<br />Minimum medical loss ratio rules<br />
Implications for Health Policy IV<br />Many FI employers in our study were using brokers, yet we find evidence of search frictions.<br />Why don’t brokers eliminate search frictions?<br />What must we change to ensure that brokers search effectively on behalf of clients?<br />