Search Frictions and the Cost and Quality of Health Insurance

Unhealthy Insurance Markets:
Search Frictions and the Cost and
Quality of Health Insurance
Randal Cebul
School of Medicine and Center for Health Care Research and Policy
Case Western Reserve University
James B. Rebitzer
Department Markets, Public Policy and Law
Boston University School of Management,
Case Western’s Center for Health Care Research and Policy,
NBER, The Levy Institute, and IZA
Lowell J. Taylor
H. John Heinz III School of Public Policy and Management
Carnegie Mellon University
Mark Votruba
Department of Economics, Weatherhead School
School of Medicine and Center for Health Care Research and Policy
Case Western Reserve University
A Prosaic Beginning: The Shopping Problem
The Health Insurance Shopping Problem
 Health Insurance is a complex multi-attribute service.
 Savvy purchasers must consider:
 which drugs are in the insurer’s formularies,
 which local physicians are part of the insurer’s provider
 what co-pays and deductibles apply to which
pharmaceuticals, providers and services
 Delivery of services under hard-to-anticipate contingencies.
 Medical underwriting and the great profusion of insurance
products increases administrative costs and search complexity.
 Overcoming these challenges entails costs and these costs
create search frictions.
The Health Insurance Shopping Problem
 In the US, large and sophisticated employers can simplify
the shopping problem by “self insuring” and hiring insurers
simply to administer their plans.
 Smaller and less sophisticated firms “fully insure”, i.e. they
buy both administrative services and insurance.
 These “fully insured” employers have a particularly
daunting shopping problem: they know less and the
service they buy is more complex.
 Brokers can, in theory, help.
 In practice broker advice influenced by the fact that
they receive commissions from insurers.
The Effects of Search Frictions
 We study the effect of search frictions on the operation of
the commercial health insurance market – especially the
“fully insured” market segment.
 Little attention has been given to the issue of search
frictions. Important exceptions:
 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.
 Frank and Lamiraud ( 2008) report evidence of
significant price dispersion for homogenous products in
Swiss health insurance markets.
The Effects of Search Frictions: Theory Results
 Burdett-Mortensen model adapted to health insurance
 Key results:
 Law of One Price doesn’t hold. Identical products priced
differently and the distribution of prices is right skewed.
 Moderate frictions  high policy-holder turnover rates
 The magnitude of frictions can be inferred from the
distribution of premiums
 Search frictions lead insurers to adopt inefficiently high
marketing expenditures.
Theory Results: Why Inefficiently High levels of
 In frictional insurance markets p> MC, so insurers always want
more clients and will spend resources to attract them.
 Insurance companies with high p gets greater return from
marketing than low price plan and so will pay higher
 The result is an arms race in marketing –especially in FI plans.
 Social welfare would be improved with lower commissions,
but no insurer will unilaterally cut their payments.
 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
Empirical Results I : Excess Insurance Turnover
 Data: Household Survey component of the Community Tracking
Study (CTS); proprietary information from the enrollment
records of a large regional insurer.
 We find
 High rates of health insurance cancellation rates (20%/year).
 Rates of turnover are higher for “fully insured” groups
(30%/year) than for self insured (14%)
 For the average “fully insured”, roughly 60% of this
turnover is in fact due to cancellations by entire
employer groups.
 For “self insured”, only 10% of turnover due to employer
group turnover.
Empirical Results II: Excess Price Dispersion
 Data: The Robert Wood Johnson Foundation Employer
Health Insurance Survey (EHIS) from 1997
 The variance in the residual distribution of premiums is
greatest in the fully insured market segment where
frictions are greatest.
 The skewness of the residual distribution is greatest for
fully insured.
Empirical Results III: Structural Estimates
 Fitting our theoretical model directly to the data yields parameter
estimates suggesting moderate search frictions.
 Market frictions are severe enough to:
 Transfer ~ 13.2% of consumer surplus to insurers (~$34B in
 Increase the insurance turnover about 64% for the average
insurance policy.
 Caveat: structural estimation presumes a correct model.
 If the fit to the data is poor or if parameter values are crazy, can
cast doubt on adequacy of the chosen model.
 Structural estimation does not rule the possibility that other
models might do as well or better.
Policy Implications
 Moderate search frictions transfer substantial surplus to
insurers; and support high levels of insurance turnover.
 Friction induced turnover reduces incentives to invest in
future health of policy holders.
 Policy Responses?
 Use IT to make comparison shopping easier.
 Reduce excess variety of plans.
 Thin the right tail of premium distribution:
 public option? Medical loss ratio regulation?
 Regulate brokers?
Plan of Talk
 Sketch out search model and its key predictions for insurance
turnover and insurance premiums.
 Examine the distribution of premiums. Is residual variance and
skewness greatest where frictions are greatest?
 Fit the theoretical model to the data to estimate “search
friction” parameter.
 Are the parameters we uncover consistent with other data?
 What implications do these parameters have for the
efficiency of insurance markets?
 What implications do these parameters have for incentives
to invest in future health. For public insurance options?
Modeling Insurance Search: Setup
 Two market actors:
 insurances companies and clients
 Clients are employers who purchase on behalf of their employees.
 Problematic Information flows
 Insurers post a premium. Offers arrive at clients via a random
process at rate, l.
 Clients choose the lowest price plan. Contracts last one year
 Clients exit the relationship in one of two ways.
 Exogenous separation: which occurs at rate d.
 Endogenous separation: the client finds a better deal elsewhere.
 Market friction parameter, g = d/l. As g increases so do frictions.
 Solve for steady state solutions in continuous time.
Modeling Insurance Search: Price Dispersion
 Insurers can reach only a limited number of clients.
 Perhaps due to the costs of marketing, e.g. the costs of
hiring sales people or paying brokers
 Perhaps due to client’s limited “mental shelf space”.
 Offers arrive randomly, so some clients will receive many offers
and others only one or two.
 This latter possibility makes it profitable for some insurers to
charge high prices for their product.
 Many, perhaps most, clients will decline these high priced
 For a few clients, however, the high priced offer will be the
best they receive.
Modeling Search Frictions: Price Dispersion
 Suppose all firms set p=c, so p=0
 A maverick firm could earn positive expected profits by
charging a discretely higher premium, p.
 The high offer will sometimes be accepted if the
contacted client receives no better offer.
 Supposed all firms set p>c, so p>0
 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.
 Insurers must therefore be playing mixed strategies.
Modeling Search Frictions: the equilibrium
distribution of premiums.
 In order for profits to be identical for all insurers, the entire
distribution of offers and acceptances must take a certain shape.
 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.
 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.
 Requiring that high price insurers make the same profit as
lower priced insurers therefore determines the shape of the
cdf of premiums, F(p)
 Somewhat miraculously, the B-M framework allows for a simple
closed-form solution for the cdf of premiums.
Modeling Search Frictions: The equilibrium
distribution of premiums
 Knowing the equilibrium cdf of premiums allows us to know the
premium that prevails at every quantile of the distribution
 Thus, the lowest premium in the distribution is:
 g 
plowest = c  
 Note: even the lowest premium exceeds cost because frictions
give insurers market power.
 As frictions increase, insurers gain market power and so the
lowest premium offered rises higher above costs.
Modeling Search Frictions: More on The
Distribution of Accepted Offers
 We can generalize the previous result for any quantile, q,
 g 
pq = c  ( p - c) 
 , p0.5 = c  ( p - c) 
 
Integrating over the distribution gives us average price
 g 
p = c   p  c
 p0.5
 g 1 
 So long as the market friction parameter is neither zero nor infinity,
the average premium exceeds the median premium, p.5
 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.
Search Frictions and Switching Costs:
 Firms switch insurers when the gains in terms of better
premiums exceed the costs of switching
 If market frictions were quite small (g ~0) or, large (g
approaching infinity), the distribution of premiums would
be narrow and gains from switching insurers would likely
not exceed the switching costs.
 High insurance turnover rates with positive switching costs
is evidence for intermediate levels of market frictions.
 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.
Premiums Data For FI and SI Plans from EHIS
Distribution of Raw Premiums: Mean premiums are
very close, but variance and skew is larger for FI
Frictions Create Premium Variation For Similar
Plans at Similar Firms
 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.
 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
 Both regressions included identical covariates measuring plan and
establishment characteristics
 Plan type (PPO/POS), deductible level, co-payment for typical
office visit, the inclusion of prescription drug coverage,
 firm and establishment size, percent of workers who are full-time,
percent female, age distribution of workers, state and mean
Distribution of Residual Premiums:
Comparison of FI and SI Premium Residuals
Figure 1:
Premium Variance in FI vs. SI by Firm Size
 We find that the variance and skewness of residual
premium distributions is greatest for the FI market
segment where search frictions are more important.
 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.
Fitting our Search Model to the Data
 g
p qi , Ei  = p  r qi , Ei  = c   p  c  
  e  Ei  .
 g  1  qi 
 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.
 We assume that e is a mean zero random variable with variance equal
to variance in residual in the SI market.
 We begin assuming that θi=Ei and then “fit” the model to the data to
get starting values of parameters.
 With these starting values we create a simulates distribution of
premiums by taking 100,000 independent draws of θi, and Ei .
 We calculate the values of θ and E at each percentile and use these to
re-fit the model.
 Results are based on 20 iterations,
Table 12. Estimates of Market Frictions
and Insurance Cost for Fully Insured
Panel A: Fitted Models
model 1
model 2
Deviation is
$1.7 / month
The Model Fitted at Each Percentile
Percentile of residual
Empirical residual
Simulated residual
Is c = $136 per month plausible?
 Estimates of c using aggregate data
 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
 The implied load factor
 If c =$136 pmpm then monthy premiums exceed costs in the FI
market by 27% in 1997.
 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.
Is PR= $433 reasonable?
 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
 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)
What does γ= 0.152 mean? Transfer of surplus
from employers to insurance companies
 The monthly consumer surplus is pR – c =
 The fraction of this accruing to insurers is γ/(g
+1) = .132
 Summing over 73.1 million policy holders in
the FI market, the implied transfer is $34.4B in
What does γ= 0.152 mean? High Rates of
 We observe the distribution of accepted offers,
but turnover is determined by the distribution
of offers.
l F ( p)
F ( p)
l F ( p)  d F ( p)  g
 The average accepted offer sits at the 27th
percentile of the distribution of offers.
 the fraction of group turnover due to
endogenous separations is
 Thus at the mean, frictions increase turnover
by .27/(.27+.152)= 64%
What does γ= 0.152 mean? Uninsurance
In the Burdett-Mortensen framework, the distribution of prices
is bounded from above by employers’ maximum willingness to
 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.
 Consistent with this expectation, our estimate of g 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.
We attribute excess price dispersion to seach
 Our calculation of excess price dispersion rests on the
assumptions that
 premiums in the self insured market reflect variations
in the marginal cost of insurance, and
 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.
 If assumption 1 is wrong, our approach leads us to
understate the extent of search frictions.
We attribute excess price dispersion to seach
 Our calculation of excess price dispersion rests on the
assumptions that
 premiums in the self insured market reflect variations
in the marginal cost of insurance, and
 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.
 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.
Implications for Health Policy I
 Make shopping easier:
 Recent IRS, HHS and DOL guidelines might help, but
recent guidelines don’t seem very effective. See here
 Clever uses of IT might be helpful.
 Reduce excessive variety of plans
Implications for Health Policy II
 In a frictional insurance market, heightened turnover and
rent transfer reduce the payoff to investing in the future
health of employees.
 True for relationship specific investments
 True general investments whether financed by
employer or employee
 This has important implications for the problem of
managing chronic diseases.
Implication for Health Policy III: Thin the Right
Tail of Price Distribution
 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.
 Lower priced plans have to match these payments to
brokers in order to attract clients.
 How to thin right tail?
 Subsidized public option
 Minimum medical loss ratio rules
Implications for Health Policy IV
 Many FI employers in our study were using brokers, yet we
find evidence of search frictions.
 Why don’t brokers eliminate search frictions?
 What must we change to ensure that brokers search
effectively on behalf of clients?

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