Adverse Selection and Inertia in Health Insurance Markets: When Nudging Hurts

TL;DR: A major change to insurance provision that occurred at a large firm is leveraged to identify substantial inertia, and a choice model is developed and estimated that also quantifies risk preferences and ex ante health risk.

Abstract: This paper investigates consumer inertia in health insurance markets, where adverse selection is a potential concern. We leverage a major change to insurance provision that occurred at a large firm to identify substantial inertia, and develop and estimate a choice model that also quantifies risk preferences and ex ante health risk. We use these estimates to study the impact of policies that nudge consumers toward better decisions by reducing inertia. When aggregated, these improved individual-level choices substantially exacerbate adverse selection in our setting, leading to an overall reduction in welfare that doubles the existing welfare loss from adverse selection. (JEL D82, G22, I13) A number of potential impediments stand in the way of efficient health insur ance markets. The most noted of these is adverse selection, first studied by Akerlof (1970) and Rothschild and Stiglitz (1976). In insurance markets, prices reflect the expected risk (costs) of the insured pool. Whether the reason is price regulation or private information, when insurers cannot price all risk characteristics riskier consumers choose more comprehensive health plans. This causes the equilibrium prices of these plans to rise and healthier enrollees to select less comprehensive coverage than they would otherwise prefer.

Figures

Table A-6: This table presents the welfare results of the ‘naive’ counterfactual inertia reduction analysis. We present the mean per employee per year dollar change in certainty equivalents and corresponding percentage welfare changes resulting from the policy reducing inertia to .25η from η. We present three alternative welfare benchmarks to assess the % impact of this these certainty equivalent changes. These metrics divide the change in certainty equivalent from the policy intervention by mean (i) total employee premiums (ii) total employee spending and (iii) the absolute value of the certainty equivalent loss. Note that since all figures are losses the certainty equivalent absolute value is larger than the total spending figure. Since we hold plan prices fixed in this exercise, the welfare changes must be positive when consumers make better individual-level decisions.

Table A-7: Table A-7 investigates the maximum extent of inertia costs consumers experience from switching plans under the range of settings where Z = 1 (full inertia) to Z = 0 (no inertia). This ‘maximum’ here corresponds to the case where the inertia we estimate comes entirely from tangible / direct costs that must be overcome to switch plans. As Z decreases, maximum inertia costs incurred are generally decreasing, though they increase from $185 per population member to $188 per population member when moving from Z = 1 to Z = 0.75. This reflects the fact that as Z decreases, maximum inertial costs per switcher are lower (by definition) but more people actually switch plans due to reduced inertia. The table presents maximum inertia costs incurred broken down across year t1 to t6, with the bottom section (also in table 8 in the main text) averaging across all six years after t0. This analysis relates to the analysis of welfare treatment of inertia, included in the bottom part of table 8 in the main text.

Table A-2: This table describes the financial characteristics for each PPO option available at the firm over time, both before and after the menu change at t0. For most medical expenses, an individual pays the full amount until he reaches the yearly plan deductible, after which he pays the coinsurance rate for all further medical expenses. Once an individual spends up to the out-of-pocket maximum, he pays no further general medical expenses. Pharmacy products and physician office visits only apply to the deductible and coinsurance for PPO1200; all other plans have fixed co-payments for these services. Mental health services apply to all plan deductibles but not the out-of-pocket maximum for each plan. Out-of-pocket maximums vary with income, presumably for equity considerations. This chart does not include out-of-network plan characteristics which account for only 2% of total expenses and don’t vary substantially across the three plans. These three plans have the same provider network and cover the same medical services.

Table A-3: This table describes plan choice at the firm between years t−1 and t1. The top panel documents the number of employees who chose each plan in each of these three years. Before the menu change about 39% of employees enrolled in a PPO and 47% in an HMO. After the menu change these numbers are essentially reversed with 47% in a PPO and 35% in an HMO. The middle panel studies the choice behavior of all employees at the firm who were enrolled in any plan in both of the years t−1 and t0. Each column corresponds to the plan an employee was in at t−1 while each row corresponds to the plan an employee was in at t0. It is clear that, when the menu of plans changed for t0, most employees in PPO−1 moved to one of the new PPO options while most employees enrolled in an HMO at t−1 still re-enroll in an HMO at t0. The bottom panel presents the analogous chart for all employees at the firm enrolled in a plan both in years t0 and t1. The vast majority of t0 PPO enrollees who switch plans at year t1 choose another PPO option at t1. These panels together reveal significant horizontal differentiation between the nest of PPOs and nest of HMOs.

Figure A-3: This figure describes the new plan enrollment levels and average costs under the ‘naive’ inertia reduction counterfactual where prices are held fixed as observed in the data. The market shares are presented for all coverage tiers combined, while the average costs are presented for the family coverage tier (employee + spouse + dependent). The figure studies these quantities as a function of the effectiveness of the policy to reduce inertia, where η signifies no reduction in inertia from our estimates and 0 signifies no inertia. In general, the market share of PPO250 is decreasing in both t1 and t2 as the policy to reduce inertia becomes more effective. The relative average cost of this plan increases as the market share declines, implying that when we allow for endogenous plan re-pricing there will be increased adverse selection on the margin.

Table A-4: This table presents the estimated parameter results for the basic version of the primary choice model presented in section 3 of the main text. The table can be thought of as an extension to Table 5, which presents our primary choice model estimates along with four robustness checks. The basic model estimates inertia, risk preferences, and persistent tastes for PPO1200 but includes only very limited observable heterogeneity for both inertia and risk preferences. The estimates in the basic specification are similar in magnitude to those in the primary specification.

Figure A-4: This figure shows market shares and average costs for PP0500 and PPO250 in years t1, t2, and t4, as a function of Z, in the environment with endogenous plan pricing. We report results for values of Z equal to 0,.25,.5, and 1. It is clear from the top panel that as Z decreases and inertia is further reduced, enrollment in PPO250 declines at the expense of enrollment in PPO500. The bottom panel reveals that as Z decreases and enrollment increases, the average costs (and total premiums) of PPO250 increase relative to those of PPO500 in each year. This is indicative of increased relative premiums for comprehensive insurance and increased adverse selection.

Figure A-2: This figure outlines the primary steps of the cost model described in Online Appendix A. It moves from the initial inputs of cost data, diagnostic data, and the ACG algorithm to the final output Fkjt which is the family, plan, time specific distribution of out-of-pocket expenditures that enters the choice model for each family. The figure depicts an example individual in the top segment, corresponding to one cell in each category of medical expenditures. The last part of the model maps the expenditures for all individuals in one family into the final distribution Fkjt.

Table A-5: This table examines the risk preference estimates from the empirical results presented in table 5 in the main text. The first section of the table is for the normally distributed risk preference estimates in the Primary specification, where the age and income coefficients are evaluated at the median values of those variables. The second section is for the model with log-normally distributed preferences studied in column 4 of table 5. The interpretation column is the value X that would make someone indifferent about accepting a 50-50 gamble where you win $100 and lose X versus a status quo where nothing happens. Our estimates are similar under both specifications with the exception that the log normal model predicts a fatter tail with higher risk aversion. These estimates are in the middle of the (wide) range found in the literature and show moderate risk aversion (relative to this literature) except at the tails in the log-normal model where consumers are quite risk averse.

Table A-1: This table describes the output of the cost model in terms of the means and medians of individual level parameters, classified by the plan actually chosen. These parameters are aggregated for these high-level groups but have more micro-level groupings, which are the primary inputs into our cost projections in the choice model. Weibull α, Weibull β, and Zero Claim Probability correspond to the cell-specific predicted total individual-level health expenses as described in more detail in Online Appendix A.

Figure A-1: This figure validates the mapping Ωj that translates the vector of total claims C into plan specific out of pocket expenditures. The two charts show Ω for PPO250, with predicted out-ofpocket spending on the x-axis and actual out-of-pocket spending on the y-axis. The top chart is the mapping actually used where claims are categorized into four categories (i) hospital and outpatient (ii) pharmacy (iii) mental health and (iv) physician office visit. Ideally, we want all points to be on the 45 degree line where the actual employee paid out of pocket equals the model predicted out of pocket. The plot is condensed around the 45 degree line so we believe this our mapping is close to the true mapping. The bottom figure adds out of network expenses to the mapping as a fifth category and does not materially improve upon the mapping used.

Full text

Online Appendix
Adverse Selection and Inertia in Health Insurance Markets:
When Nudging Hurts
Benjamin Handel
∗
August 29, 2013
Abstract
This online appendix provides supporting analysis for the primary manuscript ’Adverse Selec-
tion and Inertia in Health Insurance Markets: When Nudging Hurts’ published in the American
Economic Review. Appendix A describes the cost model setup and estimation. Appendix B de-
scribes the choice model estimation algorithm in greater detail. Appendix C discusses a robust
check allowing for moral hazard, i.e. a price elasticity of demand for medical expenditures. Ap-
pendix D discusses different interpretations of and foundations for inertia. Appendix E presents
additional supporting analyses.
∗
Department of Economics, University of California at Berkeley. Contact: handel@berkeley.edu.

Online Appendix A: Cost Model Setup and Estimation
This appendix describes the details of the cost model, which is summarized at a high-level in
section 3. The output of this model, F
kjt
, is a family-plan-time specific distribution of predicted
out-of-pocket expenditures for the upcoming year. This distribution is an important input into the
choice model, where it enters as a family’s predictions of its out-of-pocket expenses at the time
of plan choice, for each plan option. We predict this distribution in a sophisticated manner that
incorporates (i) past diagnostic information (ICD-9 codes) (ii) the Johns Hopkins ACG predictive
medical software package (iii) a novel non-parametric model linking modeled health risk to total
medical expenditures using observed cost data and (iv) a detailed division of medical claims and
health plan characteristics to precisely map total medical expenditures to out-of-pocket expenses.
1
The level of precision we gain from the cost model leads to more credible estimates of the choice
parameters of primary interest (e.g. inertia).
In order to most precisely predict expenses, we categorize the universe of total medical claims
into four mutually exclusive and exhaustive subdivisions of claims using the claims data. These
categories are (i) hospital and physician (ii) pharmacy (iii) mental health and (iv) physician office
visit. We divide claims into these four specific categories so that we can accurately characterize the
plan-specific mappings from total claims to out-of-pocket expenditures since each of these categories
maps to out-of-pocket expenditures in a different manner. We denote this four dimensional vector
of claims C
it
and any given element of that vector C
d,it
where d ∈ D represents one of the four
categories and i denotes an individual (employee or dependent). After describing how we predict this
vector of claims for a given individual, we return to the question of how we determine out-of-pocket
expenditures in plan j given C
it
.
Denote an individual’s past year of medical diagnoses and payments by ξ
it
and the demographics
age and sex by ζ
it
. We use the ACG software mapping, denoted A, to map these characteristics
into a predicted mean level of health expenditures for the upcoming year, denoted θ:
A : ξ × ζ → θ
In addition to forecasting a mean level of total expenditures, the software has an application
that predicts future mean pharmacy expenditures. This mapping is analogous to A and outputs a
prediction λ for future pharmacy expenses.
We use the predictions θ and λ to categorize similar groups of individuals across each of four
claims categories in vector in C
it
. Then for each group of individuals in each claims category, we
use the actual ex post realized claims for that group to estimate the ex ante distribution for each
individual under the assumption that this distribution is identical for all individuals within the cell.
Individuals are categorized into cells based on different metrics for each of the four elements of C:
Pharmacy: λ
it
Hospital / Physician (Non-OV): θ
it
Physician Office Visit: θ
it
Mental Health: C
MH,i,t−1
For pharmacy claims, individuals are grouped into cells based on the predicted future mean phar-
1
Features (iii) and (iv) are methodological advances. We are aware of only one previous study that incorporates
diagnostic information in cost prediction for the purposes of studying plan choice (Carlin and Town (2009)) in a
structural setup. Recent work by Einav et al. (2013) use this type of framework as well.
2

macy claims measure output by the ACG software, λ
it
. For the categories of hospital / physician
(non office visit) and physician office visit claims individuals are grouped based on their mean pre-
dicted total future health expenses, θ
it
. Finally, for mental health claims, individuals are grouped
into categories based on their mental health claims from the previous year, C
MH,i,t−1
since (i)
mental health claims are very persistent over time in the data and (ii) mental health claims are
uncorrelated with other health expenditures in the data. For each category we group individuals
into a number of cells between 8 and 10, taking into account the trade off between cell size and
precision. The minimum number of individuals in any cell is 73 while almost all cells have over
500 members. Thus since there are four categories of claims, each individual can belong to one of
approximately 10
4
or 10,000 combination of cells.
Denote an arbitrary cell within a given category d by z. Denote the population in a given
category-cell combination (d, z) by I
dz
. Denote the empirical distribution of ex-post claims in
this category for this population
ˆ
G
I
dz
(·). Then we assume that each individual in this cell has a
distribution equal to a continuous fit of
ˆ
G
I
dz
(·), which we denote G
dz
:
$ :
ˆ
G
I
dz
(·) → G
dz
We model this distribution continuously in order to easily incorporate correlations across d. Oth-
erwise, it would be appropriate to use G
I
dz
as the distribution for each cell.
The above process generates a distribution of claims for each d and z but does not model
correlations over D. It is important to model correlation over claim categories because it is likely
that someone with a bad expenditure shock in one category (e.g. hospital) will have high expenses in
another area (e.g. pharmacy). We model correlation at the individual level by combining marginal
distributions G
idt
∀ d with empirical data on the rank correlations between pairs (d, d
0
).
2
Here, G
idt
is the distribution G
dz
where i ∈ I
dz
at time t. Since correlations are modeled across d we pick the
metric θ to group people into cells for the basis of determining correlations (we use the same cells
that we use to determine group people for hospital and physician office visit claims). Denote these
cells based on θ by z
θ
. Then for each cell z
θ
denote the empirical rank correlation between claims of
type d and type d
0
by ρ
z
θ
(d, d
0
). Then, for a given individual i we determine the joint distribution
of claims across D for year t, denoted H
it
(·), by combining i’s marginal distributions for all d at t
using ρ
z
θ
(d, d
0
):
Ψ : G
iDt
× ρ
z
θ
it
(D, D
0
) → H
it
Here, G
iDt
refers to the set of marginal distributions G
idt
∀d ∈ D and ρ
z
θ
it
(D, D
0
) is the set of
all pairwise correlations ρ
z
θ
it
(d, d
0
)∀(d, d
0
) ∈ D
2
. In estimation we perform Ψ by using a Gaussian
copula to combine the marginal distribution with the rank correlations, a process which we describe
momentarily.
The final part of the cost model maps the joint distribution H
it
of the vector of total claims C
over the four categories into a distribution of out of pocket expenditures for each plan. For each
of the three plan options we construct a mapping from the vector of claims C to out of pocket
expenditures OOP
j
:
Ω
j
: C → OOP
j
This mapping takes a given draw of claims from H
it
and converts it into the out of pocket expendi-
tures an individual would have for those claims in plan j. This mapping accounts for plan-specific
2
It is important to use rank correlations here to properly combine these marginal distribution into a joint distri-
bution. Linear correlation would not translate empirical correlations to this joint distribution appropriately.
3

features such as the deductible, co-insurance, co-payments, and out of pocket maximums listed in
table A-2. I test the mapping Ω
j
on the actual realizations of the claims vector C to verify that
our mapping comes close to reconstructing the true mapping. Our mapping is necessarily simpler
and omits things like emergency room co-payments and out of network claims. We constructed our
mapping with and without these omitted categories to insure they did not lead to an incremental
increase in precision. We find that our categorization of claims into the four categories in C passed
through our mapping Ω
j
closely approximates the true mapping from claims to out-of-pocket ex-
penses. Further, we find that it is important to model all four categories described above: removing
any of the four makes Ω
j
less accurate. Figure A-1 shows the results of one validation exercise
for P P O
250
. The top panel reveals that actual employee out-of-pocket spending amounts are quite
close to those predicted by Ω
j
, indicating the precision of this mapping. The bottom panel repeats
this mapping when we add out of network expenses as a fifth category. The output in this case is
similar to that in the top panel without this category, implying that including this category would
not markedly change the cost model results.
Once we have a draw of OOP
ijt
for each i (claim draw from H
it
passed through Ω
j
) we map
individual out of pocket expenditures into family out of pocket expenditures. For families with less
than two members this involves adding up all the within family OOP
ijt
. For families with more than
three members there are family level restrictions on deductible paid and out-of-pocket maximums
that we adjust for. Define a family k as a collection of individuals i
k
and the set of families as K.
Then for a given family out-of-pocket expenditures are generated:
Γ
j
: OOP
i
k
,jt
→ OOP
kjt
To create the final object of interest, the family-plan-time specific distribution of out of pocket
expenditures F
kjt
(·), we pass the claims distributions H
it
through Ω
j
and combine families through
Γ
j
. F
kjt
(·) is then used as an input into the choice model that represents each family’s information
set over future medical expenses at the time of plan choice. Eventually, we also use H
it
to calculate
total plan cost when we analyze counterfactual plan pricing based on the average cost of enrollees.
Figure A-2 outlines the primary components of the cost model pictorially to provide a high-level
overview and to ease exposition.
We note that the decision to do the cost model by grouping individuals into cells, rather then by
specifying a more continuous form, has costs and benefits. The cost is that all individuals within a
given cell for a given type of claims are treated identically. The benefit is that our method produces
local cost estimates for each individual that are not impacted by the combination of functional form
and the health risk of medically different individuals. Also, the method we use allows for flexible
modeling across claims categories. Finally, we note that we map the empirical distribution of claims
to a continuous representation because this is convenient for building in correlations in the next
step. The continuous distributions we generate very closely fit the actual empirical distribution of
claims across these four categories.
Cost Model Identification and Estimation. The cost model is identified based on the two
assumptions of (i) no moral hazard / selection based on private information and (ii) that individ-
uals within the same cells for claims d have the same ex ante distribution of total claims in that
category. Once these assumptions are made, the model uses the detailed medical data, the Johns
Hopkins predictive algorithm, and the plan-specific mappings for out of pocket expenditures to
generate the the final output F
kjt
(·). These assumptions, and corresponding robustness analyses,
are discussed at more length in the main text.
Once we group individuals into cells for each of the four claims categories, there are two statistical
4

components to estimation. First, we need to generate the continuous marginal distribution of claims
for each cell z in claim category d, G
dz
. To do this, we fit the empirical distribution of claims G
I
dz
to a Weibull distribution with a mass of values at 0. We use the Weibull distribution instead of the
log-normal distribution, which is traditionally used to model medical expenditures, because we find
that the log-normal distribution overpredicts large claims in the data while the Weibull does not.
For each d and z the claims greater than zero are estimated with a maximum likelihood fit to the
Weibull distribution:
max
(α
dz
,β
dz
)
Π
i∈I
dz
β
dz
α
dz
(
c
id
α
dz
)
β
dz
−1
e
−(
c
id
α
dz
)
β
dz
Here, ˆα
dz
and
ˆ
β
dz
are the shape and scale parameters that characterize the Weibull distribution.
Denoting this distribution W ( ˆα
dz
,
ˆ
β
dz
) the estimated distribution
ˆ
G
dz
is formed by combining this
with the estimated mass at zero claims, which is the empirical likelihood:
ˆ
G
dz
(c) =
(
G
I
dz
(0) if c = 0
G
I
dz
(0) +
W ( ˆα
dz
,
ˆ
β
dz
)(c)
1−G
I
dz
(0)
if c > 0
Again, we use the notation
ˆ
G
iDt
to represent the set of marginal distributions for i over the
categories d: the distribution for each d depends on the cell z an individual i is in at t. We
combine the distributions
ˆ
G
iDt
for a given i and t into the joint distribution H
it
using a Gaussian
copula method for the mapping Ψ. Intuitively, this amounts to assuming a parametric form for
correlation across
ˆ
G
iDt
equivalent to that from a standard normal distribution with correlations
equal to empirical rank correlations ρ
z
θ
it
(D, D
0
) described in the previous section. Let Φ
i
1|2|3|4
denote the standard multivariate normal distribution with pairwise correlations ρ
z
θ
it
(D, D
0
) for all
pairings of the four claims categories D. Then an individual’s joint distribution of non-zero claims
is:
ˆ
H
i,t
(·) = Φ
1|2|3|4
(Φ
−1
1
(
ˆ
G
id
1
t
), Φ
−1
2
(
ˆ
G
id
2
t
), Φ
−1
3
(
ˆ
G
id
3
t
), Φ
−1
4
(
ˆ
G
id
4
t
))))
Above, Φ
d
is the standard marginal normal distribution for each d.
ˆ
H
i,t
is the joint distribution
of claims across the four claims categories for each individual in each time period. After this is
estimated, we determine our final object of interest F
kjt
(·) by simulating K multivariate draws
from
ˆ
H
i,t
for each i and t, and passing these values through the plan-specific total claims to out of
pocket mapping Ω
j
and the individual to family out of pocket mapping Γ
j
. The simulated F
kjt
(·)
for each k, j, and t is then used as an input into estimation of the choice model.
Table A-1 presents summary results from the cost model estimation for the final choice model
sample, including population statistics on the ACG index θ, the Weibull distribution parameters
ˆα
dz
and
ˆ
β
dz
for each category d, as well as the across category rank correlations ρ
z
θ
it
(D, D
0
). These
are the fundamentals inputs used to generate F
kjt
, as described above, and lead to very accurate
characterizations of the overall total cost and out-of-pocket cost distributions (validation exercises
which are not presented here).
5

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Online appendix adverse selection and inertia in health insurance markets: when nudging hurts" ?

This online appendix provides supporting analysis for the primary manuscript ’ Adverse Selection and Inertia in Health Insurance Markets: When Nudging Hurts ’ published in the American Economic Review. The authors predict this distribution in a sophisticated manner that incorporates ( i ) past diagnostic information ( ICD-9 codes ) ( ii ) the Johns Hopkins ACG predictive medical software package ( iii ) a novel non-parametric model linking modeled health risk to total medical expenditures using observed cost data and ( iv ) a detailed division of medical claims and health plan characteristics to precisely map total medical expenditures to out-of-pocket expenses. In order to most precisely predict expenses, the authors categorize the universe of total medical claims into four mutually exclusive and exhaustive subdivisions of claims using the claims data. The authors divide claims into these four specific categories so that they can accurately characterize the plan-specific mappings from total claims to out-of-pocket expenditures since each of these categories maps to out-of-pocket expenditures in a different manner. The authors denote this four dimensional vector of claims Cit and any given element of that vector Cd, it where d ∈ D represents one of the four categories and i denotes an individual ( employee or dependent ). After describing how the authors predict this vector of claims for a given individual, they return to the question of how they determine out-of-pocket expenditures in plan j given Cit.