1. Capping Risk Adjustment ?
Seminar at Leonard Davis Institute
University of Pennsylvania, Philadelphia PA,
16 March 2010
by
Peter Zweifel
(pzweifel@soi.uzh.ch)
Reference: Patrick Eugster, Michèle Sennhauser,
and Peter Zweifel (2009), Capping Risk Adjustment?
resubmitted to Journal of Health Economics

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1. Motivation
Community-rated premiums
- > incentive to select favorable risks
-> introduce risk adjustment (RA)
In Switzerland RA introduced in 1996 with two criteria,
age & gender.
Expectation: Risk selection will peter out
Fact: Volume of cross-subsidization (CS) grows faster
than HCE
Capping Risk Adjustment?

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1. Motivation
Volume of Cross-Subsidization between the Insured in
Swiss Risk Adjustment
Capping Risk Adjustment?

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1. Motivation
Two solutions proposed by Swiss parliament:
1. Introduce a third criterion “hospitalization or living in a
nursing home during the previous year“.
+ : Reduces incentives for risk selection
- : Increases the volume of CS even more
Note: CS between insured crucial, RA between insurers
visible
-> Research question 1:
How much does CS volume increase?
Capping Risk Adjustment?

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1. Motivation
2. Place a cap on the volume of CS.
+ : Exposes insurers to some financial risk
+ : Decreases amount of (unintended) CS
- : Increases incentives for risk selection
-> Research question 2:
How should a cap be designed to minimize opportunity
cost in the guise of increased incentives for risk
selection?
Capping Risk Adjustment?

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2. Data
3 large Swiss health insurers provided individual data,
2001-05 (more than 3 million individuals)
HCE function estimated to determine CS values
Socioeconomic variables: Age, gender, residence.
Ambulatory and hospital HCE, expenditure on drugs,
hospitalization during previous year, deductible, type of
managed-care plan
Capping Risk Adjustment?

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2. Data
HCE and hence CS values < Swiss average for the young
> Swiss average for the old
Market share of the 3 insurers at around 25 percent across
cantons.
Calculated nationwide CS volume CHF 4.13 bn. (2005)
Official: CHF 4.8 bn.
Calculated volume falls short of the official in all cantons.
Capping Risk Adjustment?

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3. An Additional Risk Adjuster:
Hospitalization during Previous Year
Criterion should have considerable predictive power
(see Beck et al. [2004, Ch. 10]).
With this additional criterion, calculated CS volume
increases from CHF 4.13 bn. to 5.82 bn. (+40 percent,
2005).
Every canton experiences an increase.
Highest absolute Δ in populated cantons (Zurich).
Highest relative Δ in small cantons.
Capping Risk Adjustment?

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3. An Additional Risk Adjuster:
Hospitalization during Previous Year
Capping Risk Adjustment?
Persons with a hospital stay in 2004 would receive payments from
RA regardless of age and gender in 2005. Men would receive
higher payments until age 50.

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4. Limiting the Volume of CS
Consequence of any cap is that differences in HCE
between high and low risks are not fully compensated
anymore.
Additional amount of risk borne by insurers should be
minimized. Otherwise, their incentive to „skim the
cream“ would be strengthened.
If the volume of CS were to be capped, how should this
be achieved in an optimal way (i.e. in the guise of
minimum opportunity cost due to increased risk
selection)?
Capping Risk Adjustment?

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4. Limiting the Volume of CS
Who bears the consequences of a cap?
Individuals: Pay/receive less CS, causing premiums to
converge towards risk-rated ones.
Insurers: Step up risk selection efforts , avoid
unfavorable risks, form conglomerates that simulate
risk-rated premiums.
Cantons: Pay more premium subsidies if risk structure
unfavorable.
Federal government: Pay more matching premium
subsidies.
Capping Risk Adjustment?

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4. Limiting the Volume of CS
Limitation of RA possible at three levels.
National (total) level of volume: Broken down to
individual insurer by multiplying the class-specific
amount by the number of insured.
Level of insurers: Limit amount paid/received by each
insurer.
Level of insured: Maximum transparency.
But: Premiums would have to be split into a fair
premium and a redistribution component.
-> National level most appropriate and plausible.
Capping Risk Adjustment?

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5. Optimal Implementation of a Cap
RA values based on age and gender are calculated in
the following way,
where L is HCE, a and g are subscripts for 15 age and
2 gender categories. CS volume is given by
Capping Risk Adjustment?

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5. Optimal Implementation of a Cap
If age and gender were the only determinants of HCE,
then RA would eliminate all risk induced by community
rating. Prior to capping RA, the variance borne by the
health insurer would be zero,
Capping the volume necessarily makes this variance
positive.
Objective: Minimize the increase in the variance of HCE
borne by insurers,
Capping Risk Adjustment?

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5. Optimal Implementation of a Cap
In order to avoid dealing with absolute values, the
positive and negative half-variances are minimized
separately (restriction on volume ensures zero sum).
Capping Risk Adjustment?

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5. Optimal Implementation of a Cap
A four group example: Two groups (0,1) have below
and two groups (2,3) above average HCE. Minimizing
the negative half-variance yields,
Capping Risk Adjustment?

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5. Optimal Implementation of a Cap
The first FOC can be rearranged in order to obtain,
The greater the population at risk (n), the smaller the
shadow price of the constraint.
The greater the difference between RA payments with
and without the cap, the higher the shadow price.
Capping Risk Adjustment?

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5. Optimal Implementation of a Cap
The equation system can be solved to yield
The reduction of RA values should be the same in all
“payer” categories.
Value increases with hi, the subpopulation share with
below-average HCE.
Capping Risk Adjustment?

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6. Third Criterion & a Cap
Three cases can be distinguished when the new criterion
“hospitalization” and a cap on CS are combined.
1.Benchmark case: No cap and introduction of new criterion.
Variance in HCE to be borne by insurers reduced, less risk
selection.
2.Cap initially not binding, but becomes binding due to
new criterion: Initially zero opportunity cost, then small,
then rising progressively.
3.Cap binding throughout: Constraint becomes more
binding but net HCE falling on insurers is reduced. Net
effect unclear.
Capping Risk Adjustment?

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7. Consequences of the Cap
Estimated volume of CS is
CHF 5.375 bn. (2005)
Illustration: Set cap at
CHF 4.5 bn. (-16.3%).
Recall: Optimal reductions
in RA-payments are uniform
across “payer“ and “receiver”
categories.
1
: Source: Official statistics Swiss statutory health
insurance KVG 2005
Capping Risk Adjustment?
Age CS1
Change CS new
19-25 -2347 +236 -2111
26-30 -2290 +236 -2054
31-35 -2191 +236 -1955
36-40 -2073 +236 -1837
41-45 -1800 +236 -1564
46-50 -1479 +236 -1243
51-55 -548 +236 -312
56-60 223 -223 0
61-65 1223 -435 788
66-70 2085 -435 1650
71-75 3301 -435 2866
76-80 3276 -435 2841
81-85 4851 -435 4417
86-90 7162 -435 6727
90+ 9419 -435 8985

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7. Consequences of the Cap
Financial burden drops slightly for those below 55.
Burden increases for those above 55 because of less
cross-subsidization in their favor.
Relative change is larger for men than women.
Capping Risk Adjustment?

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8. Conclusions
 Two issues addressed: (1) refining the RA-formula;
(2) capping the volume of RA or CS, respectively.
 Capping has opportunity cost in the guise of
strengthened incentives for risk selection.
 Calculated, official, and estimated HCE match
sufficiently to conduct research.
Capping Risk Adjustment?

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8. Conclusions
 Inclusion of the additional criterion inflates CS volume
by 40 percent on average.
 A cap on national (total) volume seems most
appropriate.
 Solution to optimal implementation cap is derived by
minimizing half-variances under a volume constraint.
Capping Risk Adjustment?

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8. Conclusions
 Optimal implementation calls for uniform reduction of
positive/negative RA values across groups.
 Amount depend on existing differences in RA values
between groups and on subpopulation shares with
below-average HCE.
 Age classes up to app. 55 are relieved, those above
receive less cross-subsidy.
Capping Risk Adjustment?