Parallel_Session_1_Talk_3_Beck

Department of Economics
16.09.2013 Prof. Dr. Konstantin Beck Seite 116.09.2013 Seite 1
Konstantin Beck, University of Zurich and CSS-Institute Luzern
Florian Buchner, Carinthia University & CINCH, U of Duisburg-Essen
Richard van Kleef, Erasmus University Rotterdam
Viktor von Wyl, CSS-Institute Luzern
Theory of risk adjustment –
Did we take the wrong track?
Presentation for the Swiss Health Economics Workshop 2013
Lucerne, September 13, 2013

Agenda
• Enthoven’s managed competition model
• A generalized model of risk equalization
• Discussion of four steps
• Discussion of (so called) C-variables
• Constraint solidarity in between C-variables
• C- versus R-variables
• Interaction between C- and R-variables
• Conclusions
16.09.2013 Prof. Dr. Konstantin Beck Seite 2

Back to the roots – Enthoven’s managed
competition model
Enthoven’s model was an answer to several fruitless
attempts to control costs in the health care sector.
To give insurer, physicians and insured incentives to
become prudent user of health care was in the focus
of this concept from the very beginning.
European adaption
Community rating instead of risk oriented premiums
To establish solidarity by refining risk equalization
became the focus. Efficiency was less considered

Premium differentiation
Switzerland: Individual out of pocket premiums,
community rated with many different risk classes.
The Netherlands: Community rated out of pocket for
all adults. Premium differentiation with respect to cost
containing models.
Germany: All inhabitants pay income dependent
contribution to Central Health Fund. No premiums
applied today.
Israel: No premium at all, tax funded system.

A generalized concept of Risk Equalization
RE-contribution:
Variable b is total average of community rated
premiums:
If it is the external system
[If it is the internal system]
ܴ‫ܥܧ‬௞ = ‫̅ݔ‬௞ − ܾ
ܾ = ‫̅ݔ‬
ܾ < ‫̅ݔ‬

A generalized concept of Risk Equalization (II)
HCE per insured
Risk groups
ܾ = ‫̅ݔ‬
Negative Transfers
Positive Transfers

First Step: Discussion of C-variables in RA-formula
• The dominant discussion
• C-variables: Differences in risk the insured/insurer should be
compensated for.
• In CH since 2012: Age, gender, prior hospitalization
• Power of explanation: R2 16.4%
• Current discussion: Inclusion of PCG, R2 26.1%
16.09.2013 7Prof. Dr. Konstantin Beck

2nd Step: Constrained solidarity within C-variables
Known from Switzerland and from the Affordable Care Act (US)
Swiss law recommends premium rebate for young adults (19 – 25)
Swiss RE-regulation recommends full equalization of all cost differences in
all (!) age groups.
→ appropriate rebate for young adults is CHF 0.-

Constrained solidarity in C-variables but
neglected in RE-calculation
HCE per insured
Risk groups
ܾ = ‫̅ݔ‬
Negative Transfers
Positive Transfers
Rebate impossible

Young adults
(19 – 25)
Average prem.
CHF 230Elderly adults
(26 +)
Average prem.:
CHF 266
Swiss solidarity circle
Source: von Wyl/Beck 2012
CHF 1,392 Bill.
CHF 1,164 Bill.

Constrained solidarity in C-variables calls for
differentiated points of reference (b)
HCE per insured
Risk groups
ܾଶ଺ା = ‫̅ݔ‬ଶ଺ା
ܾଵଽିଶହ = ‫̅ݔ‬ଵଽିଶହ
ܾଶ଺ା
ܾଵଽିଶହ

2nd Step : A generalized solution
if ߨଵ = ߨଶ = 0
→ Generation-Solidarity = 0
& rebate at max
if ‫̅ݔ‬ଵଽିଶହ + ߨଵ = ‫̅ݔ‬ଶ଺ା − ߨଶ
→ Gen. - solidarity at max
& rebate = 0
For solutions in between: ߨଵ = ݂(ߨଶ)
ܾଵଽିଶହ = ‫̅ݔ‬ଵଽିଶହ + ߨଵ
ܾଶ଺ା = ‫̅ݔ‬ଶ଺ା − ߨଶ

3rd Step: Riskadjustment with C- and R-variables
• The neglected discussion
• R-Variables: Differences in risk the insured/insurer should be held
responsible for.
• In CH since 1990 (!): Deductibles, Managed Care
• Power of explanation: 26.6 – 26.8% R2
• How to include?
• 3.1 Neglect?
• 3.2 Include?
• 3.3 Include and neutralize?

There are two circumstances:
‫ܥ‬௜ = 0 => young, ‫ܥ‬௜ = 1=> old
There are two coverage options (responsible variable)
ܴ௜ = 0 => managed care model chosen, ܴ௜ = 1 => mc-model not chosen
݊ = number of insured, ‫ݔ‬ = HCE
OLS regression explaining cost differences:
ܺ௜ = ߙ + ߚ‫ܥ‬௜ + ߛܴ௜ + ߝ௜
A simple model with R- and C- variables

OLS regression explaining cost differences:
ܺ௜ = ߙ + ߚ‫ܥ‬௜ + ߛܴ௜ + ߝ௜
Excluding Ri from the risk equalization-regression
=> biased estimate of and .
Including Ri into the risk equalization-regression
=> total distribution of cost reducing effect
3.1 & 3.2: How to include in risk equalization given
premium differentiation with respect to R?
ߙ ߚ

3.2: Ri included in calculation : Total redistribution
of cost reducing effect
HCE per insured
Risk groups
ܾ = ‫̅ݔ‬
Negative Transfers
Positive Transfers
R=0 R=1 R=0 R=1
C=0 C=0 C=1 C=1

3.2: Ri included in calculation – a formal proof
(C, R) - Type HCE RE-transfer Premium
(0,0) ‫ܠ‬ത૙૙ ==== હ ࢻ − ‫܊‬ ‫܊‬
(0,1) ‫ܠ‬ത૙૚ ==== હ + ઻ હ + ࢽ − ‫܊‬ ‫܊‬
(1,0) ‫ܠ‬ത૚૙ ==== હ + ઺ હ + ࢼ − ‫܊‬ ‫܊‬
(1,1) ‫ܠ‬ത૚૚ ==== હ + ઺ + ઻ હ + ઺ + ࢽ − ‫܊‬ ‫܊‬
ࢄ࢏ = ࢻ + ࢼ࡯࢏ + ࢽࡾ࢏ + ࢿ࢏ (ࢿ࢏ = ૙)
All premiums are equal
/ rebates impossible
= within cost containing model

ܴ௜ has to be included in the OLS estimation, but in a neutralized manner
Neutralization means, to distribute the additional costs ߛ of type (0,1) and
(1,1) among all insured:
(࢔૙૚ + ࢔૚૚) ∗ ࢽ
࢔
= ࣐ࢽ
3.3: Including and neutralizing R

3.3: Including a neutralized Ri
(C, R) - Type HCE RE-transfers Premium
(0,0) ‫ܠ‬ത૙૙ = α= α= α= α ࢘૙૙= α += α += α += α + φφφφγγγγ ---- bbbb bbbb ---- φφφφγγγγ
(0,1) ‫ܠ‬ത૙૚ = α+= α+= α+= α+ ઻ ࢘૙૚= α += α += α += α + φφφφγγγγ ---- bbbb b + (b + (b + (b + (1111----࣐)))) ࢽ
(1,0) ‫ܠ‬ത૚૙ = α + β= α + β= α + β= α + β ࢘૚૙= α + β += α + β += α + β += α + β + φφφφγγγγ ---- bbbb bbbb ---- φφφφγγγγ
(1,1) ‫ܠ‬ത૚૚ = α + β += α + β += α + β += α + β + ઻ ࢘૚૚= α + β += α + β += α + β += α + β + φφφφγγγγ ---- bbbb b + (b + (b + (b + (1111----࣐)))) ࢽ
• Premiums differ between insured within and without mc-model
• The difference reads: (࢈ − ࣐ࢽ) − (࢈ + (૚ − ࣐)ࢽ = ࢽ
This is exactly the cost reducing effect of the model ( = fair rebate)

Regression: All variables (R & C), without interaction
Coefficient (excerpt)
Deductible 500 CHF -45.54 ***
HMO with capitation -34.26 ***
Practitionar network -25.76 ***

RA PCG
(only C)
RA PCG
(R & C)
Diff. in
CHF./year
Faire
Rebate
Diff. in %
Rebates
Franchise
300 CHF 1'138 1'010 -128 0 *
500 CHF 607 526 -81 -546.45 15%
1000 CHF -1'305 -1'179 126 -1'162.99 -11%
1500 CHF -1'780 -1'572 208 -1'202.13 -17%
2000 CHF -2'012 -1'772 240 -1'341.09 -18%
2500 CHF -1'874 -1'652 223 -1'516.90 -15%
Managed Care
Free access to pract. 628 569 -59 0 *
HMO -692 -655 37 -411.12 -9%
Pract.-Network -1'523 -1'345 178 -309.15 -58%
Comparing RA-payment per insured with(out) R-variables

16.09.2013 22
4rth step: R & C are not uncorrelated
OLS-Formula:
With:
→ Rebates probably still biased
Prof. Dr. Konstantin Beck
iiiiii RCRCX εδγβα ++++= iiiiii RCRCX εδγβα ++++=
0≠δ 0≠δ

4rth Step: R and C not additive separable
16.09.2013 Prof. Dr. Konstantin Beck Seite 2316.09.2013 Seite 23
Ci = 0 Ci = 1
α
To be compensated
HCE
α
iiii
ii
RCR
CX
εδγ
βα
+++
+=
iiii
ii
RCR
CX
εδγ
βα
+++
+=
0α
β
α
γ
β
δ
γ
Ri = 1
(kein MC)
Ri = 0
(in MC)
We address
this problem
empirically

Regressions with & without interaction (excerpt)
Deductible 500 CHF -45.54 *** -47.01 ***
Deductible 1000 CHF -96.92 *** -83.61 ***
Deductible 1500 CHF -100.18 *** -93.41 ***
Deductible 2000 CHF -111.76 *** -107.90 ***
Deductible 2500 CHF -126.41 *** -117.39 ***
HMO with capitation -34.26 *** -17.56 *
Practitionar network -25.76 *** 3.32 n.s.
Over 60 & deductible over 500 CHF -35.97 **
Woman & deductible over 500 CHF 6.17 n.s.
PCG & deductible over 500 CHF -65.81 ***
Over 60 & MC model chosen -38.48 ***
Woman & MC model chosen 18.46 *
PCG & MC model chosen -83.69 ***

Possible rebates for senior citizens (CHF/month)
no PCG with PCG
Deductible 1000 CHF -96.92 -119.58 -185.39
Deductible 2500 CHF -126.41 -153.36 -219.17
HMO with capitation -34.26 -56.04 -139.73
Practitionar network -25.76 -38.48 -122.17
no interaction with interaction
Do we have to protect bad risks from preferred treatment ?
(higher rebates?)

Conclusion
• Premium differentiation is an important tool to stimulate
efficienct behavior of customers
• Given differentiated premiums (R-variables), all possible
rebates should be included in RE-formula and must be
neutralized thereafter (Schokkaert/van de Voorde-Solution)
• If there is restricted solidarity between C-variables (USA and
CH), we need differentiated points of references (simplified
McGuire-Solution)
• Swiss data show significant and relevant impact of cost-
reducing models. Unwanted redistribution is a problem with
respect to the young adults.
• Non additive separability exists but pragmatic solutions are
“not impossible”

Parallel_Session_1_Talk_3_Beck

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