Department of Economics
16.09.2013 Prof. Dr. Konstantin Beck Seite 116.09.2013 Seite 1
Konstantin Beck, University of Zuri...
Department of Economics
Agenda
• Enthoven’s managed competition model
• A generalized model of risk equalization
• Discuss...
Department of Economics
16.09.2013 Prof. Dr. Konstantin Beck Seite 3
Back to the roots – Enthoven’s managed
competition mo...
Department of Economics
16.09.2013 Prof. Dr. Konstantin Beck Seite 4
Premium differentiation
Switzerland: Individual out o...
Department of Economics
16.09.2013 Prof. Dr. Konstantin Beck Seite 5
A generalized concept of Risk Equalization
RE-contrib...
Department of Economics
16.09.2013 Prof. Dr. Konstantin Beck Seite 6
A generalized concept of Risk Equalization (II)
HCE p...
Department of Economics
First Step: Discussion of C-variables in RA-formula
• The dominant discussion
• C-variables: Diffe...
Department of Economics
2nd Step: Constrained solidarity within C-variables
Known from Switzerland and from the Affordable...
Department of Economics
16.09.2013 Prof. Dr. Konstantin Beck Seite 9
Constrained solidarity in C-variables but
neglected i...
Department of Economics
16.09.2013 Prof. Dr. Konstantin Beck Seite 10
Young adults
(19 – 25)
Average prem.
CHF 230Elderly ...
Department of Economics
16.09.2013 Prof. Dr. Konstantin Beck Seite 11
Constrained solidarity in C-variables calls for
diff...
Department of Economics
2nd Step : A generalized solution
if ߨଵ = ߨଶ = 0
→ Generation-Solidarity = 0
& rebate at max
if ‫̅...
Department of Economics
3rd Step: Riskadjustment with C- and R-variables
• The neglected discussion
• R-Variables: Differe...
Department of Economics
There are two circumstances:
‫ܥ‬௜ = 0 => young, ‫ܥ‬௜ = 1=> old
There are two coverage options (res...
Department of Economics
OLS regression explaining cost differences:
ܺ௜ = ߙ + ߚ‫ܥ‬௜ + ߛܴ௜ + ߝ௜
Excluding Ri from the risk e...
Department of Economics
16.09.2013 Prof. Dr. Konstantin Beck Seite 16
3.2: Ri included in calculation : Total redistributi...
Department of Economics
3.2: Ri included in calculation – a formal proof
16.09.2013 Prof. Dr. Konstantin Beck Seite 17
(C,...
Department of Economics
ܴ௜ has to be included in the OLS estimation, but in a neutralized manner
Neutralization means, to ...
Department of Economics
3.3: Including a neutralized Ri
16.09.2013 Prof. Dr. Konstantin Beck Seite 19
(C, R) - Type HCE RE...
Department of Economics
16.09.2013 Prof. Dr. Konstantin Beck Seite 20
Regression: All variables (R & C), without interacti...
Department of Economics
RA PCG
(only C)
RA PCG
(R & C)
Diff. in
CHF./year
Faire
Rebate
Diff. in %
Rebates
Franchise
300 CH...
Department of Economics
16.09.2013 22
4rth step: R & C are not uncorrelated
OLS-Formula:
With:
→ Rebates probably still bi...
Department of Economics
4rth Step: R and C not additive separable
16.09.2013 Prof. Dr. Konstantin Beck Seite 2316.09.2013 ...
Department of Economics
16.09.2013 Prof. Dr. Konstantin Beck Seite 24
Regressions with & without interaction (excerpt)
Ded...
Department of Economics
16.09.2013 Prof. Dr. Konstantin Beck Seite 25
Possible rebates for senior citizens (CHF/month)
no ...
Department of Economics
Conclusion
• Premium differentiation is an important tool to stimulate
efficienct behavior of cust...
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Parallel_Session_1_Talk_3_Beck

  1. 1. 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
  2. 2. Department of Economics 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
  3. 3. Department of Economics 16.09.2013 Prof. Dr. Konstantin Beck Seite 3 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
  4. 4. Department of Economics 16.09.2013 Prof. Dr. Konstantin Beck Seite 4 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.
  5. 5. Department of Economics 16.09.2013 Prof. Dr. Konstantin Beck Seite 5 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
  6. 6. Department of Economics 16.09.2013 Prof. Dr. Konstantin Beck Seite 6 A generalized concept of Risk Equalization (II) HCE per insured Risk groups ܾ = ‫̅ݔ‬ Negative Transfers Positive Transfers
  7. 7. Department of Economics 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
  8. 8. Department of Economics 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.- 16.09.2013 Prof. Dr. Konstantin Beck Seite 8
  9. 9. Department of Economics 16.09.2013 Prof. Dr. Konstantin Beck Seite 9 Constrained solidarity in C-variables but neglected in RE-calculation HCE per insured Risk groups ܾ = ‫̅ݔ‬ Negative Transfers Positive Transfers Rebate impossible
  10. 10. Department of Economics 16.09.2013 Prof. Dr. Konstantin Beck Seite 10 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.
  11. 11. Department of Economics 16.09.2013 Prof. Dr. Konstantin Beck Seite 11 Constrained solidarity in C-variables calls for differentiated points of reference (b) HCE per insured Risk groups ܾଶ଺ା = ‫̅ݔ‬ଶ଺ା ܾଵଽିଶହ = ‫̅ݔ‬ଵଽିଶହ ܾଶ଺ା ܾଵଽିଶହ
  12. 12. Department of Economics 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) 16.09.2013 12Prof. Dr. Konstantin Beck ܾଵଽିଶହ = ‫̅ݔ‬ଵଽିଶହ + ߨଵ ܾଶ଺ା = ‫̅ݔ‬ଶ଺ା − ߨଶ
  13. 13. Department of Economics 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? 16.09.2013 13Prof. Dr. Konstantin Beck
  14. 14. Department of Economics 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 16.09.2013 Prof. Dr. Konstantin Beck Seite 14
  15. 15. Department of Economics 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? 16.09.2013 Prof. Dr. Konstantin Beck Seite 15 ߙ ߚ
  16. 16. Department of Economics 16.09.2013 Prof. Dr. Konstantin Beck Seite 16 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
  17. 17. Department of Economics 3.2: Ri included in calculation – a formal proof 16.09.2013 Prof. Dr. Konstantin Beck Seite 17 (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
  18. 18. Department of Economics ܴ௜ 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 16.09.2013 Prof. Dr. Konstantin Beck Seite 18
  19. 19. Department of Economics 3.3: Including a neutralized Ri 16.09.2013 Prof. Dr. Konstantin Beck Seite 19 (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)
  20. 20. Department of Economics 16.09.2013 Prof. Dr. Konstantin Beck Seite 20 Regression: All variables (R & C), without interaction Coefficient (excerpt) Deductible 500 CHF -45.54 *** Deductible 1000 CHF -96.92 *** Deductible 1500 CHF -100.18 *** Deductible 2000 CHF -111.76 *** Deductible 2500 CHF -126.41 *** HMO with capitation -34.26 *** Practitionar network -25.76 ***
  21. 21. Department of Economics 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 Prof. Dr. Konstantin Beck Seite 21
  22. 22. Department of Economics 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
  23. 23. Department of Economics 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
  24. 24. Department of Economics 16.09.2013 Prof. Dr. Konstantin Beck Seite 24 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 ***
  25. 25. Department of Economics 16.09.2013 Prof. Dr. Konstantin Beck Seite 25 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?)
  26. 26. Department of Economics 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” 16.09.2013 Prof. Dr. Konstantin Beck Seite 26

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