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Agenda

Current Review of the NCCI Retro Rating Plan Greg Engl, PhD, FCAS, MAAA National Council on Compensation Insurance CAS Ratemaking Seminar March, 2004 WC-5 Latest Developments in Retrospective Rating. Agenda. Data adjustment techniques Modeling occurrences Injury type groupings

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Agenda

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  1. Current Review of the NCCI Retro Rating PlanGreg Engl, PhD, FCAS, MAAANational Council on Compensation InsuranceCAS Ratemaking Seminar March, 2004WC-5 Latest Developments in Retrospective Rating

  2. Agenda • Data adjustment techniques • Modeling occurrences • Injury type groupings • Fitting methodology

  3. Data Adjustment Basic Issues • Credibility • Differences between states

  4. Data AdjustmentCurrent Approach • Normalize by state mean: • Effectively matches first moment, i.e. mean

  5. Mean Normalization

  6. Data AdjustmentCurrent Approach • Fit loss distributions to CW mean normalized database • Assume state distributions differ only by a scale transform

  7. The Usual Standardization • Normalize by : • Effectively matches first two moments, i.e. mean and variance

  8. Data Adjustment TechniquesPrimary Approaches • Mean normalization: • Usual standardization: • Power transform:

  9. Data Adjustment TechniquesSecondary Approaches • Median normalization: • Generalized standardization:

  10. Data Adjustment Basic Idea • Adjust the data to a common basis • Combine all states adjusted data into a big database • Adjust big database as appropriate for each state

  11. Data Adjustment Techniques • Conducted extensive testing • Conclusions: • Usual standardization for F, PT • Power transform for PP, TT

  12. State Specific Distributions • More sophisticated data adjustment techniques • Give more weight to a state’s own data • Still makes use of out-of-state data • How much state data is enough?

  13. Modeling OccurrencesBasic Goal • Have per claim data • Need per occurrence ELFs

  14. Modeling OccurrencesFirst Approach • ELFo = 1.1 x ELFc • Occurrence adjustment factor was independent of • Loss limit • Mix of injury types • Could result in ELFo > 1

  15. Modeling OccurrencesSecond Approach • Occurrences cost 10% more than claims, i.e instead of r = L/, use r = L/1.1 • Adjustment factor still independent of • Loss limit • Mix of injury types

  16. Modeling OccurrencesCurrent Practice • Fit loss distributions to mean normalized data • But do not renormalize fitted distributions • This provides what Gillam and Couret called a “natural contagion load” of: • 3.9% for Fatal • 6.6% for PT/Major • 0% for TT/Minor

  17. Modeling Occurrences Hypothesis: Multi-claim occurrences differ from single claim occurrences only in that they have more claims involved.

  18. Modeling OccurrencesCollective Risk • S = X1+ +XN where • N = number of claims per occurrence • Xi = cost of ith claim . . .

  19. Claims per Occurrence For Multi-Claim Occurrences Based on PY 1997 WCSP data as of September 2002.

  20. Preliminary AnalysisDistribution of Injury Types Based on PY 1997 WCSP data as of September 2002.

  21. Preliminary AnalysisMulti-claim Occurrences Based on PY 1997 WCSP data as of September 2002.

  22. Multi-Claim Occurrences • Mix of injury types more severe • Same type of injury more severe

  23. Modeling Occurrences Revised Hypotheses: • Multi-claim occurrences have different mix of injury types • Injury type distributions for multi-claim occurrences differ only by a scale transformation

  24. Modeling Occurrences • Xi = cost of claim in multiple claim occurrence • S = X1+ . . .+ XN • Y = cost of claim in single claim occurrence • T = r . S + (1-r) . Y where • r = probability occurrence is multi-claim

  25. Impact of Occurrence ModelBased on Hypothetical Data

  26. Impact of Occurrence Model • Scaling here is about 1% • Based on least squares fit • Prior scaling: 10% • Current scaling: • Fatal 3.9% • PT/Major 6.6% • Overall 2.5%

  27. Injury Type Groupings • Separate PT from PP/Major • Use 3 years of data for F, PT • Combine PP/Major with PP/Minor • This would be unaffected by any change in critical value methodology

  28. Fitting Methods • Fit loss distributions and get ELFs indirectly • Fit ELF function directly

  29. Fit Loss Distributions • Traditional Approach • Usually based on maximum likelihood • Assumption:“good” distributions produce good ELFs

  30. Fit ELF function directly • Gets at exactly what we want: ELFs • Fit loss distributions based on ELFs—not on abstract statistical measures like likelihood function • Strong connection to traditional approach

  31. Distributions to Consider • Mixed exponential(for the tail, with an empirical base à la Howard Mahler, PCAS 1998) • All others

  32. Mixed Exponential • Semi-parametric distribution • ELF function of a mixed exponential is again mixed exponential

  33. Mixed Exponential Tail Behavior • Increasing mean residual life, i.e. is increasing in x • Lots of moments

  34. Mixed ExponentialSpecial Cases • Pareto ( mixing distribution) • Transformed Beta • Weibull • Burr • Gamma

  35. Mixed ExponentialGoodness of Fit • “a parametric procedure often produces a distribution that does not fit the data well” - Clive Keatinge • Semi-parametric mixed exponential’s flexibility should produce very good fits

  36. Other Distributions • Current distributions • Pareto-exponential • Transformed Beta • Conditional Transformed Beta • Others?

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