B.10. WC Experience Rating

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B.10. WC Experience Rating
2015-09-11 19:50:08
Workers Compensation Experience Rating Gillam Snader NCCI Venter

TIA Summary - Workers Compensation Experience Rating
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  1. Purpose of experience rating
    • relate an insured's premium to their loss experience (individual risk equity)
    • actual losses are compared with expected loses to produce Mod
    • Manual Premium * Mod = Modified Premium
    • Modified Premium * Schedule Mod = Standard Premium
  2. Characteristics of Worker's Compensation
    • company management has a great deal of control over company safety practices
    • experience rating help distinguish between risks for differences such as compensation, management, employee morale, relation to the community, etc.
    • those aspects would typically not be rating variables but can be captured with experience rating
  3. Credibility of WC Experience rating
    • credibility of experience depends on size of insured (usually measured by payroll)
    • credibility of individual risk experience also increases when there is greater between variance (variance of hypothetical means)
    • when a classification plan is very strong, the experience rating will be less important
  4. Goals of experience rating
    • predictive accuracy: degree of charge based on past experience should be the degree in which it is predictive of future losses, ensuring equity (premium relates to the insured’s loss potential) and rates that aren't unfairly discriminatory
    • safety incentive: financial incentive for loss control (safety programs, return to work programs, …)
    • enhance market competition: more companies willing to sell insurance if profit is guaranteed on all risk after the application of the experience mod
  5. Maximizing predictive accuracy
    • minimize the error between the predicted losses and actual residual losses
    • expected square error = best measure → leads to solvable equations and penalizes large errors
    • to make the math simpler, experience mod is a linear function of losses
  6. No-Split Plan
    • define A = actual historical losses, E = expected losses, Z = credibility = E / (E + KE)
    • Mod = [ZA + (1 - Z)E] / E = 1 + Z[(A - E)/E] = (A + KE) / (E + KE)
    • the term ZA + (1 - Z)E is known as the Modified Expected Losses
    • Surety Association Plans: Mod = (1 - Z) + Z/[E/P] * A/P = premium mod + adj loss multiplier * adj LR
  7. Credibility under No-Split Plans
    • KE can be a constant, a function of E, or manually chosen to achieve the desired responsiveness
    • 3 conditions: 0 ≤ Z ≤ 1, ↑ as size ↑ (d/dE(Z) ≥ 0), % charge ↓ as size ↑ (d/dE(Z/E) < 0)
    • note that condition 3 does not mean Z must increase at a decreasing rate
    • all conditions are automatically satisfied if KE is a constant
  8. Split Plans
    • actual and expected losses are split into primary and excess components; primary reflects frequency and receives the most weight, while excess reflects severity
    • Mod = (1/E) * [ZpAp + (1 - Zp)Ep + ZeAe + (1 - Ze)Ee]
    • Mod * E = Modified Expected Losses
    • using Zp/e = E / (E + Kp/e), Mod = 1 + (Ap - Ep) / (E + Kp) + (Ae - Ee) / (E + Ke)
  9. Perryman's First Formula
    • Mod = [Ap + WAe + (1 - W)Ee + B] / [E + B]
    • Bballast = (1 - W)K
    • B limits the impact of any individual large claim on the Mod
  10. Single and Multi-Split Plans
    • under a single split plan, there is 1 split point below which losses are considered primary
    • under a multi-split plan, a decreasing portion of loss increment is considered primary
    • Ap = I + (1 - d)I + (1 - d)2I + … + (1 - d)N (A - N * I), where I = $ increment, d = rate of discount
    • maximum value of Ap = I/d, and Ae = A(capped) - Ap
  11. WC Experience Rating - Pre-1940
    • used no-split plan with Mod = (A + KE) / (E + KE)
    • Venter argues that it's problematic for highly skewed, heavy-tailed distributions such as WC claims, so by splitting the losses each component becomes less heavy-tailed and more predictable
    • the flaw in the argument is that the distribution of excess losses is less heavy tailed but not necessarily more predictable (e.g. it's much easier to price a ground-up policy than an excess policy)
  12. WC Experience Rating - 1940 to 1961
    • new NCCI split-plan has Mod = [Ap + WAe + (1 - W) Ee + B] / [E + B]
    • split used to be with I = 500, d = 2/3 (primary portion = [2/3]x), with max(Ap) = I / d
    • selecting B and W: prevent large swings in the mod for small insureds; provide 100% credibility for large insureds; as a result B and K decreased as risk size increased
  13. WC Experience Rating - 1961 to 1991
    • simplified the formula with Ap = A if A ≤ 2,000, 10000A / (A + 8,000) if A > 2,000
    • as a result the maximum value of Ap is 10,000
  14. WC Experience Rating - Post 1991
    • NCCI simplified the split to a single-split plan at 5,000
    • values of B and K began to increase non-linearly with premiums; in theory constant B and K means large risks are more stable, but empirical data showed a slower decrease in variance
  15. Resulting impact on credibility
    • small risks received larger primary credibility
    • large risks received smaller primary credibility, with maximum now 91%
    • small risks received larger excess credibility, with all risks having non-zero credibility
    • large risks received much smaller excess credibility, with maximum now 57%
    • quintile test: small and large performed better, medium performed equally well
  16. Calculating a Medical Claim
    • reduce the primary medical-only portion by 70%
    • e.g. for a $7,000 loss, Ap = 5,000 * 0.3 = 1,500 and Ae = 2,000 * 0.3 = 600
  17. Dorweiler's 2 conditions for correct credibility
    • necessary: credit and debit risks show equal standard loss ratios in prospective period
    • sufficient: no way to select a subgroup of credit/debit risks on any experience basis that would produce a different loss ratio in the prospective period (more a goal than a requirement)
  18. Testing the predictive accuracy of the plan
    • conduct tests separately for each size group
    • if premium is not available for manual loss ratio, use actual losses / expected losses
    • if premium is not available for standard loss ratio, use actual losses / modified expected losses
  19. Dorweiler's Test
    • sort risk in increasing order, group in subdivisions, calculate manual and standard loss ratio for each
    • maximal loss ratio dispersion → plan correctly identifies risk differences
    • more importantly, equal standard loss ratios → plan corrects for risk differences (+ want no trend)
  20. Quintile's Test
    • essentially a quantified version of Dorweiler’s test
    • sort risks by their mods in increasing order, group in 5 quintiles, calculate manual/standard LR
    • test statistic = variance in standard loss ratios / variance in manual loss ratios
    • lower test statistics indicates better plan performance
  21. Efficiency test
    • calculate manual and standard loss ratios for all risks
    • test statistic = variance of standard loss ratios / variance of manual loss ratios
    • lower test statistic indicates better plan performance
  22. Data used for Experience Rating
    • data comes from the Workers Compensation Statistical Plan (the Unit Plan)
    • insurers report losses by injury type, payroll, and class codes for every risk up to 5th report
    • NCCI uses this information in both experience rating and class ratemaking
    • experience mod uses 3 prior years of actual loss experience
  23. NCCI modifications to the data
    • add contract medical losses to Medical-Only losses
    • separate Permanent Partial claims into Major PP and Minor PP based on $ threshold (critical value)
    • NCCI does not develop or trend actual losses, or change them to the latest benefit levels, instead they de-trend and de-develop expected losses to make them comparable to the historical actual
  24. NCCI loss groups
    • serious: includes Fatal, Permanent Total, and Major Permanent Partial indemnity
    • non-serious: includes Temporary Total and Minor Permanent Partial indemnity
    • medical: includes medical amounts from all claims
  25. Experience Rating Plan Parameters
    • state reference point (SRP): index of benefits used to calculate G and SAL (by state)
    • weighting value (W): used to limit weight of actual XS losses (varies by state and insurer size)
    • ballast (B): used to provide stability by limiting impact of single loss (varies by state and size)
    • expected loss rates (ELRs): expected loss / $100 payroll (varies by state and class)
    • discount ratios (D-ratios): expected primary % of expected loss (varies by state and class)
  26. Calculating State Reference Point
    • first calculate trended State Average Cost per Claim (SACC)
    • trended SACC = (∑ Incurred Lossesy / ∑ Claim County) * ert over the 3 years
    • Incurred for Employer’s Liability capped at $100K
    • SRP = 250 * trended SACC, rounded to the nearest $5K
    • G & SRP not allowed to decrease from last year unless there is a significant reduction in benefits
    • any change over 20% to the SRP will be further investigated
  27. Uses of SRP
    • state accident limit (SAL): per claim limit for losses in experience mod calculation = 10% * SRP
    • scale factor G: used in calculating values for B and W; G = SRP / 250,000, rounded to nearest .05
    • B = max[7500, E* (0.1E + 2500G) / (E + 700G)]
    • C = KE = max[150000, E * (0.75E + 200000G) / (E + 5100G)]
    • W = (E + B) / (E + C) rounded to the nearest 0.01
    • W also can not increase when E decreases, and 0 < W < 1, B > 0 so no insured has 100% credibility
  28. Calculating class ELR - data prep
    • should be proportional to the loss cost underlying manual rate
    • multiply class rate by PLR to remove profit, taxes, expenses
    • adjust for time frame differences (benefit level, loss development, trend)
    • adjust for the fact that claims covered by the policy have no limits, unlike claims used in rating
  29. Steps to calculating ELR
    • calculate a factor to reduce manual rates to pure premium at 2nd report
    • calculate class Hazard Group ELR and ELR; correcting for loss limitation includes:
    • calculate ratio of SAL to average loss (entry ratio by Hazard Group and Injury Type)
    • weight 3 excess ratios for each HG by injury type to get single excess ratio by HG
    • calculate HG adjustment factor = 1 - HG excess ratio
    • multiply ELR level factor by HG adjustment factor to get HG ELR factors
    • apply for HG ELR to rates and check ELRs for reasonableness
  30. Calculating D-ratios
    • use the 3 most recent single history year of statistical plan available
    • because of policy years extending over 2 calendar years, plus reporting, verification and processing, a rate filing effective Jan 1, X would generally contain D-ratios based on X-3 policy year
    • use D-ratio by class = weighted average of D-ratio Factors (partial D-ratios) by type of injury
    • Application of NCCI Experience Rating Plan
    • apply mod factor to the manual premium → differentiates loss potential within not between classes
    • having a debit ≠ stigma, it may not reflect poor safety habits; any accident is a matter of chance
  31. Off-balance factor
    • off-balance: ratio of standard premium to manual premium = weighted average of mods
    • when ELRs and D-ratios are adequate, the off-balance will be near 1 or a slight credit since risks large enough to be experience rated tend to have better loss experience
    • off-balance is not used to try and change overall premium adequacy
    • in states where rate adequacy deteriorates, problem is that rate indication is based on standard loss ratios, but changes are applied to manual rates
  32. Off-balance vs rate inadequacy
    • expected loss will be too low
    • mods will increase, increasing off-balance
    • this will increase the overall premium
    • rate indications are based on premium including mods, so it'll partially lower indication as a result of the higher off-balance
    • note that premium level contemplates no changes in off-balance factor in the prospective period
  33. Off-balance factor vs rate increase
    • assuming the rate increase is to correct inadequate rates
    • as the rates come up, the off-balance will decrease
    • this will lower the premium which increases the rate indication
    • rates will still be slightly inadequate
  34. Using the NCCI Manual
    • Rule 1.C.8 lists some reasons why a risk high have a mod of 1.0
    • Rule 2.A.2 shows premium eligibility for exp rating by state (only need to satisfy 1)
    • Rule 2.A.5 specifies interstate experience rating requirements
    • Rule 2.B.2 talks about rating effective dates
    • Rule 2.C describes all items in the experience mod formula
    • Rule 2.C.13 talks about rules to apply when different loss limits apply
    • Rule 2.D.2 gives the maximum debit mod (cap varying by risk)
    • Rule 3 explains how a change in ownership or combination of entities impact experience used
    • Rule 4.B.1/2/3 describe the correction to payroll, losses or classifications resulting in revised mods